Multivariate fault detection and isolation.

In a variety of industrial settings, many complexly related variables are monitored to ensure that a process remains in control (IC) over time. Faults that remain undetected can cause extensive damage that require costly repairs; even if the fault is detected quickly, it can be difficult to isolate the fault without the aid of data-driven diagnostic tools. Multivariate statistical process monitoring (MSPM) methods are designed to detect an abnormal process and sometimes to also isolate the shifted variables in a system. However, these methods often require assumptions such as normality, stationarity, and autocorrelation, which are not often met in practice. Additionally, the metrics used to evaluate MSPM schemes, terminology, and notation are inconsistent, making it difficult to understand and compare methods in the literature. In our first project, we propose a distribution-free, retrospective fault detection and isolation (FD&I) method for autocorrelated, nonstationary processes. First, we detrend the data using observations from an IC period to account for known causes of fluctuations in the mean. Then, we perform fused lasso to drive any small changes in the mean to zero, and we use the estimated effective sample size in the Extended Bayesian Information Criterion to account for autocorrelation in the choice of the regularization parameter. In our second project, we develop a fully integrated online FD&I method that can also handle non-normality, nonstationarity, and autocorrelation. The method is based on principal component analysis, where the shifted variables are recovered using adaptive lasso. In addition, we design an enhanced visualization technique to assist operators in fault diagnosis. In both projects, we illustrate our method’s performance in case studies with known faults from a wastewater treatment facility. In our third project, we summarize the most common metrics used to evaluate FD&I methods from a survey of MSPM literature. We offer a way to standardize the notation and language, and we synthesize their strengths and weaknesses. Then, we propose a suite of new metrics to jointly assess a method’s detection and isolation ability that allows the user to tailor the metric to a particular process based on the consequences of a missed detection.