Nonlinear system identification and fault detection using hierarchical clustering analysis and local linear models

This paper discusses the use of unsupervised learning and localized modeling to identify nonlinear dynamical systems from empirical data. A finite-order nonlinear autoregressive (AR) model is constructed to capture the system dynamics. The embedded input space for the nonlinear AR model is partitioned into overlapped regions that are fine enough so that localized modeling techniques, such as local linear modeling, can approximate system dynamics well in each region. Subsequently, unsupervised learning, such as hierarchical clustering analysis, is used for partitioning the embedded input space to achieve the tradeoff between the model complexity and the approximation error. The performance of the proposed nonlinear system identification is evaluated on two numerical examples: (i) time series prediction; (ii) identification of SISO system. Intelligent fault detection scheme is designed based on the identified linear models. Simulation results demonstrate that the proposed approach can capture the nonlinear system dynamics well and correctly detect the faults.