## 4 Results  
For a comparative assessment of the models, a measure of similarity between the real pressure waveform and the pressure generated by the model was created. The use of an additional measure to evaluate models apart from MSE was necessary because models can achieve relatively low MSE with outputs that are of constant value, since the most common value appearing in the pressure signal is 0. The measure of similarity was defined as the harmonic mean of two values:  
\[SM=\frac{2}{\sqrt{\frac{1}{\rho_{1}}+\frac{1}{\rho_{2}}}}, \tag{1}\]  
where \(\rho_{1}\) is the correlation coefficient between model and real values of the pressure waveform. The measure \(\rho_{2}\) was defined as a normalized difference in instantaneous pressure values:  
\[\rho_{2}=\frac{1}{N}\underset{i=1}{\overset{N}{\underset{i=1}{\sum}}}\frac{|r_ {i}-m_{i}|}{max(r)} \tag{2}\]  
where \(r_{i}\) is the real value of the pressure, \(m_{i}\) is the reconstructed pressure value, \(N\) is the number of samples, and \(max(r)\) is the maximum value of the entire signal. The first component of measure (1) is easy to interpret and contains information about the linear relationship between the reproduced and model waveforms but does not contain information about the difference between the pressure values generated by the model and the real ones. Hence, it is necessary to use both components. The measure was tested on many simulated waveforms and performed well in assessing waveform similarity. It is important to note that this similarity measure (SM) was (directly in model building) not used directly in model building due to potential computational complexity, which would not allow for a timely comparison of such a vast quantity of models. It was applied for a comparative assessment of the obtained results generated using different models. The best-performing model was the U-net model with an ReLU output activation function, with the output being smoothed by another U-net model and the BCE loss applied in the training of the smoothing model. The model has managed to achieve a value of 0.993 using the aforementioned similarity measure for both validation and test sets. The results of the model's prediction of the engine's pressure are visible in Figure 6.  
To generate the final pressure curve for a given rotational speed and load, the reconstructed pressure curves were averaged. Figure 7 presents a comparison of the averaged expected output and the averaged reconstructed output for the best-performing model for a random example from the validation set. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Parameters** & **Loss Functions** & **Activation Functions** \\ \hline Convolutional & 945 & MSE/BCE & ReLU \\ Model–Small & 945 & MSE/BCE & ReLU \\ \hline Simple Dense ANN & 170,960 & & \\ Convolutional Model & 724,225 & MSE/BCE & ReLU/Sigmoid \\ U-net & 65,729 & MSE/BCE & ReLU/Sigmoid \\ Autoencoder & 2,046,497 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Smoothing models. Furthermore, the performance of the model does not seem to differ for previously unseen examples, as the model still manages to achieve a very high similarity score of 0.993 for the test set. To further showcase the model's performance for unseen data, Figure 8 was included, which shows a comparison of the expected pressure values of the engine and the model's output after averaging and centring the values for a random example from the test set. Figure 6: Results of the prediction of the engine’s pressure by the U-net model with applied smoothing of the output using another U-net model and real pressure (top figure), based on the measured acceleration signals in the x, y, z axes (other waveforms in the figure) for a random example from the validation set. The model’s output is high-indistinguishable from the expected output. Figure 7: Comparison of the expected engine pressure signal and the model’s output for the best-performing model for a random example from the validation set.