Research On Efficient Reliability-based Design Optimization Methods

There are widespread uncertainties related to material properties,geometric dimensions,external loads and calculation models in actual engineering problems.The combined effect of multiple uncertain factors may cause the structure or product performance to deviate from expectations or even fail.Traditional design optimization methods use safety factors to roughly estimate the impact of uncertainty,and the optimum design may be too conservative to achieve the desired performance.Reliability-based design optimization(RBDO)combines the concept of reliability with structural optimization,which is of great importance to the outstanding products.Although scholars around the world have made a series of significant achievements in reliability analysis methods and decoupling methods between reliability analysis and design optimization,the existing research still has the following shortcomings:relatively large computational errors due to the most probable point(MPP)based reliability analysis methods;cannot solve the RBDO problem containing multimodal random variables.To solve these problems,this article explores methods to strike a balance between accuracy and efficiency.The research works are as follows:(1)In order to improve the accuracy of RBDO problems with highly nonlinear performance function,a response probability density function(PDF)based performance shift method is proposed.Firstly,by introducing a shift strategy for the response PDF of performance function,a deterministic optimization model is formulated for the RBDO problem.Secondly,the performance shift scalar is calculated through the approximate of the response PDF of performance function.Thirdly,by performing reliability analysis at current design point,the new response PDF is obtained and the actual reliability is calculated to check if all the probability constraints are satisfied.If not,the shift scalar is calculated according to the current performance function value and the response PDF,and a new deterministic optimization model is formulated for the next iteration.By solving the deterministic optimization,a new solution with higher reliability is obtained.The above procedures are performed for several iterations until all the constraints are satisfied,which means that the algorithm has achieved convergence.The accuracy,efficiency and stability of the proposed method are verified through three numerical examples and the engineering application of automobile side collision safety.(2)In order to solve the RBDO problem involving multimodal random variables efficiently,a sequential approximate optimization method is proposed.In the proposed method,the RBDO problem is decomposed into a series of sub-optimization problems.In each sub-optimization problem,by using the dimension reduction method and the maximum entropy method,the reliability assessment is performed for each constraint to calculate the response PDF of performance function.Then,by proposing an important hypothesis that the response PDF of performance function has only translational deformation when solving the RBDO problem,a deterministic optimization model is formulated to substitute the original RBDO problem.By solving deterministic optimization,a new solution with higher reliability is obtained.Next,checking if the algorithm has achieved convergence.If not,performing the reliability assessment and the deterministic optimization iteratively until the optimum solution that satisfies all the constraints is obtained.Three numerical examples and an engineering problem are used to verify the performance of the proposed method.As a result,compared with the double-loop method,the proposed method has excellent performance in terms of stability,accuracy and efficiency.