A Method for Assessing the Risks of Freeway Segments with Combined Horizontal and Vertical Curves
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摘要: 高速公路平纵曲线组合路段常出现单一平曲线和竖曲线要素满足规范，但二者相结合后存在安全隐患的情况。为评估这类组合路段的交通风险、提升组合路段安全性，综合运用可拓云理论与理想点法，提出了基于可拓云模型的交通风险评估方法。基于已有事故数据和文献，从驾驶员、道路、交通环境以及其他因素的角度出发，构建了包含15个指标的交通风险评估指标体系，并将每个指标划分为5个风险等级；利用层次分析法和熵权法确定各评估指标主、客观权重后，再通过理想点法确定各评估指标组合权重；参照公路路线设计规范及相关文献，考虑定性指标的边界模糊性划分各评估指标的风险等级，并按照等比原则实现定性指标的定量化描述；构造可拓云模型云隶属度矩阵，计算综合评判向量，最后根据最大隶属度原则确定路段风险等级。以云南省3段高速公路路段作为分析案例，利用基于可拓云模型的交通风险评估方法计算了各路段风险等级，并识别了各路段的危险性指标。结果表明：该方法与传统基于模糊综合评价法相比，评估结果相同，但信息更丰富，其综合评判模糊等级特征值的期望Exr反映了路段的安全程度；Y路段的Exr高于C路段，表明Y路段比C路段更安全；3段路段的评估结果的置信度因子θ均小于0.05，表明结果可信度较高，验证了该方法在交通风险评估过程中的适用性。Abstract: Freeway segments with combined horizontal and vertical curves might not satisfy the safety specifications of Highway Alignment Design(hereafter referred as HAD)even though each of them does so. To assess the risks of such road sections and improve road safety, a safety assessment method is proposed by using the extendable cloud theory and the ideal point method(IPM). Firstly, a road safety evaluation system is developed, which includes 15 indicators from the following five perspectives: drivers, roads, traffic, environment, and others, and each indicator is coded as one of five levels. Secondly, subjective and objective weights of the indicators are determined by the analytic hierarchy process(AHP)and entropy weight method(EWM), respectively, which are combined into one using the ideal point method.Thirdly, the risk levels of each indicator are classified based on the specifications, considering the fuzz boundaries of the qualitative indicators, and the qualitative indicators are quantified based on the principle of equal ratio. Finally, the membership evaluation matrix is developed, a comprehensive assessment vector is calculated, and the level of risk of road section is determined by the maximum membership principle. To demonstrate the proposed method, three cases from the Yunnan Province are used, and the results show that the proposed method not only provides compliant outcomes with the traditional fuzzy comprehensive assessment method but also offers more information. Specifically, the expected value of fuzzy grade eigenvalue for comprehensive assessment, i.e. Exr, reflects the safety level of the road sections; Confidence Factor θ reveals the reliability level of the result. In the studied cases, Exr of Section Y is higher than that of Section C, showing that Section Y is safer than Section C; Confidence Factor θ are all under 0.05, showing that the results are reliable. These results reveal the potential of the proposed method for road safety assessment.
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图 4 不同平纵曲线组合形式眨眼频率变化图
Figure 4. Variation diagram of blink frequency in different horizontal and vertical line combinations
图 5 不同驾驶员心率变异性变化图
Figure 5. Variation chart of heart rate variability among different drivers
图 6 Y路段视觉特性风险等级云图
Figure 6. Cloud map of risk level of visual characteristics of Section Y
图 7 各路段评估指标隶属风险等级图
Figure 7. Assessment indicators of each road section belong to the risk level map
表 1 各评估指标风险等级划分依据
Table 1. Basis for the classification of risk levels of each assessment indicator
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表 2 风险评估指标等级界限划分
Table 2. Classification of risk assessment indicators levels
评估指标 范围 分级 E级 D级 C级 B级 A级 视觉特性（眨眼频率）P1/（次/10 s）（转化为评分） (0, 100] (0, 20] (20, 40] (40, 60] (60, 80] (80, 100] 心理、生理特性(HRV) P2/ms2(转化为评分） (0, 100] (0, 20] (20, 40] (40, 60] (60, 80] (80, 100] 平曲线最小半P3/103m (0, 10] (0, 1] (1, 2] (2, 4] (4, 5] (5, 10] 凹形竖曲线最小半径P4/103m (0，） (0, 2] (2, 4] (4, 6] (6, 25] (25，） 凹形竖曲线最小半径/103m(转化为评分） (0, 100] (0, 20] (20, 40] (40, 60] (60, 80] (80, 100] 凸形竖曲线最小半径P5/103m (0，） (0, 3] (3, 11] (11, 17] (17, 30] (30，) 凸形竖曲线最小半径/103m(转化为评分） (0, 100] (0, 20] (20, 40] (40, 60] (60, 80] (80, 100] 最大纵坡（绝对值）P6/（°） (0, 6] (4, 6] (3, 4] (2, 3] (1, 2] (0, 1] 最大坡度差P7/(°) (0, 10] (8, 10] (6, 8] (4, 6] (2, 4] (0, 2] 最大坡长P8/m (0, 1 100] (900, 1 100] (800, 900] (700, 800] (600, 700] (0, 600] 竖曲线最短长度P9/m (0，） (0, 70) (70, 100] (100, 250] (250, 300] (300, ^) 竖曲线最短长度(m)(转化为评分） (0, 100] (0, 20] (20, 40] (40, 60] (60, 80] (80, 100] 最小合成坡度P10/% (0, 8] (0, 0.3] (0.3, 0.5] (0.5, 1] (1, 2] (2, 8] 最小平纵指标均衡性(竖/平）P11 (0，） (0, 5] (5, 10] (10, 15] (15, 20] (20，) 最小平纵指标均衡性(竖/平)（转化为评分）P11 (0, 100] (0, 20] (20, 40] (40, 60] (60, 80] (80, 100] 最小变坡点与平曲线的曲中错位率P12/% (0, 100] (40, 100] (30, 40] (20, 30] (10, 20] (0, 10] 大车比例p13/% (0, 100] (80, 100] (60, 80] (40, 60] (20, 40] (0, 20] 地区不良气候天数P14/% (0, 100] (80, 100] (60, 80] (40, 60] (20, 40] (0, 20] 超载率P15/% (0, 100] (80, 100] (60, 80] (40, 60] (20, 40] (0, 20]
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表 3 标准正态云模型
Table 3. Standard normal cloud model
评估指标 分级 E级 D级 C级 B级 A级 视觉特性（眨眼频率）P1 (10, 3.33, 0.333) (30,3.33,0.333) (50, 3.33, 0.333) (70, 3.33, 0.333) (90, 3.33, 0.333) 心理、生理特性(HRV) P2 (10, 3.33, 0.333) (30, 3.33, 0.333) (50, 3.33, 0.333) (70, 3.33, 0.333) (90, 3.33, 0.333) 平曲线最小半径P3 (0.5, 0.17, 0.017) (1.5, 0.17, 0.017) (3, 0.33, 0.033) (4.5, 0.17, 0.017) (7.5, 0.83, 0.083) 凹形竖曲线最小半径P4 (10, 3.33, 0.333) (30, 3.33, 0.333) (50, 3.33, 0.333) (70, 3.33, 0.333) (90, 3.33, 0.333) 凸形竖曲线最小半径P5 (10, 3.33, 0.333) (30, 3.33, 0.333) (50, 3.33, 0.333) (70, 3.33, 0.333) (90, 3.33, 0.333) 最大纵坡P6 (5, 0.33, 0.033) (3.5, 0.17, 0.017) (2.5, 0.17, 0.017) (1.5, 0.17, 0.017) (0.5, 0.17, 0.017) 最大坡度差P7 (9, 0.33, 0.033) (7, 0.33, 0.033) (5, 0.33, 0.033) (3, 0.33, 0.033) (1, 0.33, 0.033) 最大坡长P8 (1 000, 33.33, 3.333) (850, 16.67, 1.667) (750, 16.67, 1.667) (650, 16.67, 1.667) (300, 100, 10.000) 竖曲线最短长度P9 (10, 3.33, 0.333) (30, 3.33, 0.333) (50, 3.33, 0.333) (70, 3.33, 0.333) (90, 3.33, 0.333) 最小合成坡度P10 (0.15, 0.05, 0.005) (0.4, 0.03, 0.003) (0.75, 0.08, 0.008) (1.5, 0.17, 0.017) (5, 1, 0.100) 最小平纵指标均衡性(竖/平）P11 (10, 3.33, 0.333) (30, 3.33, 0.333) (50, 3.33, 0.333) (70, 3.33, 0.333) (90, 3.33, 0.333) 最小变坡点与平曲线的曲中错位率P12 (70, 10, 1.000) (35, 1.67, 0.167) (25, 1.67, 0.167) (15, 1.67, 0.167) (5, 1.67, 0.167) 大车比例P13 (90, 3.33, 0.333) (70, 3.33, 0.333) (50, 3.33, 0.333) (30, 3.33, 0.333) (10, 3.33, 0.333) 地区不良气候天数P14 (90, 3.33, 0.333) (70, 3.33, 0.333) (50, 3.33, 0.333) (30, 3.33, 0.333) (10, 3.33, 0.333) 超载率P15 (90, 3.33, 0.333) (70,3.33,0.333) (50, 3.33, 0.333) (30, 3.33, 0.333) (10, 3.33, 0.333)
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表 4 试验路段概况
Table 4. Overview of test section
路段 路段长度/km 设计速度/(km/h) 汕昆高速
(阳宗收费站一草甸收费站）8.85 80 杭瑞高速
(彩云收费站一恐龙谷收费站）21.7 80/100 杭瑞高速
(旧县收费站一马龙收费站）18.2 80/100
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表 5 线形单元划分
Table 5. Division of linear elements
线形单元编号 横断面 纵断面 1 直线 直坡 2 直线 坚曲线 3 缓和曲线 直坡 4 缓和曲线 坚曲线 5 圆曲线 直坡 6 圆曲线 坚曲线 7 直线 8 缓和曲线 9 圆曲线
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表 6 驾驶员信息
Table 6. Driver information
编号 年龄/岁 性别 驾龄/年 1 27 男 5 2 30 女 4 3 34 男 11 4 38 男 14 5 31 女 8
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表 7 路段概况及相关数据
Table 7. Road profile and related data
路段 设计速度/ (km/h) 桩号范围 路线长度/km CHVC占比/% 事故统计时间 事故绝对数 Y 80 K24+244—K33+094 8.85 37.4 2015-01—37 4 2020-12 479 C 80 K94+172—K105+852 11.68 42.3 2015-01—42.32020-12 627 H 80 K28+478—K37+268 8.79 44.1 2015-01—44.12020-12 642
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表 8 各路段评估指标值
Table 8. Assessment indicators value of each road section
风险源 评估指标 Y路段 C路段 H路段 驾驶员因素K1 视觉特性（眨眼频率）P1 /(次/10 s) 2.15 2.05 1.95 视觉特性（眨眼频率）P1(转化为评分） 82 78 74 心理、生理特性（HRV) P2/ms2 1 237 1 190 1 126 心理、生理特性(HRV) P2 (转化为评分） 78 75 71 道路条件因素K2 平曲线最小半径P3 /103 m 0.83 1.49 1.16 凹形竖曲线最小半径P4 /103 m 7.58 5.43 5.7 凹形竖曲线最小半径（103 m）P4（转化为评分） 61.66 54.3 57 凸形竖曲线最小半径P5 /103 m 15.05 10.4 11.06 凸形竖曲线最小半径P5/103 m(转化为评分） 53.5 38.5 40.2 最大纵坡(绝对值）P6/(°) 3 3 3.5 最大坡度差P7/(°) 3.5 3 4 最大坡长P8 /m 650 730 680 竖曲线最短长度P9 /m 134.6 113 96.57 竖曲线最短长度P9/m(转化为评分） 44.61 41.73 37.71 最小合成坡度P10 /% 1.2 0.8 0.9 最小平纵指标均衡性（竖/平）P11 13.17 14.83 14.26 最小平纵指标均衡性（竖/平）P11（转化为评分） 52.68 59.32 57.04 最小变坡点与平曲线的曲中错位率P12 /% 1.1 3.9 2.1 交通环境因素K3 大车比例P13 /% 16.38 21.24 18.76 其他因素K4 地区不良气候天数P14/% 14.7 18.5 13.3 超载率P15/% 4.2 6.7 5.6
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表 9 专家可信度评判标准
Table 9. Expert credibility assessment standard
评判因素 权重l 级别 分值q 职称 2 正高级 0.8 副高级 0.6 中级 0.4 学位 1 博士 0.8 硕士 0.6 学士 0.4 工龄/年 4 > 30 0.8 15~30 0.6 < 15 0.4 经历 3 有类似评估经历 0.8 无类似评估经历 0.4
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表 10 各评估指标权重
Table 10. Weighting of each assessment indicator
评估指标 主观权重wj 客观权重wj 组合权重Kj 排序 P1 0.027 2 0.065 0 0.048 4 11 P2 0.027 2 0.052 1 0.040 3 12 P3 0.091 7 0.112 6 0.099 6 3 P4 0.072 6 0.071 7 0.070 0 9 P5 0.090 9 0.080 6 0.083 3 4 P6 0.092 2 0.138 4 0.114 1 1 P7 0.096 3 0.118 2 0.104 6 2 P8 0.076 0 0.092 0 0.081 9 6 P9 0.066 9 0.077 5 0.070 2 8 P10 0.096 4 0.069 2 0.081 4 7 P11 0.104 6 0.060 1 0.082 7 5 P12 0.055 9 0.006 6 0.038 6 13 P13 0.067 8 0.023 2 0.049 2 10 P14 0.016 6 0.027 4 0.022 0 14 P15 0.019 1 0.005 3 0.013 6 15
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表 11 Y路段各评估指标隶属度评判矩阵
Table 11. Assessment matrix of membership degree of each assessment indicator in Section Y
Y路段 E级 D级 C级 B级 A级 P1 0 0 1.07×10-20 0.001 6 0.056 5 P2 0 0 5.12×10-16 0.056 5 0.001 6 P3 0.175 0 7.57×10-4 9.60×10-10 0 0 P4 0 2.82×10-20 0.0022 0.044 0 2.17×10-16 P5 0 1.70×10-11 0.576 9 4.90×10-6 1.04×10-26 P6 2.19×10-8 0.0183 0.0183 2.28×10-16 0 P7 0 3.48×10-24 4.91×10-5 0.332 1 1.07×10-12 P8 0 0 1.56×10-8 1 2.19×10-3 P9 4.34×10-24 6.87×10-5 0.271 3 2.67×10-13 0 P10 0 0 1.43×10-6 0.236 8 8.06×10-4 P11 0 9.29×10-11 0.7243 1.41×10-6 6.85×10-28 P12 0 0 0 1.19×10-15 0.066 9 P13 0 0 9.02×10-23 2.41×10-4 0.1607 P14 0 0 4.98×10-25 2.72×10-5 0.3708 P15 0 0 0 1.04×10-13 0.2208
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表 12 各路段交通风险综合评判向量
Table 12. Comprehensive assessment vector of traffic risk for each road section
路段 E级 D级 C级 B级 A级 最终风险等级 Y 0.0174 0.002 2 0.129 3 0.141 3 0.024 7 B级 C 1.78x10-8 0.105 0 0.1466 0.122 6 0.040 6 C级 H 0.0009 0.1354 0.037 4 0.041 6 0.031 8 D级
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表 13 各路段评估结果对比
Table 13. Comparison of assessment results of each road section
路段 期望值Exr 置信度因子θ 危险指标 较危险指标 Y 3.488 0 0.014 P3 无 C 3.238 4 0.031 无 P3，P5 H 2.870 6 0.027 无 P3，P6，P9
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表 14 不同方法评估结果对比
Table 14. Comparison of assessment results of different methods
路段 可拓云模型 模糊综合评价法 Y B级 B级 C C级 C级 H D级 D级
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