Virtual testing using CAE techniques is clearly a very effective approach when the underlying models are valid. In practice, however, these models are only approximations of reality. Even though a lot of attention is paid to model validation, there will always be a considerable amount of uncertainty due to various sources of error. For example, in the application in Section 27.2, "failure" in virtual testing is defined as sealing force being below a certain threshold. This definition of failure is only a surrogate for leakage, the real failure mode that can be ascertained only by physical tests. Thus, there is still a need for physical testing before final decisions on product design and reliability can be made.The goal of this chapter is to describe some variance-reduction techniques that use information from CAE models to increase the efficiency and reduce the cost of physical testing. We describe the use of two well-known techniques called importance sampling and stratified sampling for this purpose. It turns out that the use of optimal importance sampling and stratified sampling schemes requires knowledge of unknown quantities. However, knowledge of these quantities from CAE modeling and analysis can yield "prior information" that can be used to develop good sampling strategies. The actual estimators of the reliability parameter are unbiased, even if the prior information is not very good. When the prior information is reliable, however, the estimators turn out to have much smaller variance and hence can lead to a substantial reduction in the cost of physical testing.
Virtual Testing Using Computer ModelsThis section provides a mathematical description of virtual testing based on computer models. We will use a real application to motivate and discuss the ideas. Figure 27.1 is a visual representation of a finite-element analysis (FEA) model for deep thermal-shock simulation of a basic engine structure, including engine block, gasket, cylinder head, and bolts. It models, among other things, the rigidity and structure of the mating components so that one can analyze their impact on sealing performance and crack size. For internal combustion engines, the architecture of the components depends on the engine block and head designs. Choices of these designs are major determinants for downstream decisions on manufacturing facilities, which are expensive and time consuming to set up. Thus, simulation models for engine block and headjoint assembly are commonly employed to make structural decisions for optimizing reliability [3].Physical testing to validate the design integrity of head and block sealing is typically conducted in a controlled laboratory environment by running the engines with (controlled) cyclical stresses obtained FIGURE 27.1 Finite-element analysis (FEA) model for deep thermal-shock simulation of a basic engine structure.
