## 4 Simulations
### Introduction to Dataset and Experiment Parameters  
The real-world dataset used in this study was obtained from a spring factory and has been employed by multiple studies in the past [11; 18]. Figure 8a shows the architecture of this machine. Figure 8b-d illustrate its operation. It comprises a wire feeding hole in the center column and eight wire benders surrounding it. During operation, a wire is fed from the hole at a fixed speed, and the surrounding wire benders reach out at the right moments to bend the wire and form the spring shape designated by the user. To collect the data, a triaxial accelerometer was installed on the center column, as shown in Figure 8a. This sensor collects acceleration data of the vibrations along the \(X\), \(Y\), and \(\mathbf{Z}\) axes generated as the wire is fed from the hole and bent by the wire benders. The directions of three axes (\(X\), \(Y\), and \(\mathbf{Z}\)) are marked on Figure 8a with arrows. The resulting data are displayed in Figure 9: each cycle of variations in acceleration represents the production of one spring. The datasets mentioned in [11; 18] include the production data from springs of over a dozen types of lengths. For our research requirement, we only used data from springs that were 171 mm, 181 mm, 188 mm, 189 mm, 190 mm, 210 mm, and 230 mm in length. Those that were 171 mm or 181 mm long were considered to be bad products due to insufficient length; those that were 188 mm, 189 mm, or 190 mm long were considered to be good products; and those that were 210 mm or 230 mm long were considered to be bad products due to excessive length. Based on the characteristics of this dataset, we saw spring length as the difference between the basic product and the modified product and designed two experiments: (1) the basic model only detects good products and bad products that were too long while the add-on model considers three fault categories, and (2) the basic model only detects good products and bad products that were too short while the add-on model considers three fault categories. The acceleration signal values collected for the spring change periodically (as shown in Figure 9). Therefore, as suggested by previous papers [11; 18], we did not use recursive neural networks for modelling, but rather adopted a windowing approach. This method starts by extracting a window for the time series of each acceleration segment and then calculating seven features for each window's points. The seven features are mean, maximum, energy, root mean square, variance, mean absolute deviation, and standard deviation. As each item of data contains three time series (one for each of the axes, x, y, and z), we ultimately obtained 21 features for each item of data. Based on the needs of our experiment, we set the sizes of the windows and overlaps to be 150 points and 50 points, respectively. Furthermore, as we only considered the length differences between the basic and modified products, we only needed the original accelerator; i.e., there were no issues with increasing or decreasing the features. Thus, in the construction of both the basic model and the add-on model, we considered 21 features. The four models used in this experiment included (1) the RBF-DNN that determines the key features of the basic model, (2) the basic model itself, (3) the RBF-DNN that determines the key features of the add-on model, and (4) the add-on model itself. We introduce their parameter settings below. First are the two RBF-DNNs in (1) and (3). In the construction phases of the basic and add-on models, 21 features were considered, so the number of input neurons in both RBF-DNNs was 21. Next, regarding the number of neurons in the RBF layer, we referred to the settings of past studies [4; 15], in which each input neuron uses three RBF neurons to describe it. Thus, the RBF layer contained a total of 63 neurons. As for the subsequent fully connected layers, we had the number of neurons decrease to a fourth of the former number each time.