@article{lien_fang_buckner_2011, title={Hysteretic neural network modeling of spring-coupled piezoelectric actuators}, volume={20}, ISSN={["1361-665X"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-79956193310&partnerID=MN8TOARS}, DOI={10.1088/0964-1726/20/6/065007}, abstractNote={This paper discusses the development of a high-fidelity, computationally efficient model for spring-coupled piezoelectric stack actuators. The model is based on a hysteretic recurrent neural network (HRNN), and aims to balance computational tractability with physical intuition. Previous work has detailed the development and experimental validation of an HRNN model for unloaded piezoelectric actuators. This paper extends the modeling approach to incorporate coupling with linear springs, and discusses training techniques based on genetic algorithms, which provide advantages over the previously employed Levenberg–Marquardt methods in terms of accuracy and model complexity. The resulting models are computable in real time. Model validity is established by comparison with a rate-dependent threshold-discrete Prandtl–Ishlinskii model.}, number={6}, journal={SMART MATERIALS AND STRUCTURES}, author={Lien, J. P. and Fang, Tiegang and Buckner, Gregory D.}, year={2011}, month={Jun} }
 @article{lien_york_fang_buckner_2010, title={Modeling piezoelectric actuators with Hysteretic Recurrent Neural Networks}, volume={163}, ISSN={["0924-4247"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-78049473465&partnerID=MN8TOARS}, DOI={10.1016/j.sna.2010.08.013}, abstractNote={This paper describes the application of Hysteretic Recurrent Neural Networks (HRNNs) to the modeling of polycrystalline piezoelectric actuators. Because piezoelectric materials exhibit voltage/strain relationships that are hysteretic and rate-dependent, the HRNN is composed of neurons with activation functions that incorporate these characteristics. Individual neurons are shown to agree with existing models of ideal single-crystal piezoelectric behavior. The combination of many such neurons into a network allows prediction of the heterogeneous behavior of polycrystalline materials. This model is shown to approximate the strain and polarization of an unloaded commercial stack actuator at multiple loading rates. A comparison is made to a recurrent Radial Basis Function Network model, and the HRNN is demonstrated to more accurately generalize across data sets. The model is further shown to execute on a PC platform at rates over 100 Hz, fast enough to support its application to real-time control.}, number={2}, journal={SENSORS AND ACTUATORS A-PHYSICAL}, author={Lien, J. P. and York, Alexander and Fang, Tiegang and Buckner, Gregory D.}, year={2010}, month={Oct}, pages={516–525} }