Introduction to Model Validation

The discipline of mathematical model validation is increasing in importance as the value of accurate models of physical systems increases. The fundamental activity of model validation is the comparison of predictions from a mathematical model of a system to the measured behavior of the system. This discussion motivates the need for model validation and introduces some preliminary elements of model validation. This is the first in a sequence of six tutorial presentations on model validation, and will introduce five presentations to follow. Motivation and Introduction Mathematical model validation is defined as the “process of determining the degree to which a computer model is an accurate representation of the real world from the perspective of the intended model applications. ” (ASME, 2006, U.S. DOE, 2000, AIAA, 1998). It is accomplished through the comparison of predictions from a model to experimental results. There are numerous, related reasons for performing validations of mathematical models. For example: • There may be a need or desire to replace experimentation with model predictions, and, of course, a corresponding requirement that the model predictions have some degree of accuracy. The need for a model may arise from the fact that it is impossible to test system behavior or survivability in some regimes of operation. For example, a requirement of a building structure may be that it must survive a blast load, yet, for regulatory reasons, it may be impossible to test the structure in blast. • Alternately, the need for validation may arise from a necessity to prove the reliability of a structure under a broad range of operating conditions or environments. Because it may be expensive to simulate the conditions in the laboratory or realize them in the field, an accurate model is required. • Another reason for model validation is that a system may be undergoing changes in design that require analyses to assure that the design modifications yield acceptable system behavior. A validated model can be used to assess the system behavior. In all these situations it is useful to confirm analysts’ abilities to produce accurate models. The sections that follow introduce some ideas and terminology from model validation and list some steps that can be followed to perform a model validation. The paper introduces an example structure with a model to be validated, and carries it through steps involving planning, experiments, and validation comparisons. There are normally several parties or groups involved in performance of a validation. These are: • Analysts/modelers. These are persons capable of creating computational models from mathematical and conceptual models, when details of the latter are established. They are capable of anticipating the behaviors of computational models that include specific features. • Experimentalists. These are persons capable of planning and performing the calibration and validation experiments required in a validation. The experiments may be performed in the laboratory or field, and must normally be high precision experiments with high-accuracy measurements. • Validation analysts (Persons performing validation comparisons). These are persons knowledgeable about validation procedures, including means for comparing model predictions to experimental outcomes. They should possess intuition regarding the difficulty of obtaining positive validation results given various system measures of response and various means of comparison.