### Signal Processing  
When the vibratory roller moved on the test lanes, the vibration signals measured by two accelerometers (in the cab and on the drum frame) were continuous. Since the velocity of the roller was about 1 m/s, it took about 60 s for one pass. Therefore, a 60-s long vibration signal was obtained from one accelerometer in one pass. A total of 60 long signals were collected since a total of 30 passes were performed on two test lanes. Theoretically, the frequency components of the vibration signals from the cab and drum frame should be the same, even though the amplitudes may be different.  
The vibration was sampled at 2 kHz. The 60-s long signal (collected in one pass) was successively split into many 0.5-s short signals. A short signal had 1000 contiguous data samples, the first 500 values of a short signal overlapped with the last 500 values of the previous short signal. The short signals were converted into the frequency domain by using a fast Fourier transform (FFT). The Nyquist frequency was 1 kHz since the vibration was sampled at 2 kHz. The Nyquist frequency is half of the sampling rate of a discrete signal processing system. According to the Nyquist-Shannon sampling theorem, if a system uniformly samples an analog signal at a rate that exceeds the signal's highest frequency by at least a factor of two, the original analog signal can be perfectly recovered from the discrete values produced by sampling. In other words, the Nyquist frequency should be higher than the signal's highest frequency to express the signal's features accurately. The system in this study is a low-frequency system, 1 kHz Nyquist frequency is enough. By using the single-sided FFT, each short signal was converted to a frequency spectrum distributed between 0 and 1 kHz, expressed as an array of 500 elements, \(a=(a_{1},\,a_{2},\,\ldots,\,a_{500})\). Therefore, the frequency features of the vibration signal were extracted by using FFT. In this study, the amplitude was not considered as a kind of feature. To eliminate the effects of amplitudes, array \(a\) should be normalized. The normalized array \(x\) was obtained as follows.  
\[\begin{array}{l}\overline{a}=\ln(a)\\ x=\frac{\overline{a}}{|\overline{a}|_{\max}}\end{array} \tag{1}\]  
In Equation (1), some inconspicuous frequency components can be amplified by the logarithmic operation. The signal processing procedure is summarized as the following three steps:  
1. The 60-s long vibration signal collected in one pass is successively split into many 0.5-s short signals.
2. The short signals are converted into the frequency domain by using a single-sided FFT.
3. The short signals are normalized by using Equation (1).  
The signal processing method is also diagrammed in Figure 6. The input arrays, \(x\), were the samples used to train the ANN model, the elements of \(x\) were the features of the sample. Therefore, in this paper, 500 features were considered for a sample. Before the training, every sample was tagged with a target class, the signal sample's corresponding compaction level. In this study, four compaction levels were considered and represented by four target classes, as is shown in Table 2. Each sample was tagged according to the data of degree of compaction measured in the in-situ tests shown in Figure 5, then the tagged samples formed the dataset to train the ANN model.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Target Class** & **Level No.** & **Degree of Compaction (\%)** & **Target Array** \\ \hline Class 1 & 1 & \textless{}95 & (1, 0, 0, 0) \\ Class 2 & 2 & 95–96 & (0, 1, 0, 0) \\ Class 3 & 3 & 96–97 & (0, 0, 1, 0) \\ Class 4 & 4 & \textgreater{}97 & (0, 0, 0, 1) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Target class and compaction level.