装备振动功率谱密度统计归纳误差研究

Statistical induction error of equipment vibration power spectral density

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。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。

For equipment subjected to random vibration environment,power spectral density is generally taken as the vibration environment condition.For the measured power spectral density with each frequency point satisfying normal distribution,the normal unilateral tolerance upper limit method is often used to do statistical induction,and form the test spectrum.Here,to determine the relation between upper limit estimation error and sample size,combined with the definition of upper limit of normal unilateral tolerance,formulas for RMS error and percentage error of upper limit estimation of normal unilateral tolerance were derived.The correctness of function relations was verified through numerical simulation.At the same time,formulas were reasonably simplified based on engineering practice to obtain the function relation between the maximum value of upper limit estimation error and sample size.The maximum number of samples required to control upper limit estimation error was given.Finally,a comparison was made between upper limit error of self-service tolerance and upper limit error of normal unilateral tolerance under different sample sizes.The results showed that at least 20 samples are needed to ensure the upper limit estimation error of P95/50 not exceeding 10%;at least 54 samples are required to ensure the upper limit estimation error of P99/90 not exceeding 10%;the self-service tolerance upper limit method has certain advantages in small sample statistical induction.