Research On The Multi-objective Reliability-based Design Optimization Based On Probability And Interval Hybrid Model

There are various uncertain factors in the design,manufacture,operation and maintenance of product structure in engineering application.These uncertainties can be roughly divided into two distinct forms of uncertainty.The first is the random uncertainty caused by the randomness of the working environment,the non-uniformity of product materials,changes in time and space or partial differences between individuals.The other is from the cognitive uncertainty that cannot be explained by current science,personnel measurement error,unobservability or lack of knowledge.In the process of solving the reliability-based optimization design(RBDO)problem,probability model is usually used to describe the uncertainty of the variables with the above uncertainty,and the limit state function with uncertain variables is used as the constraint condition of reliability optimization design.However,the accurate probability model established for uncertain variables often needs to collect a large number of sample points.Moreover,obtaining an accurate probability density distribution function through the obtained sample points is generally accompanied by a large amount of calculation cost.Therefore,the reliability optimization design problem which only uses probability model to replace uncertain variables has some limitations in practical engineering application.In order to meet the design requirements of engineering applications,non-probabilistic model is proposed as a new reliability model.Among them,as a non-probabilistic model used to describe uncertainty,non-probabilistic convex model has the greatest advantage in the field of reliability analysis.Specifically,it is not necessary to obtain the distribution function of uncertain variables,but only to determine the upper and lower boundaries of their variables.As a common non probabilistic convex model,interval model is used to describe the changes of uncertain variables,which has strong practicability and applicability.To sum up,in the reliability optimization design of complex engineering equipment structure with high nonlinearity,most designers only use a single type model(probability model)to describe the uncertainty of variables.In fact,it is necessary to consider the reliability design optimization problem with mixed uncertain variables,that is,the uncertain variables should be described according to different models such as probability and interval.Therefore,this paper studies and discusses the solution method of multi-objective reliability optimization design problem with probability interval hybrid model.The specific research contents are as follows:(1)A multi-objective reliability optimization design method for probability interval mixed model is proposed.In this paper,an effective decoupling strategy based on KarushKuhn-Tucker(KKT)necessary condition and maximum entropy principle is proposed.The three-layer nested structure in reliability optimization design problem is transformed into a single-layer structure,which improves the solution speed of the original optimization problem and effectively avoids the computational burden caused by the three-layer nested structure optimization problem.Then,multi-objective genetic algorithm is used as the solver of multi-objective reliability optimization design problem,and its Pareto optimal solution set is obtained.Finally,the efficiency of the proposed method is verified by numerical examples and engineering application results.(2)Combining the dimension reduction method and sequential optimization method,an effective decoupling strategy is proposed to solve the reliability optimization design problem in two ways.The first is to transform the reliability optimization design problem of the original three-layer nested structure into a single-layer optimization problem;The second is to transform the original optimization design problem into a sub deterministic optimization problem,which improves the efficiency of solving the optimization problem and breaks through the limitation of time-consuming calculation of reliability optimization design problem.Then,the Pareto optimal solution set of the optimization problem is solved by multi-objective genetic algorithm,which is applied to numerical examples and engineering application problems.(3)In order to solve the problems of black box function or computational cost in reliability optimization design,a multi-objective reliability optimization design method based on adaptive approximate model technology is proposed.In this method,the radial basis function and inverse parameter method are combined to construct an approximate model,which is combined with the above two decoupling strategies to construct an approximate multi-objective reliability optimization problem,and the optimization problem is solved.Then,the Pareto optimal solution set obtained by solving the optimization problem is added to the sample space of the established approximate model through local encryption approximation technology,so as to improve the accuracy of the approximate model.Finally,the proposed method is applied to numerical examples and multi-objective reliability optimization design problems in engineering applications.