Efficient multivariate optimization of an ultrasonic transducer with genetic parallel algorithms

Abstract

Design optimization of a multilayer transducer is desired for flaw detection, biomedical and underwater applications by controlling layer thicknesses of active material and volume fractions of ceramic in each piezocomposite layer. To handle the computational complexity in solving such multivariate optimization and the complex nature of the problem, we propose a parallel genetic algorithm (GA)-based strategy. The complexity of the problem increases with the number of layers and layer-wise ceramic volume fraction to achieve an optimized transducer working efficiently in an operational frequency range as desired by the application specification. The fitness function is formulated based on the transducer response in terms of about the same value of pressure magnitude at the first three harmonics at functional frequencies. The fitness value is computed using a one-dimensional model (ODM) for PMNPT, PZT4d, and PZT5h-based materials initially, while input layer thicknesses and volume fractions are evaluated through GAs and passed to ODM. The overall scheme is maintained through parallel GAs. The simulation is performed by using 1, 4, 6, and 8 core machines to reduce time complexity. The results for parallel GA-ODMs are statistically represented in the minimum, maximum, mean and standard deviation of fitness, while graphically represented for speedup and time.