Modeling of the non-linear acoustic response of bubbles by Volterra series analysis

The ability to determine the size distribution of a field of bubbles has a wide range of practical applications. Bubbles have traditionally been detected by using either optical or acoustic techniques. Bubbles exhibit strong acoustic resonance properties dependent on their size. By probing a field of bubbles it is possible to form an estimate of the range of sizes present by analysing the scattered data. There are a number of acoustic bubble sizing methods currently available, some of which exploit the nonlinear dynamic behaviour of the bubble. By modeling this behaviour, improvements may be made to the estimation techniques. This paper presents estimates for the quadratic transfer function of a single bubble based on the Volterra series. A method of estimating the Volterra kernels using a neural network is presented which significantly reduces the quantity of data required to form an estimate of the transfer function