A piecewise affine (PWA) model identification method for nonlinear systems using hierarchical clustering based on the gap metric is proposed. The model parameter estimation is realized by clustering input-output data according to the local models. We initially introduce the gap metric to analyze the similarity between the local models from the perspective of the system, which distinguishes the proposed method from other identification methods that only focus on data features. To determine the optimal number of submodels, the hierarchical clustering aimed at the identification error minimization is addressed. Furthermore, Softmax regression is adopted to completely partition the valid region of a PWA model. Particle swarm optimization (PSO) algorithm is applied to simultaneously update the partition boundaries and model parameters in order to avoid the mismatch between them. Case studies on the multivariable pH neutralization process demonstrate that the proposed method achieves more accurate and stable identification.

提出了一种基于间隙度量的基于层次聚类的非线性系统分段仿射模型识别方法。通过根据局部模型对输入输出数据进行聚类来实现模型参数估计。首先，我们从系统的角度介绍了间隙度量，以分析局部模型之间的相似性，从而将提出的方法与仅关注数据特征的其他识别方法区分开来。为了确定子模型的最佳数量，解决了针对识别误差最小化的分层聚类。此外，采用Softmax回归来完全划分PWA模型的有效区域。应用粒子群优化（PSO）算法来同时更新分区边界和模型参数，以避免它们之间的不匹配。对多变量pH中和过程的案例研究表明，该方法可实现更准确和稳定的鉴定。