Nonlinear dynamical factor analysis for state change detection.
Changes in a dynamical process are often detected by monitoring selected indicators directly obtained from the process observations, such as the mean values or variances. Standard change detection algorithms such as the Shewhart control charts or the cumulative sum (CUSUM) algorithm are often based on such first- and second-order statistics. Much better results can be obtained if the dynamical process is properly modeled, for example by a nonlinear state-space model, and then the accuracy of the model is monitored over time. The success of the latter approach depends largely on the quality of the model. In practical applications like industrial processes, the state variables, dynamics, and observation mapping are rarely known accurately. Learning from data must be used; however, methods for the simultaneous estimation of the state and the unknown nonlinear mappings are very limited. We use a novel method of learning a nonlinear state-space model, the nonlinear dynamical factor analysis (NDFA) algorithm. It takes a set of multivariate observations over time and fits blindly a generative dynamical latent variable model, resembling nonlinear independent component analysis. We compare the performance of the model in process change detection to various traditional methods. It is shown that NDFA outperforms the classical methods by a wide margin in a variety of cases where the underlying process dynamics changes.