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

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

Nonlinear control of friction-induced limit cycle oscillations via feedback linearization

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On the influence of multiple contact conditions on brake squeal

This study focuses on squeal noise prediction for an automotive brake system. For this purpose, a stability study of a finite element model of the brake system is carried out. For the determination of the squeal propensity of a brake system via finite element models, the commonly used approach consists in considering only a friction coefficient at the pad-disc interface. However, numerous other contacts exist in a brake system. In the present study, the influence of several contacts between the caliper, the bracket, the pad and the piston is studied. It turns out that the consideration of these numerous contacts has a real impact on the stability results and can not therefore be neglected. Indeed, a high dispersion of results for the system’s eigenvalues indicating strong modifications of the stability behavior and thus of the squeal propensity is observed when different contact conditions are considered. This study insights the necessity to take into account of all contact conditions during the design process of brake systems

Model Reduction of Linear Systems with Random Parameters

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

International audienceThis 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 foralternative 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 tofriction-induced vibrations. This system is considered under two configurations defining two stability behaviors with coalescencepatterns of different complexities. Efficiency of kriging is then assessed on both configurations. In this framework, the proposedkriging surrogate approach includes a mode tracking method based on the Modal Assurance Criterion (MAC) in order to followthe physical modes of the mechanical system. Based on the numerical simulations, it is demonstrated by a comparison with thereference parameter-dependent CEA that the proposed kriging surrogate model can provide efficient and reliable predictions ofmode coupling instabilities with different complex patterns

Kriging Metamodeling in Rotordynamics: Application for Predicting Critical Speeds and Vibrations of a Flexible Rotor

Rotating machinery produces vibrations depending upon the design of the rotor systems as well as any faults or uncertainties in the machine that can increase the vibrations of such systems. This study illustrates the effectiveness of using surrogate modeling based on kriging in order to predict the vibrational behavior (i.e., the critical speeds and the vibration amplitudes) of a complex flexible rotor in the presence of uncertainties. The basic idea of kriging is to predict unknown values of a function by using a small size set of known data. The kriging estimation is based on a weighted average of the known values of the function in the neighborhood of the point for which the value of the function has to be calculated. The crucial dependence of a kriging predictor versus the correlation functions and different orders will be illustrated. This paper also shows that reducing the number of samples required to have predictive models can be achieved by performing an initial understanding of the mechanical system of interest and by considering certain characteristics directly deriving from the physics of the problem studied

Damage evaluation and tracking using kriging approaches on wave-guide dispersion curves

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Squeal analysis based on the effect and determination of the most influential contacts between the different components of an automotive brake system

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A novel hybrid surrogate model and its application on a mechanical system subjected to friction-induced vibration

International audienceA new hybrid meta-modeling approach is proposed and developed for the propagating and quantifying of uncertainties in friction-induced instabilities. According to the available knowledge about design parameters, the associated uncertainty can be described by using different models. Hence, hybrid meta-models prove to be necessary to simultaneously treat different uncertainty models. So, this study presents a novel hybrid meta-model issued from the associating of the kriging formalism together with the generalized polynomial chaos for the prediction of friction-induced instabilities submitted to interval and probabilistic uncertainties. Its assessing through the considering of a friction system, reveals suitable accuracy about the estimating of the dispersion of the occurrences of instabilities. Moreover, it offers a promising alternative to the prohibitive Monte-Carlo/scanning based methods that are usually used for the same task