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Entropy 2015, 17, 5868-5887; doi:10.3390/e17085868

OPEN ACCESS

entropy

ISSN 1099-4300

www.mdpi.com/journal/entropy

Article

Detection of Causality between Process Variables Based on

Industrial Alarm Data Using Transfer Entropy

Weijun Yu and Fan Yang *

Tsinghua National Laboratory for Information Science and Technology, Department of Automation,

Tsinghua University, Beijing 100084, China; E-Mail: zdhx@tsinghua.edu.cn

* Author to whom correspondence should be addressed; E-Mail: yangfan@tsinghua.edu.cn;

Tel.: +86-10-62771347; Fax: +86-10-62786911.

Academic Editor: Kevin H. Knuth

Received: 1 May 2015 / Accepted: 14 August 2015 / Published: 20 August 2015

Abstract: In modern industrial processes, it is easier and less expensive to conﬁgure alarms

by software settings rather than by wiring, which causes the rapid growth of the number

of alarms. Moreover, because there exist complex interactions, in particular the causal

relationship among different parts in the process, a fault may propagate along propagation

pathways once an abnormal situation occurs, which brings great difﬁculty to operators to

identify its root cause immediately and to take proper actions correctly. Therefore, causality

detection becomes a very important problem in the context of multivariate alarm analysis and

design. Transfer entropy has become an effective and widely-used method to detect causality

between different continuous process variables in both linear and nonlinear situations in

recent years. However, such conventional methods to detect causality based on transfer

entropy are computationally costly. Alternatively, using binary alarm series can be more

computational-friendly and more direct because alarm data analysis is straightforward for

alarm management in practice. The methodology and implementation issues are discussed in

this paper. Illustrated by several case studies, including both numerical cases and simulated

industrial cases, the proposed method is demonstrated to be suitable for industrial situations

contaminated by noise.

Keywords: alarm design; transfer entropy; binary alarm series; causality analysis

Entropy 2015, 17 5869

1. Introduction

Alarms are indications of abnormal situations in process industries, including food, beverages,

chemicals, pharmaceuticals, petroleum, ceramics, base metals, coal, plastics, rubber, textiles, tobacco,

wood and wood products, paper and paper products, etc, where the primary production processes are

either continuous or occur on a batch of materials that is indistinguishable [1]. In former times, due to the

limitations of high cost and low quality of industrial monitoring systems, alarms have been conﬁgured via

directly placing sensors to measure the physical quantity that needed to be monitored and transmitting

the measurements to the control panel through cables. This caused the number of alarms at that time

to remain at a low level. However, with the development of monitoring systems, modern plants in

process industries have a multitude of sensors that are recorded and archived by process historians and

monitored by distributed control systems (DCSs), supervisory control and data acquisition (SCADA)

systems or other monitoring systems. Thus, most of the process variables can be conﬁgured to have at

least one alarm and, in many cases, more than one. For example, for monitoring a pressure variable,

four alarm tags can be conﬁgured, namely high-high, high, low and low-low. As a result, the number of

alarm variables is often quite large, and hence, a large number of alarms are raised during an abnormal

situation. Moreover, there often exist complex interactions between the corresponding process variables

due to the process dynamics and the associated monitoring systems. Once an abnormal situation occurs

at some place in the process, the fault may spread to many other places through interconnections between

variables and process units. Such a situation often leads to alarm ﬂoods. In this case, it is difﬁcult for

operators to identify the type of fault or to ﬁnd its root cause to mitigate the source of the abnormality.

Without proper actions, such a situation may lead to serious and catastrophic events.

For example, in 1994, before an explosion accident happened in a ﬂuid catalytic cracking unit of a

reﬁnery of British Texaco Company, there were 1775 out of 2040 alarm tags set to be “high priority”

in DCS, and 275 alarms occurred in the last ten minutes, which caused operators not to take effective

actions, leading to a major accident [2].

There are different ways to reduce the number of alarms, in particular nuisance alarms. For univariate

methods, ﬁltering, deadband, delay-timer and many other methods can be used [3].

On the other hand, for bivariate or multivariate situations, Folmer et al. [4] summarized several

approaches. Among these approaches, it is an essential method to identify the propagation paths between

variables and, thus, to localize the root cause of the abnormal situation. Yang et al. used signed directed

graphs to identify the process topology and connectivity that help in fault diagnosis and process hazard

assessment [5,6]. Noda et al. [7] and Yang et al. [8] used event correlation analysis to design a

policy to reduce alarms. Using causality information between alarm variables is another approach in

this area. Thereby, the propagation path of the fault can be found, and this will help operators identify

the root cause [9]. This enables operators to take preventative actions immediately. Thus, the detection

of causality between variables becomes important and has received a lot of attention.

The ﬁrst experimental example of causality detection by analyzing consecutive time series was

demonstrated by Granger [10]. He formalized the causality identiﬁcation idea in linear regression

models by the following thought: we consider that there exists causality from random variable I to

Entropy 2015, 17 5870

J if the variance of the autoregressive prediction error of J can be reduced by additionally considering

the historical data of I.

After that, some more advanced techniques for causality identiﬁcation have been proposed by

different researchers, such as extended Granger causality [11], nearest neighbor methods [12] and

transfer entropy (TE) [13].

Among these methods, TE, which was proposed by Schreiber in 2000, has been considered a useful

way to describe causality between variables. The major advantage of TE is that it can be used in both

linear and nonlinear situations. What is more, TE is equivalent to Granger causality in the presence

of Gaussian noise [14], which indicates that TE is also consistent with the concept of causality in the

predictive Granger sense. Since its introduction, TE has been successfully applied to industrial data to

identify causal relationships between process variables [15]. With the further development of TE, there

have been many extensions for causality identiﬁcation. For example, Duan et al. extended the traditional

concept of TE and made it more applicable, especially for multivariate cases [16,17]. Yang et al. [18]

and Duan et al. [19] also summarized these methods for capturing causality in industrial processes.

However, TE has primarily been used for continuous time series, which can describe the whole

characteristic of the process, but is computationally quite burdensome. In the context of alarm

management, causality under abnormal situations is usually of more concern rather than the exact

dynamic relationships under all situations. Therefore, it is unnecessary to take all cases (all situations

and process data) into account, and we would rather just focus on processing data in abnormal situations

(typically processing alarm data). In addition, because some alarm variables themselves are not

generated by continuous variables, such as switch variables (e.g., ON/OFF for a pump) and state

variables, a discrete version of TE is needed. Considering the computational cost and the above issues,

it is reasonable to detect causality between variables using alarm data directly.

Although there are already some discrete extensions of TE (for example, Staniek et al. proposed

symbolic transfer entropy to reduce the computational burden to estimate TE [20]), our purpose is not

the same. The main reason for emphasizing the discrete version of TE is that alarm data are binary

by nature. For analogue alarms, the corresponding process values are compared to the thresholds for

discretization. Thus, it is natural to use such binary alarm data for causality detection.

The main contribution of this paper is a new application of TE to identify causality between

variables by using binary alarm data in general multivariate systems. The proposed method and the

above-mentioned methods are compared in both variable type and their main characteristic, as shown

in Table 1. It can be seen that the types of methods used for the discrete situation are far fewer than

methods for the continuous situation, especially using such binary alarm data, which makes the method

easy to use.

The rest of this paper is organized as follows. In Section 2, the basic deﬁnition of transfer entropy

is revisited, and related concepts are also introduced. The TE method based on binary alarm data is

proposed in Section 3. Several simulated case studies are given in Section 4 to show the effectiveness

of the proposed method for detecting the causality between variables, followed by concluding remarks

in Section 5.

Entropy 2015, 17 5871

Table 1. The comparison of the mentioned methods and the proposed method. TE, transfer

entropy.

Method Authors Variable Type Main Characteristic

signed directed graph Yang, Shah and Xiao [5,6] continuous

qualitative model to

detect the cause and

effect relationship

event correlation analysis

Noda, Higuchi,

Takai and Nishitani [7]

continuous

a data mining method

to detect statistical

similarities

Granger causality Granger [10] continuous based on AR models

extended Granger causality

Ancona, Marinazzo

and Stramaglia [11]

continuous

nonlinear extension

of Granger causality

nearest neighbor methods

Bauer, Cox, Caveness,

Downs and Thornhill [12]

discrete

data-driven and operating

on the process measurements

stored in a data historian

transfer entropy Schreiber [13] continuous based on information theory

direct transfer entropy

Duan, Yang,

Chen and Shah [16]

continuous

extension of TE to

detect direct relationship

transfer zero-entropy

Duan, Yang,

Shah and Chen [17]

continuous

avoid estimating high

dimensional pdfs using

0-entropy

symbolic transfer entropy Staniek, Lehnertz [20] discrete

avoid estimating high

dimensional pdfs using

a technique of symbolization

this paper discrete

use natural binary alarm

data for causality detection

2. Concept of Transfer Entropy

In this section, the basic deﬁnition of TE is described. In addition, estimation methods and some

related concepts are also presented.

2.1. Basic Deﬁnition

Given two continuous random variables I and J, let them be sampled at time instant t and denoted by

∈ [i

min

, i

max

] and j

∈ [j

min

, j

max

] with t = 1, 2,···, N, where N is the number of time bins.

Let i

t+h

denote the value of I at time instant t + h, which means h steps in the future from t, and

h is called the prediction horizon. Let i

(k)

= [i

, i

t−τ

, . . . , i

t−(k−1)τ

] denote the embedded vectors with

elements being the past values of I; j

(l)

= [j

, j

t−τ

, . . . , j

t−(l−1)τ

] the embedded vectors with elements

being the past values of J (thus, k is the embedding dimension of I, and l is the embedding dimension of

J); τ is the time interval, which can allow us to sample the embedded vector; f (i

t+h

, i

(k)

, j

(l)

) the joint

probability density function (pdf) of i

t+h

, i

(k)

and j

(l)

; f(i

t+h

(k)

, j

(l)

) the conditional pdf of i

t+h

given

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