# Bridge Health Monitoring Using Proper Orthogonal Decomposition and Transfer Learning
###### Abstract
In addition to issues associated with the effects of MUs on damage identification accuracy, one of the drawbacks of most conventional SHM ML techniques is the inability to use transfer knowledge from one structure under specific damage scenarios to another, similar, structure in a population, potentially one with different damage scenarios. Difficulty associated with transferring a developed and trained algorithm within a population of structures has motivated the SHM community to incorporate Population-Based SHM (PBSHM). Recently developed TL methods and their applications to SHM can provide systematic approaches to knowledge transfer within a population of structures [3; 23]. Traditionally, the main assumption in implementing these methods is that training and testing data are selected from the same distribution [24]. To overcome this limitation, TL methods generalize the classifier trained for one structure to be applicable to another structure. In the context of SHM, TL methods have been used for image processing, computer vision, and pattern recognition. [PERSON] et al. [3] proposed a PBSHM by employing TL methods in the form of Domain Adaptation (DA). They assessed TL performance with respect to labeling a target domain using Transfer Component analysis (TCA) [25], Joint Domain Adaptation (JDA) [26], and Adaptation Regularization-based TL (ARTL) [27] in classification-type problems for homogeneous- and heterogenous-type populations. The efficiency of each TL method was examined for two heterogenous populations. The first case population encompassed two numerical simulations of a three degree of freedom structure, each with different geometric and material properties, with one simulation being the source and the other the target domain. The second case involved using a numerical simulation of a structure as the source domain and an experimental replica as the target domain. Recently, [PERSON] et al. [28] proposed a TL-based method and Bayesian model updating (BMU) to reduce the effect of MUs on model updating performance. Modal parameters, including normalized frequency change ratios and mode shapes, were used as features. They utilized ARTL to transfer knowledge from a source domain consisting of an eight-floor numerically simulated structure to a target six-floor experimental structure. [PERSON] et al. [29] used JDA as a TL method to map wave signals from one plate to another and a convolutional long short-term memory (ConvLSTM) network to learn mapping relationships from the source plate so that the damage image was detected in the targeted plate. [PERSON] et al. [30] developed a structural anomaly detection framework using the transmissibility function and statistical threshold selection, and examined its robustness against uncertainty. [PERSON] et al. [31] demonstrated the better performance of the Bhattacharyya distance-driven algorithm for novelty detection against transmissibility functions that follow Gaussioan distribution. This study was motivated because research shows that a trained source domain TL-based classifier can be generalized to detect deficiencies in unlabeled target domains, and, when a JDA-kernel method is implemented, higher accuracy target domain label predictions are obtained [3]. To date, research regarding TL-based SHM, while promising,has focused on experimental and numerical simulations under controlled environments. Therefore, a need to expand this approach to bridges and examine its effectiveness for actual structures under actual load with larger feature space exists. In addition, coupling this TL method with POD provides a robust damage identification framework with minimum sensitivity to noises. This study focused on developing and studying a TL approach for transferring knowledge from a base, a modeled existing railway bridge class with known labels in the feature space, to a modeled bridge class with realistic MU and unknown labels in the feature space.