Verification & Validation: Process and Levels Leading to Qualitative or Quantitative Validation Statements

The concepts of Verification and Validation (V&V) can be oversimplified in a succinct manner by saying that “verification is doing things right” and “validation is doing the right thing”. In the world of the Finite Element Method (FEM) and computational analysis, it is sometimes said “verification means solving the equations right” and “validation means solving the right equations”. In other words, if one intends to give an answer to the equation “2+2=”, then one must run the resulting code to assure that the answer “4” results. However, if the nature of the physics or engineering problem being addressed with this code is multiplicative rather than additive, then even though Verification may succeed (2+2=4 etc), Validation will fail because the equations coded are not those needed to address the real world (multiplicative) problem. When this simple explanation of V&V is extended to the multidimensional world of nonlinear FEM with multiple application scenarios, the V&V process becomes complicated very quickly. It is essentially impossible to “fully verify a code” or “fully validate a model”. The appropriate Level of V&V is a function of the time available to do the V&V evaluations, and this should in turn be a function of the Risk that will be incurred if the V&V is not done, or the risk that will be mitigated if a given level of V&V is done. We will describe a process for V&V based on Levels (with a fractional rating system from 0 to 1). V&V “Levels” can provide a necessary first step beyond “yes or no” in answering the question of whether a capability has been verified or validated. We then discuss a 4-step quantitative implementation for V&V once a given Level has been chosen. Next, we provide short examples from metal forming, crashworthiness, and engine performance of the different process Levels for V&V, and the qualitative and quantitative statements that can be credibly made as a function of the V&V Level assessed. We suggest that one of the key end products of V&V is to provide the information needed for predictive adequacy for the intended application, and that adequacy is a balance between rigor and expediency obtained from risk management.