Nonlinear latent variable regression methods

Detecting anomalies is crucially important for improving the operation, reliability, and profitability of complex industrial processes. Traditional linear data-driven methods, such as the principal component analysis (PCA) and partial least squares (PLS) method, are extensively exploited for detecting anomalies in multivariate correlated processes. Since most of the data observed in practical applications are innately nonlinear, the development of models able to learn such nonlinearity are indispensable. In this chapter, in order to handle nonlinearity, we use nonlinear latent variable regression (LVR) modeling methods, which are powerful tools for processing nonlinearities. First, we use nonlinear functions using polynomials an adaptive network-based fuzzy-inference system as an inner model of the LVR model (i.e., nonlinear relation between latent variables and output). We then offer a brief overview of nonlinear LVR-based monitoring approaches and how they can be used for anomaly detection. We also present an alternative for dealing with nonlinearities in-process data by using kernel PCA, which captures the nonlinear features in high-dimensional feature spaces via nonlinear kernel functions. Lastly, the methods presented are applied to simulated synthetic data, plug flow reactor data, and real data from a wastewater treatment plant located in Saudi Arabia.