China Safety Science Journal ›› 2026, Vol. 36 ›› Issue (7): 199-206.doi: 10.16265/j.cnki.issn1003-3033.2026.07.1583
• Public Safety and Emergency Management • Previous Articles Next Articles
Chen Yuguang1,2(
), Hai Lingtao1, Yang Bin1, Guo Yanyong2, Xiao Haicheng1,**(
)
Received:2026-02-03
Revised:2026-05-10
Online:2026-07-28
Published:2027-01-28
Contact:
Xiao Haicheng
CLC Number:
Chen Yuguang, Hai Lingtao, Yang Bin, Guo Yanyong, Xiao Haicheng. ISMA-BP neural network algorithm for vehicle operation risk prediction[J]. China Safety Science Journal, 2026, 36(7): 199-206.
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URL: http://www.cssjj.com.cn/EN/10.16265/j.cnki.issn1003-3033.2026.07.1583
Table 1
CEC2017 test function
| 表达式 | 范围 | 维数 | 最优值 |
|---|---|---|---|
| ${f}_{1}=\sum _{i=1}^{n-1}\left(\mathrm{s}\mathrm{i}{\mathrm{n}}^{2}\left(\sqrt{{x}_{i}^{2}+{x}_{i+1}^{2}}\right)-0.5\right)+1$ | [-10,10] | 30/30/800 | 0 |
| ${f}_{2}=\frac{1}{4\mathrm{ }000}\sum _{i=1}^{n}{x}_{i}^{2}-{\prod }_{i=1}^{n}\mathrm{c}\mathrm{o}\mathrm{s}\left({x}_{i}/\sqrt{i}\right)+1$ | [-20,20] | 30/30/800 | 0 |
| ${f}_{3}=10n+\sum _{i=1}^{n}[{x}_{i}^{2}-10\mathrm{c}\mathrm{o}\mathrm{s}\left(2\mathrm{\pi }{x}_{i}\right)]$ | [-10,10] | 30/30/800 | 0 |
| ${f}_{4}=-20\mathrm{e}\mathrm{x}\mathrm{p}\left(0.2\sqrt{\frac{1}{n}\sum _{i=1}^{n}{x}_{i}^{2}}\right)-\mathrm{e}\mathrm{x}\mathrm{p}\left(\sum _{i=1}^{n}\mathrm{c}\mathrm{o}\mathrm{s}\right(2\mathrm{\pi }{x}_{i}\left)\right)+20+\mathrm{e}$ | [-30,30] | 30/30/800 | 0 |
| $\begin{array}{l}{f}_{5}=\mathrm{s}\mathrm{i}{\mathrm{n}}^{2}\left(\pi {w}_{1}\right)+\sum _{i=1}^{n-1}({w}_{i}-1\left)\right[1+10\mathrm{s}\mathrm{i}{\mathrm{n}}^{2}(\pi {w}_{1}+1)]+\\ \left({w}_{n}{-1)}^{2}\right[1+\mathrm{s}\mathrm{i}{\mathrm{n}}^{2}\left(2\pi {w}_{n}\right)],{w}_{i}=\frac{3+{X}_{i}}{4}\end{array}$ | [-30,30] | 30/30/800 | 0 |
| ${f}_{6}=\sum _{i=1}^{n}{x}_{i}^{2}$ | [-10,10] | 30/30/800 | 0 |
Table 2
Optimization results of ablation experiment function
| 测试函数 | 误差指标 | G1 | G2 | G3 | G4 |
|---|---|---|---|---|---|
| f1 | M | 2. 039 7 | 0. 788 0 | 0. 502 0 | 0. 500 1 |
| S | 0. 352 5 | 0. 077 7 | 0. 000 9 | 0. 000 3 | |
| f2 | M | 1. 659 9 | 1. 673 2 | 0. 000 8 | 0. 000 5 |
| S | 0. 040 6 | 0. 033 0 | 0. 000 7 | 0. 000 5 | |
| f3 | M | 931. 289 4 | 948. 473 7 | 0. 001 0 | 0. 000 9 |
| S | 70. 572 2 | 49. 289 1 | 0. 000 4 | 0. 000 5 | |
| f4 | M | 20. 159 0 | 20. 210 8 | 0. 001 1 | 0. 000 8 |
| S | 0. 148 8 | 0. 200 9 | 0. 000 8 | 0. 000 4 | |
| f5 | M | 1 745. 266 3 | 1 620. 807 0 | 2. 138 8 | 1. 962 5 |
| S | 408. 265 8 | 316. 976 5 | 0. 067 9 | 0. 048 4 | |
| f6 | M | 671. 428 2 | 555. 231 3 | 0. 004 1 | 0. 002 3 |
| S | 34. 315 2 | 33. 728 7 | 0. 001 8 | 0. 001 5 |
Table 3
Multiple algorithm optimization results
| 测试函数 | 误差指标 | PSO | SO | BA | GWO | ISMA |
|---|---|---|---|---|---|---|
| f1 | M | 0. 801 2 | 0. 769 8 | 0. 787 0 | 1. 493 8 | 0. 500 0 |
| S | 0. 141 2 | 0. 035 8 | 0. 139 9 | 0. 396 8 | 0. 000 3 | |
| f2 | M | 0. 039 1 | 0. 983 7 | 0. 273 6 | 0. 004 4 | 0. 001 3 |
| S | 0. 026 4 | 0. 077 6 | 0. 041 5 | 0. 005 5 | 0. 003 1 | |
| f3 | M | 80. 359 8 | 324. 510 7 | 328. 730 8 | 38. 935 4 | 0. 002 1 |
| S | 20. 931 0 | 71. 686 4 | 51. 230 8 | 14. 267 0 | 0. 001 1 | |
| f4 | M | 8. 627 2 | 10. 424 5 | 19. 830 4 | 0. 002 0 | 0. 001 2 |
| S | 2. 127 7 | 1. 519 5 | 0. 288 8 | 0. 003 5 | 0. 001 7 | |
| f5 | M | 112. 715 9 | 64. 917 0 | 670. 731 5 | 2. 992 5 | 1. 828 4 |
| S | 36. 547 9 | 14. 768 6 | 114. 758 5 | 1. 010 3 | 0. 174 8 | |
| f6 | M | 7. 424 1 | 157. 417 0 | 5. 410 7 | 0. 003 4 | 0. 001 9 |
| S | 4. 560 2 | 43. 681 5 | 0. 362 2 | 0. 00 2 | 0. 000 8 |
Table 5
Parameter configurations of comparative algorithms
| 预测模型 | 种群规模 | 维度 | 最大迭代次数 | 初始范围 | 关键参数 |
|---|---|---|---|---|---|
| PSO-BP | 30 | 30 | 300 | [-20,20] | 惯性权重W=0.5,学习因子c1=c2=1.5 |
| SO-BP | 30 | 30 | 300 | [-20,20] | 惯性权重W=0.5,分量r=0.5 |
| SMA-BP | 30 | 30 | 300 | [-20,20] | 距离衰减g=1.0,吸引度b =1.0 |
| GWO-BP | 30 | 30 | 300 | [-20,20] | 领导者数k=3,系数A1,A2,A3 ∈ [-1,1] |
| BA-BP | 30 | 30 | 300 | [-20,20] | 响度A=0.5,脉冲率R=0.5 |
| ISMA-BP | 30 | 30 | 300 | [-20,20] | 距离衰减g=1.0,吸引度b = 1.0 |
Table 6
Prediction errors of vehicle operation risk for multiple models
| 序号 | 车辆运行风险 | 相对误差/% | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 对照值 | PSO-BP | SO-BP | SMA-BP | GWO-BP | BA-BP | ISMA-BP | PSO-BP | SO-BP | SMA-BP | GWO-BP | BA-BP | ISMA-BP | ||
| 1 | 1.572 | 1.772 | 1.594 | 1.580 | 1.587 | 1.610 | 1.569 | 12.71 | 1.333 | 0.461 | 0.910 | 2.355 | 0.249 | |
| 2 | 1.624 | 1.772 | 1.636 | 1.618 | 1.614 | 1.642 | 1.618 | 9.157 | 0.781 | 0.365 | 0.623 | 1.103 | 0.364 | |
| ︙ | ︙ | ︙ | ︙ | ︙ | ︙ | ︙ | ︙ | ︙ | ︙ | ︙ | ︙ | ︙ | ︙ | |
| 2749 | 1.544 | 1.772 | 1.552 | 1.542 | 1.542 | 1.565 | 1.521 | 14.829 | 0.547 | 0.103 | 0.123 | 1.400 | 1.461 | |
| 2750 | 1.588 | 1.772 | 1.586 | 1.593 | 1.594 | 1.596 | 1.582 | 11.609 | 0.120 | 0.313 | 0.349 | 0.482 | 0.360 | |
Table 8
Comparison of function evaluations
| 预测模型 | FEs计算 公式 | 单次试验 FEs值 | 计算依据 | |||
|---|---|---|---|---|---|---|
| PSO-BP | P + I·P | 9 030 | 初始化P, 迭代每代P | |||
| SO-BP | P +I·P | 9 030 | 初始化P, 迭代每代P | |||
| SMA-BP | P + I·P | 9 030 | 初始化P, 迭代每代P | |||
| GWO-BP | I·P | 9 000 | 每代统一 评估P | |||
| BA-BP | P + I·(P + 1) ~ P + I·(2P + 1) | 9 330~ 18 330 | 每代P +最优1 (触发局部 搜索再+P) | |||
| ISMA-BP | I·(2P + 1) | 18 330 | 每代P + 精英变异1 | |||
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