An optimally located network of sensors is a prerequisite for successful application of fault diagnosis techniques. Most of the previous work in the area of fault diagnosis deals with methodologies for identifying possible faults, given sensor data. Available literature suggests that very little work has been done on methods for optimally locating the sensors for efficient fault diagnosis. Some algorithms based on the concepts of observability and resolution were discussed in our previous work (ref 1: Raghuraj et al. AIChE J. 1999, 45 (2), 310). These algorithms are based on a digraph (DG) representation of the process. In this article, the sensor location work is extended to use the signed directed graph (SDG) representation of the process. Various issues involved in utilizing the SDG of the process for the problem of sensor location are discussed. Algorithms for sensor network design based on the SDG of the process are detailed and applied to two chemical engineering case studies. It is shown that better design can be obtained by using the SDG instead of the DG.

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.

The objectives of this part of the two part paper are (i) development of signed digraph (SDG) models for control loops and (ii) discussion of a framework for application of graph-based approaches at a flowsheet level. Further, two case studies are used to explain the methods developed in part 1 1 (Ind. Eng. Chem. Res. 2003, 42, in press) and this paper. The first case study (continuous stirred tank reactor case study) explains the basic concepts of the generate and test method for SDG analysis, generation of redundant equations using algebraic manipulation, and analysis of systems with a single control loop. Case study 2 (flash vaporizer case study) deals with different methods of generating redundant equations and the analysis of systems with multiple interacting control loops.