0
TECHNICAL PAPERS

System Identification of Nonlinear Mechanical Systems Using Embedded Sensitivity Functions

[+] Author and Article Information
Chulho Yang

 Arvin Meritor CTC, 950 W. 450 S. Bldg. 2, Columbus, IN 47201chulho.yang@arvinmeritor.com

Douglas E. Adams1

 Purdue University, School of Mechanical Engineering, Ray W. Herrick Laboratories, 140 S. Intramural Drive, West Lafayette, IN 47907-2031deadams@purdue.edu

Sam Ciray

 ArvinMeritor, A&ET, 950 W 450 S, Columbus, IN 47201mehmet.ciray@arvinmeritor.com

1

Telephone: (765) 496-6033; Fax: (765) 494-0787.

J. Vib. Acoust 127(6), 530-541 (Feb 18, 2005) (12 pages) doi:10.1115/1.2110815 History: Received March 17, 2004; Revised February 18, 2005

A novel method of experimental sensitivity analysis for nonlinear system identification of mechanical systems is examined here. It has been shown previously that embedded sensitivity functions, which are quadratic algebraic products of frequency response function data, can be used to identify structural design modifications for reducing vibration levels. It is shown here that embedded sensitivity functions can also be used to characterize and identify mechanical nonlinearities. Embedded sensitivity functions represent the rate of change of the response with variation in input amplitude, and yield estimates of system parameters without being explicitly dependent on them. Frequency response functions are measured at multiple input amplitudes and combined using embedded sensitivity analysis to extract spectral patterns for characterizing systems with stiffness and damping nonlinearities. By comparing embedded sensitivity functions with finite difference frequency response sensitivities, which incorporate the amplitude-dependent behavior of mechanical nonlinearities, models can be determined using an inverse problem that uses system sensitivity to estimate parameters. Expressions for estimating nonlinear parameters are derived using Taylor series expansions of frequency response functions in conjunction with the method of harmonic balance for periodic signals. Using both simulated and experimental data, this procedure is applied to estimate the nonlinear parameters of a two degree-of-freedom model and a vehicle exhaust system to verify the approach.

Copyright © 2005 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Schematic of a three degree-of-freedom linear system model with a parameter labeling format used to indicate coupling

Grahic Jump Location
Figure 2

Brief overview of the characterization and identification process for nonlinear systems using embedded sensitivity functions

Grahic Jump Location
Figure 3

Schematic of a two degree-of-freedom nonlinear system model with cubic/quadratic stiffness or quadratic/Coulomb friction damping nonlinearity between masses 1 and 2

Grahic Jump Location
Figure 4

The embedded (—) and finite difference (---) sensitivities (a) dH21∕dK12 showing nearly the same magnitude in the entire frequency range, and (b) dH21∕dK01 showing different magnitude in the entire frequency range

Grahic Jump Location
Figure 5

The graph of numerator [H21l-H21s] and denominator [dH21∕dK12(Y21l-Y21s)] for the nonlinear parameter calculation showing nearly parallel curves with constant magnitude difference (—: Numerator, ---: Denominator)

Grahic Jump Location
Figure 6

Graph of the estimated nonlinear parameter in the frequency range of interest; for a single nonlinearity, the estimated curve is flat throughout the entire frequency range

Grahic Jump Location
Figure 7

(a) The embedded (—) and finite difference (---) sensitivities dH21∕dK12 showing different magnitude. (b) Graph of the estimated nonlinear parameter; the estimated curve is not flat for the case when the characterized type of nonlinearity is not correct

Grahic Jump Location
Figure 8

Graphs of restoring forces (Acceleration Y21a) of quadratic stiffness parameter at 34Hz with respect to relative displacement Y11–Y21 for given parameters: 7e5 [(a): simulated, (b): estimated], 7e7 [(c): simulated, (d): estimated]

Grahic Jump Location
Figure 9

Restoring forces (Acceleration Y21a) for Coulomb friction damping parameter obtained from simulation and estimation process; the constant value of Coulomb friction parameter was well estimated (∗: Simulation, 엯: Estimation)

Grahic Jump Location
Figure 10

Shaker and de-coupler of vehicle exhaust system

Grahic Jump Location
Figure 11

Frequency response function H21(ω) in x direction obtained using a broadband random signal showing distortions in FRFs around 200 and 350Hz (—: input level 1, ---: input level 2, ∙∙∙∙: input level 3)

Grahic Jump Location
Figure 12

Frequency response functions H12 in x direction obtained using a sine sweep signal from 190to240Hz in 50s; distortion in FRFs around 200Hz was examined (—: input level 1, ---: input level 2, ∙∙∙∙: input level 3)

Grahic Jump Location
Figure 13

Graphs of the numerator [H12l-H12s] and denominator [dH12∕dK12(X12l2̱X12s2)] for the nonlinear parameter calculation in the de-coupler of an exhaust system showing similar spectral patterns (---: Numerator,—: Denominator)

Grahic Jump Location
Figure 14

The estimated nonlinear parameter of the bellows in exhaust system; even though the estimated parameter curve is not constant, the average taken for specific frequency range of interest provides a relatively accurate value

Grahic Jump Location
Figure 15

Restoring forces (Acceleration X11a) obtained from experiment (---) and estimation process (∙∙∙∙); slight asymmetry in test data is caused by skewed front end of the de-coupler

Grahic Jump Location
Figure 16

Time signals of acceleration X11a, obtained by test data (-엯-) and reconstructed from the estimated value of the nonlinear parameter (-∗-); note that these two graphs match well except for the bottom of the cycle due to asymmetry in test data caused by skewed front end of the decoupler

Grahic Jump Location
Figure 17

The estimated nonlinear parameter of the bellows in the exhaust system; even though the estimated parameter curve varies, the average value is used to obtain accurate estimate

Grahic Jump Location
Figure 18

Restoring forces (Acceleration Y12a) obtained from experiment (—) and estimation process (-◻-) showing good match in overall friction behavior

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In