Spatial frequency control for the systematic generation of optimal candidate designs having various topological complexities

In practical engineering design problems, there are some design and manufacturing considerations that are difficult or infeasible to express in terms of an objective function or a constraint. Among them, we pay attention to the topological complexity of optimized designs which are difficult to quantify. In this situation, a set of optimal candidate designs having different topological complexities, not just a single optimal design, is preferred. In this work, the mean spatial frequency is proposed as a means to measure the topological complexity of an optimized design. To maximize the system performance and to control the mean spatial frequency, the topology design optimization in the M-band wavelet transformed multiscale design space is proposed. In the proposed scheme, the mean frequency is controlled effectively by choosing different design space resolution in the multiscale design space, and the performance maximization is treated as the objective function of the topology optimization. The procedure to transform the original design space into the multiscale design space by the M-band Daubechies wavelet is also explained in some details.