Chapter 8 discussed the methods for using numerical methods to optimize systems designed using black box software such as finite element analysis. In some cases, there is no engineering model available, whether in a black box or equations. In these cases, parameter values are determined from engineering standards, experience, or trial and error. This chapter presents a method for creating empirical models to estimate system outputs. There are many methods for doing this, but the method presented here emphasizes efficient experimentation. If the cost or time to perform experiments is not prohibitive, this method can be altered.
The first step when developing an empirical model is determining which parameters (or factors) to include in the model. A two-level fractional factorial experiment efficiently identifies relevant factors by assuming linearity.
A full factorial experiment requires LF trials, where L is the number of levels and F is the number of factors. An advantage of using a full factorial experiment is that all components of the model can be estimated. The disadvantage of a full factorial is the number of experimental trials required. A two-level full factorial experiment with seven factors requires 128 trials. A two-level full factorial experiment with five factors requires 32 trials. Table 10.1 shows the number of experimental trials required to estimate the components of a two-level, five-factor experiment.