#111: What is the “Fractional Error of Approximation”?

#111: What is the “Fractional Error of Approximation”?

This number refers to the differences in values between the objective function after approximate optimization, and the corresponding value after a subsequent analysis update.

As discussed in the Nastran Design Sensitivity and Optimization User’s Guide, the optimizer works with structural response approximations.
A measure of the approximation’s quality could then be computed as:
E=(Fopt-Ftrue)/Ftrue
where Fopt = objective function value returned from the optimizer, Ftrue = true objective function computed via a finite element analysis of the current design.

However, be aware that this is based on the objective function only and not on any of the constraints. Often, this error is small since a common design objective is weight, which frequently is linear in the design variables (e.g., linearly proportional to plate thicknesses, bar areas, and so on). The constraint approximations may not be as good since they are often based on responses, such as stresses, which generally are nonlinear functions of the design variables. Thus, it could be a mistake to increase move limits (DELP) in order to increase the rate of convergence based solely on this error measure.