(204f) Optimal Sensor Placement for Fault Diagnosis By Using Magnitude Ratio and Fault Propagation Time

Early detection of faults in process plants can help in improving plant safety, achieving higher efficiency and attaining longer equipment life.  One or more process variables may get affected due to occurrence of a fault in process plants.  However, measurement of every variable is neither economically and practically feasible nor necessary. An optimal set of sensors can be selected to diagnose the faults. However, placing an optimal number of sensors for detection and identification of faults becomes challenging for large and complicated processes.

Most of the sensor placement (SP) problems for large processes have been solved in the existing literature by using qualitative models of the plant because of easy conversion of the cause-effect (CE) relations into graphical and mathematical representations. Among various qualitative model-based SP approaches, the directed graph (DG) and signed directed graph (SDG) based approaches are widely used.  In the DG and SDG based approaches, variables are chosen for fault observabilty and resolution from the sets of variables that respond due to the faults. However, for fault resolution, variables are selected from the sets of responding variables for a pair of faults. In the DG based approach, when two or more different faults yield same set of responding variables, those faults cannot be distinguished from each other. Even the SDG based approach cannot distinguish these faults if the responding variables deviate in the same direction in each set.

To improve the effectiveness of the sensor network in resolving faults and to obtain a measurement network with fewer sensors, a SP algorithm is developed by including the magnitude of deviation of the responding variables and the propagation time of faults through the process variables. Even though two different faults may yield the same set of responding variables with the same directionality for each variable, the magnitude of deviation can be very different for each fault. The pair-wise ratio of the magnitude of deviation of the responding variables is found to be successful in distinguishing between faults that could not be resolved with the DG or SDG based approaches. In addition different process variables can respond to the same fault at different times. For a particular fault, one variable may respond earlier than another variable. Selection of this pair of variables for the sensor network helps to identify that particular fault.

In this work, a sensor placement algorithm has been developed by using magnitude ratios and fault propagation times for fault resolution. A set cover problem is formulated subject to fault observability and resolution. The proposed algorithm is employed to find optimal sensor network for a simple CSTR as well as the Tennessee Eastman process.