## 1 Introduction  
The urban rail transit system is a reliable and environmentally friendly way of transport; it generates low pollution, has high passenger capacity and is not prone to delays. The traction converter (TC) in the EMU provides motive and electric braking power through traction motors. TC's switching IGBTs are high-power devices that are prone to failure compared to other components [1]. Switching device fault accounts for more than 10% of the total TC failures. In most cases, fatigue causes the failure of the switching device [2]. If the fatigue state of the switching device can be predicted and manually maintained or replaced in the device [3], the train failure caused by the failure of the switching device can be reduced. The switching device in the TC is usually a package module composed of an IGBT and an FWD. The fatigue of the switching device is mainly manifested by package failure, including two main forms: Wire liftoffs and solder layer cracking [4; 5]. Wire liftoffs and solder layer cracking are caused by shear thermal stresses that are produced by temperature drift inside the device. In the intermittent operation of the device when it is turned on, heat is generated by current; when it is turned off, i.e., the current is cut off, the heat is dissipated. In such a way, the device is heated and cooled periodically. The internal temperature of the device (not only the IGBT junction temperature \(T_{\rm j}\), however also the temperature of each single layer) would increase and decrease accordingly. One switching device consists of multiple layers (as shown in Figure 1) with different coefficients of thermal expansion (CTE) of each layer. The relationship between thermal stress and the change of CTE is shown in Equation (1). \[S=f(\Delta CTE,\Delta T) \tag{1}\]  
\(S\) is the thermal stress, \(\Delta CTE\) is the difference of \(CTE\) and \(\Delta T\) is junction temperature variation. Equation (1) shows that the thermal stress is caused by the difference of \(CTE\) and \(\Delta T\). Such temperature change is caused by internal thermal resistance (such as \(R_{\text{th-c\_1}}\) and \(R_{\text{th-c\_2}}\) in Figure 1) and heat flow, as is shown in Equation (2)  
\[\Delta T=P\bullet Rth \tag{2}\]  
In Equation (2), \(P\) is the heating power. \(R_{\text{th}}\) is the thermal resistance. Temperature changes causes shear thermal stress, while shear thermal stress causes liftoffs and cracks [6]. Due to the encapsulation, internal liftoffs and cracks cannot be observed directly; several sensitive parameters have been considered to represent the fatigue characteristics instead, such as the IGBT saturation voltage drop (\(U_{\text{CES}}\)) [7], SOA [8], thermal resistance between IGBT junction and device substrate (\(R_{\text{th}}\)[9], threshold voltage of the IGBT gate [10], etc. These methods are based on the one-to-one relationship between fatigue signatures and fatigue levels. However, these parameters are difficult to obtain reliably in the situation of high power and high EMI (Electromagnetic Interference), such as converters. In other cases, liftoffs and cracks can be estimated by experimental data where a certain number of thermal cycles and Temperature drift (obtained from the mission profile) are applied to the IGBT under test; we call it AFT (accelerated fatigue test). Then, the model is built based on fatigue observations from the AFT. The model that is established by the AFT is the fitting relationship between the fixed working conditions and the fatigue life of switching devices. An AFT tests a DUT with a predetermined time-effect force and obtains data showing the fatigue characteristics of it. However, the existing fatigue model requires stable and fixed operating conditions because these models were established under the AFT results of fixed experimental conditions [4; 11; 12]. Therefore, the existing model cannot be fully applied to the changing conditions of the actual operating conditions, and this is the actual application of the TC.