Deep Gaussian Process for the Approximation of a Quadratic Eigenvalue Problem: Application to Friction-Induced Vibration

Vibration

Isabelle Turpin¹  El-Ghazali Talbi²  Franck Massa³  Thierry Tison³  Jeremy Sadet³ 

[1] CERAMATHS, Hauts-de-France Polytechnic University, F-59313 Valenciennes, France;CRIStAL UMR CNRS 9189, University of Lille, Inria-Lille Nord Europe, F-59000 Lille, France;LAMIH UMR CNRS 8201, Hauts-de-France Polytechnic University, F-59313 Valenciennes, France;

关键词: friction-induced vibration;    squeal;    uncertainty;    surrogate modelling;    Gaussian process;    deep Gaussian process;   

DOI  :  10.3390/vibration5020020

来源: DOAJ

【 摘 要 】

Despite numerous works over the past two decades, friction-induced vibrations, especially braking noises, are a major issue for transportation manufacturers as well as for the scientific community. To study these fugitive phenomena, the engineers need numerical methods to efficiently predict the mode coupling instabilities in a multiparametric context. The objective of this paper is to approximate the unstable frequencies and the associated damping rates extracted from a complex eigenvalue analysis under variability. To achieve this, a deep Gaussian process is considered to fit the non-linear and non-stationary evolutions of the real and imaginary parts of complex eigenvalues. The current challenge is to build an efficient surrogate modelling, considering a small training set. A discussion about the sample distribution density effect, the training set size and the kernel function choice is proposed. The results are compared to those of a Gaussian process and a deep neural network. A focus is made on several deceptive predictions of surrogate models, although the better settings were well chosen in theory. Finally, the deep Gaussian process is investigated in a multiparametric analysis to identify the best number of hidden layers and neurons, allowing a precise approximation of the behaviours of complex eigensolutions.

【 授权许可】

Unknown