A Nonlinearity-Sensitive Approach for Early Damage Detection Using NOFRFs and the Hybrid-LSTM Model

Early damages have become a latent source of catastrophic failure of structures, while the nonlinearity of systems at the early failure stage is hard to detect. Combining the physical interpretability of nonlinear output frequency response functions (NOFRFs) and the strong nonlinear modeling ability of deep neural networks, a sensitive approach for early damage detection is proposed. Inspired by the parallel idea of ResNet and considering that nonlinear system responses can be divided into linear and nonlinear parts, this article proposes the Hybrid-long short-term memory (LSTM) model to build the surrogate model of nonlinear structural systems being investigated. In Hybrid-LSTM, the feed-forward neural network (FFNN) applies the linear transformation to the features generated by the convolutional layer and the LSTM structure performs the nonlinear transformation. Using this strategy, the Hybrid-LSTM network has stronger nonlinear modeling ability than convolutional neural network (CNN)-LSTM models, especially when the system nonlinearity is weak. In addition, to avoid the impact of the excitation frequency of single-tone harmonic excitation, we adopt the multisine signal as the system excitation to investigate the features of nonlinear systems, which makes the damage detection evaluation more stable and reliable. Numerical simulations indicate that the proposed method can successfully detect early damages when the relative depth of the crack is less than 5%. The effectiveness and applicability of the novel proposed method in practical structures are further verified using the experimental studies of the breathing beam and the bolted connection structure.