Management of water resource systems in the presence of uncertainties by nonlinear approximation techniques and deterministic sampling

Baglietto, Marco; Cervellera, Cristiano; Sanguineti, Marcello; Zoppoli, R.

doi:10.1007/s10589-008-9221-6

Cited by 15 publications

(7 citation statements)

References 51 publications

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“…Dealing with moderate and high dimensional stochastic spaces is actually one of the most important problem in uncertainty quantification (UQ) community. Several methods are proposed in Agarwal and Aluru (2009), Baglietto et al (2010), Blatman andSudret (2011), Caflisch et al (1997), Cao et al (2003), Foo et al (2008), Ma and Zabaras (2010) and Wang and Sloan (2003), but their accuracy on realistic problems with highly non-linear effects is still not proven. This problem is even more challenging when coupled to the robust design optimization, where conventional optimization procedures aims at taking in account uncertainty in the design procedures (for a detailed review see Verstraete and Périaux (2010) and Schuëller and Jensen (2008)).…”

Section: Introductionmentioning

confidence: 99%

TSI metamodels-based multi-objective robust optimization

Congedo¹,

Geraci²,

Abgrall

et al. 2013

Engineering Computations

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Purpose – This paper aims to deal with an efficient strategy for robust optimization when a large number of uncertainties are taken into account. Design/methodology/approach – ANOVA analysis is used in order to perform a variance-based decomposition and to reduce stochastic dimension based on an appropriate criterion. A massive use of metamodels allows reconstructing response surfaces for sensitivity indexes in the design variables plan. To validate the proposed approach, a simplified configuration, an inverse problem on a 1D nozzle flow, is solved and the performances compared to an exact Monte Carlo reference solution. Then, the same approach is applied to the robust optimization of a turbine cascade for thermodynamically complex flows. Findings – First, when the stochastic dimension is reduced, the error on the variance between the reduced and the complete problem was found to be roughly estimated by the quantity (1-T¯TSI)×100, where T¯TSI is the summation of TSI concerning the variables respecting the TSI criterion. Second, the proposed strategy allowed obtaining a converged Pareto front with a strong reduction of computational cost by preserving the same accuracy. Originality/value – Several articles exist in literature concerning robust optimization but very few dealing with a global approach for solving optimization problem affected by a large number of uncertainties. Here, a practical and efficient approach is proposed that could be applied also to realistic problems in engineering field

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Section: Introductionmentioning

confidence: 99%

TSI metamodels-based multi-objective robust optimization

Congedo¹,

Geraci²,

Abgrall

et al. 2013

Engineering Computations

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“…In this section, we report the simulation tests carried out to investigate the effectiveness of LPSs for sampling the state space in the ADP algorithm. Specifically, we focus on the optimal control of a water reservoirs network, which is a classic example for testing ADP algorithms . The aim of the problem is to maximize the benefit related to water releases, while keeping the water levels as close as possible to given target values.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…Specifically, we focus on the optimal control of a water reservoirs network, which is a classic example for testing ADP algorithms. 6,24 The aim of the problem is to maximize the benefit related to water releases, while keeping the water levels as close as possible to given target values. The considered network consists of 5 basins, interconnected as depicted in Figure 4.…”

Section: Simulation Resultsmentioning

confidence: 99%

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Lattice point sets for state sampling in approximate dynamic programming

Cervellera

Gaggero

Macciò

2017

Optim Control Appl Methods

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Summary This paper investigates the use of lattice point sets as an efficient method to sample uniformly the state space of discrete‐time dynamic systems for the solution of finite‐horizon optimal control problems using approximate dynamic programming. Lattice point sets are a kind of discretization method, commonly employed for efficient numerical integration, providing a regular and balanced sampling of the state space based on the repetition of elementary unit cells. A convergence analysis of the approximate solution of the control problem to the optimal one is provided, pointing out that such sampling schemes allow one to efficiently exploit possible regularities of the cost‐to‐go functions. Furthermore, it is shown that a higher accuracy may be obtained through suitable transformations of the state vector of the dynamic system. Another advantage of lattice point sets over other sampling schemes is the possibility of evaluating a priori the goodness of a given set over another through the explicit computation of a specific parameter. Simulation results concerning the optimal control of a water reservoirs system are presented to show the effectiveness of the proposed approach.

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“…Brown et al in [3] present an irrigation scheduling decision support method. In [1] the authors center on the study of optimal water reservoirs management using non-linear one-hidden-layer networks.…”

Section: Introductionmentioning

confidence: 99%

Analytical Study for Different Extremal State Solutions of an Irrigation Optimal Control Problem with Field Capacity Modes

Lemos-Paião

Lopes

Pinho

2022

Int. J. Appl. Comput. Math

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In this paper we study the problem of daily irrigation of an agricultural crop using optimal control. The dynamics is a model based on field capacity modes, where the state, x, represents the water in the soil and the control variable, u, is the flow rate of water from irrigation. The variation of water in the soil depends on the field capacity of the soil, $$x_{FC}$$ x FC , weather conditions, losses due to deep percolation and irrigation. Our goal is to minimize the amount of water used for irrigation while keeping the crop in a good state of preservation. To enforce such requirement, the state constraint $$x(t) \ge x_{\min }$$ x ( t ) ≥ x min is coupled with the dynamics, where $$x_{\min }$$ x min is the hydrological need of the crop. Consequently, the problem under study is a state constrained optimal control problem. Under some mild assumptions, we consider several basic profiles for the optimal trajectories. Appealing to the Maximum Principle (MP), we characterize analytically the solution and its multipliers for each case. We then illustrate the analytical results running some computational simulations, where the analytical information is used to partially validate the computed solutions. The need to study irrigation strategies is of foremost importance nowadays since 80% of the fresh water used on our planet is used in agriculture.

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Management of water resource systems in the presence of uncertainties by nonlinear approximation techniques and deterministic sampling

Abstract: Water resources management, Stochastic optimal control, Dynamic programming, Curse of dimensionality, Deterministic sampling, Stochastic approximation,

Cited by 15 publications

References 51 publications

TSI metamodels-based multi-objective robust optimization

TSI metamodels-based multi-objective robust optimization

Lattice point sets for state sampling in approximate dynamic programming

Analytical Study for Different Extremal State Solutions of an Irrigation Optimal Control Problem with Field Capacity Modes

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