Scale factor

To aid convergence of the optimization algorithm, it is beneficial to include a scale factor that will automatically scale all design variables to produce a structure that will satisfy at least one constraint equation exactly. To illustrate, the current problem will use displacement measurements as constraints. At the beginning of each iteration, the displacements will be calculated using the same load cases used to produce the measured displacements for the damaged structure. The most violated displacement will be used as the basis for the scale factor. For example, say at the beginning of the first iteration, where all design variables start at those of the healthy structure, the calculated displacement at the first degree of freedom is half as large as the measured displacement at that same degree of freedom. In order for the calculated and measured displacements to match, all design variables must be cut in half, thus reducing the stiffness of the structure by a factor of 2. As a result, the displacement constraint on the first DOF will automatically be satisfied. A scale factor is calculated and applied to the initial design variables of each iteration.