Wavelet Applications in Chemical Engineering

Increasing emphasis on safety, productivity and quality control has provided an impetus to research on better methodologies for fault diagnosis, modeling, identification, control and optimization ofchemical process systems. One of the biggest challenges facing the research community is the processing of raw sensordata into meaningful information. Wavelet analysis is an emerging field of mathematics that has provided new tools and algorithms suited for the type of problems encountered in process monitoring and control. The concept emerged in the geophysical field as a result ofthe need for time-frequency analytical techniques. It has since been picked up by mathematicians and recognized as a unifying theory for many ofthe methodologies employed in the past in physics and signal processing. l Meyer states: "Wavelets are without doubt an exciting and intuitive concept. The concept brings with it a new way of thinking, which is absolutely essential and was entirely missing in previously existing algorithms. " The unification ofthe theory from these disciplines has led to applications of wavelet transforms in many areas ofscience and engineering including: • pattern recognition • signal analysis • time-frequency decomposition • process signal characterization and representation • process system modeling and identification • control system design, analysis and implementation • numerical solution ofdifferential equations • matrix manipulation About a year ago, in talking to various colleagues and co-workers, it became clear that a number of chemical engineers were fascinated with this new concept.

Résumé
Gives an insight into the many possible applications of time-frequency decomposition to the discipline of chemical engineering. This book includes tutorial chapters introducing wavelets and providing computational examples which will be helpful to readers new to the field.

Contenu
I Introduction to Wavelet Transformation and Time Frequency Analysis.- 1. General Introduction.- 2. Time Frequency Distributions.- 3. Fourier Transform and Short-Time Fourier Transform.- 4. Wavelet Theory.- 5. Conclusion.- 6. References.- II Computational Aspects of Wavelets And Wavelet Transforms.- 1. Introduction.- 2. Wavelets - Classification and Properties.- 3. Wavelet Transformation.- 4. Graphical Display of the Wavelet Transformation.- 5. Other Public Domain Wavelet Software.- 6. Concluding Remarks.- 7. Notation.- 8. References.- 9. Appendix I: Matlab Routines for Discrete Wavelet Transformation.- III Trend Analysis Using the Frazier-Jawerth Transform.- 1. Introduction.- 2. Background.- 3. Terminology.- 4. The FJ Decomposition and the FJT.- 5. Example.- 6. FJT Algorithms.- 7. On-line Implementation of the FJT.- 8. Conclusions.- 9. Acknowledgment.- 10. References.- IV Process Signal Features Analysis.- 1. Introduction.- 2. Signal Patterns on the Phase Plane.- 3. Signal Dependent Basis.- 4. Application Examples.- 5. Conclusion.- 6. References.- V Learning at Multiple Resolutions: Wavelets as Basis Functions in Artificial Neural Networks and Inductive Decision Trees.- 1. Introduction.- 2. Learning and Approximation Theory.- 3. Multi-Resolution Functional Approximation Using Wavelets.- 4. Theory of Wave-Nets.- 5. Extracting Rules from Wave-Nets.- 6. Conclusions and Discussion.- 7. References.- VI Application of Wavelets in Process Control.- 1. Introduction.- 2. Wavelets: A Process Control Perspective.- 3. Model Predictive Control: A Wavelet Domain Solution.- 4. Conclusions.- 5. References.- VII Use of Wavelets For Numerical Solution of Differential Equations.- 1. Introduction.- 2, Multiresolution Analysis.- 3. Wavelet Bases.- 4. Wavelet-Galerkin Method.- 5. Two-ScaleMethods.- 6. The Laplace Transform Wavelet Methods.- 7. Discussion.- 8. Conclusions.- 9. References.- VIII A Parallel Two-Dimensional Wavelet Packet Transform and Some Applications in Computing and Compression Analysis.- 1. Introduction.- 2. Parallel Wavelet Packet Decomposition.- 3. Parallel Wavelet Packet Best Basis Selection.- 4. Parallel Wavelet Packet Reconstruction.- 5. Parallel Matrix-Vector Multiplication in the Wavelet Packet Basis Expansion.- 6. Applications of the Wavelet Packet Transform to the Compression and Analysis of a Two-Dimensional Turbulent Flow.- 7. Acknowledgment.- 8. References.- 9. Annexes: Algorithms Written in Pseudo-Code.