Parameter calibration and inadequacy modeling in a computer experiment

Deterministic simulation is a popular tool used to numerically solve complex mathematical models in engineering applications. These models often involve parameters in the form of numerical values that can be calibrated when real-life observations are available. This paper presents a systematic approach in parameter calibration using Response Surface Methodology (RSM). Additional modeling by considering correlation in error structure is suggested to compensate the inadequacy of the computer model and improve prediction at untried points. Computational Fluid Dynamics (CFD) model for manure storage ventilation is used for illustration. A simulation study shows that in comparison to likelihood-based parameter calibration, the proposed parameter calibration method performs better in accuracy and consistency of the calibrated parameter value. The result from sensitivity analysis leads to a guideline in setting up factorial distance in relation to initial parameter values. The proposed calibration method extends RSM beyond its conventional use of process yield improvement and can also be applied widely to calibrate other types of models when real-life observations are available. Moreover, the proposed inadequacy modeling is useful to improve the accuracy of simulation output, especially when a computer model is too expensive to run at its finest level of detail.