Copula based dependence analysis of functional data for validation and calibration of dynamic aircraft models

基于 Copula 的功能数据依赖性分析，用于动态飞机模型的验证和校准

基本信息

批准号：
314284122
负责人：
Professorin Dr. Claudia Czado
金额：
--
依托单位：
Lehrstuhl für Flugsystemdynamik
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2016
资助国家：
德国
起止时间：
2015-12-31 至 2019-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/314284122?language=en
关键词：
Copula based dependence analysis functional

项目摘要

Physical models of aircraft motion are cast into a set of differential equations describing the relationship between several variables of interest. They are crucial tools for the analysis of flight risks, such as Hard Landings or Runway Excursions. We investigate - in a statistical sense - if the catalog of currently used physical models appropriately captures the dependencies between recorded variables in real data. To get a comprehensive view of the models' adequacy, the analysis will be run on different time scales.The most powerful tool for the statistical analysis of dependencies is the copula. It captures the dependencies in a finite-dimensional vector of random variables. On some time scales, however, the recorded variable trajectories in our data have to be interpreted as random functions (i.e., infinite-dimensional) of time. For such situations, we develop a copula-based modeling framework for the dependence between random functions. We find finite-dimensional representations of the infinite-dimensional random functions using functional principal component scores. These scores can then be equipped with a flexible vine copula model that describes the dependencies. Using real data from operational flights, this dependence model can be used to assess several state of the art physical models of aircraft motion. One goal is to use the dependence characterization for physical model calibration. Thereby, the dependence structure between time series is estimated for both, the recorded data and the model output. Subsequently, initial parameters of the physical model are updated in several iterations so that the estimated dependence structures match more closely. It is investigated, whether this parameter estimation technique improves over state of the art methods. In case the parameter estimation can not be done adequately, the analyses of the dependence structure will be used to enhance the physical model by modifying the corresponding differential equations to give a more appropriate representation of relationships between the variables.

飞机运动的物理模型被转化为一组微分方程，描述了几个感兴趣的变量之间的关系。它们是分析飞行风险（例如硬着陆或跑道偏离）的重要工具。我们从统计意义上调查当前使用的物理模型的目录是否适当地捕获了实际数据中记录的变量之间的依赖关系。为了全面了解模型的充分性，分析将在不同的时间尺度上运行。用于依赖性统计分析的最强大的工具是 copula。它捕获随机变量的有限维向量中的依赖性。然而，在某些时间尺度上，我们数据中记录的变量轨迹必须被解释为时间的随机函数（即无限维）。对于这种情况，我们开发了一个基于 copula 的建模框架，用于随机函数之间的依赖关系。我们使用函数主成分分数找到无限维随机函数的有限维表示。然后，这些分数可以配备一个灵活的 vine copula 模型来描述依赖性。使用来自运营飞行的真实数据，这种依赖性模型可用于评估飞机运动的几种最先进的物理模型。目标之一是使用依赖性表征进行物理模型校准。因此，可以估计记录数据和模型输出的时间序列之间的依赖结构。随后，物理模型的初始参数在多次迭代中更新，使得估计的依赖结构更加匹配。研究了这种参数估计技术是否比最先进的方法有所改进。如果参数估计不能充分完成，则依赖结构的分析将用于通过修改相应的微分方程来增强物理模型，以给出变量之间关系的更合适的表示。