Sequential Experiment Design Method Based on Uniformity and Distortion of Responses

• Published in: Acta Mathematicae Applicatae Sinica 2023-07, Vol.39 (3), p.778-790
• Main Authors: Huang, Qian-yi, Qi, Liang-wei, Zhang, Jing-ke, Tang, Yu
• Format: Article
• Language: English
• Subjects: Algorithms; Applications of Mathematics; Continuity (mathematics); Design of experiments; Design optimization; Design techniques; Distortion; Electronic countermeasures; Entropy (Information theory); Experiments; Jamming; Math Applications in Computer Science; Mathematical and Computational Physics; Mathematics; Mathematics and Statistics; Military aviation; Radar; Simulated annealing; Theoretical
• ISSN: 0168-9673; 1618-3932
• DOI: 10.1007/s10255-023-1065-4

With the development of modern electronic countermeasure technology, the fight between radar jamming and anti-jamming in aviation military has become increasingly fierce. There are some special requirements for radar countermeasure experiments. For example, such experiments are often divided into several stages, and responses of the previous stages will become factors of the next stages. Moreover, the experiment design can only consider some typical level values of the factors. However, the experiment factors are mostly continuous variables. Thus when there are some jumps in the response, and the value granularity of the factor level is large, the responses fail to reflect the distortion process, which makes it difficult to explore the radar performance boundary. Therefore, it is necessary to study the sequential experiment design method with the optimization goals of response uniformization and response distortion process characterization. In this paper, a sequential experiment design strategy based on Kriging model is established. Firstly, Kriging model is used to fit the initial experimental data to obtain the response surface. In order to enhance the uniformity of response distribution, Shannon entropy is applied to the objective function as the measure of uniformity. While for the situation of response distortion, we consider replacing the existing experiment points with those whose corresponding responses have a larger gradient norm. It means that the response value near these points will change rapidly, so they are more valuable for research. Then we use the peak surface in the three-dimensional space to intuitively verify the effect of the above algorithms on response uniformization and response distortion process characterization, and use the simulated annealing algorithm to solve them. The simulation results show that our sequential experiment strategy has a good effect. Finally, we apply the strategy to the practical problem of radar countermeasure experiment, and the obtained results also perform well.