As a structural health monitoring (SHM) system can hardly measure all the needed responses, estimating the target response from the measured responses has become an important task. Deep neural networks (NNs) have a strong nonlinear mapping ability, and they are widely used in response reconstruction works. The mapping relation among different responses is learned by a NN given a large training set. In some cases, however, especially for rare events such as earthquakes, it is difficult to obtain a large training dataset. This paper used a convolution NN to reconstruct structure response under rare events with small datasets, and the main innovations include two aspects. Firstly, we proposed a multi-end autoencoder architecture with skip connections, which compresses the parameter space, to estimate the unmeasured responses. It extracts the shared patterns in the encoder and reconstructs different types of target responses in varied branches of the decoder. Secondly, the physics-based loss function, derived from the dynamic equilibrium equation, was adopted to guide the training direction and suppress the overfitting effect. The proposed NN takes the acceleration at limited positions as input. The output is the displacement, velocity, and acceleration responses at all positions. Two numerical studies validated that the proposed framework applies to both linear and nonlinear systems. The physics-informed NN had a higher performance than the ordinary NN with small datasets, especially when the training data contained noise.
Civil engineering structures will exhibit hysteretic behavior due to damage caused by dynamic loads. Identifying the hysteretic behavior of structures is a practical and challenging problem that involves observing vibration data to determine strength and stiffness degradation. This paper proposes a modified square root central difference Kalman filter (MSRCD-KF) method to track this behavior. By combining the QR decomposition and strong tracking filtering technology, the proposed method makes the recursive calculation process unconditionally stable, while enabling the tracking of abrupt changes in structural parameters. A three degree-of-freedom (3-DOF) Duffing system is used in the simulation to verify the effectiveness of the proposed method. Numerical results show that the proposed method can converge to the true value quickly and accurately. Then, the proposed method is used to identify the structural parameters of a two-story concrete frame structure under different seismic loading sequences. In the first example, the structure is simplified as a 2-DOF linear system for which the equivalent stiffness and damping under different damage levels are identified. This information is then used to obtain the stiffness variation trend, damping ratio, and frequency. The second example uses the Bouc–Wen model to consider the stiffness and strength degradation of the structure. Finally, the experimental results demonstrate that the proposed method can accurately identify the structural parameters of nonlinear systems, and the identified hysteresis curves are in good agreement with the experimental ones.
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