# A Hydraulic Semi-Active Suspension Based on Road Statistical Properties and Its Road Identification
## 4 Test Verification
### Results Analysis
#### 4.3.2 Influence Factor Analysis of Identification Results  
The Influence of the Acceleration Signal Length  
The road identification method proposed is based on Formula (8). It is assumed that the road input is regarded as white noise, but the actual pavement is not. Theoretically, many samples are needed when the RMS acceleration \(\sigma_{z_{2}}\) is calculated. That is, longer times result in predicted PSD \(G_{q}(n_{0})\) values closer to the actual road surface. However, it cannot be infinitely long in the practical application. According to the experimental results, the PSD \(G_{q}(n_{0})\) value of the highway can be effectively identified  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \multicolumn{3}{c}{**Road Condition**} & \multirow{2}{*}{**Damping**} & \multicolumn{3}{c}{**Identifified \(G_{q}(n_{0})\)/(10\({}^{-6}\)m\({}^{3}\))**} \\ \hline
**Road Section** & **Length (m)** & **Real \(G_{q}(n_{0})\)/(10\({}^{-6}\)m\({}^{3}\))** & \multicolumn{3}{c}{_C/(Ns/m)_} & **40 km/h** & **60 km/h** & **80 km/h** \\ \hline \multirow{3}{*}{Highway} & \multirow{3}{*}{460.0} & \multirow{3}{*}{2.0–10.0} & 1032 & 6.5 & 6.8 & 6.3 \\  & & & 1806 & 6.4 & 6.9 & 6.7 \\  & & & 2613 & 6.1 & 6.2 & 6.6 \\ \hline \multirow{3}{*}{Cement road} & \multirow{3}{*}{615.5} & \multirow{3}{*}{50.0–85.0} & 1032 & 68.3 & 62.7 & 65.4 \\  & & & 1806 & 65.3 & 64.8 & 68.0 \\  & & & 2613 & 62.1 & 63.9 & 61.8 \\ \hline \multirow{3}{*}{Sand road} & \multirow{3}{*}{1075.0} & \multirow{3}{*}{400.0–500.0} & 1032 & 446.2 & 423.1 & 430.3 \\  & & & 1806 & 457.3 & 419.4 & 425.9 \\ \cline{1-1}  & & & 2613 & 418.6 & 438.7 & 446.5 \\ \hline \end{tabular}
\end{table}
Table 2: The identified PSD \(G_{q}(n_{0})\) values.  
Figure 9: The measured cab floor vertical acceleration signals under the sand road for: (**a**) \(v\) = 80 km/h; (**b**) \(v\) = 60 km/h; and (**c**) \(v\) = 40 km/h.  
by using the length 41.4 s of the acceleration signal for \(v\) = 40 km/h. Moreover, taking 20.7 s is enough for \(v\) = 80 km/h. According to the experiment results, the effective perception of road conditions can be realized within 1.0 min at the speed of 40-100 km/h on the highway. In the actual running process, the road grade is basically unchanged for a period. Therefore, it can meet the requirements of practical applications using 20 s as the identification interval. To further analyze the influence of the acceleration signal length, the PSD \(G_{q}(n_{0})\) values of the highway for the three runs for \(v\) = 80 km/h were identified using 10 s, respectively. The identified results are 5.9, 6.2, and 6.1 \(\times\) 10\({}^{-6}\) m\({}^{3}\), respectively. The identified values are smaller than those identified using 20 s. The longer the acceleration signal length is, the more effectively the low-frequency excitation components of the road surface can be reflected. Thus, the cause may be that the contribution of the low frequency excitations cannot be totally contained.  
The Influence of the Running Speed Change  
According to Equation (7), when the vertical acceleration \(\bar{z}_{2}\) is measured, the cars need to run at a constant speed for a period, but the running speed is fluctuating for the actual car in operation. In most cases, it is basically fluctuating within a constant velocity range. According to Formula (8), the PSD \(G_{q}(n_{0})\) is inversely proportional to the running speed \(v\). If the vehicle speed fluctuates \(\pm\)5% within a period, the identification result fluctuates \(\mp\)5%. The proposed method of the road identification is based on road statistical characteristics. The slight fluctuation of the running speed \(v\) has little effect on the statistical characteristics of road conditions.