Smart or active materials expand or deform as a response to external pressure, temperature, or electromagnetic field. The most commonly used active material in actuators is piezoelectric as it relates the electric field to mechanical compression and elongation. However, mathematical modeling of such actuators is tedious and complicated because of the nonlinear behavior. Therefore, there is a need to employ appropriate identification algorithms in order to capture the modeling process of such actuators. In this paper, ultrasonic transducer that is used in ultrasonically assisted machining is adopted as a case study. A component-based model for the piezoelectric is derived and the dynamic response is analyzed. Then, two identification techniques, ARX and ANN, are used to obtain models that mimic the system's dynamic response with minimal error.