Global error estimation in CFD mesh coarsening process for uncertainty quantification methods

Due to high performance of modern computers, Uncertainty Quantification is becoming an important part of engineering design. Every non intrusive Uncertainty Quantification method requires a considerable number of evaluations of the model, meaning that the design process is more expensive in terms of computational resources/time. In Computational Fluid Dynamics, the usual practice is to reduce the computational time by reducing the number of nodes of the used mesh. Each coarsening of the mesh leads to the increase of the error measured as the difference between the real solution and the solution provided by the computational model. In this work, an approach for quantification of the global error around the stochastic domain, in a mesh reduction process, is described and results obtained for a test case are detailed. The method is based on a comparison of the high accurate mesh against coarse mesh with lower accuracy, but less expensive in terms of computational time. The global error is defined as a volume difference between surrogate models created in the stochastic domain. The stochastic domain is given by pre-specified input variables with appropriate boundaries. Surrogate models are used and a non intrusive polynomial chaos model is created with response samples from high and low accuracy mesh. For the chosen test case, the input variables, related to the stochastic space, were the free stream pressure and free stream Mach number. A hypersonic flow solver developed at the von Karman Institute, Cosmic, was used to compute properties of a flow around the reentry spacecraft. A computational expensive mesh was used as a reference mesh. Due to computational resources, it was impossible to use expansive mesh for Monte Carlo simulation or high order Polynomial Chaos. Therefore, the global error estimation approach was applied to find an accurate and relatively inexpensive mesh for Uncertainty Quantification in hypersonic simulation. Multiple meshes with different coarsening were tested, based on expert knowledge of the problem. The global error estimation method allowed for finding a final mesh, with an error on the mean value 0.48% and on the standard deviation 5.89%, which was 4 times faster than the reference mesh

Aero-thermal re-entry sensitivity analysis using DSMC and a high dimensional model representation-based approach

This paper presents a sensitivity analysis for the hypersonic aero-thermal convective heat transfer from the free molecular to the slip-flow regime for cylindrical and cubic geometries. The analyses focus on a surface-averaged heat transfer coefficient at various atmospheric conditions. The sensitivity analyses have been performed by coupling a High Dimensional Model Representation based approach and a Direct Simulation Monte Carlo code. The geometries have been tested with respect to different inputs parameters; altitude, attitude, wall temperature and geometric characteristics. After the initial sensitivity analyses, the N-dimensional surrogate models of the surface-averaged heat transfer coefficient have been defined and tested. Hereby, a shape-based DSMC mesh refinement correction factor for reducing the overall analyses computational times is also presented

Debris re-entry modeling using high dimensional derivative based uncertainty quantification

Well-known tools developed for satellite and debris re-entry perform break-up and trajectory simulations in a deterministic sense and do not perform any uncertainty treatment. In this paper, we present work towards implementing uncertainty treatment into a Free Open Source Tool for Re-entry of Asteroids and Space Debris (FOSTRAD). The uncertainty treatment in this work is limited to aerodynamic trajectory simulation. Results for the effect of uncertain parameters on trajectory simulation of a simple spherical object is presented. The work uses a novel uncertainty quantification approach based on a new derivation of the high dimensional model representation method. Both aleatoric and epistemic uncertainties are considered in this work. Uncertain atmospheric parameters considered include density, temperature, composition, and free-stream air heat capacity. Uncertain model parameters considered include object flight path angle, object speed, object mass, and direction angle. Drag is the only aerodynamic force considered in the planar re-entry problem. Results indicate that for initial conditions corresponding to re-entry from a circular orbit, the probabilistic distributions for the impact location are far from the typically used Gaussian or ellipsoids and the high probability impact location along the longitudinal direction can be spread over ∼2000 km, while the overall distribution can be spread over ∼4000 km. High probability impact location along the lateral direction can be spread over ∼400 km

Surrogate model for probabilistic modeling of atmospheric entry for small NEO's

Near Earth Objects (NEOs) enter the Earths atmosphere on a regular basis. Depending on the size, object and entry parameters; these objects can burn-up through ablation (complete evaporation), undergo fragmentation of varying nature, or impact the ground unperturbed. Parameters that influence the physics during entry are either unknown or highly uncertain. In this work, we propose a probabilistic approach for simulating entry. Probabilistic modeling typically requires an expensive Monte Carlo approach. In this work, we develop and present a novel engineering approach of developing surrogate models for simulation of the atmospheric entry accounting for drag, ablation, evaporation, fragmentation, and ground impact

Sensitivity analysis and probabilistic re-entry modeling for debris using high dimensional model representation based uncertainty treatment

Well-known tools developed for satellite and debris re-entry perform break- up and trajectory simulations in a deterministic sense and do not perform any uncertainty treatment. The treatment of uncertainties associated with the re-entry of a space object requires a probabilistic approach. A Monte Carlo campaign is the intuitive approach to performing a probabilistic analysis, however, it is computationally very expensive. In this work, we use a recently developed approach based on a new derivation of the high dimensional model representation method for implementing a computationally efficient probabilistic analysis approach for re-entry. Both aleatoric and epistemic uncertainties that affect aerodynamic trajectory and ground impact location are considered. The method is applicable to both controlled and uncontrolled re-entry scenarios. The resulting ground impact distributions are far from the typically used Gaussian or ellipsoid distributions

Comparison of non-intrusive approaches to uncertainty propagation in orbital mechanics

The paper presents four different non-intrusive approaches to the propagation of uncertainty in orbital dynamics with particular application to space debris orbit analysis. Intrusive approaches are generally understood as those methods that require a modification of the original problem by introducing a new algebra or by directly embedding high-order polynomial expansions of the uncertain quantities in the governing equations. Non-intrusive approaches are instead based on a polynomial representations built on sparse samples of the system response to the uncertain quantities. The paper will present a standard Polynomial Chaos Expansion, an Uncertain Quantification-High Dimensional Model Representation, a Generalised Kriging model and an expansion with Tchebycheff polynomials on sparse grids. The work will assess the computational cost and the suitability of these methods to propagate different type of orbits

A novel model for uncertainty propagation analysis applied for human thermal comfort evaluation

The comfort sensation is mainly affected by six variables: air temperature, mean radiant temperature, air velocity, relative humidity, personal metabolism and clothing insulation. These are characterized by different mean values and distributions. To analyze the uncertainty propagation three numerical models are used: the Fully Monte Carlo Simulation MCSs, the Monte Carlo Simulation Trials MCSt, and a novel model named "Adaptive Derivative based High Dimensional Model Representation" (AD-HDMR). In the paper these three different methods are applied to the thermal comfort evaluation, through the PMV Index, they are analyzed and their efficiency was verified in terms of computational time. To allow a revision of this index, the effect of the different variables was then analyzed

OPTICAL NERVE SEGMENTATION USING THE ACTIVE SHAPE METHOD

The paper deals with the segmentation procedure for optical nerve localization and the consequent determination of geometrical parameters such as optical nerve area, radius and diameter. An extraction of these geometrical parameters is especially important for clinical practice particularly in the case where retinal lesions are present. On the base of the optical nerve extraction, we are capable of comparing it with area of retinal lesions. Via this approach it is possible to track time evaluation of retinal lesions. The proposed algorithm for segmentation of optical nerve area is performed within two main steps. In the first step, the active contour method is used specially for the localization of the optical nerve. This part of the algorithm generates mathematical model of the optical nerve in binary form. Consequently, on the base of this mathematical model of the optical nerve respective geometrical parameters are worked out for future comparison with retinal lesions. Image preprocessing is an integral part of the segmentation procedure, improving the observability of the optical nerve to ensure as relevant detection of the optical nerve as possible

A MATLAB-BASED GUI FOR REMOTE ELECTROOCULOGRAPHY VISUAL EXAMINATION

In this work, a MATLAB-based graphical user interface is proposed for the visual examination of several eye movements. The proposed solution is algorithm-based, which localizes the area of the eye movement, removes artifacts, and calculates the view trajectory in terms of direction and orb deviation. To compute the algorithm, a five-electrode configuration is needed. The goodness of the proposed MATLAB-based graphical user interface has been validated, at the Clinic of Child Neurology of University Hospital of Ostrava, through the EEG Wave Program, which was considered as “gold standard” test. The proposed solution can help physicians on studying cerebral diseases, or to be used for the development of human-machine interfaces useful for the improvement of the digital era that surrounds us today

Failure modes and criticality analysis of the preliminary design phase of the Mars Desert Research Station considering human factors

This work presents an extension to the traditional FMECA (Failure Modes, Effects and Criticality Analysis) method to include the effects of human factors concerning accessibility/repairability, probability of contact and degree of contact. The authors refer to this extension to the traditional FMECA as the Human Design Approach (HDA). All data used in this study was collected during the stay of two of the authors at the Mars Desert Research Station (MDRS) in the Utah desert, USA. The MDRS is a laboratory for carrying out research in order to understand and investigate the difficulties of how to live and work on another planet. The results show that following the HDA can enhance the safety and reliability of the MDRS. There is still a significant amount of research required concerning reliability analysis of the space habitat in terms of the selection of optimum designs, the modification of systems, as well as access, inspection and maintenance strategies, human factors and environmental impacts. This preliminary study will assist the design engineers with the selection of an optimum configuration for space habitats and can be extended to any case where humans can influence function of an environment