Identify Structural Parametrers Based On Bayesian Theory Nested Sampling

Structural health monitoring refers to damage detection and identification of engineering structures,and the ultimate goal is to determine the extent and location of structural damage after a disaster occurred.Structural damage identification based on Bayesian theory is the more popular and advanced method among uncertainty methods.In the past two decades,the research on model update based on Bayesian theory has developed rapidly.In order to solve the problem of high-dimensional posterior probability density,Beck proposed that the Bayesian theory uses Markov Monte Carlo sampling(MCMC)to solve the problem.But in fact,if the Bayesian method is based on the model update of the time history signal,the structural parameters will increase significantly.In addition,as today’s buildings become more and more complex,the parameters will also increase significantly due to the complexity of the structure.Although the increase of these parameters has upgrate the accuracy of the recognition results in some respects,the difficulty of recognition will also increase.At this time,the traditional Markov Monte Carlo(MCMC)method encountered a crush in solving the Bayesian problem.At first,this article introduces the research status of structural damage identification and structural damage identification based on Bayesian theory,and establishes the probability function relationship of Bayesian theory based on acceleration time history.In order to solve the model update based on Bayesian estimation,traditional MCMC often has the problem of low sampling efficiency and non-convergence when solving the problem of high-dimensional probability density function.Nested sampling method commonly used in astronomy is bring in to solve the high-dimensional posterior joint probability density function in Bayesian theory.The main contents of this paper are as follows:1.Apply the nested sampling method in the Bayesian theory structure parameter identification to solve the problem that the Bayesian theory’s high-dimensional posterior probability density function is difficult to solve.Parameter identification using nested sampling method based on Bayesian theory.When sampling through algorithms,the results often deviate from the prior distribution and produce outliers due to the convergence condition being limited by the likelihood function.The introduction does not affect the overall probability value The uniform distribution limits the sampling range,improves the sampling efficiency,and realizes the application of the nested sampling method that does not produce singular values.2.Through the use of nested sampling method to identify the parameters of the numerical structure model,and compare with other methods to show the advantages and characteristics of this method.A 10-layer shear numerical model is established,the acceleration response is obtained by the Newmark method and the white noise error is added to simulate the actual measured value of the acceleration response.The nested sampling method is used for recognition,and the recognition results are respectively compared with the recognition results of the advanced SCAM method in MCMC sampling.The comparison shows the advantages of the method in terms of stability and accuracy.In addition,a certain shaking table test model is also identified for some working conditions.By comparing the identification results of the model with other people,it is shown The feasibility of the method identified in the actual structure.3.Design and complete the shaking table test,identify the parameters of the layer model simplified from the test model,and compare the data collected by the test with the various methods of test phenomena to prove the reliability of the method in actual engineering.Summarized and sorted out the experimental phenomena under different damage states in the test process,and used the nested sampling method to identify the structural parameters of the RC frame under different damage states,and showed the expression of the parameters in the uncertainty.Through the identified parameters,the damage assessment of the structure was carried out,and the correlation between the structure parameters and the experimental phenomenon was analyzed.The structural modal parameters and acceleration response are inversely calculated by identifying the physical parameters of the structure,and the inverse calculated value is used as a simulation value to compare the actual modal parameters and acceleration response of the structure.The comparison results show the various advantages and reliability of the method.