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

• Applicants: Professorin Dr. Claudia Czado; Professor Dr.-Ing. Florian Holzapfel
• Subject Area: Mathematics ; Traffic and Transport Systems, Intelligent and Automated Traffic
• Term: from 2016 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 314284122

• Final Report Year: 2020

Final Report Abstract

Operational safety in aviation is, amongst other measures, monitored by an airline’s mandatory flight data monitoring (FDM) program. FDM evaluates operational flight data, which is recorded during conducted flights. This project investigated advanced statistical models in the form of enhanced multivariate copula structures (vine copulas) for the description of dependence structures in operational flight data. The statistical models support the analysis of residual dependencies between measured time series which currently used physical models can not reflect. First, to enable the joint work of both participating institutions, a means of providing specifically structured operational flight data to the mathematical statisticians needed to be established. Additionally, interfaces from MATLAB to statistical tools written in R and C++ were implemented. An enhancement of multivariate copula structures was the extension of the generalized additive modelling (GAM) framework for conditional copulas to pair-copula constructions (PCCs) in the form of regular vines (R-vine). Multivariate copula parameters are thereby conditioned on exogenous covariates. One study dealt with the application of the Rauch-Tung-Striebel (RTS) smoother to FDM data. The effects of allowing the covariance matrix of the measurement noise to vary in time were analysed. Furthermore, the study analysed how well the Kálmán filter assumption of normally distributed, zero mean noise is reflected in residuals. This is accomplished by fitting multivariate vine copula to the data for quantification of nonlinear dependencies. The proposal suggested a macro level view on flight data as functional data. Using the Karhunen- Loève (KL) expansion as functional principal component analysis (FPCA), wind data in the final approach was statistically modelled. The description allows to generate wind data with the same statistical characteristics as found in the recorded data.

Publications

• “Generalized Additive Models for Pair-Copula Constructions” Journal of Computational and Graphical Statistics, Vol. 27(4), pp. 715-727, 2018
  Vatter, T., Nagler, T.
  
• “Statistical Dependence Analyses of Operational Flight Data Used for Landing Reconstruction Enhancement“, 22nd Air Transport Research Society World Conference, Seoul, Südkorea, 2018
  Höhndorf, L., Nagler, T., Koppitz, P., Czado, C., Holzapfel, F.
  
• “Modeling of Stochastic Wind Based on Operational Flight Data Using Karhunen-Loeve Expansion Method”, MDPI Sensors Open Access Journal, Vol. 20
  Wang, X. , Beller, L., Czado, C., Holzapfel, F.