Generation of mode-dependent ARRs from a bond graph of a mode switching LTI model

In model-based fault detection and isolation (FDI), Analytical Redundancy Relations (ARRs) play a key role. Residuals as the result of their numerical evaluation serve as fault indicators. This paper proposes a novel approach to the generation of ARRs from a diagnostic bond graph (DBG) of a mode switching linear time invariant (LTI) model with ideal switches that hold for all modes of operation. Devices or phenomena with fast state transitions such as electronic diodes and transistors, clutches, or hard mechanical stops are modelled by ideal switches giving rise to variable causalities. Nevertheless, fixed causalities are assigned only once such that a DBG with storage elements in derivative causality and sensors in inverted causality is obtained. That is, the BG reflects the configuration for a specific system mode. From such a DBG with fixed causalities, a unique system of ARRs is derived from the DBG that holds for all system modes. The ARRs are implicitly given. In order to evaluate them, first, a set of algebraic or Differential Algebraic Equations (DAEs) must be solved. A formal matrix based approach that starts from the partitioning of a BG into fields is used for the general case. For illustration, two small system examples are considered. Their equations and the ARRs are directly derived from the DBG by following causal paths.