Simultaneous Determination of Tuning and Calibration Parameters for Computer Experiments.

Area of Science:

• Computational Science
• Statistical Modeling
• Engineering Simulation

Background:

• Computer simulations require tuning and calibration to accurately represent physical phenomena.
• Simultaneous determination of tuning and calibration parameters is challenging, especially with limited data.
• Existing methods may not fully leverage available experimental data for parameter estimation.

Purpose of the Study:

• To introduce a novel statistical methodology for the simultaneous determination of tuning and calibration parameters.
• To improve the representativeness of computer simulation codes to physical phenomena.
• To provide a framework for integrating data from both computer codes and physical experiments.

Main Methods:

• A hierarchical Bayesian model is employed to determine the distribution of calibration parameters.
• Tuning parameters are optimized by minimizing a discrepancy measure.
• Gaussian stochastic processes with hyperpriors are used to model simulation output.
• Markov chain Monte Carlo (MCMC) simulation is utilized to draw from the posterior distribution.

Main Results:

• The proposed methodology effectively integrates tuning and calibration parameter estimation.
• The Bayesian approach provides a robust framework for uncertainty quantification in parameters.
• Demonstrated improved simulation representativeness compared to an alternative approach in examples.
• Successfully applied to a biomechanical engineering problem.

Conclusions:

• The developed statistical methodology offers a powerful approach for simultaneous tuning and calibration.
• This method enhances the reliability and accuracy of computer simulations in engineering applications.
• Availability of supplemental software and a user manual facilitates practical implementation.