Fault Diagnosis Using Dynamic Time Warping
Owing to the superiority of Dynamic Time Warping as a similarity measure of time series, it can become an effective tool for fault diagnosis in chemical process plants. However, direct application of Dynamic Time Warping can be computationally inefficient
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Chemical Engineering Division, National Chemical Laboratory, Pune-411008, India {bd.kulkarni,vk.jayaraman}@ncl.res.in 2 Department of Chemical Engineering, Indian Institute of Technology, Kharagpur-721302, India
Abstract. Owing to the superiority of Dynamic Time Warping as a similarity measure of time series, it can become an effective tool for fault diagnosis in chemical process plants. However, direct application of Dynamic Time Warping can be computationally inefficient, given the complexity involved. In this work we have tackled this problem by employing a warping window constraint and a Lower Bounding measure. A novel methodology for online fault diagnosis with Dynamic Time Warping has been suggested and its performance has been investigated using two simulated case studies.
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Introduction
The process deviation from the normal operating range leads to deterioration in product quality and can be source of potential hazard. The control of such deviations comes under abnormal event management (AEM) in chemical process industry. The first step in AEM consists of timely detection and diagnosis of fault, so that it can lead to situation assessment and planning of supervisory decisions to bring the process back to a normal and safe operating state. However due to the size and complexity involved in the modern process plants, traditional method of complete reliance on human operators has become insufficient and unreliable. The advent of computer based control strategies and its success in process control domain has lead to several automated fault diagnosis methodologies. Currently available fault diagnosis techniques can be classified into three broad categories: quantitative model based, qualitative model based and process history based approaches. In this work, a novel process history based approach for fault detection has been proposed. It employs the concept of Dynamic time warping (DTW) for the similarity measurement. Direct application of DTW leads to poor computational efficiency of the methodology. This problem has been rectified in this work by using window warping constraint in DTW with the application of lower bounding technique. We demonstrate the efficiency of our proposed methodology by performing online fault diagnosis on two simulated case studies.
Corresponding author.
A. Ghosh, R.K. De, and S.K. Pal (Eds.): PReMI 2007, LNCS 4815, pp. 57–66, 2007. c Springer-Verlag Berlin Heidelberg 2007
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Rajshekhar et al.
Dynamic Time Warping
Consider two multivariate time series Q and C, of length n and m respectively, Q = q1 , q2 , q3 , . . . . . . , qi , . . . . . . , qn
(1)
C = c1 , c2 , c3 , . . . . . . , cj , . . . . . . , cm
(2)
such that, qi , cj ∈ IRp . Since the DTW measure is symmetric with respect to the order of the two time series, without any loss of generality we can assume that n ≥ m in our work. To align these two sequences using DTW, we construct a n − by − m matrix where the (ith , j th ) element of the matrix corresponds to the squared distance, r=p d(i, j) = (qi,r − cj,r )2 (3) r=1
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