Model Error: Estimating Uncertainty if Your Analysis Lacks the Needed Physics.

摘要

Traditional uncertainty analysis will usually underestimate errors if the 'model' being used does not capture all of the real physical phenomena. This applies to both experimental data analysis and computational models of physical processes. In the first case, some equation is used to calculate the quantity of interest from the measured data. In the second case, data is used to calibrate a mechanics model (for example a constitutive model), which is then used to predict some behavior. In both cases, traditional uncertainty analysis would propagate uncertainties in the measured data through the equations/calculations to produce an uncertainty in the final answer. That will underestimate errors. The 'model error' issue is illustrated on a real example. An experimental measurement method is studied where measured strains are used to calculate residual stresses through the solution of an elastic inverse problem. To evaluate model error, the method is simulated using finite elements so that the error sources can be controlled. It is shown that when the elastic inverse solution has the precisely correct physics, a standard propagation analysis gives the correct uncertainties in the final values. Conversely, when some physics are missing (which is usually the case), the uncertainties are significantly underestimated. For this particular example, a novel method is presented for correctly estimating the real uncertainties. The implications for the broader issue of general model error are discussed.