ASME VVUQ 10.2:2021 pdf download

ASME VVUQ 10.2:2021 pdf download The Role of Uncertainty Quantification in Verification and Validation of Computational Solid Mechanics Models
Understanding the differences between these sources of uncertainties is important because different characterizationand analysis techniques are often used to quantify the uncertainties originating from different sources and to propagatethese uncertainties through the model.Uncertainty propagation is the process of using the knowledge about uncertaintyin model input variables to quantify the uncertainty in output variables.Iln para. 3.1, a brief discussion is provided of thesources of uncertainties in physics-based and empirical models.In para.3.2,several methods foruncertainty propagationare discussed.
3.1 Sources of Uncertainty in Modeling
There are three sources of uncertainty in physics-based computational models: the model form, the model inputs,andthe numericalsolution.Uncertainties in the model form arise from assumptions or approximations in the formulation of aspecific set of mathematical equations to represent the reality of interest. Model input uncertainties represent theuncertainties in the nondeterministicinputvariables and parameters associated with the selected model form.Numericalsolution uncertainties arise, for example, due to discretization approximations, iterative solution algorithms, and par-ticular computational platform characteristics.
The uncertainties in empirical models originate primarily from three sources: the model form, the model inputs, andthe model-basis data. As in the physics-based models, the uncertainties in the model form result from assumptions andapproximations in the selection or formulation of a specific set of mathematical equations to represent the reality ofinterest. The uncertainties in the model-basis data arise from errors, both systematic and random, in the experimentaldata used to develop the model,as well as from limited sample size and a number of other limitations associated with themodel-basis data sets.Unlike in the physics-based models, such uncertainties are a major, and often a dominant, source ofuncertainties in the empirical models.Uncertainties associated with the model parameters (and the numerical solution, ifapplicable) typically play a smaller role in the empirical models than in the physics-based models.
3.1.1 Uncertainties in Model Form.Because the true form of the model is not known, the selection of a specificmathematical form for a given modeling application will lead to some level of model-form uncertainty.In theprocess of developing a model, there are numerous questions that must be considered, such as
(a) what can and should be modeled mathematically?
b) What are the important features that the model must accurately represent?
(c) What role do computational constraints, model dimensionality, and code maturity play in the complexity of themodel?
(d) what physical principles or data is the model derived from?
(e) Is the model expected to be adequate in the entire prediction or application space?
Model-form uncertainty isgenerally treatedas an epistemic uncertainty because it stems from the inexact nature of themodeling process.Physics intentionally ignored or unintentionally missed in the idealized mathematical representationalways exists. One example of missed physics is modeling the boundary condition of a cantilever beam as fully fixed, whenin reality there is some rotational movement.Another example of model-form uncertainty involves the computer-aidedconstruction of a model, in which the part geometry is defeatured (simplified by removal of selected details) based on itsrelevance to the fidelity of the simulation and before meshing.The extent of defeaturing may be driven by engineeringintuition, formal geometry feature sensitivity, or both.
ln theory, model-form uncertainty can be reduced through model enhancements, such as incorporation of additionalmechanisms in a physics-based model or additional terms in an empirical model. An example of adding terms to anempirical model was discussed in para. 2.8, where the base model formulation eq.(2-8)with a single input variable,S,wasamended with additional terms representing the effects of additional explanatory variables.The model-form uncertaintycontributes to the residual uncertainty in the empirical models. Therefore, reducing the model-form uncertainty byadding appropriate terms to the model formulation results in a reduction of the residual uncertainty, as shown inFigure 2.8-1.Of course,the model-form uncertainty is reduced only if the input variables added to the model formulationhave statistically significanteffects on the response variable being modeled.Ilt is also recognized that adding fidelity tothemodel will often introduce additional nondeterministic input variables and parameters, and the uncertainties in theseadded inputs will contribute to the uncertainty in the model output.
ln practice, however, model enhancements have important limitations.Adding new physical mechanisms increasescomputational expense or may require new code development. Additional physical mechanisms may require modifica-tions to the underlying equations as different mechanisms are often treated with different mathematical formalisms.Many molecular scale mechanisms, for example,are not easily modeled using continuum mechanics.Meanwhile, addingterms to an empirical model may lead to difficulties with simultaneous estimation of many model parameters,commonlyreferred to as overparameterization or overfitting-