# Application of the Residue Method in Steam Superheater Fault Detection
## 2 Methods of Fault Detection  
Manufacturing systems consist of various machine tools, robots, and conveyor systems, all of which need to serve their purpose correctly to ensure efficient, high-quality production. In the literature, failure represents deterioration in operating performance and plant or automation equipment disruptions [14; 15; 16]. In a general sense, a fault changes a system's behavior so that it no longer satisfies the purpose for which it was designed. On the one hand, it can be an internal event in the system that stops the power supply, breaks a link, or creates a leak in a pipe, or it can be a wrong command given by the human operator that takes the system out of the desired operating point, or it can be a system design error that has gone undetected until the system reaches a specific operating point where this error significantly reduces the performance of the system. In either case, the fault is the leading cause of change in system structure or parameters, ultimately leading to reduced system performance or even loss of system function. Fault detection involves determining the occurrence of a malfunction of plant components or automation components (transducers, actuators, controllers) based on the plant's response to standard commands. According to studies, including [14], fault detection can be carried out using:  
* Measurements taken from transducers (usual or special) installed at key points of the installation, based on their information, the protection, signaling, and interlocking systems work in any industrial installation;
* Analytical methods based on dedicated models and structures allow the detection and location of faults not detectable in the first case. These methods are based on current measurements existing in the monitoring and control system of the industrial plant. According to the scientific paper by [PERSON] et al. and cited in the publication [16], it has been determined that multiplicative faults can emerge due to the influence of product terms of process variables on the overall process. This means that these faults arise due to the interdependent nature of multiple variables that simultaneously affect the process. In other words, such faults can be linked to the fact that certain variables can have a more significant impact when combined with other variables, with the overall effect on the process being more than the sum of their individual impacts. Conversely, additive faults occur when the process is influenced by adding process variables, which can also significantly impact the overall process. Faults can be represented as unknown inputs acting on the system (additive faults) or as changes in plant parameters (multiplicative faults). This particular classification of faults as additive or multiplicative is usually carried out according to their nature, or sometimes it can be carried out arbitrarily. As will be seen, additive defects are simple to address; therefore, defects should be defined as additive defects whenever they can be reasonably justified. The different types of faults and disturbances and the relationships between them are centralized and presented in Table 1:Most detection and diagnosis schemes consist of two levels: a symptom generation level and a diagnostic level. The first level indicates the status of the process (presence or absence of the defect). With the fault signature, the second level is used to diagnose faults. The difficulty in constructing fault detection and diagnosis schemes is finding those significant manifestations robust to noise, disturbances, modeling uncertainties, and static operating point change. Modern approaches are based on process models and exploit mathematical relationships between different signals measured in the process. They allow a high-depth diagnosis but require accurate mathematical models of the process.