Parameter Optimization of Vibratory Sorter using Neural Network and Particle Swarm Optimization
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摘要: 针对废旧铅酸蓄电池回收预处理工艺中极群分离问题设计了振动式分选机，并应用椭圆基神经网络近似模型和粒子群算法研究了振动式分选机参数优化问题。首先，以降低质量、降低应力和提高第3阶固有频率为目标，利用灵敏度分析获得影响程度最高的结构参数；其次，采用具有最高拟合度的椭圆基神经网络构建试验设计样本的最佳近似模型，并采用优化效果更佳的粒子群算法进行数值优化；最后，对优化前后的结构进行可靠性分析。结果表明：优化后结构质量降低了9.7%，最大等效应力降低了36.7%，第3阶固有频率提高了12.9%，结构可靠度提高了5.9%。Abstract: A vibratory sorter was designed for the separation of polar groups in the recycling pretreatment process of used lead-acid batteries, and the ellipsoid basis function(EBF)neural network approximation model and particle swarm optimization(PSO)algorithm were used to optimized structural parameters of the vibratory sorter. Firstly, to reduce the mass, reduce the stress and increase the third-order natural frequency, the sensitivity analysis is done to obtain the structural parameters with the highest degree of influence. Secondly, the optimal approximation model of the experimental design sample is constructed by using EBF neural networks with the highest fitting degree, and PSO algorithm with better optimization effect is adopted for numerical optimization. Finally, the reliability analysis was performed on the structures before and after the optimization. The results show that the quality of the optimized values is reduced by 9.7%, the maximum equivalent stress is reduced by 36.7%, the third-order natural frequency is increased by 12.9%, and the structural reliability is increased by 5.9%.
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表 2 前6阶固有频率和振型
阶数 固有频率/Hz 模态振型描述 1 5.95 入口沿YZ平面左右摆动 2 6.98 整体沿XZ平面上下平动 3 20.097 出口沿YZ平面左右摆动 4 23.843 整体沿XY平面上下摆动 5 37.235 整体沿YZ平面上下摆动 6 45.269 整体沿Z轴扭动 
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表 3 设计变量的初始值和范围
变量 参数定义 初始值/mm 取值范围/mm t1 出入口上板厚度 5 3≤t1≤7 t2 侧方连接板厚度 10 4≤t2≤12 t3 弹簧处连接板厚度 6 4≤t3≤12 t4 振动电机上方加强板厚度 15 5≤t4≤18 t5 下主梁厚度 5 3≤t5≤7 t6 上主梁厚度 4 3≤t6≤7 t7 调距横梁厚度 15 5≤t7≤18
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表 4 设计变量的灵敏度
变量 灵敏度 质量M 最大等效应力S 第3阶固有频率F3 t1 0.0043 -0.064 3 -0.007 6 t2 0.1089 -0.103 6 -0.043 8 t3 0.06 -1.373 3 0.077 6 t4 0.0187 -0.041 1 0.020 3 t5 0.0488 -0.123 3 0.130 1 t6 0.0365 -0.411 5 -0.018 9 t7 0.0807 -0.097 -0.017
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表 5 近似模型拟合效果评估
类型 决策系数 平均误差/10-2 最大误差/10-2 M S F3 F2 M S F3 F2 M S F3 F2 RSM 1 0.949 0.937 0.999 0.001 6.03 4.275 0.149 0.008 20.58 15.065 0.51 Kriging 0.949 0.95 0.938 0.949 3.97 5.26 3.761 3.742 21.11 24.98 23.89 17.968 RBF 0.999 0.933 0.952 0.998 0.662 6.96 3.769 0.831 3.467 22.549 12.684 3.92 EBF 1 0.984 0.972 0.999 0.104 3.22 2.662 0.87 0.349 10.55 11.176 3.683
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表 6 基于EBF近似模型的数值优化对比
参数 初始值 PSO优化 NSGA-II优化 x1/mm 10 4 4.011 7 x2/mm 6 9.151 5 9.327 x3/mm 5 6.286 4 6.318 5 x4/mm 4 5.959 7 5.927 6 x5/mm 15 5 5.052 8 M/kg 173.54 156.61 156.93 S/MPa 125.99 76.807 76.648 F3/Hz 20.097 22.616 22.611
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表 7 优化值相对误差分析
目标 M/kg S/MPa F3/Hz 优化前初始值 173.54 125.99 20.097 有限元计算值 156.77 79.757 22.628 PSO算法优化值 156.61 76.807 22.616 计算相对误差/% 0.1 3.7 0.05
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