# The Cluster Computation-Based Hybrid FEM-Analytical Model of Induction Motor for Fault Diagnostics
## 1 Introduction  
Electrical machines, particularly induction motors, are indispensable in almost all sectors of our modern-day society. In the form of conveyor belt movers, compressors, electric vehicles, fans, and pumps, etc., they consume more than 50% of the total generated energy worldwide [1]. This fact makes their predictive maintenance very important, to avoid any catastrophic situation. As the world is moving towards industry 4.0, predictive maintenance is becoming more important--as contrasted to preventive or reactive maintenance. Unlike preventive or reactive maintenance, in predictive maintenance we monitor the behavior of an electrical machine and anticipate failures before they occur. Predictive maintenance allows the servicing of the machine when it needs. By doing so, the system's downtime can exponentially decrease with a resultant decrease in the maintenance cost. A variety of conventional condition-monitoring techniques have been discussed in literature over the past few decades, such as motor current signature analysis (MCSA) [2; 3; 4; 5], thermal analysis [6; 7; 8], vibration [9], acoustics [10; 11], stray flux monitoring [12; 13], partial discharges [14], air-gap flux monitoring [15], etc. Although these techniques are well-established, compatible with a variety of signal-processing techniques, and require fewer computational resources, they possess several drawbacks. The mostprominent drawbacks are relevant to expensive sensors--such as in the case of thermal analysis and the poor legibility of fault-based frequency components at the incipient stage, as in motor current signature analysis (MCSA)-based techniques. Moreover, these techniques depend upon various constraints such as machine structure, the industrial environment, external noise, bad load-coupling, poor foundation, and the impact of the drive controller, etc. The segregation of frequency components when there is more than one fault is another challenging task in MCSA-based diagnostic techniques. It becomes worse when the industrial inverters inject several frequency components as well. The industrial inverters with complex control algorithms are becoming a crucial part of a drive system. In this case, the definition of faults goes beyond the domain of simple machine equations. The use of conventional diagnostic techniques, while neglecting all subsystems of the drive, can increase the false or missed alarm rate. To avoid all those problems and to make diagnostic algorithms more reliable, advanced model-dependent and artificial intelligence (AI) based techniques can give promising results. The majority of rotating machine faults are degenerative, which makes fault diagnosis a pattern recognition problem. Due to a variety of global signals and different faults, pattern recognition is not a straightforward problem. Therefore, a reliable diagnostic algorithm can be a combination of data processing for feature extraction and recognition through AI techniques. Various AI techniques such as probability-based, classification, statistical learning, mathematical optimization, and convex optimization can be found in the literature [16]. The statistical and classification-based methods are gaining increasing popularity in uses such as support vector machines (SVM) [17; 18; 19], artificial neural networks (ANN) [20; 21; 22], Bayesian classifiers, Naive Bayes classifiers [23; 24; 25], machine learning [26; 27], k-nearest neighbor algorithm [28; 29; 30], etc. Almost all AI-based diagnostic techniques need a large number of data samples under various conditions. Those conditions may include signals under healthy, faulty, loaded, and no-load conditions. Moreover, various kinds of faults with different severity levels under a variety of loading conditions can better train advanced AI-based techniques. The collection of large amounts of data with different constraints is practically impossible both from industry and laboratory environments.