Statistical induction error of equipment vibration power spectral density

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Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (17) : 188-193.

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

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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.

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upper normal one-sided tolerance limit / statistical induction / estimated error / sample size / numerical simulation

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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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