Determination of Dynamic Model Parameters Using Quasilinearization

Ramaker, Brian L.; Smith, Cecil L.; Murrill, Paul W.

doi:10.1021/i160033a005

Cited by 10 publications

(5 citation statements)

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“…A considerable amount of work has been directed to solve the problem of the small region of convergence or the problem of convergence to nonglobal optima (Ramaker et al, 1970;Hwang andSeinfeld, 1972 Donnelly andQuon, 1970;Nieman and Fisher, 1972).…”

Section: Procedures For Good Initial Estimatesmentioning

confidence: 99%

“…Bard (1970) compared several gradient methods and concluded that Marquardt's modification of Gauss-Newton method is the best. Ramaker et al (1970) used Marquardt's modification in quasilinearization to expand the region of convergence. However, they found that the efficiency of the algorithm is greatly influenced by the starting value of the directional parameter and the rate at which it is varied.…”

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confidence: 99%

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Simplification of quasilinearization method for parameter estimation

Kalogerakis

Luus

1983

AIChE Journal

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Section: Procedures For Good Initial Estimatesmentioning

confidence: 99%

mentioning

confidence: 99%

Simplification of quasilinearization method for parameter estimation

Kalogerakis

Luus

1983

AIChE Journal

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“…However, these methods often converge to local optima and convergence is rather slow, if at all. On the other hand, the efficiency of Marquardt's modification is greatly influenced both by the starting value of µ and the rate at which µ is varied (Ramaker et al, 1970;Osborne, 1972).…”

Section: Information Indexmentioning

confidence: 99%

“…This problem has received much attention recently. Ramaker et al (1970) suggested the incorporation of Marquardt's modification to expand the region of convergence. Donnelly and Quon (1970) proposed a procedure whereby the given data are perturbed if divergence occurs and a series of problems are solved until the model trajectories "match" the original data.…”

Section: Introductionmentioning

confidence: 99%

Improvement of Gauss-Newton method for parameter estimation through the use of information index

Kalogerakis¹,

Luus²

1983

Ind. Eng. Chem. Fund.

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In parameter estimation for systems described by ordinary differential equations, the region of convergence for the Gauss-Newton method can be substantially enlarged through the use of an "Information Index" and an optimal step-size policy. The information index provides a measure of the available sensitivity information as a function of time, thereby locating the most appropriate section of data to be used for parameter estimation. The use of the chosen section of data significantly improves the conditioning of the linear algebraic equations that are solved at the end of each iteration In the Gauss-Newton method, and the region of convergence is thus expanded. If observations are unavailable in the most appropriate section of data, artificial data can be generated by data smoothing and interpolation. The effectiveness of the approach is illustrated by four examples depicting typical chemical engineering systems. The proposed procedure is especially attractive for systems described by stiff differential equations.

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“…The regression method may be improved according to various proposals suggested in recent literature. Some of these include: ( 1 ) the methods of Ramaker et al (1970) for increasing convergence regions, (2) Tanner's (1972) fast algorithm for generating starting parameter values for quasilinearization, and ( 3 ) a n algorithm of Hwang and Seinfeld (1972) requiring fewer integrations per iteration to replace quasilinearization.…”

Section: Improvement Of the Algorithmmentioning

confidence: 99%

Application of quasilinearization to methane pyrolysis

Denis¹,

Daubert²

1974

AIChE Journal

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The rate constants appearing in differential equations derived from proposed mechanisms for methane pyrolysis were estimated from published integral conversion data. Quasilinearization, capable of fitting the differential equation solutions directly to the integral data and therefore not requiring differentiation or transformations, was used. Since differential equations representing free radical reactions have coefficients varying over many orders of magnitude, implicit numerical integration was used to obtain the numerous particular and homogeneous solutions required in the execution of the algorithm. Convergence was achieved by replacing the concentrations after each iteration with values near the solution at that point and by repeatedly estimating a small number of parameters in a cyclic manner in order to improve starting estimates of all parameters simultaneously. The mechanisms attempted were considered plausible when they led to adequate data fits and reasonable rate constant estimates. The major contribution of the work is that the algorithm is capable of testing a mechanistic model over a relatively wide range of conditions with minimal experimental data.

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Determination of Dynamic Model Parameters Using Quasilinearization

Cited by 10 publications

References 1 publication

Simplification of quasilinearization method for parameter estimation

Simplification of quasilinearization method for parameter estimation

Improvement of Gauss-Newton method for parameter estimation through the use of information index

Application of quasilinearization to methane pyrolysis

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