Optimal control applied to water flow using second order adjoint method

Shichitake, Masanori; Kawahara, Mutsuto

doi:10.1080/10618560802077814

Cited by 6 publications

(7 citation statements)

References 28 publications

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“…Thus, the stability condition can be expressed by Equation (31). In the case of a quadratic performance function and linear state equation, Equation (31) is always valid, as reported by Shichitake and Kawahara 14. However, in the case of general non‐linear state equations, Equation (31) is not always valid.…”

Section: Trust Region Methodsmentioning

confidence: 77%

“…Second‐order adjoint equation methods are utilized in various fields in science and engineering. Some recent applications include temperature uncertainty 4, 5, data assimilation of meteorogical and ocean models 2, viscoplastic model 6, chemical reactions 7, air traffic flow 8, four‐dimensional data assimilation 9, global CO 2 fluxes 10, data assimilation of oceans 11, 12, conduit flow 13, reflective waves on reservoir surfaces 14, and water purification 14. The directional second‐order adjoint method was discussed by Ozyurt and Barton 7.…”

Section: Introductionmentioning

confidence: 99%

“…In Japan, local governments recently established plans to purify an area with polluted water via the flow of additional waters from other rivers. Shichitake and Kawahara [14] have presented a control system for the Sasame, Shobu, and Kamitoda rivers. We applied the present method to the Teganuma river.…”

Section: Introductionmentioning

confidence: 99%

“…Our assertion is that the stability of control should be determined by the second variation of the extended performance function. The derivation in a previous paper [14] is limited in the case of a linear advection diffusion equation; in contrast, the formulation in this paper is extended to the advection diffusion equation with the shallow water equation.…”

Section: Introductionmentioning

confidence: 99%

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Computational water purification controls using second‐order adjoint equations with stability confirmation

Sekine

Kawahara

2011

Numerical Methods in Fluids

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SUMMARY This paper presents a computational method for water purification using second‐order adjoint equations. In Japan, the waters of polluted rivers are purified by conveying the waters from other rivers into the main rivers or by using outflows from sewage plants. The shallow water flow equation based on the water velocity and elevation and the advection diffusion equation of COD concentration are governing equations. The control problem involves finding a flow velocity into the main river that can reduce the COD concentration as close to the target value as possible. In other words, the problem is to find a water velocity to minimize the performance function, which is the square sum of the discrepancy between the computed and the observed COD concentrations. The present research was motivated by the need to apply water purification controls to practical projects. We have found that the controls occasionally tend to be unstable, and the stability of control must be ensured. By expanding the extended performance function into the Taylor series, the necessary condition for the stationary state is derived. Based on this condition, the first‐and second‐order adjoint equations can be obtained. The backward solution of the adjoint equation leads to the gradient and the Hessian product; these serve as the basis of the quasi‐Newton method. From the condition that the performance function must be minimum, the stability confirmation index can be determined. Using this index, we have derived the trust region method, the computation of which confirms the stability of control. Verification was carried out using a simple channel model. By varying the peak value of the inflow velocity, the outlet velocity has been determined such that the water elevation at the target point is zero. Depending on the peak value of the inflow, unstable control arises; this is determined by the stability confirmation index presented in this paper. The trust region method with the stability confirmation index is shown to be adaptable to judge the stability of control. The present method was applied to the water purification of Teganuma river in Japan. The steady fundamental state was computed with the inflow, outflow, and COD concentration at the inlet being specified. The control velocity at the control point can be determined for a fixed control duration with and without the stability confirmation index. The inflow, outflow, and COD concentration are specified as functions of time. It is shown that this method is suitable for practical use because control stability can be ensured. Moreover, it is also noted that the maximum flow velocity for stable control depending on the given control duration can be obtained. Copyright © 2011 John Wiley & Sons, Ltd.

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Section: Trust Region Methodsmentioning

confidence: 77%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Computational water purification controls using second‐order adjoint equations with stability confirmation

Sekine

Kawahara

2011

Numerical Methods in Fluids

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“…Osabe and Kawahara (2006) and Shimamura and Kawahara (2007) have used the timedelay function to treat the drainage basin. A secondorder control problem has been presented by Shichitake and Kawahara (2008). However, the optimal control of a moving boundary has never been investigated.…”

Section: Introductionmentioning

confidence: 98%

Optimal control of drainage basin considering moving boundary

Miyaoka

Kawahara

2008

International Journal of Computational Fluid Dynamics

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The purpose of this article is to present a technique to optimally control river flood using a drainage basin considering a moving boundary. The main theme of this article is to obtain outflow discharge from the drainage basin that maintains the water level at a downstream point and empties the drainage basin as soon as possible. The water flow phenomenon inside the drainage basin when a river flood occurs is considered. This phenomenon can be analysed by the finite element method considering a moving boundary. The optimal control theory can be implemented to obtain the optimal control discharge. The finite element analysis with a moving boundary is introduced in the optimal control theory. A new boundary condition on the downstream side of the river is proposed. This condition is formulated by the solitary wave condition based on the basic water level being capable of representing natural water surface. As a numerical study, optimal control of shallow water flow is carried out for the Tsurumi River and its drainage basin model.

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Input disturbance predictive control of shallow water flows

Samizo

Kawahara

2014

Computer Methods in Applied Mechanics and Engineering

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Optimal control applied to water flow using second order adjoint method

Cited by 6 publications

References 28 publications

Computational water purification controls using second‐order adjoint equations with stability confirmation

Computational water purification controls using second‐order adjoint equations with stability confirmation

Optimal control of drainage basin considering moving boundary

Input disturbance predictive control of shallow water flows

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