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

Abstract

Parametric studies for dynamic systems are of high interest to detect instability domains. This prediction can be demanding as it requires a refined exploration of the 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 proposed as an efficient indicator of non-regular behavior. 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.

PI/PID controller stabilizing sets of uncertain nonlinear systems: an efficient surrogate model-based approach

“…To reduce the computational cost due to the sampling approach, a kriging surrogate model is adopted based on an efficient adaptive sampling technique called Monte Carlo intersite Voronoi (MiVor) [24]. Used for the stability analysis of a friction-induced oscillator of Duffing's type, it has shown to yield accurate results for complex binary classification problems [25]. MiVor relies on the interpolation of observations by the socalled ordinary kriging technique which is defined by Gaussian processes.…”

Efficient surrogate strategy for investigating stick‐slip instability

“…Indeed, it can be seen that the surrogate classification provides an accurate classification for 99.9% of reference points for both classes from 50 observations. The proposed strategy appears robust for various parametric response surfaces investigated in [3]. The approach can be employed for more complex applications such as multiple outputs [2].…”

A Pointwise Evaluation Metric to Visualize Errors in Machine Learning Surrogate Models

“…Although, some of these local errors, such as the pointwise cross validation error [28], may not be necessarily reliable surrogates for the point errors of test samples, but they still can increase the overall performance, while with possibly higher computational costs [29]. Few studies [30][31][32] defined pointwise metrics to measure and precisely visualize errors of samples, but they have not been used to study the correlation between the numerical model and these errors. In this paper, we propose a similar pointwise metric, but it is used only for testing to keep the training fast while we use it to especially interpret the relationship between the numerical and ML models.…”