Least Bumpiness Calibration With Extrapolative Bias Correction

Bias correction is important for model calibration to obtain unbiased calibration parameter estimates and make accurate prediction. However, calibration often relies on insufficient samples, and so bias correction often mostly depends on extrapolation. For example, bias correction with twelve samples in nine-dimensional box generated by Latin Hypercube Sampling (LHS) has less than 0.1% interpolation domain in the box. Since bias correction is coupled with calibration parameter estimation, calibration with extrapolative bias correction can lead a large error in the calibrated parameters. This paper proposes an idea of calibration with minimum bumpiness correction. The bumpiness of bias correction is a good measure of assessing the potential risk of a large error in the correction. By minimizing bumpiness, the risk of extrapolation can be reduced while the accuracy of parameter estimates can be achieved. It was found that this calibration method gave more accurate results than Bayesian calibration for an analytical example. It was also found that there are common denominators between the proposed method and the Bayesian calibration with bias correction.