Model-Based Optimal Adaptive Monitoring of Oil Spills

Abstract

This article presents a novel model-based adaptive monitoring framework for the estimation of oil spills using mobile sensors. In the first of a four-stage process, simulation of a combined ocean, wind, and oil model provides a state trajectory over a finite time horizon, used in the second stage to solve an adjoint optimization problem for sensing locations. In the third stage, a reduced-order model is identified from the state trajectory, utilized alongside measurements to produce smoothed state estimates in the fourth stage, which update and re-initialize the first-stage simulation. In the second stage, sensors are directed to optimal sensing locations using the solution of a partial differential equation (PDE)-constrained optimization problem. This problem formulation represents a key contributory idea, utilizing the definition of spill uncertainty as a scalar PDE to be minimized subject to sensor, ocean, wind, and oil constraints. Spill uncertainty is a function of uncertainty in 1) the bespoke model of the ocean, wind, and oil spill; 2) the reduced order model identified from sensor data; and 3) the data assimilation method employed to estimate the states of the environment and spill. The uncertainty minimization is spatiotemporally weighted by a function of spill probability and information utility, prioritizing critical measurements. A numerical case study spanning a 2500-km <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> coastal area is presented, with four mobile sensors arriving 12 h after an oil leak. Compared to industry standard “ladder pathing,” the proposed method achieves an 80% reduction in oil distribution error and a 62% reduction in sensor distance traveled.