Estimation of random vibration signals with small samples using bootstrap maximum entropy method

The precise estimation of random vibration signals (RVS) is the important guarantee for safety and stability in flight. But in testing phase, RVS with small samples are obtained under the condition of unknown probability distribution. The current estimation methods based on statistical theory could not be used to estimate this kind of small samples. In this paper, a novel bootstrap maximum entropy method (BMEM) is proposed, which combines the advantages of bootstrap method (BM) and maximum entropy method (MEM). In addition, the proposed method is innovatively used for estimating RVS in the frequency domain with small samples. The estimation indices include the estimated expected value, estimated interval and expanded uncertainty. The estimation performance is quantified by the relative error and reliability. Firstly, BMEM is employed to analyze estimated expected value and estimated interval. The estimation results of BMEM are compared with MEM's and BM's quantitatively. Secondly, BMEM is employed to estimate expanded uncertainty. The adaptability of BMEM is proved by simulation experiments for different probability distributions. And the estimation precision of BMEM is demonstrated more accurate than grey system theory (GST), MEM and the conventional statistical methods. Finally, the real and simulation experiments results show that the proposed method is appropriate and effective for estimating RVS with small samples.