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Time-Optimal Path Planning in Uncertain Flow Fields Using Stochastic Dynamically Orthogonal Level Set Equations

Wei, Q.J., 2015. Time-Optimal Path Planning in Uncertain Flow Fields Using Stochastic Dynamically Orthogonal Level Set Equations, B.S. Thesis, Massachusetts Institute of Technology, Dept. of Mechanical Engineering, June 2015.

Path-planning has many applications, ranging from self-driving cars to flying drones, and to our daily commute to work. Path-planning for autonomous underwater vehicles presents an interesting problem: the ocean flow is dynamic and unsteady. Additionally, we may not have perfect knowledge of the ocean flow. Our goal is to develop a rigorous and computationally efficient methodology to perform path-planning in uncertain flow fields. We obtain new stochastic Dynamically Orthogonal (DO) Level Set equations to account for uncertainty in the flow field. We first review existing path-planning work: time-optimal path planning using the level set method, and energy-optimal path planning using stochastic DO level set equations. We build on these methods by treating the velocity field as a stochastic variable and deriving new stochastic DO level set equations. We use the new DO equations to simulate a simple canonical flow, the stochastic highway. We verify that our results are correct by comparing to corresponding Monte Carlo results. We explore novel methods of visualizing the results of the equations. Finally we apply our methodology to an idealized ocean simulation using Double-Gyre flows.

Time-optimal Path Planning for Sea-surface Vehicles Under the Effects of Strong Currents and Winds

Hessels, B., 2014. Time-optimal Path Planning for Sea-surface Vehicles Under the Effects of Strong Currents and Winds.. BS Thesis, Massachusetts Institute of Technology, Department of Mechanical Engineering, June 2014.

A path-planning methodology that takes into account sea state fields, specifically wind forcing, is discussed and exemplified in this thesis. This general methodology has been explored by the Multidisciplinary Simulation, Estimation, and Assimilation Systems group (MSEAS) at MIT, however this is the first instance of wind effects being taken into account. Previous research explored vessels and isotropy, where the nominal speed of the vessel is uniform in all directions. This thesis explores the non-isotropic case, where the maximum speed of the vessel varies with direction, such as a sailboat. Our goal in this work is to predict the time-optimal path between a set of coordinates, taking into account flow currents and wind speeds. This thesis reviews the literature on a modified level set method that governs the path in any continuous flow to minimize travel time. This new level set method, pioneered by MSEAS, evolves a front from the starting coordinate until any point on that front reaches the destination. The vehicles optimal path is then gained by solving a particle back tracking equation. This methodology is general and applicable to any vehicle, ranging from underwater vessels to aircraft, as it rigorously takes into account the advection effects due to any type of environmental flow fields such as time-dependent currents and dynamic wind fields.

Generation of High Quality 2D Meshes for Given Bathymetry

Colmenero J., 2014. Generation of High Quality Meshes for Given Bathymetry. BS Thesis, Massachusetts Institute of Technology, Department of Mechanical Engineering, June 2014.

This thesis develops and applies a procedure to generate high quality 2D meshes for any given ocean region with complex coastlines. The different criteria used in determining mesh element sizes for a given domain are discussed, especially sizing criteria that depend on local properties of the bathymetry and relevant dynamical scales. Two different smoothing techniques, Laplacian conditioning and targeted averaging, were applied to the fields involved in calculating the sizing matrix. The L^2 norm was used to quantify which technique had the greatest preservation of the original field. In both the reduced gradient and gradient cases, targeted averaging had a lower L^2 norm. The sizing matrices were used as inputs for two mesh generators, Distmesh and GMSH, and their meshing results were presented over a set of ocean domains in the Gulf of Maine and Massachusetts Bay region. Further research into the capabilities of each mesh generator are needed to provide a detailed evaluation. Mesh quality issues near coastlines revealed the need for small scale feature size recognition algorithms that could be implemented and studied in the future.

Missiles & Misconceptions: Why We Know More About the Dark Side of the Moon than the Depths of the Ocean

Young, G.C., 2014. Missiles & Misconceptions: Why We Know More About the Dark Side of the Moon than the Depths of the Ocean. BS Thesis, Massachusetts Institute of Technology, Department of Mechanical Engineering, June 2014.

We know more about the dark side of the moon than the depths of the ocean. This is startling, considering how much more tangible the ocean is than space, and more importantly, how much more critical it is to the health and survival of humanity. Tens of billions of dollars are spent on manned and unmanned missions probing deeper into space, while 95% of Earth’s oceans remain unexplored. The result is a perilous dearth in knowledge about our planet at a time when rapid changes in our marine ecosystems profoundly affect its habitability.
The more intensive focus on space exploration is a historically recent phenomenon. For millennia until the mid-20th century, space and ocean exploration proceeded roughly at the same pace, driven by curiosity, military, and commerce. Both date back to early civilization when star-gazers scanned the skies, and sailors and free-divers scoured the seas. Since the 1960s when Don Walsh and Jacques Piccard descended to the deepest point on the ocean floor, and Neil Armstrong ascended to the moon, however, the trajectories of exploration diverged dramatically. Cold War-inspired geopolitical-military imperatives propelled space research to en extraordinary level, while ocean exploration stagnated in comparison. Moreover, although the Cold War ended more than 20 years ago, the disparity in effort remains vast despite evidence that accelerating changes in our marine ecosystems directly threatens our well being. Misconception about the relative importance of space and ocean exploration caused, and continues to sustain, this knowledge disparity to our peril.
In this thesis, we first review in section 2 the history of space and ocean exploration before the Cold War, when the pace of exploration in each sector was more or less comparable for thousands of years. We show in section 3, however, how the relative paces and trajectories of exploration diverged dramatically during the Cold War and continue to the present. In section 4 we seek to dispel the persistent misconceptions that have led to the disparity in resources allocated between space and ocean exploration, and argue for prioritizing ocean research. Finally, in section 5 we highlight the urgent imperative for expanding our understanding of the ocean.

Stochastic Modeling of Flows behind a Square Cylinder with uncertain Reynolds numbers

Wamala, J., 2012. Stochastic Modeling of Flows behind a Square Cylinder with uncertain Reynolds numbers. BS Thesis, Massachusetts Institute of Technology, Department of Mechanical Engineering, June 2012.

In this thesis, we explore the use of stochastic Navier-Stokes equations through the Dynamically Orthogonal (DO) methodology developed at MIT in the Multidisciplinary Simulation, Estimation, and Assimilation Systems Group. Specifically, we examine the effects of the Reynolds number on stochastic fluid flows behind a square cylinder and evaluate computational schemes to do so. We review existing literature, examine our simulation results and validate the numerical solution. The thesis uses a novel open boundary condition formulation for DO stochastic Navier-Stokes equations, which allows the modeling of a wide range of random inlet boundary conditions with a single DO simulation of low stochastic dimensions, reducing computational costs by orders of magnitude. We first test the numerical convergence and validating the numerics. We then study the sensitivity of the results to several parameters, focusing for the dynamics on the sensitivity to the Reynolds number. For the method, we focus on the sensitivity to the: resolution of in the stochastic subspace, resolution in the physical space and number of open boundary conditions DO modes. Finally, we evaluate and study how key dynamical characteristics of the flow such as the recirculation length and the vortex shedding period vary with the Reynolds number.

Technological Review of Deep Ocean Manned Submersibles

Vaskov, A.K., 2012. Technological Review of Deep Ocean Manned Submersibles. BS Thesis, Massachusetts Institute of Technology, Department of Mechanical Engineering, June 2012.

James Cameron’s dive to the Challenger Deep in the Deepsea Challenger in March of 2012 marked the first time man had returned to the Mariana Trench since the Bathyscaphe Trieste’s 1960 dive. Currently little is known about the geological processes and ecosystems of the deep ocean. The Deepsea Challenger is equipped with a plethora of instrumentation to collect scientific data and samples. The development of the Deepsea Challenger has sparked a renewed interest in manned exploration of the deep ocean.
Due to the immense pressure at full ocean depth, a variety of advanced systems and materials are used on Cameron’s dive craft. This paper provides an overview of the many novel features of the Deepsea Challenger as well as related features of past vehicles that have reached the Challenger Deep. Four key areas of innovation are identified: buoyancy materials, pilot sphere construction/instrument housings, lighting, and battery power. An in depth review of technological development in these areas is provided, as well as a glimpse into future manned submersibles and their technologies of choice.

Upwelling Dynamics off Monterey Bay: Heat Flux and Temperature Variability, and their Sensitivities

Kaufman, M.R.S., 2010. Upwelling Dynamics off Monterey Bay: Heat Flux and Temperature Variability, and their Sensitivities. BS Thesis, Massachusetts Institute of Technology, Department of Mechanical Engineering, May 2010.

Understanding the complex dynamics of coastal upwelling is essential for coastal ocean dynamics, phytoplankton blooms, and pollution transport. Atmospheric- driven coastal upwelling often occurs when strong alongshore winds and the Coriolis force combine to displace warmer surface waters offshore, leading to upward motions of deeper cooler, nutrient-dense waters to replace these surface waters. Using the models of the MIT Multidisciplinary Simulation, Estimation, and Assimilation System (MSEAS) group, we conduct a large set of simulation sensitivity studies to determine which variables are dominant controls for upwelling events in the Monterey Bay region. Our motivations include determining the dominant atmospheric fluxes and the causes of high-frequency fluctuations found in ocean thermal balances. We focus on the first upwelling event from August 1- 5, 2006 in Monterey Bay that occurred during the Monterey Bay 06 (MB06) at-sea experiment, for which MSEAS data-assimilative baseline simulations already existed.

Using the thermal energy (temperature), salinity and momentum (velocity) conservation equations, full ocean fields in the region as well as both control volume (flux) balances and local differential term-by-term balances for the upwelling event events were computed. The studies of ocean fields concentrate on specific depths: surface-0m, thermocline-30m and undercurrent-150m. Effects of differing atmospheric forcing contributions (wind stress, surface heating/cooling, and evaporation-precipitation) on these full fields and on the volume and term-by-term balances are analyzed. Tidal effects are quantified utilizing pairs of simulations in which tides are either included or not. Effects of data assimilation are also examined.

We find that the wind stress forcing is the most important dynamical parameter in explaining the extent and shape of the upwelling event. This is verified using our large set of sensitivity studies and examining the heat flux balances. The assimilation of data has also an impact because this first upwelling event occurs during the initialization. Tidal forcing and, to a lesser extent, the daily atmospheric and data assimilation cycles explain the higher frequency fluctuations found in the volume averaged time rate of change of thermal energy.