Estimating Parametric, Model Form, and Solution Contributions Using Integral Validation Uncertainty Quantification Page: 4 of 12
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Model validation is the process of determining whether a model of a physical process is
adequate from the perspective of the real world use of the model. This is true whether the
model is a simple curve fit or a nonlinear finite element solution. Quantitative model
validation typically involves uncertainty quantification, in order to develop quantitative
measures of confidence intervals and prediction intervals over the range of validation of
the model (comparison against test data), and outside the range of data (predictive
capability estimates). Two forms of validation are commonly used. These may be called
Hierarchical and Integral validation. Hierarchical validation (also called bottom-up2) is
described as a process where the model is built in steps, with uncertainty quantification at
each level. Integral validation (also called top-down) is a process where a model of the
top-level quantity of interest is built, and the model assessed against top level data. The
hierarchical method provides more information about the way that subsystems and
parametrics affect the final quantity of interest. Furthermore, hierarchical models are
often less ad-hoc, so it is possible to achieve a highly physics-based model instead of a
top level curve fit. The downside of the hierarchical method is time, cost, and possibly
even drift, as bias errors in the hierarchical path may stack up to form a bias in the top
level solution. Because of this, it is of value to use both hierarchical and integral model
validation and uncertainty quantification. We find that integral models, while they may
contain more free parameters, can be quickly compared to available referent data, and top
level confidence bounds can be constructed if we account properly for the existence of
free (fitting) parameters in the model'4'5'6. The integral model is useful as a screening
tool or a pilot to guide future work on more detailed, physically based hierarchical
models. The integral model also provides a bias check; ideally, the mean and confidence
bounds on the hierarchical and integral models should align very closely. If not, one or
the other (or both) contain bias errors or uncertainties not properly quantified.
Even while using these "integral models" as screening and planning assessment tools, we
desire to gain a feeling for the components of uncertainty contributed by each major
factor in the model. For example, a finite element model will have uncertainties due to:
" [A] Plan simulations: Assess existing output data uncertainty, codes, code errors
" [B] Solution Verification (spatial, temporal, iterative convergence)
" [C] Parametric Variability (experimental scatter in the input quantities)
" [C] Parametric Uncertainty (lack of information - not enough data)
" [D] Model Form or Physics Uncertainty (lack of knowledge about the physics
We have denoted each of these aspects with the letters A, B, C, or D, corresponding to an
"ABCD" process for Model Verification & Validation (V&V) described in previous
works7. The letters "ABCD" can represent both the process used for model V&V, but
also reflect specific types of uncertainty terms which may be quantified using the same
"ABCD" breakout. We can make a direct analogy between our interpretation of the
"ABCD" process for assuring accurate FEA simulations, and one proposed process by
Coleman and Sterng for validation with uncertainties at confidence. For clarity we follow
the nomenclature as proposed', but will use standard uncertainties (u) instead of
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2/28/2006 4:31 PM
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Logan, R W; Nitta, C K & Chidester, S K. Estimating Parametric, Model Form, and Solution Contributions Using Integral Validation Uncertainty Quantification, report, February 28, 2006; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc891341/m1/4/: accessed January 23, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.