# The Cluster Computation-Based Hybrid FEM-Analytical Model of Induction Motor for Fault Diagnostics
## 1 Introduction
Because, first, in industries there are few faulty machines and, secondly, the type and level of faults in industry machines are unknown at first--which is necessary information for training the diagnostic algorithms. In the laboratory, conducting a large number of destructive tests is not economically feasible. The only optimal way is to rely on the accurate mathematical models of the machine. Using mathematical models, almost any kind of fault in any type of machine with different natures of load can be simulated to train the diagnostic algorithm. A variety of machine modeling techniques are available in the literature, which can be broadly classified into two categories; analytical and numerical. The two-axis theory-based models [31; 32; 33] are being effectively utilized for control and analysis. Although those models are simple to understand, comprehensive, and fast, they are not suitable for fault simulations because of various approximations such as sinusoidal stator and rotor windings distribution, uniform air gap, no inter-bar currents, and no material saturation, etc. The multiple coupled circuit theory-based models such as winding function analysis (WFA) [34; 35], modified winding function analysis (MWFA) [36; 37], and extended MWFA [37] allow the inclusion of practical stator and rotor winding functions, the stator and rotor slots openings, and non-linear functions for material saturation. Those models can be used to simulate the majority of faults with very much less simulation time and computational complexity, but they do not remain straightforward while dealing with different types of machines with complex geometrical features. Similarly, other analytical models such as magnetic equivalent circuit [38], generalized harmonic analysis [39], voltage behind reactance [40], and convolution theorem [41] can be used for the simulation of various faults in induction machines but at the cost of material and geometry-related approximations. Having the ability to deal with almost all kind of geometries and material properties, and the compatibility to solve various kinds of problems, the finite element method (FEM)-based modeling techniques are gaining heightened popularity. Using FEM, a vast variety of electromagnetic [42; 43],thermal [44], fluid dynamics [45], structural [46], and related problems can be solved with incredible accuracy. In FEM, the geometry of the system is divided into a considerable number of mesh elements represented by nodes and the solution of each node leads toward the final solution. Indeed, it requires significantly powerful computational resources and a large memory to save intermediate results. Although modern computers with advanced processors are very strong, they need a long time, from several minutes to days, for the solution of highly unsymmetrical machines. The saving of simulation time for fault diagnostics is very important for the collection of vast amounts of data, which can be used as a benchmark for advanced fault diagnostic techniques. Many methods to diminish these problems have been presented in the literature such as; the hybrid analytical-FEM model [47; 48], the model order reduction [49; 50; 51], and sparse subspace learning (SSL) [52], etc. These methods have their own limitations as they rely on statistical and interpolation techniques, which are different for different kinds of machines. Problems such as the reducibility of the model and the precision of the input grid can lead to the increased complexity of the model. As the world is moving towards industry 4.0 standards and cloud computation, the computational resources are becoming unlimited. These resources can be in the form of software applications, processing power, and data storage. All these resources are very important for big data-based advanced diagnostic techniques such as machine learning [53], deep learning [54], parallel autonomous mining [55], image processing [56], online wireless monitoring through smart sensors [57], and neural networks [58; 59; 60], etc.