## 3 Methodology and Experimental Setup  
### Proposed Methodology  
The proposed methodology to diagnose different levels of severity of short-circuit faults in a transformer under transient and steady state regimes of operation through the analysis of vibration signals is shown in Figure 3. In general, this proposal is based on the adroit integration of several methods that effectively addresses the needs of this application, e.g., noise rejection, removal of harmonic oscillation components during transformer energization, appropriate selection and use of fault indicators to characterize the fault severity, and low-complex but efficient pattern recognition algorithms for automatic classification. In this regard, the proposed methodology consists of the following stages:  
Stage 1--Noise reduction in the vibration signals. According to Section 2.2, a wavelet denoising stage is developed, removing frequencies with amplitude fluctuation that are not related to the fault condition and, consequently, highlighting the frequency components which can provide useful information for the diagnosis. After extensive experimentation, it was determined that a Daubechies 45 (db45) mother wavelet, a decomposition level of 7, the threshold estimator, sqtwolog, and soft thresholding provide satisfactory results in the denoising task.  
Stage 2--Removal of stationary frequency components from a transient signal. Once the noise has been removed, the clean vibration signals are analyzed in both transient and steady states. It is important to remark that this work presents a methodology to diagnose SCTs faults in both regimes, allowing the condition monitoring and fault detection in a wider range of transformer applications. For the transient signals, the comb filter presented in Section 2.5 is first applied in order to remove the stationary frequency components, i.e., integer multiples of 60 Hz. This process allows the analysis of the transient regimen without affecting the harmonic changes and their duration.  
Stage 3--Time-frequency and frequency-domain analysis. For the transient signal, its time-frequency representation is obtained through the STFT. In this case, with the elimination of stationary frequency components in stage 2, the frequency components related to the energization transient of the transformer are only retained. On the other hand,  
Figure 3: Proposed methodology.  
in the case of the steady-state signals, the frequency components of the vibration signals are obtained using the FT. This regimen is considered stationary since the parameters of the harmonic components remain constant. In this stage, the mathematical formulation of Section 2.3 is used.  
Stage 4--Index calculation. Due to the nature of the two types of analysis (transient and stable), two different indices are proposed. For the case of transient state, the ENE index is used and, for the case of steady state, the THD index is calculated according to Equations (6) and (7).  
Stage 5--Classification and diagnosis. Finally, once the indices have been obtained for each transformer operating condition (transient state regimen and steady state regimen), two independent ANNs are designed and trained to perform the automatic transformer diagnosis. The metrics used to evaluate the performance of the ANNs are presented in Section 2.6 and their settings are presented in Section 4.4.