{"title":"A \"data-driven uncertainty\" computational method to model and predict instabilities of a frictional system.","authors":"Farouk Maaboudallah, Noureddine Atalla","doi":"10.1186/s40323-023-00241-3","DOIUrl":null,"url":null,"abstract":"<p><p>Most of the recently developed methods for predicting instabilities of frictional systems couple stochastic algorithms with the finite element method (FEM). They use random variables to model the uncertainty of input parameters through standard probability laws. Regardless of the fact that advanced numerical schemes are available nowadays, a systematic and accurate method to describe finely the uncertainties upstream the model, and thus predict its response is still missing. In this contribution, we present a data-driven stochastic finite element scheme to predict the dynamic behavior of a rubbing system. The proposed framework relies on data-driven approach and uses four steps. In the first, the measured data are integrated directly, for the uncertainty quantification, by means of the random balance design (RBD). In the second step, the generated stochastic data are evaluated in an iterative way to solve friction-induced vibration problem. In the third step, the resulted data are reordered in such a way that the corresponding values of each measured input parameters are ranked in ascending order. Finally, the Fourier spectrum is introduced on the reordered results to compute the sensitivity indices. Thus, instead of Monte Carlo-based formalism or Fourier Amplitude Sensitivity Test (FAST), the computational cost of the proposed method is kept down to <math><mrow><mi>O</mi> <mo>(</mo> <mi>N</mi> <mo>)</mo></mrow> </math> with <i>N</i> the number of samples. We investigate the efficiency of the suggested solver on a reduced brake system. Altogether, the suggested procedure achieves excellent accuracy at a much reduced computational time compared to the methods available in the literature.</p>","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":null,"pages":null},"PeriodicalIF":2.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9925556/pdf/","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advanced Modeling and Simulation in Engineering Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1186/s40323-023-00241-3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
Most of the recently developed methods for predicting instabilities of frictional systems couple stochastic algorithms with the finite element method (FEM). They use random variables to model the uncertainty of input parameters through standard probability laws. Regardless of the fact that advanced numerical schemes are available nowadays, a systematic and accurate method to describe finely the uncertainties upstream the model, and thus predict its response is still missing. In this contribution, we present a data-driven stochastic finite element scheme to predict the dynamic behavior of a rubbing system. The proposed framework relies on data-driven approach and uses four steps. In the first, the measured data are integrated directly, for the uncertainty quantification, by means of the random balance design (RBD). In the second step, the generated stochastic data are evaluated in an iterative way to solve friction-induced vibration problem. In the third step, the resulted data are reordered in such a way that the corresponding values of each measured input parameters are ranked in ascending order. Finally, the Fourier spectrum is introduced on the reordered results to compute the sensitivity indices. Thus, instead of Monte Carlo-based formalism or Fourier Amplitude Sensitivity Test (FAST), the computational cost of the proposed method is kept down to with N the number of samples. We investigate the efficiency of the suggested solver on a reduced brake system. Altogether, the suggested procedure achieves excellent accuracy at a much reduced computational time compared to the methods available in the literature.
期刊介绍:
The research topics addressed by Advanced Modeling and Simulation in Engineering Sciences (AMSES) cover the vast domain of the advanced modeling and simulation of materials, processes and structures governed by the laws of mechanics. The emphasis is on advanced and innovative modeling approaches and numerical strategies. The main objective is to describe the actual physics of large mechanical systems with complicated geometries as accurately as possible using complex, highly nonlinear and coupled multiphysics and multiscale models, and then to carry out simulations with these complex models as rapidly as possible. In other words, this research revolves around efficient numerical modeling along with model verification and validation. Therefore, the corresponding papers deal with advanced modeling and simulation, efficient optimization, inverse analysis, data-driven computation and simulation-based control. These challenging issues require multidisciplinary efforts – particularly in modeling, numerical analysis and computer science – which are treated in this journal.