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

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 appropriate 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 expansion 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 validation 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.