Damage Identification In Frame Structure Based On Statistical Moment And Bayesian Theory Using A Two Step Method

In recent years,with the rapid development of China’s infrastructure,the number of building structures has increased greatly.In addition to the impact of harsh environment,the active building structure is also affected by its own load for a long time,which leads to structural damage.With the passage of time,the damage will gradually accumulate until the structural failure.Therefore,it is very necessary to carry out regular inspection of the structure.However,due to the complexity of the actual engineering structure and the influence of uncertain factors,it is still difficult to apply in the actual engineering.In this paper,a two-step method is proposed to identify the damage of frame structure based on statistical moment.Firstly,the damage location of the structure is identified by integrating the fourth-order displacement response statistical moment and the eighth order acceleration response statistical moment index,and the damage identification method which can not be identified by using the eighth order acceleration response statistical moment index only under the condition of no model is improved;secondly,based on the fusion of the fourth-order displacement response statistical moment and the eighth order acceleration response statistical moment,the damage identification method is improved;secondly,based on the fusion of the fourth-order displacement response statistical moment and the eighth order acceleration response statistical moment,the damage location of the structure is improved;secondly The acceleration response statistical moment index and MH Gibbs algorithm are used to identify the structural damage degree.The main research contents are as follows（1）Firstly,the statistical moment theory is derived,and the damage identification effect of each order of statistical moment is illustrated from the sensitivity to stiffness and anti noise.The model free structural damage identification method which combines the fourth order of displacement response statistical moment and the eighth order of acceleration response statistical moment is improved,which is verified by the numerical simulation of frame structure.（2）Based on Bayesian method,the posterior probability density function of structural modification parameters with statistical moment as index is derived,and MH Gibbs hybrid sampling algorithm is proposed to identify the location and degree of structural damage.Considering that the traditional Bayesian method needs multiple sampling,which is time-consuming and laborious,the optimal single sampling time of MH Gibbs hybrid sampling algorithm is determined by orthogonal design experiment,and only one sampling is needed for structural damage identification.On this basis,the damage indexes of the fourth-order displacement response statistical moment,the fusion of the sixth order displacement response statistical moment and the sixth order acceleration response statistical moment,the fusion of the fourth-order displacement response statistical moment and the eighth order acceleration response statistical moment are compared and analyzed,which shows the advantages of the fusion of the fourth-order displacement response statistical moment and the eighth order acceleration response statistical moment Finally,the feasibility of the method is verified.（3）The two-step method of structural damage identification is introduced: firstly,the location of structural damage is identified based on the model free method of fusing the fourth-order displacement response statistical moment and the eighth order acceleration response statistical moment;secondly,the location and degree of structural damage are identified based on the model free method of fusing the fourth-order displacement response statistical moment and the eighth order acceleration response statistical moment.By comparing with the Bayesian method in reference [53],the recognition accuracy and computational efficiency are analyzed,and the advantages of the two-step method are illustrated.（4）Based on the shaking table test data of 12 story frame structure in Tongji University,the applicability of the two-step method to identify structural damage is illustrated by three typical cases.