## 1 Introduction  
The induction motor fed by an inverter is presently a common and practically irreplaceable element in most industrial sectors and in electric traction. The inverter allows operation at variable speeds, a functionality required in many applications, and also allows a considerable reduction in the current demanded during startup. However, the presence of the inverter also has some drawbacks [1]. As far as maintenance work is concerned, its influence is mainly in two aspects: changing the failure mechanisms and making diagnosis more difficult [2]. The change in the electrical starting conditions and during continuous operation of the motor changes in turn the failure mechanisms. Focusing on the problems associated with the rotor, the fact that the starting current is much lower decreases stresses on the rotor cage [3]. Still, other problems arise mainly associated with the higher harmonic content, which increases the level of vibrations and the harmonic torques and temperature in the cage [4, 5, 6]. The fact that inverters allow operation with repetitive cycles also has a negative influence. These stresses will be higher in cases where regenerative braking is used. From a diagnostic point of view, as already reflected in the literature, inverters make it more difficult to identify characteristic fault frequencies due to a higher noise level and interharmonics and subharmonics around the first component [7; 8]. The commutation mechanism of the converter produces harmonics that can be confused with the one characteristic of motor failure and, in addition, usually generates a signal with a higher noise level. In addition, the harmonic content will vary significantly from one inverter to another, or even within the same inverter, depending on the type of control applied and the switching frequency chosen [9]. Detection of faults in inverter-fed induction motors operating at fixed speed has already been studied in [6; 10; 11; 12; 13]. However, inverter-fed motors may operate in non-stationary regimes due to the particularities of the industrial application. If this is the case, it is not possible to employ the Fourier transform of the stator current for fault detection, and the use of time-frequency transforms is essential. Furthermore, motor operation tends to be under low slip condition, which in cases such as broken bars, where the characteristic harmonics of failure in operation at high load are very close to the fundamental harmonic, makes it difficult to identify these characteristic failure frequencies [14; 15]. These characteristics of the operation of the induction motor with an inverter increase the possibility of false positives. These diagnostic errors can have significant economic consequences in addition to gradually leading to a lack of confidence in the diagnostic tasks. This paper proposes a two-step methodology to overcome the difficulties in the diagnosis inherent to inverter-fed motors, providing a reliable method to diagnose the condition of the motor. The first step is to apply the Dragon Transform, which has been recently developed by the authors [16]. This transform provides the adequate time and frequency resolution to be able to follow the fault-related harmonics, which, in the case of broken bars, evolve very close to the main harmonic. This feature is obtained by the definition of atoms whose shape adapt to the trajectory of the fault harmonics [16]. It should be noted that just as in the stationary state there are preset fault frequencies that depend exclusively on the operating speed, in the case of diagnosis in transient state during the start of the motor, the path of the fault harmonics is also previously known. Therefore, if an adapted mathematical tool is available to separate the trajectory of the fault harmonics from that of the main harmonic, it will be possible to carry out this monitoring in a suitable way, as has already been demonstrated in [17].