1st Edition

# Wavelet Analysis in Civil Engineering

224 Pages 90 B/W Illustrations
by CRC Press

224 Pages 90 B/W Illustrations
by CRC Press

224 Pages 90 B/W Illustrations
by CRC Press

Also available as eBook on:

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

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