# IoT System for Detecting the Condition of Rotating Machines Based on Acoustic Signals
## 4 Experimental Results
### Preliminary Results without Hyperparameter Tuning  
For initial analysis, the hyperparameter tuning step will be omitted and feature extraction and classification parameters will be set bearing in mind the complexity of the problem and the nature of acoustic signals. By adopting \(dwt\_lwl=6\), 7 different DWT coefficients are generated, and the frequency bandwidth of each coefficient can be determined from Table 1. Figure 13 illustrates how the recorded signal looks in the frequency domain, on lower frequencies (up to 500 Hz) with corresponding DWT coefficients. One important thing that is worth mentioning is that the main rotary frequency of the mill (which is 12.5 Hz) is lower than the passband frequency of the microphone as stated in Table 2. For that reason, the spectral component which corresponds to this frequency is significantly weakened and the amplitude of its first harmonic (at the frequency of 25 Hz) is actually more pronounced, as can be seen in Figure 13. This means that although one of the dominant frequencies of the rotary mill is lower than the passband of the microphone, the information that this component yield is not lost since it can be captured in its higher harmonics. By analyzing the frequency characteristics of the signal, it is clear that the most informative dynamic of the signal is captured with coefficients \(a_{6}\) and \(d_{5}\). Here, level 5 detail coefficients (\(d_{5}\)) contain frequencies between 75 and 150 Hz, while approximate coefficients (\(a_{6}\)) contain frequencies from 0 to 37.5 Hz, thus yielding the information about the basic rotary frequency of the mill and one higher harmonic. The power of each coefficient is used as a feature, so there are seven inputs to the NN classification algorithm. This means that the structure of the network does not need to be complex (furthermore, the complex structure can result in overfitting). Therefore, a neural network with two hidden layers and five neurons in each layer is selected (\(nn\_layers=[5,5]\)). With these hyperparameters, the neural network is trained using recordings several minutes long for each of the appointed classification outputs, resulting in over 30 min worth of audio signals recorded in the period of two months. These recordings reflected all the appointed states of the particular rotary machine. Choosing the so-called ground truth (i.e., which of the four classes corresponds to each of the recorded signals) was challenging and was conducted with the help of the site operators. Namely, recordings that are obtained less than a week before the maintenance was conducted are denoted as class four recordings (i.e., they reflect extremely worn impact plates of the mill), whereas the recordings obtained in the first two weeks after the maintenance are denoted as class 1 recordings (reflecting completely healthy machine components). Class 2 roughly corresponds to recordings obtained between 2 and 4 weeks after the maintenance, while class 3 corresponds to  
Figure 13: Frequency characteristics of the recorded signal. Gray areas represent the frequency bandwidth of the corresponding DWT coefficients: \(a_{6}\), \(d_{6}\), \(d_{5}\), \(d_{4}\) and lower frequency parts of \(d_{3}\). recordings obtained around five weeks after the maintenance. It is important to mention that ground truth information about classes is always best when obtained with the input of the domain expert, and it should be carefully chosen for each rotary machine for which the algorithm is used. When initial segmentation of recordings is conducted using the proposed hyperparameters, the training set consisted of a total of 638 samples in a 7-dimensional feature space. Out of these, 134 correspond to class 1, 190 to class 2, 188 to class 3, and 126 to class 4. The training set is divided into training segments (80%) and validation segments (20%). After the training of the neural network is conducted, the testing is performed on new recordings which were previously not seen by the network.