Sensitivity analysis and Kriging based models for robust stability analysis of brake systems

Nechak, Lyès; Gillot, F; Besset, Sébastien; Sinou, Jean-Jacques

doi:10.1016/j.mechrescom.2015.08.001

Cited by 52 publications

(27 citation statements)

References 46 publications

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“…As explained in previous papers [9,11,12], both approaches have their pros and cons. However CEA based methods and the calculations of self-excited vibrations may become too costly when parametric analysis and/or 2 Shock and Vibration uncertainty propagation are needed for engineering design problems [13]. In these cases, it may be worthwhile to work towards the development of sophisticated methods based on surrogate models in order to perform design optimization or design space approximation (i.e., emulation).…”

Section: Introductionmentioning

confidence: 99%

Kriging Surrogate Models for Predicting the Complex Eigenvalues of Mechanical Systems Subjected to Friction-Induced Vibration

Denimal

Nechak

Sinou

et al. 2016

Shock and Vibration

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This study focuses on the kriging based metamodeling for the prediction of parameter-dependent mode coupling instabilities. The high cost of the currently used parameter-dependent Complex Eigenvalue Analysis (CEA) has induced a growing need for alternative methods. Hence, this study investigates capabilities of kriging metamodels to be a suitable alternative. For this aim, kriging metamodels are proposed to predict the stability behavior of a four-degree-of-freedom mechanical system submitted to friction-induced vibrations. This system is considered under two configurations defining two stability behaviors with coalescence patterns of different complexities. Efficiency of kriging is then assessed on both configurations. In this framework, the proposed kriging surrogate approach includes a mode tracking method based on the Modal Assurance Criterion (MAC) in order to follow the physical modes of the mechanical system. Based on the numerical simulations, it is demonstrated by a comparison with the reference parameter-dependent CEA that the proposed kriging surrogate model can provide efficient and reliable predictions of mode coupling instabilities with different complex patterns.

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Section: Introductionmentioning

confidence: 99%

Kriging Surrogate Models for Predicting the Complex Eigenvalues of Mechanical Systems Subjected to Friction-Induced Vibration

Denimal

Nechak

Sinou

et al. 2016

Shock and Vibration

Self Cite

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“…sensitivity analysis by Nechak et al [13] where similar criteria is considered. Thus the minimization of the criteria with respect to the shape parameters represents the least possibility or lower magnitude of the squeal noise for a given range of parameters.…”

Section: Stability Criteriamentioning

confidence: 99%

Shape optimization of a disc-pad system under squeal noise criteria

et al. 2020

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This paper deals with the parametric shape optimization of a simplified model of brake system under squeal noise criteria. As brake squeal phenomenon induces under-quality perception for industrial structures such as cars and trains, its understanding and management are important challenges for future systems design. Hence, we expose an optimization methodology based on meta-model for a proposed computationally expensive stability criteria representing the squeal noise. Sensitivity analysis is first conducted to assess and validate the chosen geometrical parameters. Then, a Pareto front is obtained through optimization of the system, leading to a set of optimal solutions for the considered multi-objective case.

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“…The finite element model of the simplified brake system used in this study is illustrated in Figure 1. This model is taken from [15] and the parameters are listed in Table 1. Figure 1.…”

Section: Finite Element Model Of the Brake Systemmentioning

confidence: 99%

“…Kriging [11] is an interpolation-based approach in which the model is assumed to be a realization of a Gaussian process. Since metamodel-based methods can be applied to various levels of uncertainty, numerous studies have utilized them to solve stochastic eigenvalue problems in brake systems [12][13][14][15].However, despite previous studies, it remains challenging to apply PCE and kriging to brake systems with the mode-coupling phenomenon. Since eigenvalues exhibit nonsmooth behavior around the bifurcation point, PCE is not adequate for capturing local solution accuracy.…”

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A Combined Nonstationary Kriging and Support Vector Machine Method for Stochastic Eigenvalue Analysis of Brake Systems

Lee

Park

2019

Applied Sciences

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This paper presents a new metamodel approach based on nonstationary kriging and a support vector machine to efficiently predict the stochastic eigenvalue of brake systems. One of the difficulties in the mode-coupling instability induced by friction is that stochastic eigenvalues represent heterogeneous behavior due to the bifurcation phenomenon. Therefore, the stationarity assumption in kriging, where the response is correlated over the entire random input space, may not remain valid. In this paper, to address this issue, Gibb's nonstationary kernel with step-wise hyperparameters was adopted to reflect the heterogeneity of the stochastic eigenvalues. In predicting the response for unsampled input, the support vector machine-based classification is utilized. To validate the performance, a simplified finite element model of the brake system is considered. Under various types of uncertainties, including different friction coefficients and material properties, stochastic eigenvalue problems are investigated. Through numerical studies, it is seen that the proposed method improves accuracy and robustness compared to conventional stationary kriging.Carlo simulation (MCS), a sensitivity-based approach, polynomial chaos expansion (PCE), and kriging (Gaussian process). MCS [8] is a sampling-based technique which is considered the most robust method for uncertainty quantifications. However, since a large number of samples must be drawn to obtain sufficient accuracy, the computational cost becomes prohibitive. The sensitivity-based method [9] is a low-order Taylor expansion method that approximates the solution near the input parameters. Although this method is computationally efficient, the obtained solution will be inaccurate under large parameter variabilities.PCE and kriging are metamodel (surrogate model) -based techniques that replace the original model with an easy-to-evaluate function. PCE [10], also known as a spectral approach, is a regression-based methods that approximates the model by multivariate polynomials. Kriging [11] is an interpolation-based approach in which the model is assumed to be a realization of a Gaussian process. Since metamodel-based methods can be applied to various levels of uncertainty, numerous studies have utilized them to solve stochastic eigenvalue problems in brake systems [12][13][14][15].However, despite previous studies, it remains challenging to apply PCE and kriging to brake systems with the mode-coupling phenomenon. Since eigenvalues exhibit nonsmooth behavior around the bifurcation point, PCE is not adequate for capturing local solution accuracy. Several studies have tackled this issue by applying multi-element PCE [16], a wavelet basis [17]. Although kriging interpolates each sample and reflects the local characteristics, to the authors' knowledge, previous studies have all been based on the stationarity assumption, which means that the smoothness of response is entirely correlated throughout the random input space. Therefore, for mode-coupling problems where the stationarity a...

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Sensitivity analysis and Kriging based models for robust stability analysis of brake systems

Cited by 52 publications

References 46 publications

Kriging Surrogate Models for Predicting the Complex Eigenvalues of Mechanical Systems Subjected to Friction-Induced Vibration

Kriging Surrogate Models for Predicting the Complex Eigenvalues of Mechanical Systems Subjected to Friction-Induced Vibration

Shape optimization of a disc-pad system under squeal noise criteria

A Combined Nonstationary Kriging and Support Vector Machine Method for Stochastic Eigenvalue Analysis of Brake Systems

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