Derivative extraction from a neuro‐fuzzy model

Many engineering optimisation problems are difficult to describe mathematically and as such can not be easily optimised. Recently attention has focussed on developing methods to create approximations of the real object function using numerical model data instead. The approximated function can then be optimised using a suitable optimisation method. This paper describes the extraction of derivative information from a neuro‐fuzzy system. Subsequently, this permits the application of classic deterministic optimisation methods in order to identify the global minimum of any approximated objective function. For non‐differentiable functions this approach is of great benefit. Results from an analytical optimisation example, in which the objective function and the solution are known, and a two variable loudspeaker optimisation problem are discussed. In both cases, the neuro‐fuzzy system worked well to model the physical problem and the extracted derivative served to locate the minimum.