An Interval Multi-objective Optimization Method Considering The Dependency Of Variables And It's Application

The optimization problem exists extensively in practical engineering problems,and usually contains multiple contradictory optimization goals.Therefore,multi-objective optimization is needed.The errors caused by the coupling of multiple uncertain information contained in multi-objective optimization problems will affect the stability of the system structure.Interval methods studied in recent years have greatly improved efficiency and engineering applicability when representing uncertain parameters.At the same time,due to the existence of multi-source uncertainty,each parameter is related and independent.In order to obtain more accurate optimization results,this paper takes the correlation between uncertain parameters into account for the solution of interval multi-objective optimization problems,and studies an interval multi-objective optimization method considering the parameter correlation.The main work is as followed:First of all,this paper studies a new optimization method of interval multi-objective considering the correlation of parameters for dealing with uncertain problems.The method uses interval structure analysis method to deal with the uncertain objective function.Taylor expansion is performed by using the midpoint value of the uncertain variable,and then the natural function is expanded to obtain the upper and lower bounds of the objective function.The method uses the interval probability model to deal with the uncertain constraint function,transforming the uncertain constraint into the deterministic constraint through the model of reliability-based possibility degree of interval.Based on the multidimensional parallelepiped model,the problem with correlated parameters is transformed into a general interval problem by affine coordinate system and transformation matrix.Through the above processing,the non-linear interval multi-objective problem eventually transforms into a deterministic multi-objective problem.Finally,a micro multi-objective genetic algorithm is used to solve the deterministic multi-objective optimization problem after conversion.Secondly,this paper validates the performance of the method studied in the paper through two numerical examples and a structural optimization example of a classic ten-truss structure.By comparing the optimization result considering the correlation of the parameters with the optimization result without considering the correlation,the validity of the method is verified.Thirdly,the research method was applied to the optimization of crashworthiness of the composite tube.The papers uses the optimal Latin hypercube test design method,selects design sample points and performs finite element simulation analysis;Considering the fiber thickness at different ply angles as a design variable,and the density,longitudinal elastic modulus and transverse elastic modulus of the material are regarded as uncertain parameters.There is a correlation between the parameters.To optimize the target of specific energy absorption and peak collision force of the composite tube,and to verify the optimization method by comparing the optimization results.Finally,the method is combined with the car crashworthiness optimization design.Considering the safety and lightness of automobiles at the same time,the body space and body weight at the time of collision are the optimization goals.The thickness of the main energy-absorbing parts of the vehicle is directly used as a design variable,and the elastic modulus and density are used as uncertain parameters which are relevant.At last,the paper uses a multi-objective genetic algorithm to find the optimal solution of the problem.The calculation results show that the method has good engineering practicality.