  Nonlinearities in piezoelectric systems can arise from internal factors such
as nonlinear constitutive laws or external factors like realizations of
boundary conditions. It can be difficult or even impossible to derive detailed
models from the first principles of all the sources of nonlinearity in a
system. As a specific example, in traditional modeling techniques that use
electric enthalpy density with higher-order terms, it can be problematic to
choose which polynomial nonlinearities are essential. This paper introduces
adaptive estimator techniques to estimate the nonlinearities that can arise in
certain piezoelectric systems. Here an underlying assumption is that the
nonlinearities can be modeled as functions in a reproducing kernel Hilbert
space (RKHS). Unlike traditional modeling approaches, the approach discussed in
this paper allows the development of models without knowledge of the precise
form or structure of the nonlinearity. This approach can be viewed as a
data-driven method to approximate the unknown nonlinear system. This paper
introduces the theory behind the adaptive estimator and studies the
effectiveness of this approach numerically for a class of nonlinear
piezoelectric composite beams.
