Diagnostic and Bicausal Bond Graphs for FDI

Abstract

The analytical redundancy relation (ARR) derivation method presented in Chapter 5 follows the causality inversion of detectors (putting them as sources) to derive a closed form ARR expression. In this chapter, we show that closed form expressions for ARRs cannot be derived for all kinds of processes with all kinds of instrumentation because it may not be possible in certain cases to eliminate unknown variables from the model through symbolic algebra. We develop a few substitutions in this chapter which results in a new model structure to directly evaluate the residuals. The modified method leads to the same set of residuals which can be obtained through classical means, if the equations are symbolically resolvable. It also generates only the structurally independent residuals, and thus, reduces the computation time. Furthermore, the developed method leads to a numerical residual generation scheme which can be applied to all situations, irrespective of whether the set of equations can be symbolically resolved, or not.