基于Gamma过程的加速退化试验多目标优化设计

doi:10.13229/j.cnki.jdxbgxb20211100

吉林大学学报(工学版) ›› 2022, Vol. 52 ›› Issue (2): 361-367.doi: 10.13229/j.cnki.jdxbgxb20211100

• 车辆工程·机械工程 • 上一篇

基于Gamma过程的加速退化试验多目标优化设计

张立杰^1,^2,³(),阿喜塔^1,²,田笑^1,²,李稳^1,^2,³()

^1.燕山大学先进锻压成形技术与科学教育部重点实验室，河北秦皇岛 066004
^2.燕山大学河北省重型机械流体动力传输与控制重点实验室，河北秦皇岛 066004
^3.高端工程机械智能制造国家重点实验室，江苏徐州 221004

收稿日期:2021-10-23 出版日期:2022-02-01 发布日期:2022-02-17
通讯作者: 李稳 E-mail:ljzhang@ysu.edu.cn;liwen9933@126.com
作者简介:张立杰（1969-），男，教授，博士.研究方向：液压测控技术，机器人技术.E-mail：ljzhang@ysu.edu.cn
基金资助:
国家自然科学基金项目(51875499)

Multi⁃objective optimization design of accelerated degradation test based on Gamma process

Li-jie ZHANG^1,^2,³(),Xi-ta A^1,²,Xiao TIAN^1,²,Wen LI^1,^2,³()

^1.Key Laboratory of Advanced Forging & Stamping Technology and Science，Ministry of Education of China，Yanshan University，Qinhuangdao 066004，China
^2.Hebei Key Laboratory of Heavy Machinery Fluid Power Transmission and Control，Yanshan University，Qinhuangdao 066004，China
^3.State Key Laboratory of Intelligent Manufacturing of Advanced Construction Machinery，Xuzhou 221004，China

Received:2021-10-23 Online:2022-02-01 Published:2022-02-17
Contact: Wen LI E-mail:ljzhang@ysu.edu.cn;liwen9933@126.com

摘要/Abstract

摘要：

为得到加速退化试验优化设计中兼顾多个优化目标的相对最优试验配置，提出一种恒定应力加速退化试验多目标优化设计方法。基于Gamma过程建立了加速退化模型，通过极大似然估计方法求解未知参数。综合考虑模型拟合精度及寿命估计精度构建了多目标优化模型，通过NSGA-II对模型进行求解，建立兼顾多个优化目标的Pareto前沿集。以单目标优化目标函数值为基准，计算Pareto前沿集中的各目标函数相对比重。在此基础上，采用层次分析法对拟进行的加速退化试验进行专家决策，得出各目标函数的权重。以目标函数相对比重与目标函数权重误差最小为评价标准，选出Pareto前沿集中的相对最优试验配置。最后，以碳膜电阻的加速退化试验数据为实例验证了本文方法的有效性。

关键词: 加速退化试验, 多目标优化设计, Gamma过程, 层次分析法

Abstract:

In order to obtain the relative optimal test configuration considering multiple optimization objectives in the optimization design of accelerated degradation test， a multi-objective optimization design method of constant stress accelerated degradation test is proposed. The accelerated degradation model is established based on gamma process， and the unknown parameters are solved by maximum likelihood estimation method. Considering the model fitting accuracy and life estimation accuracy， a multi-objective optimization model is constructed. The model is solved by NSGA-II， and a Pareto frontier set considering multiple optimization objectives is established. The relative proportion of each objective function in Pareto frontier set is calculated based on the value of single objective optimization objective function. On this basis， the Analytic Hierarchy Process is used to make expert decision on the accelerated degradation test to be carried out， and the weight value of each objective function is obtained. Taking the minimum error between the relative proportion of the objective function and the weight value of the objective function as the evaluation standard， the relatively optimal test configuration in the Pareto front set is selected. Finally， the effectiveness of the proposed method is verified by the accelerated degradation test data of carbon film resistance.

Key words: accelerated degradation test, multi-objective optimization design, Gamma process, analytic hierarchy process

中图分类号:

TB114.3

张立杰,阿喜塔,田笑,李稳. 基于Gamma过程的加速退化试验多目标优化设计[J]. 吉林大学学报(工学版), 2022, 52(2): 361-367.

Li-jie ZHANG,Xi-ta A,Xiao TIAN,Wen LI. Multi⁃objective optimization design of accelerated degradation test based on Gamma process[J]. Journal of Jilin University(Engineering and Technology Edition), 2022, 52(2): 361-367.

图/表 4

图1

表1

CSADT单目标优化设计结果"

目标函数	n₁	n₂	n₃	S₁	S₂	S₃	函数值
I（θ）	11	15	4	50	200	119	1.03×10⁸
$A v a r (M T T F ?)$	14	3	13	90	200	91	1.44×10⁹

表1

表2

表3

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基于Gamma过程的加速退化试验多目标优化设计

Multi⁃objective optimization design of accelerated degradation test based on Gamma process

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参考文献 23

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方案	n₁	n₂	n₃	S₁	S₂	S₃	R₁	R₂
1	14	3	13	90	200	91	0.2296	0.7704
2	14	4	12	90	200	92	0.2787	0.7213
3	13	4	13	92	200	94	0.2789	0.7211
4	13	5	12	92	200	94	0.3212	0.6788
5	7	6	17	50	200	105	0.3752	0.6248
6	7	6	17	50	200	106	0.3758	0.6242
7	7	6	17	50	200	107	0.3763	0.6237
8	6	7	17	50	200	105	0.4057	0.5943
9	6	7	17	50	200	107	0.4065	0.5935
10	7	7	16	50	200	105	0.4078	0.5922
11	7	7	16	50	200	107	0.4086	0.5914
12	7	8	15	50	200	106	0.4372	0.5628
13	7	8	15	50	200	107	0.4375	0.5625
14	8	8	14	50	200	108	0.4400	0.5600
15	8	9	13	50	200	109	0.4664	0.5336
16	9	9	12	50	200	110	0.4689	0.5311
17	9	9	12	50	200	113	0.4700	0.5300
18	9	10	11	50	200	110	0.4924	0.5076
19	8	11	11	50	200	112	0.5119	0.4881
20	9	11	10	50	200	108	0.5135	0.4865
21	9	11	10	50	200	111	0.5140	0.4860
22	9	12	9	50	200	111	0.5335	0.4665
23	9	12	9	50	200	114	0.5340	0.4660
24	9	13	8	50	200	112	0.5515	0.4485
25	10	13	7	50	200	110	0.5537	0.4463
26	10	13	7	50	200	118	0.5548	0.4452
27	10	14	6	50	200	114	0.5705	0.4295
28	10	15	5	50	200	113	0.5856	0.4144
29	10	15	5	50	200	114	0.5857	0.4143
30	11	15	4	50	200	119	0.5884	0.4116

方案	n₁	n₂	n₃	S₁	S₂	S₃	μ₁	μ₂
1	14	3	13	90	200	91	0.364 170	0.205 823
2	14	4	12	90	200	92	0.228 190	0.128 972
3	13	4	13	92	200	94	0.227 640	0.128 659
4	13	5	12	92	200	94	0.110 500	0.062 500
5	7	6	17	50	200	105	0.039 000	0.022 100
6	7	6	17	50	200	106	0.040 709	0.023 010
7	7	6	17	50	200	107	0.042 094	0.023 790
8	6	7	17	50	200	105	0.123 511	0.069 810
9	6	7	17	50	200	107	0.125 727	0.071 060
10	7	7	16	50	200	105	0.129 327	0.073 090