## 3 Experiment Setup  
For evaluation purposes, a visual inspection of the proposed filtering methodology was initially performed for inner race faults at variable speed, employing a simulated envelope spectrum computed from the tested vibration signal. As outlined in Figure 1, after completing the shared procedures of segmentation and spectrogram estimation, we also assessed the proposed filtering approach's influence by appraising the classification accuracy of failures in parallel with testing both filtering approaches for impulsive components: spectral kurtosis and spectral entropy. Thus, the validation of the proposed filtering methodology was achieved in three real-world vibration-signal collections (the tailored software to support the validating pipeline of the proposed short-time/-angle spectral analysis is now publicly available at [[https://github.com/juccaicedoac03/tf-Comp-ex_vib](https://github.com/juccaicedoac03/tf-Comp-ex_vib)]([https://github.com/juccaicedoac03/tf-Comp-ex_vib](https://github.com/juccaicedoac03/tf-Comp-ex_vib))): (1) The SAFRAN dataset, which holds a challenging record of aircraft engines dealing with variable speed in a run-up test. (2) the Case Western Reserve University (CWRU) dataset, which consists of 59 records from two damaged bearings at constant speed; and (3) the Universidad Nacional de Colombia (UNC) dataset, which holds 42 variable-speed signals, including a concrete set of testing bearing failures. For the above datasets, each vibration signal was mapped into the angular domain to remove the shaft speed's influence before validating the filtering approaches, the baseline versions (SK and SE) and their proposed sliding versions (SSK and SSE). We also fixed the set parameter as shown in Table 1, namely, the sliding STFT window \(\mathbf{w}_{\tau}\) to compute SK and SE (as suggested in [29]), and length \(M\) of the segment \(\mathbf{x}_{M}\) to calculate SSE and SSK. To feed the classifier, the single-trial feature vectors extracted from SK and SE are: \(\mathbf{\xi}_{1}[k]\), and \(\mathbf{\xi}_{2}[k]\) (see Equations (4) and (5)). To deal with the poor time alignment of time-frequency sets \(\mathbf{\Xi}[l,k]\), the mean and standard deviation (STD) through time index \(l\) were extracted as a feature from SSK and SSE. The classification procedure was implemented using Python library Scikit-learn, and the following working parameters were selected. The initial feature-selection step employed a support vector machine with \(C=0.1\) (selecting features with nonzero coefficients and stochastic gradient descent optimization), and cross-validation was carried out through a leave-one-out scheme handling 100 trials. Simulation Framework of Rolling-Element Bearing Faults  
To reproduce records with constant instantaneous angular speed (IAS) to be tested, we initially created a fault record with a rolling-element bearing (REB) using a superposition of periodic impulses at the fault frequency (i.e., the average time between impacts) using the model suggested in [30]: \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **Simulation** & **SAFRAN** & **CWRU** & **UNC** \\ \hline \(\mathbf{w}_{\tau}\) & 256 & 256 & 256 & 256 \\ \(M\) & 2048 & 4096 & 8192 & 32,768 \\ Samples per revolution & 128 & 256 & 400.67 & 1024 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Testing dataset parameters: \(\mathbf{w}_{\tau}\), sliding short-time Fourier transform (STFT) window; \(M\), length segment for computation of either sliding spectral entropy (SSE) or sliding spectral kurtosis (SSK) estimator. All parameters measured in samples. Figure 1: Validating pipeline of proposed short-time/-angle spectral analysis for vibration monitoring.