On the use of weighting matrices to improve harmonic balance parameter identification results

• Published in: Journal of sound and vibration 2013-06, Vol.332 (12), p.2941-2953
• Main Authors: Tweten, Dennis J., Mann, Brian P.
• Format: Article
• Language: English
• Subjects: Gaussian; Harmonics; Mathematical analysis; Matrices; Matrix methods; Oscillators; Strategy; Weighting
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2013.01.010

This paper investigates the use of weighting matrices to improve the harmonic balance identification (HBID) method for identifying nonlinear oscillators. While the notation for adding weighting matrices has been previously introduced, typical strategies for developing weighting matrices cannot be applied to the HBID method since the variance structure of each observation is identical. A new approach is presented based on the signal to noise ratio of each harmonic. This new weighting strategy is shown to improve the accuracy of the estimated parameters from data with Gaussian, uniform, and Laplacian noise distributions. In addition, the paper explores the relationship between the accuracy of the estimated parameters and the range of phase space transversed by a steady-state response. It is shown that small oscillations in a double well oscillator can be used to accurately estimate the system parameters. ► We compare the use of weighting matrices to improve harmonic balance identification. ► Parameters are identified using simulated data with multiple noise distributions. ► We introduce a new weighting matrix based on the signal to noise ratio of harmonics. ► The new weighting matrix is shown to improve the accuracy of estimated parameters. ► We show how to accurately identify parameters in a reduced phase space.