Towards timed fuzzy Petri net algorithms for chemical abnormality monitoring

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Abstract

One critical problem in the operations of chemical processes is the occurrence of abnormal events. Therefore, an effective process monitoring methodology that can help detect, diagnose and predict abnormal events becomes potentially very useful. For the purpose of knowledge representation of chemical abnormality, a specified type of timed fuzzy Petri net (tFPN) approach is explicitly introduced in this paper. The dominant feature of tFPN metrics can be recognized from the fact that a timing factor is assigned to each transition, as well as a degree of reliability is associated with each place, which allows accurately representing the dynamic nature of fuzzy knowledge pertaining to abnormal events. Following a procedure towards abnormal event monitoring, two efficient algorithms in terms of abnormality prognostication and diagnosis are exploited by means of reachability analysis of tFPN. The benefits of derived techniques and solutions are illustrated through a case study consisting in a polypropylene reactor.

Research highlights

► A type of timed fuzzy Petri net (tFPN) is introduced for knowledge representation of chemical abnormality. ► Enabling algorithms using tFPN metrics are presented for abnormal event monitoring. ► Case studies consisting in a polypropylene reactor are performed to exemplify the approaches.

Introduction

In chemical engineering practice, abnormal event monitoring is driven by increasing concerns for diagnosing faults, ensuring safe and smooth operations. Abnormality of varying magnitudes could result in incipient faults, near-misses, incidents, or even forced shutdown of plants. In recent years, fault diagnosis of chemical process has become an active area in both academia and industry. Whereas, monitoring of abnormal events in terms of predicting consequences, compensating and correcting abnormal situations has found only a limited reports.

Generally speaking, abnormal event is referred to as a departure from an admissible range of an observed variable or a calculated parameter associated with a process. Failures in equipments may cause abnormalities, while mal-operations and larger process disturbances may also give rise to them. Thus, in realistic production environment, it is usually difficult for operators to identify the causes of abnormal events so as to achieve effective solutions in time.

Incorporating fuzzy philosophy in Petri net, fuzzy Petri net (FPN) is acknowledged to have inherited the key advantages of both graphical power and fuzzy reasoning capability, which has been extensively studied and widely circulated in the literature (Bugarn and Barro, 1994, Cao and Sanderson, 1995, Chen et al., 1990, Garg et al., 1991). Nevertheless, employed as a tool to handle dynamic knowledge pertaining to abnormal events, FPN still suffers a couple of deficiencies, such as:

  • Difficulty in describing sharing behavior of abnormality propagation: in FPN model, token is regarded as a flow resource moved with fuzzy inferring. As a consequence, the firing of transition leads to not only occurrence of subsequent symptoms but also disappearance of the former, which is not in accordance with the mechanism of abnormality evolutions.

  • Difficulty in describing temporal behavior of abnormality evolution: owing to the intrinsic dynamic nature of chemical process, abnormal event always travels with time going on. However, temporal factor appears nowhere in the structure of conventional FPN.

Several approaches have been presented to modify FPN in knowledge representations. For instance, when fuzzy Petri net is used to model production rule, flow of token is regarded as generation other than consumption of resources. To address this issue, Nazareth (1993) suggested that, when output places capture new tokens, the tokens in input places should keep unchanged and a control place should be additionally added to each transition to prevent transition being fired endless. Pedrycz and Camargo (2003) provided a kind of timed extension of fuzzy Petri nets by means of associating temporal fuzzy sets to either transitions or places. Thus, the influence of time factor on performance of Petri net can be recognized. In addition, a type of fuzzy timed Petri net model was introduced and successively investigated by Ding et al. (2005) and Ding et al. (2006). In their studies, each transition is associated with a fuzzy number representing the firing time, and each place is provided with a time dependent mark distribution function. In order to represent dynamic knowledge, a termed adaptive fuzzy Petri net was initially proposed by Li and Lara-Rosano (2000) and further investigated by Chiang, Tai, and Hou (2009), which is identified to have both the features of a fuzzy Petri net and learning ability of a neural network. Nevertheless, to the best of our knowledge, industrial relevance of the fuzzy Petri nets with characteristics of dynamic knowledge representation has scarcely circulated in the literature ever since.

Motivated by effectively describing incipient abnormality evolution in chemical process, a novel temporal version of fuzzy Petri net, designated timed fuzzy Petri Net (tFPN), is presented in this paper. With emphasis on fuzzy knowledge representation, the input and output places of each transition are used to describe the antecedent and consequent propositions of the fuzzy production rules, respectively. Additionally, a timing factor is assigned to each transition and a degree of reliability is associated with each place to capture the dynamic nature of abnormality, which allows the automatic inference of reliability and undergoing time of abnormal events. After that, together with a procedure towards abnormal event monitoring, two efficient algorithms in regard to abnormality prognostication and diagnosis are exploited by employing reachability analysis of tFPN. The benefits of the derived techniques and solutions are illustrated through a case study consisting in a polypropylene reactor.

The paper is organized as follows. In Section 2, some definitions related with tFPN are highlighted, together with schemes of tFPN based knowledge representations. This is followed in Section 3 by dealing with some crucial issues of abnormal event monitoring, including analysis of abnormal event evolution, as well as the diagnostic and prognostic inference algorithms. Section 4 contains a case study that helps exemplify the proposed techniques. Section 5 concludes the paper and discusses areas for future work.

Section snippets

Definitions of timed fuzzy Petri nets

Definition 1

A timed fuzzy Petri net is a tuple:tFPN=(P,T,E,I,O,f,α,β,D,TS,M0),where

  • P = {p1, p2, …, pn} denotes a finite set of places;

  • T = {t1, t2, …, tn} denotes a finite set of transitions, where P  T = Φ;

  • E = {e1, e2, …, en} denotes a finite set of propositions, where ∣P = E∣;

  • I:P × T  {0, 1} is an input function, representing a mapping from input places to transitions;

  • O:T × P  {0, 1} is an output function, representing a mapping from transitions to output places;

  • f:T  [0, 1] is a relationship function with respect to transition t,

Methodologies

The major tasks involved in abnormal event monitoring can be categorized into two aspects:

  • (1)

    Diagnosis: find the underlying causes of abnormal events, including disturbances stemmed from process operations or hard failures in equipments; and

  • (2)

    Prognostication: analyze the evolutions of abnormal events and forecast the possible consequences.

As we know, reachability analysis is a potentially useful tool particularly in Petri net application issues. With respect to tFPN, it may offer an opportunity to

Case studies

A polymerization takes place in a polypropylene reactor as shown in Fig. 5, where the monomer propylene, dissolvent hexane and catalyst are fed as liquid state. Due to the poignant exothermic characteristics of the polymerization, the temperature must be strictly enforced within the range of 70 ± 1 °C. Over high temperature will speed up the reaction that can lead to great release of heat as well as increase reaction temperature sharply. So, it follows that the natural positive-feedback

Conclusions

As a methodological foundation of abnormal event monitoring, we introduced a termed timed fuzzy Petri net along with its representation of temporal fuzzy deductive rule initially. The key idea behind this contribution consists in that a timing factor is assigned to each transition and a degree of reliability is associated with each place, which allows effectively capturing the dynamic nature of abnormality evolution. Together with a procedure towards abnormality monitoring, two algorithms

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