Study On Numerical Simulation Based Sequential Approximate Optimization

Optimization design based on high-precision numerical simulation is a promising approach for the refined design of aircraft.However,the time-consuming calculation coupled with a large number of iterations in optimization process make it quite difficult for high-precision model to be fully adopted in aircraft optimization design.Throuth introducing surrogate model and updating dynamically,Sequential Approximation Optimization method could get satisfactory design results with limited number of model simulations,which is an effective way to solve aircraft optimization design problems based on high-precision simulation models.Based on surrogate model theory and Sequential Approximation Optimization method,this paper studies how to improve the efficiency of aircraft optimization design based on time-consuming simulation models.By analyzing the drawbacks of the existing black-box surrogate-based methods,an optimization design theory coupling numerical simulation and optimization search is proposed to efficiently utilize the large amount of data generated in the simulation process.Consequently,the efficiency of aircraft optimization design is significantly improved and the theory of aircraft optimization design is enriched.The specific research work is as follows:Aiming at the optimization problems based on high-precision numerical simulation of boundary value differential equations,a physical field approximation model method is proposed according to the characteristics of iterative solution process and the effect of reasonable initial field on accelerating the convergence of boundary value simulations.By learning the boundary value problem solution of existing sample points,the changes of the problem solution with changes of input variables is predicted,and the approximate model of physical field is established.In the process of sequence sampling,the new sample points are initialized directly on the basis of the existing approximate model to avoid repeated simulation in each iteration,and the computational complexity of new sample solution in the process of sequence sampling is consequently decreased.Aiming at the inverse design problem of initial value problem,a collaborative iteration method coupling numerical simulation of initial value problem and inverse design method is proposed according to the divisibility of inverse design problem and the characteristics of one-way recurrence and no aftereffect in initial value problem solution process.In the process of Sequential Approximation Optimization,the potential optimal solution prediction and inferior solution elimination are realized based on incomplete simulation information and inaccurate sampling criteria and the waste of computing resources caused by inferior solution simulation is effectively avoided.It can effectively save computing resources and achieve collaborative iteration between simulation and optimization.A low-correlation Latin hypercube direct construction method is proposed and its homogeneity is optimized.Because of the introduction of direct construction method,the complexity of optimization is greatly reduced,thus the scattering of sample points is highly improved and the ability of sample points to capture the full spatial characteristics is increased.On this basis,an optimized Latin hypercube experimental design sequence expansion method is proposed.By reasonably designing the new sample points,the new sample points can be filled evenly among the existing samples,which ensures the optimum distribution of the whole sample set and increases the availability of simulation results.Aiming at a large number of explicit constraints in optimization design,an optimal Latin hypercube design method for constrained domain is proposed.By weighting infeasible points and feasible points respectively,the uniform distribution of sampling points in the feasible region is realized,while the distribution of infeasible points is ignored.The feasibility of sample points is improved and the simulation of infeasible points is avoided.A calculation method for shape parameters of radial basis function(RBF)based on local density is proposed.By introducing the concept of local density according to the density of sample points,the determination of multiple shape parameters is transformed into the determination of one single parameter.In this process,the firstorder and second-order moments of the radial basis function approximation model are explicitly solved,which significantly reduces the computational complexity and improves the approximation accuracy.Based on Sobol' decomposition,an orthogonal decomposition method for radial basis function(RBF)approximation model is proposed.The sensitivity of each order of the approximation model is solved explicitly.The efficiency of sensitivity analysis for complex and time-consuming models is improved,and the main influencing factors can be quickly identified.A self-adaptive parallel sampling criterion based on imprecise search is proposed.The idea of imprecise one-dimensional search in classical gradient optimization field is used for reference and introduced into the optimization process based on approximate model.The approximate model search is stopped at the appropriate time instead of searching exhaustively,which saves the amount of search calculation and avoids the misleading from initial rough approximate model.On this basis,the requirements for exploration and exploitation in different stages of optimization are analyzed,and a self-adaptive determination method for the number of sample points is proposed to realize the adaptive adjustment between exploration and development.As a result,the ineffective exploration in the later stage of optimization could be avoided,and the number of simulation model calculation is reduced,which significantly improves the optimization efficiency.Based on the proposed optimization design theory coupling numerical simulation and optimization search,the aerodynamic optimization design of hypersonic lifting body and the performance matching design of solid rocket motor are completed.The engineering application of this method is realized,and the feasibility and efficiency of the proposed method are verified.