## 3 Road Surface Grade Identification
### Feature Extraction  
Feature extraction involves identifying the most relevant attributes from raw data. In this paper, the Pied Kingfisher Optimizer (PKO) [19] is used to remove irrelevant or redundant features, thus improving the model's performance, reducing the computational cost, and optimizing the system's performance. After mathematical modeling, feature selection becomes a multi-objective optimization task, with the fitness function defined as follows:  
\[fit=(l-\rho)\times E+\rho\times\frac{\mid I\mid}{\mid L\mid} \tag{8}\]  
where \(E\) is the classifier's classification error rate, \(\rho\) is the weight coefficient, \(\mid l\mid\) represents the number of feature subsets selected by the algorithm, and \(\mid L\mid\) represents the feature count in the initial dataset. The PKO achieves intrinsic fitness for the feature selection task through its unique bio-behavioral metaphor: The algorithm maps \(x_{i}\), the component of each individual's position vector (\(\vec{X}\in[0,1]^{D}\)), to the feature importance's confidence and generates a binary subset, \((\tau=0.5)\), of features based on a threshold function, \(\phi(x_{i})=(x_{i}>\tau)\), where overhead water striking provides global exploration capability to avoid the locally optimal feature combinations. Dive fishing achieves local exploitation capability to refine the quality feature subset, and the other symbiosis mechanism improves the convergence efficiency through an inter-population feature subset's information exchange. For the dynamic characteristics of multi-speed conditions, PKO adopts an independent optimization kernel to generate an exclusive feature mask (\(M_{\text{p}}\)) for each speed \(v\), which oscillation factor enhances the global feature combination's evaluation ability at the low-speed stage and focuses on the high-frequency feature optimization at the high-speed stage. At the same time, it introduces a speed robustness penalty term (\(R_{\text{p}}\)) to ensure the feature subset's continuity when the algorithm is switched. This bio-inspired dynamic balancing strategy, combined with the features' mutual information-guiding mechanism, overcomes the inherent defects of the \begin{table}
\begin{tabular}{l l} \hline \hline
**Feature** & **Physical Meaning** \\ \hline RMS & Road profile’s root-mean-square value \\ \(\kappa\) & Peak characteristics in vibration signals indicate impact events \\ \(\mu\) & Permanent load redistribution \\ \(\sigma\) & Dispersion of vibration signals, exhibits a positive correlation with the \\  & amplitude variability of the surface roughness \\ \(f_{do}\) & Spectral location of the peak power density, corresponds to the \\  & fundamental excitation frequency component in vibratory systems \\ \(E_{sp}\) & Normalized energy content within the frequency band, provides a \\  & comprehensive characterization of the overall vibrational intensity \\  & Normalized power content within a specified frequency band, \\ BER & a discriminative feature for characterizing frequency-resolved roughness \\  & distributions \\ Max PSD & Peak magnitude of the power spectral density, indicates the maximum \\  & excitation intensity within the system \\ WER & Distribution of the multiscale signal energy, a diagnostic feature for \\  & detecting transient impulses \\ IFM & Temporal average of the instantaneous frequency, characterizes \\  & time-varying spectral properties \\ SE & A metric for signal complexity quantification, where higher entropy \\  & correlates with irregular vibration patterns \\ H & Long-range correlation index, reflects spatial aggregation effects of road \\  & irregularities \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Relationship of characteristics to pavement grading. traditional optimizer, fixes the exploration-exploitation ratio, and ignores the features' statistical dependency and the assumption of a static environment.