# Recognition of Acoustic Signals of Commutator Motors
## 2 Proposed Fault Detection Approach Using a Smartphone and Acoustic Signals
### Masaf-Ratio-27-Multiiexpanded-4-Groups  
It is difficult to see changes of signals in the time domain; this is a reason to use the frequency domain. The MSAF-RATIO-27-MULTIEXPANDED-4-GROUPS (Method of Selection of Amplitudes of Frequency Ratio 27% Multiexpanded 4 Groups) method computed the FFT (Fast Fourier Transform) spectra. Next, the method computed feature vectors of the analysed states of the electric impact drill. The method used the differences of the FFT spectra. The proposed method used the following steps:  
1. Compute the FFT spectra of the analysed states of the electric impact drill. Each FFT spectrum had 16,384 values. These values formed 16,384 elements of the vector. Vectors were denoted as follows: healthy electric impact drill--**hd** = [_hd_1, _hd_2,..., _hd_16,384], electric impact drill with damaged gear train--**ddgt** = [_ddgt_1, _ddgt_2,..., _ddgt_16,384], electric impact drill with a faulty fan (5 broken rotor blades)--**dffive** = [_dffive_1, _dffive_2,..., _dffive_16,384], electric impact drill with a faulty fan (10 broken rotor blades)--**dten** = [_dten_1, _dten_2,..., _dten_16,384],
2. Find difference between the FFT spectra: **hd** -- **ddgt**, **hd** -- **dfive**, **hd** -- **dten**, **ddgt** -- **dfive**, **ddgt** -- **dten**, **dfive** -- **dten**. 3. Compute absolute values: |**hd** -- **ddgt**!, |**hd** -- **dfive**!, |**hd** -- **dten**!, |**ddgt** -- **dfive** -- **dten**!. 4. Compute _Ratio_ from Equation (1) for all absolute values: \[Ratio=(100\%)AV_{i}/MaxAV\] (1) where _MaxAV_ is the maximum absolute value of the difference between FFT spectra, \(AV_{i}\) is the absolute value of the difference between FFT spectra with index \(i\), and _Ratio_ is the threshold of the difference between FFT spectra. The RATIO-27 means that 27% of the maximum absolute value of the difference between FFT spectra was the threshold. First, the ratio is defined, and next, it is fixed to a specific threshold. All frequency components larger than the threshold were used for the further steps of processing. Figure 10: **(a)** Diagram of the experimental setup of the measurements using the smartphone. **(b)** Experimental setup of the blender and electric impact drill. Compute common frequency components using the parameter _TCF_ (_Threshold of common frequency components_) = (_number of required common frequency components_)/(number of all differences_). An example of using _TCF_ is presented as follows. There are the following differences of the FFT spectra: \(|\,\mathbf{hd}-\mathbf{ddgt}|\), \(|\,\mathbf{hd}-\mathbf{dfive}|\), \(|\,\mathbf{hd}-\mathbf{dten}|\), \(|\,\mathbf{ddgt}-\mathbf{dfive}|\), \(|\,\mathbf{ddgt}-\mathbf{dten}|\), \(|\,\mathbf{dfive}-\mathbf{dten}|\). Frequency components of 100 and 150 Hz are selected 3 times for \(|\,\mathbf{hd}-\mathbf{ddgt}|\). Frequency components of 100 and 200 Hz are selected 3 times for \(|\,\mathbf{hd}-\mathbf{dfive}|\). Frequency components of 100 and 300 Hz are selected 3 times for \(|\,\mathbf{hd}-\mathbf{dten}|\). Frequency components of 400 and 450 Hz are selected 3 times for \(|\,\mathbf{ddgt}-\mathbf{dfive}|\). Frequency components of 400 and 500 Hz are selected 3 times for \(|\,\mathbf{ddgt}-\mathbf{dten}|\). Frequency components of 400 and 600 Hz are selected 3 times for \(|\,\mathbf{dfive}-\mathbf{dten}|\). It can be noticed that the best frequency components are 100 and 400 Hz, being found 9 times (if _TCF_ = 9/18 = 0.5, it assumes, that 9 required common frequency components are set and there are 18 differences between 4 states, it assumes there are 3 training sets, then it will have 18 differences). The MSAF-RATIO-27-MULTIEXPANDED-4-GROUPS finds none of the frequency components (if _TCF_ = 11/18 = 0.6111 - 11 required common frequency components/18 differences). 6. Group the common frequency components. The MSAF-RATIO-27-MULTIEXPANDED-4-GROUPS used 1-4 groups of the best common frequency components. In the mentioned example, the best group had the common frequency components of 100 and 400 Hz. 7. Use 1-4 of the found groups. 8.