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摘要:
为了精确评估数控系统伺服驱动单元的可靠性，提出了一种多阶段退化数据融合的可靠性建模方法。通过分析多种退化过程模型，针对不同伺服驱动单元之间存在的个体差异特点，引入随机效应并给出了考虑个体差异的可靠性模型建立方案；采用贝叶斯方法通过考虑多种退化过程，将不同退化的数据进行融合，建立了多阶段退化数据融合的伺服驱动单元可靠性模型，并采用马尔可夫链蒙特卡罗方法完成模型参数估计；在实验室环境下搭建伺服驱动单元加载测试平台，采集实验数据验证了模型的有效性。
Abstract:In order to accurately evaluate the reliability of the servo drive unit of a computer numerical control (CNC) system, a reliability modeling method with multi-stage degradation data fusion was proposed. Firstly, by analyzing multiple degradation process models, random effects were introduced, and a reliability model building scheme considering individual differences was given for the characteristics of individual differences existing between different servo drive units. Then, a Bayesian approach was adopted to fuse different degradation data by considering multiple degradation processes, and a reliability model of servo drive units with multi-stage degradation data fusion was established. Moreover, a Markov chain Monte Carlo (MCMC) method was used to complete the model parameter estimation. Finally, a servo drive unit loading test platform was built in the laboratory environment to collect experimental data and verify the validity of the model.
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Key words:
- degradation process /
- data fusion /
- Bayesian approach /
- servo drive unit /
- reliability modeling
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图 3 水平及竖直振动退化累积曲线
Figure 3. Horizontal and vertical vibration degradation accumulation curves
图 4 维纳过程参数后验分布概率密度函数及自相关性
Figure 4. Probability density function and auto-correlation of posterior distribution of Wiener process parameters
图 5 伽马过程参数后验分布概率密度函数及自相关性
Figure 5. Probability density function and auto-correlation of posterior distribution of gamma process parameters
图 6 逆高斯过程参数后验分布概率密度函数自相关性
Figure 6. Probability density function and auto-correlation of posterior distribution of inverse Gaussian process parameters
图 7 维纳过程参数的历史迭代轨迹图
Figure 7. Historical iterative trajectory of Wiener process parameters
图 8 伽马过程参数的历史迭代轨迹图
Figure 8. Historical iterative trajectory of Gamma process parameters
图 9 逆高斯过程参数的历史迭代轨迹图
Figure 9. Historical iterative trajectory of inverse Gaussian process parameters
图 10 融合多阶段退化数据后模型后验分布概率密度函数
Figure 10. Probability density function of posterior distribution of model after fusing multi-stage degradation data
图 11 融合多阶段退化数据后模型关键参数自相关性
Figure 11. Auto-correlation of key model parameters after fusing multi-stage degradation data
表 1 伺服驱动单元初期试验退化数据
Table 1. Initial test degradation data of servo drive unit
时间/h 水平退化/g 竖直退化/g 时间/h 水平退化/g 竖直退化/g 时间/h 水平退化/g 竖直退化/g 0 0 0 0 0 0 0 0 0 493 0.080 0.095 574 0.053 0.059 488 0.058 0.053 806 0.125 0.150 996 0.090 0.101 958 0.116 0.103 1 218 0.190 0.227 1 554 0.143 0.156 1 439 0.169 0.155 1 544 0.246 0.276 1 972 0.184 0.202 2 044 0.240 0.222 1 998 0.320 0.396 2 498 0.234 0.257 2 399 0.282 0.261 2 685 0.446 0.556 3 115 0.294 0.323 2 961 0.353 0.327 3 279 0.569 0.696 3 529 0.338 0.370 3 362 0.405 0.377 
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表 2 伺服驱动单元后期试验退化数据
Table 2. Post-test degradation data of servo drive unit
时间/h 水平退化/g 竖直退化/g 时间/h 水平退化/g 竖直退化/g 时间/h 水平退化/g 竖直退化/g 5 000 1.045 1.346 5 000 0.512 0.570 5 000 0.666 0.614 5 215 1.113 1.466 5 226 0.542 0.609 5 246 0.706 0.660 5 434 1.214 1.580 5 518 0.586 0.662 5 517 0.760 0.706 5 742 1.361 1.785 5 748 0.619 0.704 5 693 0.796 0.741 5 998 1.492 1.943 6 021 0.664 0.759 5 914 0.849 0.785 6 259 1.632 2.128 6 256 0.702 0.808 6 285 0.941 0.865 6 517 1.794 2.346 6 543 0.749 0.871 6 514 0.999 0.922 6 698 1.911 2.492 6 796 0.799 0.933 6 738 1.069 0.977 6 979 2.102 2.750 7 081 0.865 1.010 7 002 1.148 1.056 7 284 2.333 3.029 7 286 0.914 1.085 7 240 1.244 1.140 7 518 2.529 3.303 7 518 0.971 1.173 7 532 1.368 1.261 7 752 2.737 3.615 7 693 1.017 1.236 7 733 1.469 1.353 8048 2.999 4.003 7 978 1.131 1.389 7 969 1.640 1.482 8244 3.222 4.293 8 258 1.258 1.582 8 259 1.899 1.700 8517 3.534 4.780 8 488 1.384 1.811 8 529 2.196 1.987
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表 3 3种模型的相关参数估计结果
Table 3. Three model parameter estimation results
模型 参数 均值 标准差 MCMC误差 维纳
退化过程δ 0.283 0.210 0.007 58 μ 5. 336×103 261.000 2.020 θ 3.757×10−5 5.831×10−5 1.425×10−6 伽马
退化过程δ 1.018 0.445 0.011 9 η 83.470 13.920 0.258 γ 66.560 23.580 0.612 逆高斯
退化过程α 0.027 4 0.183 0.008 77 δ 8.439×10−4 0.0227 8.463×10−4 λ 4.613×109 3.385×109 1.534×108
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表 4 融合模型参数估计结果
Table 4. Results of fusion model parameter estimation
参数 均值 标准差 MCMC误差 95%置信区间 ω(样本1) 19.3 5.87 0.06595 [11.09,33.54] ω(样本2) 0.6146 0.2624 0.003225 [ 0.2946 ,1.2570 ]ω(样本3) 2.366 0.8213 0.007614 [1.238,4.403] Rω(样本1) 0.05616 0.01554 1.677×10−4 [ 0.02981 ,0.09016 ]Rω(样本2) 1.871 0.6728 0.00691 [ 0.7952 ,3.3940 ]Rω(样本3) 0.4692 0.1487 0.001214 [ 0.2271 ,0.8075 ]μ(样本1) 3.286×10−4 1.32×10−4 9.051×10−7 [6.723×10−5,5.883×10−4] μ(样本2) 1.252×10−4 2.279×10−5 1.668×10−7 [8.0×10−5,1.702×10−4] μ(样本3) 1.922×10−4 4.661×10−5 2.767×10−7 [9.719×10−5,2.848×10−4] δ 0.2314 0.1796 0.002692 [ 0.02694 ,0.70420 ]γ 1.242 0.7701 0.01149 [ 0.2735 ,3.1560 ]θ 2.284 1.672 0.01465 [0.334,6.557]
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