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Modeling Dynamical Causal Interactions with Fuzzy Temporal Networks for Process Operation Support Systems Gustavo Arroyo-Figueroa and Raúl Herrera-Avelar Gerencia de Sistemas Informáticos, Instituto de Investigaciones Eléctricas, Av. Reforma 113, Col. Palmira, 62490 Temixco Morelos Mexico KEVVS]S$MMISVKQ\ LXXT[[[MMISVKQ\

Abstract. Fossil Power Plants are faced with ever-increasing requirements for better quality, higher production profits, safer operation and stringent environment regulation. New technologies are required to reduce the operator’s cognitive load and to achieve more consistent operations. The research described in this work intended to develop an efficient reasoning methodology for operation support systems. The proposed approach is based on a novel fuzzy reasoning to deal uncertainty and time, know as Fuzzy Temporal Network (FTN). A FTN is a formal and systematic structure (DAG), used to model dynamical causal interactions between the occurrence of events. The mechanism of possibility propagation is based on Mamdani inference method (fuzzy logic control methodology). The proposed approach is applied to fossil power plant diagnosis through a case study: the diagnosis and prediction of events in the drum level system.

1

Introduction

Computer systems and information technology have been extensively used in power plant process operation. This trend is motivated by increasing requirements for higher productions profits, safer operation and stringent environment regulation. Distributed control systems (DCS) and management information systems have been playing an important role in increase this requirements. However, in nonroutine operations such as fault diagnosis, human operators have to rely on their own experience. During disturbances, the operator must determine the best recovery action according to the type and sequence of the signals received. In a major upset, the operator may be confronted with a large number of alarms, but very limited help from the system, concerning the underlying plant condition. Faced with vast amount of raw process data, human operators find it hard to contribute a timely and effective solutions. The power plants require new technologies to reduce the cognitive load placed upon operators. Analytical solution methods exist for many power operation and control problems. However, the mathematical formulations of real-word processes are obtained under certain restrictive assumptions, and even with these assumptions the resolution of C.A. Coello Coello et al. (Eds.): MICAI 2002, LNAI 2313, pp. 440–449, 2002. © Springer-Verlag Berlin Heidelberg 2002

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power-plant problems is not trivial. On the other hand, there are many uncertainties in the process, because power plants are large, complex and influenced by unexpected events and the evolution of time. Intelligent operational systems were born for this industrial need and deal with the uncertainties. As an effort towards the development of an intelligent operation support system for power plant [1,2,3], the knowledge representation and the reasoning mechanism used for efficient problem solving are being investigated. Fuzzy logic has shown its ability to handle this kind of uncertain in industrial automation, such as diagnostic systems [4, 5]; fuzzy classification [6]; and decision support systems [7]; this indicates its potential role in solving power-plant problems. In this study, the dealing of uncertainty and time are covered through a fuzzy temporal net. Using fuzzy logic each linguistic causal-temporal sentence can be defined by a possibility distribution. We propose building a events network that facilitates temporal representation and reasoning with uncertainty and time. The temporal model is called “Fuzzy Temporal Network”. In this directed acyclic graph model, each temporal node represents an event or state change of a variable and the arcs represent causal – temporal relationships between the nodes. The proposed approach is applied to fossil power plant operation for prediction task.

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Fuzzy Temporal Reasoning

2.1

Temporal expressions

In the context of industrial process, the knowledge is described in an imprecise and vague path using ill-defined linguistic terms such as “about 3 minutes”. Each of such linguistic terms can be described by a possibility distribution, for instance: “when the speed of the feedwater pump increase, there is increase in the feedwater flow “about 3 minutes after the increase of the speed”. Figure 1 shows the triangular possibility distribution that represent the temporal representation of the event “about 3 minutes”.

 (t − 1) / 2 if 1 ≤ t < 3  π about 3 min (t ) = (5 − t ) / 2 if 3 ≤ t < 5 0 Otherwise  Fig. 1. Temporal triangular possibility distribution for a event occurrence

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Gustavo Arroyo-Figueroa and Raúl Herrera-Avelar

2.2 Temporal Relationships Allen´s interval algebra and its thirteen relations provide the temporal basis of the temporal systems [8]. Each event has an associated interval denoted [a,b], where “a” is the starting time point and “b” is the ending point. A fuzzy time point can be represented by a normalized possibility distribution associated with each punctual event. Hence, a time interval is a representation of two fuzzy time points, there are three kinds of temporal relationships between points and intervals: those between two points, those between a point and interval, and those between two intervals. Defined the temporal elements (points and intervals) as normalized possibility distribution, the relationship between two temporal elements is measured by the possibility and necessity, which are two principal measures in possibility theory [9]. The relations between two fuzzy time points are defined by the conditional possibility. There are three possible relationships between two fuzzy time points: before, at the same time, and after. The possibility of the relation  between any couple of fuzzy time points τ1 y τ2 is given by:

Π((τ1, τ2)=max{min[πτ1(τ1), πτ2(τ2)]} τ1 6τ1 τ2 6τ2 τ1  τ2 The necessity measure is computed by the definition of necessity: N(p) = 1 - Π(~p) N ((τ1, τ2)=1- max{min[πτ1(τ1), πτ2(τ2)]} τ1 6τ1 τ2 6τ2 τ1 (~) τ2 where ~ is the complement of . As a fuzzy time interval can be defined by a couple of fuzzy time points, temporal relations between intervals can therefore be defined based on those between fuzzy time points. There are two kinds of relations between intervals: those between a time point and a time interval, and those between two time intervals. Given a fuzzy time interval i = {τid, τif} and a fuzzy time point τ, five mutually exclusive temporal relations are possible between them. By definition the end has to be after its beginning: Π(τid < τif) = 1; N(τid < τif) = 1. Table 1 defines the temporal relations between a fuzzy time interval and a fuzzy time point. The relations between two time intervals are defined by Allen´ interval algebra. There are thirteen mutually exclusive temporal relations between two intervals. The definition of each relations between two fuzzy time intervals can be made by their respective extreme points [9]. Table 2 shows the thirteen relations between two fuzzy time intervals.

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Table 1. Temporal relations between a fuzzy time interval and a fuzzy time point τ before I i after τ τ after I i before τ τ start i i started by τ τ during i i contained τ τ finish i i finished by τ

ττ τ>i i