The Research On Structural Damage Identification Method Based On Principal Component Analysis

Damage identification of structures has always been a key work and a hot issue in the field of engineering.In view of the characteristics of structural engineering,once an accident occurs,it will cause great losses to human life and property.Therefore,it is of great significance to study damage identification of structural systems.In this paper,the frequency response function and curvature mode are taken as the research data,and the principal component analysis method is used to identify the structural damage,which is validated on a simply supported beam model.The results show that damage identification can be realized by principal component analysis based on frequency response function,and damage location can be achieved by principal component analysis based on curvature mode.The main work and achievements of this paper are as follows:(1)The feasibility of damage identification by combining frequency response function with principal component analysis is analyzed theoretically,and verified on a simply supported beam model.The results show that the method can realize damage identification,and has the characteristics of easy access to analytical data and sensitivity to minor damage.(2)Principal component analysis based on frequency response function defines four damage indices as follows:the sum of Euclidean distances constructed by correlation matrix between damage state and health state is used as damage index;the sum of Euclidean distances constructed by damage state and health state is used as damage index;and the vector angle between damage state and health state is used as damage index.The maximum eigenvalue in different states is taken as the damage index.The damage index constructed by principal component analysis uses the idea of principal component analysis dimensionality reduction,and the damage index constructed by correlation matrix and eigenvalue uses the idea of further analysis of variables generated in the process of principal component analysis.By comparing and analyzing the results of four damage indices,it is found that all four indices can be used for damage identification.The damage indices defined by the sum of Euclidean distances constructed by the principal components of the damage state and the health state are more sensitive to the damage than the other three indices,which can be used to accurately judge whether the damage occurs or not.Compared with the other three indexes,the damage index defined by the maximum eigenvalue under different states avoids the complicated numerical calculation,the identification process is simple,and the identification result has both figures,but the index is insensitive to damage.Therefore,the index can be used in the rapid preliminary damage identification of structural systems.(3)The feasibility of damage identification by combining principal component analysis with Hotelling T~2 statistics is analyzed theoretically.Based on the curvature mode as the research data,a damage identification method is proposed by combining the principal component analysis with Hotelling T~2 statistics.This method is verified by a simple supported beam example.The results show that the damage location of the simply supported beam model can be achieved under the condition of single damage and two damage elements at the same time under different damage degrees.The method is simple and feasible,and the research data are easy to obtain.