Sensor Fault Detection in Uncertain Large-Scale Systems Using Interval-Valued PCA Technique

Abstract

Principal component analysis (PCA)-based fault detection and diagnosis (FDD) is a well-established, data-driven method that has shown remarkable performance. Despite the excellent reputation of the PCA, it is not an optimal solution, mainly due to the effect of system parameters’ uncertainties and imprecise measurements. These drastically affect the decision-making concerning the operating state of the process. In this article, the data collected by different sensors are transformed from a single value to an interval value form by which errors and uncertainties in the measurements are quantified satisfactorily. Then, the process modeling based on the PCA technique has been duly performed for interval-valued. Afterward, the well-known fault detection statistics <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${T}^{\,{2}}$ </tex-math></inline-formula>, Q, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Phi $ </tex-math></inline-formula> are obtained under an interval-valued representation. The developed technique is tested in the cement rotary kiln process. Its performance in terms of false and missed alarms and detection delay is compared with that of other techniques through an actual involuntary system fault and other different types of sensor faults. The obtained results show high superiority in detecting accurately and quickly distinct faults in a stochastic environment, including unknown and uncontrolled uncertainties. Consequently, the results have been reduced by more than 33%, 85%, and 45% for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${T}^{\,{2}}$ </tex-math></inline-formula>, Q, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Phi $ </tex-math></inline-formula>, respectively, compared with the best results of the studied methods.