Research On Multidisciplinary Design Optimization Modeling And Solving Methods Based On Process Analysis

Modern complex engineering problems usually involve a number of design variables,nonlinear constraints,and diverse coupled disciplines.Traditional methods could not satisfy the design requirements of these large-scale coupled systems.According decomposition and coordination strategies,Multidisciplinary Design Optimization(MDO)method decomposes a complex optimization problem into one or several sub-problems,which can be solved in parallel,and employs specific coordination methods to enforce the multidisciplinary feasibility.To solve these coupled systems,a number of MDO frameworks are proposed,and many integrated software platforms are developed to support engineering applications.However,several problems should be further addressed in the research and application of MDO.The solving efficiency of most MDO methods is low,and the research on the global optimization on MDO problems is less focused on because of the complexity of these problems.Also,current MDO platforms are hard to support flexible implementation of different MDO frameworks.By analysizing the coupling relationships in MDO,the paper will research how to enhance the solving efficiency,implement global optimization on MDO problems based on response surface methods,and carry out modular MDO process modeling and solving in multidisciplinary integrated platforms.The main contributions of the research are as follows.Firstly,a multidisciplinary design system analysis method based on minimal solving strategy is proposed.When solving the coupled system with many disciplines and coupling variables,the multidisciplinary system analysis(MDSA)could be time-consuming.To address this problem,the paper decomposes a complex coupled system into several minimal solving units and solves them sequentially.When solving each solving unit,based on the integrated discipline dependence structural matrix,feedback coupling relationships are selected to be broken,and a least-square problem is constructed to minimize the difference of these broken relationships,and to find the multidisciplinary feasible solution.Thus,by reducing the number of disciplines and unknowns in each unit,the MDSA problem size is decreased,and the solving efficiency is enhanced.Secondly,an optimal discipline sequencing method based on discipline dependence structural matrix is proposed.With the number of disciplines and the number of coupling variables increasing,the resulting problem of Multidisciplinary Feasible(MDF)or Individual Discipline Feasible(IDF)could become too large to be solved efficiently.Based on Discipline Dependence Structural Matrix,the paper builds an optimal discipline sequencing model to minimize the number of feedback coupling variables,and to select less coupling variables to construct MDF or IDF problem.Furthermore,the paper maps all the discipline permutations into a group of integers based on Cantor Expansion,and converts the optimal sequencing model into an unconstraint integer programming.Also,DIviding RECTangle algorithm is modified to solve the integer programming globally.Thirdly,a Response surface-based MDF Global Optimization(RB-MDF-GO)method is proposed.The paper introduces the sequential sampling strategy based on quasi-sampling density function,improves its ability of global exploration,and implements global optimization on MDF problem.Subject to approximate constraints,the product of predictive objective function and the quasi-sampling density is minimized to obtain the next sampling point to enhance the accuracy of response surface and in turn to improve the solution.An approximate multidisciplinary feasibility constraint is added to drive the sampling point away from the region where no multidisciplinary feasible solution exists.If there is no feasible solution in the initial sampling points,sequential sampling minimizing the approximate constraint violations is implemented until a feasible solution is found.Quasi-sampling density function is used to balance the global exploration and the local exploitation.Fourthly,a Response surface-based IDF Global Optimization(RB-IDF-GO)method is proposed.As IDF adds compatibility consistent equal constraints to coordinate broken couplings,the global optimization algorithms based on swarm,or the algorithms based on response surface,are hard to solve the IDF problems with time-consuming discipline analyses.Based on the features of IDF problem,the paper constructs the response surface of compatibility consistent constraints with respect to design variables and coupling variables,and employs a two-phase framework to solve the problem.In the first phase,sequential sampling minimizing the approximate equal constraint violations is implemented,so that the response surface of compatibility consistent constraint boundary could be approximate to the true boundary.In the second phase,sequential sampling is carried out in the region where the objective could be improved and the approximate equal constraints are satisfied to enhance the accuracy of response surface and improve the solution found.Quasi-sampling density function is employed to balance the global exploration and local exploitation during both phases.Fifthly,an optimization process modeling method based on response surface modulars is proposed.The sequential sampling optimization process based on response surface is hard to be implemented in the current integrated MDO platforms.The paper analyzes the general optimization process based on response surface,and designs three type of components,including Design of Experiment(DOE)component,Response Surface Model(RSM)component and Reference RSM component,to model the sequential sampling process,together with discipline components and other design tools.The method could construct response surface-based design optimization process according to specified engineering flowchart.Sixthly,the process modeling and solving of MDO frameworks are implemented in a multidisciplinary integrated platform.As a class of framework-based solving methods,MDO usually involves discipline analysis models,response surface models,diverse design exploration methods and software tools,and solving strategies.In fact,the implementation is to combine all these models and methods following specified flowchart.The paper analyzes the basic functions in MDO,designs them as a serial of functional components in a MDO platform,and constructs different MDO implementations using these components to solve engineering coupling problems.Finally,the main contributions of the research are summarized,the limitations are addressed,and the future works are presented.