Substructural Time History Response Sensitivity-based Structural Damage Identification

The finite element model updating-based damage identification method which is understandable and has physical meaning,can identify the location and extent of damage meanwhile.However,this is an optimization problem,and requires calculation of structural response and response sensitivity many times,which will consume numerous computational time and memory.Substructuring method is effective to analyze large-scale structure,which analyzes the structure in a piece-wise manner rather than analyzes it as a whole.The exist research focuses on developing substructuring method to eigensolutions,while there exists less research on substructuring method to time history response and its sensitivity.The research in this dissertation is supported by National Natural Science Foundation of China(Damage identification of civil structures,NSFC,51922046)and National Natural Science Foundation of China(Substructuring method to nonlinear finite element model updating and damage identification,NSFC,51778258).This dissertation focuses on the substructural sensitivity based structural damage identification,and is combined with time domain model updating and uncertainty analysis for fast damage identification of large-scale structure,including the following parts:(1)The substructuring method which considers the elastic effects of slave modes is proposed to calculate time history response and first order time response sensitivity.The proposed method is an extension of traditional substructuring method in calculation of features in frequency domain to time domain.The motion equation of global structure with respect to substructural lower order master modes is established,where the elastic effects of slave modes are considered by a first order residual flexibility matrix.Only a few master modes are required for accurate calculation of structural time history response,and first order master mode derivative of one substructure is required for accurate calculation of first order time history response sensitivity.This accelerates the time efficiency.(2)Based on the substructuring method considering elastic effects of slave modes,the enhanced substructuring method which considers the inertial effects of slave modes is proposed.The transformation matrix is derived to relate slave modes to master modes,and then equivalent modal mass matrix which is related to master modes and transformation matrix is derived for the consideration of inertial effects of slave modes.Due to the contribution of slave modes is considered more accurately compared with the substructuring method considering elastic effects of slave modes,structural time history response and its sensitivity are accurately required without increasing the number of master modes.(3)The substructuring method which considers the inertial effects of slave modes is proposed to calculate second order time history response sensitivity.Based on the motion equation which considers the inertial effects of slave modes,the reduced second order sensitivity equation with respect to master modes is derived.Only a few master modes and master mode derivatives of a few concerned substructures are required for accurate calculation of second order time history response sensitivity,which can improve the time efficiency.(4)The global-based finite element model updating method is time consuming.To improve the time efficiency,the substructure-based model updating method in time domain to damage identification is proposed.The eigensensitivity-based criterion for determining critical area is proposed.The elemental stiffness parameters of critical area are selected as updating parameters.Master modes of a few concerned substructures are repeatedly required to calculate structural response for constructing objective function.Analyzing master mode derivative of one substructure repeatedly to calculate first order time history response senisitivity for constructing sensitivity matrix.This avoids analyzing the whole structure repeatedly in the optimization process.(5)A substructure and perturbation-based damage identification method with the consideration of measurement uncertainty and modelling uncertainty is proposed.The zero order and first order perturbation equations are derived based on the damage identification equation.Time history response and its first order and second order sensitivity are calculated by the substructuring method rapidly.The mean,deviation,and damage probability of elemental stiffness parameters are solved from perturbation equations.Thus,the time efficiency of damage identification with consideration of uncertainty is improved.