A "data-driven uncertainty" computational method to model and predict instabilities of a frictional system

Area of Science:

• Computational mechanics
• Applied mathematics
• Mechanical engineering

Background:

• Predicting instabilities in frictional systems often combines stochastic algorithms with the finite element method (FEM).
• Current methods struggle with accurately quantifying uncertainties in input parameters, limiting predictive accuracy.
• A need exists for systematic and precise methods to model upstream uncertainties for improved system response prediction.

Purpose of the Study:

• To introduce a novel data-driven stochastic finite element scheme for predicting the dynamic behavior of rubbing systems.
• To develop a computationally efficient framework for uncertainty quantification and sensitivity analysis in frictional systems.

Main Methods:

• A four-step data-driven approach integrating measured data via random balance design (RBD) for uncertainty quantification.
• Iterative evaluation of stochastic data to solve friction-induced vibration problems.
• Reordering results and applying Fourier spectrum analysis to compute sensitivity indices, reducing computational cost significantly compared to Monte Carlo or FAST methods.

Main Results:

• The proposed method achieves excellent accuracy in predicting the dynamic behavior of a reduced brake system.
• Demonstrated significant reduction in computational cost, with complexity related to the number of samples (N), not N^2 or N^3.
• The framework effectively quantifies uncertainties and computes sensitivity indices.

Conclusions:

• The developed data-driven stochastic finite element scheme offers a highly accurate and computationally efficient solution for predicting instabilities in frictional systems.
• This approach overcomes limitations of existing methods by systematically handling uncertainties.
• The findings suggest a promising new direction for the analysis and design of systems prone to friction-induced vibrations.