This research result consists of two parts: one is general theory on causality assignment for hybrid bond graph (HBG) and another is application of this concept to the quantitative fault diagnosis. From Low et al., 2008, a foundation for quantitative bond graph-based fault detection and isolation (FDI) design using HBG is laid. Useful causality properties pertaining to the HBG from FDI perspectives, and the concept of diagnostic hybrid bond graph (DHBG) which is advantageous for efficient and effective FDI applications are proposed. This paper is a continuation of our previous paper (Low et al., 2008). Here, the DHBG is exploited to analyze the hybrid system's fault detectability and fault isolability. Additionally, a quantitative FDI framework for effective fault diagnosis for hybrid systems is proposed. Simulation and experimental results are presented to validate some key concepts of the quantitative hybrid bond graph-based FDI framework. Note to Practitioners-Many complex industrial systems combine subsystems of different dynamical nature. Some of the system's components exhibit continuous behavior (e. g., electric motors, gears, pistons), while others compel sudden configuration changes (e. g., clutches, switches, on/off valves). Such systems are referred to as hybrid dynamical systems (or hybrid systems, for short). Industrial system's failures may cause to heavy losses and damages, this can be significantly decreased using online system's health monitoring. There are many methods for system's health monitoring and here we focus on the model-based quantitative techniques. The model describes the system's healthy condition and the method measures the distinction between the system and the model. In this work, we utilize the HBG modeling approach. Using the HBG for system's health monitoring requires derivation of analytical redundancy relations (ARRs) which described constraint relations between known system's variables. Fortunately, by the bond graph modeling approach these constraints relations can be derived algorithmically, however when the system is hybrid a separate derivation process was required for every system's operating mode. To overcome this, we introduced (Low et al., 2008) the DHBG, and explained how to develop a DHBG from a given HBG. In this work, we explain who to use the DHBG for health monitoring of hybrid systems. The method is based on a set of global analytical redundancy relations (GARRs), which describe the system behavior at all of its operating modes. Based on these new tools we propose a complete quantitative health monitoring framework for hybrid systems. In addition, a method to assess offline the performances of the monitoring system is proposed based on new monitoring ability definitions for hybrid systems. Using these definitions, a designer can find the weaknesses of his design and modify the monitoring system to suit his needs.
