A model validation method based on the orthogonal polynomial transformation and area metric

作     者：Huan Zhang Wei Li Ping Ma Ming Yang 

作者机构：Control and Simulation Center Harbin Institute of Technology HarbinP.R.China 

出 版 物：《International Journal of Modeling, Simulation, and Scientific Computing》 (建模、仿真和科学计算国际期刊（英文）)

年 卷 期：2022年第13卷第2期

页      面：215-232页

核心收录：

学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 

基　　金：The research is supported by National Key R&D Program of China(Grant No.2018YFB1701600). 

主　　题：Model validation dynamic response uncertainty orthogonal polynomial area metric 

摘      要：Modeling and Simulation Technology has become an important means to study various complex systems with its extensive application.Thus,the accuracy of the simulation models becomes a critical problem and needs to be assessed by employing an appropri-ate model validation method.The simulation models often have multivariate dynamic responses with uncertainty,while most of the existing validation methods concentrate on the validation of the static responses.Hence,a new validation method is proposed in this paper to validate the dynamic responses of the simulation models over the time domain at a single validation site and multiple validation sites through introducing the discrete Chebyshev polynomials and area metric.For each time series,the orthogonal expan-sion coefficients are extracted primarily by representing the time series with the discrete orthogonal polynomials.Then,the area metric and the u-pooling metric are employed to validate all the uncorrelated coefficients at a single validation site and multiple vali-dation sites,respectively,and the final validation result is obtained by summarizing the metric values.The feasibility and effectiveness of the proposed model validation method are illustrated through the example of the terminal guidance stage of the flight vehicle.