Simultaneous identification of a single pollution point-source location and contamination time under known flow field conditions

Milnes, Ellen; Perrochet, Pierre

doi:10.1016/j.advwatres.2007.05.013

Cited by 45 publications

(29 citation statements)

References 26 publications

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“…To the authors' knowledge, the research of mathematical methods for this kind of problem are not published in literature although similar problems for groundwater pollution is intensively studied (see, e.g., [14] and the references therein). In [14] following the adjoint approach of Neupauer and Wilson [15] and in the terminology of location probability density function, the authors proposed a method for solving the groundwater pollution problem based on a fundamental property of the forward and backward location probability density functions, which is not proved analytically.…”

Section: A Methods For the Identification Of Location And Time Of Oil mentioning

confidence: 99%

“…In [14] following the adjoint approach of Neupauer and Wilson [15] and in the terminology of location probability density function, the authors proposed a method for solving the groundwater pollution problem based on a fundamental property of the forward and backward location probability density functions, which is not proved analytically. The same method is also used in [3] for the identification of contaminant point source in surface waters although the authors of this work do not refer to [14]. It should be mentioned that all the authors of the three above-mentioned papers only proposed method for solving the problem from technical point of view, and a rigorous mathematical justification is absent there.…”

Section: A Methods For the Identification Of Location And Time Of Oil mentioning

confidence: 99%

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Mathematical Modeling and Numerical Algorithms for Simulation of Oil Pollution

Dang¹,

Ehrhardt

Tran

et al. 2011

Environ Model Assess

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This paper deals with the mathematical modeling and algorithms for the problem of oil pollution. For solving this task, we derive the adjoint problem for the advection-diffusion equation describing the propagation of oil slick after an accident, which we call the main problem. We prove a fundamental equality between the solutions of the main and the adjoint problems. Based on this equality, we propose a novel method for the identification of the pollution source location and the accident time of oil emission. This approach is illustrated on an example for an accident in the offshore of the central part of the Vietnamese coast. Numerical simulations demonstrate the effectiveness of the proposed method. Besides, the method is verified for 1D model of substance propagation.

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Section: A Methods For the Identification Of Location And Time Of Oil mentioning

confidence: 99%

Section: A Methods For the Identification Of Location And Time Of Oil mentioning

confidence: 99%

Mathematical Modeling and Numerical Algorithms for Simulation of Oil Pollution

Dang¹,

Ehrhardt

Tran

et al. 2011

Environ Model Assess

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“…Finally, Milnes and Perrochet [24] tackle the problem of source identification by using an adjoint backward time PDE with velocity reversed, but keeping the diffusion operator positive (much as Neupauer and Wilson, op. cit.).…”

Section: Environmental and Groundwater Literaturementioning

confidence: 99%

Anti-diffusion and source identification with the ‘RAW’ scheme: A particle-based censored random walk

2009

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This paper presents a novel methodology for time reversal in advective-diffusive pollutant transport in groundwater systems and other environmental flow systems (specifically: time reversal of diffusive terms). The method developed in this paper extends previous particle-based approaches like the Reversed Time Particle Tracking Method of Bagtzoglou [6]. The reversal of the 'diffusive' and/or 'macrodispersive' component of pollutant migration is especially under focus here. The basis of the proposed scheme for anti-diffusion is a continuous time, censored, non-local random walk capable of tracking groundwater solute concentration profiles over time while conserving the (reverse) Fickian properties of the anti-diffusing particle cloud in terms of moments. This scheme is an alternative to the direct solution of the eulerian concentration-based diffusion PDE, which is notoriously unstable in reverse time. Our analysis leads to the conclusion that an adaptive time stepping scheme-with decreasing time step-is necessary in order to maintain a constant amount of anti-diffusion (the reverse form of Fick's law). Specifically, we study the relations between the following parameters: time step evolution vs. time (or vs. number of steps); variance evolution (decrease rate); total time (or number of steps) required to reach a fully anti-diffused solution. The proposed approach is shown to be quite efficient; typically, for every ten time steps, one to two orders of magnitude reduction of the dispersion width of the plume can be attained. Furthermore, the method is shown to be asymptotically exact for reverse Fickian diffusion. The method is applied with success to several situations involving the diffusive transport of a conservative solute in the following cases: (i) Single source recovery in onedimensional space with constant diffusion parameters (this example serves as a validation test for the theory); (ii) Single source recovery in two-dimensional space with constant isotropic diffusion (this example also serves as a test for the theory); (iii) Multiple source recovery R. Ababou (B) · A. Mallet 123 42 Environ Fluid Mech (2010) 10:41-76in two-dimensional space, assuming isotropic diffusion. It is expected that the methodology tested in this paper is applicable more generally to complex environmental pollution problems involving multiple sources, anisotropic hydrodynamic dispersion, and space-time variable advection-diffusion flow systems; the modeling of reverse diffusion/dispersion in such systems is currently under investigation.

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“…Methods able to handle heterogeneous geological media can be classified into two groups: backward-or forward-solverbased approaches. The backward solvers consist of reversing the flow problem (Skaggs and Kabala, 1995;Milnes and Perrochet, 2007;Ababou et al, 2010) and solving the advection dispersion equation backward in time to localize the source and identify the release history. In this group of methods, both the flow field and the contaminant plume are assumed to be perfectly known.…”

Section: Introductionmentioning

confidence: 99%

Contaminant source localization via Bayesian global optimization

Pirot

Krityakierne

Ginsbourger

et al. 2019

Hydrol. Earth Syst. Sci.

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Contaminant source localization problems require efficient and robust methods that can account for geological heterogeneities and accommodate relatively small data sets of noisy observations. As realism commands hi-fidelity simulations, computation costs call for global optimization algorithms under parsimonious evaluation budgets. Bayesian optimization approaches are well adapted to such settings as they allow the exploration of parameter spaces in a principled way so as to iteratively locate the point(s) of global optimum while maintaining an approximation of the objective function with an instrumental quantification of prediction uncertainty. Here, we adapt a Bayesian optimization approach to localize a contaminant source in a discretized spatial domain. We thus demonstrate the potential of such a method for hydrogeological applications and also provide test cases for the optimization community. The localization problem is illustrated for cases where the geology is assumed to be perfectly known. Two 2-D synthetic cases that display sharp hydraulic conductivity contrasts and specific connectivity patterns are investigated. These cases generate highly nonlinear objective functions that present multiple local minima. A derivative-free global optimization algorithm relying on a Gaussian process model and on the expected improvement criterion is used to efficiently localize the point of minimum of the objective functions, which corresponds to the contaminant source location. Even though concentration measurements contain a significant level of proportional noise, the algorithm efficiently localizes the contaminant source location. The variations of the objective function are essentially driven by the geology, followed by the design of the monitoring well network. The data and scripts used to generate objective functions are shared to favor reproducible research. This contribution is important because the functions present multiple local minima and are inspired from a practical field application. Sharing these complex objective functions provides a source of test cases for global optimization benchmarks and should help with designing new and efficient methods to solve this type of problem.

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Simultaneous identification of a single pollution point-source location and contamination time under known flow field conditions

Cited by 45 publications

References 26 publications

Mathematical Modeling and Numerical Algorithms for Simulation of Oil Pollution

Mathematical Modeling and Numerical Algorithms for Simulation of Oil Pollution

Anti-diffusion and source identification with the ‘RAW’ scheme: A particle-based censored random walk

Contaminant source localization via Bayesian global optimization

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