Effects of operational variability and damage on structural response signals: A method based on LMS radar image and residual-permutation entropy

Abstract

The study investigates the residual sequence from time series “black box” models and evaluates the nonlinear and non-stationary characteristics of the residual sequence using Lagrange Multiplier (LM) test. The Lagrange Multiplier Statistics (LMS) radar map is performed to analyze and clarify the corresponding relationship between the residual sequence and structural safety condition. Then, the permutation entropy is proposed to measure the complexity, randomness and fluctuation of the residual sequence, and the correlation is established between the residual-permutation entropy (R-PE), structural abnormal response signal and safety state. The effects of operational variability, damage, coupling disturbance of operational variability and damage on R-PE are analyzed in detail.In this paper, the proposed methodology is verified by vibration response signals of a three-storey shear-type frame in experiment and a six-storey shear-type frame in numerical simulation. The results indicate that i) LMS = 0.9n can be considered as the classification threshold for undamaged and damaged state of the structure using LMS radar map. ii) When the R-PE value is close to 1, it indicates that the structure is undamaged or not influenced by operational variability. iii) When the R-PE value is less than 1, it may be disturbed by operational factors, damage factors, or coupling disturbance of the two. iv) The R-PE value is very robust as the decrease of the R-PE value caused by operational disturbance is small, while the decrease of R-PE value caused by damage is significant. v) There is a significant difference of the R-PE value between small damage and operational impact on the structure.