(421e) Reliability Based Sensor Network Design for Fault Diagnosis

An appropriately designed sensor network is a prerequisite for safe and optimal operation of any plant. Over the last couple of decades, the problem of sensor network design has received considerable attention in literature. The problem of sensor network design as considered in this work is to choose locations of variables to be measured in a plant as well as the number of sensors to be used to measure a variable. In literature, for the purpose of sensor network design, objectives related to fault detection and diagnosis, state and parameter estimation, and process control have been considered typically in the presence of constraints on the total cost of the sensor network. In the area of fault detection and diagnosis, constrained optimization based approaches which minimize the system unreliability of detection, have been proposed for sensor network design (Bhushan and Rengaswamy, 2002; Bhushan et al., 2008). In this approach the aim was to minimize the probability of a fault occurring and remaining undetected. A fault would remain undetected if it occurred and simultaneously all the sensors affected by that fault fail. This probability was defined as unreliability of detection of that fault. Given several faults in the process, the overall system unreliability was defined to be the maximum unreliability of detection amongst all the faults. The sensor network design problem was posed as a constrained optimization (integer linear programming) problem with minimization of this system unreliability as the objective function and constraint on the total allowed cost of chosen sensors. This definition of system unreliability was based on the philosophy that a ?chain is as strong as its weakest link?. This philosophy has also been used by other researchers in the area of sensor network design, such as the work of Ali and Narasimhan (1993) on reliable estimation of variables. However, while this definition of system unreliability may be acceptable from a design perspective, it does not has any obvious probabilistic interpretation.

In this work we propose an alternate definition of the system unreliability of detection which can be interpreted to be the probability of atleast one fault in the system remaining undetected. The derivation of this system unreliability expression is not straightforward due to the fact that the unreliabilities of detections of various faults are not independent since a given variable in the process is usually affected by several faults. Computation of system unreliability is shown to be the problem of finding the probability of union of a set of events. We use the well known inclusionexclusion principle for deriving this expression. Sensor network design can then be performed to maximize this objective function. The resulting problem turns out to be a nonlinear integer programming problem.

The proposed approach is applied to an illustrative example and the resulting sensor network is compared with that obtained by the earlier (Bhushan and Rengaswamy, 2002) approach. Stochastic simulations, where fault occurrence and sensor failures are simulated, are performed to investigate the performance of the two networks. To demonstrate the applicability of the proposed way of defining system unreliability, the approach is also applied to perform sensor network design for reliable estimation of process variables. The aim in such cases is to choose sensors so that the probability of not being able to estimate any variable (due to sensor failures) is minimized. The results are compared to those available in literature (Ali and Narasimhan, 2003) where sensors were chosen so as to maximize the minimum reliability of estimation amongst all process variables.

References

1) Ali Y. and Narasimhan S. Sensor Network Design for Maximizing Reliability of Linear Processes. AIChE J., 39, 820-828, 1993.

2) Bhushan M. and Rengaswamy R. Comprehensive Design of a Sensor Network 2 for Chemical Plants Based on Various Diagnosability and Reliability Criteria: I. Framework. Ind. Eng. Chem. Res., 41, 1826?1839, 2002.

3) Bhushan M., Narasimhan S. and Rengaswamy R. Robust Sensor Network Design for Fault Diagnosis. Comput. Chem. Engng., 32, 1067?1084, 2008.