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

Abstract

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

CLC Number:

TH213

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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References 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

数据	最优 RBC	步数/路径	类型	3种γ取值类型
数据	最优 RBC	步数/路径	类型	常数	增量	PID
A =[32321]， T = [12222]	V =[11122]， V = [11121]	6/3.6 6/3.6	无效	4	1	0
			有效	21	21	20
			最优	5	8	10
A =[22222]， T = [21212]	V =[21112]， V = [11212]	4/1.8 4/1.8	无效	5	6	0
			有效	17	16	21
			最优	8	8	9
A =[22223]， T = [12222]	V =[11113]， V = [11112]	8/3.6 8/3.6	无效	0	0	0
			有效	10	5	7
			最优	20	25	23
A =[21212]， T = [23221]	V =[11211]， V = [11212]	5/2.7 5/2.7	无效	1	0	0
			有效	17	17	15
			最优	12	13	15
A =[22331]， T = [12222]	V =[11122]， V = [11121]	7/3.6 7/3.6	无效	21	11	0
			有效	2	8	17
			最优	7	11	13
A =[21331]， T = [12222]	V =[11121]， V = [11122]	6/3.15 6/3.15	无效	23	12	0
			有效	2	7	17
			最优	5	11	13
平均无效解/%				0.300	0.167	0
平均有效解/%				0.384	0.410	0.539
平均最优解/%				0.316	0.423	0.461

	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

Telescoping path optimization of a single-cylinder pin⁃type multi⁃section boom based on Hopfield neural network

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