# A Diagnosability-Integrated Design Approach Based on Graph Theory
## 1 Introduction  
With the development of science and technology, the systems involved in people's production and life are developing in the direction of complexity, large-scale and modularization. This change in the system poses a challenge for the fast and accurate detection and isolation of faults in the system and, so, how to improve the fault diagnosis capability of the system, so as to improve the reliability and utilization of the system, has become a hot spot for researchers to study. The concept of diagnosability has been introduced in order to improve the fault diagnosis capability of the system. Diagnosability is a property that indicates the extent to which system faults can be accurately and efficiently identified [1]. The diagnosability concept was originally established to uncover deeper information about fault diagnosis, such as how difficult or costly it is to detect and isolate a fault, from a system perspective. The current research concluded that the diagnosis capability of the system is suitable to be improved by designing fault diagnosis methods only when the fault of the system can be diagnosed. If the system fault itself is difficult to diagnose or even undiagnosable, it is meaningless to improve the performance of the diagnosis algorithm for this kind of fault [1]. Therefore, taking the difficulty of fault diagnosis into the scope of fault diagnosis, that is, considering the diagnosability of the system, can fundamentally improve the diagnosis capability of the system. Research work on diagnosability can be divided into two aspects: diagnosability evaluation [2; 3; 4] and diagnosability design [5; 6]. Diagnosability evaluation refers to the processof measuring the degree to which system faults can be identified deterministically and efficiently, mainly revealing how difficult the fault can be diagnosed. High diagnosability means that the system is more capable of fault diagnosis, while low diagnosability means that the system is less capable of fault diagnosis. Diagnability design refers to a design technique that takes diagnosability as an optimization index in the design stage of system and diagnosis algorithm [1]. It can be seen that the diagnosability design is a key step in improving the system's ability to diagnose faults. Depending on the object of diagnosability design, diagnosability design can be further categorized into the design of system structure and the design of diagnosis methods. 1. Design of the system structure. Researchers in this direction focus on optimizing the design of the system's structure to improve the system's ability to respond to faults and, thus, improve the system's diagnosis capability, while satisfying the premise of system diagnosability. Since the location and number of sensors can affect the effectiveness of fault identification and isolation [7], the current research direction focuses on changing the structure of the system by optimizing the configuration of the sensors in order to improve the diagnosis capability of the system. The optimal configuration of sensors is essentially a multi-objective decision-making (MODM) problem in the multi-criteria decision-making (MCDM) problem [8]. Various objectives such as system cost [9], reliability, number of sensors, redundancy between sensor information [10], system diagnosability [5; 11; 12; 13], and the degree of hazard of missed faults are considered in different sensor configuration schemes to select one of them that is suitable for the system by balancing the conflicts between multiple objectives and reducing information redundancy [14], making the system inherently more capable of acquiring fault information. 2. Design of the diagnosis method of the system. [PERSON] [6] evaluated the false alarm rate, fault detection rate and fault detection time based on a stochastic algorithm, and based on this, proposed a design method for observer-based fault detection system, and [15] proposed an adaptive application strategy that combines system diagnosability analysis with actual fault diagnosis.