Crack identification by multifractal analysis of a dynamic rotor response

Litak, Grzegorz; Sawicki, Jerzy T.

doi:10.1002/zamm.200900226

Cited by 5 publications

(3 citation statements)

References 23 publications

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“…Multifractal analysis, including singular spectrum and generalized dimensions, has aroused more attentions in the field of mechanical fault identification [7][8][9][10][11]. Box-counting (BC) method is the most popular tool for estimating the generalized dimensions due to its ease to understand and implement.…”

Section: Introductionmentioning

confidence: 99%

Morphological covering based generalized dimension for gear fault diagnosis

Zhang

Wang³

et al. 2011

Nonlinear Dyn

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This investigation presents a new generalized dimension estimation method based on morphological covering (MC) technique for characterizing the nonlinearity and complexity of vibration signals measured from gearbox. A synthetic fractal signal is employed to evaluate and compare the proposed MC technique with the traditional box-counting (BC) method and a similar approach developed in literature. Results revealed that the presented MC method is the one providing the most reliable generalized dimension estimation results. Furthermore, we applied this scheme to analyze the vibration signals from a gearbox with three operation states. The estimated general dimensions are used as the input feature vector for classifiers to the gear working states. Experimental results showed that our presented scheme achieves the best performance on discriminating the gear conditions. We also explore the calculational efficiency of B. Li ( ) · P.-l. Zhang the MC method. Results demonstrated that the MC method requires much less computational cost than BC method and seems to be more suitable for on-line condition monitoring of gearboxes.

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Section: Introductionmentioning

confidence: 99%

Morphological covering based generalized dimension for gear fault diagnosis

Zhang

Wang³

et al. 2011

Nonlinear Dyn

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“…Following the multifractal procedure [2][3][4][5] we performed the Taylor expansion of the time series in the small vicinity the instant i:…”

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confidence: 99%

“…The estimated critical exponent distributions D(h) [3][4][5] of the different noise level σ (σ ∈ [0.1, 2.0]) are presented in Fig. 2c.…”

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confidence: 99%

Noisy and chaotic conditions of a pendulum motion

Borowiec

Litak

2009

Proc Appl Math and Mech

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The effect of noise on the rotational mode of a pendulum which is excited kinematically in vertical direction has been analyzed. We have applied the multifractal analysis to distinguish chaotic and noisy solutions in transitions from the oscillations to rotations motion of a pendulum. During increasing the noisy disturbance of the system we analyzed the basic multifractals criteria of the system as correlation and complexity. Using the example of a parametric pendulum [1] we analyzed the noisy and chaotic conditions of a nonlinear system. Starting from pendulum which is subjected to a simple kinematic excitation with noisy disturbance:where vertical harmonic excitation x = A cos (Ω t + Ψ ) effected by a random Winer process Ψ = Ψ (t).The others values: A, Ω -forcing amplitude and frequency, m -the point mass, l -the length of the pendulum, g -gravitational constant, ω 0 = g/l -natural frequency of free oscillations (Fig. 1a). Introducing dimensionless variables; τ = ω 0 t, Ω = Ω /ω 0 , Ψ(τ ) = Ψ (t), the equation of motion reads:here β = k/(ml 2 ) and γ = A/l. In the our recent paper [1] we classified the different oscillatory and rotational motions by a rotation number. This was possible because of the appearance of the phase lock phenomenon due to the system nonlinearities. However in the region of chaos and/or in limit of fairly strong noise this phenomenon disappeared. Here we focus on their other problem. We examine the complexity parameter in the presence of noisy conditions. Namely, increasing the square deviation of the noise Gaussian distribution we follow the changes in the time series based of Poincaré points by estimation complexity and correlation parameters.

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