Evaluation of cost functions for FEA based transducer optimization

Abstract

For a finite element analysis (FEA) based transducer optimization a global cost function is needed to evaluate the simulated model. This global cost function can be composed of several cost functions which describe a certain characteristic of the transducer. By adding weights to these cost functions it is possible to give each characteristic a priority for the optimization.The goal of this work is to find optimal cost functions for certain transducer characteristics (like bandwidth, sensitivity, sound pressure distribution, angle of beam). For the investigation a simple transducer design consisting of four layers (backing, piezoelectric and two matching layers) is used. Diameter and thickness of each layer are variable.For the evaluation process a Matlab® script generates different simulation models by modifying the dimensions of transducer layers. For each transducer design four simulation models are generated to determine different criteria: the integrated displacement of the transducer surface, the electrical impedance and the receiver signal assuming two identical transducers by transmission measurement in water. The fourth criterion, the sound field is used for checking purpose only. Each criterion represents a set of cost functions (e.g. for the receiver signal criterion: rise time, maxima, envelope shape…). The significance of the cost functions for different transducer characteristics is evaluated by comparing their results during the different simulations with each other and with the resulting sound field. In this contribution the usability of different cost functions for the abovementioned optimization approach will be presented by means of some examples with different objectives of transducer design.