Reliability-Based Optimization Design With Bayesian Inference Under Incomplete Information

There are many uncertainties in practical engineering,such as material properties,external loads,dimensional tolerances of manufacturing.Therefore,reliability-based analysis method can be used to evaluate the structural performance from the perspective of probability,which always needs complete information of probability distributions of variables and parameters or a large amount of statistical sample data.However,the number of sample experiments is limited due to the experiment conditions and cost in areas of weapon development and aerospace,which may lead to incomplete information.In this case,the results obtained by the traditional reliability analysis method often fail to reflect the true reliability information.In order to solve this problem,the Bootstrap method and Bayesian theory are often used to process small sample data information.The Bootstrap method can transform small sample problems into large sample problems by resampling,and replace the characteristics of real population samples with the statistical properties of experimental data.Bayesian theory can filter and process known data,update the information with subsequent experimental data to make a reasonable estimate of small sample information.In order to solve reliability-based design optimization(RBDO)problem under incomplete information,this paper improves the existing Bayesian inference based RBDO under the framework of reliability index approach(RIA),and proposes Bayesian inference based RBDO under the framework of performance measure approach(PMA).1.Estimate the parameters of random variables with incomplete information using Bootstrap method and Bayesian method.The small sample problem is transformed into a large sample problem by resampling,and the distribution parameters of samples are estimated by the Bootstrap method.Using the Bayesian method,the posterior samples are generated by Gibbs sampling,and the parameter distribution of samples is obtained by fitting from the posterior samples.The examples show that the Bayesian method can obtain a more stable result,which has a better agreement with the true sample distribution.2.Combining Bayesian theory with RIA and PMA to perform structural reliability optimization design with incomplete information,which means the probability distribution functions of some random variables or parameters are known,while only a finite number of samples are given for other random variables or parameters without known.In Bayesian inference based RBDO with RIA,all known samples are taken as parameters to solve the reliability index by the first order reliability method,which is used as the prior information,then the RBDO process is completed.In Bayesian inference based RBDO with PMA,the Bayesian method is used to determine the parameter distribution of random variables.Compare Bayesian methods with classical statistical results of normal and the non-normal random variables,the optimization results obtained by the Bayesian method are less volatile and more stable.3.Perform the Bayesian inference based RBDO with PMA of the stiffened panels with curvilinear stiffeners in airplane,when the elastic modulus distribution of the material is unknown and only the finite sample is available.Firstly,Latin Hypercube Sampling is used to generate the sample points to construct the Kriging model,and then combined with the Bayesian theory RBDO is conducted by PMA to obtain the optimal solution.By comparing with the original results,the feasibility in practical application of the proposed method is verified.