## 4 Analysis and Discussion  
### Accuracy Verification of Road Longitudinal Slope Automatic Detection  
To ensure that the longitudinal slope results collected by the vehicular detection system are within the allowable error range, the accuracy of longitudinal slope automatic detection should be verified before the formal test. Before this, the distance automatic measurement test was carried out according to the accuracy verification requirements in the Specifications of Automatic Pavement Condition Survey [26]. The test results meet the specifications requirements, which require that the distance automatic measurement error does not exceed 0.1%. The following experiments are conducted in accordance with the standard specifications of the Specifications of Automatic Pavement Condition Survey [26] regarding the automated longitudinal slope detection. The MOT Standard [26] stipulates that the automated longitudinal slope detection of pavement needs to meet the following two points: the absolute error of 95% detection value \(\leq\)1.5% or relative error \(\leq\)10%, and the absolute error of all detection values \(\leq\)6%. According to the provisions of the MOT Standard [26], a straight-line test section with a length of 150 m and a significant longitudinal slope change is selected to mark the section's starting and ending positions and a measuring point position every 10 m along the driving direction. DSZ05 leveler is used to measure the elevation of two adjacent measuring points along the driving direction. According to Formula (16), Figure 5a,b, the longitudinal slope value between two adjacent measuring points is calculated, and the result is used as the known longitudinal slope between the two measuring points. Moreover, the vehicular detection system detects the test section at a constant speed of 20 km/h, 30 km/h, and 40 km/h. As illustrated in Figure 5c, the system collects longitudinal slope data at an interval of 0.1 m and outputs the average longitudinal slope every 10 m as the automatic measurement results. \[S^{\prime}_{HM}=\frac{\frac{h_{AB}}{d_{AB}}}{\sqrt{1-\left(\frac{h_{AB}}{d_{ AB}}\right)^{2}}} \tag{16}\]  
where \(S_{HM}\) denotes the longitudinal slope value (%) between two adjacent measuring points measured manually, \(h_{AB}\) denotes the height (m) between two adjacent measuring points measured by the leveler, and \(d_{AB}\) represents the distance (m) between two adjacent measuring points, which was taken as 10 m in this case. In order to better develop the bridge slope generality test, it is necessary to calibrate the automatic test results, as shown in Equation (17). \[S_{AM}=\alpha*S_{AM}^{\prime}+\beta \tag{17}\]  
where \(\alpha\) and \(\beta\) is the empirical correction factor, in this work, we fix the focusing parameter \(\alpha\) as 1.02 and \(\beta\) as 0.03. \(S_{AM}^{\prime}\) is the automatic longitudinal slope measurement before calibration, and \(S_{AM}\) is the automatic longitudinal slope measurement after calibration. Error analysis is carried out on the measurement results, and the absolute error and relative error are selected as the accuracy verification parameters of longitudinal slope automatic measurement, whose calculation formulas are as follows:  
\[E_{AE}=|S_{AM}-S_{HM}| \tag{18}\]  
\[E_{RE}=\frac{|S_{AM}-S_{HM}|}{|S_{HM}|}\times 100\% \tag{19}\]  
where \(E_{AE}\) denotes the absolute error (%) of the longitudinal slope measurement between two adjacent measuring points, \(E_{RE}\) denotes the relative error (%) between two adjacent measuring points, and \(S_{AM}\) is the average longitudinal slope value (%) between two adjacent measuring points output by the vehicular detection system every 10 m.  
The analysis results are shown in Table 2. There are 15 groups of longitudinal slope results measured automatically and manually, distributed every 10 m, namely, 0-10 m, 10-20 m,..., 140-150 m. It can be seen from Table 2 that the absolute error \(E_{AE}\) of 15 groups of longitudinal slope measurement results under three speeds are all less than 6%.