Gray bootstrap method for estimating frequency-varying random vibration signals with small samples

 During environment testing, the estimation of random vibration signals (RVS) is an important technique for the airborne platform safety and reliability. However, the available methods including extreme value envelope method (EVEM), statistical tolerances method (STM) and improved statistical tolerance method (ISTM) require large samples and typical probability distribution. Moreover, the frequency-varying characteristic of RVS is usually not taken into account. Gray bootstrap method (GBM) is proposed to solve the problem of estimating frequency-varying RVS with small samples. Firstly, the estimated indexes are obtained including the estimated interval, the estimated uncertainty, the estimated value, the estimated error and estimated reliability. In addition, GBM is applied to estimating the single flight testing of certain aircraft. At last, in order to evaluate the estimated performance, GBM is compared with bootstrap method (BM) and gray method (GM) in testing analysis. The result shows that GBM has superiority for estimating dynamic signals with small samples and estimated reliability is proved to be 100% at the given confidence level.