电磁干扰信号的数学表征方法与理论研究

The phenomenon of electromagnetic interference (EMI) can severely deteriorate the performance of electronic equipment in complex electromagnetic environments. Most of existing models for EMI analysis are constructed on strict mathematical hypotheses, which can merely deal with EMI signals in ideal conditions. As a consequence, how to propose an adaptive and universal mathematical framework and representation methods of EMI signals has emerged as one of the most critical scientific problems in EMI analysis. To address the aforementioned problem, this application aims to study the mathematical representation methods of severely coupled EMI signals. Specifically, the adaptive signal separation methods will be firstly studied to solve the undetermined blind identification problem of nonlinearly mixed signals. Subsequently, based on the generative adversarial network, the classification approaches will be proposed to model the nonlinear discriminative patterns of sparsely labeled signals with extremely high dimensions. Based on the separation and classification results, the basis function space can be built and optimized, by leveraging the empirical model decomposition model. Furthermore, considering the face that EMI signals are often stored by large-scale matrices, fast and scalable matrix computation methods will be presented, in order to improve the efficiency of the signal separation, classification and the basis function space construction. Finally, an adaptive and universal mathematical framework for representation EMI signals will be constructed, which can provide a solid mathematical foundation for the top-level design of the electromagnetic compatibility in complex electromagnetic environments.

复杂电磁环境中电磁干扰严重影响了电子设备的正常运行，现有方法模型假设性较强，仅适用于理想情况下的电磁干扰分析，如何从数学理论和表征方法上解决复杂电磁干扰信号处理模型和分析技术的自适应性和普适性是亟待解决的关键科学问题。本课题拟围绕上述问题，针对高密度耦合电磁干扰信号，研究其数学表征方法与理论。首先针对混合信号的欠定盲辨识问题，研究高密度耦合电磁干扰信号的自适应分离方法。针对高维混合信号特征空间中标注数据稀疏分布的特点，研究基于对抗生成网络的电磁干扰信号非线性分类模式表征方法。在此基础上，通过信号的经验模态分解，研究混合电磁干扰信号基函数空间构建与优化方法。此外，本课题将基于高维数据的大规模矩阵表示，研究混合电磁干扰信号的高效数学表征理论，提高信号分离、分解及基函数构建方法的计算效率。最终构建具有自适应性和普适性的电磁干扰信号数学表征方法和理论体系，为我国电磁兼容顶层设计提供数学支撑。

本项目以国家复杂电子系统为背景，对电磁干扰信号的数学表征方法与理论进行了深入系统的研究，提出了基于信号分解、分离、分类和量化的电磁干扰信号处理模型和分析方法，研究电磁干扰信号基函数空间构建与优化方法。对电磁兼容分析中高密度耦合电磁干扰信号的自适应分解和分离方法进行了探索研究；改进了现有的特征提取方法，增强信号编码的表征能力和普适性；从预处理角度分析了信号滤波器性质，利用特殊矩阵结构设计快速求解算法，计算效率得到显著地改善。本项目探索并创新性地提出了复信号量化和表征的理论体系，并应用至复杂电磁干扰信号场景中，为电磁兼容总体设计、预测、环境防护和评估等国防安全领域提供更多可行的应用解决方案。.项目执行期间研究成果共计35项，其中在Applied Mathematics and Computation, IEEE Communications Letters和Circuits, Systems, and Signal Processing等国际权威学术期刊上发表SCI检索论文14篇，在国际学术会议上发表EI论文16篇，教材专著1本，授权专利2项。代表性成果有：.1) 提出三次三角B样条和分段有理三次样条的包络修正经验模态分解，避免插值中过冲和欠冲问题；构建经验模态分解预处理框架，利用掩码信号处理含噪声情况下的模态混叠问题；分析基于包络修正经验模态分解的滤波器组性质。.2) 提出基于形态多样性的双低秩字典学习方法，解决异常值干扰下多通道信号分离问题；采用经验模态分解和独立成分分析，设计一系列一站式盲源分离方法；利用智能算法加速等变自适应独立分离算法收敛。.3)为处理含噪声信号的高维、非线性、非平稳、采样时空不一致等不良因素，利用小波变换、多维缩放映射、经验模态分解、自组织映射、自编码器等工具实现多个高效的电磁干扰要素的分类器，大幅提高识别精度.4) 研究复数域中对称双圆盘上复高斯随机变量问题的数值解，设计新的二维复金角量化方法，降低传统量化模型的均方误差失真率。.5) 提出基于Schur补和Hessian矩阵分解的改进块预处理器，设计预处理算法求解大型块状稀疏线性方程组，进一步分析预处理系数矩阵的特征值性质和边界。.本项目按计划完成研究内容，构建可应用于电磁干扰要素的数学框架，完成了论文发表。期间在数学、信息及交叉方向培养了博士10名，硕士16名，超额完成人才培养任务。