基于群智算法优化的ME车辙预测模型

刘佳佳; 李卓轩; 张伟光; 曹进德

doi:10.21656/1000-0887.460045

基于群智算法优化的ME车辙预测模型

doi: 10.21656/1000-0887.460045

刘佳佳^1,,
李卓轩^{1, 2,},
张伟光^3,,
曹进德^{1, 2, ,}

1.
东南大学数学学院，南京 211189
2.
中华人民共和国交通运输部综合交通运输理论交通运输行业重点实验室(南京现代综合交通实验室), 南京 211135
3.
东南大学交通学院，南京 210096

(我刊编委曹进德来稿)

基金项目:

国家重点研发计划 2020YFA0714300

南京现代综合交通实验室开放课题 MTF2023004

详细信息

作者简介:
刘佳佳(2001—)，女，硕士生(E-mail: 3046838001@qq.com)

李卓轩(1997—)，男，博士生(E-mail: 230229338@seu.edu.cn)

张伟光(1986—)，男，副教授(E-mail: wgzhang@seu.edu.cn)

通讯作者:
曹进德(1963—)，男，教授(通信作者. E-mail: jdcao@seu.edu.cn)

中图分类号: U416.217; TP18
计量
- 文章访问数: 49
- HTML全文浏览量: 13
- PDF下载量: 19
- 被引次数: 0
出版历程
- 收稿日期: 2025-03-10
- 修回日期: 2025-04-22
- 刊出日期: 2026-05-01

Optimization of the ME Rutting Depth Prediction Model Using Swarm Intelligence Algorithms

LIU Jiajia^1
,,
LI Zhuoxuan^{1, 2
,},
ZHANG Weiguang^3
,,
CAO Jinde^{1, 2
, ,}

1.
School of Mathematics, Southeast University, Nanjing 211189, P. R. China
2.
Key Laboratory of Transport Industry of Comprehensive Transportation Theory (Nanjing Modern Multimodal Transportation Laboratory), Ministry of Transport of the People's Republic of China, Nanjing 211135, P. R. China
3.
School of Transportation, Southeast University, Nanjing 210096, P. R. China

(Contributed by CAO Jinde, Member of the Editorial Board of AMM)

摘要

摘要: 车辙，作为沥青路面的一种常见病害，不仅影响着道路的行驶质量和安全性，还在许多国家沥青路面结构设计中占据着举足轻重的地位. 为了更准确地预测和评估车辙的演变趋势，对现有车辙预测模型进行改进和优化显得尤为重要. 因此，基于RIOHTrack足尺路面加速加载试验环道长期观测数据，对《公路沥青路面设计规范》(JTG D50—2017)中的力学经验车辙性能预测模型进行了全面的调整和优化，引入三个校准参数，分别对常数项系数、温度和累计载荷次数进行校准，以提升模型的预测准确性和泛化能力. 接着，提出了一种多策略自适应粒子群算法，引入邻域突变策略，并融合指数自适应惯性权重和正弦自适应学习因子，有效平衡了局部搜索和全局搜索的能力，使得粒子可以更高效地找到最优解. 使用该算法求解三个校准参数的值，进一步提升模型的精准度. 最后，以RIOHTrack中19种沥青路面的车辙数据为例，使用本文提出的MAPSO-RME模型进行车辙预测. 实验发现，相对于《公路沥青路面设计规范》(JTG D50—2017)中的力学经验车辙预测模型，其拟合性能显著提升，模型预测均方误差MSE大幅降低.
- 沥青路面 /
- 车辙 /
- 参数校准 /
- 多策略自适应粒子群算法
Abstract: Rutting, a common disease of asphalt pavement, not only compromises the road quality and safety, but also plays a critical role in the structural design of asphalt pavement in many countries. To achieve more accurate prediction and evaluation of rutting evolution trends, it is particularly important to improve and optimize the existing rutting depth prediction model. Therefore, based on the long-term observation data of the RIOHTrack full-scale pavement acceleration loading test loop, the mechanical-empirical rutting depth prediction model in the Highway Asphalt Pavement Design Specifications (JTG D50—2017) was comprehensively adjusted and optimized. Three calibration parameters were introduced to calibrate the constant coefficients, temperatures, and cumulative load times, respectively, to improve the prediction accuracy and generalization ability of the model. Subsequently, a multi-strategy adaptive particle swarm optimization (MAPSO) algorithm incorporating a neighborhood mutation strategy and fusing exponential adaptive inertia weights with sinusoidal adaptive learning factors, was proposed. Then this algorithm was used to estimate the values of three calibration parameters to further improve the accuracy of the model. Finally, with the rutting data of 19 types of asphalt pavements in the RIOHTrack as an example, the MAPSO-RME model proposed in this article was applied for rutting depth prediction. The experimental results demonstrate that, compared with the mechanical-empirical rutting depth prediction model in the Highway Asphalt Pavement Design Specifications (JTG D50—2017), the MAPSO-RME model achieves remarkable improvement in fitting performance with a significant reduction in mean squared error (MSE) of prediction.
- asphalt pavement /
- rutting /
- parameter calibration /
- multi-strategy adaptive particle swarm optimization
edited-by

edited-by
注释:

1) (我刊编委曹进德来稿)

HTML全文

图 1 自适应学习因子c₁和c₂变化曲线

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 1. Change curves of adaptive c₁, c₂

下载: 全尺寸图片幻灯片

图 2 自适应惯性权重变化曲线

Figure 2. The change curve of adaptive w

下载: 全尺寸图片幻灯片

图 3 RIOHTrack的路段布局和不同测试路段的结构

Figure 3. The layout and structure of RIOHTrack

下载: 全尺寸图片幻灯片

图 4 使用不同PSO算法校准参数时RME车辙模型预测箱线图

Figure 4. The boxplots of the RME rutting model with different PSO algorithms

下载: 全尺寸图片幻灯片

图 5 传统ME与MAPSO-RME模型车辙数据拟合图

Figure 5. Fitting diagram of rutting data for the traditional ME and MAPSO-RME models

下载: 全尺寸图片幻灯片

表 1 RIOHTrack原始车辙数据(rutting/mm)

Table 1. Original rutting data of RIOHTrack (rutting/mm)

loading date	cycle number	STR1	STR2	…	STR19
2016-11-30—2016-12-10	N1	1.556	1.567	…	1.844
2016-12-13—2016-12-24	N2	1.585	1.598	…	1.704
2016-12-27—2017-01-09	N3	1.495	1.481	…	1.857
2017-01-12—2017-02-23	N4	1.515	1.636	…	1.892
2017-02-26—2017-03-10	N5	0.633	0.853	…	0.848
2017-03-13—2017-03-23	N6	1.529	1.656	…	1.881
					
2023-11-09—2023-11-20	N157-mid	9.477	10.326	…	7.347
2023-11-30	N157	6.819	10.696	…	7.071
2023-11-25—2023-12-05	N158-mid	8.465	10.336	…	5.203
2023-12-19	N158	7.684	10.614	…	7.827
2023-12-10—2023-12-24	N159	8.558	10.689	…	6.543

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表 2 使用不同PSO算法校准参数时RME车辙模型预测MSE

Table 2. MSE of the RME rutting model with different PSO algorithms

structure	STR	dataset	PSO	PSO-w	PSO-c	PSO-cw	MAPSO
semi-rigid base	1	training set	0.410 595	0.185 487	0.203 388	0.178 934	0.152 480
		validation set	0.696 990	0.582 992	0.596 342	0.563 521	0.530 709
		test set	2.509 542	1.177 000	1.474 362	1.221 109	0.967 856
	2	training set	0.606 712	0.412 764	0.253 175	0.209 692	0.166 210
		validation set	0.912 542	0.659 501	0.842 561	0.703 448	0.564 336
		test set	4.624 047	2.848 571	2.979 764	2.420 495	1.861 227
	3	training set	0.425 854	0.390 227	0.209 142	0.202 680	0.196 218
		validation set	0.877 747	0.729 117	0.965 374	0.837 196	0.709 018
		test set	3.169 630	1.315 188	1.194 343	1.374 164	1.553 986
	6	training set	0.516 525	0.865 394	0.258 599	0.258 599	0.258 600
		validation set	0.988 402	0.712 187	1.570 256	1.140 831	0.711 407
		test set	2.715 440	2.239 869	1.114 442	1.121 091	1.127 740
	7	training set	1.134 145	0.553 150	0.362 448	0.362 255	0.362 062
		validation set	1.736 897	0.932 510	1.050 403	0.992 835	0.935 268
		test set	3.799 113	1.899 565	0.782 371	0.776 644	0.770 918
	8	training set	1.553 299	0.691 531	0.410 541	0.402 776	0.395 011
		validation set	1.715 339	1.052 580	1.331 017	1.210 249	1.089 482
		test set	5.949 349	3.498 445	1.564 804	1.333 661	1.102 519
	9	training set	0.882 199	1.019 762	0.413 015	0.392 358	0.371 702
		validation set	1.573 723	0.946 857	1.806 158	1.401 802	0.997 447
		test set	3.765 739	2.775 897	1.338 344	1.196 726	1.055 109
composite base	4	training set	0.451 810	0.338 917	0.342 544	0.340 038	0.337 533
		validation set	0.728 057	0.603 934	0.588 322	0.595 650	0.602 979
		test set	2.374 773	1.245 610	1.231 211	1.265 825	1.300 439
	5	training set	0.407 643	0.256 997	0.235 612	0.235 594	0.235 576
		validation set	0.927 610	0.778 510	0.740 710	0.740 252	0.739 794
		test set	2.108 517	0.614 362	0.922 068	0.928 251	0.934 434
inverted base	10	training set	1.247 075	0.651 788	0.424 257	0.424 231	0.424 206
		validation set	1.737 176	1.260 077	1.096 066	1.095 811	1.095 556
		test set	2.791 466	1.431 539	0.430 544	0.430 167	0.429 791
	12	training set	0.755 677	0.377 483	0.375 019	0.367 551	0.360 083
		validation set	1.334 464	0.991 834	1.009 769	1.019 796	1.029 823
		test set	1.892 574	1.394 988	1.273 527	1.257 019	1.240 511
thick asphalt mixture	11	training set	0.980 259	0.274 138	0.277 521	0.274 496	0.271 471
		validation set	1.598 245	1.016 558	1.021 496	1.023 717	1.025 939
		test set	3.625 655	0.944 324	0.954 184	0.906 389	0.858 595
	13	training set	0.482 084	0.215 051	0.214 200	0.213 234	0.212 268
		validation set	0.968 232	0.711 305	0.725 866	0.721 866	0.717 867
		test set	1.332 715	1.068 594	1.053 880	0.881 943	0.710 006
	14	training set	0.919 257	2.194 195	0.488 585	0.488 584	0.488 584
		validation set	1.438 904	3.026 559	0.992 537	0.992 513	0.992 489
		test set	1.057 984	2.576 982	0.777 095	0.677 353	0.577 611
	15	training set	0.764 079	0.356 896	0.225 591	0.224 920	0.224 249
		validation set	1.272 832	0.940 174	0.835 076	0.834 197	0.833 318
		test set	1.596 950	1.413 084	1.396 155	1.351 480	1.306 806
	16	training set	0.608 094	0.284 710	0.273 694	0.273 691	0.273 689
		validation set	1.028 781	0.686 561	0.699 881	0.699 583	0.699 285
		test set	1.733 118	1.539 418	1.400 808	1.402 209	1.403 611
	17	training set	0.550 707	0.390 883	0.291 573	0.289 111	0.286 650
		validation set	0.847 637	0.730 998	0.585 582	0.578 780	0.571 979
		test set	1.012 510	0.702 791	0.764 194	0.722 844	0.681 495
full-depth structure	18	training set	1.340 227	0.738 468	0.625 697	0.449 693	0.273 689
		validation set	1.454 363	1.040 647	0.517 088	0.608 186	0.699 285
		test set	2.683 918	0.860 402	1.123 262	0.961 056	0.798 851
	19	training set	0.508 108	0.319 305	0.316 766	0.316 469	0.316 172
		validation set	0.893 133	0.780 262	0.773 359	0.773 730	0.774 101
		test set	1.288 807	0.524 418	0.461 374	0.488 395	0.515 417
mean value	1-19	training set	0.765 492	0.326 387	0.553 534	0.310 785	0.310 075
		validation set	1.196 372	0.811 559	1.089 961	0.870 209	0.801 145
		test set	2.633 255	0.901 943	1.387 940	1.090 359	0.779 180

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表 3 MAPSO-RME与其他车辙模型预测MSE

Table 3. MSE of MAPSO-RME and other rutting depth prediction models

structure	STR	dataset	conventional ME	MEPDG	ALF	MAPSO-RME
semi-rigid base	1	training set	3.028 442	3.220 613	4.558 947	0.152 479
		validation set	3.354 868	3.476 885	4.660 625	0.530 709
		test set	7.871 037	8.784 877	11.996 429	0.967 855
	2	training set	5.035 846	5.373 725	7.524 113	0.166 209
		validation set	5.187 335	5.436 588	7.334 865	0.564 335
		test set	12.489 605	14.480 936	19.786 438	1.861 226
	3	training set	4.200 122	4.133 276	5.785 925	0.196 217
		validation set	4.644 348	4.548 648	6.066 975	0.709 017
		test set	8.951 187	9.881 610	13.793 160	1.553 985
	6	training set	3.851 698	3.912 073	5.471 450	0.258 599
		validation set	4.605 777	4.585 073	6.072 855	0.711 406
		test set	8.568 350	9.525 019	13.199 786	1.127 739
	7	training set	9.181 578	9.733 199	13.474 390	0.362 061
		validation set	9.123 794	9.457 739	12.786 435	0.935 267
		test set	18.169 156	20.029 062	28.020 197	0.770 917
	8	training set	12.190 578	13.114 549	17.864 043	0.395 010
		validation set	12.072 149	12.829 842	17.080 704	1.089 481
		test set	25.204 567	28.628 111	39.376 308	1.102 518
	9	training set	6.695 091	6.958 968	9.569 548	0.371 701
		validation set	7.276 596	7.378 902	9.768 586	0.997 446
		test set	13.834 582	15.589 380	21.664 890	1.055 108
composite base	4	training set	2.384 208	2.298 905	3.132 093	0.337 532
		validation set	3.096 253	3.002 693	3.855 451	0.602 978
		test set	5.716 098	6.388 276	8.682 817	1.300 438
	5	training set	3.130 139	3.087 029	4.298 696	0.235 576
		validation set	4.091 722	4.032 026	5.240 113	0.739 793
		test set	6.591 538	7.237 353	10.104 716	0.934 434
inverted base	10	training set	9.858 078	10.559 385	14.721 283	0.424 205
		validation set	10.173 588	10.479 296	14.155 547	1.095 555
		test set	18.439 777	19.492 381	27.630 661	0.429 790
	12	training set	6.654 381	6.828 003	9.563 298	0.360 082
		validation set	7.561 562	7.462 090	9.994 335	1.029 822
		test set	12.120 562	12.274 365	17.467 073	1.240 511
thick asphalt mixture	11	training set	8.495 938	9.050 297	12.662 660	0.271 471
		validation set	9.100 457	9.356 417	12.565 171	1.025 939
		test set	17.356 242	18.876 424	26.457 632	0.858 594
	13	training set	4.662 731	4.631 565	6.501 461	0.212 267
		validation set	5.319 145	5.171 455	6.923 511	0.717 866
		test set	7.352 789	7.553 253	11.084 846	0.710 006
	14	training set	7.039 255	7.123 291	9.966 689	0.488 583
		validation set	7.551 967	7.317 617	9.933 316	0.992 488
		test set	11.478 991	11.088 329	16.034 980	0.577 611
	15	training set	7.632 578	7.900 890	11.054 452	0.224 248
		validation set	7.466 344	7.589 090	10.355 889	0.833 317
		test set	12.051 865	12.430 074	18.060 955	1.306 805
	16	training set	5.671 963	5.695 424	7.906 122	0.273 688
		validation set	5.853 698	5.768 754	7.767 493	0.699 284
		test set	9.810 330	10.187 734	14.532 253	1.403 611
	17	training set	5.550 707	6.291 573	6.390 883	0.286 650
		validation set	6.847 637	6.585 582	6.730 998	0.571 979
		test set	10.831 145	11.403 217	15.675 145	0.681 495
full-depth structure	18	training set	8.340 227	8.625 697	9.738 468	0.273 689
		validation set	9.135 367	9.594 851	13.285 677	0.699 285
		test set	18.337 959	19.304 372	27.317 153	0.798 851
	19	training set	3.629 191	3.594 874	4.946 199	0.316 171
		validation set	4.196 426	4.177 939	5.464 795	0.774 100
		test set	6.105 749	6.265 470	8.901 877	0.515 416

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基于群智算法优化的ME车辙预测模型

doi: 10.21656/1000-0887.460045

作者简介:
刘佳佳(2001—)，女，硕士生(E-mail: 3046838001@qq.com)

李卓轩(1997—)，男，博士生(E-mail: 230229338@seu.edu.cn)

张伟光(1986—)，男，副教授(E-mail: wgzhang@seu.edu.cn)

通讯作者:
曹进德(1963—)，男，教授(通信作者. E-mail: jdcao@seu.edu.cn)

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Optimization of the ME Rutting Depth Prediction Model Using Swarm Intelligence Algorithms

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留言板

基于群智算法优化的ME车辙预测模型

doi: 10.21656/1000-0887.460045

作者简介: 刘佳佳(2001—)，女，硕士生(E-mail: 3046838001@qq.com) 李卓轩(1997—)，男，博士生(E-mail: 230229338@seu.edu.cn) 张伟光(1986—)，男，副教授(E-mail: wgzhang@seu.edu.cn)

通讯作者: 曹进德(1963—)，男，教授(通信作者. E-mail: jdcao@seu.edu.cn)

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出版历程

Optimization of the ME Rutting Depth Prediction Model Using Swarm Intelligence Algorithms

计量

出版历程

目录

作者简介:
刘佳佳(2001—)，女，硕士生(E-mail: 3046838001@qq.com)

李卓轩(1997—)，男，博士生(E-mail: 230229338@seu.edu.cn)

张伟光(1986—)，男，副教授(E-mail: wgzhang@seu.edu.cn)

通讯作者:
曹进德(1963—)，男，教授(通信作者. E-mail: jdcao@seu.edu.cn)