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首页> 外文期刊>Mechanical systems and signal processing >Clarifying and quantifying the geometric correlation for probability distributions of inter-sensor monitoring data: A functional data analytic methodology
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Clarifying and quantifying the geometric correlation for probability distributions of inter-sensor monitoring data: A functional data analytic methodology

机译：澄清和量化传感器间监视数据的概率分布的几何相关性：一种功能数据分析方法

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摘要

In structural health monitoring (SHM), revealing the underlying correlations of monitoring data is of considerable significance, both theoretically and practically. In contrast to the traditional correlation analysis for numerical data, this study seeks to analyse the correlation of probability distributions of inter-sensor monitoring data. Due to induced by some commonly shared random excitations, many structural responses measured at different locations are usually correlated in distributions. Clarifying and quantifying such distributional correlations not only enables a more comprehensive understanding of the essential dependence properties of SHM data, but also has appealing application values; however, statistical methods pertinent to this topic are rare. To this end, this article proposes a novel approach using functional data analysis techniques. The monitoring data collected by each sensor are divided into time segments and later summarized by the corresponding probability density functions (PDFs). The geometric relations of the PDFs in terms of their shape mappings between sensors are first characterized by warping functions, and they are subsequently decomposed into finite functional principal components (FPCs); one FPC of the warping functions characterizes one deformation pattern in the transformation of the shapes of the PDFs from one sensor to another. Using this principle, the inter-sensor geometric correlation patterns of PDFs can be clarified by analysing the correlation of the FPC scores of warping functions to the PDFs from one sensor. To overcome the challenge of correlation quantification for real-valued samples (FPC scores) coupled with their functional counterparts (PDFs), a novel nonparametric functional regression (NFR)-based correlation coefficient is defined. Both simulation and real data studies are conducted to illustrate and validate the proposed method.
机译：在结构健康监测（SHM）中，揭示监测数据的潜在相关性在理论上和实践上都具有重要意义。与传统的数值数据相关性分析相反，本研究旨在分析传感器间监测数据的概率分布的相关性。由于一些共同共享的随机激发的诱导，在不同位置测得的许多结构响应通常在分布中相关。澄清和量化这种分布相关性，不仅可以更全面地了解SHM数据的基本依赖性，而且具有诱人的应用价值;但是，与该主题相关的统计方法很少见。为此，本文提出了一种使用功能数据分析技术的新颖方法。每个传感器收集的监视数据被分为多个时间段，然后通过相应的概率密度函数（PDF）进行汇总。根据传感器之间的形状映射，PDF的几何关系首先通过翘曲函数进行表征，然后将它们分解为有限功能的主成分（FPC）;弯曲功能的一个FPC表征了PDF形状从一个传感器转换为另一个传感器时的一种变形模式。使用此原理，可以通过分析翘曲函数的FPC分数与一个传感器的PDF的相关性来阐明PDF的传感器间几何相关性模式。为了克服对实值样本（FPC分数）及其功能对应项（PDF）进行相关量化的挑战，定义了一种基于非参数功能回归（NFR）的新型相关系数。仿真和实际数据研究都进行了说明和验证所提出的方法。

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