Professor and Chair in Mathematics
Education
B.S.: Mathematics, National Taiwan University, (1975)
Ph. D.: Mathematics, Johns Hopkins University, (1982)
Contact Information
Pearce 214, Department of Mathematics
Phone: (989) 774-3596
e-mail: lin1e @ cmich.edu
Research Fields
Wavelets and Applications, Signal and Image Processing
Numerical solutions of PDE and Integral Equations, Compressed sensing.
Current Research Projects
One of my ongoing research projects is wavelet based Preisach modeling of hysteresis for piezoceramic actuator system which is described as follows. Smart materials such as piezoceramics are being widely used as actuators and sensors to achieve the micro-positioning and active control purposes. However, a major limitation of piezoceramic actuators is their lack of accuracy due to hysteresis. Applications, from electric motors to transformers and permanent magnets, from various types of electronic devices to magnetic recording, rely heavily on particular aspects of hysteresis. The Preisach model is one of the most useful models to handle hysteresis and has recently been applied to the piezoceramic material systems. The main objective is to develop and use the Preisach technique to model the hysteresis for piezoceramic actuator for the micro-position and active control purposes. Since most of the previous applications of the Preisach model are in the ferromagnetic area, the models developed by using the identification and numerical implementation approaches are based on the ferromagnetic material properties. Due to the differences in the hysteresis behavior between the magnetic and piezoceramic, some modifications on the Preisach model are needed. It is expected that the performance of the improved model will be achieved by choosing proper wavelet basis and wavelet parameters. Since any finite energy function can be represented by a wavelet basis, no specific parametric form is needed and hence, the wavelet approach can be effectively applied to virtually any physical system and greatly simplify the process of numerical implementations.
Selected Publications
E. B. Lin, Multi-scaling Approximation for Eigenvalue Problems of Fredholm Integral Operators, Journal of Applied Functional Analysis 2(4) 461-460 (2007).
E. B. Lin and P. Liu, A Discrete Wavelet Analysis of Freak Waves in the Ocean, Journal of Applied Mathematics, 5, 379-394, (2004).
E. B. Lin and Y. Ling, Image Compression and Denoising via Nonseparable Wavelet Approximation, Journal of Computational and Applied Mathematics, 155, 131-152, (2003).
E. B. Lin and X. Zhou, Connection coefficients on an interval and numerical solution of the Burgers equation, Journal of Computational and Applied Mathematics, 135, 63-78, (2001).
Y. Yu, Z. Xiao, E. B. Lin, N. Naganathan, Analytic and Experimental Studies of A Wavelet Identification of Preisach Model of Hysteresis, Journal of Magnetism and Magnetic Materials, 208(3), 255-263, (2000).
E. B. Lin, A Survey on Scaling Function Interpolation and Approximation, Applied Math. Review, 1, 559-607, (2000).
T. Bielecki, J. Chen, E. B. Lin and S. Yau, Wavelet Representations of General Signals, Journal of Nonlinear Analysis, 35, 125-141, (1999).
