Specifying the Directionality of Fault Propagation Paths Using Transfer Entropy

Abstract

In continuous chemical processes, variations of process variables usually travel along propagation paths in the direction of flow. The aim of this study was to find a data-driven method for identifying the direction of variation propagation using historical process data. Transfer entropy is a recently proposed method based on the probability density function (PDF) that measures directionality of variation with respect to time. An industrial case study illustrates the method which detects the influence of a temperature controller on downstream temperature measurements. A reversal of directionality was noted during a disturbance and a physical explanation offered.

Finding the Direction of Disturbance Propagation in a Chemical Process Using Transfer Entropy

“…For surrogate time series construction, the iterative amplitude adjusted Fourier transform (iAAFT) method as described by Schreiber and Schmitz [26], is used in all the following computations. The significance level is then defined as (6) where and are mean and standard deviation of . A sixsigma threshold for the significance level is chosen here to give a robust decision rather than a two or three sigma test as in [27].…”

“…For example, the bubble on the intersection of row PI2 column TI1 is 13 which means that PI2 causes TI1. The lower plot shows all transfer entropy values for which the significance level exceeds the threshold of 6 [see (6)]. Rearranging the transfer entropy matrix according to the first step described the reordering algorithm in Section V with all elements above the main diagonal, see Table IV.…”

“…This paper describes a solution through the application of transfer entropy, a method due to Schreiber [5] that exploits conditional probabilities to determine cause and effect relationships in process data. The possibility of a transfer entropy test was introduced in an earlier conference paper [6] which showed that it was possible to determine causes and effects using the process measurements collected during routine operation of a plant. The key advance in this paper compared to [6], is the detailed description and optimization of the method to give default parameters to facilitate its application to a large-scale plant.…”

“…The possibility of a transfer entropy test was introduced in an earlier conference paper [6] which showed that it was possible to determine causes and effects using the process measurements collected during routine operation of a plant. The key advance in this paper compared to [6], is the detailed description and optimization of the method to give default parameters to facilitate its application to a large-scale plant. A further contribution of this paper is to give fundamental insights into its operation and to extend it to additional case studies.…”

Information Theory Analysis of Cascading Process in a Synthetic Model of Fluid Turbulence

“…TE was soon adopted as a time series analysis tool in many complex system fields, such as space physics [9,10] and industrial chemistry [11], even if Kaiser and Schreiber developed a criticism and presented many caveats to the extension of the TE to continuous variables [12]. Since then, however, many authors have been using TE to detect causality, for example, in stock markets [13], symbolic dynamics [14], biology and genetics [15] and meteorology [16,17].…”