An anisotropic fast marching method applied to path planning for Mars rovers

This paper presents the application of the Anisotropic Fast Marching Method to the path planning problem of mobile robots moving in outdoors environments, such as Mars. Considering that at any point on a 3D surface there are two main slopes: the maximum, which is the slope of the gradient, and the minimum, the height map of a terrain can be considered as a tensor filed. Using the Anisotropic Fast Marching Method, the resulting trajectory of the path planning takes the tensor field into account so that the slopes in the trajectory are minimized. Numerical simulations are presented to show the advantage of this method over its isotropic version. Besides, the influence of the anisotropic index and the traversability of the resultant paths are analyzed.This work was supported in part by the projects: "RoboCity2030-III-CM project (Robótica aplicada a la mejora de la calidad de vida de los ciudadanos. fase III; S2013/MIT-2748), in part by Programas de Actividades I+D en la Comunidad de Madrid and cofunded by Structural Funds of the EU" and in part by "Investigación para la mejora competitiva del ciclo de perforación y voladura en minería y obras subterráneas, mediante la concepción de nuevas técnicas de ingeniería, explosivos, prototipos y herramientas avanzadas (TUÑEL)"

Modeling the effect of soil meso- and macropores topology on the biodegradation of a soluble carbon substrate

Soil structure and interactions between biotic and abiotic processes are increasingly recognized as important for explaining the large uncertainties in the outputs of macroscopic SOM decomposition models. We present a numerical analysis to assess the role of meso- and macropore topology on the biodegradation of a soluble carbon substrate in variably water saturated and pure diffusion conditions . Our analysis was built as a complete factorial design and used a new 3D pore-scale model, LBioS, that couples a diffusion Lattice-Boltzmann model and a compartmental biodegradation model. The scenarios combined contrasted modalities of four factors: meso- and macropore space geometry, water saturation, bacterial distribution and physiology. A global sensitivity analysis of these factors highlighted the role of physical factors in the biodegradation kinetics of our scenarios. Bacteria location explained 28% of the total variance in substrate concentration in all scenarios, while the interactions among location, saturation and geometry explained up to 51% of it

Optimality and robustness in path-planning under initial uncertainty

Classical deterministic optimal control problems assume full information about the controlled process. The theory of control for general partially-observable processes is powerful, but the methods are computationally expensive and typically address the problems with stochastic dynamics and continuous (directly unobserved) stochastic perturbations. In this paper we focus on path planning problems which are in between -- deterministic, but with an initial uncertainty on either the target or the running cost on parts of the domain. That uncertainty is later removed at some time $T$, and the goal is to choose the optimal trajectory until then. We address this challenge for three different models of information acquisition: with fixed $T$, discretely distributed and exponentially distributed random $T$. We develop models and numerical methods suitable for multiple notions of optimality: based on the average-case performance, the worst-case performance, the average constrained by the worst, the average performance with probabilistic constraints on the bad outcomes, risk-sensitivity, and distributional-robustness. We illustrate our approach using examples of pursuing random targets identified at a (possibly random) later time $T$.Comment: 24 pages, 14 figures. Keywords: optimal control, path-planning, Hamilton-Jacobi PDEs, uncertainty, robustness, delayed information acquisitio

Transient Study of the Wetting Films in Porous Media Using 3D X-Ray Computed Micro-Tomography: Effect of Imbibition Rate and Pore Geometry

Imbibition in porous media is governed by the complex interplay between viscous and capillary forces, pore structure and fluid properties. Understanding and predicting imbibition is important in many natural and engineered applications; it affects the efficiency of oil production operations, the moisture and contaminant transport in soil science, and the formation of defects in certain types of composite materials. Majority of the studies published on the transient imbibition behavior in a porous medium were conducted in the simplified 2D transparent micromodels or the 2D projection visualization (X-ray or visible light) of the 3D porous medium. However, the pore level transient imbibition studies have not been reported on real three dimensional porous medium. The main challenge arises from the slowness of the present 3D imaging techniques in comparison with the speed of the pore filling events. To overcome these difficulties, we have developed a novel experimental technique using UV-induced polymerization, which allows the fluid phase distributions to be frozen in place during transient imbibition. Pore-scale structure of the front can then be examined in the 3D microscopic details using the X-ray Computed micro-Tomography (XCT). We have also developed a suite of advanced image segmentation programs to segment the grayscale XCT data. Image-based physically representative pore network generation techniques were unitized to quantify the geometry and topology of pore, wetting and nonwetting phase structure. Using UV initiated polymerization technique and image-based quantitative analysis tools; we have studied the effects of capillary number, pore structure and surface roughness on the structure of the transient imbibition front

Geomorphic Landform Design as an Alternative for Conventional Valley Fill Surface Mine Reclamation: Assessing Conceptual Design, Groundwater Modeling, and Contaminant Desorption

This research aimed to evaluate the potential of applying geomorphic landform design (GLD) principles to valley fill reclamation, specifically in southern West Virginia, central Appalachia, USA. When constructing reclaimed landforms, GLD aims to mimic the geomorphology of reference landforms that are stable and in erosive and hydrologic equilibrium. Challenges with the technique have been identified related to use in central Appalachia. Reference landform design values vary by location and need to be quantified at a local scale for site-specific design. Due to the steep slopes of existing valleys, constructing engineered landforms that naturally blend in with the surrounding environment may not ensure stability. Less steep, more stable slopes of geomorphic landforms could create greater stream disturbance to maintain fill volumes. Potential benefits of GLD with respect to groundwater movement and contaminant desorption have also not been quantified. This research presents three major objectives to assess geomorphic landform design in central Appalachia: 1) define the geomorphic characteristics of mature landform reference sites in southern West Virginia; 2) quantify the issues associated with implementing geomorphic reclamation on a field scale at an existing valley fill; and, 3) compare models of groundwater movement and desorption of selenium in reclamation alternatives for a southern WV surface mine. Geomorphic properties of drainage length and drainage density for mature landforms in central Appalachia were 408 ft and 62 ft/ac, respectively. Slopes were steep (\u3e20%), aspects were well distributed in all directions, vegetation was predominately dense core forest, and ephemeral channel heads developed where erosive surface processes created concentrated flow and sediment transport. Potential issues associated with implementing GLD in central Appalachia with respect to landform stability, stable channel mitigation, and mass balance were confirmed. No geomorphic design was able to satisfy all three criteria when the permitted area of impact was maintained. Expanding the area of impact beyond permit boundaries promoted more success in meeting design criteria, but did not comply with reclamation regulations governing excess spoil placement and constructed hillslopes. A quantitative comparison of the groundwater movement and selenium desorption between alternative reclamation designs confirmed potential benefits to geomorphic reclamation. Selenium desorption was reduced by 23-39% in geomorphic fills and was attributed to improved groundwater movement. Geomorphic reclaimed landforms exhibited 23-45% lower infiltration volumes, 12-63% lower groundwater discharge volumes, and approximately 50% shorter groundwater residence times. These findings will be used to provide recommendations to government agencies and the surface mining industry on the practicality of implementing geomorphic reclamation as an alternative to conventional valley fill reclamation in central Appalachia

Adaptive Haar wavelets for the angular discretisation of spectral wave models

A new framework for applying anisotropic angular adaptivity in spectral wave modelling is presented. The angular dimension of the action balance equation is discretised with the use of Haar wavelets, hierarchical piecewise-constant basis functions with compact support, and an adaptive methodology for anisotropically adjusting the resolution of the angular mesh is proposed. This work allows a reduction of computational effort in spectral wave modelling, through a reduction in the degrees of freedom required for a given accuracy, with an automated procedure and minimal cost

Method of fragments (MoF) solutions for double-walled, circular and rectangular cofferdam seepage problems

Cofferdams are temporary structures used in construction sites. Long-narrow (double-walled), circular, square and rectangular are the commonly seen cofferdam shapes, and flow rate and maximum exit hydraulic gradient are two of the main design parameters required. Commonly, these are evaluated through the 2D ground water flow model solved using flow nets or numerical methods. However, when the flow pattern is 3D, such as flow into the square or rectangular cofferdams, predictions by the 2D models underestimate the flow rate and maximum exit hydraulic gradient values considerably. Method of fragment (MoF) is an approximate technique which can be used for quick estimates of the flow rate and maximum exit hydraulic gradient values for double-walled cofferdams. The accuracy of the MoF solutions depends on the validity of the assumption that the equipotential line at the tip of the cut-off wall is vertical, dividing the flow domain into two fragments. In this research, validity of this assumption was assessed through the extensive numerical simulations, and it was found that, MoF predictions are within acceptable limits, and the effect of deviating from the assumption is always onto the conservative side. Further, MoF was extended to solve circular cofferdam problems, defining two new axisymmetric fragment types. Through a range of numerical simulations, design charts were developed to obtain the required axisymmetric form factors and normalised exit hydraulic gradient values. These were validated against detailed numerical solutions, analytical solutions, and experimental results reported in the literature. Also, a small-scale laboratory model was developed for analysing the circular cofferdam, and using that, series of tests were carried out. Then, the experimental results were compared against solutions derived using the proposed MoF solutions and showed a good agreement. Further, simple analytical expressions were developed and validated for the form factors and normalised exit gradient estimations of both double-walled and circular cofferdams enabling quicker computations and the MoF be implemented in spreadsheets. In addition, a simple method for evaluating the cofferdam safety against possible piping failure is presented. Through a series of finite element simulations, simple expressions were developed and validated to estimate the maximum exit hydraulic gradient for both double-walled and circular cofferdams considering only the shortest seepage path, known as creep length. The proposed solutions, including mean, lower and upper bound values for the exit hydraulic gradient at a given creep length can be applied in both isotropic and anisotropic soil conditions. Using them, a first-order estimate of the required creep length to limit the exit hydraulic gradient to a specific value can be determined. Alternatively, for a given configuration of the cofferdam, the exit hydraulic gradient can also be estimated. These equations can be valuable tools for back-of-the-envelope calculations in the preliminary analysis while selecting the dimensions in a cofferdam. Furthermore, simple expressions were developed and validated for accurately estimating the flow rate and maximum exit hydraulic gradient values of square and rectangular cofferdams founding on an isotropic and homogeneous soil medium. However, when the soil medium is anisotropic and homogeneous, proposed solutions are still applicable with a reasonable level of accuracy. In the proposed solutions, the 3D flow effects of square and rectangular cofferdams have been incorporated through the correction factors. Suggestions are made to improve the expressions given in the Canadian Foundation Engineering Manual, widely used in practice. The solutions proposed in this research can be very useful as a design tool in providing realistic first estimates of the flow rate and maximum exit hydraulic gradients of cofferdams, especially in preliminary assessments and for carrying out parametric studies, before going for a detailed analysis

Methodology investigations for shear wave splitting analysis

Over the past several decades, shear wave splitting analyses have been increasingly utilized to delineate mantle structure and probe mantle dynamics. However, the reported splitting parameters (fast polarization orientations and splitting times) are frequently inconsistent among different studies, partially due to the different techniques used to estimate the splitting parameters. Here the study conduct research on methodology investigations for shear wave splitting analysis, which are composed of two sub-topics, i.e., a systematic comparison of the transverse minimization (TM) and the splitting intensity (SI) techniques and applicability of the multiple-event stacking technique (MES). Numerical experiments are conducted using both synthetic and observed data. In addition, crustal anisotropy beneath 71 broadband seismic stations situated at the eastern Tibetan Plateau and adjacent areas is investigated based on the sinusoidal moveout of P-to-S conversions from the Moho and an intra-crustal discontinuity with an average splitting time of 0.39 ± 0.19 s and dominantly fracture-parallel fast orientations. The crustal anisotropy measurements support the existences of mid/lower crustal flow in the southern Songpan-Ganzi Terrane and crustal shortening deformation beneath the Longmenshan fault zone --Abstract, page iv

Bayesian Methods applied to Reflection Seismology

Quantifying uncertainty in models derived from observed seismic data is an important issue in exploration geophysics. In this research we examine the geological structure of the subsurface of the Earth using controlled source seismology which consists of data recorded in time and the distance between acoustic sources and receivers. There are a number of inversion tools to map data into depth models, but a full exploration of the uncertainty of such models is rarely done because of the lack of robust strategies available for the analysis of large non-linear complex systems. In reflection seismology, there are three principal sources of uncertainty: the first comes from the input data which is noisy and band-limited, the second is from the modeling assumptions used to approximate the physics of the problem in order to make the problem tractable, and the last is from the ambiguity in data and model selection. The latter is by far the hardest source of uncertainty to assess, not only are there a large number of models which are appropriate for a given seismic profile and still physically and geologically plausible, but also the judgement related to the acceptability of a model varies according to the expert handling the data. The fact that there are many possible solutions, depending on how the problem is treated, adds a new layer of uncertainty to the question. Here we propose a Bayesian approach to assess the uncertainty in velocity models derived from seismic reflection data. We have developed a method used to identify and track seismic events called the Seismic Event Tracking algorithm. We then created the BRAINS (Bayesian Regression Analysis in Seismology) class of models used to estimate velocities, travel times and depths with associated measures of uncertainty for each identified horizon. Since the experts' prior judgements and problem requirements vary according to the situation being analysed, the Bayesian methodology is the most appropriate to create a gray box that accepts the input of prior knowledge but that is also able to cope with vague or no prior information; here each model in the BRAINS class can be used at different stages of seismic processing, depending on the inputs necessary for the next step of modeling. Moreover, each estimate produced has an uncertainty model attached that can be explored before making a decision. In order to investigate the robustness of the models proposed, we analysed a series of single and multigathered synthetic examples, some of which had attributes that differ from the modeling assumptions or carried ambiguities derived from the limitations of data recording. Finally, we analysed a 2D real data set part of a seismic survey acquired over the Naturaliste Plateau and Mentelle Basins off the south west coast of Australia. We show the efficiency of the BRAINS approach on real data and recover velocity and depth models with posterior depth standard errors of at most 0.4% relative to posterior depth means, and posterior RMS velocity standard errors of at most 1.7% relative of posterior RMS velocity means. We also observe that variations in interval velocities is higher with an average of 2.4% for the posterior interval velocity standard deviation and mean ratio which reaches a maximum of 23.7% in areas of high uncertainty