Issam S. Strub

Quadratic programming based data assimilation with passive drifting sensors for shallow water flows

We present a method for assimilating Lagrangian sensor measurement data into a shallow water equation model. The underlying estimation problem (in which the dynamics of the system are represented by a system of partial differential equations) relies on the formulation of a minimisation of an error functional, which represents the mismatch between the estimate and the measurements. The corresponding so-called variational data assimilation problem is formulated as a quadratic programming problem with linear constraints. For the hydrodynamics application of interest, data is obtained from drifting sensors that gather position and velocity. The data assimilation method refines the estimate of the initial conditions of the hydrodynamic system. The method is implemented using a new sensor network hardware platform for gathering flow information from a river, which is presented in this article for the first time. Validation of the results is performed by comparing them to an estimate derived from an independent set of static sensors, some of which were deployed as part of our field experiments.

Comparison of two data assimilation algorithms for shallow water flows

This article presents the comparison of two algorithms for data assimilation of two dimensional shallow water flows. The first algorithm is based on a linearization of the model equations and a quadratic programming (QP) formulation of the problem. The second algorithm uses Ensemble Kalman Filtering (EnKF) applied to the non-linear two dimensional shallow water equations. The two methods are implemented on a scenario in which boundary conditions and Lagrangian measurements are available. The performance of the methods is evaluated using twin experiments with experimentally measured bathymetry data and boundary conditions from a river located in the Sacramento Delta. The sensitivity of the algorithms to the number of drifters, low or high discharge and time sampling frequency is studied.

Optimal Control of Air Traffic Networks Using Continuous Flow Models

in the National Airspace System using an Eulerian description of the network with hyperbolic partial dierential equations. Existence and uniqueness (well-posedness) of a solution to the system of partial dierential equations on a network is established. Subsequently, an optimal control problem is studied with the junction coecients as control variables. We use a fully discretised adjoint approach and we implement it on a network with 16 links and 5 junctions created from the enroute high altitude jetways between the Oakland and Salt Lake City air trac control centers. The aircraft flows on the final link of the network with and without control are compared and the results demonstrate the eciency of the method developed in the article.

Quadratic Programming based data assimilation with passive drifting sensors for shallow water flows

We present a method for assimilating Lagrangian sensor measurement data into a Shallow Water Equation model. Using our method, the variational data assimilation problem is formulated as a Quadratic Programming problem with linear constraints. Drifting sensors that gather position and velocity information in the modeled system can then be used to refine the estimate of the initial conditions of the system. A new sensor network hardware platform for gathering flow information is presented. We summarize the results of a field experiment designed to demonstrate the capabilities of our assimilation method with data gathered from the sensors. Validation of the results is performed by comparing them to an estimate derived from an independent set of static sensors.

Mixed initial-boundary value problems for scalar conservation laws: application to the modeling of transportation networks

This article proves the existence and uniqueness of a weak solution to a scalar conservation law on a bounded domain. A weak formulation of hybrid boundary conditions is needed for the problem to be well posed. The boundary conditions are represented by a hybrid automaton with switches between the modes determined by the direction of characteristics of the system at the boundary. The existence of the solution results from the convergence of a Godunov scheme derived in this article. This weak formulation is written explicitly in the context of a strictly concave flux function (relevant for highway traffic). The numerical scheme is then applied to a highway scenario with data from the I210 highway obtained from the California PeMS system. Finally, the existence of a minimizer of travel time is obtained, with the corresponding optimal boundary control.

Continuous adjoint method for Air Traffic Flow Management

This article develops a model of air traffic flow using an Eulerian description with hyperbolic partial differential equations. Existence and uniqueness (well-posedness) of a solution to the system of partial differential equations on a network is established. Subsequently, an optimal control problem is studied with the junction coefficients as control variables. We use a continuous adjoint approach and we implement it on a network with 16 links and 5 junctions, demonstrating the computational efficiency of this method