Damage Identification of Plate Structures Based on a Non-Convex Approximate Robust Principal Component Analysis

Abstract

Structural damage identification has been one of the key applications in the field of Structural Health Monitoring (SHM). With the development of technology and the growth of demand, the method of identifying damage anomalies in plate structures is increasingly being developed in pursuit of accuracy and high efficiency. Principal Component Analysis (PCA) has always been effective in damage identification in SHM, but because of its sensitivity to outliers and low robustness, it does not work well for complex damage or data. The effect is not satisfactory. This paper introduces the Robust Principal Component Analysis (RPCA) model framework for the characteristics of PCA that are too sensitive to the outliers or noise in the data and combines it with Lamb to achieve the damage recognition of wavefield images, which greatly improves the robustness and reliability. To further improve the real-time monitoring efficiency and reduce the error, this paper proposes a non-convex approximate RPCA (NCA-RPCA) algorithm model. The algorithm uses a non-convex rank approximation function to approximate the rank of the matrix, a non-convex penalty function to approximate the norm to ensure the uniqueness of the sparse solution, and an alternating direction multiplier method to solve the problem, which is more efficient. Comparison and analysis with various algorithms through simulation and experiments show that the algorithm in this paper improves the real-time monitoring efficiency by about ten times, the error is also greatly reduced, and it can restore the original data at a lower rank level to achieve more effective damage identification in the field of SHM.