Research On Sequential Multi-objective Robust Design Optimization Methods Using Kriging Under Mixed Uncertainties

Multi-objective robust optimization is a commonly used and effective method to solve complex engineering product design optimization problems.It can take into account the influence of input uncertainties in actual engineering problems in the design stage,and avoid uncertainties causing objectives or constraints to fluctuate beyond the allowable range,so as to obtain the optimal solution set that is not sensitive to uncertainty.However,most of the existing multi-objective robust design optimizations only consider the existence of input uncertainties in the form of irreducible intervals,ignoring the probabilistic uncertainties that often exist in actual engineering problems,which may make the robust analysis inaccurate,resulting in poor quality of the solution.In addition,the optimization objectives and constraints in actual engineering design optimization problems usually do not have display expressions.Expensive finite element simulation analysis is required to obtain the objective and constraint response values.This often leads to the long calculation cycle required for the optimization process and the high design cost.Therefore,in order to solve the multi-objective robust design optimization problem of complex engineering products with lower computational cost and higher efficiency while ensuring the quality of optimized solutions,this paper has carried out the following related research work:Firstly,a multi-objective robustness design optimization method considering interval reduction under mixed uncertainties has been proposed in this paper.This method adopts a robust design optimization framework based on the worst possible point constraint cut to avoid unnecessary robustness analysis of intermediate design solutions,resulting in a waste of computing resources.At the same time,the "Statistical Worst Case Concept" to quantify the negative impact caused by the probability uncertainty in the robust design optimization problem.In addition,considering that some interval uncertainties in actual engineering problems can usually be partially reduced or eliminated by investing a certain cost,the proposed method introduces a cost investment function as an additional optimization objective,thereby simultaneously optimizing the uncertainty reduction scheme during the optimization process,so as to provide designers with more choices and avoid the Pareto optimal solution obtained from being too conservative.Comparison results illustrate that the proposed method is more efficient and effective than other optimization methods for both numerical and engineering problems.Secondly,aiming at the engineering design optimization problem that relies on expensive finite element simulation analysis,this paper introduces Kriging surrogate model technology to build a Kriging model that meets the accuracy requirements with a small amount of sample data to predict the objective and constraint response values of unknown sample points.In addition,in order to balance the contradiction between model accuracy and modeling cost more reasonably,this paper proposes a sequential modeling method based on the robustness non-misjudgment criterion,combining it with the previous research work,and further proposes a Kriging-assisted sequential multi-objective robust design optimization method considering interval reduction under mixed uncertainties.The proposed method is then tested and verified by mathematical examples,three-bar truss design and micro-aircraft fuselage structure design optimization engineering examples.The results illustrate that this method can largely cut down the amount of calculation required for the optimization process and significantly improve the optimization efficiency.At the same time,it can ensure the quality and robustness of the obtained Pareto optimal solution,which verifies the effectiveness and superiority of the proposed method in engineering applications.