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

SU(2) gluon propagator on a coarse anisotropic lattice

We calculated the SU(2) gluon propagator in Landau gauge on an anisotropic coarse lattice with the improved action. The standard and the improved scheme are used to fix the gauge in this work. Even on the coarse lattice the lattice gluon propagator can be well described by a function of the continuous momentum. The effect of the improved gauge fixing scheme is found not to be apparent. Based on the Marenzoni's model, the mass scale and the anomalous dimension are extracted and can be reasonably extrapolated to the continuum limit with the values $\alpha\sim 0.3$ and $M\sim 600MeV$. We also extract the physical anisotropy $\xi$ from the gluon propagator due to the explicit $\xi$ dependence of the gluon propagator.Comment: LaTeX, 14 pages including 4 ps figure

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

Towards Validation of an Adaptive Flight Control Simulation Using Statistical Emulation

Traditional validation of flight control systems is based primarily upon empirical testing. Empirical testing is sufficient for simple systems in which a.) the behavior is approximately linear and b.) humans are in-the-loop and responsible for off-nominal flight regimes. A different possible concept of operation is to use adaptive flight control systems with online learning neural networks (OLNNs) in combination with a human pilot for off-nominal flight behavior (such as when a plane has been damaged). Validating these systems is difficult because the controller is changing during the flight in a nonlinear way, and because the pilot and the control system have the potential to co-adapt in adverse ways traditional empirical methods are unlikely to provide any guarantees in this case. Additionally, the time it takes to find unsafe regions within the flight envelope using empirical testing means that the time between adaptive controller design iterations is large. This paper describes a new concept for validating adaptive control systems using methods based on Bayesian statistics. This validation framework allows the analyst to build nonlinear models with modal behavior, and to have an uncertainty estimate for the difference between the behaviors of the model and system under test

Why Do Shoppers Choose your Pack? The Impact of Product Package Design on Consumers’ Brand Stereotypes and Purchase Intention

Given the pivotal role of product package design in the visual representation of brands, we argue that its associated aesthetic, functional and symbolic values may affect brand stereotypes, i.e. warmth and competence, hence consumer purchase intention. We also argue that such effects are conditional on consumers’ centrality of visual product aesthetics (CVPA), representing consumers’ aesthetical sensitivity and dominance when evaluating the product’s presentation. Through a survey (n=661) examining consumers’ reactions toward new packaging designs, we find that only symbolic and functional dimensions positively influence brand warmth and competence. Only brand warmth significantly affects and mediates these effects on purchase intention. CVPA elevates the effect of symbolism on brand warmth while negatively moderating the effect of aesthetics on brand warmth. The results contribute to the product package design literature and the practical implications of these findings are discussed

Effect of low-Raman window position on correlated photon-pair generation in a chalcogenide Ge11.5As24Se64.5 nanowire

We investigated correlated photon-pair generation via spontaneous four-wave mixing in an integrated chalcogenideGe11.5As24Se64.5photonicnanowire. The coincidence to accidental ratio, a key measurement for the quality of correlated photon-pair sources, was measured to be only 0.4 when the photon pairs were generated at 1.9 THz detuning from the pump frequency due to high spontaneous Raman noise in this regime. However, the existence of a characteristic low-Raman window at around 5.1 THz in this material's Raman spectrum and dispersion engineering of the nanowire allowed us to generate photon pairs with a coincidence to accidental ratio of 4.5, more than 10 times higher than the 1.9 THz case. Through comparing the results with those achieved in chalcogenide As2S3waveguides which also exhibit a low Raman-window but at a larger detuning of 7.4 THz, we find that the position of the characteristic low-Raman window plays an important role on reducing spontaneous Raman noise because the phonon population is higher at smaller detuning. Therefore the ultimate solution for Raman noise reduction in Ge11.5As24Se64.5 is to generate photon pairs outside the Raman gain band at more than 10 THz detuning

Yet another breakdown point notion: EFSBP - illustrated at scale-shape models

The breakdown point in its different variants is one of the central notions to quantify the global robustness of a procedure. We propose a simple supplementary variant which is useful in situations where we have no obvious or only partial equivariance: Extending the Donoho and Huber(1983) Finite Sample Breakdown Point, we propose the Expected Finite Sample Breakdown Point to produce less configuration-dependent values while still preserving the finite sample aspect of the former definition. We apply this notion for joint estimation of scale and shape (with only scale-equivariance available), exemplified for generalized Pareto, generalized extreme value, Weibull, and Gamma distributions. In these settings, we are interested in highly-robust, easy-to-compute initial estimators; to this end we study Pickands-type and Location-Dispersion-type estimators and compute their respective breakdown points.Comment: 21 pages, 4 figure

Decay rate estimations for linear quadratic optimal regulators

Let $u(t)=-Fx(t)$ be the optimal control of the open-loop system $x'(t)=Ax(t)+Bu(t)$ in a linear quadratic optimization problem. By using different complex variable arguments, we give several lower and upper estimates of the exponential decay rate of the closed-loop system $x'(t)=(A-BF)x(t)$. Main attention is given to the case of a skew-Hermitian matrix $A$. Given an operator $A$, for a class of cases, we find a matrix $B$ that provides an almost optimal decay rate. We show how our results can be applied to the problem of optimizing the decay rate for a large finite collection of control systems $(A, B_j)$, $j=1, \dots, N$, and illustrate this on an example of a concrete mechanical system. At the end of the article, we pose several questions concerning the decay rates in the context of linear quadratic optimization and in a more general context of the pole placement problem.Comment: 25 pages, 1 figur

In-situ micro-tensile testing of AA2024-T3 fibre laser welds with digital image correlation as a function of welding speed

In this paper, the influence of welding speed on tensile properties of AA2024-T3 fibre laser welds was investigated by monitoring the deformation behaviour during tensile loading. In-situ micro-tensile testing combined with a high-resolution optical microscope and DIC was used to measure strain distribution in narrow weld regions showing characteristics of fibre laser beam welding with limited metallurgical modifications. A chemical etching technique was used to generate a micro-scale random speckle pattern by revealing the weld microstructure. Such pattern enabled a sufficient spatial resolution of strain while keeping the weld seam visible during deformation. The results of microstructural and mechanical properties determined under numerous welding speeds indicated that increasing the welding speed led to the transition of weld pool shape from circular to elliptical to teardrop with a greater fraction of equiaxed dendrites. The weaker strength of the weld, as measured by local lower micro-hardness values, constrained significant plasticity development locally within the weld. Tensile tests revealed that increasing the welding speed resulted in greater yield strength and ultimate tensile strength, whereas, total elongation to failure dropped. The tensile properties improved with increasing welding speed as the fraction of equiaxed dendrites increased

Renewable fuel production from hydropyrolysis of residual biomass using molybdenum carbide-based catalysts: An analytical Py-GC/MS investigation

Fast hydropyrolysis of lignocellulosic biomass was studied by using an analytical pyrolyzer coupled with a gas chromatography/mass spectrometry set-up (Py-GC/MS). Under pure H2 stream, Canadian pinewood was rapidly heated up to 500 °C and the generated vapors passed through a catalytic bed at 500 °C. Experiments were carried out in order to compare the catalytic performance of MoC/Al2O3 catalyst to a reference catalyst based on noble metal (1.5 wt.% Pt/Al2O3). The effect of different supports (Al2O3, ZrO2 and MgO) on the carbide performance and product formation was investigated. The results showed that the performance of MoC/Al2O3 was similar to that of 1.5 wt.% Pt/Al2O3. Both of them deoxygenated the hydropyrolysis vapors and led exclusively to hydrocarbons formation. However, the proportion of aliphatic and aromatic hydrocarbons was different: MoC/Al2O3 catalyst produced more aliphatics (57%) than the Pt catalyst. The supports have demonstrated influence on the product distribution. Acidity of the support seems to play an important role in the deoxygenation of the vapors. While there was complete removal of oxygen when MoC/Al2O3 and MoC/ZrO2 were used, the same did not take place for the more basic MoC/MgO catalyst