A physics-augmented deep learning framework for structural dynamic load identification with FRF-guided state expansion

Xinhao An

doi:10.1016/j.ymssp.2026.113965

2026-02-06

PRE

DOI：10.1016/j.ymssp.2026.113965

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摘要

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Structural load identification is a critical technique that facilitates safety monitoring and performance assessment of engineering structures, activities that hold significant engineering importance. Current mainstream methods face two major challenges: traditional physical model inversion techniques require precise knowledge of structural parameters and thus are highly sensitive to modeling errors, while purely data-driven approaches based deep learning offer powerful nonlinear mapping capabilities but lack integration with physical laws and rely heavily on large volumes of labeled data. To address these issues, this paper proposes a physics-augmented deep learning (PADL) framework for structural dynamic load identification. First, based on the measured dynamic response of the structure and a simplified structural model, an initial load estimate is obtained through the frequency response function (FRF) inversion technique. Additionally, frequency-domain relationships between different types of responses are exploited to approximately reconstruct unmeasured responses, which further augments available information under the constraints of physical laws. Notably, the physical model employed in this process does not require precise structural parameters: even a simplified, inaccurate model is sufficient to provide the necessary physical constraints. Next, the augmented data is fed into a lightweight LSTM network for residual error compensation, with the output layer designed as a linear mapping without an activation function. This design overcomes the limitation of output boundedness, enabling load extrapolation beyond the extreme values of the training data through an explicit scaling mechanism in the weight matrix. Finally, numerical simulations and laboratory tests are performed to demonstrate the effectiveness of the proposed PADL framework in identification of structural dynamic loads.

Keyword:

structural load identification

physics-augmented deep learning

frequency response function

LSTM network

dynamic load estimation