TY - JOUR

T1 - Surrogate model approach for investigating the stability of a friction-induced oscillator of Duffing’s type

AU - Fuhg, Jan N.

AU - Fau, Amélie

N1 - Funding Information: The authors acknowledge the financial support from the Deutsche Forschungsgemeinschaft under Germany?s Excellence Strategy within the Cluster of Excellence PhoenixD (EXC 2122, Project ID 390833453). The results presented in this paper were partially carried out on the cluster system at the Leibniz University of Hannover, Germany.

PY - 2019/11

Y1 - 2019/11

N2 - Parametric studies are required to detect instability regimes of dynamic systems. This prediction can be computationally demanding as it requires a fine exploration of large parametric space due to the disrupted mechanical behavior. In this paper, an efficient surrogate strategy is proposed to investigate the behavior of an oscillator of Duffing’s type in combination with an elasto-plastic friction force model. Relevant quantities of interest are discussed. Sticking time is considered using a machine learning technique based on Gaussian processes called kriging. The largest Lyapunov exponent is considered as an efficient indicator of chaotic motion. This indicator is estimated using a perturbation method. A dedicated adaptive kriging strategy for classification called MiVor is utilized and appears to be highly proficient in order to detect instabilities over the parametric space and can furthermore be used for complex response surfaces in multi-dimensional parametric domains.

AB - Parametric studies are required to detect instability regimes of dynamic systems. This prediction can be computationally demanding as it requires a fine exploration of large parametric space due to the disrupted mechanical behavior. In this paper, an efficient surrogate strategy is proposed to investigate the behavior of an oscillator of Duffing’s type in combination with an elasto-plastic friction force model. Relevant quantities of interest are discussed. Sticking time is considered using a machine learning technique based on Gaussian processes called kriging. The largest Lyapunov exponent is considered as an efficient indicator of chaotic motion. This indicator is estimated using a perturbation method. A dedicated adaptive kriging strategy for classification called MiVor is utilized and appears to be highly proficient in order to detect instabilities over the parametric space and can furthermore be used for complex response surfaces in multi-dimensional parametric domains.

KW - Adaptive sampling

KW - Dry friction

KW - Lyapunov exponents

KW - Machine learning

KW - Non-smooth system

KW - Stick–slip instability

KW - Surrogate model

UR - http://www.scopus.com/inward/record.url?scp=85074435106&partnerID=8YFLogxK

U2 - 10.1007/s11071-019-05281-2

DO - 10.1007/s11071-019-05281-2

M3 - Article

AN - SCOPUS:85074435106

VL - 98

SP - 1709

EP - 1729

JO - Nonlinear dynamics

JF - Nonlinear dynamics

SN - 0924-090X

IS - 3

ER -