Method And Application Of Experimental Design In Complex Test Space

Equipment tests are comprehensive practices to determine the performances and effectiveness of equipment and to discover the problems and defects.Experimental design is the key link of equipment test,which requires that an optimized test scheme should be made according to the test purpose,and the most effective test data can be obtained at a lower cost.However,due to the influence of equipment structure and function and complex combat environment,equipment test has the characteristics of a large number of factors,constraints among factors,different importance of factors and factor levels,diversification of factor types and so on,which makes the equipment test space very complex,showing the characteristics of irregular space shape and unbalanced regional characteristics.The current experimental design methods are difficult to solve the problem of equipment test design in the complex test space mentioned above.This paper studies the problems widely existing in equipment test design,such as constraints between factors,different importance of space regions,multiple types of factors,sequential supplement of test samples and so on.In general,our main contributions in this thesis are summarized as follows:(1)We propose methods for experimental design with constraints between factors.For the cases that the response model being unknown or known,based on the approximate orthogonal space filling criterion and D-optimal design criterion respectively,the coordinate exchange rules of design matrix are proposed,and the optimization algorithm based on improved coordinate exchange is developed to solve the experimental design problem of complex constraint space.The experimental results show that the proposed method is suitable for many types of constraints,such as linear and nonlinear constraints,convex and non-convex constraints,analytical and non-analytical constraints and so on.Compared with the existing methods for constrained space,the proposed method has a significant improvement in operation efficiency and the superiority of the test plan,and the performance of the method shows more obvious advantages with the increase of factors.(2)We propose methods for experimental design with different important regions of space.For the situation that the importance of the space regions are different due to the different importance of factor levels,the space filling experimental design method and the weighted D-optimal experimental design method based on importance weighting are proposed.In view of the different degree of nonlinearity of the response model,a comprehensive experimental design method is proposed,in which the nonlinear region of the response model is explored based on the simulation experiments,and the regional importance is quantified by the nonlinear degree.Then the test plan is constructed based on the non-analytical constraint experimental design method.The experimental results demonstrate that,compared with the existing adaptive sampling experimental design methods,our method has stronger model applicability and can obtain a higher precision model.(3)We propose methods for experimental design with multiple types of factors.For the case that experimental design with qualitative and quantitative factors,when the model is unknown,a coordinate exchange algorithm for multiple types of factors based on maximum projection design criterion is proposed.When the model is known,a maximum entropy design criterion based on Gaussian process model of mixed factors and the corresponding point exchange algorithm are proposed.The experimental results show that,compared with the existing experimental design methods with multiple types of factors,our method can obtain a better test plan under different number of factors and sample sizes.(4)We propose sequential design methods of supplementing test points..In order to solve the problem of sequentially supplementing new test points on the basis of current test information,two types of sequential design methods based on input and output are proposed.Among them,the input-based method does not consider the test response,only based on the current set of test points and constraints,we propose a space-filling sequential design method based on coordinate exchange strategy.The output-based method,considering the current test points and responses,using Gaussian process model of mixed factors,a comprehensive design criterion based on model prediction error and gradient approximation is constructed,and the genetic algorithm is used to select the new point.The experimental results demonstrate that,the input-based method can generate the test plan quickly and has good adaptability to the case of high-dimensional space and large sample size;the output-based method can effectively solve the experimental design problem of complex response modeling in the case of limited sample size.(5)Case application.A case study on the experimental design of a ship-to-air missile is carried out,the test response and factors in the actual situation are analyzed,and a complex test space with multiple types of factors,constraints between factors and different importance of regions is constructed.Single-stage test plan and two sequential test plans are designed and compared to verify the effectiveness of our methods.