基于非均匀采样数据的复杂非线性系统的多模型辨识方法研究

The modeling of complex nonlinear systems with non-uniformly sampled data under a frame period is a theoretical research with a wide range of practical applications. This kind of system has the characteristics of strong nonlinearity, uncertainty and multiple working regions, which lead to the difficulties of direct application of the existing non-uniformly sampled data nonlinear system identification methods. In this project, based on the “divide and conquer” principle of multi-models modeling，the whole work region of non-uniformly sampled data nonlinear systems can be divided into multiple finite sub-regions to be described by local linear sub-models. The fuzzy rules are employed to merge local sub-models into the global model to describe the whole dynamic process of non-uniformly sampled data nonlinear systems. According to the non-uniformly sampled process, the transformation relationships of the system models are deeply analyzed, and the mult-models of these nonlinear systems are described under the unified framework. In order to solve the problems of model structure identification, parameter identification, algorithm convergence and global optimization, we use fuzzy clustering, hierarchical identification, martingale convergence theories, intelligent optimization algorithms and other tools to explore and research. Then, the research results are applied to the non-uniformly sampled data industrial systems, and the identification modeling and model test verification are completed. This study provides an effective analysis and design method for modeling complex nonlinear systems with non-uniformly sampled data, and the results can be applied in non-uniformly sampled industrial production, which provides a feasible solution for multi-model identification theory to solve practical problems.

含有框架周期的非均匀采样数据的复杂非线性系统建模是具有广泛实际应用前景的理论研究。该系统具有强非线性、不确定性、多工况等特点，导致现有非均匀采样数据非线性系统辨识方法很难直接应用。本项目基于“分解-合成”多模型建模思想，将非均匀采样数据非线性系统的输入空间划分为有限个子空间，每个子区间上用一个局部线性模型来描述，通过模糊规则将局部模型融合成整体来描述系统的全局动态过程。根据非均匀采样过程，深入分析系统模型转换关系，提出在统一框架下描述此类非线性系统的多模型。探索研究利用模糊聚类、递阶辨识、鞅收敛理论、智能优化算法等工具解决模型结构辨识、参数辨识、算法收敛性和全局最优化等问题。进而，将研究结果应用于非均匀采样数据实际系统中，完成辨识建模和模型试验验证。本研究为非均匀采样数据复杂非线性系统建模提供有效的分析和设计方法，并在非均匀采样工业生产中应用，为多模型辨识理论解决实际问题提供方案

含有框架周期的非均匀采样数据的复杂非线性系统建模是具有广泛实际应用前景的理论方法研究。该系统具有强非线性、不确定性、多工况等特点，导致现有非均匀采样数据非线性系统辨识方法很难直接应用，是当前系统辨识建模的热点难点问题。在国家自然科学基金资助下，研究了非均匀采样数据驱动下的多种多模型框架，构思了多模型建模技术路线和建模途径，设计了多种建模方法，用严谨数学证明揭示了辨识算法的建模原理和收敛机制，从而建立了非均匀采样多模型建模理论体系，获得一批原创的学术成果和成功应用的工程案例。具体研究工作为：首先，结合非均匀采样数据，构建了模糊多模型的建模架构、基于切换原理的多模型建模架构、分数阶非线性系统的建模架构；其次，结合系统辨识理论、鞅收敛系统理论、切换系统理论、多智能体控制理论、群智优化算法、分数阶微积分等数学理论和优化方法，深入研究了最小二乘类算法、多新息类估计算法、梯度下降类算法、递阶类辨识算法、群智类优化、分数阶类优化等算法在辨识中的模型结构确定、参数估计等应用，分析了算法性能、复杂度和收敛性等，并设计了适合不同多模型类型的控制策略；最后，通过仿真算例和工程实例，对所提出的基于多模型辨识方法和控制策略展开技术验证，发表了第1标注的影响因子较高的学术论文30篇，其中SCI检索9篇，EI检索9篇，获得和申请专利5项、软著3项，培养26名研究生，24名已毕业，完成项目预定的研究目标。通过不断努力，相信项目中提出的理论、方法和技术一定有着广阔的应用前景。