Determining growth rates of instabilities from time-series vibration data: Methods and applications for brake squeal

Stender, Merten; Tiedemann, Merten; Hoffmann, Lando; Hoffmann, Norbert

doi:10.1016/j.ymssp.2019.04.009

Cited by 22 publications

(6 citation statements)

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“…SNR dB = 10 log 10 P clean P noise (11) where x clean is the noiseless signal, x noise is the added noise, N is the number of observations and the SNR is expressed in decibels. As an error metric the difference in the signals' standard deviations is used.…”

Section: Noise-contaminated Datamentioning

confidence: 99%

“…To this end, many strategies have been developed for system identifications generally based on linear theory, such as modal analysis [6][7][8]. It is superfluous to note that, in a sense, all real systems are nonlinear and may be described by linear models only within some restricted ranges of the governing parameters, or under particular conditions [9][10][11]. For example, almost all engineering applications are constituted by jointed structures [12][13][14][15][16] where frictional dissipation takes place [17,18].…”

Section: Introductionmentioning

confidence: 99%

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Reconstruction of Governing Equations from Vibration Measurements for Geometrically Nonlinear Systems

et al. 2019

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Data-driven system identification procedures have recently enabled the reconstruction of governing differential equations from vibration signal recordings. In this contribution, the sparse identification of nonlinear dynamics is applied to structural dynamics of a geometrically nonlinear system. First, the methodology is validated against the forced Duffing oscillator to evaluate its robustness against noise and limited data. Then, differential equations governing the dynamics of two weakly coupled cantilever beams with base excitation are reconstructed from experimental data. Results indicate the appealing abilities of data-driven system identification: underlying equations are successfully reconstructed and (non-)linear dynamic terms are identified for two experimental setups which are comprised of a quasi-linear system and a system with impacts to replicate a piecewise hardening behavior, as commonly observed in contacts.

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Section: Noise-contaminated Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reconstruction of Governing Equations from Vibration Measurements for Geometrically Nonlinear Systems

et al. 2019

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“…complicating the picture of stability drastically. Previous work [19] on extracting the instantaneous growth rates, i.e. quantifying linear stability and instantaneous damping, from experimental data illustrates high sensitivity of the effective damping with respect to loading conditions.…”

Section: Input-output Behavior Of Dynamical Systemsmentioning

confidence: 99%

“…During the last two decades, research activities, cf. Figure 1 (a), have addressed fundamental instability mechanisms [5,6,7], design countermeasures [8,9], advanced computational modeling [10,11,12,13,14], signal analysis [15,16,17,18,19,20], uncertainty analysis [21,22,23,24] and many more using experimental data and numerical models. However, until today the numerical prediction quality is in most cases unsatisfactory [25,26].…”

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confidence: 99%

Deep learning for brake squeal: vibration detection, characterization and prediction

Stender,

Tiedemann,

Spieler

et al. 2020

Preprint

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Despite significant advances in numerical modeling of brake squeal, the majority of industrial research and design is still conducted experimentally. In this work we report on novel strategies for handling data-intensive vibration testings and gaining better insights into brake system vibrations. To this end, we propose machine learning-based methods to detect and characterize vibrations, understand sensitivities and predict brake squeal. Our aim is to illustrate how interdisciplinary approaches can leverage the potential of data science techniques for classical mechanical engineering challenges. In the first part, a deep learning brake squeal detector is developed to identify several classes of typical sounds in vibration recordings. The detection method is rooted in recent computer vision techniques for object detection. It allows to overcome limitations of classical approaches that rely on spectral properties of the recorded vibrations. Results indicate superior detection and characterization quality when compared to state-of-the-art brake squeal detectors. In the second part, deep recurrent neural networks are employed to learn the parametric patterns that determine the dynamic stability of the brake system during operation. Given a set of multivariate loading conditions, the models learn to predict the vibrational behavior of the structure. The validated models represent virtual twins for the squeal behavior of a specific brake system. It is found that those models can predict the occurrence and onset of brake squeal with high accuracy. Hence, the deep learning models can identify the complicated patterns and temporal dependencies in the loading conditions that drive the dynamical structure into regimes of instability. Large data sets from commercial brake system testing are used to train and validate the deep learning models.

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“…Once the system enters another basin of attraction, severe jumping phenomena may occur. Typically, such jumps are related to a change from a stable steady sliding state to high-intensity periodic vibrations or stick-slip cycles [27,28], or from one periodic solution to another periodic solution [11].…”

Section: Introductionmentioning

confidence: 99%

The Basin Stability of Bi-Stable Friction-Excited Oscillators

Stender¹,

Hoffmann²,

Papangelo³

2020

Preprint

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Stability considerations play a central role in structural dynamics to determine states that are robust against perturbations during the operation. Linear stability concepts, such as the complex eigenvalue analysis, constitute the core of analysis approaches in engineering reality. However, most stability concepts are limited to local perturbations, i.e. they can only measure a state’s stability against small perturbations. Recently, the concept of basin stability has been proposed as a global stability concept for multi-stable systems. As multi-stability is a well-known property of a range of nonlinear dynamical systems, this work studies the basin stability of bi-stable mechanical oscillators that are affected and self-excited by dry friction. The results indicate how the basin stability complements the classical binary stability concepts for quantifying how stable a state is given a set of permissible perturbations.

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Determining growth rates of instabilities from time-series vibration data: Methods and applications for brake squeal

Cited by 22 publications

References 22 publications

Reconstruction of Governing Equations from Vibration Measurements for Geometrically Nonlinear Systems

Reconstruction of Governing Equations from Vibration Measurements for Geometrically Nonlinear Systems

Deep learning for brake squeal: vibration detection, characterization and prediction

The Basin Stability of Bi-Stable Friction-Excited Oscillators

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