装备振动功率谱密度统计归纳误差研究

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振动与冲击 ›› 2023, Vol. 42 ›› Issue (17) : 188-193.

论文

装备振动功率谱密度统计归纳误差研究

申加康1，徐俊1，张建军1，李贺1，万军2

作者信息 +

Statistical induction error of equipment vibration power spectral density

SHEN Jiakang1, XU Jun1, ZHANG Jianjun1, LI He1, WAN Jun2

Author information +

文章历史 +

摘要

承受随机振动环境的装备，一般采用功率谱密度作为振动环境条件。对于各频点幅值满足正态分布的实测功率谱密度，常采用正态单边容差上限方法进行统计归纳形成试验谱。为确定上限估计误差与样本量的关系，结合正态单边容差上限的定义，推导了正态单边容差上限估计的均方根误差和百分比误差的公式，并结合数值仿真校验了此函数关系的正确性，同时结合工程实际对公式合理简化，得到上限估计误差的最大值与样本量的函数关系式，并给出了控制上限估计误差所需的最大样本个数。最后，对比了不同样本量下自助容差上限和正态单边容差上限误差，结果表明：至少需要20个样本才能使得P95/50上限估计误差不超过10%；至少需要54个样本才能使得P99/90上限估计误差不超过10%；自助容差上限方法在小样本统计归纳时有一定优势。

Abstract

For equipment subjected to random vibration environment, power spectral density is generally used as the vibration environment condition. For the measured power spectrum density whose amplitudes of each frequency point satisfy the normal distribution, the upper normal one-sided tolerance limit is often used to perform statistical induction to form the test spectrum. To determine the relationship between estimated error and sample size, combined with the definition of upper normal one-sided tolerance limit, the mathematical formulas of root mean square error and percent error are deduced. And combined with numerical simulation to verify the correctness of this function relationship. At the same time, the formula is reasonably simplified in combination with the engineering practice, and the function relationship between the upper normal one-sided tolerance limit estimate error and the number of samples is obtained. Meanwhile, the maximum number of samples required for the upper limit estimation error is given. Finally, the upper tolerance limit based bootstrap method and the upper limit of normal unilateral tolerance were compared with different sample sizes. The results show that: at least 20 samples are needed to make the P95/50 estimated error not exceed 10%. at least 55 samples are required to make the P95/50 estimated error not exceed 10%. the upper tolerance limit based bootstrap method has certain advantages in statistical induction of small samples.

导出引用

申加康1，徐俊1，张建军1，李贺1，万军2. 装备振动功率谱密度统计归纳误差研究[J]. 振动与冲击, 2023, 42(17): 188-193

SHEN Jiakang1, XU Jun1, ZHANG Jianjun1, LI He1, WAN Jun2. Statistical induction error of equipment vibration power spectral density[J]. Journal of Vibration and Shock, 2023, 42(17): 188-193

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