Study On Structural Nonlinear Damage Identification Based On Time Series Analysis Method And Permutation Entropy

Constructing a damage-sensitive factor(DSF)is one of the key steps in structural damage detection.In this paper,innovation series extracted from the auto-regressive conditional heteroscedasticity(ARCH)model are proposed to construct two DSFs,which are respectively defined as the standard deviation of innovation(SDI)and the permutation entropy of innovation(PEI).The experimental data of a three-story shear building structure and the simulation of a six-story shear structure are used to demonstrate and verify the performance of the proposed methods,and the results are compared with the standard deviation of residual(SDR)and the permutation entropy of residual(PER)based on the auto-regressive(AR)model.This study focuses on analyzing the accuracy of fitting AR model and ARCH model to vibration response data via the normal probability distribution and fitting analysis,and identifying the characteristics of the original data,residual and innovation series.The mean squared error(MSE)is used as the loss function to calculate the loss on residual and innovation series from the AR model and ARCH model,respectively.The results demonstrate that the structural nonlinear DSFs,which is established based on innovation series,can accurately describe nonlinear damage features of structures.In the proposed method,the AR model is firstly established using the acceleration responses obtained from the reference structure and the structures at the test states.The residual series are then extracted for fitting the SDR and PER.Subsequently,the ARCH model is constructed based on the residual series from the AR model,and two new DSFs of SDI and PEI are defined.Secondly,the DSFs are constructed based on the ARCH model,and the AR model are analyzed and evaluated in terms of nonlinear damage identification performance.Finally,the normal probability distribution and fitting analysis are used to analyze the original data series,the residual series from the AR model and the innovation series from the ARCH model,and the loss function values are further determined via the loss function method.The results show that the SDR and PER can realize structural nonlinear damage identification,however,they are not ideal for extracting nonlinear damage characteristics of structures.The proposed SDI and PEI can better realize structural nonlinear damage identification.The innovation series based on the ARCH model are promising for expressing and constructing nonlinear DSFs.