## 3 Deep Learning Architecture and Signal Reconstruction  
### Dataset  
The dataset comprises vibration measurements along the x, y, and z axes, accompanied by pressure readings (considering overpressure relative to atmospheric pressure). Each signal was segmented using a sliding window approach into input arrays of shape (10,000 samples, three channels) with a 50% overlap (5000 samples). The data were partitioned into training (70%), validation (15%), and test (15%) sets, resulting in 4495 training, 963 validation, and 964 testing examples. It should be noted that data splitting was performed before window sampling to avoid data leak. Two preprocessing techniques were applied to the input data:  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline  & & **Load [Nm]** & \\ \hline \hline  & 0 & 22.5 & 45.0 & 67.5 & 90.0 \\ Rotational speed [rpm] & 700 & & 1000, 1200, 1500, 1700 & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Engine operating conditions variations.  
Figure 1: Measurement system diagram (**a**), vibration signal acquisition location (**b**).  
Min-Max Scaling: normalizes data to a [0, 1] range;
* Standardization: transforms data to have zero mean and unit variance.  
Corresponding pressure outputs were scaled using parameters derived from the training set and applied consistently across validation and test sets with the vibration and pressure signals processed independently for all of the sets. The expected output of the model, corresponding to the pressure values, was also available in the normalized and standardized versions using maximal, minimal, standard deviation, and mean values extracted from the training set and later applied to validation and test sets. The task of the tested models was to produce an output for the whole signal--10,000 floating point numbers representing the pressure of the engine based on the measured x, y, z vibrations--meaning that the three channels with 10,000 floating point measurements were mapped by the model to the 10,000 floating point values representing the pressure (signal-to-signal processing task). To allow for an extensive comparison of the architectures, several models based on commonly utilized architectures were used: autoencoder (AE) [20], U-net [21], Generative Adversarial Network (GAN) [22], and a novel smoothing network (SmM) setup. Furthermore, all models were trained on both the normalized and standardized data to allow for further comparisons. The brief overview of implementations is as follows:  
**Autoencoder:**  
* Implemented in two sizes: small (17,121 parameters) and large (188,193 parameters);
* Tested with ReLU and Sigmoid activation functions at the output layer;
* ReLU was considered for data without a fixed upper bound, while Sigmoid was suited for normalized data within [0, 1].  
**U-Net:**  
* Adapted for 1D signal processing;
* Two configurations: small (2,046,545 parameters) and large (16,992,849 parameters);
* Tested with both ReLU and Sigmoid output activations.  
**Generative Adversarial Network:**  
* Generators based on U-Net architectures with ReLU activation;
* Discriminator implemented as a CNN, classifying inputs as real or fake;
* Loss functions included the following:  
* Discriminator Loss (Binary Cross-Entropy);
* Weighted combinations of Discriminator Loss with MAE or MSE (weights: 0.6 for Discriminator Loss, 0.4 for MAE/MSE) [23].  
**Smoothing Models:**  
* Post-processing model for removing output from the earlier-tested models;
* Dense, convolutional neural network (CNN) [24], U-Net, and Autoencoder architectures were tested;
* Trained on Binary-Cross Entropy and MSE losses;
* Tested with Sigmoid and ReLU output activations.