Sensor clustering-based approach for structural damage identification under ambient vibration
Introduction
Civil engineering infrastructures such as bridges and buildings play important roles in providing essential welfare for society. However, the resistance of the in-service infrastructures deteriorates with time, owing to many factors such as exposure to the harsh environment, long-term fatigue and natural hazard i.e. earthquake and storm. These factors accumulate damage that leads to a huge investment in retrofitting or at worst, can cause catastrophic structural failure that involves severe economic and human life losses. In this regard, a condition assessment via Structural Health Monitoring (SHM) system is essential to assure structural reliability and safety.
Damage detection is indeed a fundamental part of SHM, thus has been explored extensively, particularly in making use of vibrational parameters to identify damage existence (Level I), location (Level II) and severity (Level III) [1]. The underlying theory of vibration-based damage detection is that structural damage affects the structure's physical properties such as stiffness and mass, which in turn will result in changes of its vibration properties i.e. frequency, mode shapes, acceleration and displacement [2]. There are many vibration-based damage detection methods that have been successfully developed, which can be classified into three categories, depending on the type of vibration parameters which are modal-based, frequency-based and time-series-based methods. As for the first category, damage detection is made based on modal parameters (i.e. natural frequencies and mode shapes) [[3], [4], [5], [6], [7]] which requires modal extraction from measured vibration data. Although this category has gained significant attention in the SHM field, there are some arguments on the suitability of modal data in damage detection, for instance: (i) reliability of damage identification results is likely dependent on the accuracy of the extracted parameters because errors are inherent in the modal extraction [8]; (ii) modal data is not sensitive to local damage and minor damage because damage is a local phenomenon while modal data is a structural global feature [9,10]; (iii) higher modes are more correspond to local changes, but measuring high vibration modes is even more difficult in real practice especially for large civil structures under ambient excitation which usually low in frequency [11]; (iv) very susceptible to environmental and operational variability [12]. On contrary, frequency response function (FRF) [13,14] which falls in the frequency-based method provides more information as compared to modal data, but its prime drawback is the requirement of known input [15], hence limiting its practicability for in-service structures as the excitation under operation conditions is generally difficult to measure. Moreover, the conversion from time-domain to frequency-domain data discards some information contained in the measured response [16]. On the other hand, the third category which is based on time-series performs damage identification by direct analysis of the time-series response captured by sensors. Therefore, this category of methods is advantageous for an automated SHM system not only because it is simpler and faster but also avoids uncertainties due to modal extraction.
For the above-mentioned reasons, great research efforts have been devoted recently to the development and application of time-series-based methods. In the methods, the measured dynamic responses such as accelerations, velocity, and displacement of a structure are fitted into time-series models (i.e., autoregressive (AR) model, AR with exogenous inputs (ARX) model, AR moving average (ARMA) model, ARMA with exogenous input (ARMAX) model) and damage detection is then undertaken by extracting damage sensitive feature (DSF) from model coefficients [[17], [18], [19], [20]] or model residual errors [[21], [22], [23], [24]]. Some studies on time-series methods assigned nonlinear model instead of the linear time-series models mentioned above. For example, Wei et al. [25] proposed delamination detection for multi-layer composite system by considering both excitation signal and acceleration response for nonlinear ARMAX (NARMAX) modelling. The time-series methods not only have potential to identify damage at its early stage where changes of natural frequencies are almost unperceivable [21] but also allow damage detection to be conducted in an unsupervised way. Unlike supervised learning that requires data from undamaged and different damaged states in the training phase, unsupervised learning uses data only from the undamaged structure [24,26,27]. Since obtaining data from all possible damaged scenarios is very challenging in most applications, unsupervised learning is more widely used in time-series-based damage detection. However, most of the time-series-based methods are focused only on Level I and Level II damage identification while the implementations up to Level III are somewhat limited.
In this regard, the concept of sensor clustering introduced by Gul and Catbas [28] seems promising to provide three levels of damage identification as the method resulted in good sensitivity to damage existence, location, and relative severity. In the study, acceleration responses obtained from impact test were used in autoregressive with exogenous inputs (ARX) modelling for different sensor clusters and two DSFs were derived from the model coefficient and fit ratio to detect damage in a steel grid structure. Later, similar structure and DSFs were used by Mei and Gül [29] with the improvement of using a fixed-order time-series model via equation of motion. For a real application, Farahani and Penumadu [30] evaluated ARX model and sensor clustering approach with a new DSF extracted from model residuals to identify damage in a full-scale five-girder bridge utilising velocity of free-vibration response generated by sandbag drop-weight test. Azim and Gul [31] presented sensor clustering-based time-series method for damage detection of steel girder railway bridges under operational train loading. Although the proposed methodology demonstrated great potential, the study was conducted based on numerical simulation problem and the considered signals were free-vibration responses as the responses were obtained after the train has fully passed over the bridge. All these remarkable works have proved that sensor clustering concept has potential in damage detection due to capability of enhancing the time-series-based methods up to Level III damage identification. However, the existing applications are efficient under the free-vibration response obtained from impact test. One flaw of impact test is that it may not practical since its execution will disturb the normal operation of structures i.e. traffic suspension. Hence, the output response from ambient vibration is favoured for most civil structures. An attempt to apply sensor clustering for ambient vibration has also shown promising results [32]; however, the raw measured signals need to be transformed into pseudo-free responses before time-series modelling. In the present study, the sensor-clustering based method is improved so that it can be used directly using the measured signal under ambient vibration. Adams and Farrar [33] applied ARX models using frequency domain data, in which model coefficients were used for quantifying damage severity and distinguishing data linearity/nonlinearity. Huang et al. [34] used time-varying autoregressive with exogenous input (TVARX) model to extract instantaneous modal parameters. The method was utilised to identify the instantaneous natural frequencies and damping ratio of an experimental model subjected to base excitation input. The input acceleration and displacement response were used as the input and output of the model, respectively. Yan et al. [35] employed the substructural technique in conjunction with NARX neural network. For damage detection, the change in variance of prediction error was assessed using a statistical inference standard F test. The model prediction error was processed with statistical inference where the error was randomly reshuffled, divided into equal segments and computed the sum of each segment. The variance of the sum was taken as damage indicator in the proposed method.
Considering the limitation of impact test in real field applications, the aim of this study is to explore the sensor clustering-based damage detection beyond the free-vibration limitation to allow for straightforward usage of ambient vibration in time-series response, without extraction of dynamic properties. In this study, the ability of artificial neural network (ANN) in learning linear and nonlinear systems is used for time-series modelling of NARX model in conjunction with sensor clustering using output-only data, which is the ambient acceleration response. To provide the first three levels of damage identification as defined by Rytter [1], a new DSF extracted from the model prediction error is proposed. The experimental datasets of an 8 degree-of-freedom (DOF) mass-spring system and steel arch laboratory models are used to validate the efficiency and applicability of the proposed methodology. Results indicate that the proposed method is efficiently successful to detect, locate and relatively estimate the severity of structural damage, which is a significant improvement over previous sensor clustering-based methods because the demonstration is under ambient vibration and does not involve data transformation of the raw signal.
Section snippets
Methodology
As mentioned earlier, the adoption of time-series approach is to overcome the problems in the conventional modal-based damage identification. The approach presented here is an output-only and non-model damage detection where it solely based on the measured acceleration responses without any need of excitation information nor details of physical structural properties. In conjunction with sensor clustering, the aim of the approach is to fit the measured time-series responses into mathematical
Case study I: 8-DOF mass-spring system
In this section, the proposed method is verified using experimental data of an 8-DOF system designed by Los Alamos National Laboratory (LANL) which are available online on LANL website [43]. As shown in Fig. 6, the undamaged system comprises of 8 translating masses (m1 = 559.3 g, m2–8 = 419.4 g) connected by springs with an identical constant (k1–7 = 56.7 kN/m). To generate ambient vibration, a 215 N peak force shaker is attached to the first mass. The horizontal acceleration responses with a
Case study II: Experimental steel arch
In this section, the applicability of the proposed damage detection approach is further verified using experimental data obtained from lab-tested steel arch structures as shown in Fig. 10 are used. The test structures are 180° circular arches with radius of 500 mm to the centroid and cross-sectional area of 50 mm × 9 mm. The support system is provided by welding each end of the arch to a steel plate that is bolted to a ground-fixed thick plate.
For dynamic test, the arch is uniformly divided
Conclusion
This study develops a damage identification approach based on the integration of sensor clustering and nonlinear autoregressive exogenous (NARX) neural networks. In the proposed algorithm, ambient acceleration responses measured from the undamaged structure are collected and directly used to train the NARX neural network of each sensor cluster. Compared to the intact condition, the trained NARX neural networks provide higher prediction error when the responses from damaged states are fed to the
Declaration of Competing Interest
No potential conflict of interest was reported by the authors.
Acknowledgment
The authors would like to thank the Ministry of Higher Education of Malaysia and Universiti Teknologi Malaysia for their financial support through the research grant vote number of 16J24, 4L705 and 4B498.
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