## 2 Diagnostics and Prediction of Faults in Pumps  
Prognostics and health management (PHM) is a significant field of study since it forms the basis for advanced prediction technologies [34]. It aids not only by determining how well the apparatus functions but also by predicting when a failure will occur and minimizing the effects of these unforeseen failures [34]. Forecasting is a significant focus of PHM applications, which also aids in determining the system's remaining useful life (RUL). Additionally, it supports creating a current maintenance strategy [34]. The conceptual difference between a diagnosis and a prognosis is significant in terms of time. Diagnosis is identifying the nature and cause of a specific phenomenon. This method is used to identify the underlying cause of a system failure after it has occurred [34]. Prognosis, on the other hand, is derived from a Greek word that denotes foreknowledge and fore-sensing [34]. It aids in the prediction of faults before they can occur. The primary goal of the prognosis is to forecast the event before it may happen; hence, time is a crucial aspect in this scenario, rather than diagnosis. Meanwhile, Figure 3 represents an overview of condition-based maintenance (CBM), relating to diagnostic and prognostic maintenance, as in the work of [PERSON] et al. [35]. CBM is achieved in three primary processes, as illustrated in Figure 4, including data collecting with sensors, signal processing employing various data approaches, and feature extraction via the collection of characteristics that will assist in determining the present condition of the observed equipment. As demonstrated in Figure 3, the system's information from current and past status, obtained from the data, can be used to detect or predict faults in pumps. Corrective maintenance is performed once a defect is diagnosed, to address the failures. If, on the other hand, a failure is predicted, preventative maintenance is performed before the fault occurs. Additionally, faults in pumps may be operationally created, system faults, mechanically caused, or any combination of these. Mechanical pump problems are brought on by malfunctioning components, such as bent rotors, misalignments, and bearing issues. System flaws, on the other hand, involve improper installation and leaking. However,operationally generated faults--primarily obstruction, cavitation, and flow-related issues--occur while the pump is functioning [36]. According to [PERSON] [1], due to the pressure below the vapor pressure suction, cavitation is reported to be the typical fault that most frequently develops in pumps, as described in several studies [1, 36, 37, 38, 39, 40, 41, 42, 43]. Apart from cavitation, another recurring problem in pumps is damage to the casing and impeller, which can be caused due to the pulsation of pressure that is associated with internal recirculation. A further problem is the blockage of the suction and discharge pipe caused by solid elements and impurities in the liquid being pumped. Regardless of the pump's condition, these faults can progress at any phase of its operation. A study by [PERSON] [44] shows a breakdown of the causes of failure in pumps, with a description of the repair cost for each failure, as demonstrated in Figure 4.  
Traditionally, fault diagnoses have been achieved by physically evaluating the health of equipment. This adds to the labor intensity while also affecting the accuracy of the diagnosis. At the most fundamental level, fault diagnosis methods may be categorized as either model-based or data-driven. Model-based fault diagnosis methods utilize a mathematical model  
Figure 4: Failure causes and repair cost-distribution analysis. Figure 3: An overview of condition-based maintenance. of the observed system. Using such a model, estimations of system/process outputs can be developed, which are then contrasted against actual process outputs to provide a residual signal or innovation.