Increasing the size of region of convergence for parameter estimation through the use of shorter data-length

Wang, Bi-Chong; Luus, Rein

doi:10.1080/00207178008961094

Cited by 20 publications

(7 citation statements)

References 16 publications

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“…Kalogerakis and Luus recognized the existence of local minima and the poor convergence regions of the previous approaches . They presented an algorithm which uses a direct search method to determine good initial guesses for either a quasi-linearization or a Gauss−Newton type minimization.…”

Section: Introductionmentioning

confidence: 99%

Global Optimization for the Parameter Estimation of Differential-Algebraic Systems

Esposito

Floudas

2000

Ind. Eng. Chem. Res.

178

168

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The estimation of parameters in semiempirical models is essential in numerous areas of engineering and applied science. In many cases these models are represented by a set of nonlinear differential-algebraic equations. This introduces difficulties from both a numerical and an optimization perspective. One such difficulty, which has not been adequately addressed, is the existence of multiple local minima. In this paper, two novel global optimization methods will be presented which offer a theoretical guarantee of convergence to the global minimum for a wide range of problems. The first is based on converting the dynamic system of equations into a set of algebraic constraints through the use of collocation methods. The reformulated problem has interesting mathematical properties which allow for the development of a deterministic branch and bound global optimization approach. The second method is based on the use of integration to solve the dynamic system of equations. Both methods will be applied to the problem of estimating parameters in differential-algebraic models through the error-in-variables approach. The mathematical properties of the formulation which lead to specialization of the algorithms will be discussed. Then, the computational aspects of both approaches will be presented and compared through their application to several problems involving reaction kinetics.

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Section: Introductionmentioning

confidence: 99%

Global Optimization for the Parameter Estimation of Differential-Algebraic Systems

Esposito

Floudas

2000

Ind. Eng. Chem. Res.

178

168

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“…A limited knowledge of the unknown parameters requires a considerable amount of work to obtain optimal parameters and might induce the problem of convergence to the local optimum instead of the global optimum (Wang and Luus, 1980). In this study, each unknown parameter has its minimum and maximum bounds obtained by field observation, laboratory experimentation, and previous modeling studies (Bowie et al, 1985;HydroQual, 1987;Ambrose et al, 1994;Cerco and Cole, 1995;Park et al, 1995;Chapra, 1997;DiToro, 2001;Jorgensen, 2001b;Phlips et al, 2004).…”

Section: Estimation Of Water Quality Model Parametersmentioning

confidence: 99%

Estimation of water quality model parameters

Kim

Sheng

2010

KSCE J Civ Eng

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A modified Gauss-Newton method was utilized to estimate water quality model parameters, which is important in the modeling of water quality transport process. This method served the unknown parameters of three engineering problems exceptionally well. We applied this method to obtain a set of water quality parameters by solving the kinetic equations for dissolved and particulate water quality species during episodic events in the Indian River Lagoon, FL. The method was successful in producing water quality model parameters, and the relative errors between measurements and model predictions are below 46.4% and 39.4% for all dissolved and particulate water quality state variables, respectively. In this study we evaluated a good capability of suggested parameter estimation method by comparing a couple of water quality model simulations: (1) water quality model simulation using model parameters produced by the modified Gauss-Newton method and (2) water quality model simulation employing model parameters obtained by the trial-and-error method. The average relative error and ROC score between observed data and water quality model results using model parameters calculated by the modified Gauss-Newton method are 58.3% and 0.565, respectively. In the case of water quality model simulation using model parameters obtained by the trial-and-error method, the average relative error and ROC score are 60.5% and 0.555, respectively. This suggests that the modified Gauss-Newton method efficiently yields water quality model parameters resulting in better or similar model prediction errors when compared to the trial-and-error method.

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“…The simple one parameter model used by Hwang and Seinfeld (1972) and Wang and Luus (1980) which demonstrates the difficulty of obtaining the global minimum is used here. The system is given by However, in the present work we assume that there is a nonlinear relationship between the observed and state variables given by…”

Section: Examplementioning

confidence: 99%

“…Nieman and Fisher (1972) incorporated linear programming into quasilinearization and suggested the solution of a series of constrained parameter estimation problems where the search is restricted in a small parameter space around the chosen initial guess. Recently, Wang and Luus (1980) proposed the use of shorter data length to substantially enlarge the region of convergence, thereby also avoiding the problem of convergence to nonglobal optima. More specifically, only portions of the data length are used during the early iterations when the estimated values for the parameters are far from their optimum values.…”

mentioning

confidence: 99%