China Safety Science Journal ›› 2025, Vol. 35 ›› Issue (12): 78-87.doi: 10.16265/j.cnki.issn1003-3033.2025.12.0140
• Safety engineering technology • Previous Articles Next Articles
HONG Liang(
), CHEN Zhihao, LIU Peng
Received:2025-08-14
Revised:2025-10-23
Online:2025-12-27
Published:2026-06-28
CLC Number:
HONG Liang, CHEN Zhihao, LIU Peng. Optimal design of school bus intelligent airbags for enhanced safety of middle-sized children[J]. China Safety Science Journal, 2025, 35(12): 78-87.
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URL: http://www.cssjj.com.cn/EN/10.16265/j.cnki.issn1003-3033.2025.12.0140
Table 1
IGD mean and standard deviation of improved NSGA-III and other algorithms under DTLZ
| 测试 函数 | 目 标 | MOEAD-DU | MOMBI-II | NSGA-III | 改进型NSGA-III |
|---|---|---|---|---|---|
| DTLZ1 | 3 | 2.066 2×10-2(8.17×10-5) - | 2.084 6×10-2(1.66×10-4) - | 2.065 5×10-2 (1.03×10-4)- | 2.055 6×10-2 (1.23×10-6) |
| 5 | 7.024 5×10-2(5.87×10-4) - | 8.586 8×10-2(3.20×10-2) - | 6.828 2×10-2 (2.49×10-4)- | 5.272 7×10-2 (4.93×10-5) | |
| 8 | 1.093 0×10-1 (1.69×10-3) - | 2.725 0×10-1 (2.31×10-2) - | 1.244 5×10-1 (4.08×10-2) - | 1.057 8×10-1 (1.63×10-2) | |
| 10 | 1.149 3×10-1 (6.92×10-4) - | 2.039 4×10-1 (3.74×10-2) - | 1.111 3×10-1 (6.60×10-3) ≈ | 1.139 6×10-1 (1.65×10-2) | |
| 15 | 2.098 2×10-1 (1.60×10-2) - | 2.704 4×10-1 (1.59×10-2) - | 1.863 1×10-1 (1.46×10-2) ≈ | 1.904 7×10-1 (2.08×10-2) | |
| DTLZ2 | 3 | 5.585 5×10-2 (6.17×10-4) - | 5.504 6×10-2 (2.73×10-4) - | 5.448 4×10-2 (1.01×10-5) - | 5.447 0×10-2 (2.20×10-5) |
| 5 | 2.216 2×10-1 (1.74×10-3) - | 2.184 5×10-1 (1.46×10-3) - | 2.123 0×10-1 (5.74×10-5) - | 1.651 1×10-1 (2.63×10-5) | |
| 8 | 3.899 8×10-1 (1.59×10-3) - | 4.610 1×10-1 (1.09×10-1) - | 4.366 8×10-1 (7.85×10-2) - | 3.229 2×10-1 (3.84×10-2) | |
| 10 | 4.314 0×10-1 (8.69×10-4) + | 4.376 0×10-1 (5.59×10-3) - | 4.224 3×10-1 (9.30×10-3) ≈ | 4.321 2×10-1 (3.64×10-2) | |
| 15 | 6.369 8×10-1 (1.24×10-2) ≈ | 8.562 9×10-1 (8.33×10-2) - | 6.412 5×10-1 (2.03×10-2) ≈ | 6.400 0×10-1 (1.81×10-2) | |
| DTLZ3 | 3 | 5.482 4×10-2 (2.84×10-4) - | 5.485 8×10-2 (3.43×10-4) - | 5.462 5×10-2 (1.72×10-4) - | 5.446 4×10-2 (7.20×10-7) |
| 5 | 2.210 2×10-1 (2.18×10-3) - | 2.217 5×10-1 (2.37×10-2) - | 2.130 3×10-1 (5.42×10-4) - | 1.652 0×10-1 (7.36×10-5) | |
| 8 | 3.932 2×10-1 (1.50×10-3) + | 8.937 4×10-1 (4.04×10-2) - | 6.816 6×10-1 (6.60×10-1) - | 5.733 0×10-1 (6.53×10-1) | |
| 10 | 4.307 2×10-1 (7.21×10-4) + | 6.116 7×10-1 (1.37×10-1) - | 4.802 2×10-1 (8.20×10-2) + | 5.035 1×10-1 (1.23×10-1) | |
| 15 | 6.300 0×10-1 (1.34×10-3) + | 1.037 1×100 (2.39×10-2) - | 1.019 0×100 (7.49×10-2) - | 7.313 5×10-1 (6.33×10-2) | |
| DTLZ4 | 3 | 5.461 5×10-2 (7.11×10-5) - | 7.181 2×10-2 (8.88×10-2) - | 1.491 2×10-1 (2.26×10-1) - | 5.446 5×10-2 (2.05×10-6) |
| 5 | 2.173 5×10-1 (1.31×10-3) - | 2.956 5×10-1 (1.17×10-1) - | 3.144 6×10-1 (1.20×10-1) - | 1.651 2×10-1 (1.13×10-5) | |
| 8 | 4.493 0×10-1 (5.90×10-2) - | 5.196 4×10-1 (1.03×10-1) - | 4.887 4×10-1 (8.95×10-2) - | 3.151 2×10-1 (1.08×10-4) | |
| 10 | 4.324 4×10-1 (1.77×10-3) - | 4.523 5×10-1 (5.33×10-4) - | 4.287 6×10-1 (2.98×10-2) - | 4.204 5×10-1 (2.86×10-4) | |
| 15 | 6.318 6×10-1 (5.09×10-3) - | 6.480 0×10-1 (1.19×10-2) - | 6.417 5×10-1 (1.87×10-2) - | 6.228 3×10-1 (7.09×10-3) | |
| SDTLZ1 | 3 | 5.623 8×10-2 (6.61×10-4) - | 5.234 7×10-2 (4.47×10-4) - | 5.173 9×10-2 (2.66×10-4) - | 5.148 2×10-2 (2.79×10-6) |
| 5 | 3.526 4×10-1 (3.86×10-3) + | 3.854 8×10-1 (2.18×10-3) - | 3.831 8×10-1 (9.07×10-4) ≈ | 3.831 1×10-1 (4.21×10-4) | |
| 8 | 3.688 1×100 (1.11×10-1) + | 4.762 7×100 (1.44×100) - | 3.580 7×100 (7.50×10-1) + | 3.772 6×100 (9.80×10-1) | |
| 10 | 1.324 3×101 (3.06×10-1) + | 1.678 7×101 (3.11×100) - | 1.229 8e×101 (1.89×100) + | 1.437 8×101 (3.17×100) | |
| 15 | 5.558 6e×102 (3.73×101) - | 1.146 5×103 (5.80×102) - | 4.50 20×102 (9.46×101) + | 5.404 0×102 (9.91×101) | |
| SDTLZ2 | 3 | 1.420 2×10-1 (2.13×10-3) - | 1.307 9×10-1 (3.81×10-4) - | 1.299 3×10-1 (6.82×10-5) ≈ | 1.299 0×10-1 (3.21×10-5) |
| 5 | 1.047 8×100 (9.83×10-3) - | 9.854 9×10-1 (4.37×10-3) ≈ | 9.854 5×10-1 (8.22×10-4) ≈ | 9.858 2×10-1 (1.83×10-3) | |
| 8 | 1.143 1×101 (2.66×10-1) - | 1.060 1×101 (1.39×10-1) + | 1.052 6×101 (4.03×10-1) + | 1.136 6×101 (2.80×100) | |
| 10 | 4.250 7×101 (8.25×10-1) - | 4.000 0×101 (8.42×10-1) + | 3.971 8×101 (3.07×100) - | 3.950 0×101 (2.02×10-1) | |
| 15 | 2.016 6×103 (7.98×101) - | 2.787 1×103 (7.26×102) - | 1.580 5×103 (2.10×102) - | 1.559 7×103 (1.91×102) | |
| +/-/≈ | — | 7/22/1 | 2/27/1 | 5/18/7 | — |
Table 3
Injury criteria of head, thorax and femurs of middle-sized children under six sitting postures
| 儿童坐姿 | HIC15 | IP/kPa | THPC/mm | LP/kPa | FL/N | FR/N | WICC |
|---|---|---|---|---|---|---|---|
| NP(原工况) | 807.38 | 372.9 | 2.81 | 198.0 | 474.55 | 477.68 | 1.3881 |
| NP(优化前) | 157.29 | 138.5 | 5.54 | 162.2 | 428.87 | 436.85 | 0.4976 |
| NP(优化后) | 51.19 | 90.5 | 1.70 | 132.7 | 379.27 | 390.65 | 0.2997 |
| 变化率1/% | -93.66 | -75.73 | -39.50 | -32.98 | -20.08 | -18.22 | -78.41 |
| 变化率2/% | -67.46 | -34.66 | -69.31 | -18.19 | -11.57 | -10.58 | -39.77 |
| FP10(原工况) | 754.25 | 293.9 | 1.04 | 151.6 | 459.92 | 462.98 | 1.1717 |
| FP10(优化前) | 75.88 | 144.1 | 3.60 | 125.8 | 420.11 | 414.50 | 0.4140 |
| FP10(优化后) | 26.18 | 108.7 | 4.95 | 122.4 | 377.51 | 368.91 | 0.3196 |
| 变化率1/% | -96.53 | -63.01 | +375.96 | -19.26 | -17.92 | -20.32 | -72.72 |
| 变化率2/% | -65.50 | -24.57 | +37.50 | -2.70 | -10.14 | -11.00 | -22.80 |
| FP20(原工况) | 501.12 | 242.2 | 2.85 | 230.4 | 442.75 | 450.52 | 0.9633 |
| FP20(优化前) | 30.17 | 129.7 | 10.87 | 135.5 | 406.12 | 401.47 | 0.3939 |
| FP20(优化后) | 14.49 | 90.5 | 11.28 | 101.8 | 356.12 | 358.81 | 0.2918 |
| 变化率1/% | -97.11 | -62.63 | +295.79 | -55.82 | -19.57 | -20.36 | -69.71 |
| 变化率2/% | -51.97 | -30.22 | +3.77 | -24.87 | -12.31 | -10.63 | -25.92 |
| RP5(原工况) | 477.99 | 326.8 | 1.34 | 140.9 | 467.74 | 451.71 | 1.0228 |
| RP5(优化前) | 198.01 | 158.2 | 6.22 | 148.6 | 412.64 | 422.29 | 0.5542 |
| RP5(优化后) | 69.24 | 107.3 | 0.67 | 137.5 | 367.68 | 371.49 | 0.3408 |
| 变化率1/% | -85.51 | -67.17 | -50.00 | -2.41 | -21.39 | -17.76 | -66.68 |
| 变化率2/% | -65.03 | -32.17 | -89.23 | -7.47 | -10.90 | -12.03 | -38.51 |
| RP10(原工况) | 450.91 | 327.8 | 2.37 | 324.7 | 492.61 | 424.51 | 1.1412 |
| RP10(优化前) | 138.79 | 154.6 | 4.19 | 147.5 | 430.15 | 408.95 | 0.4958 |
| RP10(优化后) | 36.53 | 94.3 | 0 | 136.5 | 386.71 | 369.90 | 0.2911 |
| 变化率1/% | -91.90 | -71.23 | -100.00 | -57.96 | -21.50 | -12.86 | -74.49 |
| 变化率2/% | -73.68 | -39.00 | -100.00 | -7.46 | -10.10 | -9.55 | -41.29 |
| SP(原工况) | 598.67 | 291.4 | 0 | 166.5 | 413.41 | 427.02 | 1.0609 |
| SP(优化前) | 167.28 | 128.3 | 7.78 | 184.8 | 389.80 | 397.52 | 0.5123 |
| SP(优化后) | 97.08 | 97.0 | 2.08 | 110.0 | 349.45 | 350.20 | 0.3292 |
| 变化率1/% | -83.78 | -66.71 | N/A | -33.93 | -15.47 | -17.99 | -68.97 |
| 变化率2/% | -41.97 | -24.40 | -73.26 | -40.48 | -10.35 | -11.90 | -35.74 |
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