Detection method of unlearned pattern using support vector machine in damage classification based on deep neural network

Deep neural networks (DNNs) are a powerful tool for structural health monitoring because they can automatically identify features that are useful for classifying and recognizing damage patterns of a target structure with high accuracy. However, it can misclassify input data of an unlearned damage pattern as any of the learned damage patterns. To address this shortcoming, this paper presents a method to detect unlearned damage patterns by using the collective decision of support vector machines (SVMs). SVMs are constructed using feature vectors from training data, which are stored in the output layer of a DNN. To validate the proposed method, we used two different datasets, one containing experimental data of a steel frame structure and the other containing simulated and experimental data of a wooden house. In both cases, it correctly identified data of both learned and unlearned damage patterns. The proposed method can enhance the effectiveness of structural health monitoring (SHM). In addition, because it does not employ SHM‐specific characteristics, it can be used in various pattern recognition applications, such as image and audio processing.


| INTRODUCTION
The use of artificial neural networks affords significant advantages in the mathematical modeling of nonlinear relationships between input and output data. Consequently, their utility in structural health monitoring (SHM) for civil engineering structures using vibration observation data has recently been extensively investigated. Although neural networks require a large training dataset for establishing useful relationships between input and output, simulated data, such as results obtained from time-history response analysis of a numerical structural model, can be used in lieu of actual observation data.
Wu et al. 1 proposed a neural network-based monitoring system and adopted the Fourier spectra of the computed acceleration response of a building frame model. Their proposed neural network outputs the damage states of each member. Additionally, Elkordy et al. 2 proposed the use of a neural network for structural monitoring and adopted displacement-mode shapes, and they used numerical analysis results of a frame model as well as a finite element model for network training. Stephens and Vanluchene 3 proposed a neural network that categorizes the safety conditions of structures after an earthquake, that is, safe, lightly damaged, damaged, or critically damaged. They considered damage indices, such as maximum displacement ratio and cumulative dissipated energy, as input for a neural network that was trained using data from shaking table tests. Barai and Pandey 4 adopted analytically generated vibration signatures from a vehicle moving on a bridge structure as input data, which was simulated using the finite element technique. Their proposed neural network generates member stiffness as output. Masri et al. 5 also used neural networks to detect structural damage based on prediction errors, and their proposed network was applied to linear and nonlinear models subject to ambient Gaussian white noise vibration. Zhao et al. 6 considered natural frequencies and parameters based on mode shapes as input to their neural network to detect damage and support movement in bridge structures. Damage was simulated by reducing the Young's moduli values of members, and training data were obtained using finite element analysis. Yun et al. 7 considered measured modal properties as input to their neural network, which outputs joint damage severities. The connection stiffness of a beam-to-column joint in a steel frame structure was represented by the stiffness of a zero-length rotational spring placed at the end of a beam element. Their proposed method was verified through numerical simulations of a two-bay 10-story steel frame and an experiment on a two-story frame. Huang et al. 8 used experimental data for training a neural network capable of predicting the acceleration response of a five-story steel frame to input base excitations. Damage caused by strong excitations was detected based on the modal assurance criterion-an index of the modal shape correlation-and mean absolute errors incurred between the predicted neural network output and measured response. Lee et al. 9 considered the differences or ratios between mode shape components before and after damage to assess element-level damages, thereby reducing the effect of modeling errors in the baseline finite element model. Additionally, their proposed method was employed in two numerical simulations involving a simple beam and multigirder bridge. Yeung and Smith 10 used Fourier spectra derived from time histories at nodes and modal peaks of the first five vibration modes, which were calculated using a finite element model of a suspension bridge subjected to 23 independent damage scenarios involving a vehicle moving over it at different speeds and different heat conditions. Jiang and Adeli 11 introduced a dynamic fuzzy wavelet neural network and proposed the power density pseudospectrum approach to detect damage occurrence in high-rise buildings. In their study, a large structure was divided into a series of substructures around a few preselected floors with sensors deployed for measurements. Mehrjoo et al. 12 adopted the natural frequency and mode shapes of a truss bridge structure as input data to a neural network. Their proposed neural network outputs a damage percentage for the related joint. Morfidis and Kostinakis 13 created a training dataset using a nonlinear time-history analysis of 30 reinforced concrete buildings with different structural characteristics. The buildings were subjected to 65 actual ground motions. They proposed a neural network that takes structural parameters-number of stories, structural eccentricity, and so forth-and ground motion parameters-peak ground acceleration, peak ground velocity, and so forth-as input to identify damage classes, which were assessed based on the maximum interstory drift ratio.
Owing to the invention of the autoencoder [14][15][16][17][18] and many other techniques, the deep neural network (DNN) 19, 20 has become a powerful tool for pattern recognition. An autoencoder is an algorithm to compress the dimensions of input data into a small size while remaining sufficiently large to recover the original data, and it is considered as a type of nonlinear principal component analysis. Therefore, the algorithm can automatically find features that are useful for classifying input data into trained patterns and replacing conventional features that were sought by researchers based on logical considerations and scientific insights. A DNN can be trained using results obtained by an autoencoder as initial data to generate useful and effective features as well as classify input data as one of the learned patterns with high accuracy. DNNs have been applied in many fields, such as image analysis, audio and speech recognition, and natural language processing, and SHM of building structures based on vibration measurements is no exception. 21,22 In past studies on structural damage detection and classification, many researchers have made tremendous efforts to identify reliable features calculated from a vibration record. Examples include maximum responses, such as floor accelerations, story drifts, and column curvatures, along with mechanical and dynamic characteristics, such as stiffness, damping factors, natural periods, and mode shapes. However, features obtained using a DNN can replace the above-mentioned conventional features. Further, convolutional neural networks for pattern recognition especially in visual images have been employed in vibration-based monitoring. [23][24][25][26][27] The National Research Institute for Earth Science and Disaster Resilience (NIED) and the Mizuho Information and Research Institute developed an artificial intelligence system for damage pattern recognition that identifies damage patterns within a structure using a DNN based on time-history response data. 28 The DNN is trained by supervised learning techniques using a large amount of training data. Once the DNN training is completed, the configured feature values in a hidden layer adjacent to the output layer in the DNN are transferred from the hidden layer to the output layer. The feature values are used as the arguments to a softmax function, which outputs probabilities that the input data belong to each learned pattern. The input data are attributed to the pattern with the highest probability. For the training data, time-history responses of a target structure can be employed, and the authors have confirmed the detection accuracy to be very high. 29 Although the DNN is a powerful tool for pattern recognition, a supervised learning-based DNN will erroneously classify input data of an unlearned pattern as that of a learned pattern. For example, if a DNN has been trained using cat and dog images, it will classify a rabbit image as either a cat or a dog. In practical SHM scenarios, this drawback may result in the failure of damage pattern recognition, which could cause false alarms for building damage or lead to inappropriate decision making in the event of a disaster.
The authors' research group proposed a method to detect the input data of an unlearned damage pattern based on the Mahalanobis distance. 29 However, that method has limited detection accuracy for unlearned damage patterns owing to the assumption that the probability distribution of feature values follows a Gaussian distribution. In a DNN, a nonlinear activation function, such as a rectified linear unit (ReLU), ϕ(x) = max(x, 0), is used at the nodes (also called units) in hidden layers to distort the distribution of input values, which could follow a Gaussian distribution. Consequently, feature values in the output layer do not follow a Gaussian distribution. Therefore, alternate approaches are required to devise a reliable method to detect the input data of an unlearned damage pattern. In this paper, we propose the use of a support vector machine (SVM) 30,31 to detect an unlearned damage pattern based on the feature data of a DNN, which can be obtained automatically as a byproduct of deep learning by a DNN to identify damage patterns. The proposed method is validated on two different datasets: (i) measurement data from shaking table tests of a steel frame structure and (ii) simulated training data and measurement data from shaking table tests of a wooden house.

| Overview of proposed SHM system
We propose an SHM system to recognize the damage patterns of a structure during earthquakes. The system considers two phases: a design and construction phase and an operation phase; flowcharts of these phases are depicted in Figure 1. In the design and construction phase of a building structure, a numerical model of the target structure is first constructed; this model can reproduce structural responses to strong earthquake ground motions via dynamic simulations. Subsequently, time-history response analysis is performed using the prepared model and input ground motions to generate a large amount of simulated records. We assume some damage patterns within the target structure, and a model with one of these assumed damage patterns is utilized for time-history response analysis. When extracting the simulation results, to obtain the simulated records, we consider the type of sensor, location of observation, direction of the measuring component, and so forth. Using the simulated records, a deep learning technique is employed for the supervised training of a DNN, and this is used for damage pattern recognition. Upon completion of deep learning, we extract feature data, which are the data input to the output layer nodes in the trained DNN. Based on the extracted feature data, we construct an SVM to detect unlearned damage pattern data. After the target building is constructed, an SHM system with the proposed damage pattern recognition framework is installed in the building, and the sensor network is deployed and connected to the SHM system.
To reduce the time and cost of creating a large damage dataset, we propose reusing the results of the time-history response analysis in the design stage of a target structure. Various types and intensities of ground motions are input to a model of the target structure in a particular structural design, employing numerical simulations that particularly aim at performance-based design. It is noteworthy that the observed fluctuations in the structural response owing to the influence of temperature and other parameters can be somewhat alleviated by introducing them into numerical models used for generating training data via dynamic analysis. In addition, the discrepancy between the dynamic properties of a numerical model based on design-stage information and an actual constructed building can be resolved by updating the numerical model with response data recorded during small earthquakes and vibration excitation tests in the operation phase. In this case, the DNN must be retrained using the updated numerical model.
In the operation phase of a building, seismic response is monitored continuously. During earthquakes, the sensor measurements are provided as input to the trained DNN. Feature data are subsequently extracted and input to the constructed SVM. If the SVM detects unlearned damage pattern data, the proposed SHM system indicates the occurrence of an unlearned damage pattern. If not, the SHM system indicates the occurrence of a damage pattern (or no damage) recognized by the DNN from the assumed damage patterns. However, the proposed damage pattern classification method faces a major limitation in that it cannot accurately identify damage patterns when the response is influenced by the simultaneous occurrence of strong winds and an earthquake. In such a case, accurate identification of an unlearned pattern and classification of damage patterns cannot be guaranteed.

| Deep learning method of DNN
For damage pattern recognition, we use a DNN comprising one input, one output, and three hidden layers (five, in total), as shown in Figure 2.
Prior to explaining the algorithm used in the proposed damage pattern recognition system, multiclass classification is first explained. Suppose we want to distinguish which class the input data x belongs to among Classes C 1 , C 2 , …, C K (K classes in total), which correspond to the damage patterns examined in this study. We define output vector y = {y 1 , y 2 , …, y K } T , and y k (k = 1, 2, …, K) represents the probability that input data x belongs to class C k such that To obtain the regression formula y = G(x), we repeat the estimation and update of the DNN parameter set, w. Upon completion of the DNN learning process, we can classify input data x into Class C kmax by identifying the largest y kmax among y 1 , y 2 , …, y K . In the implementation of the DNN, we use the deep learning framework Chainer 3.1.0 32 , which can be used to create Python programs to facilitate DNN handling. For dimensionality reduction of the hidden layers, we employ a deep autoencoder, and the stochastic gradient descent method is applied to update the DNN parameter set w. Additionally, ReLU is used as the activation function of nodes within the hidden layers. ReLU can be expressed as In the output layer, we use the following softmax function to calculate output value y k : where u k denotes a feature value stored at an output node k. Feature data (or feature vector) u = {u 1 , u 2 , …, u K } is an intermediate product of the DNN to calculate output y from input x and can be represented by u = g(x).
During the learning process, we minimize errors between the training data and estimated classes by updating the parameter w, and the following cross entropy is used as a loss function E(w), that is, an objective function to be minimized: where N denotes the number of input data, and d nk denotes the correct class data, which is equal to 1 when input data x n belongs to Class C k and 0 otherwise.

| Method to detect data of an unlearned damage pattern using SVMs
For the detection of unlearned damage pattern data, we use SVMs based on the unsupervised learning of feature data u used in Equation 3. We construct a one-class SVM with a radial basis function (RBF) kernel (Gaussian kernel), which is defined as follows: where σ represents a scale parameter optimized to achieve the prescribed expected proportion (5% in this study) of outliers in the training data. The purpose of the one-class SVM is to identify a rule that returns +1 when data u is normal (i.e., corresponding to a learned damage pattern) and − 1 when it is an anomaly (i.e., corresponding to an unlearned damage pattern). We assume the function f(u|x) to implement this rule: where u j denotes feature data given by input data x j ; a 1 ,a 2 ,…,a M (0 ≤ a j ≤ 1 8 j = 1,2,…,M) denote estimated SVM parameters; and M denotes the number of support vectors. Using f(u|x), a judgment is made as follows: f ujx ð Þ≥0 ) normal; input data x belongs to a learned damage pattern: ð7aÞ f ujx ð Þ< 0 ) anomaly;input data x belongs to an unlearned damage pattern: The value of Equation 6 (hereinafter, referred to as the decision score) represents a signed distance between u and decision boundaries, and the values of parameters a 1 , a 2 , …, a M can be determined such that f(u|x) provides the most accurate judgment possible. This is achieved by maximizing the margin between support vectors u j (j = 1, 2, …, M) and a hyperplane to discriminate between the normal (learned damage pattern) and anomalous (unlearned damage pattern) data. The ratio of margin errors, ν, represents the tolerance to permit a wrong decision in training data and ν = 0.02 in this study. This parameter ensures an upper limit for the ratio of margin error and a lower limit for the ratio of support vectors in the training data. Suppose a series of input data,x n n = 1,2,…, N s ð Þ , is given. To detect the input data of an unlearned damage pattern, we propose the following criteria: where n(L) denotes a function that returns the number of elements in a set L; sgn(Á) denotes a signum function that returns values of 1, 0, or −1 when its argument is a positive, zero, or negative, respectively; and f Di (u) is a function that returns the decision score in terms of the damage pattern Di, that is, an SVM constructed using feature vectors of pattern Di data in the training data. The contents of Equations 8a and 8b can be described as follows. A series of N s input data is first evaluated sequentially to check whether it represents normal data in terms of the damage pattern Di using a function f Di (Á). Subsequently, a collective decision is made using a summation of signum function values; the summation result is positive when the majority of N s input data is recognized as normal in terms of damage pattern Di, and the index i is stored in a set L. Finally, we determine whether a series of data belongs to a learned or unlearned damage pattern class. We consider the data to belong to a learned damage pattern when the set L contains a single element. When L contains any other number of elements (including zero), the data are considered representative of an unlearned damage pattern. It was observed in this study that some unlearned damage pattern data that are similar to multiple learned damage pattern data corresponded to the presence of two or more elements in set L.
When the number of elements in set L satisfies Equation 8a, we consider the series of input data as belonging to one of the learned damage patterns and then continue to the next step to identify a damage pattern from the learned damage patterns by using a trained DNN. Otherwise, in the case of Equation 8b, we consider the series of input data as belonging to an unlearned damage pattern. Essentially, the set of learned damage patterns includes a "no damage" condition, and unlearned damage pattern data thus imply a certain damage occurrence that differs from those in learned damage patterns.

| Overview of shaking table tests
Simulated response data are used for training the DNN and SVMs in the proposed SHM system. To investigate the validity of the proposed method, we first used measurements from shaking table tests of a steel frame structure ( Figure 3) rather than simulated response data. Details of the target structure are described in Yamashita (2016) 33 , and the specimen is a 1:3 scaled model with a story height of 1.157 m and first natural period of 0.21 s under the condition that all braces are removed. The original scale structure was supposed to be a four-story steel structure with a height of 14 m and a slab of 6 × 12 m. Uniaxial shaking table tests were conducted using the large-scale shaking table at NIED, Tsukuba. Four braces are attached in the second layer of the specimen, and we emulated multiple damage patterns by fastening and relaxing the brace turnbuckles, as shown in Figure. 4. Responses to x-direction table motion were measured using MEMS sensors with a sampling frequency of 500 Hz. Figure 5 illustrates the locations of the sensors used in this study. Although the sensors measure three translational accelerations and three angular velocities, we used only acceleration in the x-direction, indicated by the red circles in Figure 5, as the input data for the DNN.
One hundred different simulated ground motions with small to large amplitudes and short to long durations were input to the specimen for each damage pattern; Figure 6 shows examples of the simulated ground motions. In the tests, multiple ground motions were connected sequentially to have a total duration of approximately 10 min for reducing F I G U R E 3 Specimen of a steel frame structure F I G U R E 4 Damage patterns of braces F I G U R E 5 Locations of sensors in steel frame specimen (cyan and red circles) with blue parts denoting weights the time and effort of measurement. The measured acceleration records were divided into samples with lengths of 1 s (Figure 7), which were used as the input data for the neural network. This time length was determined based on a parameter study. 29

| Results for three learned damage patterns (Case DP3)
First, we conducted a validation analysis for the case of three learned damage patterns (D1, D3, and D5). We used the data of damage pattern D4 as the unlearned damage pattern. The neural network consisted of five layers: an input layer with 1,500 nodes, three hidden layers with 500, 250, and 125 nodes, and an output layer with three nodes. The shaking table tests yielded 6,600 samples; we first used 3,300 randomly selected samples for training and the other 3,300 samples for validation to calculate the accuracy rate of damage pattern classification. Then, the sample datasets were interchanged, and the accuracy rate was recalculated. We monitored the evolution of the average of the above-mentioned two accuracy rates during validation and adopted a neural network at epoch 90, before overfitting occurred ( Figure 8). Table 1 lists the aggregated classification results for the two validation phases. The average accuracy rate reached 99.0%.
We extracted the feature vectors when training data were input to the DNN; Figure 9 shows the distributions of feature vectors, where each color denotes a damage pattern of the training data. Based on the feature vectors of each damage pattern, we constructed one-class SVMs with 3,300 samples of training data, and Figure 10 shows the support vectors, which comprise a classification boundary for each SVM. Note that we set the parameter ν = 0.02 and confirmed that approximately 5% of the feature vectors had a negative score, even for the test data.
Using a series of acceleration responses with a total duration of 10 s (i.e., N s = 10, 10 samples of input data), we validated the proposed method. Figures 11-14 show the distributions of decision scores for the test data of damage patterns D1, D3, D4, and D5, respectively, and we confirmed that the scores of the test data are distributed in a similar manner to the damage patterns of the training data. Because all the summation results are negative, L = and n(L) = 0, the test data are identified as data of an unlearned damage pattern. Because data of both learned and unlearned damage patterns were identified properly, the above results support the validity of the proposed method.

| Results for six learned damage patterns (Case DP6)
Next, we validate the proposed method for the case where the DNN learns the six damage patterns D1, D3, D4, D5, D6, and D8 (Case DP6). The numbers of hidden layers and hidden layer nodes were the same as for Case DP3. The classification accuracy of the trained DNN (epoch size: 90) is shown in Table 3. We constructed six one-class SVMs with ν = 0.02. Again, a series of acceleration responses with a total duration of 10 s (N s = 10) was used as the input data of the DNN. Table 4 lists the results of the summation in Equation 8a. For learned damage patterns, we observed a test data yield n(L) = 1 for all cases, and they were identified correctly as belonging to a learned damage pattern. For the test data of damage pattern D7, L = {4, 8} and n(L) = 2, which is different from 1. Consequently, the data were identified correctly as those of an unlearned damage pattern.

| Results for eight learned damage patterns (Case DP8)
Finally, we validated the proposed method for the case that the DNN learns all eight damage patterns from D1 to D8 (Case DP8). Again, the numbers of hidden layers and hidden layer nodes were the same as in Case DP3. The classification accuracy of the trained DNN (epoch size: 80) is shown in Table 5. We constructed eight one-class SVMs with ν = 0.02. As test data, we synthesized reverse damage patterns of D9, D10, D11, and D12, which are mirror-symmetric patterns of D4, D5, D6, and D7, respectively. The acceleration data were synthesized using the records measured at the sensors indicated by cyan dots in Figure 5. A series of acceleration responses with a total duration of 10 s (N s = 10) was used as the input data of the DNN. Table 6 lists the results of the summation in Equation 8a. For learned damage patterns, we observed a test data yield n(L) = 1 for all cases, and they were correctly identified as belonging to a learned damage pattern. For unlearned damage patterns, all cases resulted in n(L) = 0, and they were identified correctly as belonging to unlearned damage patterns.

| Overview of shaking table tests
In the previous section, we reported the training of the DNN and construction of SVMs using real observed measurements. However, this approach is not applicable to ordinary buildings. Therefore, we used simulated responses to synthesized ground motions as training data for the DNN and SVMs. Subsequently, real observed measurements from shaking table tests were used to validate the proposed method. The target building (Figure 15) was the wooden house of Specimen 4 in Project: Experiments for Verification of the Design Methods for Three-Story Wooden Houses by Post and Beam Construction. 34 We obtained the experimental data from the Archives of Shaking table Experimentation dataBase and Information (ASEBI), which is disseminated by the Hyogo Earthquake Engineering Research Center, NIED. 35 The specifications of the house are listed in Table 7, and they conform to Seismic Grade 1 of a Housing Performance Indication System in the Housing Quality Assurance Act, which satisfies the minimum requirements of the Building Standard Law of Japan.
During shaking table tests, uniaxial shaking was applied to the shorter axis direction of the house. The ground motion specified in the Building Standard Law for the ground type 2 (hereafter referred to as BSL) was input to the house with a duration of 20 s and amplification factors of 112.5% and 150%. The three-story house was designed using an amplification factor of 90% of the safety limit specified in the limit strength calculation design method of the Building Standard Law.

| Simulation model of specimen house
A three-dimensional frame model (Figure 16) was constructed considering the material nonlinearity of braces, walls, joints, and floor diaphragms. The numerical analysis program wallstat ver. 3.3.11, which was developed by the Building Research Institute and is based on a discrete element method, was used for the time-history response analysis. 36,37 Walls and diaphragms were substituted by braces (truss elements), and beams and columns were modeled using an elastic beam with elasto-plastic rotational springs. Member joints were modeled using an elastoplastic rotational spring and an axial spring. Figure 17 shows an example skeleton curve of a brace. Note that skeleton curves are modeled based on the averaged load-displacement relation of multiple test results of elements. For the horizontal diaphragm, we amplified the capacity by 2.86 based on the experimental results of Yoshikawa et al. 38 We considered three damage patterns: D1, no damage; D2, moderate damage; and D3, severe damage. Damage patterns D2 and D3 correspond to the state after experiencing BSL with amplification factors of 112.5% and 150%, respectively ( Figure 18). Figures 19 and 20 show comparisons between the acceleration time histories and floor response spectra (5% damping) of the experimental and simulated results when excited by BSL 5%, and Table 8 compares the maximum acceleration responses; the simulation results indicate smaller maximum responses in the positive direction, which is mainly due to the difference between the natural periods of the specimen and simulation model, as observed in the floor response spectrum. Figure 21 compares between the story deformation time histories of the experimental and simulated results when excited by BSL 112.5%; the simulation results do not match well owing to the above-mentioned property difference. The test results of the structural elements revealed large dispersion, and the averaged load-displacement relation adopted F I G U R E 1 5 Photo of specimen house 35

T A B L E 7
Overview of the target wooden house for the simulation model did not reproduce the dynamic characteristics of the specimen in consideration of the above comparisons. Despite the model discordance, the proposed simulation model was employed in this study to investigate the classification ability of DNNs. This is because discordance is inevitable when applying the proposed method to an actual wooden house. It must be noted that long-term monitoring data could be used to improve the numerical model if an SHM system is operated.

| Training and test datasets
To generate training data for deep learning, we simulated the response to nonsevere ground motion, which does not expand the damage. One hundred ground motions were simulated while following the design ground motion for the damage limitations specified in the Building Standard Law of Japan; a random phase was adopted for synthesizing ground motion with a duration of 60 s, and the ground motions were assumed to be at the engineering bedrock level. Several amplification factors were applied to achieve various amplitude levels of ground motions. Figure 22 shows an example input ground motion used in the simulation, which was created by combining 12 waves. Simulated responses were acquired to replicate the test measurements, which use the servo-accelerometer Tokyo Keiki TA-25E with a sampling frequency of 100 Hz.
In the validation tests for the proposed method to detect unlearned damage pattern data, acceleration records measured in the shaking table test were used; 10-s duration records taken in the response decaying phase are extracted; we focused on the condition of the house experiencing severe ground motion. Figures 23-25 show the records used.

| Construction of DNN and SVMs
We first constructed the DNN with three hidden layers to classify damage patterns D1 and D3. Considering that the first natural period of the wooden house is shorter than 1 s, the input data were designed to have a length of 1 s. The DNN contained an input layer with 400 nodes (= 4 ch × 100 Hz × 1 s), three hidden layers with 200, 100, and 50 nodes, and an output layer with two nodes. Figure 26 displays the evolutions of accuracy rates in the training and test data. We used the DNN at epoch 80 for the classification results for the test data of the simulated responses and test data of the shaking table tests, as shown in Tables 9 and 10, respectively; the accuracy rates reached 98.6% and 90%, respectively. Subsequently, feature vectors were derived from the training data; Figure 27 presents the distributions of the feature vectors. Using the feature vectors, one-class SVMs were constructed with parameter ν = 0.02 to detect the data of the learned damage patterns of D1 and D3. The distribution of the support vectors is shown in Figure 28

| Validation results
We input 10-s input data to construct the DNN and SVMs. Figure 29 shows the decision score distributions of the test data when evaluated by each SVM. The calculation results using the proposed method are as follows: F I G U R E 2 5 Experimental data used in the validation of damage pattern D3

T A B L E 9
Damage classification result and average accuracy rate for simulated response data and we successfully determined that the input data belong to learned damage pattern D3. Consequently, we confirmed that the proposed method can correctly classify data of learned and unlearned damage patterns. The successful classification of D3 damage despite the predominant period difference between F I G U R E 2 9 Decision score distribution of the test data when evaluated by an SVM based on each training data floor response spectra of the actual specimen and simulation model can be attributed to the proposed DNN's acquisition of features intrinsic to the nonlinear response during training. An example of such features is the nonoval shape of the hysteresis loop. To validate this hypothesis, the authors are currently developing a method to interpret trained DNNs. The said method would, in turn, help improve the accountability of the DNN-based classification process.

| CONCLUSION
For the purpose of SHM based on vibration measurement, a DNN is a powerful tool to classify the damage patterns of a target structure. However, it will misclassify input data of an unlearned damage pattern as that of any of its learned damage patterns. To overcome this drawback, we proposed a method to detect unlearned damage patterns by using the collective decision of SVMs. To detect the data of an unlearned damage pattern, one-class SVMs were constructed using feature vectors of training data, which are stored in the output layer of a DNN. To validate the proposed method, we used two different datasets, namely, the experimental data of a steel frame structure and the simulated and experimental data of a wooden house.
For the steel frame structure, we used measurements from shaking table tests of a steel frame structure both for constructing a DNN to classify damage patterns and SVMs to detect the data of an unlearned damage pattern and for validating the ability of the proposed method to detect data of an unlearned damage pattern. The steel frame structure was a 1:3 scaled model with a natural period of 0.21 s under the condition without braces. Four braces were fastened or loosened to replicate multiple damage patterns. We employed a five-layer neural network for the classification of multiple damage patterns. We studied three different cases with respect to the numbers of learned patterns: three, six, and eight damaged and undamaged patterns. In all three cases, the proposed method could correctly classify the data learned and unlearned damage patterns.
For the wooden house, we conducted a time-history response analysis by using synthesized ground motions, and simulated responses were used as training data for the construction of a DNN to classify damage patterns and SVMs to detect the data of an unlearned damage pattern. To verify the proposed method, we used an open dataset of measurements from in shaking table tests for a real-scale wooden house. A DNN was trained to classify two damage states, namely, no damage and severe damage, and two one-class SVMs were constructed using feature vectors. The proposed method correctly identified response data of no damage and severe damage as data of a learned damage pattern, and it successfully detected data of moderate damage as data of an unlearned damage pattern. However, excessively weak ground motions will decrease the accuracy of unlearned pattern detection and damage classification. A guideline is required to extract appropriate samples that are input to the DNN from observed records.
Our results validate the effectiveness of the proposed method in detecting data of an unlearned pattern. Moreover, the proposed method does not use any vibration-specific or SHM-specific characteristics, so it can be applied to damage classification using computer vision [39][40][41][42] and moreover pattern recognition in other fields, such as image, audio, and speech recognition.
Future studies should investigate the following. A validation study is required for cases where the input ground motion possesses drastically different characteristics, such as in pulse-like ground motions. We should develop a design procedure for hyperparameters such as the ratio of margin erroνrs, in the construction of SVMs and N s , the number of input data series. In addition, for a general method using a DNN in SHM, the accountability of feature vectors should be improved to explain the rationality and reliability of the damage pattern recognition results deduced by the DNN.