Sensor location problem for large-scale complex systems in the framework of the dynamic Signed Directed Graph

Fault detection in large-scale systems is conducted by the use of sensors, thus the sensor location influences the performances of fault detection directly. As the scale of systems increases, traditional input-output models may not work well or may even not be applicable. The signed directed graph (SDG) concept is used to describe large-scale complex systems and the cause-effect relationships among variables. However, SDG cannot express the dynamic propagation properties when describing the fault propagation phenomena. In this paper, time parameters are taken into account within the branches of an SDG, in order to approximately denote the propagation time of the variable changes in the systems. An SDG constructed this way is called a dynamic SDG. As to sensor location, because of the economic and technical limitations, the number of sensors should be limited while meeting the demands of fault detection. We analyzed the main criteria of the fundamental demand such as reachability, detectability and identifiability of faults in the framework of dynamic SDG, and presented an algorithm to describe the fault propagation process using forward inference and obtained a way to locate sensors. These indices guarantee that the faults can be detected in time and identified from each other. The criteria change when the faults propagate; they are much closer to the reality than those in the framework of a traditional SDG. Some general results, which extend the results obtained in the framework of a traditional SDG, were presented. An algorithm was presented to describe the fault propagation process using forward inference and a way to locate the sensors was obtained. Finally, an example of a boiler system was used out to illustrate the proposed method and results.