Levenberg-Marquardt algorithm for optimization of mathematical models according to minimax objective function of measurement systems

• Autorzy: Tomczyk K.
• Języki publikacji: EN

Abstrakty

EN

The paper presents an application of Levenberg-Marquardt algorithm to parametric optimization of the minimax type of measurement systems. For the assumed objective function given by the integral square error, optimization of the third-order model is carried out and explained in detail. The optimization procedure is realized in three stages. The optimization method presented in the paper can find broad application in the process of determining optimum models of systems, especially for those that operate in dynamic states.

Słowa kluczowe

EN

minimax optimization; Levenberg-Marquardt algorithm; dynamic error

• Wydawca: Komitet Metrologii i Aparatury Naukowej PAN
• Czasopismo: Metrology and Measurement Systems
• Rocznik: 2009
• Tom: Vol. 16, nr 4
• Strony: 599--606
• Opis fizyczny: Bibliogr. 8 poz., rys., wykr., wzory

Twórcy

autor

Tomczyk K.

• Cracow University of Technology, Faculty of Electrical and Computer Engineering, Warszawska 24, 31-155 Kraków, Poland,

Bibliografia

• [1] A. Bobon, J. Kudla, C. Ondrusek: „Zastosowanie algorytmu genetycznego i metody Levenberga-Marquardta do aproksymacji indukcyjności widmowych maszyny synchronicznej”. Zeszyty Naukowe Politechniki Śląskiej Elektryka, vol. 168, Gliwice, 1999, pp. 113-124. (in Polish)
• [2] E. Layer: Modelling of Simplified Dynamical Systems. Springer-Verlag. Berlin Heidelberg New York, 2002.
• [3] E. Layer: “Non-standard input signals for the calibration and optimization of the measuring systems”. Measurement, vol. 34, issue 2, 2003, pp.179-186.
• [4] N.K. Rutland: “The Principle of Matching: Practical Conditions for Systems with Inputs Restricted in Magnitude and Rate of Change”. IEEE Trans. Autom. Control., vol. 39, 1994, pp. 550-553.
• [5] N.K. Sinha, G.T. Bereznai: “Optimum approximation of high-order systems by low order model”. Int. J. Control., no. 21, 1971, pp. 951-959.
• [6] K. Tomczyk: „Optymalizacja parametrow matematycznych modeli wzorcow ze względu na transformacje niezniekształcajaca”. Proc. V Symp. Dynamical Measurement, Szczyrk, 2005, pp.119-128. (in Polish)
• [7] K. Tomczyk: “Application of genetic algorithm to measurement system calibration intended for dynamic measurement”. Metrol. Meas. Syst., vol. XIII, no. 1, 2006, pp. 193-103.
• [8] V. Zakian: “Perspectives of the Principle of Matching and the Method of Inequalities”. Int. J. Control, vol. 65, 1996, pp. 147-175.