Application of the Nonlinear Least Squares Frequency Domain Method to the Estimation of Modal Model Parameters

• Autorzy: Iwaniec J. , Uhl T.
• Języki publikacji: EN

Abstrakty

EN

The least squares method is the most popular algorithm for solving linear as well as nonlinear systems of equations. In the paper the theoretical basis of the Gauss-Newton and the Levenberg-Marquardt algorithms for solution estimation with the use of the nonlinear least squares method are presented. The discussed schemes of proceeding usually allow the user to improve the quality of the estimated solutions. The analysis of frequency data measured on a real structure with the use of the created software realizing the Gauss-Newton algorithm in the Matlab environment is presented. The comparison of the analysis results estimated by the use of the proposed software and the LSCE (least squares complex exponential) algorithm implemented in the VIOMA toolbox is also included.

Słowa kluczowe

EN

modal analysis; nonlinear squares frequency domain method; Gauss-Newton algorithm; model estimation

• Wydawca: Oficyna Wydawnicza Politechniki Warszawskiej
• Czasopismo: Machine Dynamics Problems
• Rocznik: 2003
• Tom: Vol. 27, No. 2
• Strony: 37--54
• Opis fizyczny: bibliogr. 12 poz.

Twórcy

autor

Iwaniec J.

• Department of Robotics and Machine Dynamics, AGH University of Science and Technology, Krakow

autor

Uhl T.

• Department of Robotics and Machine Dynamics, AGH University of Science and Technology, Krakow

Bibliografia

• 1. Balmés, E., 1996, Frequency domain identification of structural dynamics using the pole/residue parametrization, International Modal Analysis Conference, Dearbom.
• 2. Balmés, E., 1997, Structural Dynamics Toolboxfor Use With Mat/ab, User's Guide, Version 3, Scientific Software Group, Sevres, France.
• 3. Giergiel, J., Uhl, T., 1990, Identification of mechanical systems (original title in Polish: Identyfikacja ukałów mechanicznych), PWN, Warszawa.
• 4. Heylen, W., Lammens, S., Sas, P., 1994, Modal Analysis Theory and Testing, KUL Leuwen.
• 5. Kurowski, P., 2001, Identification of modal models of mechanical structures on the basis of the in-operational measurements (original title in Polish: Identyfikacja modeli modalnych konstrukcji mechanicznych w warunkach eksploatacji), Ph.D. thesis, AGH, Kraków.
• 6. Kurowski, P., Ligęza, J., Ubi, T., 2001, The usage of the Matlab environment for modal model parameters estimation for single degree offreedom systems (original title in Polish: Zastosowania MATLABa do estymacji parametrów modalnych metoda SDOF), 5 th Scientific Conference: Experimental methods in machine design and exploitation, Wrocław-Szklarska Poręba, 65-77.
• 7. Ligęza J., 2002, lmplementation of modal analysis algorithms in Matlab (original title in Polish: Implemenatcja algorytmów analizy modalnej w Pakiecie MATLAB), Master 's thesis, AGH, Kraków.
• 8. MathWorks Inc., 2003 , Optimization Toolbox User's Guide, http://www.mathworks.com/access/helpdesk/help/toolbox/optim/optim.shtrnl.
• 9. Mrozek B., Mrozek Z., 1998, Matlab 5.x Simulink 2.x user guide (original title in Polish: MATLAB 5.x SIMULINK 2.x. Pozdręcznik Uzytkownika), PLJ, Warszawa.
• 10. Norton J. P., 1992, An Introduction to Identification, AP (Academic Press), London.
• 11. Ubl T., 1997, Computer aided identification of mechanieal structure models (original title in Polish: Komputerowe wspomaganie identyfikacji modeli konstrukcji mechanicznych), WNT, Warszawa.
• 12. Ubl T., Lisowski W., Kurowski P., 2000, ln-operation modal analysis and its applications, Katedra Robotyki i Dynamiki Maszyn, AGH, Kraków.