Physics-Augmented Deep Learning Approach for Identification of Structural Excitations

Xinhao An, J. Hou, L. Jankowski, Qingxia Zhang

Load identification is a crucial topic in structural health monitoring (SHM). Existing approaches involve a trade-off between the amount of data required and the fidelity of available parametric physical models. Purely data-driven methods require extensive labeled training data for reliable identification and lack physical interpretability. Methods based on physical model inversion techniques are interpretable, but their accuracy depends on precise knowledge of the structural model and its parameters, which requires extensive model-tuning procedures. This contribution presents and discusses a physics-augmented deep learning (PADL) framework, intended for identification of structural dynamic excitations and aimed at striking the balance between data and model precision demands. A long short-term memory (LSTM) neural network is used as the basic identification tool. However, in contrast to typical data-driven methods, its input consists of not only measured structural responses. It includes also the results of FRF-based inverse processing performed with a simplified, reduced-order model of the monitored structure, yielding inexact estimates of the unknown input and state vector. In this way, the typical data-based input is augmented with a physically consistent data that indirectly embeds and provides information about the physical structure and its equations of motion. Such a dual-input design effectively addresses the trade-off noted above: on the one hand, the required structural model can be very coarse, inexact and reduced-order, on the other, the physical consistency of the information it provides (even if it is strongly simplified and approximate) significantly reduces the amount of training data required. Moreover, the employed FRF-based approximate model inversion is sensor-agnostic, which enables applications with heterogeneous sensor networks. A specific data normalization scheme ensures applicability across a range of excitation amplitudes. The proposed PADL framework is verified in numerical simulations and laboratory experiments using random and impulsive excitation profiles. The tests demonstrate that PADL outperforms purely physics-based and purely data-driven baseline methods and that high identification accuracy can be achieved even with very small training sets and highly simplified structural models and inaccurate parameters. An ablation study confirms that including the approximate state vector in the input data, in addition to the computed approximate excitation, provides additional physically consistent information and is important for the accuracy of the obtained identification results.