A Multi-objective Optimization Method For Uncertain Structures Based On Ellipsoidal Convex Model And Its Application In Vehicle Engineering

With the rapid development of economy and industry,the optimization method has been widely used.However,there are many multi-objective optimization problem in engineering optimization,which makes it difficult to obtain a set of optimal design variables to meet all the objectives.Therefore,the traditional single objective optimization method has many limitations in dealing with such optimization problems.At the same time,Because of the errors of manufacture,installation and measurement,the deterministic parameters will fluctuate in the actual operation and optimization problem,which will reduce the accuracy of the deterministic optimization methods.The stochastic and fuzzy programming methods and convex set model method can be used to deal with this kind of optimization problems.However,The stochastic and fuzzy programming methods need to obtain accurate distribution information,which limits its application in engineering optimization.The convex model includes interval model and ellipsoid convex model.Non-probabilistic interval optimization method can be used to solve this kind of optimization problem that the interval is used to replace the uncertain parameters.However,the interval method can only optimized the independent variables,and the non-probabilistic ellipsoidal convex model method can be used to solve it.Therefore,the multi-objective optimization method based on ellipsoidal convex model is presented to solve the uncertain optimization problem,The research is carried out in the following aspects:Firstly,a nonlinear multi-objective uncertain transformation model based on ellipsoidal convex model is proposed to solve the uncertain optimization problem,which transform it into a deterministic optimization problem.Then,the local-dendifying approximation model method is applied to improve the efficiency of the multi-objective optimization method.Finally,the multi-objective optimization method is applied to solve the practical problems in engineering design.Based on this,the specific research ideas in the paper are as follows:1?A multi-objective optimization method based on ellipsoidal convex model is proposed in this part.In order to treat the uncertain variables in optimization problems,the order interval and possibility degree strategies are used to transform the uncertain objective and constraint function into deterministic optimization problem,respectively.The penalty function method is applied to transform the deterministic optimization problem into an unconstrained optimization problem.The micro multi-objective genetic algorithm(?MOGA)is used to treat design parameters in the outer layer.The intergeneration projection genetic algorithm(IP-GA)strategy is used to treat uncertain vectors in the inner layer.Finally,a numerical example is given to illustrate the effectiveness of the proposed algorithm.2.A multi-objective optimization method based on the local-densifying approximation model method is proposed in this part.Firstly,The LDH method is used to obtain the sample in the sampling space and calculate the response value.Furthermore,The radial basis function model of objective functions and constraints are constructed.In each iteration step,the approximate model value is used to instead of the real model.The local-densifying approximation model method is introduced to obtain high optimization accuracy with the fewer sample points which improves the accuracy and efficiency of optimization by using the optimization results of the current steps as the sample points.Finally,a numerical example is calculated and compared to test the local approximation method.3.The optimization method is applied to solve the vehicle suspension system optimization problem.The numerical model of automobile suspension system is constructed,which is used to expressed as multi-objective optimization problem.Finally,the optimal Pareto solution is obtained by using the multi-objective optimization method based on ellipsoidal convex model.A multi-objective optimization method based on local-densifying approximation model is applied to the optimization problem of vehicle occupant restraint system.The simulation model of occupant restraint system is constructed and the design parameters and uncertain parameters are selected to construct the multi-objective optimization model.The optimal design variables and Pareto solutions are obtained by using the multi-objective optimization method based on local-densifying approximation model.Finally,the effects of different parameters on the optimization results are discussed and verify the effectiveness of the method.