Duthinh Dat, Pintar Adam L, Simiu Emil
National Institute of Standards and Technology, Gaithersburg, MD. 20899.
National Institute of Standards and Technology, Gaithersburg, MD. 2089.
Eng Struct. 2017;3. doi: 10.1061/AJRUA6.0000933.
Estimating properties of the distribution of the peak of a stationary process from a single finite realization is a problem that arises in a variety of science and engineering applications. Further, it is often the case that the realization is of length while the distribution of the peak is sought for a different length of time, > . Current methods for estimating peaks of time series have drawbacks that motivated the development of a new procedure, based on the method, an advantage of which is that it often results in an increased size of the relevant extreme value data set compared with procedures. For further comparison, the approach depends upon the estimate of the marginal distribution of a non-Gaussian time series, which is typically difficult to perform reliably. The epochal procedure for estimating peaks combined with Best Linear Unbiased Estimates (BLUE) of the Gumbel parameters was found to depend, in some cases very significantly, upon the number of partitions being used. The proposed procedure is based on a Poisson process model for the thresholded pressure coefficient , with threshold . The estimated peak depends upon the choice of the threshold. However, unlike for the choice of the number of partitions for the epochal procedure, a criterion is available that allows the analyst to make an optimal choice (according to a chosen metric) of the threshold value. Two versions of the proposed new procedure have been developed. One version, denoted by FpotMax, includes estimation of a tail length parameter with a similar interpretation to the generalized extreme value distribution tail length parameter. The second version, denoted by GpotMax, assumes that the tail length parameter vanishes, resulting in a tail of the Gumbel distribution type.
从单个有限实现估计平稳过程峰值分布的性质是一个在各种科学和工程应用中都会出现的问题。此外，通常的情况是，实现的长度为 ，而要寻找的峰值分布对应的时间长度为 ，且 > 。当前估计时间序列峰值的方法存在缺陷，这促使人们基于 方法开发一种新的程序，该方法的一个优点是，与 程序相比，它通常会使相关极值数据集的规模增大。为了进行进一步比较， 方法依赖于对非高斯时间序列边际分布的估计，而这通常很难可靠地进行。人们发现，估计峰值的时期程序与耿贝尔参数的最佳线性无偏估计（BLUE）相结合，在某些情况下对所使用的分区数量非常敏感。所提出的程序基于阈值压力系数 的泊松过程模型，阈值为 。估计的峰值取决于阈值的选择。然而，与时期程序中分区数量 的选择不同，有一个标准可供分析师根据所选指标对阈值进行最优选择。已经开发了所提出的新程序的两个版本。一个版本记为FpotMax，包括对一个尾长参数的估计，其解释与广义极值分布尾长参数类似。第二个版本记为GpotMax，假设尾长参数为零，从而得到耿贝尔分布类型的尾部。
