loader graphic

Loading content ...

Three-dimensional Time-Optimal Path Planning in the Ocean

Kulkarni, C.S. and P.F.J. Lermusiaux, 2020. Three-Dimensional Time-Optimal Path Planning in the Ocean, Ocean Modelling, 152, 101644. doi:10.1016/j.ocemod.2020.101644

Autonomous underwater vehicles (AUVs) operate in the three-dimensional and time-dependent marine environment with strong and dynamic currents. Our goal is to predict the time history of the optimal three-dimensional headings of these vehicles such that they reach the given destination location in the least amount of time, starting from a known initial position. We employ the exact differential equations for time-optimal path planning and develop theory and numerical schemes to accurately predict three-dimensional optimal paths for several classes of marine vehicles, respecting their specific propulsion constraints. We further show that the three-dimensional path planning problem can be reduced to a two-dimensional one if the motion of the vehicle is partially known, e.g. if the vertical component of the motion is forced. This reduces the computational cost. We then apply the developed theory in three-dimensional analytically known flow fields to verify the schemes, benchmark the accuracy, and demonstrate capabilities. Finally, we showcase time-optimal path planning in realistic data-assimilative ocean simulations for the Middle Atlantic Bight region, integrating the primitive-equation of the Multidisciplinary Simulation Estimation and Assimilation System (MSEAS) with the three-dimensional path planning equations for three common marine vehicles, namely propelled AUVs (with unrestricted motion), floats (that only propel vertically), and gliders (that often perform sinusoidal yo-yo motions in vertical planes). These results highlight the effects of dynamic three-dimensional multiscale ocean currents on the optimal paths, including the Gulf Stream, shelfbreak front jet, upper-layer jets, eddies, and wind-driven and tidal currents. They also showcase the need to utilize data-assimilative ocean forecasts for planning efficient autonomous missions, from optimal deployment and pick-up, to monitoring and adaptive data collection.


Advection without Compounding Errors through Flow Map Composition

Kulkarni, C.S. and P.F.J. Lermusiaux, 2019. Advection without Compounding Errors through Flow Map Composition. Journal of Computational Physics, 398, 108859. doi:10.1016/j.jcp.2019.108859

We propose a novel numerical methodology to compute the advective transport and diffusion-reaction of tracer quantities. The tracer advection occurs through flow map composition and is super-accurate, yielding numerical solutions almost devoid of compounding numerical errors, while allowing for direct parallelization in the temporal direction. It is computed by implicitly solving the characteristic evolution through a modified transport partial differential equation and domain decomposition in the temporal direction, followed by composition with the known initial condition. This advection scheme allows a rigorous computation of the spatial and temporal error bounds, yields an accuracy comparable to that of Lagrangian methods, and maintains the advantages of Eulerian schemes. We further show that there exists an optimal value of the composition timestep that yields the minimum total numerical error in the computations, and derive the expression for this value. We develop schemes for the addition of tracer diffusion, reaction, and source terms, and for the implementation of boundary conditions. Finally, the methodology is applied in three flow examples, namely an analytical reversible swirl flow, an idealized flow exiting a strait undergoing sudden expansion, and a realistic ocean flow in the Bismarck sea. New benchmark problems for advection-diffusion-reaction schemes are developed and used to compare and contrast results with those of classic schemes. The results highlight the theoretical properties of the methodology as well as its efficiency, super-accuracy with minimal numerical errors, and applicability in realistic simulations.

Risk-Optimal Path Planning in Stochastic Dynamic Environments

Subramani, D.N. and P.F.J. Lermusiaux, 2019. Risk-Optimal Path Planning in Stochastic Dynamic Environments. Computer Methods in Applied Mechanics and Engineering, 353, 391–415. doi:10.1016/j.cma.2019.04.033

We combine decision theory with fundamental stochastic time-optimal path planning to develop partial-differential-equations-based schemes for risk-optimal path planning in uncertain, strong and dynamic flows. The path planning proceeds in three steps: (i) predict the probability distribution of environmental flows, (ii) compute the distribution of exact time-optimal paths for the above flow distribution by solving stochastic dynamically orthogonal level set equations, and (iii) compute the risk of being suboptimal given the uncertain time-optimal path predictions and determine the plan that minimizes the risk. We showcase our theory and schemes by planning risk-optimal paths of unmanned and/or autonomous vehicles in illustrative idealized canonical flow scenarios commonly encountered in the coastal oceans and urban environments. The step-by-step procedure for computing the risk-optimal paths is presented and the key properties of the risk-optimal paths are analyzed.


MIT –WHOI 50th anniversary

Read more about the MIT-WHOI Joint program and the anniversary here.

Sensitivity of the Bay of Bengal upper ocean to different winds and river input conditions

Jana, S., A. Gangopadhyay, P.F.J. Lermusiaux, A. Chakraborty, S. Sil, and P.J. Haley Jr., 2018. Sensitivity of the Bay of Bengal Upper Ocean to Different Winds and River Input Conditions. Journal of Marine Systems, 187, 206–222. doi:10.1016/j.jmarsys.2018.08.001

The sensitivity of the Bay of Bengal (BoB) upper ocean circulation and thermohaline structure to varying wind strengths and river salinity conditions is investigated using a set of long-term mesoscale simulations. The Regional Ocean Modeling System (ROMS) simulations differ in their forcing fields for winds (strong vs. weak) and in their representations of river input salinity conditions (seasonally varying estuarine salinity vs. zero salinity). The sensitivities are analyzed in terms of the responses of the surface circulation, thermohaline structure, freshwater plume dispersion, and the coastal upwelling along the western boundary. All the simulations reproduce the main broad-scale features of the Bay, while their magnitudes and variabilities depend on the forcing conditions. The impact of stronger wind is felt at greater depths for temperature than for salinity throughout the domain; however, the impact is realized with vertical distributions that are different in the northern than in the southern Bay.

As expected, the stronger wind-induced enhanced mixing lowers (enhances) the upper ocean temperature (salinity) by 0.2C (0.3 psu), and weakens the near-surface stratification. Moreover, stronger wind enhances eddy activity, strengthens the springtime Western Boundary Current (WBC) and enhances coastal upwelling during spring and summer along the east coast of India. The fresher river input reduces the surface salinity and hence enhances the spreading and intensity of the freshwater plume, stratification, and barrier layer thickness. The lower salinity simulation leads to an eddy-dominant springtime WBC, and enhances the freshness, strength, and southward extent of the autumn East India Coastal Current (EICC). The stronger wind simulations appear to prevent the spreading of the freshwater plume during the summer monsoon due to enhanced mixing. Fresher river input reduces the overall surface salinity by ~0.4 psu; however, it significantly underestimates the salinity near the river mouths, whereas the estuarine salinity river input simulations are closer to reality. These results highlight the importance of river input salinity and realistic strong winds in reducing model biases of high-resolution simulations for the Bay of Bengal.


Florian Feppon awarded the Médaille Louis-Édouard Rivot of the French Académie des Sciences

Congratulations to Florian Feppon for being awarded the Médaille Louis-Édouard Rivot of the French Académie des Sciences. This is in recognition for the scientific research on “Design and optimization for Wear of Bi-Material Composite Surfaces” that he performed at Lehigh University (Bethlehem, PA) as a visiting research scholar, under the direction of Prof. Grégoire Allaire (Centre de Mathématiques Appliquées, École Polytechnique) and Prof. Vermaak (Mechanical Engineering, Lehigh University).

Two papers published on using Gaussian Mixture Models for Data Assimilation

Two papers by Sondergaard and Lermusiaux have been accepted for publication in Monthly Weather Review. These papers are on Data Assimilation with Gaussian Mixture Models using the Dynamically Orthogonal Field Equations. The first describes the theory and scheme, while the second discusses applications.

Prof. Lermusiaux receives the “Ruth and Joel Spira Award for Distinguished Teaching”

March 2010: Prof. Pierre Lermusiaux received an MIT School of Engineering teaching award, the “Ruth and Joel Spira Award for Distinguished Teaching”. This award is given to one faculty member each in Electrical Engineering and Computer Science, Mechanical Engineering, and Nuclear Science and Engineering to acknowledge “the tradition of high quality engineering education at MIT”.

Melissa Kaufman accepted as Ph.D. student at URI

December 2009: Ms. Melissa Kaufman (a MechE undergraduate UROP student in our group) has been accepted as a PhD student at the Graduate School of Oceanography of the University of Rhode Island. Congratulations Melissa!

MREA Workshop at NATO Undersea Research Centre

Prof. Pierre Lermusiaux co-chaired the workshop on Maritime Rapid Environmental Assessment Conference: Quantifying, Predicting, Exploiting Uncertainties in Marine Environments at the NATO Undersea Research Center in Lerici, Italy

A multigrid methodology for assimilation of measurements into regional tidal models

Logutov, O.G., 2008. A multigrid methodology for assimilation of measurements into regional tidal models. Ocean Dynamics, 58, 441-460, doi:10.1007/s10236-008-0163-4.

This paper presents a rigorous, yet practical, method of multigrid data assimilation into regional structured-grid tidal models. The new inverse tidal nesting scheme, with nesting across multiple grids, is designed to provide a fit of the tidal dynamics to data in areas with highly complex bathymetry and coastline geometry. In these areas, computational constraints make it impractical to fully resolve local topographic and coastal features around all of the observation sites in a stand-alone computation. The proposed strategy consists of increasing the model resolution in multiple limited area domains around the observation locations where a representativeness error is detected in order to improve the representation of the measurements with respect to the dynamics. Multiple high-resolution nested domains are set up and data assimilation is carried out using these embedded nested computations. Every nested domain is coupled to the outer domain through the open boundary conditions (OBCs). Data inversion is carried out in a control space of the outer domain model. A level of generality is retained throughout the presentation with respect to the choice of the control space; however, a specific example of using the outer domain OBCs as the control space is provided, with other sensible choices discussed. In the forward scheme, the computations in the nested domains do not affect the solution in the outer domain. The subsequent inverse computations utilize the observation-minus-model residuals of the forward computations across these multiple nested domains in order to obtain the optimal values of parameters in the control space of the outer domain model. The inversion is carried out by propagating the uncertainty from the control space to model tidal fields at observation locations in the outer and in the nested domains using efficient low-rank error covariance representations. Subsequently, an analysis increment in the control space of the outer domain model is computed and the multigrid system is steered optimally towards observations while preserving a perfect dynamical balance. The method is illustrated using a real-world application in the context of the Philippines Strait Dynamics experiment.

Prediction Systems with Data Assimilation for Coupled Ocean Science and Ocean Acoustics

Robinson, A.R. and P.F.J. Lermusiaux, 2004. Prediction Systems with Data Assimilation for Coupled Ocean Science and Ocean Acoustics, Proceedings of the Sixth International Conference on Theoretical and Computational Acoustics (A. Tolstoy, et al., editors), World Scientific Publishing, 325-342. Refereed invited Keynote Manuscript.

Ocean science and ocean acoustics today are engaged in coupled interdisciplinary research on both fundamental dynamics and applications. In this context interdisciplinary data assimilation, which melds observations and fundamental dynamical models for field and parameter estimation is emerging as a novel and powerful methodology, but computational demands present challenging constraints which need to be overcome. These ideas are developed within the concept of an interdisciplinary system for assessing sonar system performance. An end-to-end system, which couples meteorology-physical oceanography-geoacoustics-ocean acoustics-bottom-noise-target-sonar data and models, is used to estimate uncertainties and their transfers and feedbacks. The approach to interdisciplinary data assimilation for this system importantly involves a full, interdisciplinary state vector and error covariance matrix. An idealized end-to-end system example is presented based upon the Shelfbreak PRIMER experiment in the Middle Atlantic Bight. Uncertainties in the physics are transferred to the acoustics and to a passive sonar using fully coupled physical and acoustical data assimilation.

Rapid real-time interdisciplinary ocean forecasting using adaptive sampling and adaptive modeling and legacy codes: Component encapsulation using XML

Evangelinos C., R. Chang, P.F.J. Lermusiaux and N.M. Patrikalakis, 2003. Rapid real-time interdisciplinary ocean forecasting using adaptive sampling and adaptive modeling and legacy codes: Component encapsulation using XML. Lecture Notes in Computer Science, 2660, 375-384.

We present the high level architecture of a real-time interdisciplinary ocean forecasting system that employs adaptive elements in both modeling and sampling. We also discuss an important issue that arises in creating an integrated, web-accessible framework for such a system out of existing stand-alone components: transparent support for handling legacy binaries. Such binaries, that are most common in scientific applications, expect a standard input stream, maybe some command line options, a set of input files and generate a set of output files as well as standard output and error streams. Legacy applications of this form are encapsulated using XML. We present a method that uses XML documents to describe the parameters for executing a binary.