Dynamical Response of a Planetary Gear System with Faults Using Recurrence Statistics

Ambrożkiewicz, Bartłomiej; Guo, Yu; Litak, Grzegorz; Wolszczak, Piotr

doi:10.1007/978-981-13-9463-8_9

Cited by 6 publications

(5 citation statements)

References 11 publications

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“…The recurrence analysis is very popular and widely applied among a variety of sciences such as physiology [62,63], geology [64,65], finances [66,67]. The subject of study is also the diagnostics of the mechanical systems [68][69][70] and recurrences are an alternative method to the standard frequency and time-based methods. In the following subsections, the fundamentals of the recurrence-based methods are presented, i.e., recurrence plots (RP) and Recurrence Quantification Analysis (RQA).…”

Section: Recurrence Analysismentioning

confidence: 99%

Analysis of Dynamic Response of a Two Degrees of Freedom (2-DOF) Ball Bearing Nonlinear Model

et al. 2021

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Often the input values used in mathematical models for rolling bearings are in a wide range, i.e., very small values of deformation and damping are confronted with big values of stiffness in the governing equations, which leads to miscalculations. This paper presents a two degrees of freedom (2-DOF) dimensionless mathematical model for ball bearings describing a procedure, which helps to scale the problem and reveal the relationships between dimensionless terms and their influence on the system’s response. The derived mathematical model considers nonlinear features as stiffness, damping, and radial internal clearance referring to the Hertzian contact theory. Further, important features are also taken into account including an external load, the eccentricity of the shaft-bearing system, and shape errors on the raceway investigating variable dynamics of the ball bearing. Analysis of obtained responses with Fast Fourier Transform, phase plots, orbit plots, and recurrences provide a rich source of information about the dynamics of the system and it helped to find the transition between the periodic and chaotic response and how it affects the topology of RPs and recurrence quantificators.

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Section: Recurrence Analysismentioning

confidence: 99%

Analysis of Dynamic Response of a Two Degrees of Freedom (2-DOF) Ball Bearing Nonlinear Model

et al. 2021

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“…Angle delay δ and embedding dimension d were determined by the FNN and mutual-information function, respectively. Threshold ε was determined by the standard deviation of the observed angular-domain signal [11]. The vertical distance between these lines can be seen in Figure 4, signals' intermittent behavior with a characteristic angle scale [21] of components caused by faults.…”

Section: Data Preprocessingmentioning

confidence: 99%

“…Recurrence-plot (RP) analysis [9] is a powerful tool to locate nonstationary structural changes and transitions occurring in the dynamic system. It can be employed to study the response of a planetary-gear set and visualize the recurrence behavior of a faulty system [10,11]. RP results are 2D images that make the RP and CNN combination convenient.…”

Section: Introductionmentioning

confidence: 99%

Planetary-Gearbox Fault Classification by Convolutional Neural Network and Recurrence Plot

Wang

Guo

et al. 2020

Applied Sciences

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Recurrence-plot (RP) analysis is a graphical tool to visualize and analyze the recurrence of nonlinear dynamic systems. By combining the advantages of the RP and a convolutional neural network (CNN), a fault-classification scheme for planetary gear sets is proposed in this paper. In the proposed approach, a vibration is first picked up from the planetary-gear test rig and converted into an angular-domain quasistationary signal through computed order tracking to eliminate the frequency blur caused by speed fluctuations. Then, the signal in the angular domain is divided into several segments, and each segment is processed by the RP to constitute the training sample. Moreover, a two-dimensional CNN model was developed to adaptively extract faulty features. Experiments on a planetary-gear test rig with four conditions under three operating speeds were carried out. The results of measured vibration demonstrated the validity of CNN and recurrence plot analysis for the fault classification of planetary-gear sets.

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“…Recurrence-based techniques allow the quantification of temporal structure and generalized autocorrelation properties of individual time series (Webber and Zbilut, 1994;Zbilut and Webber, 1992), the quantification of bivariate relationships, and coupling between two time series (Zbilut et al, 1998;, as well as the quantification of multidimensional dynamics of multivariate time series (Wallot et al, 2016b;Wallot and Mønster, 2018). Recurrence-based techniques originate from the description and analysis of dynamical systems (Marwan et al, 2007; and have been widely applied to data from physics (Alex et al, 2015;Ambrożkiewicz et al, 2019;Donner and Thiel, 2007;Hilarov, 2017;Zolotova and Ponyavin, 2006), physiology Langbein et al, 2004;Thomasson et al, 2001;Mestivier et al, 2001;Mønster et al, 2016;Timothy et al, 2017), and psychology (Abney et al, 2014;Coco et al, , 2016Shockley et al, 2003;Wijnants et al, 2012;Pagnotta et al, 2020), to name a few fields.…”

Section: Introductionmentioning

confidence: 99%

Unidimensional and Multidimensional Methods for Recurrence Quantification Analysis with crqa

Coco¹,

Mønster²,

Leonardi³

et al. 2021

The R Journal

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Recurrence quantification analysis is a widely used method for characterizing patterns in time series. This article presents a comprehensive survey for conducting a wide range of recurrencebased analyses to quantify the dynamical structure of single and multivariate time series and capture coupling properties underlying leader-follower relationships. The basics of recurrence quantification analysis (RQA) and all its variants are formally introduced step-by-step from the simplest autorecurrence to the most advanced multivariate case. Importantly, we show how such RQA methods can be deployed under a single computational framework in R using a substantially renewed version of our crqa 2.0 package. This package includes implementations of several recent advances in recurrencebased analysis, among them applications to multivariate data and improved entropy calculations for categorical data. We show concrete applications of our package to example data, together with a detailed description of its functions and some guidelines on their usage.

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Dynamical Response of a Planetary Gear System with Faults Using Recurrence Statistics

Cited by 6 publications

References 11 publications

Analysis of Dynamic Response of a Two Degrees of Freedom (2-DOF) Ball Bearing Nonlinear Model

Analysis of Dynamic Response of a Two Degrees of Freedom (2-DOF) Ball Bearing Nonlinear Model

Planetary-Gearbox Fault Classification by Convolutional Neural Network and Recurrence Plot

Unidimensional and Multidimensional Methods for Recurrence Quantification Analysis with crqa

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