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经典的统计学方法无法解决乏信息数据的评估问题。结合自助法和灰色系统理论,提出一种实现乏信息空间机械臂随机振动数据估计的灰自助方法。运用自助法对乏信息振动功率谱密度进行自助再抽样得到大量样本数据;利用灰色系统理论和最大熵理论建立灰自助模型,构建振动功率谱密度在不同频率点的灰自助分布。利用灰自助方法得到随机振动功率谱密度的真值估计和区间估计。提出了可靠度偏差和区间准确度2个指标对区间估计进行评价。灰自助方法与灰色方法和自助法的对比与测量实例表明,真值估计平均相对误差小于5%,在不同置信度水平下区间估计的准确度高于97%。
Classical statistical methods can not solve the problem of assessing the lack of information. Combining with the self-help method and the gray system theory, a gray self-help method is proposed to realize the random vibration data estimation of the arm with the lack of information. Self-help resampling of the vibration power spectral density of the scarcity information is used to obtain a large amount of sample data by using the self-help method. A gray self-help model is established by using the gray system theory and the maximum entropy theory to construct a gray self-help distribution of vibration power spectral density at different frequency points. Using the gray self-help method to get the true value and interval estimation of random vibration power spectral density. Two indicators of reliability deviation and interval accuracy are proposed to evaluate interval estimation. The comparison between gray self-help method and gray method and self-help method and measurement examples show that the average relative error of true value estimation is less than 5%, and the accuracy of interval estimation is higher than 97% under different confidence levels.