1st Edition

Wavelet Analysis in Civil Engineering

By Pranesh Chatterjee Copyright 2015
    224 Pages 90 B/W Illustrations
    by CRC Press

    224 Pages 90 B/W Illustrations
    by CRC Press

    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


    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