A machine learning–based approach for adaptive sparse time–frequency analysis used in structural health monitoring

Time–frequency analysis is an essential subject in nonlinear and non-stationary signal processing in structural health monitoring, which can give a clear illustration of the variation trend of time-varying parameters. Thus, it plays a significant role in structural health monitoring, such as data analysis, and nonlinear damage detection. Adaptive sparse time–frequency analysis is a recently developed method used to estimate an instantaneous frequency, which can achieve high-resolution adaptivity by looking for the sparsest time–frequency representation of the signal within the largest possible time–frequency dictionary. However, in adaptive sparse time–frequency analysis, non-convex least-square optimization is the most important and difficult part of the algorithm; therefore, in this research the powerful optimization capabilities of machine learning were employed to solve the non-convex least-square optimization and achieve the accurate estimation of the instantaneous frequency. First, the adaptive sparse time–frequency analysis was formalized into a machine-learning task. Then, a four-layer neural network was designed, the first layer of which was used for training the coefficients of the envelope of each basic functions in a linear space. The next two merge layers were used to solve the complex calculation in a neural network. Finally, the real and imaginary parts of the reconstructed signal were the outputs of the output layer. The optimal weights in this designed neural network were trained and optimized by comparing the output reconstructed signal with the target signal, and a stochastic gradient descent optimizer was used to update the weights of the network. Finally, the numerical examples and experimental examples of a cable model were employed to illustrate the ability of the proposed method. The results show that the proposed method which is called neural network–adaptive sparse time–frequency analysis can give accurate identification of the instantaneous frequency, and it has a better robustness to initial values when compared with adaptive sparse time–frequency analysis.