A Data-driven Analysis On Bridging Techniques

Multi-scale strategies have been widely used to improve the accuracy and efficiency of modeling and simulation of engineering problems.Generally,in the process of multiscale modeling,a fine model built in the key zone for a precise simulation and a coarse model built in the rest zone for low computation costs are coupled by a bridging technique.The Arlequin method or the so-called the bridging domain method is a simple,flexible and powerful multi-scale coupling method.It allows the superposition of various mechanical models.By means of energy partition functions and Lagrange multipliers,different models are glued in a coupling zone.The bridging domain method has been rapidly developed and widely used since it was proposed.However,the definition of the following key parameters remains unclear: the energy partition functions,the characteristic length of the coupling operator and the size of the coupling zone,which greatly affect the coupling accuracy.Therefore,it is necessary and important to study the optimal range of these coupling parameters.Based on the Global Sensitivity Analysis(GSA),this paper proposes a data-driven method for the optimization of the coupling parameters in the bridging domain method.The data-driven method aims to investigate quantitatively and qualitatively the influences of these factors on the coupling accuracy,find the most influencing factors and offer quantitative guides for the choice of these parameters.To this end,adequate samples consisting of coupling parameters and model responses are drawn according to the multi-scale model.Based on these samples,a data-driven model that approximates the input/output behavior of the numerical model is built by using the Sparse Polynomial Chaos Expansion(SPCE)methodology.Then,Sobol’indices that quantify the sensitivity of the input factors are calculated analytically from the data-driven model with a negligible additional computational cost.Interaction effects among different parameters are also captured.Using this approach,several benchmark tests,including a coarse-fine bar model,a particle-continuum model and a 2D-1D sandwich beam model,are considered to explore the optimal settings of the coupling factors.