Optimal sensor placement for model-based fault detectability and isolability - Chi, Guoyi (2014)
This dissertation investigates the sensor placement issue in a dynamic system for fault detectability and isolability. A degree of detectability (respectively, isolability) which accounts for faults in a dynamic system under consideration, is defined and then optimized over the admissible set of candidate sensors. In this study, emphasis will be placed upon how to achieve fault detectability and isolability in a first principle model using the least number of candidate sensors. The definitions for model-based fault detectability and isolability have two types, and they are made according to whether or not have reference to residual generators. One is termed performance-based fault detectability and isolability which is expressed in terms of the signature of the faults on the residuals. Alternatively, the other is named intrinsic fault detectability and isolability that is known as a structural property of the investigated system. The latter type (of fault detectability and isolability) captures the signature of the faults on the system other than the residuals. This dissertation studies the optimization problem of sensor placement with respect to both types: performance-based and intrinsic. One research work presented in this dissertation is to propose a novel and highly efficient approach of sensor placement for performance-based fault detectability and fault isolability. In the parity space, all possible residuals, called analytical redundancy relations (ARRs), are generated by some sophisticated methods. This new approach rests on the basic facts that faults and candidate sensors are embedded in ARRs. Therefore, fault detectability is expressed in terms of a set of ARRs which response to a specified fault; meanwhile fault isolability is to find out a unique set of ARRs regarding to a specified fault. From this discovery, the sensor placement problem constraint (fault detectability and isolability) can be expressed as a minimal isolating (MI) set where each fault under consideration is isolable. Immediately, the senor placement problem is formulated as an optimization problem with respect to MI sets. For high-efficiency, a low complexity dynamic programming (LCDP) is developed and it serves to seek the optimal MI set for system faults (which is related to the least number of candidate sensors). Besides isolability of system faults, sensor faults are taken into consideration. Note that sensor faults are always varied as different sensor configurations are assigned to system faults. Then, a dedicated procedure is designed to solve this issue. This approach can solve the sensor placement issue for isolability of system faults and sensor faults in a linear or nonlinear model. However, the approach involves the risk that a lot of ARRs need to be constructed and most of them are impossibly utilized in the design of a fault diagnosis system. To completely avoid generating residuals, sensor placement for intrinsic fault detectability and isolability is exploited. Until now, most of the publications discuss intrinsic fault detectability and isolability in a linear dynamic system. In this dissertation, the bond graph modelling technique is used to model a linear dynamic system. Different from the state space representation, graphical connections between faults and junctions are built by causal paths on a bond graph. Causal paths provide a powerful tool to analyze which junction can be used for fault detectability and isolability. So the sensor placement issue is restricted by junctions. Incorporating the restriction of junctions into fault detectability and isolability is investigated and thus relevant conditions of fault detectability and isolability are provided. Using fault detectability and isolability conditions, a sensor placement algorithm is developed to determine an optimal set of junctions that should be equipped with sensors. In this sensor placement algorithm, the basic building block is realized by solving a set of differential-algebraic equations (DAEs) which results from constitutive relations of a bond graph. For instance, if Q faults are considered for isolability, this basic building block need to be invoked (Q^2+Q)/2 times. Consequently, the sensor placement algorithm is computationally intensive. To design a more efficient algorithm for sensor placement, the structural characteristics of a bond graph are further investigated. With the aid of causal paths, this study provides a simpler condition for intrinsic fault detectability which is a necessary and sufficient condition. Based on this simpler condition for fault detectability, this study derives another simpler condition for distinguishability of two faults. However, this fault distinguishability condition is a necessary condition so as not to directly determine where should place sensors. Therefore, this fault distinguishability condition serves as the basis of the optimization formulation for isolability on a fault set. For high-efficiency, a dynamic programming algorithm is developed to attain the optimal solution from a pre-enumerated set of junctions.