Additional Virtual Mass Damage Identification Method Based On Damage Sparsity

Structural health monitoring for major structures has become the current trend.As a key step,damage identification has great research significance.There are many problems in the test data,such as noise,low sensitivity to damage and incomplete data,and the damage distribution has the characteristics of sparsity.Therefore,this paper proposes the additional virtual mass damage identification method based on damage sparsity.Acceleration responses of the new structure is constructed by the additional virtual mass method,which makes the number of test data increased,and ensures that the constructed data has a higher sensitivity to damage.On the basis,combined with the characteristics of damage sparsity,the regularized damage identification method is studied.The advantages and disadvantages of l0 norm method,l1 norm method and l2 norm method are analyzed.At the same time,the OMP method in l0 norm method is improved,and the improved OMP method is proposed.Through numerical simulation of simply supported beams with variable cross-section,it is found that the recognition accuracy of regularized damage identification method is higher than that of ordinary damage identification method,and the best one is improved OMP method.Although the improved OMP method has the highest recognition accuracy,it is easy to obtain the local optimal solution due to its calculation method.Therefore,a sparse greedy elimination method based on residual principal component analysis is proposed.This method determines the number of substructures that may be damaged by analyzing the overall damage residual matrix and carries out damage identification.From the global point of view,it avoids the local optimal problem,and at the same time,it is easier to determine the sparsity of damage.Through the numerical simulation of simply supported beam with variable cross-section,the superiority of sparse greedy elimination method based on residual principal component analysis is illustrated by comparing the improved OMP method.The regularization method can not completely eliminate the influence of data error on damage identification.At the same time,the regularization parameter is introduced,which makes the calculation more complex.Therefore,the sparse Bayesian method is studied to reduce the above errors from the perspective of probability and statistics,and to simplify the calculation steps.Based on the prior probability of data,damage factor and sparsity control parameter,the posterior probability distribution of damage factor and sparsity control parameter is derived by Bayesian formula,and the damage of structure is identified.The reliability and high accuracy of sparse Bayesian method are verified by three-layer frame numerical simulation.In order to verify the effectiveness and practicability of the virtual mass damage identification method based on damage sparsity,a three-layer frame test was carried out.The results show that the proposed method can identify the damage within the engineering accuracy requirements.The highest recognition accuracies are l0 norm method and sparse Bayesian method,and the lowest is l2 norm method.