Probabilistic Framework-based Uncertainty Quantification Methods For Complex Simulation Model

In the fields of aeronautics and astronautics,a large number of uncertain factors are involved in the simulation model.These factors will lead to the variation of model response and have a critical influence on its performance.With the increasing requirement of model accuracy,simulation model is typically characterized by complexity,high dimensionality,high nonlinearity,and high computational demand.Taking electromagnetic railgun for instance,the velocity of railgun projectile can reach 2km/s.During the flight,projectile suffers from the influence of random wind,aerodynamic influence,and erosion.Running the model of electromagnetic railgun is a time-consuming work,which requires several ten hours for computing the accurate results.Besides,the uncertain parameters are coupled with each other in the model of electromagnetic railgun,which leads to a great influence on the flight performance.How to effectively quantify the uncertainty is a great challenge in the complex simulation model.Due to the expensive computational costs of complex simulation model,it is required to study the computational method of response property with high efficiency.Various uncertain parameters are included in the complex simulation model,the importance analysis is also required to screen significant factors and reduce model uncertainty.Besides,since uncertain parameters will influence the solution of optimization design,the optimization design under uncertainty is deserved to study for improving design quality.Therefore,to improve the computational accuracy and efficiency in the uncertainty quantification,the uncertainty propagation,derivative-based sensitivity analysis,multi-response sensitivity analysis,reliability-based design optimization,and their applications to electromagnetic railgun model are studied.Overall,the details are summarized as follows:To deal with the low accuracy and poor efficiency issues of uncertainty propagation in the complex simulation model,optimal Latin hypercube design(LHD)based on local search-based genetic algorithm(LSGA)and response moment computational method based on polynomial chaos expansion(PCE)have been proposed.In the LSGA,the modified order crossover,probabilistic mutation,and adaptive selection operators and local search strategy are proposed to improve optimization efficiency.On the other hand,according to the orthogonality of PCE polynomial terms,the low-order moments of simulation model response in different probability distributions are derived,which can improve the computational accuracy and efficiency in the uncertainty propagation.Since various uncertain factors and intensive computational efforts are involved in the complex simulation model,derivative-based global sensitivity measure(DGSM)using radial basis function(RBF)metamodel is proposed to screen important factors.The RBF metamodel is used to replace original simulation model and can transform DGSM index into the computation of Gaussian integrals.This approach employs RBF metamodel to derive the computational expression of DGSM index,which effectively reduce the computational costs and improve screening efficiency.In the complex simulation model,a multi-PCE sensitivity analysis method using asymptotic covariance determinant-based sequential design(ACDSD)is proposed to deal with the low computational efficiency of multi-response sensitivity analysis.The scalar response PCE approach is firstly extended to the case of multi-response.Then,the coefficients of PCE and asymptotic property of sensitivity index have been derived.To improve the computational efficiency,ACDSD is proposed to select optimal design points,which can effectively reduce the computational burden of sensitivity analysis.The computational efficiency is a great challenge in reliability-based design optimization(RBDO)of complex simulation model.Therefore,a polynomial chaos enhanced radial basis function(PCE-RBF)metamodel is proposed to relief the computation.The optimal LHD method is used to construct initial PCE-RBF metamodel.Then,a sequential sampling approach based on local variation with minimum distance,is proposed to refine the local accuracy of metamodel.PCE-RBF method can capture the global accuracy of PCE and local nonlinearity of RBF,which significantly improve the computational accuracy and efficiency in the RBDO.Since electromagnetic railgun suffers from structure complexity,high dimensionality,and time-consuming issue,the proposed methods are employed to quantify the uncertainty.Firstly,the optimal LHD and PCE-based response moment computation method is carried out to propagate the uncertainty.Then,RBF and ACDSD-based PCE methods are used to compute DGSM and multi-response sensitivity indices.At last,PCE-RBF method is used to address RBDO problem.Compared with traditional method,the proposed methods can effectively improve the computational accuracy and efficiency,and has a fine prospect in the engineering application.