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1. 北京航空航天大学 仪器科学与光电工程学院, 北京 100083;
2. 中国科学院光电研究院, 北京 100094

Estimation of space manipulator random vibration signals with poor information based on grey bootstrap method
WANG Qiyue1, WANG Zhongyu1 , WANG Yanqing1,2, YAO Zhenjian1
1. School of Instrumentation Science & Opto-electronics Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China;
Received: 2015-04-29; Accepted: 2015-06-26; Published online: 2015-08-03 14:23
Foundation items: Aeronautical Science Foundation of China (20100251006)
Corresponding author. Tel.: 010-82338881 E-mail: mewan@buaa.edu.cn
Abstract: The classic statistical methods based on statistical theory can not solve the estimation of poor information data. A novel method based on grey bootstrap model for space manipulator random vibration signals with poor information was presented. The random vibration measurement data was processed by the bootstrap sampling．The bootstrap sequence was derived from the bootstrap distribution, and then the system theory was used to establish a bootstrap model. The true value and the interval of the space manipulator random vibration signals with poor information were estimated．grey bootstrap method is compared with grey method and bootstrap method. Experimental results show that grey bootstrap method has high accuracy. The validity of the proposed method is examined．The mean value of estimated relative errors are less than 5%, meanwhile, the estimated interval accuracy calculated with different confidence levels are more than 97%.
Key words: poor information     space manipulator     grey bootstrap method     random vibration     estimation

1 灰自助方法 1.1 灰自助建模

1.2 估计指标

1) 真值估计

2) 区间估计

2 实例分析

 图 1 空间机械臂结构示意图 Fig. 1 Schematic of space manipulator structure
2.1 实例评估 2.1.1 真值估计

 图 2 不同方法对固结端振动信号的真值估计和估计误差 Fig. 2 Estimated values and estimated errors of fixed-end vibration signals by different methods

 % 方法 Emax Emin Erm 灰自助方法 15.84 0.11 3.83 自助法 17.01 0.25 6.45 GM(1,1) 38.22 1.69 13.56
2.1.2 区间估计

 图 3 灰自助方法计算得到的区间估计 Fig. 3 Estimated intervals calculated by grey bootstrap method
 图 4 自助法计算得到的区间估计 Fig. 4 Estimated intervals calculated by bootstrap method

 图 5 灰自助方法与自助法区间估计的可靠度偏差比较 Fig. 5 Comparison of estimated interval reliability deviation by grey bootstrap method and bootstrap method

 P/% Pr/% 自助法 灰自助方法 80 67.58 97.99 85 69.87 98.11 90 73.98 98.89 95 75.12 97.92 99 75.01 97.47
2.2 实例验证

 图 6 不同方法对自由端振动信号的真值估计和估计误差 Fig. 6 Estimated values and estimated errors of free-end vibration signals by different methods

 % 方法 Emax Emin Erm 灰自助方法 12.59 0.02 3.08 自助法 20.94 0.10 6.22

 P/% Pr/% 自助法 灰自助方法 80 69.16 97.01 85 75.87 99.74 90 79.81 99.01 95 79.91 98.61 99 79.69 97.33
3 结 论

1) 将灰自助方法应用于乏信息随机振动信号的分析中,构建了灰自助模型,拓展了随机振动信号估计方法,提出了相应的估计指标。利用灰自助方法对空间机械臂固结端振动功率谱密度进行真值估计,并与自助法和GM(1,1)比较,实例表明灰自助方法估计效果最好,在全频域真值估计的平均相对误差小于5%,验证了灰自助方法在真值估计中的优越性。

2) 利用灰自助方法对空间机械臂活动端振动功率谱密度进行区间估计,并与自助法比较说明其区间估计的特性,实例表明灰自助方法的区间估计准确度较自助法方法要好,区间估计准确度高于97%。

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#### 文章信息

WANG Qiyue, WANG Zhongyu, WANG Yanqing, YAO Zhenjian

Estimation of space manipulator random vibration signals with poor information based on grey bootstrap method

Journal of Beijing University of Aeronautics and Astronsutics, 2016, 42(4): 858-864.
http://dx.doi.org/10.13700/j.bh.1001-5965.2015.0270