A Systematic Framework for the Development and Analysis of Signed Digraphs for Chemical Processes. 1. Algorithms and Analysis

Abstract

In the recent past, graph-based approaches have been proposed by various researchers for safety analysis and fault diagnosis of chemical process systems. Though these approaches have shown promise, there are a number of important issues that have not been adequately addressed in the literature. The issue of systematic development of graph representations for chemical processes has not been addressed in the literature. This is an important issue because the development of digraphs is error-prone and time-consuming. Further, little attention has been paid toward understanding the conceptual relationship between the underlying mathematical description and the analysis procedures for the graph model. Also, the utility of these graphbased approaches at a flowsheet level has not been studied. With these issues in perspective, in this first part of the two-part paper, we focus on the systematic development of graph models and the conceptual relationship between the analysis of graph models and the underlying mathematical description of the process. The elimination of spurious solutions through the use of noncausal redundant equations and thorough analysis of inverse and compensatory response is also discussed.

Model Based Diagnostic Module for a FCC Pilot Plant

“…other authors (see for instance Maurya et al, 2003, for a recent work) for fault detection. The arcs contain knowledge about the signs of the influences, from which propagation of faults is deduced (too high or too low variables' values).…”

Root cause analysis in multivariate statistical process monitoring: Integrating reconstruction-based multivariate contribution analysis with fuzzy-signed directed graphs

“…An SDG model could be constructed by using quantitative knowledge, e.g. mathematical models (Maurya, Rengaswamy & Venkatasubramanian, 2003), or qualitative process knowledge or experiences (Vedam & Venkatasubramanian, 1999;Lee, Han & Yoon, 2004). In the present work, the SDG is constructed through qualitative analysis of the process flow sheet, since the accurate quantitative equations are not available.…”

Signed directed graph based modeling and its validation from process knowledge and process data

“…Although the modeling of SDGs can be based on mathematical equations (Maurya et al, 2003a;2003b;, it can also be undertaken practically from process knowledge that is readily available from Piping and Instrumentation Diagrams (P&IDs). Although simple, SDGs are able to capture fairly precise process connectivity information from the direct relationship between variables, as based on causality.…”

“…The following three types of relationships between these variables can be described as DAEs: DEs, which reflect dynamic causal relationships (Type I), AEs with causal meaning, which include driving force equations, functional relationships, and other algebraic equalities (Type II), and AEs with no causal relationships (Type III) (Yang et al, 2010b). For the first two types, Maurya et al (2003a) summarized the modeling methods. The third type can be used as redundant constraints to remove irrelevant solutions (Oyeleye and Kramer, 1988).…”