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参数 | 数值 |
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密度/(kg/m3) | 2 800 | 弹性模量/GPa | 69 | 泊松比 | 0.33 | 抗拉强度/MPa | ≥390 | 伸长率/% | ≥8 |
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Table 1 Material property parameters of ZL201A aluminum alloy
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Fig.1 Finite element model of steel car door
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Fig.2 Finite element model of cast aluminum integrated car door
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Fig.3 Sinking stiffness condition of cast aluminum integrated car door
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Fig.4 Upper torsional stiffness condition of cast aluminum integrated car door
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Fig.5 Lower torsional stiffness condition of cast aluminum integrated car door
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Fig.6 Modal simulation results of cast aluminum integrated car door
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Fig.7 Modal test point arrangement for cast aluminum integrated car door
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Fig.8 Modal test results of cast aluminum integrated car door
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模态 | 频率/Hz | 相对误差/% |
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仿真值 | 试验值 |
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一阶弯曲模态 | 36.62 | 37.87 | 3.4 | 一阶扭转模态 | 54.59 | 56.49 | 3.5 |
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Table 2 Comparison of modal simulation and test results of cast aluminum integrated car door
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Fig.9 Sampling strategies of different Latin hypercube experimental design methods
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Fig.10 Schematic of thickness of each component in cast aluminum integrated car door
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试验编号 | 设计变量 | m/kg | f1/Hz | f2/Hz | d1/mm | d2/mm | d3/mm |
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T1/mm | T2/mm | T3/mm | T4/mm | T5/mm |
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1 | 2.069 | 3.862 | 2.828 | 3.103 | 3.448 | 12.90 | 25.72 | 46.06 | 2.073 | 3.145 | 1.301 | 2 | 2.207 | 3.172 | 2.276 | 3.241 | 2.276 | 11.49 | 27.17 | 47.50 | 3.588 | 2.860 | 1.174 | 3 | 3.448 | 2.276 | 3.241 | 4.000 | 3.103 | 15.83 | 37.35 | 58.59 | 1.857 | 1.378 | 0.460 | 4 | 3.034 | 3.793 | 2.345 | 3.862 | 2.966 | 13.63 | 34.36 | 54.94 | 2.252 | 1.616 | 0.604 | 5 | 2.483 | 2.345 | 2.000 | 2.483 | 3.172 | 10.97 | 29.55 | 50.20 | 4.699 | 2.448 | 0.951 | ? | ? | ? | ? | ? | ? | ? | ? | ? | ? | ? | ? | 28 | 2.000 | 2.966 | 3.586 | 2.552 | 2.483 | 14.05 | 24.82 | 45.34 | 2.295 | 2.426 | 1.416 | 29 | 3.655 | 4.000 | 2.897 | 2.690 | 3.241 | 16.19 | 38.58 | 60.32 | 1.281 | 1.199 | 0.444 | 30 | 3.586 | 3.724 | 3.655 | 3.793 | 2.759 | 17.75 | 38.11 | 59.71 | 1.009 | 1.214 | 0.426 |
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Table 3 Experimental design scheme and results of deterministic optimization for cast aluminum integrated car door
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响应 | RBF神经网络近似模型 | 二阶响应面近似模型 |
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d1 | 0.974 86 | 0.931 54 | d2 | 0.980 79 | 0.979 53 | d3 | 0.970 83 | 0.961 69 | f1 | 0.999 21 | 0.999 93 | f2 | 0.999 43 | 0.999 50 | m | 0.999 11 | 0.999 98 |
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Table 4 Accuracy evaluation results of approximation model of each response of cast aluminum integrated car door
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参数 | 数值 |
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种群数/个 | 100 | 迭代数/次 | 50 | 交叉率 | 0.9 | 交叉分布指数 | 10 | 突变分布指数 | 20 |
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Table 5 Parameter setting for NSGA-II
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参数 | 数值 |
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迭代数/次 | 50 | 粒子数/个 | 100 | 惯性权重 | 0.9 | 全局增量 | 0.9 | 粒子增量 | 0.9 |
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Table 6 Parameter setting for MOPSO algorithm
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参数 | 数值 |
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种群数/个 | 50 | 岛屿数/个 | 10 | 迭代数/次 | 10 | 交叉率 | 1.0 | 变异率 | 0.01 | 迁移率 | 0.01 |
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Table 7 Parameter setting for MIGA
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参数 | 初始值1) | 优化值 |
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NSGA-Ⅱ | MOPSO | MIGA |
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T1/mm | 0.70 | 3.716 2 | 3.730 8 | 3.738 8 | T2/mm | 1.40 | 2.000 6 | 2.000 0 | 2.003 7 | T3/mm | 0.65 | 2.000 1 | 2.000 0 | 2.017 2 | T4/mm | 0.70 | 3.999 1 | 3.990 8 | 3.980 5 | T5/mm | 1.80 | 3.999 7 | 4.000 0 | 3.973 9 | d1/mm | 4.402 | 1.843 5 | 1.837 9 | 1.866 9 | d2/mm | 2.904 | 1.115 3 | 1.104 1 | 1.100 7 | d3/mm | 1.443 | 0.352 1 | 0.347 9 | 0.347 1 | f1/Hz | 49.22 | 40.00 | 40.11 | 40.17 | f2/Hz | 75.53 | 61.21 | 61.33 | 61.41 | m/kg | 17.46 | 13.322 | 13.350 | 13.406 |
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Table 8 Deterministic optimization results of cast aluminum integrated car door based on RBF neural network approximation model
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参数 | 初始值1) | 优化值 |
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NSGA-Ⅱ | MOPSO | MIGA |
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T1/mm | 0.70 | 3.726 8 | 3.722 8 | 3.747 0 | T2/mm | 1.40 | 2.000 7 | 2.000 0 | 2.014 5 | T3/mm | 0.65 | 2.000 0 | 2.000 0 | 2.007 9 | T4/mm | 0.70 | 3.301 3 | 3.469 2 | 3.469 3 | T5/mm | 1.80 | 3.994 1 | 3.948 8 | 3.982 5 | d1/mm | 4.402 | 2.551 3 | 2.566 8 | 2.546 4 | d2/mm | 2.904 | 1.172 1 | 1.170 3 | 1.160 2 | d3/mm | 1.443 | 0.390 4 | 0.388 7 | 0.386 6 | f1/Hz | 49.22 | 40.01 | 40.03 | 40.21 | f2/Hz | 75.53 | 61.38 | 61.35 | 61.56 | m/kg | 17.46 | 13.302 | 13.302 | 13.376 |
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Table 9 Deterministic optimization results of cast aluminum integrated car door based on second-order response surface approximation model
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参数 | RBF神经网络近似模型 | 二阶响应面近似模型 |
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NSGA-II | MOPSO | MIGA | NSGA-II | MOPSO | MIGA |
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Q | R | Q | R | Q | R | Q | R | Q | R | Q | R |
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d2/mm | 8 | 1 | 8 | 1 | 8 | 1 | 8 | 1 | 8 | 1 | 8 | 1 | d3/mm | 8 | 1 | 8 | 1 | 8 | 1 | 8 | 1 | 8 | 1 | 8 | 1 | f1/Hz | 0.678 | 0.503 | 0.937 | 0.651 | 1.065 | 0.713 | 0.694 | 0.512 | 0.738 | 0.539 | 1.192 | 0.767 | f2/Hz | 3.869 | 0.999 | 4.231 | 0.999 | 4.417 | 0.999 | 4.373 | 0.999 | 4.294 | 0.999 | 4.888 | 0.999 |
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Table 10 Quality level and reliability of deterministic optimization results of cast aluminum integrated car door
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参数 | 初始值1) | 优化值 |
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NSGA-Ⅱ | MOPSO | MIGA |
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T1/mm | 0.70 | 3.998 0 | 3.941 6 | 3.961 3 | T2/mm | 1.40 | 2.135 1 | 2.000 0 | 2.066 5 | T3/mm | 0.65 | 2.018 9 | 2.000 0 | 2.031 3 | T4/mm | 0.70 | 3.968 8 | 4.000 0 | 3.948 0 | T5/mm | 1.80 | 3.986 6 | 4.000 0 | 3.990 7 | d1/mm | 4.402 | 1.696 6 | 1.680 1 | 1.744 4 | d2/mm | 2.904 | 0.910 7 | 0.964 1 | 0.952 2 | d3/mm | 1.443 | 0.276 2 | 0.278 8 | 0.280 1 | f1/Hz | 49.22 | 42.45 | 42.31 | 42.35 | f2/Hz | 75.53 | 64.18 | 63.91 | 63.98 | m/kg | 17.46 | 14.154 | 13.786 | 13.983 |
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Table 11 Reliability optimization results of cast aluminum integrated car door based on RBF neural network approximation model
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参数 | NSGA-II | MOPSO | MIGA |
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Q | R | Q | R | Q | R |
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d2 | 8 | 1 | 8 | 1 | 8 | 1 | d3 | 8 | 1 | 8 | 1 | 8 | 1 | f1 | 7.57 | 1 | 6.17 | 1 | 6.55 | 1 | f2 | 8 | 1 | 8 | 1 | 8 | 1 |
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Table 12 Quality level and reliability of reliability optimization results of cast aluminum integrated car door based on RBF neural network approximation model
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参数 | 优化值 | 仿真值 | 相对误差/% |
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d1/mm | 1.680 1 | 1.650 0 | 1.8 | d2/mm | 0.964 1 | 0.936 7 | 2.8 | d3/mm | 0.278 8 | 0.282 4 | 1.3 | f1/Hz | 42.31 | 41.76 | 1.3 | f2/Hz | 63.91 | 63.21 | 1.1 | m/kg | 13.786 | 13.761 | 0.2 |
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Table 13 Simulation verification of reliability optimization results of cast aluminum integrated car door based on RBF neural network approximation model and MOPSO algorithm
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Fig.11 Fitting surfaces of reliability optimization results of cast aluminum integrated car door based on RBF neural network approximation model and MOPSO algorithm
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参数 | 初始值1) | 优化值 |
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NSGA-Ⅱ | MOPSO | MIGA |
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T1/mm | 0.70 | 3.951 9 | 3.954 7 | 3.953 2 | T2/mm | 1.40 | 2.040 7 | 2.000 0 | 2.007 9 | T3/mm | 0.65 | 2.0013 | 2.000 0 | 2.033 3 | T4/mm | 0.70 | 3.861 0 | 3.182 5 | 3.494 7 | T5/mm | 1.80 | 3.670 3 | 3.900 8 | 3.993 2 | d1/mm | 4.402 | 2.558 3 | 2.521 4 | 2.476 6 | d2/mm | 2.904 | 1.110 9 | 1.112 0 | 1.101 7 | d3/mm | 1.443 | 0.383 9 | 0.384 0 | 0.378 7 | f1/Hz | 49.22 | 42.22 | 42.02 | 42.04 | f2/Hz | 75.53 | 63.71 | 63.73 | 63.73 | m/kg | 17.46 | 13.894 | 13.851 | 13.924 |
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Table 14 Reliability optimization results of cast aluminum integrated car door based on second-order response surface approximation model
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参数 | NSGA-II | MOPSO | MIGA |
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Q | R | Q | R | Q | R |
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d2 | 8 | 1 | 8 | 1 | 8 | 1 | d3 | 8 | 1 | 8 | 1 | 8 | 1 | f1 | 6.80 | 1 | 6.18 | 1 | 6.41 | 1 | f2 | 8 | 1 | 8 | 1 | 8 | 1 |
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Table 15 Quality level and reliability of reliability optimization results of cast aluminum integrated car door based on second-order response surface approximation model
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参数 | 优化值 | 仿真值 | 相对误差/% |
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d1/mm | 2.521 4 | 2.526 4 | 0.2 | d2/mm | 1.112 0 | 1.119 0 | 0.7 | d3/mm | 0.384 0 | 0.388 4 | 1.1 | f1/Hz | 42.02 | 41.66 | 0.9 | f2/Hz | 63.73 | 63.35 | 0.6 | m/kg | 13.851 | 13.734 | 0.8 |
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Table 16 Simulation verification of reliability optimization results of cast aluminum integrated car door based on second-order response surface approximation model and MOPSO algorithm
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Fig.12 Fitting surfaces of reliability optimization results of cast aluminum integrated car door based on second-order response surface approximation model and MOPSO algorithm
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