城市轨道交通土建工程造价非线性预测与反演

孟春成; 亐道远; 段晓晨

doi:10.3969/j.issn.0258-2724.20230209

城市轨道交通土建工程造价非线性预测与反演

doi: 10.3969/j.issn.0258-2724.20230209

1.
石家庄铁道大学管理学院，河北石家庄 050043
2.
石家庄铁道大学经济与法律学院，河北石家庄 050043

基金项目: 国家自然科学基金项目（72071133）

详细信息

作者简介:
孟春成（1996—），男，博士研究生，研究方向为工程管理，E-mail：2202203001@student.stdu.edu.cn

通讯作者:
段晓晨（1962—），男，教授，博士生导师，研究方向为工程经济与造价管理，E-mail：duanxch888@sohu.com

中图分类号: U121
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- 文章访问数: 216
- HTML全文浏览量: 56
- PDF下载量: 42
- 被引次数: 0
出版历程
- 收稿日期: 2023-05-04
- 修回日期: 2023-11-27
- 网络出版日期: 2024-07-25
- 刊出日期: 2023-12-05

Nonlinear Prediction and Inversion of Civil Engineering Cost of Urban Rail Transit

1.
School of Management, Shijiazhuang Tiedao University, Shijiazhuang 050043, China
2.
School of Economics and Law, Shijiazhuang Tiedao University, Shijiazhuang 050043, China

摘要

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.
- 城市轨道交通 /
- 土建工程 /
- 造价预测 /
- GWO-ELM模型 /
- 反分析
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 optimizer (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.
- urban rail transit /
- civil engineering /
- cost prediction /
- GWO-ELM model /
- anti-analysis

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图 1 因素自变量与造价因变量间的拟合关系

Figure 1. Fitting relationship between independent variable of factor and dependent variable of cost

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图 2 模型建构与优化流程

Figure 2. Model construction and optimization process

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图 3 训练集对比

Figure 3. Comparison of training sets

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图 4 检验集对比

Figure 4. Comparison of test sets

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图 5 不同模型相同环境下性能对比

Figure 5. Performance comparison of different models in the same environment

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图 6 相同模型不同环境下性能对比

Figure 6. Performance comparison of same model in different environments

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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

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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

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表 3 各因素最优拟合函数式

Table 3. Optimal fitting functions of different factors

影响因素	拟合函数式	R²
地下线长度	f(x)=2.317 0 − 0.216 0cos 0.142 6x − 0.113 9sin 0.142 6x + 0.153 4cos 0.285 2x + 0.048 5 × sin 0.285 2x + 0.247 2cos 0.427 8x + 0.125 4sin 0.427 8x + 0.007 9cos 0.570 4x − 0.085 2 × sin 0.570 4x + 0.214 8cos 0.713 0x + 0.007 5sin 0.713 0x − 0.042 0cos 0.855 6x + 0.009 1 × sin 0.855 6x + 0.025 3cos 0.998 2x − 0.164 8sin 0.998 2x − 0.089 6cos 1.140 8x + 0.066 4sin 1.140 8x	0.645 2
高架线长度	f(x)=− 6 409 + 10⁴cos 0.998 9x + 8 473sin 0.998 9x − 2 120cos 1.997 8x − 12 500sin 1.997 8x − 5 779cos 2.996 7x + 8 477sin 2.996 7x + 7 112cos 3.995 6x − 720.100 0sin 3.995 6x − 3 340cos 4.994 5x − 2 932sin 4.994 5x + 463.200 0cos 5.993 4x + 1 899sin 5.993 4x + 74.800 0cos 6.992 3x − 395.100 0sin 6.992 3x	0.488 5
地下车站数	f(x)=− 3.368 0 10⁹ + 5.946 0 10⁹cos 0.046 2x + 2.665 0 10⁹sin 0.046 2x − 3.327 0 10⁹cos 0.092 4x − 4.480 0 10⁹sin 0.092 4x + 1.306 0 10⁸cos 0.138 6x + 3.879 0 10⁹sin 0.138 6x + 1.234 0 10⁹cos 0.184 8x − 1.667 0 10⁹sin 0.184 8x − 7.959 0 10⁸cos 0.231 0x + 1.796 0 10⁸sin 0.231 0x + 1.940 0 10⁸cos 0.277 2x + 1.099 0 10⁸sin 0.277 2x − 1.126 0 10⁷cos 0.323 4x − 3.620 0 10⁷sin 0.323 4x − 1.356 0 10⁶cos 0.369 6x + 2.710 0 10⁶sin 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 10¹⁰cos 0.811 8x − 5.568 0 10¹¹sin 0.811 8x − 4.067 0 10¹¹cos 1.623 6x − 2.742 0 10¹⁰sin 1.623 6x − 2.242 0 10¹⁰cos 2.435 4x + 2.381 0 10¹¹sin 2.435 4x + 1.096 0 10¹¹cos 3.247 2x + 1.231 0 10¹⁰sin 3.247 2x + 4.558 0 10⁹cos 4.059 0x − 3.827 0 10¹⁰sin 4.059 0x − 9.559 0 10⁹cos 4.870 8x − 1.067 0 10⁹sin 4.870 8x − 1.333 0 10⁸cos 5.682 6x + 1.521 0 10⁹sin 5.682 6x + 1.157 0 10⁸cos 6.494 4x + 5.302 0 10⁶sin 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 8sin 1.571 0x	0.068 9
国内生产总值	f(x)=1.751 0 + 0.189 1cos 2.361 0x − 1.345 0sin 2.361 0x + 1.109 0cos 4.722 0x + 0.535 3sin 4.722 0x − 1.252 0cos 7.083 0x + 0.429 1sin 7.083 0x + 1.131 0cos 9.444 0x − 0.997 2sin 9.444 0x − 0.349 1cos 11.805 0x + 1.747 0sin 11.805 0x − 0.817 2cos 14.166 0x − 1.829 0sin 14.166 0x + 1.257 0cos 16.527 0x + 0.705 4sin 16.527 0x − 0.434 9cos 18.888 0x + 0.305 6sin 18.888 0x	0.526 1
居民消费价格指数	f(x)=2.185 0 + 0.058 3cos 5.835 0x − 0.145 6sin 5.835 0x − 0.203 1cos 11.670 0x + 0.237 2sin 11.670 0x + 0.050 6cos 17.505 0x + 0.138 8sin 17.505 0x + 0.106 0cos 23.340 0x − 0.051 0sin 23.340 0x + 0.179 2cos 29.175 0x − 0.239 2sin 29.175 0x − 0.027 0cos 35.010 0x + 0.246 6sin 35.010 0x + 0.021 3cos 40.845 0x − 0.346 3sin 40.845 0x + 0.231 5cos 46.680 0x − 0.089 9sin 46.680 0x	0.486 7

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