## 3 Methodology  
In this section, the GA-based methodology for suppressing the FFC from the current signals of the IM is described. The proposed methodology can estimate the amplitude, frequency, and phase shift that describe the FFC in order to suppress it, or at least highly reduce it. By attenuating the energy of the FFC, it is possible to better appreciate the failure harmonics because they are not overshadowed nor hidden by spectral leakage. In Figure 2, a diagram of the proposed methodology is observed. Figure 1: Flow diagram of the Genetic algorithm (GA). The methodology was performed through three steps: signal acquisition, suppression of the FFC, and residual signal (RS) spectrum. In the first step, the current signals of the IM operating at steady state were acquired using a proprietary data acquisition system (DAS). The current signals for the three phases, _Ia_, _Ib_, and _Ic_, of the IM were simultaneously acquired; however, they were processed one at a time. In the second step, the current signal \(i(t)\) was sent to the GA in order to estimate the amplitude (Am), frequency (f), and phase (\(\Phi\)) that better described the FFC. Since the methodology was designed for working with the motor signals at steady state, the first seconds of the current signal containing the transient were not taken into account. Thus, in order to perform the parameter estimation, a population of 30 individuals was considered in the implementation of the GA. Every individual was composed by the union of three different genes: the first represented the amplitude (Am), the second the frequency (f), and the third one the phase (\(\Phi\)). To ensure that the individuals fell within an acceptable range, the next boundaries were set for the genes: 0 to 3 for the amplitude considering that peak current in steady state always remain in this range; 19 to 32 for the frequency since the two operating frequencies used in this work (20 and 31 Hz) were between these two values; and -\(\pi\) to \(\pi\) for the phase. The objective function is a pure sinusoidal wave; therefore, each individual was assessed using (5):  
\[fc(t)=Am\times\sin(2\pi ft+\Phi). \tag{5}\]  
After assessing the individuals, it was necessary to organize them by applying (3) and (4). This sorting was performed with the aim of obtaining the best member of the current population (\(G_{1}\)), which is the one with the highest fitness value. This individual must be conserved in the next generation. The missing individuals in the new population needed to be generated using the crossover operation. To simplify the calculation of this operation, in this particular work, the crossover was reduced to an average value as shown in (6):  
\[G_{n}(i)=(G_{1}+G_{c}(i))/2, \tag{6}\]  
where \(i=2,\ldots,30\); \(G_{c}(i)\) is the i-th individual of the current population; and \(G_{n}(i)\) is the i-th individual of the next population. To add diversity in the population and to avoid local maxima stagnation, a mutation probability \(Pm=0.2\) was introduced in order to randomly exchange some individuals. Figure 2: Block diagram of the proposed methodology. These operations were performed a total of 300 times because it was experimentally demonstrated that this number of iterations was enough to ensure the convergence of the GA every time. The genes Am, f, and \(\Phi\) from the best individual in the last iteration were considered as the parameters of the FFC. These parameters were substituted in (5) and the resulting signal \(fc(t)\) was considered as the FFC. The \(fc(t)\) signal was subtracted from the current signal \(i(t)\) and the result was called the RS. This signal contained all the harmonics and interharmonics from the original signal. It must be mentioned that the methodology cannot completely remove the FFC, a small amount of its energy may be preserved in the RS. Notwithstanding, the remaining energy was much lower than in the original signal because it had been attenuated by the GA-suppression technique.