A Probabilistic Damage Identification Method Based On An Improved Approximate Bayesian Computation

Damage identification is the core of structural health monitoring.Due to uncertainties inevitably existing in real-world engineering structures,traditional deterministic damage identification methods often fail when they are applied to practical problems.Therefore,this thesis develops a probabilistic method that incorporates the merits of the approximate Bayesian computation,the Markov chain Monte Carlo sampling and the stochastic response surface.By this means,the solution of likelihood functions is avoided and the probabilistic properties of responses can be fast calculated.Moreover,the solution process for estimating parameter posterior distributions is considerably simplified with the improvement in computational efficiency.The main contents and the research fruits of this thesis include the following aspects:The basic concepts of the traditional Bayesian theory and the approximate Bayesian computation are first introduced.The primary advantage of the latter lies in the absence of likelihood functions during the estimation of parameter posterior probability distributions,which greatly reduces the solution difficulty.Meanwhile,the Markov chain Monte Carlo sampling is adopted in order to avoid the calculation of the complex definite integral in the Bayesian formula.Simultaneously,stochastic response surfaces are also employed for fast calculation of the probabilistic properties of sample responses,providing great improvement in computational efficiency.Through the incorporation of the three different methods,their merits are effectively used to reduce solution difficulty of a Bayesian damage identification problem.At the same time,the estimation accuracy of parameter posterior distributions is also guaranteed with the great improvement in computational efficiency.Hence,the practicability of the developed method is enhanced.Subsequently,in order to verify the feasibility of the developed method,a numerical steel beam and a numerical reinforced concrete beam were first investigated.The stiffness parameters of the two beams were reduced to simulate the desirable damage.And the modal frequencies and mode shapes were adopted as the responses.The analysis results demonstrated that the proposed method could precisely identify the damage locations and severities.In addition,after compared with traditional Bayesian method,it was found that the proposed method also effectively reduced the solution difficulty and improved the computational efficiency without losing the estimation accuracy of parameter posterior probability distributions.Thus the superiority of the proposed method has been proved.Lastly,modal testing was performed on an experimental steel beam and also on an experimental reinforced concrete beam.Damage was simulated by cutting the steel beam or applying a static load to the reinforced concrete beam until the cracks appeared.Then based on the measured modal frequencies and mode shapes of the undamaged and damaged beams,the proposed method was successfully used to identify the damage.Meanwhile,the analysis results were also compared with those given by the traditional Bayesian method.It was found that the proposed method could accurately identify the locations and severities of the two experimental beams.Therefore,the feasibility and reliability of the method on real-world structures have been validated to an extent.In a word,the method developed in this thesis may effectively enhance the practicability of Bayesian theories in the research realm of probabilistic damage identification methods.Therefore,the method presents its own contributions to the relevant topic.