# From Modeling to Failure Prognosis of Permanent Magnet Synchronous Machine
## 1 Introduction  
Nowadays, conventional automobile transportation is in a crisis due to the high price of gasoline. It is expected that this crisis will worsen gravely due to a diminishing oil supply. Moreover, climate change has turned out to be a very powerful motivator for research to head toward energy efficiency and emission reduction goals. According to the yearly consumption of oil and gas, studies state that oil will run out in 2052 and gas will run out in 2060 [1]. On the other hand, the Intergovernmental Panel on Climate Change (IPCC) assesses that CO\({}_{2}\) emissions should be reduced by up to 85% by 2050 in order to limit the global temperature rise [2]. Accordingly, the only envisaged solution is to switch to green transportation technology. Electric vehicles (EV) and hybrid electric vehicles (HEV) are a good alternative for conventional vehicles. However, HEVs have earned higher popularity over EVs due to EVs' problems linked to their battery capacity, reliability and lifecycle. This is why the idea of combining conventional technology with environmentally friendly technology is more salable. It is assessed that the production and use of HEVs will increase in the coming years and divert the situation [3; 4; 5]. To increase the integration of HEVs in the domestic market, research should be upgraded to assure reliability, availability, health and proper operation of HEVs. Much research has focused on the diagnosis of the different elements in the HEV; the evolution in the field drives us to prognosis, to predict the fault before it occurs. In this article, prognosiswill be applied to ensure the proper health and operation of HEVs' electrical machine. The type of the selected electrical machine is the permanent magnet machine due to its high power density and efficiency, robust construction and low weight [6; 7; 8]. The types of faults that will be encountered are demagnetization, turn-to-turn short circuit and eccentricity [9]. Executing prognostic analysis and studies for electric machines in HEVs are very important and justified, knowing their high cost with respect to the cost of the whole system. Prognosis will help in predicting the coming fault before the relative component fails. It will also help in regulating the maintenance schedule and in predicting the remaining useful life of the machine. In all cases, prognostic studies are very beneficial in saving money [10]. The author in [11] states that, in HEV application, a forward-looking diagnosis and prognosis technologies are required to promptly sense and isolate faults in network-embedded automotive systems so that proactive corrective maintenance actions can be taken to evade failures and increase the availability of the vehicle. After a survey on the available prognostic techniques that may be applied to assure an optimal and convenient operation of electrical machines in hybrid electric vehicles, it has been agreed that a hidden Markov model (HMM) be adopted [12; 13]. A hidden Markov model is a data-driven prognostic approach since it attempts to derive models directly from collected condition monitoring (CM) data; they get predictive output directly in terms of CM data. It's a stochastic signal model [14]. An experimental prototype containing the permanent magnet machine where faults are easily integrated and measured data are progressively collected is not available. Hence, the need for an accurate machine model arises. The selected machine is a surface permanent magnet machine (SPMM) used in hybrid electric vehicles [15; 16]. Its specifications and parameters are illustrated in Table 1, and its laminated sheet is illustrated in Figure 1.