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: A dam may be damaged by occasional extreme loads such as major earthquakes or terrorist attacks during its service. According to the needs of emergency assessment, this paper studies a rapid damage identiﬁcation method for damage location and damage degree in concrete arch dams which is based on the dynamic characteristics of concrete arch dam data, using wavelet transform, wavelet packet decomposition, a BP neural network and D-S evidence theory for damage identiﬁcation and related experimental veriﬁcation. The results show that the relative difference of the curvature mode ( δϕ k ), the wavelet coefﬁcient ( W f k ) and the relative difference of the wavelet packet energy ( δ K k ) can effectively identify the damage position of the arch dam, and ϕ k in the ﬁrst four modalities has the best overall recognition effect; W f k requires a high number of measurement points, which should be at least 64 or as close as possible; δ K k has a better damage recognition effect than the ﬁrst two at the same number of measurement points. D-S evidence theory signiﬁcantly improves the damage identiﬁcation effect and reduces the misjudgment of the single-damage method. The trained neural network can effectively identify the damage degree based on the data of one measuring point when there is a single damage instance, and the number of measuring points should be no fewer than two when there is double damage. The test results verify the feasibility of the method in this paper, which can provide a theoretical basis for a post-disaster emergency assessment information system of concrete arch dams.


Introduction
With the rapid development of today's society, traditional non-renewable energy sources such as coal have had difficulty meeting the pace of modern development. Therefore, emerging clean energy sources such as solar energy, water energy and wind energy are gradually replacing the traditional consumption type of energy and could become extremely important development strategies for resource and energy development for the country. Among them, water is a clean energy source with early development and large output. When building large dams, the possible risks should not be ignored while paying attention to the safety of people's lives and the economic benefits brought by the dams. The structures will be affected by various environmental factors such as water flow and temperature for a long time and may even be damaged by super floods, major earthquakes or terrorist attacks. If the damage and defects of a dam cannot be identified, evaluated and repaired in time, they can cause it to continue to deteriorate. In the lightest case, this may affect the dam's water storage and the functional operation of the hydropower station. In the worst case, it may cause the dam to break and harm the downstream area, posing a huge threat to the lives of people in the downstream area and nearby, causing a large amount of property loss and causing serious damage to the ecological environment and social stability. In order to ensure the safety of a dam during its service, in addition to the daily monitoring and evaluation of the dam, it is also necessary to quickly identify structural damage in an emergency to ensure that structural defects are discovered and repaired in time.
Structural evaluation and recognition based on dynamic testing [1,2] are generally favored and valued by researchers because the method can obtain a better grasp of the overall information of civil engineering structures through limited measuring point information. The combination of digital signal analysis technology and various mathematical methods for structural evaluation and detection is becoming an important method of health monitoring and detection in the field of civil engineering. In the current research and development of damage identification methods in civil engineering, using processing vibration signals for damage identification is the most popular and applicable damage identification method. Its main research methods include wavelet transforms [3][4][5], wavelet packet decomposition [6,7], neural networks [8][9][10], multi-source data fusion [11] methods, etc.
Mohammad Ali Lotfollahi-Yaghini [12] used the inconsistency between a certain point or several points in the wavelet transform map and other related points to identify damage. The method was found to have a high ability to identify inconsistencies. When identifying discrete and incongruous situations, such as stiffness changes caused by cracks in a dam, damage locations can be accurately identified. Han Dong [13] took the finite element numerical simulation of a high-arch dam as an example, using wavelet transforms to calculate the wavelet coefficient residual as the structural damage index to identify the cracks in the dam body; the resulting analysis shows that the method has good effect and practicability for crack damage identification in high-arch dams. Wang Baisheng et al. [14] simulated cracks with different degrees of cracking and numbers of cracks at multiple positions of the dam body and obtained the natural frequencies and mode shapes of the corresponding damage conditions, using neural networks to identify damage in different damage conditions; the results show that damage detection using vibration data is feasible. Zhang Jianwei [15] aimed at the possible lack of test data and defect identification accuracy problems in the damage diagnosis of arch dam structures and used multi-source data fusion to evaluate the damage identification of arch dam structures to improve the identification accuracy. Zhu X [16] carried out damage identification on bridges under moving loads and found that using wavelet packet energy can not only identify damage accurately, but also reduce environmental components that may blur damage characteristics, improving the identification effect. Jungwhee Lee et al. [17] proposed a double-layer damage identification and evaluation algorithm that takes structural vibration responses as input and uses neural networks to perform classification, and they applied the algorithm to a bridge test model to verify the feasibility of the algorithm. Zhang J.C. et al. [18] used an improved D-S evidence theory for damage identification in pipelines. Through experimental comparison, it was found that the damage identification performance after the fusion using D-S evidence theory was more accurate than that of a single identification method, and it could improve the damage recognition performance of single-damage and double-damage scenarios. Karalar, M.; Cavusli, et al. [19,20] considered the ground motion of different faults in the structural design of the vertical displacement and shear strain of the fill dam, and evaluated the three-dimensional seismic damage performance of the dam. They also used FLAC3D software based on the finite difference method to model and analyze the dam, and studied the nonlinear seismic behavior of concrete gravity (CG) dams considering different epicentral distances. From the perspective of comprehensive research status, most of the domestic and foreign studies on damage identification for arch dam structures have studied the step of whether the damage occurs, and there are still few studies on the identification of the damage degree and damage location. Wavelet transforms, artificial intelligence and multi-source data fusion are gradually being used as tools in damage identification for civil engineering structures, and damage identification for beams, slabs and other structures has continuously achieved results. However, there is a lack of relevant research on large-scale hydraulic structures such as high-arch dams and a lack of methods for rapid damage identification and assessment at critical moments.
In this paper, the dynamic characteristic data of an arch dam model are obtained through numerical simulation, combined with wavelet transforms, wavelet packet decomposition, a neural network and multi-source data fusion to study a damage identification method that is suitable for emergency treatment and is fast and accurate, taking into account both damage location and damage value. In addition, for the arch dam-reservoirfoundation model, the damage identification analysis of whether there is a water level, different damage positions and different damage degrees of the dam body is carried out, and finally test verification is carried out to provide a basis for the subsequent related information system production. The main research contents are as follows: (1) Obtain the modal data of numerically simulated empty storage without a water level and with a simulated water level, respectively, obtain the mode shape data when intact and damaged, calculate the modal curvature, obtain the wavelet coefficient by wavelet transforming the mode shape data, and then locate the damage. Then, the acceleration time history data with or without a water level are obtained through transient analysis, the total energy of all frequency bands is obtained through wavelet packet decomposition, and then the wavelet packet energy index is obtained to locate the damage.
(2) D-S evidence theory is used for multi-source data fusion for the modal curvature index and wavelet packet energy index obtained with or without a water level, and the damage identification effect after fusion and before fusion is compared.
(3) Similarly, the acceleration time-history data with and without a water level are obtained, and then the energies of different characteristic frequency bands are respectively obtained by wavelet packet decomposition, and the energy ratio deviation ERVD is obtained by calculation. Then, the BP neural network whose input set is ERVD and whose output set is the damage degree is trained, the damage degree is identified, and the obtained data are processed with noise to test the anti-noise interference ability of ERVD and the BP neural network.
(4) A concrete arch dam vibration test is carried out to verify the above method.

Damage Location Identification
The concrete arch dam model is referenced in [21], and the length, width and height of the test model are reduced by half to obtain the test dam model in this paper. The height of the dam body is 400 mm, the central angle of the dam crest is 120 • , the outer radius is 530 mm, the inner radius is 500 mm, the central angle of the dam bottom is 60 • , the outer radius is 530 mm, and the inner radius is 475 mm. The dam abutment expands outward by one multiple of the dam height, extends upstream by four times the dam height [22] and extends downstream by one multiple of the dam height. The model size is 2400 mm long, 1800 mm wide and 800 mm high, with a density of 2.02 × 10 3 kg/m 3 . The volume is 2.2 × 10 4 Mpa, and the finite element model of the arch dam is shown in Figure 1. When the finite element simulation of the arch dam structure with water leve eling is carried out, this paper uses the Westergaard additional mass model meth the fluid-solid coupling model method to simulate the influence of a 300 mm wat on the arch dam structure. The additional mass model does not consider the compressibility of reservoir According to the "Code for Seismic Design of Hydraulic Structures", the Westergaa ANSYS modeling is divided into no-water-level modeling and water level modeling. When modeling without a water level, two assumptions are set. One is to assume that Buildings 2023, 13, 1417 4 of 34 the dam body is a linear elastic material for modal calculation, and different properties such as an elastic modulus can be added to the elements of different parts according to the actual situation. Second, in the dynamic analysis of arch dams, it is usually necessary to consider the influence of the foundation on the dynamic characteristics of the structure. The massless foundation model suggested by R.W. Clough is adopted, and only the stiffness of the foundation is considered, while the influence of its mass on the dynamic characteristics of the structure is ignored. ANSYS APDL finite element software was used to establish the equivalent finite element model of the test model, solid45 solid element was used to generate hexahedral mesh, and the peripheral constraints of the dam foundation were taken as fixed hinge supports. The finite element model is shown in Figure 1.
When the finite element simulation of the arch dam structure with water level modeling is carried out, this paper uses the Westergaard additional mass model method and the fluid-solid coupling model method to simulate the influence of a 300 mm water level on the arch dam structure.
The additional mass model does not consider the compressibility of reservoir water. According to the "Code for Seismic Design of Hydraulic Structures", the Westergaard formula is used to calculate the additional mass. In the case of an arch dam (non-gravity dam), the calculation result of the formula is halved. In ANSYS, the mass21 unit is used to simulate the additional mass of hydraulic pressure, and 672 mass21 units are added to the upstream dam surface of the dam body model. The finite element model is shown in Figure 2, and the additional mass of the unit with a height of more than 300 mm in the figure is 0. When the finite element simulation of the arch dam structure with water leve eling is carried out, this paper uses the Westergaard additional mass model meth the fluid-solid coupling model method to simulate the influence of a 300 mm wat on the arch dam structure. The additional mass model does not consider the compressibility of reservoir According to the "Code for Seismic Design of Hydraulic Structures", the Westerga mula is used to calculate the additional mass. In the case of an arch dam (nondam), the calculation result of the formula is halved. In ANSYS, the mass21 unit is simulate the additional mass of hydraulic pressure, and 672 mass21 units are adde upstream dam surface of the dam body model. The finite element model is shown ure 2, and the additional mass of the unit with a height of more than 300 mm in th is 0.
When the fluid-solid coupling model is used to simulate the influence of wat sure on the structure, the compressibility of water will be considered. In ANSYS, ervoir is simulated with the fluid30 unit, and the SF (FSI) command is used to rea fluid-solid coupling at the interface between the reservoir and the dam. The wate parameter density is 1000 kg/m 3 , and the sound velocity in the water body is 14 There are 9300 fluid30 units in the model, and the finite element model is shown in 2. When the structure is partially damaged, the impact on the overall quality structure is very small, mainly involving a change of stiffness; thus, the structural d is realized by reducing the stiffness, and the degree of damage is manifested as a d in the elastic modulus (For example, damage of 15% means that the modulus of el When the fluid-solid coupling model is used to simulate the influence of water pressure on the structure, the compressibility of water will be considered. In ANSYS, the reservoir is simulated with the fluid30 unit, and the SF (FSI) command is used to realize the fluid-solid coupling at the interface between the reservoir and the dam. The water body parameter density is 1000 kg/m 3 , and the sound velocity in the water body is 1460 m/s. There are 9300 fluid30 units in the model, and the finite element model is shown in Figure 2.
When the structure is partially damaged, the impact on the overall quality of the structure is very small, mainly involving a change of stiffness; thus, the structural damage is realized by reducing the stiffness, and the degree of damage is manifested as a decrease in the elastic modulus (For example, damage of 15% means that the modulus of elasticity decreases by 15%.). Furthermore, the reduction of the elastic modulus is only centralized in the damage zone. Figure 3 shows the location of the damage and the location of the measuring point. In order to reflect the two locations more clearly, only the dam body part is shown in the figure, and the dam foundation part is not shown. The blue line is the location of the measuring point. Each node from left to right is measuring point 1, measuring point 2, . . . , measuring point 32. The red area unit is the damage position, as decreases by 15%.). Furthermore, the reduction of the elastic modulus is on in the damage zone. Figure 3 shows the location of the damage and the l measuring point. In order to reflect the two locations more clearly, only the d is shown in the figure, and the dam foundation part is not shown. The b location of the measuring point. Each node from left to right is measuring p uring point 2, …, measuring point 32. The red area unit is the damage posit in Figure 3. The depth of the damage position unit is half of the thickness of t The left-side position is Lesion 1, and the one near the middle is Lesion 2.
(a) (b) The curvature of any point on a plane curve can be approximated as [2 In the formula, w is the bending deformation deflection of the structur ordinate along the length direction of the structure.
The curvature mode cannot be directly measured, but it can be obtain through the structural mode shape. On the basis of the mode shape data, the curvature mode can be obtained through the center difference calculation kj Z denote the curvature mode of the structure state and the displacement tively; the curvature mode is: In the formula, k is the structural node number; j is the modal order distance between two adjacent measuring points k − 1 and k.
Let u ϕ and d ϕ be the curvature modes of the structure before and respectively. The relative difference of the curvature mode at point k on the responding to the two states is used as an index to locate the damage, which as:  The curvature of any point on a plane curve can be approximated as [23]: In the formula, w is the bending deformation deflection of the structure; x is the coordinate along the length direction of the structure.
The curvature mode cannot be directly measured, but it can be obtained indirectly through the structural mode shape. On the basis of the mode shape data, the approximate curvature mode can be obtained through the center difference calculation. Let ϕ kj and Z kj denote the curvature mode of the structure state and the displacement mode, respectively; the curvature mode is: In the formula, k is the structural node number; j is the modal order; and d is the distance between two adjacent measuring points k − 1 and k.
Let ϕ u and ϕ d be the curvature modes of the structure before and after damage, respectively. The relative difference of the curvature mode at point k on the structure corresponding to the two states is used as an index to locate the damage, which is calculated as:

Wavelet Packet Energy Curvature
The characteristic information of the structural damage is obtained through effective extraction and calculation from the wavelet packet energy spectrum, and a feature vector suitable for structural damage identification is formed [24].
The total energy E i obtained after decomposing the j layer with the wavelet packet is obtained by Formula (4): In the formula, j is the number of decomposition layers, i is the frequency band number, and E i j is the energy of the corresponding frequency band. Calculate the energy curvature at the k point using the second-order difference method: The relative difference of the energy curvature before and after the damage is: In the formula, K u k and K d k are the wavelet packet energy curvatures of the k measuring point before and after the damage, respectively.

Modulus of Curvature
Set the damage according to the damage position in Figure 3, first reduce the elastic modulus of the damage 1 unit by 15% and 30%, respectively, and use the modal analysis function of the ANSYS finite element software to obtain the first 4 orders from measuring point 1 to measuring point 32. The mode shape data are in the y-direction of the mode (the x-direction is the width direction of the dam, the y-direction is the direction of the reservoir, and the z-direction is the height direction). Calculate the obtained mode shape data to obtain the δϕ k of each measuring point; the result is shown in Figure 4. In the first-order mode, the results of measuring point 8 and measuring point 9 are significantly higher than those of the other measuring points, which are just at the position of damage 1, and the damage identification results are remarkable; in the second-order mode, the result of 9 is greater than that of the adjacent measuring point, but there is an obvious misjudgment at measuring point 3, and it is greater than measuring point 8 and measuring point 9; in the third-order mode, it is similar to the second-order mode, although measuring point 8 and the result of measuring point 9 are obviously higher than those of other measuring points, but there is an obvious misjudgment at measuring point 5; in the results of the fourth-order mode, the results of measuring point 8 and measuring point 9 are significantly higher than other measuring points, and the damage identification results are significant. Therefore, it is feasible to use δϕ k to identify the damage location, but because the damage identification results will be affected by the structural shape and mode shape during calculation, misjudgment may occur, resulting in a decrease in the accuracy of damage identification or even an error in identification. According to Figure 3, two damage locations are set at the same time, and the elastic moduli of the damage 1 and damage 2 elements are reduced by 15% and 30%, respectively; the first four vibration modes in the y direction are also obtained and calculated as δϕ k . The calculation results are shown in Figure 5.
It can be seen from Figure 5 that, similar to the case of a single damage, the first-order mode and the fourth-order mode have obvious peaks at measuring points 8, 9, 17 and 18, which are damage 1 and damage 2. The position of 2 can be used to identify the damage position in the case of double damage, but in the first-order mode, the identification effect of damage 1 is lower than that of damage 2. The second-order mode and the third-order mode had obvious misjudgment problems at measuring point 3 and measuring point 13, respectively, and damage 2 was not identified in the second-order mode. Therefore, it is feasible to use δϕ k to identify the damage location. According to Figure 3, two damage locations are set at the same time, an moduli of the damage 1 and damage 2 elements are reduced by 15% and 30%, r the first four vibration modes in the y direction are also obtained and calcula The calculation results are shown in Figure 5.
It can be seen from Figure 5 that, similar to the case of a single damage, th mode and the fourth-order mode have obvious peaks at measuring points 8, which are damage 1 and damage 2. The position of 2 can be used to identify position in the case of double damage, but in the first-order mode, the identifi of damage 1 is lower than that of damage 2. The second-order mode and the mode had obvious misjudgment problems at measuring point 3 and measuri respectively, and damage 2 was not identified in the second-order mode. Th feasible to use k δϕ to identify the damage location.    According to Figure 3, two damage locations are set at the same time, and th moduli of the damage 1 and damage 2 elements are reduced by 15% and 30%, resp the first four vibration modes in the y direction are also obtained and calculated The calculation results are shown in Figure 5.
It can be seen from Figure 5 that, similar to the case of a single damage, the fi mode and the fourth-order mode have obvious peaks at measuring points 8,9,17 which are damage 1 and damage 2. The position of 2 can be used to identify the position in the case of double damage, but in the first-order mode, the identificati of damage 1 is lower than that of damage 2. The second-order mode and the thi mode had obvious misjudgment problems at measuring point 3 and measuring respectively, and damage 2 was not identified in the second-order mode. There feasible to use k δϕ to identify the damage location.

Wavelet Coefficient
Perform a wavelet transform on the mode shape obtained above, in which c is selected as the wavelet base, two layers are decomposed and the detail coeffic taken. For the convenience of comparison, the absolute value of the wavelet coe k Wf ) is obtained. The elastic moduli of the damage 1 and damage 2 units were

Wavelet Coefficient
Perform a wavelet transform on the mode shape obtained above, in which coif3 [12] is selected as the wavelet base, two layers are decomposed and the detail coefficient d 1 is taken. For the convenience of comparison, the absolute value of the wavelet coefficient (|W f k |) is obtained. The elastic moduli of the damage 1 and damage 2 units were respectively reduced by 30%, and the damage position was identified by using wavelet coefficients in the case of double damage. The absolute values of the wavelet high-frequency coefficient d1 of the first two vibration modes were calculated, as shown in Figure 6. Almost no damage was identified in the first-order mode. Although the result of damage 2 at measuring point 17 was higher than that of the adjacent points, there were too many misjudgments, and it was larger than the damage, so it was difficult to identify the damage to the structure. In the second-order mode, the wavelet coefficients of measuring point 7 and measuring point 17 are larger than those of the adjacent points, but as shown with measuring point 15 and measuring point 16, the misjudgment still exists, there is an obvious edge problem, and the wavelet coefficients at the edge are larger. Because the wavelet high-frequency coefficients are used for damage identification, the structure formed by the measuring points needs to be smooth enough, and the damage judgment is performed through singular points.

Wavelet Coefficient
Perform a wavelet transform on the mode shape obtained above, in which is selected as the wavelet base, two layers are decomposed and the detail coeffic taken. For the convenience of comparison, the absolute value of the wavelet co k Wf ) is obtained. The elastic moduli of the damage 1 and damage 2 units wer tively reduced by 30%, and the damage position was identified by using wave cients in the case of double damage. The absolute values of the wavelet high-f coefficient d1 of the first two vibration modes were calculated, as shown in Figu most no damage was identified in the first-order mode. Although the result of d at measuring point 17 was higher than that of the adjacent points, there were t misjudgments, and it was larger than the damage, so it was difficult to identify the to the structure. In the second-order mode, the wavelet coefficients of measurin and measuring point 17 are larger than those of the adjacent points, but as sho measuring point 15 and measuring point 16, the misjudgment still exists, there is ous edge problem, and the wavelet coefficients at the edge are larger. Because th high-frequency coefficients are used for damage identification, the structure fo the measuring points needs to be smooth enough, and the damage judgment is p through singular points. Because the use of wavelet high-frequency coefficients for damage identific quires that the structure formed by the measuring points be smooth enough, thi the reason for the poor identification results, Therefore, the 32 measuring points bled and expanded to 64 measuring points, and the damage position and measur position are rearranged as shown in the blue curve in Figure 7. The measuring p Because the use of wavelet high-frequency coefficients for damage identification requires that the structure formed by the measuring points be smooth enough, this may be the reason for the poor identification results, Therefore, the 32 measuring points are doubled and expanded to 64 measuring points, and the damage position and measuring point position are rearranged as shown in the blue curve in Figure 7. The measuring points are measuring point 1 and measuring point 2, . . . . . . , measuring point 64 from left to right, where the red unit area ##1 is damage 1 and ##2 is damage 2. The elastic moduli of the ##1 and ##2 units are reduced by 30%, and in order to reduce the influence of the edge effect, the symmetric data expansion is first performed on the mode shape data before calculating the wavelet coefficients; the wavelet coefficients are obtained as shown in Figure 8. After doubling the number of measuring points, the calculation results of measuring points 34, 35 and measuring points 55, 56 of the first-order mode and second-order mode are larger than other adjacent measuring points, and the measuring point is exactly the ##1 and ##2 damage locations. Damage identification can be carried out, but at the measuring point at the edge, the absolute value of the wavelet high-frequency coefficient is relatively large because there will be obvious edge effects when performing wavelet transform [25], so when using this method for damage identification, there must be a sufficient number of measuring points first so that the mode shape data of the measuring points can form a smooth curve. At the same time, the measuring points should be a power series of 2 to the extent that it is possible, so the recommended measuring points should be as numerous as possible. However, when identifying damage locations, the edge effect of wavelet transforming may affect the identification of damage at the edge. number of measuring points first so that the mode shape data of the m form a smooth curve. At the same time, the measuring points should 2 to the extent that it is possible, so the recommended measuring poi merous as possible. However, when identifying damage locations, the let transforming may affect the identification of damage at the edge.

Wavelet Packet Energy
Because the wavelet packet energy needs to be obtained by wav position of the acceleration time-history data, there are two transient ANSYS, the mode superposition method (Mode Superpos'n) and the The complete method has a faster solution speed and takes up less the modal superposition method is used for transient analysis of the shows the location of the excitation, and the direction of action is alon the arch dam. Figure 10 shows the applied excitation. The action time 2 to the extent that it is possible, so the recommended measuring points sho merous as possible. However, when identifying damage locations, the edge eff let transforming may affect the identification of damage at the edge. Because the wavelet packet energy needs to be obtained by wavelet pa position of the acceleration time-history data, there are two transient analysi ANSYS, the mode superposition method (Mode Superpos'n) and the full m The complete method has a faster solution speed and takes up less memor the modal superposition method is used for transient analysis of the struct shows the location of the excitation, and the direction of action is along the w the arch dam. Figure 10 shows the applied excitation. The action time is 0.002

Wavelet Packet Energy
Because the wavelet packet energy needs to be obtained by wavelet packet decomposition of the acceleration time-history data, there are two transient analysis methods in ANSYS, the mode superposition method (Mode Superpos'n) and the full method (Full). The complete method has a faster solution speed and takes up less memory. Therefore, the modal superposition method is used for transient analysis of the structure. Figure 9 shows the location of the excitation, and the direction of action is along the water flow to the arch dam. Figure 10 shows the applied excitation. The action time is 0.002 s, the size is 10,000 N, the damping ratio ALPHAD = 0.02, the acquisition interval of the time history signal is 0.1 ms, and the acquisition time is 1000 ms; the displacement time history curve of the measuring point is obtained, the velocity displacement curve is obtained by derivation, and the derivative is obtained again as an acceleration time-history curve. Taking no damage as an example, Figure 11 is the displacement time-history curve of measuring point 1, and Figure 12 is its acceleration time-history curve.
Buildings 2023, 13, x FOR PEER REVIEW 10 10,000 N, the damping ratio ALPHAD = 0.02, the acquisition interval of the time his signal is 0.1 ms, and the acquisition time is 1000 ms; the displacement time history c of the measuring point is obtained, the velocity displacement curve is obtained by de tion, and the derivative is obtained again as an acceleration time-history curve. Takin damage as an example, Figure 11 is the displacement time-history curve of measu point 1, and Figure 12 is its acceleration time-history curve.         The obtained acceleration time-history curve is decomposed by wavelet packet d composition, and the wavelet basis function is selected as db3 [24] to decompose thr layers. The energy of the wavelet packet is calculated, and the relative difference of t energy k K δ of the wavelet packet is calculated, as shown in Figure 12. The obtained acceleration time-history curve is decomposed by wavelet packet decomposition, and the wavelet basis function is selected as db3 [24] to decompose three layers. The energy of the wavelet packet is calculated, and the relative difference of the energy δK k of the wavelet packet is calculated, as shown in Figure 12. Figure 13a shows the δK k calculation results when only damage 1 is set. It can be seen that the results at measuring point 4 and measuring point 8 are significantly larger than those at other points, and measuring point 8 is exactly the location of damage 1, which can be used for damage identification. Compared to the use of modal curvature for damage position identification, except for the δK k , the calculation results of the measuring points at the damage position are much smaller than those at the measuring point. The recognition effect is better than using δK k , but there is a misjudgment of the position of measuring point 4, which will reduce recognition accuracy; except for the misjudgment of measuring point 4, the damage δK k is 6.23 times the maximum value of the non-damage. Figure 13b shows the δK k calculation results when damage 1 and damage 2 are set at the same time. The calculation results of measurement point 8 and measurement point 18 are larger than other points, and double damage can be identified, but measurement point 4 still appears to be misjudged; excepting the misjudgment at point 4, δK k at the damage site is 5.18 and 4.95 times the maximum value at the non-damage site. At the same time, it can be found that when the damage degree increases from 15% to 30%, the calculated δK k of each measuring point increases by about once over. The obtained acceleration time-history curve is decomposed by wavelet pa composition, and the wavelet basis function is selected as db3 [24] to decompo layers. The energy of the wavelet packet is calculated, and the relative differenc energy k K δ of the wavelet packet is calculated, as shown in Figure 12. Figure 13a shows the k K δ calculation results when only damage 1 is set. I seen that the results at measuring point 4 and measuring point 8 are significantl than those at other points, and measuring point 8 is exactly the location of da which can be used for damage identification. Compared to the use of modal curva damage position identification, except for the k K δ , the calculation results of the ing points at the damage position are much smaller than those at the measurin The recognition effect is better than using k K δ , but there is a misjudgment of the of measuring point 4, which will reduce recognition accuracy; except for the misju of measuring point 4, the damage k K δ is 6.23 times the maximum value of the no age. Figure 13b shows the  This method uses the wavelet packet to decompose the dynamic response of the damaged structure, so as to obtain the energy distribution of the signal on each scale and to form a singular value by amplifying the characteristics of the damage location by forming the damage identification index of the wavelet packet energy. Because of the large change in the damage identification structure, the result at the damage location is larger than that at other locations, which is the same as the calculation result in the figure.
Using three wavelet bases of db3, sym3 and coif3, the damage recognition results of decomposing layers 1 to 8 for the above single-damage situation are shown in Figure 14. It can be found that all three wavelet bases can identify the damage, and there is a misjudgment of measuring point 4. There is little difference in the recognition effect of different wavelet bases and different decomposition layers. Among them, db3 and sym3 increase as the number of decomposition layers increases, the k at the damage site increases gradually, and the damage identification effect improves slightly. When the decomposition layer count exceeds seven layers, the δK k of each measuring point remains basically unchanged, and coif3 also basically remains unchanged after reaching seven layers. As the number of wavelet decomposition layers increases, more signal components are obtained, and the analysis results are more refined, so the damage identification results are improved accordingly. At the same time, if the number of decomposition layers is too high, problems such as overfitting may occur, and the amount of calculation will increase sharply, so it needs to be analyzed according to the specific situation.
unchanged, and coif3 also basically remains unchanged after reaching seven layers. As the number of wavelet decomposition layers increases, more signal components are obtained, and the analysis results are more refined, so the damage identification results are improved accordingly. At the same time, if the number of decomposition layers is too high, problems such as overfitting may occur, and the amount of calculation will increase sharply, so it needs to be analyzed according to the specific situation.

Modal Curvature
Because the arch dam structure cannot ignore the influence of water pressure, the fluid-solid coupling method is used in ANSYS to simulate the influence caused by the high water level of the 3/4 dam, and the modal solution method is an asymmetric solution. Reduce the elastic modulus of the damage 1 unit by 15% and 30%, and calculate δϕ k in the same way as when there is no water level. The single-damage identification results are shown in Figure 15. Similar to the no-water-level scenario, in the first-order mode, the results of measuring point 8 and measuring point 9 are significantly higher than other measuring points, which is the location of damage 1, and the damage identification results are remarkable. Neither the third-order mode nor the fourth-order mode can clearly identify the damage position, and the identification level is poor. Differently from the case of no water level, in the second-order, third-order and fourth-order mode shapes, there were misjudgments at different positions, which seriously reduced the recognition accuracy. The positive correspondence shows that the the mode shape will affect the damage identification effect of δϕ k , and generally, the more complicated the shape is, the worse the identification result will be. second-order mode still has an obvious misjudgment at measuring point 3, and the second-order mode does not identify damage 2. The third-order mode does not identify damage 1, which is different from the no-water-level scenario. The fourth-order mode has an obvious misjudgment at measuring point 20.  The double-damage scenario is also similar to the case of no water level; the elastic moduli of damage 1 and damage 2 are lowered by 15% and 30%, respectively, and the damage identification results are shown in Figure 16. The first-order mode has obvious peaks at measuring point 8, measuring point 9, measuring point 17 and measuring point 18, which are the positions of damage 1 and damage 2, and double damage can be identified, but in the first-order mode, Lesion 1 is less effective in recognition than Lesion 2. The second-order mode still has an obvious misjudgment at measuring point 3, and the secondorder mode does not identify damage 2. The third-order mode does not identify damage 1, which is different from the no-water-level scenario. The fourth-order mode has an obvious misjudgment at measuring point 20.

Wavelet Packet Energy
When using the fluid-solid coupling method to obtain the acceleration time-history data of the measurement point, the fluid30 unit is used, and the sound velocity of water is set. Therefore, only asymmetric solutions can be used for modal solutions, and the modal superposition method cannot be used for the results of asymmetric solutions, so in the transient analysis of the fluid-solid coupling method, the mode is no longer solved, but the complete method is directly used for the transient solution. The rest of the operations are the same as the anhydrous level. After the acceleration time-history curve is obtained, it is decomposed by wavelet packets, and then k K δ is calculated.
As with the water level, the calculation results of

Wavelet Packet Energy
When using the fluid-solid coupling method to obtain the acceleration time-history data of the measurement point, the fluid30 unit is used, and the sound velocity of water is set. Therefore, only asymmetric solutions can be used for modal solutions, and the modal superposition method cannot be used for the results of asymmetric solutions, so in the transient analysis of the fluid-solid coupling method, the mode is no longer solved, but the complete method is directly used for the transient solution. The rest of the operations are the same as the anhydrous level. After the acceleration time-history curve is obtained, it is decomposed by wavelet packets, and then δK k is calculated.
As with the water level, the calculation results of δK k are shown in Figure 17. Similarly, the results of measuring point 8 in the case of a single damage are significantly higher than those of other measuring points, and the calculation results of measuring point 8 and measuring point 18 in the case of double damage are significantly higher than other measuring points. However, there are still misjudgments at measuring point 4. Except for the misjudged measurement point 4, the δK k at the damaged site under the single-damage condition is 11.15 times the maximum value at the non-damaged site, and the δK k at the damaged site under the double-damage condition is 5.45 and 4.09 times the maximum value at the non-damaged site.
other measuring points. However, there are still misjudgments at measuring poi cept for the misjudged measurement point 4, the k K δ at the damaged site under gle-damage condition is 11.15 times the maximum value at the non-damaged site, k K δ at the damaged site under the double-damage condition is 5.45 and 4.09 ti maximum value at the non-damaged site. When there is a water level, compared with the use of δϕ k , there are more misjudgments, and some modes do not even recognize the damage. Except for the misjudgment at measuring point 4, the damage position identification ability of δK k is still very strong, and it can clearly and accurately identify the locations of single damages and double damages, which is better than using curvature mode identification.

Data Fusion Damage Identification of Arch Dam
From Section 2.3, we can see that when using δϕ k and δK k for damage identification in arch dam structures, although the two damage indicators can basically identify the damage location, misjudgment of different positions may occur during the identification process, thus affecting the accuracy of damage identification. Therefore, D-S evidence theory is used to improve the recognition accuracy. Using D-S evidence theory to fuse the δϕ k and δK k obtained in the second chapter, the feature-level data are calculated, and the fusion result is obtained. In order to verify the damage identification ability of the D-S data fusion results, the δϕ k and δK k calculation results of the first mode when the damage is 15% are used to calculate the fusion results with or without a water level and with single or double damage. Figure 18 shows the fusion results of single damage and double damage when there is no water level in the arch dam structure. It can be seen that in the case of single damage, the fusion result of measuring point 7 at the damage position is 8.75 times the maximum value at the non-damage point, and the relative δK k is increased by 40.4%. The fusion results at the non-damaged position are close to 0, and the misjudgment of measuring point 4 is cleared when δK k is used. In the double-damage scenario, the fusion result of measuring point 7 at the damage position is 10.10 times that of the maximum measuring point 4 at the non-damage point, the fusion result of measuring point 18 is 5.02 times that of measuring point 4, and the relative δK k increases by 94.9% and 14.1%. Similarly, the fusion results at the non-damaged position are almost all close to 0, the misjudgment of measuring point 4 is eliminated when δK k is used, the misjudgment of measuring point 15 is eliminated when δϕ k is used, and there is no misjudgment phenomenon. Figure 19 shows the fusion results of single damage and double damage when the fluid-solid coupling method is used to simulate a water level of 300 mm for the arch dam structure. It can be seen that it is similar to the case of no water level. Except for the measurement point of the damage position, the fusion results of the other measurement points are almost 0. In the case of single damage, the fusion result of measuring point 7 at the damaged position is 15.36 times that of measuring point 4 at the non-damaged position, and the relative δK k is increased by 37.8%. The fusion result of double-damage measuring point 7 is 17.50 times that of measuring point 10, the fusion result of measuring point 18 is 19.23 times that of measuring point 10, and the relative δK k increases by 221.1% and 370.2%. The accuracy of damage identification is greatly improved, and the misjudgment at measurement point 4 is also eliminated when only δK k is used.
Therefore, the use of D-S evidence theory for data fusion can greatly improve the accuracy of damage identification regardless of whether the arch dam has a water level or single or double damage, and it can eliminate the possible misjudgment of the singledamage identification method.
value at the non-damage point, and the relative Therefore, the use of D-S evidence theory for data fusion can greatly improv accuracy of damage identification regardless of whether the arch dam has a water le single or double damage, and it can eliminate the possible misjudgment of the s damage identification method.

Identification of Damage Degree of Arch Dam
Change the mesh division of the finite element model in ANSYS so that the m nodes correspond to the positions of the test sensors, and modify the mesh divisi other positions accordingly to obtain a new finite element model, as shown in Figu Apply the same excitation as in the second chapter, and Figure 21 shows the applie citation position and measuring point position.

Identification of Damage Degree of Arch Dam
Change the mesh division of the finite element model in ANSYS so that the model nodes correspond to the positions of the test sensors, and modify the mesh division of other positions accordingly to obtain a new finite element model, as shown in Figure 20. Apply the same excitation as in the second chapter, and Figure 21 shows the applied excitation position and measuring point position. Therefore, the use of D-S evidence theory for data fusion can greatly improve the accuracy of damage identification regardless of whether the arch dam has a water level o single or double damage, and it can eliminate the possible misjudgment of the single damage identification method.

Identification of Damage Degree of Arch Dam
Change the mesh division of the finite element model in ANSYS so that the mode nodes correspond to the positions of the test sensors, and modify the mesh division o other positions accordingly to obtain a new finite element model, as shown in Figure 20 Apply the same excitation as in the second chapter, and Figure 21 shows the applied ex citation position and measuring point position.   Therefore, the use of D-S evidence theory for data fusion can greatly improve the accuracy of damage identification regardless of whether the arch dam has a water level or single or double damage, and it can eliminate the possible misjudgment of the singledamage identification method.

Identification of Damage Degree of Arch Dam
Change the mesh division of the finite element model in ANSYS so that the model nodes correspond to the positions of the test sensors, and modify the mesh division of other positions accordingly to obtain a new finite element model, as shown in Figure 20. Apply the same excitation as in the second chapter, and Figure 21 shows the applied excitation position and measuring point position.   When the wavelet basis function is selected, the SymN (SymletN, N = 2, 3, 4, . . . 8) wavelet basis function has good time-frequency information localization ability and can effectively reduce the influence of noise in the acceleration signal. The more N increases, the greater the order of the vanishing distance of the Sym wavelet basis function is, the greater the local capability of the wavelet is, and the clearer the frequency band formed, so it is advised to choose as large an N value as possible [26]. In this article, Sym8 is chosen.
When choosing the number of decomposition layers of the wavelet base, it should be considered that the energy entropy obtained by processing the data should be as small as possible, and at the same time, the time cost should be considered. Taking the acceleration time-history data of measuring point 1 without damage as an example, Table 1 shows the calculation results of the total energy entropy and the time used for different numbers of decomposition layers. Considering the influence of the two factors comprehensively, the number of wavelet packet decomposition layers is determined to be 13 layers.

Defect Introduction
Use the deleted damage position unit to simulate the damage of the cavity in the structure, and keep the rest of the position unchanged. The greater the damage, the larger the volume of the unit that is deleted. Figure 22 is a finite element model for simulating single damage, and Figure 23 is a finite element model for simulating double damage.
Buildings 2023, 13, x FOR PEER REVIEW time-history data of measuring point 1 without damage as an example, Table 1 s calculation results of the total energy entropy and the time used for different nu decomposition layers. Considering the influence of the two factors comprehens number of wavelet packet decomposition layers is determined to be 13 layers.

Defect Introduction
Use the deleted damage position unit to simulate the damage of the cavi structure, and keep the rest of the position unchanged. The greater the damage, t the volume of the unit that is deleted. Figure 22 is a finite element model for si single damage, and Figure 23 is a finite element model for simulating double da

ERVD Calculation Results
After applying excitation to the excitation point, output the acceleration tim data in the y direction of the three measurement points, and then perform wavel decomposition and calculate the energy of each frequency band. Because low-en quency bands are more susceptible to noise, and the noise is evenly distributed frequency band [27], only the first 10% of the energy bands are calculated, and the ing frequency bands with lower energy are discarded. Finally, the damage p ERVD of different damage volumes is calculated, and the damage volume is 1.8 ×  Table 1 s calculation results of the total energy entropy and the time used for different nu decomposition layers. Considering the influence of the two factors comprehens number of wavelet packet decomposition layers is determined to be 13 layers.

Defect Introduction
Use the deleted damage position unit to simulate the damage of the cav structure, and keep the rest of the position unchanged. The greater the damage, the volume of the unit that is deleted. Figure 22 is a finite element model for s single damage, and Figure 23 is a finite element model for simulating double da

ERVD Calculation Results
After applying excitation to the excitation point, output the acceleration tim data in the y direction of the three measurement points, and then perform wave decomposition and calculate the energy of each frequency band. Because low-e quency bands are more susceptible to noise, and the noise is evenly distribute frequency band [27], only the first 10% of the energy bands are calculated, and th ing frequency bands with lower energy are discarded. Finally, the damage p ERVD of different damage volumes is calculated, and the damage volume is 1.8

ERVD Calculation Results
After applying excitation to the excitation point, output the acceleration time-history data in the y direction of the three measurement points, and then perform wavelet packet decomposition and calculate the energy of each frequency band. Because low-energy frequency bands are more susceptible to noise, and the noise is evenly distributed on each frequency band [27], only the first 10% of the energy bands are calculated, and the remaining frequency bands with lower energy are discarded. Finally, the damage parameter ERVD of different damage volumes is calculated, and the damage volume is 1.8 × 10 3 mm 3 to 54 × 10 3 mm 3 . Figure 24a,b are the calculation results of ERVD with no water level and the water level of 300 mm imitated by the fluid-structure interaction method, respectively. It can be seen that regardless of whether there is water level or different measuring points, ERVD increases with the increase of the damage volume, and the relationship is not linear. From the solution process of ERVD, it can be found that ERVD represents the discrete situation of existing data and original data, When the damage increases, the gap between the structure and the lossless structure increases, and the energy between different wavelet packet frequency bands and the original complete structure will change, so the ERVD will also increase with the increase of the damage volume.
Buildings 2023, 13, x FOR PEER REVIEW the structure and the lossless structure increases, and the energy between differen let packet frequency bands and the original complete structure will change, so th will also increase with the increase of the damage volume.

BP Neural Network Fitting Prediction
For the case of single damage, use the ANSYS software to expand to 50 sets Let the ERVD obtained from measuring point 1 be ERVD1, the ERVD obtained from uring point 2 be ERVD2 and the ERVD obtained from measuring point 3 be ERV input layer of the neural network is ERVD1, the output layer is the damage volu the neuron data of the hidden layer are selected according to the empirical Form [24] for neural network training: h m n a = + + In the formula, h is the number of nodes in the hidden layer, m is the number o in the input layer, n is the number of nodes in the output layer, and a is a constan to 10. The data set is divided into three parts, which are the training set, verifica and test set. The training set is used to train the BP neural network, and the ver set is used to adjust the complexity and network structure of the network. The te used to evaluate the trained network, including 34 training sets, 8 verification se test sets.
In the case of no water level, the neural network iterates 23 times in total. F regression results in Figure 25a, it can be seen that the regression results of the set, verification set and test set basically fall on the straight line L, with a high coin degree. In the case of the water level, the neural network iterates a total of 19 time be seen from Figure 25b that the regression results of the same training set, verifica and test set basically fall on the straight line L. The correlation coefficient R of the without the water level is 0.999995, and the correlation coefficient R of the test set water level is 0.999992, indicating that the trained network can predict the degree age more accurately.

BP Neural Network Fitting Prediction
For the case of single damage, use the ANSYS software to expand to 50 sets of data. Let the ERVD obtained from measuring point 1 be ERVD 1 , the ERVD obtained from measuring point 2 be ERVD 2 and the ERVD obtained from measuring point 3 be ERVD 3 . The input layer of the neural network is ERVD 1 , the output layer is the damage volume, and the neuron data of the hidden layer are selected according to the empirical Formula (7) [24] for neural network training: In the formula, h is the number of nodes in the hidden layer, m is the number of nodes in the input layer, n is the number of nodes in the output layer, and a is a constant from 1 to 10. The data set is divided into three parts, which are the training set, verification set and test set. The training set is used to train the BP neural network, and the verification set is used to adjust the complexity and network structure of the network. The test set is used to evaluate the trained network, including 34 training sets, 8 verification sets and 8 test sets.
In the case of no water level, the neural network iterates 23 times in total. From the regression results in Figure 25a, it can be seen that the regression results of the training set, verification set and test set basically fall on the straight line L, with a high coincidence degree. In the case of the water level, the neural network iterates a total of 19 times. It can be seen from Figure 25b that the regression results of the same training set, verification set and test set basically fall on the straight line L. The correlation coefficient R of the test set without the water level is 0.999995, and the correlation coefficient R of the test set with the water level is 0.999992, indicating that the trained network can predict the degree of damage more accurately.
In the actual test, there will be various factors which will lead to errors in the measured data and reduce the training effect of the neural network. Therefore, it is necessary to add a noise-adding step to the results of the array simulation. Thus, Gaussian white noise is added at three levels of 1%, 5% and 10% to the original acceleration data, and then the neural network is used for fitting prediction. Figure 26 shows the regression analysis results of the neural network after adding three kinds of horizontal white noise under the conditions of no water level and a 300 mm water level, respectively. It can be seen that although the individual predicted value-target value points gradually deviate slightly from the straight line L with the increase of the noise level, most of the points still fall on the straight line L or near the straight line L. Table 2 shows the mean square error MSE and correlation coefficient R of the test set at different noise levels of no water level and a 300 mm water level. From the table, it can be found that with the increase of the noise level, MSE increases continuously, and the correlation coefficient R decreases continuously. When the noise level is 10%, the correlation coefficients R of the conditions of no water level and a 300 mm water level are 0.99972 and 0.99945, respectively, both of which are greater than 0.999, which can effectively identify the degree of damage. In the actual test, there will be various factors which will lead to errors in the measured data and reduce the training effect of the neural network. Therefore, it is necessary to add a noise-adding step to the results of the array simulation. Thus, Gaussian white noise is added at three levels of 1%, 5% and 10% to the original acceleration data, and then the neural network is used for fitting prediction. Figure 26 shows the regression analysis results of the neural network after adding three kinds of horizontal white noise under the conditions of no water level and a 300 mm water level, respectively. It can be seen that although the individual predicted value-target value points gradually deviate slightly from the straight line L with the increase of the noise level, most of the points still fall on the straight line L or near the straight line L. Table 2 shows the mean square error MSE and correlation coefficient R of the test set at different noise levels of no water level and a 300 mm water level. From the table, it can be found that with the increase of the noise level, MSE increases continuously, and the correlation coefficient R decreases continuously. When the noise level is 10%, the correlation coefficients R of the conditions of no water level and a 300 mm water level are 0.99972 and 0.99945, respectively, both of which are greater than 0.999, which can effectively identify the degree of damage.

ERVD Calculation Results
After setting the double damage according to the positions shown in Figure 21, the acceleration time-history data of the numerical simulation are also calculated to obtain the damage parameter ERVD at different damage volumes, and the damage volume is 1.8 × 10 3 mm 3 to 54 × 10 3 mm 3 . The calculation results of ERVD are shown in Figures 27 and 28. It can be seen that ERVD increases continuously with increasing damage volume. Similar to the damage, the magnitude of the increase will decrease with increasing lesion volume.   Output ~= 0.96*Target + 1.2e+03 10 4 Test: R=0.99981 Output ~= 0.99*Target + 3.7e+02 10 4 All: R=0.99958 Data Fit Y = T Figure 26. Neural network regression results after adding white noise to a single damage.

ERVD Calculation Results
After setting the double damage according to the positions shown in Figure 21, the acceleration time-history data of the numerical simulation are also calculated to obtain the damage parameter ERVD at different damage volumes, and the damage volume is 1.8 × 10 3 mm 3 to 54 × 10 3 mm 3 . The calculation results of ERVD are shown in Figures 27 and 28. It can be seen that ERVD increases continuously with increasing damage volume. Similar to the damage, the magnitude of the increase will decrease with increasing lesion volume.

ERVD Calculation Results
After setting the double damage according to the positions shown in Figure 21, the acceleration time-history data of the numerical simulation are also calculated to obtain the damage parameter ERVD at different damage volumes, and the damage volume is 1.8 × 10 3 mm 3 to 54 × 10 3 mm 3 . The calculation results of ERVD are shown in Figures 27 and 28. It can be seen that ERVD increases continuously with increasing damage volume. Similar to the damage, the magnitude of the increase will decrease with increasing lesion volume.

BP Neural Network Fitting Prediction
In the ANSYS finite element software, the damage conditions were expanded to 900 groups, which were input into the BP neural network for training, and the number of neurons in the hidden layer was determined to be 90 by Formula 7. In the case of no water level, the result ERVD 1 of measuring point 1 and the result ERVD 2 of measuring point 2 are used as the input set, and the damage volume of the two positions is used as the output set for network training. The regression results obtained are shown in Figure 29. It is found that the relevant test points of the training set, verification set and test set deviate seriously from the straight line L, and the correlation coefficient R is only about 0.7. The trained neural network cannot meet the requirements and cannot effectively identify the degree of damage.
Both ERVD 1 and ERVD 2 are used as input sets to train the neural network. Figure 30a is the regression result in the case of no water level, and Figure 30b is the regression result in the case of a 300 mm water level. It can be found that when the ERVD of the two measurement points is used as the input set for training at the same time, the regression results of the neural network are greatly improved, and the training set, verification set, test set and overall related test points all fall near the straight line L; the regression curve formed by the test points and the straight line L have a great coincidence degree, the size of the test set R is about 0.9999, the correlation coefficient R of the overall data set without a water level exceeds 0.99999, and the correlation coefficient R of the overall data set with a water level exceeds 0.9999. This shows that the trained neural network can meet the prediction requirements. However, the recognition accuracy of double damage is lower than that of single damage, and the recognition effect is weaker than that of single damage.

BP Neural Network Fitting Prediction
In the ANSYS finite element software, the damage conditions were expanded to 900 groups, which were input into the BP neural network for training, and the number of neurons in the hidden layer was determined to be 90 by Formula 7. In the case of no water level, the result ERVD1 of measuring point 1 and the result ERVD2 of measuring point 2 are used as the input set, and the damage volume of the two positions is used as the output set for network training. The regression results obtained are shown in Figure 29. It is found that the relevant test points of the training set, verification set and test set deviate seriously from the straight line L, and the correlation coefficient R is only about 0.7. The trained neural network cannot meet the requirements and cannot effectively identify the degree of damage. Both ERVD1 and ERVD2 are used as input sets to train the neural network. Figure 30a is the regression result in the case of no water level, and Figure 30b is the regression result in the case of a 300 mm water level. It can be found that when the ERVD of the two measurement points is used as the input set for training at the same time, the regression results of the neural network are greatly improved, and the training set, verification set, test set and overall related test points all fall near the straight line L; the regression curve formed by the test points and the straight line L have a great coincidence degree, the size of the test set R is about 0.9999, the correlation coefficient R of the overall data set without a water level exceeds 0.99999, and the correlation coefficient R of the overall data set with a water level exceeds 0.9999. This shows that the trained neural network can meet the prediction requirements. However, the recognition accuracy of double damage is lower than that of single damage, and the recognition effect is weaker than that of single damage. White noise is also added to the case of double damage to verify the anti-noise interference ability of ERVD in the case of double damage. The level of white noise added is 1%, 5% and 10%, as in the case of single damage, the anti-noise ability of ERVD calculation is judged, and its neural network regression results are shown in Figure 31. When white noise is added, the impact of noise is more serious than in the case of single damage. When the noise level reaches 10%, some test points deviate from the straight line L, but most of the test points still fall on the straight line L. The correlation coefficient R of the neural network is above 0.99 when there is no water level and when there is a water level, which shows that the quantitative identification of double damage using ERVD has a good ability to resist noise interference. Output ~= 1*Target + 11 10 4 All: R=0.99996 White noise is also added to the case of double damage to verify the anti-noise interference ability of ERVD in the case of double damage. The level of white noise added is 1%, 5% and 10%, as in the case of single damage, the anti-noise ability of ERVD calculation is judged, and its neural network regression results are shown in Figure 31. When white noise is added, the impact of noise is more serious than in the case of single damage. When the noise level reaches 10%, some test points deviate from the straight line L, but most of the test points still fall on the straight line L. The correlation coefficient R of the neural network is above 0.99 when there is no water level and when there is a water level, which shows that the quantitative identification of double damage using ERVD has a good ability to resist noise interference.
White noise is also added to the case of double damage to verify the anti-noise interference ability of ERVD in the case of double damage. The level of white noise added is 1%, 5% and 10%, as in the case of single damage, the anti-noise ability of ERVD calculation is judged, and its neural network regression results are shown in Figure 31. When white noise is added, the impact of noise is more serious than in the case of single damage. When the noise level reaches 10%, some test points deviate from the straight line L, but most of the test points still fall on the straight line L. The correlation coefficient R of the neural network is above 0.99 when there is no water level and when there is a water level, which shows that the quantitative identification of double damage using ERVD has a good ability to resist noise interference. Output ~= 1*Target + 41 10 4 All: R=0.99955

Experiment Method
The physical picture of the scale model used in the tests in this chapter is shown in Figure 32. The dam foundation is made of C15 commercial concrete with a density of 2.02 × 10 3 kg/m 3 and an elastic modulus of 2.2 × 10 4 Mpa. Because the thickness of the dam body

Experiment Method
The physical picture of the scale model used in the tests in this chapter is shown in Figure 32. The dam foundation is made of C15 commercial concrete with a density of 2.02 × 10 3 kg/m 3 and an elastic modulus of 2.2 × 10 4 Mpa. Because the thickness of the dam body in the scale model is small, in order to prevent the coarse aggregate in the concrete from affecting the molding, the dam body part is made of M10 cement mortar [19], with a density of 2.1 × 10 3 kg/m 3 and an elastic modulus of 1.60 × 10 4 Mpa. In order to prevent the model from cracking in advance, a steel wire mesh with a diameter of 1 mm is added to the dam body.

Damage Location Identification
The modal test is carried out on the poured arch dam structure. The accelerat sor is a 1A111E-type acceleration sensor, the signal collection device is a Jiangsu D Test DH5922D (12CH) collection device, and the acquisition system is a Jiangsu D Test DHDAS dynamic signal acquisition system. The structure is excited by a h the acceleration time-history curve is obtained in the acquisition system, and th information is obtained in the FFT window. Figure 33 shows the acceleration sens their layout. A total of 11 acceleration sensors are placed at an average distance of from the dam crest.  Figure 34 shows the first fou tion modes obtained from the test. The first vibration mode is antisymmetric, the vibration mode is positively symmetrical, the third vibration mode is positively s rical, and the fourth vibration mode is antisymmetric, which verifies the correctne finite element numerical model in the second chapter. This test is divided into four groups: the first and second groups are the no-water-level test group and the water-level test group with single damage, respectively; the third group and the fourth group are the no-water-level test group and the water-level test group with double damage, respectively, as shown in the Table 3.

Damage Location Identification
The modal test is carried out on the poured arch dam structure. The acceleration sensor is a 1A111E-type acceleration sensor, the signal collection device is a Jiangsu Donghua Test DH5922D (12CH) collection device, and the acquisition system is a Jiangsu Donghua Test DHDAS dynamic signal acquisition system. The structure is excited by a hammer, the acceleration time-history curve is obtained in the acquisition system, and the modal information is obtained in the FFT window. Figure 33 shows the acceleration sensors and their layout. A total of 11 acceleration sensors are placed at an average distance of 100 mm from the dam crest.

Damage Location Identification
The modal test is carried out on the poured arch dam structure. The acc sor is a 1A111E-type acceleration sensor, the signal collection device is a Jian Test DH5922D (12CH) collection device, and the acquisition system is a Jian Test DHDAS dynamic signal acquisition system. The structure is excited b the acceleration time-history curve is obtained in the acquisition system, an information is obtained in the FFT window. Figure 33 shows the acceleration their layout. A total of 11 acceleration sensors are placed at an average distan from the dam crest.  Figure 34 shows the fir tion modes obtained from the test. The first vibration mode is antisymmetri   Figure 34 shows the first four vibration modes obtained from the test. The first vibration mode is antisymmetric, the second vibration mode is positively symmetrical, the third vibration mode is positively symmetrical, and the fourth vibration mode is antisymmetric, which verifies the correctness of the finite element numerical model in the second chapter.  Figure 34 shows the first four v tion modes obtained from the test. The first vibration mode is antisymmetric, the se vibration mode is positively symmetrical, the third vibration mode is positively sym rical, and the fourth vibration mode is antisymmetric, which verifies the correctness o finite element numerical model in the second chapter.

No Water Level
In the test operation, the stiffness of the material cannot be directly changed bec when the concrete spalls or cracks to cause local damage, it mainly causes the local ness to change; it is difficult to set the crack and it is difficult to control. Therefore damage form is chosen to simulate the void of the structure. The cavity damage of di ent volume conditions is set on the dam body. Figure 35 shows the damage location measuring point layout: the blue location is the damage location, the single damage i as damage 1, and the double damage is damage 1 + damage 2. Because individual a eration sensors in the single-damage test group (group 1 and group 2) did not obtain c plete test data due to operational errors, it was impossible to identify subsequent dam locations. However, because the damage is caused by destroying the concrete to f damage, the double-damage test group involves destroying two positions of the mo and a set of complete data of all sensors is also collected when the first position is stroyed. Therefore, when performing damage location, the data of the double-damage group (groups 3 and 4) used when only one damage occurred were used to verify single damage, and the physical map of the damage is shown in Figure 36.

No Water Level
In the test operation, the stiffness of the material cannot be directly changed because when the concrete spalls or cracks to cause local damage, it mainly causes the local stiffness to change; it is difficult to set the crack and it is difficult to control. Therefore, the damage form is chosen to simulate the void of the structure. The cavity damage of different volume conditions is set on the dam body. Figure 35 shows the damage location and measuring point layout: the blue location is the damage location, the single damage is set as damage 1, and the double damage is damage 1 + damage 2. Because individual acceleration sensors in the single-damage test group (group 1 and group 2) did not obtain complete test data due to operational errors, it was impossible to identify subsequent damage locations. However, because the damage is caused by destroying the concrete to form damage, the doubledamage test group involves destroying two positions of the model, and a set of complete data of all sensors is also collected when the first position is destroyed. Therefore, when performing damage location, the data of the double-damage test group (groups 3 and 4) used when only one damage occurred were used to verify the single damage, and the physical map of the damage is shown in Figure 36.

No Water Level
In the test operation, the stiffness of the material cannot be directly changed because when the concrete spalls or cracks to cause local damage, it mainly causes the local stiff ness to change; it is difficult to set the crack and it is difficult to control. Therefore, the damage form is chosen to simulate the void of the structure. The cavity damage of differ ent volume conditions is set on the dam body. Figure 35 shows the damage location and measuring point layout: the blue location is the damage location, the single damage is se as damage 1, and the double damage is damage 1 + damage 2. Because individual accel eration sensors in the single-damage test group (group 1 and group 2) did not obtain com plete test data due to operational errors, it was impossible to identify subsequent damage locations. However, because the damage is caused by destroying the concrete to form damage, the double-damage test group involves destroying two positions of the model and a set of complete data of all sensors is also collected when the first position is de stroyed. Therefore, when performing damage location, the data of the double-damage tes group (groups 3 and 4) used when only one damage occurred were used to verify the single damage, and the physical map of the damage is shown in Figure 36.   According to the obtained mode shape, the curvature mode of each point is also culated, and then the relative difference k δϕ between each damage state and the cur ture when the structure is complete is obtained as a damage index for judgment. Fig  37a shows   According to the obtained mode shape, the curvature mode of each point is also calculated, and then the relative difference δϕ k between each damage state and the curvature when the structure is complete is obtained as a damage index for judgment. Figure 37a shows the recognition of the first third-order δϕ k damages in the case of single damage, and Figure 37b shows the recognition of the first third-order δϕ k damages in the case of double damage. It can be seen that in the case of single damage, the first three modes have obvious peaks at measuring point 3 and measuring point 4, and damage 1 can be identified. Among the first three modes, the second-order mode has the best damage identification effect, the δϕ k of the first-order mode is relatively large at measuring point 7 and measuring point 8, and there is a case of misjudgment. The δϕ k of the third-order mode at measuring point 7, measuring point 10 and measuring point 17 is relatively large, and there is a misjudgment situation. In the case of double damage, the damage at measuring point 4 and measuring point 7 at the first third-order mode can be clearly identified, and the second-order mode of damage 1 still has a better identification effect. Damage 2 shows the best identification effect of the first-order mode, and the damage identification effects of different order modes are quite different. In order to keep the excitation size and excitation time consistent for each tes reduce the error caused by different excitations, a vibrator is used to apply the same of excitation to the dam body each time. Figure 38 shows the instrument used for excitation. After the instruments use excitation are ready, the same excitation is applied to the arch dam specimen. Takin state of no water level, intact and undamaged and the case of single damage as exam the first 0.5 s of each excitation cycle is taken, and the acquisition frequency is 10,00 The obtained acceleration time-history data are decomposed by wavelet packet decom sition, and the wavelet basis function is db3, decomposed into three layers. The tota quency band energy of each measuring point under different damage conditions i tained, and k K δ is calculated. Figure 39 shows the damage recognition results unde ferent conditions. In order to keep the excitation size and excitation time consistent for each test and reduce the error caused by different excitations, a vibrator is used to apply the same level of excitation to the dam body each time. Figure 38 shows the instrument used for excitation. After the instruments used for excitation are ready, the same excitation is applied to the arch dam specimen. Taking the state of no water level, intact and undamaged and the case of single damage as examples, the first 0.5 s of each excitation cycle is taken, and the acquisition frequency is 10,000 Hz. The obtained acceleration time-history data are decomposed by wavelet packet decomposition, and the wavelet basis function is db3, decomposed into three layers. The total frequency band energy of each measuring point under different damage conditions is obtained, and δK k is calculated. Figure 39 shows the damage recognition results under different conditions. state of no water level, intact and undamaged and the case of single damage as examp the first 0.5 s of each excitation cycle is taken, and the acquisition frequency is 10,000 The obtained acceleration time-history data are decomposed by wavelet packet decom sition, and the wavelet basis function is db3, decomposed into three layers. The total quency band energy of each measuring point under different damage conditions is tained, and k K δ is calculated. Figure 39 shows the damage recognition results under ferent conditions.  It can be seen from Figure 39 that, similar to the modal curvature results, k K δ a has a more significant effect on the identification of damage 1 in the case of single dama and compared with the curvature mode, the ratio of the value of the damaged part to non-damaged part is larger. For example, the k K δ of measuring point 4 in the dama area is about 5.2 times that of the maximum measuring point 9 in the non-damaged a and the recognition effect is better. In the case of double damage, the calculation resul measuring point 4 is still much larger than that of other measuring points, and the fi damage can be accurately identified. Although the calculation results of measuring po 6 and measuring point 7 are larger than the adjacent measuring points, they are m smaller than measuring point 4, being only 1/5 of its size.
Therefore, the test results show that the conclusion of the numerical simulatio correct, but it may be difficult to achieve the perfect effect in the numerical simulation actual operation. When using k K δ for single-damage recognition, it has a strong rec nition ability, but when double damage is used, the recognition effect of one damage m be much higher than that of the other, and the damage may be missed.

With Water Level
Raising the reservoir water level of the arch dam system to 3/4 of the dam height ( mm), the damage setting method and the sensor arrangement are the same as when th is no water level. Figure 40 shows the layout of each damage under the 300 mm w level.  It can be seen from Figure 39 that, similar to the modal curvature results, δK k also has a more significant effect on the identification of damage 1 in the case of single damage, and compared with the curvature mode, the ratio of the value of the damaged part to the non-damaged part is larger. For example, the δK k of measuring point 4 in the damaged area is about 5.2 times that of the maximum measuring point 9 in the non-damaged area, and the recognition effect is better. In the case of double damage, the calculation result of measuring point 4 is still much larger than that of other measuring points, and the first damage can be accurately identified. Although the calculation results of measuring point 6 and measuring point 7 are larger than the adjacent measuring points, they are much smaller than measuring point 4, being only 1/5 of its size.
Therefore, the test results show that the conclusion of the numerical simulation is correct, but it may be difficult to achieve the perfect effect in the numerical simulation in actual operation. When using δK k for single-damage recognition, it has a strong recognition ability, but when double damage is used, the recognition effect of one damage may be much higher than that of the other, and the damage may be missed.

With Water Level
Raising the reservoir water level of the arch dam system to 3/4 of the dam height (300 mm), the damage setting method and the sensor arrangement are the same as when there is no water level. Figure 40 shows the layout of each damage under the 300 mm water level.
From the damage identification when there is no water level, it can be seen that the wavelet coefficient method cannot be effectively employed because the number of measuring points is too small. Thus, the wavelet coefficient method is no longer used for identification; only the modal curvature method and wavelet packet energy method are used to identify the damage location.
The curvature modal results obtained at a water level of 300 mm are shown in Figure 41. In the test results, the recognition effect of the first two modes on damage 2 is poor, and the recognition effect of the third mode is better than that of the first two modes. Measuring point 3 and measuring point 4 are obviously larger than other measuring points in the case of single damage, and measuring point 3, measuring point 4 and measuring point 7 of double damage are obviously larger than other measuring points. The damage position can be identified, but there is a misjudgment of measuring point 8. correct, but it may be difficult to achieve the perfect effect in the numerical simulat actual operation. When using k K  for single-damage recognition, it has a strong r nition ability, but when double damage is used, the recognition effect of one damag be much higher than that of the other, and the damage may be missed.

With Water Level
Raising the reservoir water level of the arch dam system to 3/4 of the dam heigh mm), the damage setting method and the sensor arrangement are the same as when is no water level. Figure 40 shows the layout of each damage under the 300 mm level. From the damage identification when there is no water level, it can be seen th wavelet coefficient method cannot be effectively employed because the number of uring points is too small. Thus, the wavelet coefficient method is no longer used for tification; only the modal curvature method and wavelet packet energy method are to identify the damage location. The wavelet packet energy results obtained at a water level of 300 mm are sho Figure 42. In the case of single damage, the k K δ of the three measuring points is g than that of other adjacent measuring points, but the amplitude is smaller than that case of no water level. In the case of double damage, the k K δ of the same meas point 3 is greater than that of other adjacent measuring points, and the first damag be identified. However, although the k K δ at measuring point 6 is greater than t other adjacent points, it is only about 1/2 of that at measuring point 3, and the iden tion effect on damage 2 is weak. Therefore, although the results of the actual test operation are weaker than the age identification results of the numerical simulation, in the 300 mm water level tes single-damage identification effect is better, and the double-damage process can also tify the damage position, which validates the rationality of the numerical simulatio the damage identification method. However, in the case of double damage, the rec tion effect of the same damage is much higher than that of the other, and the recogn The wavelet packet energy results obtained at a water level of 300 mm are shown in Figure 42. In the case of single damage, the δK k of the three measuring points is greater than that of other adjacent measuring points, but the amplitude is smaller than that of the case of no water level. In the case of double damage, the δK k of the same measuring point 3 is greater than that of other adjacent measuring points, and the first damage can be identified. However, although the δK k at measuring point 6 is greater than that at other adjacent points, it is only about 1/2 of that at measuring point 3, and the identification effect on damage 2 is weak. The wavelet packet energy results obtained at a water level of 300 mm are sh Figure 42. In the case of single damage, the k K δ of the three measuring points is than that of other adjacent measuring points, but the amplitude is smaller than tha case of no water level. In the case of double damage, the k K δ of the same me point 3 is greater than that of other adjacent measuring points, and the first dam be identified. However, although the k K δ at measuring point 6 is greater than other adjacent points, it is only about 1/2 of that at measuring point 3, and the ide tion effect on damage 2 is weak. Therefore, although the results of the actual test operation are weaker than th age identification results of the numerical simulation, in the 300 mm water level single-damage identification effect is better, and the double-damage process can als tify the damage position, which validates the rationality of the numerical simulat the damage identification method. However, in the case of double damage, the r tion effect of the same damage is much higher than that of the other, and the reco effect of one damage is weaker. Therefore, although the results of the actual test operation are weaker than the damage identification results of the numerical simulation, in the 300 mm water level test, the singledamage identification effect is better, and the double-damage process can also identify the damage position, which validates the rationality of the numerical simulation and the damage identification method. However, in the case of double damage, the recognition effect of the same damage is much higher than that of the other, and the recognition effect of one damage is weaker.

Multi-Source Data Fusion
Using the calculated test data, the calculation result of the second-order mode shape is used for the no-water-level δϕ k , and the calculation result of the third-order mode shape is used for the water-level δϕ k , which is normalized with δK k and fused using D-S evidence theory. The data fusion results without a water level and with a water level are shown in Figures 43 and 44

Multi-Source Data Fusion
Using the calculated test data, the calculation result of the second-order mo is used for the no-water-level k δϕ , and the calculation result of the third-ord shape is used for the water-level k δϕ , which is normalized with k K δ and fu D-S evidence theory. The data fusion results without a water level and with a w are shown in Figure 43 and Figure 44 respectively. From Figure 43a, it can be found that the fusion calculation result of measur 4 is much larger than those of other measuring points, the damage probability of uring point without damage is almost 0, and the damage recognition ability damage is significantly improved compared with that before fusion. From Figu can be found that damage 1 can still be clearly identified when there are double Although the fusion result of measurement point 7 at damage 2 is larger than t adjacent measurement point, it is much smaller than that of measurement poi about 1/6 of the fusion result of measuring point 4, and the misjudgment of k δϕ uring point 10 is cleared. It can be seen from Figure 44 that single and double da be effectively identified when there is a water level, but the recognition effect on 1 is better than damage 2, and the misjudgment effect of k K δ at measuring reduced.
Therefore, the test results are similar to the numerical simulation results damage identification ability is also improved, which verifies that the numerica tion results are reasonable and that the data fusion method is applicable to dam tification in arch dam structures.

Multi-Source Data Fusion
Using the calculated test data, the calculation result of the second-order mo is used for the no-water-level k δϕ , and the calculation result of the third-or shape is used for the water-level k δϕ , which is normalized with k K δ and fu D-S evidence theory. The data fusion results without a water level and with a w are shown in Figure 43 and Figure 44 respectively. From Figure 43a, it can be found that the fusion calculation result of measu 4 is much larger than those of other measuring points, the damage probability of uring point without damage is almost 0, and the damage recognition ability damage is significantly improved compared with that before fusion. From Figu can be found that damage 1 can still be clearly identified when there are double Although the fusion result of measurement point 7 at damage 2 is larger than t adjacent measurement point, it is much smaller than that of measurement po about 1/6 of the fusion result of measuring point 4, and the misjudgment of k δϕ uring point 10 is cleared. It can be seen from Figure 44 that single and double da be effectively identified when there is a water level, but the recognition effect o 1 is better than damage 2, and the misjudgment effect of k K δ at measuring reduced.
Therefore, the test results are similar to the numerical simulation results damage identification ability is also improved, which verifies that the numeric tion results are reasonable and that the data fusion method is applicable to dam tification in arch dam structures. From Figure 43a, it can be found that the fusion calculation result of measuring point 4 is much larger than those of other measuring points, the damage probability of the measuring point without damage is almost 0, and the damage recognition ability for single damage is significantly improved compared with that before fusion. From Figure 43b, it can be found that damage 1 can still be clearly identified when there are double damages. Although the fusion result of measurement point 7 at damage 2 is larger than that of the adjacent measurement point, it is much smaller than that of measurement point 4. It is about 1/6 of the fusion result of measuring point 4, and the misjudgment of δϕ k at measuring point 10 is cleared. It can be seen from Figure 44 that single and double damage can be effectively identified when there is a water level, but the recognition effect on damage 1 is better than damage 2, and the misjudgment effect of δK k at measuring point 2 is reduced. Therefore, the test results are similar to the numerical simulation results, and the damage identification ability is also improved, which verifies that the numerical simulation results are reasonable and that the data fusion method is applicable to damage identification in arch dam structures.

Identification of Damage Degree
Because in the single−damage test group there are problems with individual sensors due to improper operation, the test data of the third and fourth groups are used in the test verification, but when the damage is quantified, only the data of one or two acceleration sensors are needed, so the first and second sets of test data can still be used for single damage. The damage degree (volume) of the arch dam test model is gradually increased. Figure 45 shows the specific conditions of the three damage degrees. Figure 45a-c respectively shows the damage degree 1, damage degree 2 and damage degree 3 when there is a single damage (the picture takes no water level as an example), and the damage degrees are respectively expressed as small damage, medium damage and large damage (The test failed to accurately obtain the specific damage volume, and it qualitatively described the three damage degrees.). The locations of the measuring points are the same as in the numerical simulation, as shown in Figure 46. After the damage setting is completed, the acceleration time-history curve of the sensor at measuring point 1 is also obtained by using the exciter and other instruments.

Identification of Damage Degree
Because in the single−damage test group there are problems with individual s due to improper operation, the test data of the third and fourth groups are used in t verification, but when the damage is quantified, only the data of one or two accel sensors are needed, so the first and second sets of test data can still be used for damage. The damage degree (volume) of the arch dam test model is gradually inc Figure 45 shows the specific conditions of the three damage degrees. Figure 45a-c tively shows the damage degree 1, damage degree 2 and damage degree 3 when t a single damage (the picture takes no water level as an example), and the damage d are respectively expressed as small damage, medium damage and large damage (T failed to accurately obtain the specific damage volume, and it qualitatively describ three damage degrees.). The locations of the measuring points are the same as in t merical simulation, as shown in Figure 46. After the damage setting is completed, celeration time-history curve of the sensor at measuring point 1 is also obtained by the exciter and other instruments.  The calculated ERVD is shown in Figure 47, which is the same as the numeric ulation results. As the damage degree increases, the ERVD increases both when t no water level and when there is a water level.

Identification of Damage Degree
Because in the single−damage test group there are problems with individual sensors due to improper operation, the test data of the third and fourth groups are used in the test verification, but when the damage is quantified, only the data of one or two acceleration sensors are needed, so the first and second sets of test data can still be used for single damage. The damage degree (volume) of the arch dam test model is gradually increased. Figure 45 shows the specific conditions of the three damage degrees. Figure 45a-c respectively shows the damage degree 1, damage degree 2 and damage degree 3 when there is a single damage (the picture takes no water level as an example), and the damage degrees are respectively expressed as small damage, medium damage and large damage (The test failed to accurately obtain the specific damage volume, and it qualitatively described the three damage degrees.). The locations of the measuring points are the same as in the numerical simulation, as shown in Figure 46. After the damage setting is completed, the acceleration time-history curve of the sensor at measuring point 1 is also obtained by using the exciter and other instruments.  The calculated ERVD is shown in Figure 47, which is the same as the numerical simulation results. As the damage degree increases, the ERVD increases both when there is no water level and when there is a water level. The calculated ERVD is shown in Figure 47, which is the same as the numerical simulation results. As the damage degree increases, the ERVD increases both when there is no water level and when there is a water level.
The ERVD obtained from the above calculation is input into the neural network completed by numerical simulation training in Chapter 4, and the corresponding predicted damage volume is obtained, as shown in Table 4. It can be seen that with the increase of the damage degree, ERVD increases, and then the prediction value of neural network also increases; there is a positive correlation between the three. Because the specific value of the damage size and the specific size and duration of the excitation applied in the test are not obtained, the excitation situation in the numerical simulation is different from that in the test, so the prediction value of the neural network obtained in this test verification cannot carry out accurate quantitative analysis of the damage degree; only qualitative analysis of the data can be carried out. Later, the damage method can be changed or other methods can be used to obtain the specific value of the damage degree, and the excitation size and duration can be determined so as to obtain the accurate damage degree of the corresponding structure. The ERVD obtained from the above calculation is input into the neural network completed by numerical simulation training in Chapter 4, and the corresponding predicted damage volume is obtained, as shown in Table 4. It can be seen that with the increase of the damage degree, ERVD increases, and then the prediction value of neural network also increases; there is a positive correlation between the three. Because the specific value of the damage size and the specific size and duration of the excitation applied in the test are not obtained, the excitation situation in the numerical simulation is different from that in the test, so the prediction value of the neural network obtained in this test verification cannot carry out accurate quantitative analysis of the damage degree; only qualitative analysis of the data can be carried out. Later, the damage method can be changed or other methods can be used to obtain the specific value of the damage degree, and the excitation size and duration can be determined so as to obtain the accurate damage degree of the corresponding structure. The damage degree identification of the double-damage condition adopts the test data of the third group and the fourth group. Figure 48 shows the damage degree setting in the case of double damage (the picture takes the water level as an example). From the numerical simulation results, we know that at least two measuring points are required for double damage, and the ERVD obtained by the two methods cannot be consistent due to the abovementioned excitation inconsistency between the test and the numerical simulation. Therefore, it is impossible to use the network trained by numerical simulation to identify the damage degree of the double-damage situation. Using the acceleration data obtained from the third and fourth groups of the test, the ERVD of the double-damage measurement point 1 is calculated as shown in Table 5, the ERVD of measurement point 2 is shown in Table 6, and the neural network is no longer used for prediction.
It can be seen from Tables 5 and 6 that there are errors in the individual data of the test; for example, when there is no water level at measuring point 1, damage 1 is small damage, and the ERVD when damage 2 is no damage is greater than the ERVD when the  The damage degree identification of the double-damage condition adopts the test data of the third group and the fourth group. Figure 48 shows the damage degree setting in the case of double damage (the picture takes the water level as an example). From the numerical simulation results, we know that at least two measuring points are required for double damage, and the ERVD obtained by the two methods cannot be consistent due to the abovementioned excitation inconsistency between the test and the numerical simulation. Therefore, it is impossible to use the network trained by numerical simulation to identify the damage degree of the double-damage situation. Using the acceleration data obtained from the third and fourth groups of the test, the ERVD of the double-damage measurement point 1 is calculated as shown in Table 5, the ERVD of measurement point 2 is shown in Table 6, and the neural network is no longer used for prediction.
It can be seen from Tables 5 and 6 that there are errors in the individual data of the test; for example, when there is no water level at measuring point 1, damage 1 is small damage, and the ERVD when damage 2 is no damage is greater than the ERVD when the damage volume is larger. When there is a water level, damage 1 is large damage, and damage 2 is medium damage. However, the overall trend of ERVD is still gradually increasing with the increase of the damage degree, and the calculation result of measuring point 2 is similar to that of measuring point 1, which is the same as the law of the numerical simulation. test; for example, when there is no water level at measuring point 1, damage 1 is small damage, and the ERVD when damage 2 is no damage is greater than the ERVD when the damage volume is larger. When there is a water level, damage 1 is large damage, and damage 2 is medium damage. However, the overall trend of ERVD is still gradually increasing with the increase of the damage degree, and the calculation result of measuring point 2 is similar to that of measuring point 1, which is the same as the law of the numerical simulation.

Conclusions
This paper studies a damage identification method of rapid damage location and damage degree discernment of a concrete arch dam, based on the dynamic characteristic data of the concrete arch dam and using wavelet transforms, wavelet packet decomposition, a BP neural network and D-S evidence theory for damage identification; related test verification is also performed. The main conclusions are as follows:

Conclusions
This paper studies a damage identification method of rapid damage location and damage degree discernment of a concrete arch dam, based on the dynamic characteristic data of the concrete arch dam and using wavelet transforms, wavelet packet decomposition, a BP neural network and D-S evidence theory for damage identification; related test verification is also performed. The main conclusions are as follows:

•
When there are enough measuring points, δϕ k , W f k and δK k can all effectively identify the damage location. When the δϕ k method is used for damage identification, the damage identification effect of the first mode of the four modes the best. When using the W f k method for damage identification, it is found that this method needs enough measuring points to be able to carry out effective damage identification; the number of measuring points should be no less than 64, and the edge effect of this method is obvious. When the δK k method is used for damage identification, the effect of damage identification is better than the first two types when the number of measuring points is the same, and the three wavelet bases of db, coif and sym can be used for effective identification. When the number of wavelet base decomposition layers is increased, the effect of damage identification using db and sym is improved, but the improvement effect is not obvious after more than seven layers.

•
After the D-S evidence theory data fusion method is applied to the arch dam structure, the damage probability of the non-damaged position is close to 0 after fusion, which eliminates the misjudgment of the single-damage recognition method and improves the damage recognition effect. • ERVD is sensitive to the damage degree of the arch dam structure, and the ERVD value increases with the increase of the damage degree. When there is a single damage, the trained BP neural network can identify the degree of damage. In the case of double damage, only one measuring point's data are used for neural network training, and the recognition effect of the trained neural network is very poor. In the case of double damage, using data from two test points is better than using one test point's data for neural network training and recognition. In addition, the BP neural network based on ERVD has good anti-noise robustness. • δK k and δϕ k can effectively identify the damage location in a concrete arch dam. After the δK k and δϕ k obtained from the test are fused with multiple data using D-S evidence theory, the influence of misjudgment is reduced compared with the single-damage recognition method, and the damage recognition ability is improved. The method imports the ERVD obtained from the test data into the neural network trained by the numerical simulation data and conducts qualitative analysis on the identification of the damage degree. As the actual damage degree increases, the ERVD increases, and the prediction results of the neural network also improve.
In this paper, wavelet transforms, wavelet packet decomposition and a BP neural network algorithm are used to process vibration characteristic information, and D-S evidence theory is used for data fusion. A damage identification method that takes into account both localization and quantification is given, and a model test is carried out to verify the feasibility of the method. The method in this paper can be used to provide emergency auxiliary decision-making and provide a theoretical basis for a subsequent information system of arch dam emergency evaluation.