Research And Application Of Interval Uncertainty Optimization Method Based On Quasi-Sparse Response Surface

Uncertainties caused by many factors such as material characteristics and manufacturing tolerances are common in the process of complex product design,which may have a greater impact on performance and reliability of product.Therefore,it is of great significance to study uncertain optimization methods.Because the upper and lower bounds of these uncertainties are often known information,interval numbers can be used to describe them,and then the uncertain optimization problem can be transformed into the interval uncertain optimization problem.However,many times of expensive simulations are required to solve this problem,which leads to low efficiency.The interval uncertainty optimization method based on response surface improves the optimization efficiency to some extent,but there are still some problems such as the number of sampling points is too large,the accuracy is too low.Therefore,this paper will study the interval uncertainty optimization method based on response surface with lower sampling cost and higher efficiency.The specific research contents are as follows:Firstly,interval numbers are used to describe uncertain design variables and uncertain parameters with known upper and lower bounds.Meanwhile,the interval uncertain optimization problem is transformed into a nested two-layer deterministic optimization problem,in which the outer layer searches the optimum and the inner layer seeks the maximum value of the objective function and the constraints in the uncertain interval of design variable.Then,the optimization model of interval uncertain optimization problem is constructed.Secondly,to solve the problem that the existing researches require too many times of expensive simulation,which leads to inefficient optimization,an interval uncertainty optimization method based on quasi-sparse response surface is proposed to effectively reduce the times of simulation.The orthogonal Legendre polynomials are chosen as the basis functions for quasi-sparse response surface,and the number of basis functions is multiplied by the number of sampling points,which improves the expression ability of the basis functions.Then,add7)₁ norm penalty term and7)₂ norm penalty term to least squares method,the7)₁norm penalty only select the basis functions which are important to describe the simulation model,so as to remove the redundant basis functions,find the sparse representation of the simulation model,and avoid overfitting.The7)₂ norm penalty term encourages to select a set of similar basis functions to enhance the stability of response surface.Thus,a high-precision global quasi-sparse response surface can be constructed stably with a small number of sampling points.Thirdly,based on quasi-sparse global response surface,the double-loop optimization process is used to solve the interval uncertainty optimization problem.In the outer loop optimization,the multi-island genetic algorithm（MIGA）is used to search global optimum,and constantly update the design points.In the inner loop optimization,Mode-Pursuing Sampling（MPS）algorithm is used to find the maximum value of objective function and constraints in the uncertain interval of the current design point.Since the quasi-sparse response surface has the characteristics of less sampling points and high precision,the times of simulation of the entire optimization process are reduced,and the optimization efficiency is improved.Finally,three numerical cases and two application cases are employed to test the interval uncertainty optimization method based on quasi-sparse response surface in three aspects:accuracy,optimization ability and number of sampling points.The experimental results show that the proposed method only needs 0.05%sampling points of the existing research,and has higher accuracy and optimization ability.