EAPSI:Investigating a Nonparametric Method to Predict Longevity of Engineering Monitoring Systems

随着工程中的系统不断变得更大、更复杂，为了更准确地预测系统故障和开发防止灾难性后果的系统，对这类系统的实时状态监测仍然是一个重要的研究领域。利用概率和统计工具，这项研究将开发一种稳健的方法来预测被分析系统的长期条件，并在未知先验分布的条件下这样做。研究将在国立台湾大学郑明彦教授的指导下进行。在贝叶斯方法中，假设先验分布，然后根据先验分布和模型的假设建立后验分布。因此，我们可以通过适当的阈值故障时间来求出概率，从而获得系统的长期状态。然而，当先验未知时，重要的是能够从由信号时间产生的样本中估计先验。本文研究的重点是将未知先验分布与基于核函数和带宽序列的光滑经验分布函数进行拟合，以估计未知先验分布。这项研究将在台湾大学数学系著名统计学家郑明彦教授的指导下进行。东亚和太平洋暑期学院项目下的这个奖项支持一名美国研究生的暑期研究，由NSF和台湾科技部联合资助。

As systems in engineering continue to become larger and more complex in nature, real time condition monitoring of such systems continues to be an important area of study in order to more accurately predict system failure and develop systems to prevent catastrophic consequences. Using probability and statistics tools, this research will develop a robust method to predict long term conditions of the systems being analyzed and to do so under conditions of unknown prior distributions. The research will be conducted under the mentorship of Professor Ming-Yen Cheng of National Taiwan University.In the Bayesian approach, prior distributions are assumed, and posterior distributions are then established from assumptions of the prior and the model. Hence, we can find the probability via the appropriate threshold failure time and access the long-term condition of the system. When the prior is unknown, however, it is then important to be able to estimate the prior from samples generated by the signal time. The focus of this research proposal is to fit the unknown prior distribution with a smooth empirical distribution function based on kernel function and sequence of bandwidths to estimate the unknown prior distribution. The research will be conducted under the mentorship of Professor Ming-Yen Cheng, a noted statistician of National Taiwan University Department of Mathematics.This award under the East Asia and Pacific Summer Institutes program supports summer research by a U.S. graduate student and is jointly funded by NSF and the Ministry of Science and Technology of Taiwan.