Rey, David | Search NASA

DOE OSTI2022

Application of Recursive Estimation to Heat Tracing for Groundwater/Surface‐Water Exchange

Abstract We present and demonstrate a recursive‐estimation framework to infer groundwater/surface‐water exchange based on temperature time series collected at different vertical depths below the sediment/water interface. We formulate the heat‐transport problem as a state‐space model (SSM), in which the spatial derivatives in the convection/conduction equation are approximated using finite differences. The SSM is calibrated to estimate time‐varying specific discharge using the Extended Kalman Filter (EKF) and Extended Rauch‐Tung‐Striebel Smoother (ERTSS). Whereas the EKF is suited to real‐time (“online”) applications and uses only the past and current measurements for estimation (filtering), the ERTSS is intended for near‐real time or batch‐processing (“offline”) applications and uses a window of data for batch estimation (smoothing). The two algorithms are demonstrated with synthetic and field‐experimental data and are shown to be efficient and rapid for the estimation of time‐varying flux over seasonal periods; further, the recursive approaches are effective in the presence of rapidly changing flux and (or) nonperiodic thermal boundary conditions, both of which are problematic for existing approaches to heat tracing of time‐varying groundwater/surface‐water exchange.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Disjunctive linear separation conditions and mixed-integer formulations for aircraft conflict resolution

In this paper, we address the aircraft conflict resolution problem in air traffic control. We introduce new mixed-integer programming formulations for aircraft conflict resolution with speed, heading and altitude control which are based on disjunctive linear separation conditions. We first examine the two-dimensional aircraft conflict resolution problem with speed and heading control represented as continuous decision variables. We show that the proposed disjunctive linear separation conditions are equivalent to the classical nonlinear conditions for aircraft separation. Further, we characterise conflict-free trajectories based on aircraft velocity bounds and propose a simple pre-processing algorithm to identify aircraft pairs which are either always conflict-free, or which cannot be separated using speed and heading control only. We then incorporate altitude control and propose a lexicographic optimisation formulation that aims to minimise the number of flight level changes before resolving outstanding conflicts via two-dimensional velocity control. The proposed mixed-integer programming formulations are nonconvex, and we propose convex relaxations, decomposition methods and constraint generation algorithms to solve the two-dimensional and lexicographic optimisation formulations to guaranteed optimality. Numerical experiments on four types of conflict resolution benchmarking instances are conducted to test the performance of the proposed mixed-integer formulations. Further, the proposed method is compared against two benchmarks based on state-of-the-art approaches for the aircraft conflict resolution problem. Our numerical results show that the proposed method largely outperforms both benchmarks in terms of runtime and is able to solve significantly more instances to global optimality.

97 MATHEMATICS AND COMPUTING↗