The harmonic probing method for output-only nonlinear mechanical systems

Scussel, Oscar; Silva, Samuel da

doi:10.1007/s40430-017-0723-y

Cited by 7 publications

(2 citation statements)

References 35 publications

(71 reference statements)

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“…However, for the reason that the number of frequency interactions increases quickly with the order of GFRFs [10][11][12], explicit expressions of frequency interactions required in the extended approach become very complicated when the order is higher than two or three. Another way to evaluate the GFRFs was by applying parametric modeling techniques, typically involving orthonormal basis expansion [13], analytical derivation [14], and harmonic probing [15][16][17][18][19] which has been applied to detecting cracks in rotor-bearing systems and cantilever beams [20]. Although the methods of para-metric modeling can obtain any order GFRF theoretically, they require not only the output data •3• available but also the knowledge of governing motion equations of system, and inherently have the problem of convergence in iteration processes [21,22].…”

Section: Introductionmentioning

confidence: 99%

A Digital Method of Evaluating Nonlinear Frequency Response Functions Based on Conditioned Spectral Analyses

Zhang

Wang

2021

Preprint

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This paper focuses on the issue of evaluating nonlinear frequency response functions (NOFRFs) of the nonlinear systems with a general input. A new digital approach of evaluating NOFRFs is proposed based on the method of conditioned spectral analysis (CSA). Firstly, a multiple-input/single-output (MISO) linear system with a series of power characterized inputs is obtained by decomposing a nonlinear system according to the NOFRFs theory. Secondly, the correlations among the inputs of various orders are removed by applying CSA method, obtaining an algorithm of identifying the NOFRFs and evaluating the contributions of different order nonlinearities to the output of the system. In the CSA procedure, the different order inputs are conditioned in the sequence from the first order to the highest order. Lastly, two kinds of nonlinear systems with a general input are simulated to verify the effectiveness of the proposed approach on evaluating the frequency response properties of nonlinear systems. It is shown that the results reached by the proposed method are very close to the numerical results obtained by the fourth order Runge-Kutta method, verifying that the proposed method is very effective on the evaluation of NOFRFs.

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Section: Introductionmentioning

confidence: 99%

A Digital Method of Evaluating Nonlinear Frequency Response Functions Based on Conditioned Spectral Analyses

Zhang

Wang

2021

Preprint

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“…Among the different methods for nonlinearities identification, the Volterra series stands out, because it is a generalization of the linear convolution concept, allowing the separation of the system response in linear and nonlinear components [31]. The main procedure to estimate the Volterra kernels is the Harmonic Probing method, that was extensively used in system identification problems [32,33] and damage characterization [34]. The limitation of the approach is the dependence of a parametric model of the system.…”

Section: Introductionmentioning

confidence: 99%

Damage detection in uncertain nonlinear systems based on stochastic Volterra series

Villani

Silva

Cunha

2019

Mechanical Systems and Signal Processing

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The damage detection problem in mechanical systems, using vibration measurements, is commonly called Structural Health Monitoring (SHM). Many tools are able to detect damages by changes in the vibration pattern, mainly, when damages induce nonlinear behavior. However, a more difficult problem is to detect structural variation associated with damage, when the mechanical system has nonlinear behavior even in the reference condition. In these cases, more sophisticated methods are required to detect if the changes in the response are based on some structural variation or changes in the vibration regime, because both can generate nonlinearities. Among the many ways to solve this problem, the use of the Volterra series has several favorable points, because they are a generalization of the linear convolution, allowing the separation of linear and nonlinear contributions by input filtering through the Volterra kernels. On the other hand, the presence of uncertainties in mechanical systems, due to noise, geometric imperfections, manufacturing irregularities, environmental conditions, and others, can also change the responses, becoming more difficult the damage detection procedure. An approach based on a stochastic version of Volterra series is proposed to be used in the detection of a breathing crack in a beam vibrating in a nonlinear regime of motion, even in reference condition (without crack). The system uncertainties are simulated by the variation imposed in the linear stiffness and damping coefficient. The results show, that the nonlinear analysis done, considering the high order Volterra kernels, allows the approach to detect the crack with a small propagation and probability confidence, even in the presence of uncertainties.

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Damage detection through nonparametric models using Kautz filters

Silva

Hansen

2021

Meccanica

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The harmonic probing method for output-only nonlinear mechanical systems

Abstract: to describe a prediction of vibrating systems in nonlinear regime of motion.

Cited by 7 publications

References 35 publications

A Digital Method of Evaluating Nonlinear Frequency Response Functions Based on Conditioned Spectral Analyses

A Digital Method of Evaluating Nonlinear Frequency Response Functions Based on Conditioned Spectral Analyses

Damage detection in uncertain nonlinear systems based on stochastic Volterra series

Damage detection through nonparametric models using Kautz filters

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