Parameter estimation using linear programming and quasilinearization

Abstract

A generalized algorithm for the estimation of parameters in a process model from experimental data is preseuted in this paper. The algorithm, which combines linear programming with quasilinearization, is formulated and its advantages and limitations are discussed. Examples are included to illustrate application of the algorithm to real engineering problems, one of which was encountered in industry and another of which was encountered in a control study. The examples demonstrate the incorporation of constraints, convergence promotion and reliability estimates into the identification.ne of the most common problems in engineering 0 analysis is the determination of parameters in a mathematical model such that the model response satisfactorily reproduces or "best" fits experimental data taken from the physical system of interest. A promising and general approach to parameter estimation problems is to formulate them as nonlinear boundary value problems to which techniques such as quasilinearization can be The quasilinearization technique converts the nonlinear problem into a series of linear boundary value problems which hopefully converge to the actual solution of the original problem.In this paper a generalized algorithm, which combines linear programming with quasilinearization, is formulated and some of the practical aspects of its implementation, including constraints, convergence and reliability estimates of parameters are explored. FormulationA convenient representation for the mathematical model of many dynamic systems is the vector differential equation :

Batch Crystallizers

“…Although several other approaches have been suggested to overcome the small region of Brought to you by | Ariz Health Sciences Library Authenticated | 150.135.135.70 Download Date | 12/30/12 4:31 PM convergence(Donnelly and Quon, 1970;Nieman and Fisher, 1972;Wang and Luss, 1980;Hwang and Seinfeld, 1972;Bergmann et al, 1976;Xugen and Svrcek, 1977; …”

Iterative parameter estimation for extraction of crystallization kinetics of potassium chloride from batch experiments

“…- Nieman and Fisher (1972) in solving quasi-linearization parameter estimation problems, had also found the necessity of imposing artificial parameter bounds on each parameter. Their reason for imposing these was the small region of convergence.…”

The application of an on-line model error tolerant sub-optimal controller to a chemical reactor

“…The suboptimal controller minimised P over the next control interval of 30 s (that is the index limit n = 1) and assumed that the control vector u was piecewise constant. Under these conditions, the method of quasilinearisation, which has been used previously to solve the full optimal control (Sbaiti and Sage, 1972;Yeo, 1976;Rothenberger and Lapidus, 1967b ;Lee, 1968) and parameter identification (Nieman and Fisher, 1972;Donnelly and Quon, 1970) problems, can be employed.…”