scholarly journals Comparisons between harmonic balance and nonlinear output frequency response function in nonlinear system analysis

2008 ◽  
Vol 311 (1-2) ◽  
pp. 56-73 ◽  
Author(s):  
Z.K. Peng ◽  
Z.Q. Lang ◽  
S.A. Billings ◽  
G.R. Tomlinson
Keyword(s):  
Nonlinear System ◽  
Frequency Response ◽  
Response Function ◽  
Harmonic Balance ◽  
Frequency Response Function ◽  
System Analysis ◽  
Output Frequency ◽  
Nonlinear System Analysis

Relationship between harmonic balance method and non-linear output frequency response function approach

2007 ◽  
Vol 221 (12) ◽  
pp. 1533-1543 ◽  
Author(s):  
Z K Peng ◽  
Z Q Lang
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Harmonic Balance ◽  
Frequency Response Function ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Output Frequency ◽  
Non Linear ◽  
Harmonic Components ◽  
The Relationship

The current paper is concerned with the investigation of the relationship between the harmonic balance method (HBM) and the non-linear output frequency response function (NOFRF) approach in the analysis of non-linear systems. Both are applied to the Duffing's oscillator to demonstrate their relationships. The results reveal that, if the Volterra series representation of a non-linear system is convergent, the harmonic components calculated by the NOFRFs are a solution of the HBM. Moreover, the simulation studies show that, in the convergent cases, the NOFRF method can give more accurate results for the higher-harmonic components than the HBM. The relationship investigated in the current study between the two methods should help researchers and engineers to understand the HBM and the NOFRF methods.

A Note on the Estimation of Nonlinear System Damping

2003 ◽  
Vol 70 (3) ◽  
pp. 449-450 ◽  
Author(s):  
P. J. Torvik
Keyword(s):  
Nonlinear System ◽  
Frequency Response ◽  
Response Function ◽  
Loss Factor ◽  
Frequency Response Function ◽  
Maximum Amplitude ◽  
Single Mode ◽  
Half Power

System damping for a single mode in resonance is often estimated from a measurement of the bandwidth of the frequency response function. While the bandwidth is customarily measured between the half-power frequencies, it is also possible to choose any other fraction of the maximum amplitude. If the damping is linear, i.e., if the loss factor is independent of amplitude, the same damping will be found with any such choice. While intuition might suggest that the damping of a nonlinear system would be better estimated from a bandwidth taken closer to the maximum amplitude, this is shown to be false.

The Improved Frequency Response Function and its Effect on Modal Circle Fits

1984 ◽  
Vol 51 (3) ◽  
pp. 657-663 ◽  
Author(s):  
K. B. Elliott ◽  
L. D. Mitchell
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
System Analysis ◽  
Resonance Region ◽  
Random Excitation ◽  
Structural Parameter ◽  
Parameter Estimates ◽  
Average Percentage ◽  
Fitting Error

When structures are excited by random force excitation the circle fits of the data around resonance are usually poor. The structural parameter estimates, which result from this fit, are usually erroneous. No matter how elegant the circle or the multimodal fit, the results will be poor if the frequency response function (FRF) is a poor representation of the actual structural response. In general for the random excitation case, this is the case. The conventional fast Fourier transform (FFT) method which is used to estimate the frequency response function, is given by H1 (f) = Gxy/Gxx. This produces poor results when the coherence of the data falls in the resonance region. A drop in the coherence usually indicates noise at the input of the structure for this case. H1 (f) is quite sensitive to such noise giving erroneous estimates. This paper investigates an alternative method for computing the frequency response function, H2 (f) = Gyy/Gyx, and its impact on the accuracy of the circle fit procedure used in modal analysis. This new estimator is not sensitive to input noise like the currently used H1 (f). H2(f) provides the best estimate at or around resonance even in the presence of noise on the input signal. If one defines the average percentage fit error in the circle fit operation as 100 times the average radial deviation of the data points from the radius of the statistically fit circle divided by the fit circle radius, one can compute the circle fit accuracy for each of the proposed methods of data treatment. Typically, the percentage fitting error for H1 (f) might be 10 percent while the fitting error for H2 (f) using exactly the same data will be 0.5 percent. Thus, the proposed method eliminates long-standing system analysis errors through the use of a simple revision of the way the data are treated in the FFT processor around the resonance regions.

scholarly journals A Novel Method for Fault Diagnosis of the Two-Input Two-Output Nonlinear Mass-Spring-Damper System Based on NOFRF and MBPCA

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Jialiang Zhang ◽  
Jie Wu ◽  
Xiaoqian Zhang
Keyword(s):  
Principal Component Analysis ◽  
Fault Diagnosis ◽  
Nonlinear System ◽  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
Principal Component ◽  
Component Analysis ◽  
Novel Method ◽  
Mass Spring

For fault diagnosis of the two-input two-output mass-spring-damper system, a novel method based on the nonlinear output frequency response function (NOFRF) and multiblock principal component analysis (MBPCA) is proposed. The NOFRF is the extension of the frequency response function of the linear system to the nonlinear system, which can reflect the inherent characteristics of the nonlinear system. Therefore, the NOFRF is used to obtain the original fault feature data. In order to reduce the amount of feature data, a multiblock principal component analysis method is used for fault feature extraction. The least squares support vector machine (LSSVM) is used to construct a multifault classifier. A simplified LSSVM model is adopted to improve the training speed, and the conjugate gradient algorithm is used to reduce the required storage of LSSVM training. A fault diagnosis simulation experiment of a two-input two-output mass-spring-damper system is carried out. The results show that the proposed method has good diagnosis performance, and the training speed of the simplified LSSVM model is significantly higher than the traditional LSSVM.

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