Abstract: The real-time residual life prediction based on kernel density estimation does not make any assumptions about the data distribution form,but studies the distribution characteristics by the data itself,which avoids the problem that many existing data-driven prediction models need model structure assumption and parameter estimation but leads to inaccurate life prediction.However,when the traditional kernel density estimation is used to estimate the probability density of bounded variables,the estimation deviation will occur at the boundary of the interval,which will affect the accuracy of the remaining life prediction.For the above problems,a real-time residual life prediction method based on kernel diffeomorphism transformation estimation was proposed.The diffeomorphism transformation was used to transform the bounded random variable to the whole real number domain,and then transformed it to the kernel density estimation problem in the traditional sense.The feasibility and effectiveness of the proposed method was verified with real-time monitoring data,and the influence of the optimal initial sample size on the accuracy of real-time residual life prediction was analyzed.

Key words: nonparametric estimation, kernel density estimation, kernel diffeomorphism transformation, adaptive window width, residual life prediction

摘要： 基于核密度估计的实时剩余寿命预测,不对数据分布形式做任何假设,而从数据本身出发研究其分布特征,避免了现有许多数据驱动方法需要进行模型结构假设及参数估计,但会导致寿命预测不够准确的问题,而传统核密度估计用于有界变量的概率密度估计时,会在区间边界处产生估计偏差,进而影响剩余寿命预测的准确性。针对以上问题,本文提出一种基于核微分同胚估计的实时剩余寿命预测方法。该方法利用微分同胚变换将有界随机变量变换到整个实数域,从而转换为传统意义上的核密度估计问题进行求解。最后,通过实例验证了该方法的可行性和有效性,并对最优初始样本数对实时剩余寿命预测准确性的影响进行了分析。

关键词: 非参数估计, 核密度估计, 核微分同胚估计, 自适应窗宽, 剩余寿命预测