# A Diagnosability-Integrated Design Approach Based on Graph Theory
## 1 Introduction
For different degrees of diagnosability, different diagnosis methods are used to detect and isolate faults, so as to achieve a balance between time efficiency and diagnosis accuracy; [16; 17] defined K-gap and used it to give performance indexes of fault detection and isolation for use in the analysis of fault diagnosis capability. Literature [18] proposes a strategy for verifying the diagnosability of discrete-time systems using conjunctive regular expressions, and illustrates the construction of diagnoser and the verification of diagnosability in a real-world case. The diagnosability design of the diagnosis method is mainly to take the diagnosability of the system into account, combined with the fault pattern recognition method [19; 20], relying on the model or signal of the system, so that the fault of the system can be exposed as much as possible, in order to achieve the purpose of improving the diagnosability of the system. From the above analysis, it can be seen that the diagnosability design method starts from the system structure design and diagnosis method design to improve the fault diagnosis capability of the system, in which the system structure design is mainly for the design of the system's sensors, which mainly solves the problem of extracting information from the system; after all, only by extracting high-quality information from the system can reflect the change of the system fault and the system fault be quickly diagnosed. The diagnosis method design mainly solves the problem of how to utilize the information, by transforming the sensor information, extracting the features and other operations, the fault information can be exposed and the diagnosis of the fault can be realized. Thus, both aspects can have an impact on the diagnosability of a system, but the two factors are currently considered separately when designing for diagnosability. The current process for diagnosability design is shown in Figure 1a. In this process, the design of system structure and diagnosis method are two successive steps, which do not affect each other. Diagnosis method and system structure are separated. However, it is clear from the above analysis that the design of the system structure determines what diagnosis algorithm is used, and the choice of diagnosis algorithm affects the design of the system structure. If both factors are taken into account in the diagnosability design, the degree of fit between the fault diagnosis method and the system structure can be greatly improved, and, thus, the diagnosis capability of the system can be enhanced. Based on the above ideas, an integrated design process was utilized in this paper when performing diagnosability design to improve system fault diagnosis, and the flow of this design method is shown in Figure 1b, in which the mutual influence between the diagnosis method and the system structure was considered, and the degree of fit between the two factors was improved by considering the specificity of each measurement point for fault diagnosis. Thus, the fault diagnosis performance of system is greatly improved [21]. Relying on this process, a diagnosability integration design method based on graph theory was proposed in this paper. In the current literature, it is rare to see an approach that enhances the diagnostic capability of a system by considering both system architecture design and diagnostic algorithms at the same time. The method was divided into three main steps: 1. Measurement point determination. The diagnosis plot of measurement point was drawn based on the diagnosability evaluation results, the maximal clique in the plot was extracted, and the maximal clique set was obtained according to the edge covering theorem, so that the set could cover the fault mode of the system. 2. Diagnosis method determination. The method of setting a cascade classifier on a maximal clique set was studied, and the  
Figure 1: Comparison of two diagnosability design processes. (**a**) General flow of diagnosability design; (**b**) the flow of integrated diagnosability design.