Wavelets as a Powerful Signal Processing Tool
The principles of wavelets can be applied to a range of problems in civil engineering structures, such as earthquake-induced vibration analysis, bridge vibrations, and damage identification. This book is particularly useful for graduate students and researchers in vibration analysis, especially those dealing with random vibrations.
Wavelet Analysis in Civil Engineering
explains the importance of wavelets in analyzing nonstationarities in ground motions. The example of a tank is considered to develop the problem and the model (based on linear assumptions) and several case studies are explored—fixed base, flexible base, lateral and rocking motions of foundations, with and without fluid—to explain how to account for ground motion nonstationarities. Bridge vibrations caused by vehicle passage are explored, as is structural damage identification. Wavelet analytic techniques starting from single degree of freedom systems to multiple degree of freedom systems are set out and detailed solutions of more complicated problems involving soil and fluid interactions are presented. Separate chapters have been devoted to explaining the basic principles of the wavelet-based random nonstationary vibration analysis of nonlinear systems, including probabilistic analysis.Comprised of seven chapters, this text:
- Introduces the concept and utility of wavelet transform
- Describes the discretization of ground motions using wavelet coefficients
- Explains how to characterize nonstationary ground motions using statistical functionals of wavelet coefficients of seismic accelerations
- Develops the formulation of a linear single-degree-of-freedom system
- Shows stepwise development of the formulation of a structure idealized as a linear multi-degree-of-freedom system in terms of wavelet coefficients
- Defines wavelet domain formulation of a nonlinear single-degree-of-freedom system
- Introduces the concept of probability in wavelet-based theoretical formulation of a nonlinear two-degree-of-freedom system
- Covers a variety of case studies highlighting diverse applications
Wavelet Analysis in Civil Engineering
explains the importance of wavelets in terms of non-stationarities of ground motions, explores the application of wavelet analytic techniques, and is an excellent resource for users addressing wavelets for the first time.Introduction to Wavelets
History of Wavelets
Fourier transform
Random Vibration
Wavelet Analysis
A brief review of wavelet properties
Vibration Analysis of SDOF and MDOF Systems in Wavelet Domain
Wavelet based discretization of ground motions
Time-frequency characteristics of wavelets
Formulation of SDOF system equation in wavelet domain
Wavelet basis function for ground motion process
Wavelet domain stochastic response of SDOF system
Statistical parameters and non-stationary peak responses
Wavelet domain stochastic response of MDOF system
Ground Motion Characterization and PSA Response of SDOF system
Characterization of ground motions
PSA response spectrum
Time history simulation by Runge-Kutta fourth-order method
Fixed base analysis of a tank
Basic assumptions
Equations of motion
Numerical study
Ground motion characterization
Validation – PSA response
Validation – structural response
Wavelet analysis – structural response
Wavelet based analysis of linear MDOF system
Description of the model
Equations of motion
Wavelet domain formulation of tank-liquid-foundation system
Wavelet based non-stationary system responses
Solution of transfer functions
Expected largest peak response
Numerical Example
Impulsive response
MDOF analysis results
Wavelet based non-stationary vibration analysis of a simple nonlinear system
Nonlinear system
Duffing oscillator
Perturbation method
Solution of Duffing equation
Nonlinear system subjected to random vibration
Wavelet based probabilistic analysis
Model and soil nonlinearity
General equations of Motion
Equations based on yield conditions
Transfer functions
Response of the structure
Probability evaluation
Validation and results
General applications
B-WIM NOR signal analysis
Bridge and vehicle model
Wavelet analysis of experimental NOR data
Stiffness degradation analysis
Description of the analytical model
Numerical approach to wavelet based damage detection
Finite element model
Wavelet based analysis of numerical results
Soil-structure-soil interaction analysis
Responses at tank base
Finite element model of the system
Biography
Dr Pranesh Chatterjee has earned undergraduate and postgraduate degrees in civil engineering and subsequently adoctorate in engineering from Jadavpur University, India. Dr Chatterjee took up post-doctoral fellowship in structural mechanics at Katholieke Universiteit te Leuven in Belgium and then was selected as prestigious Pierse Newman Scholar at University College Dublin in Ireland. He is working as Manager of Plasticity and Tribology group of Tata Steel Europe in the Netherlands. He is active in research and publication of research works.
"I believe that this book will be an important contribution in the area of structural dynamics, particularly pertaining to civil engineering. …the content is crisp yet highly comprehensive and most importantly explains wavelet from a civil engineering outlook."
—Mira Mitra, Associate Professor, Department of Aerospace Engineering, Indian Institute of Technology Bombay, Mumbai, India