Validating an Air Traffic Management Concept of Operation Using Statistical Modeling

Validating a concept of operation for a complex, safety-critical system (like the National Airspace System) is challenging because of the high dimensionality of the controllable parameters and the infinite number of states of the system. In this paper, we use statistical modeling techniques to explore the behavior of a conflict detection and resolution algorithm designed for the terminal airspace. These techniques predict the robustness of the system simulation to both nominal and off-nominal behaviors within the overall airspace. They also can be used to evaluate the output of the simulation against recorded airspace data. Additionally, the techniques carry with them a mathematical value of the worth of each prediction-a statistical uncertainty for any robustness estimate. Uncertainty Quantification (UQ) is the process of quantitative characterization and ultimately a reduction of uncertainties in complex systems. UQ is important for understanding the influence of uncertainties on the behavior of a system and therefore is valuable for design, analysis, and verification and validation. In this paper, we apply advanced statistical modeling methodologies and techniques on an advanced air traffic management system, namely the Terminal Tactical Separation Assured Flight Environment (T-TSAFE). We show initial results for a parameter analysis and safety boundary (envelope) detection in the high-dimensional parameter space. For our boundary analysis, we developed a new sequential approach based upon the design of computer experiments, allowing us to incorporate knowledge from domain experts into our modeling and to determine the most likely boundary shapes and its parameters. We carried out the analysis on system parameters and describe an initial approach that will allow us to include time-series inputs, such as the radar track data, into the analysi

Bayesian Statistics and Uncertainty Quantification for Safety Boundary Analysis in Complex Systems

The analysis of a safety-critical system often requires detailed knowledge of safe regions and their highdimensional non-linear boundaries. We present a statistical approach to iteratively detect and characterize the boundaries, which are provided as parameterized shape candidates. Using methods from uncertainty quantification and active learning, we incrementally construct a statistical model from only few simulation runs and obtain statistically sound estimates of the shape parameters for safety boundaries

A Hardware Model Validation Tool for Use in Complex Space Systems

One of the many technological hurdles that must be overcome in future missions is the challenge of validating as-built systems against the models used for design. We propose a technique composed of intelligent parameter exploration in concert with automated failure analysis as a scalable method for the validation of complex space systems. The technique is impervious to discontinuities and linear dependencies in the data, and can handle dimensionalities consisting of hundreds of variables over tens of thousands of experiments

From chains to networks: An adaptive, coarse -grained method for simulating elastomers at the rubbery plateau

Computational modeling for elastomers still faces unique challenges due to the fact that phenomena of interest require a large range of length scales in order to capture material properties. Behaviors like crazing and the strength of double network hydrogels require length scales smaller than chain length to appropriately model. However, a typical elastomer has on the order of 10 19 crosslinks in one mL of volume, which means that a simulation that is entirely resolved to the scale of chain lengths is computationally prohibitive. To study these behaviors computationally requires a new method that can bridge a wide range of length scales while still preserving the underlying physics of the problem. This work presents a new, multi-scale, adaptive method for the simulation of deformation in elastomer networks. Recent research has indicated that elastomer networks do not deform perfectly affinely although large regions of the network can be approximated as doing so. We assume that topographically local parts of the network deform affinely, and have developed a very fast interpolation method that allows us to find the energy, forces, and stiffness in these affine parts of the network. By iteratively refining our network and testing our affinity assumption, we end up with networks in which many crosslinks can be described with relatively few degrees of freedom, and the positions of some crosslinks are determined explicitly. The advantage of this method is that large networks can be computationally simulated while still preserving fine scales in regions of interest