## 5 Discussion and Conclusions  
The presented study set out to determine whether purely external vibration measurements can be transformed, without any handcrafted features, into high-fidelity reconstructions of in-cylinder pressure. There, well-established signal-to-signal deep-learning architectures (autoencoders, U-Nets, and GANs) were benchmarked. Additionally, a novel two-stage model composed of a \"base\" U-Net followed by a dedicated smoothing network (SmN) was introduced. The proposed two-stage method for reconstructing the pressure curve in the engine cylinder based on vibration measurements using a smoothing network delivers the best result among the tested models (SM = 0.9935). The reconstruction errors are minimal and insignificant when averaging. The proposed method can serve as a highly effective tool for diagnosing engine damage that affects the pressure curve. However, several key limitations of the study should be noted, due to the vast number of deep-learning architectures being available, this work was focused on only a small number of those most relevant to the problem. However, several other architectures could \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & **Activation** & **Smoothing** & \begin{tabular}{c} **Smoothing Model** \\ **Output Activation** \\ **Function** \\ \end{tabular} & \
\begin{tabular}{c} **Smoothing Model** \\ **Model Loss Function** \\ **Function** \\ \end{tabular} &
\begin{tabular}{c} **Similarity Measure for the Test Set** \\ **Test Set** \\ \end{tabular} \\ \hline U-net–small & ReLU & U-net & ReLU & BCE & 0.9935 \\ \hline Autoencoder–small & ReLU & U-net & ReLU & BCE & 0.9909 \\ \hline GAN (generator–U-net small) & ReLU & U-net & ReLU & BCE & 0.9783 \\ \hline U-net–big & ReLU & - & - & - & 0.9918 \\ \hline Autoencoder–small & ReLU & - & - & - & 0.9673 \\ \hline GAN (generator–U-net big) & - & - & - & - & 0.9232 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of similarity measures for the best models with various architectures. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & **Activation** & **Smoothing** & \begin{tabular}{c} **Smoothing Model** \\ **Output Activation** \\ **Function** \\ \end{tabular} & \
\begin{tabular}{c} **Smoothing Model** \\ **Loss Function** \\ \end{tabular} &
\begin{tabular}{c} **Similarity Measure** \\ **for the Test Set** \\ \end{tabular} \\ \hline U-net–small & ReLU & U-net & ReLU & BCE & 0.9935 \\ U-net–small & ReLU & U-net & ReLU & MSE & 0.9929 \\ U-net–small & ReLU & U-net & Sigmoid & MSE & 0.9920 \\ U-net–big & ReLU & - & - & - & 0.9918 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The four best-performing models for recreating internal engine pressure based on vibration signals, with values provided for the test set. be tested, such as recurrent networks utilizing LSTM [27] or GRU [28] layers. Transformer architecture could also be a promising direction for future analysis [29]. Furthermore, only the steady-state performance of a single engine was tested; to propose a more universal tool a more robust analysis with the aforementioned methodology should be applied to a more varied dataset. Regardless, the potential of the smoothing technique applied to the signal processed by a deep-learning model was demonstrated. Several other observations can be drawn from this work:  
1. Importance of architecture depth vs. capacity: Larger networks did not systematically outperform smaller ones once the SmN was introduced; the small U-Net + SmN (\(\sim\)2 M + 66 k parameters) slightly surpassed the 17 M-parameter \"big\" U-Net. Thus, hierarchical receptive fields matter more than sheer width for this task. 2. Role of the similarity function: The custom metric SM (harmonic mean of correlation and normalized amplitude error) proved essential. Pure MSE rewarded flat, low-variance outputs, whereas SM penalised such trivial solutions, causing clear ranking shifts among otherwise comparable models.