基于Hopfield神经网络的单缸插销式伸缩臂伸缩路径优化

doi:10.13229/j.cnki.jdxbgxb20181272

摘要/Abstract

摘要：

提出了单缸插销式伸缩臂伸缩路径优化问题，采用Hopfield神经网络构建了数学模型。由于能量方程中的约束项罚参数λ和目标项罚参数γ的确定往往相互矛盾：当λ占优时，能量方程更多朝向满足约束方向收敛，得到的有效解往往不是高质量解；当γ占优时，则可能收敛到无效解。为此，提出了λ为向上梯度递增、γ为向下梯度递减的曲线形式；对于λ和γ的增量确定，提出了一种基于约束边界偏差控制的PID自适应增量法，通过对约束边界偏差的PID控制使有效解的生成可控。实验结果表明：路径优化后伸缩效率能提升10%~30%。神经网络模型优化效果较好，几乎能100%收敛到有效解，同时由于PID控制使解聚集到约束边界，最优解生成率也较高，接近50%。

关键词: 机械设计, Hopfield神经网络, 单缸插销式伸缩臂, 伸缩路径优化, PID控制器

Abstract:

The issue of Telescoping Path Optimization (TPO) of Single-cylinder Pin-type Multi-section Boom (SPMB) was raised and its model is proposed by using Hopfield Neural Network (HNN). In an energy equation, it is difficult to balance the parameter λ of constrained term and the parameter γ of objective term. When λ dominates, network converges toward constraint satisfaction and a valid solution is often of poor quality. Whereas when γ dominates, network might converge to an invalid solution. To solve this problem, this paper proposes that the λ is gradient rising and the γ is gradient falling. A PID hybridized method based on Constraint Boundary Gap (CBG) control is presented to adaptively regulate the increments of λ and γ. Experimental results show that the telescoping efficiency improves 10%~30% after path optimization. TPO model achieves good optimization effect, and enables network converge almost 100% to a valid solution. The generation proportion of the optimal solution remains high at about 50% seeing that PID control often imposes a solution to the constraint boundary.

Key words: mechanical design, Hopfield neural network, single-cylinder pin-type multi-section boom, telescoping path optimization, proportional integral derivative(PID) controller

中图分类号:

TH213

毛艳,成凯. 基于Hopfield神经网络的单缸插销式伸缩臂伸缩路径优化[J]. 吉林大学学报(工学版), 2020, 50(1): 53-65.

Yan MAO,Kai CHENG. Telescoping path optimization of a single-cylinder pin⁃type multi⁃section boom based on Hopfield neural network[J]. Journal of Jilin University(Engineering and Technology Edition), 2020, 50(1): 53-65.

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参考文献 20

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步数	实例A				实例B
步数	未优化	臂节	优化后	臂节	未优化	臂节	优化后	臂节
0	1 4 4 1 1	——	1 4 4 1 1	——	2 2 2 2 2	——	2 2 2 2 2	——
1	1 1 4 1 1	II	1 1 4 1 1	II	1 2 2 2 2	I	1 2 2 2 2	I
2	1 1 1 1 1	III	1 1 2 1 1	III	1 1 2 2 2	II	1 1 2 2 2	II
3	1 1 1 1 2	V	1 1 2 1 2	V	1 1 1 2 2	III	1 1 2 1 2	IV
4	1 1 1 2 2	IV	1 1 2 2 2	IV	1 1 1 1 2	IV	2 1 2 1 2	I
5	1 1 2 2 2	III	1 2 2 2 2	II	1 1 2 1 2	III
6	1 2 2 2 2	II	2 2 2 2 2	I	2 1 2 1 2	I
7	2 2 2 2 2	I

HNN γ参数恒定,γ=常数	HNN γ定常数衰减;Δγ= K_γ ·γ(t)	HNN γ PID;Δγ见式（5）
B=5, C=5	B=5, C=5	B=5, C=5
μ=μ_γ = 0.000 1	μ_λ =μ_γ =0.000 1	μ_λ =μ_γ =0.000 1
K _p _λ =10,K _i _λ =0.1,K _d _λ =1	K _p _λ =10,K _i _λ =0.1,K _d _λ =1	K _p _λ =10,K _i _λ =0.1,K _d _λ =1
γ=[1010101010]	K_γ =10	K _p _γ =0.1,K _i _γ =0.01, K _d _γ =1
λ(0)=0	λ(0)=0,γ(0)=1 000	λ(0)=0,γ(0)=1 000

	工况
算法	n=5， A =[21212] T =[23221]		n=6， A =[212121] T =[233221]		n=8， A =[21212121] T =[23333221]		n=10， A =[2121212121] T =[2333333221]
算法	有效解比 /最优解比	t/s	有效解比 /最优解比	t/s	有效解比 /最优解比	t/s	有效解比 /最优解比	t/s
排列组合	100% /100%	0.012	100% /100%	0.012	100% /100%	0.036	100% /100%	0.168
动态规划	100% /100%	0.053	100% /100%	0.059	-	-	-	-
HNN	90% /50%	0.519	90% /40%	0.640	80% /30%	0.641	80% /10%	0.632

	工况
算法	n=5， A =[22222] T =[21212]		n=6， A =[222222] T =[212121]		n=6， A =[22222222] T =[21212121]		n=10， A =[2222222222] T =[2121212121]
算法	有效解比 /最优解比	t/s	有效解比 /最优解比	t/s	有效解比	t/s	有效解比 /最优解比	t/s
排列组合	100% /100%	0.014	100% /100%	0.014	100% /100%	0.016	100% /100%	0.035
动态规划	100% /100%	0.053	100% /100%	0.059	--	--	--	--
HNN	100% /30%	0.634	90% /80%	0.639	100% /80%	0.635	90% /60%	0.637