Nonlinear Prediction and Inversion of Civil Engineering Cost of Urban Rail Transit
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摘要:
为解决城市轨道交通土建工程传统造价预测模型缺乏决策信服力的问题,首先,运用特征选择与知识判断方法提取城市轨道交通土建工程造价关键影响因素并建立工程案例数据库;然后,通过粒子群优化(PSO)聚类算法筛选相似案例,采用基于灰狼优化算法(GWO)的极限学习机(ELM)建立土建工程造价非线性预测模型并设计双环境对比实验;最后,将Sobol'全局敏感性分析和Curve Fitting分析用于模型解释性反演,并以成都市轨道交通10号线1期工程为例验证模型优越性. 研究结果表明:模型平均绝对误差与均方根误差分别为0.113 9和0.127 4,平均绝对百分比误差为4.14 %,非线性造价预测模型预测效果优于线性模型,同时采用因素优化与案例聚类方法所得预测效果更好;全局敏感性分析发现,地下线长度和地下车站数的总敏感度明显高于其他因素,可作为方案优化重点调节因素;采用Curve Fitting分析提高了机器学习智能预测模型作用机理“黑箱”效应33.70 %~64.52 %的解释性.
Abstract:The traditional prediction model for the civil engineering cost of urban rail transit lacks decision-making credibility. To address this issue, First, critical factors affecting the civil engineering cost of urban rail transit were retrieved utilizing the feature selection and knowledge judgment methods, and an engineering case database was created. Then, similar cases were screened using the particle swarm optimization (PSO) clustering algorithm, and a nonlinear prediction model of civil engineering cost was established using the extreme learning machine (ELM) based on gray wolf optimization (GWO), followed by a dual environment comparison experiment. Finally, Sobol’s global sensitivity analysis and curve fitting analysis were conducted to invert the model and validate its superiority by using the Chengdu Rail Transit Line 10 Phase 1 Project as an example. The results show that the prediction model’s mean absolute error and root mean square error are 0.113 9 and 0.127 4, respectively, and the mean absolute percentage error is 4.14%. The prediction effect of the nonlinear cost prediction model is better than that of the linear model, and the better prediction effect is obtained by simultaneously using the factor optimization and case clustering methods. The global sensitivity study reveals that the total sensitivity of the subterranean line length and the number of underground stations is much larger than the other factors, making them the major factors to be adjusted for the scheme optimization. The “black box” effect of intelligent predictive modeling mechanism based on machine learning is better understood by 33.70%–64.52% when curve fitting analysis is used.
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Key words:
- urban rail transit /
- civil engineering /
- cost prediction /
- GWO-ELM model /
- anti-analysis
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表 1 全局敏感性分析结果
Table 1. Global sensitivity analysis results
影响因素 地下线长度 高架线长度 地下车站数 地上车站数 平均站距 编组 工程环境及
地质条件国内生产总值 居民消费
价格指数总敏感度 0.653 6 0.060 3 0.223 6 0.012 4 0.008 3 0.019 3 0.000 8 0.003 1 0.018 2 表 2 线性拟合函数式及其对比
Table 2. Linear fitting functions and their comparison
影响因素 拟合函数式 拟合函数式影响因素
与土建造价相关性原始数据中影响因素
与土建造价相关性对比结果 地下线长度 f(x)=0.007 1x + 2.179 0 正相关 0.203 1(正相关) 一致 高架线长度 f(x)=−0.059 2x + 2.467 0 负相关 −0.498 8(负相关) 一致 地下车站数 f(x)=0.014 0x + 2.114 0 正相关 0.255 4(正相关) 一致 地上车站数 f(x)=−0.101 4x + 2.455 0 负相关 −0.443 6(负相关) 一致 平均站距 f(x)= −0.073 3x + 2.491 0 负相关 −0.167 1(负相关) 一致 编组 f(x)= 0.080 2x + 1.781 0 正相关 0.266 0(正相关) 一致 工程环境及地质条件 f(x)= 0.065 4x + 2.205 0 正相关 0.127 0(正相关) 一致 国内生产总值 f(x)= 0.000 1x + 2.202 0 正相关 0.253 5(正相关) 一致 居民消费价格指数 f(x)= 0.039 1x−1.636 0 正相关 0.138 8(正相关) 一致 表 3 各因素最优拟合函数式
Table 3. Optimal fitting function of each factor
影响因素 拟合函数式 R2 地下线长度 f(x)=2.317 0-0.216 0 cos(0.142 6x)-0.113 9 sin(0.142 6x) + 0.153 4 cos(0.285 2x) + 0.048 5 sin(0.285 2x) + 0.247 2 cos(0.427 8x) + 0.125 4 sin(0.427 8x) + 0.007 9 cos(0.570 4x)-0.085 2 sin(0.570 4x) + 0.214 8 cos(0.713 0x) + 0.007 5 sin(0.713 0x)-0.042 0 cos(0.855 6x) + 0.009 1 sin(0.855 6x) + 0.025 3 cos(0.998 2x)-0.164 8 sin(0.998 2x)-0.089 6 cos(1.140 8x) + 0.066 4 sin(1.140 8x) 0.645 2 高架线长度 f(x)=-6 409 + 104 cos(0.998 9x) + 8 473 sin(0.998 9x)-2 120 cos(1.997 8x)-12 500 sin(1.997 8x)-5 779 cos(2.996 7x) + 8 477 sin(2.996 7x) + 7 112 cos(3.995 6x)-720.100 0 sin(3.995 6x)-3 340 cos(4.994 5x)-2 932 sin(4.994 5x) + 463.200 0 cos(5.993 4x) + 1 899 sin(5.993 4x) + 74.800 0 cos(6.992 3x)-395.100 0 sin(6.992 3x) 0.488 5 地下车站数 f(x)=-3.368 0 109 + 5.946 0 109 cos(0.046 2x) + 2.665 0 109 sin(0.046 2x)-3.327 0 109 cos(0.092 4x)-4.480 0 109 sin(0.092 4x) + 1.306 0 108 cos(0.138 6x) + 3.879 0 109 sin(0.138 6x) + 1.234 0 109 cos(0.184 8x)-1.667 0 109 sin(0.184 8x)-7.959 0 108 cos(0.231 0x) + 1.796 0 108 sin(0.231 0x) + 1.940 0 108 cos(0.277 2x) + 1.099 0 108 sin(0.277 2x)-1.126 0 107 cos(0.323 4x)-3.620 0 107 sin(0.323 4x)-1.356 0 106 cos(0.369 6x) + 2.710 0 106 sin(0.369 6x) 0.486 8 地上车站数 f(x)=0.007 9x5-0.139 2x4 + 0.823 5x3-1.875 0x2 + 1.143 0x + 2.530 0 0.337 0 平均站距 f(x)=3.088 0 1011 + 1.954 0 1010 cos(0.811 8x)-5.568 0 1011 sin(0.811 8x)-4.067 0 1011 cos(1.623 6x)-2.742 0 1010 sin(1.623 6x)-2.242 0 1010 cos(2.435 4x) + 2.381 0 1011 sin(2.435 4x) + 1.096 0 1011 cos(3.247 2x) + 1.231 0 1010 sin(3.247 2x) + 4.558 0 109 cos(4.059 0x)-3.827 0 1010 sin(4.059 0x)-9.559 0 109 cos(4.870 8x)-1.067 0 109 sin(4.870 8x)-1.333 0 108 cos(5.682 6x) + 1.521 0 109 sin(5.682 6x) + 1.157 0 108 cos(6.494 4x) + 5.302 0 106 sin(6.494 4x) 0.579 1 编组 f(x)=-0.008 9x4 + 0.226 1x3-2.071 0x2 + 8.206 0x-9.692 0 0.089 3 工程环境及
地质条件f(x)=2.320 0-0.266 6cos(1.571 0x)-0.118 8 sin(1.571 0x) 0.068 9 国内生产总值 f(x)=1.751 0 + 0.189 1 cos(2.361 0x)-1.345 0 sin(2.361 0x) + 1.109 0 cos(4.722 0x) + 0.535 3 sin(4.722 0x)-1.252 0 cos(7.083 0x) + 0.429 1 sin(7.083 0x) + 1.131 0 cos(9.444 0x)-0.997 2 sin(9.444 0x)-0.349 1 cos(11.805 0x) + 1.747 0 sin(11.805 0x)-0.817 2 cos(14.166 0x)-1.829 0 sin(14.166 0x) + 1.257 0 cos(16.527 0x) + 0.705 4 sin(16.527 0x)-0.434 9 cos(18.888 0x) + 0.305 6 sin(18.888 0x) 0.526 1 居民消费价格指数 f(x)=2.185 0 + 0.058 3 cos(5.835 0x)-0.145 6 sin(5.835 0x)-0.203 1 cos(11.670 0x) + 0.237 2 sin(11.670 0x) + 0.050 6 cos(17.505 0x) + 0.138 8 sin(17.505 0x) + 0.106 0 cos(23.340 0x)-0.051 0 sin(23.340 0x) + 0.179 2 cos(29.175 0x)-0.239 2 sin(29.175 0x)-0.027 0 cos(35.010 0x) + 0.246 6 sin(35.010 0x) + 0.021 3 cos(40.845 0x)-0.346 3 sin(40.845 0x) + 0.231 5 cos(46.680 0x)-0.089 9 sin(46.680 0x) 0.486 7 -
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