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Damage Models and Algorithms for Assessment of Structures under Operating Conditions

Structures and Infrastructures Book Series, Vol. 5

By Siu-Seong Law, Xin-Qun Zhu

Series Editor: Dan M. Frangopol

CRC Press – 2009 – 340 pages

Series: Structures and Infrastructures

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    978-0-415-42195-9
    September 17th 2009

Description

Extensive amounts of operational data are generated over time by the health monitoring system of a structure’s management system, yet there are few analysis algorithms which can tell the exact working state of the structure on-line. Good maintenance engineers need to know the exact location and state of the structural components after an earthquake or some attack or accident involving the structure, possibly within a matter of hours, and the client also demands a rapid diagnosis of the structure before making decisions on any necessary remedial work.

This book is devoted to the condition assessment of a structure under operational loading, with most of the illustrations related to a bridge deck under a group of moving vehicular loads. More generally, a wide variety of excitation forces can be exerted on a structure, from earthquake excitation, wind loading, vehicular loading or ambient excitation at the supports. Different algorithms may be used to enable real time identification with deterministic results on the state of the structure. This book also covers a group of damage-detection-oriented-models developed by the author, including a new decomposition of the system matrices of the beam element and plate element. Methods for extending the deterministic condition assessment to provide statistical information are also included. The methods and algorithms described can be implemented for the on-line condition assessment of a structure through model updating of the structure during the course of extreme loading such as an earthquake, or when under normal ambient excitation or operation excitation. Different sample structures are described and analysed, supplemented with major references.

This leading-edge work will be especially useful for researchers and graduate students, and it is also heavily rooted in advanced engineering practice.

Series: Structures and Infrastructures Series

Structures and Infrastructures comprises advanced-level books dealing with the maintenance, management, and cost analysis of structures and infrastructures. Topics treated include research, development and application of the most advanced technologies for analyzing, predicting, and optimizing the performance of structures and infrastructures, such as buildings, bridges, dams, underground construction, offshore platforms, pipelines, naval vessels, ocean structures, and nuclear power plants, as well as airplanes, aerospace, and automotive structures.

Themes featured are mathematical modeling, computer and experimental methods, practical applications in assessment and evaluation, construction and design for durability, decision making, deterioration modeling and aging, failure analysis, field testing, financial planning, inspection and diagnostics, life-cycle analysis and prediction, loads, maintenance strategies, management systems, nondestructive testing, maintenance and management optimization, specifications and codes, structural safety and reliability, system analysis, time-dependent performance, rehabilitation, repair, replacement, reliability and risk management, service life prediction, strengthening and whole life costing.

Contents

1. Introduction

  • Condition monitoring of civil infrastructures
  • Background to the book
  • What information should be obtained from the structural health monitoring system?
  • General requirements of a structural condition assessment algorithm
  • Special requirements for concrete structures
  • Other considerations
  • Sensor requirements
  • The problem of a structure with a large number of degrees-of-freedom
  • Dynamic approach versus static approach
  • Time-domain approach versus frequency-domain approach
  • The operation loading and the environmental effects
  • The uncertainties
  • The ideal algorithm/strategy of condition assessment

2. Mathematical concepts for discrete inverse problems

  • Introduction
  • Discrete inverse problems
  • Mathematical concepts
  • The ill-posedness of the inverse problem
  • General inversion by singular value decomposition
  • Singular value decomposition
  • The generalized singular value decomposition
  • The discrete Picard condition and filter factors
  • Solution by optimization
  • Gradient-based approach
  • Genetic algorithm
  • Simulated annealing
  • Tikhonov regularization
  • Truncated singular value decomposition
  • Generalized cross-validation
  • The L-curve
  • General optimization procedure for the inverse problem
  • The criteria of convergence
  • Summary

3. Damage description and modelling

  • Introduction
  • Damage models
  • Model on pre-stress
  • Damage-detection-oriented model
  • Beam element with end flexibilities
  • Hybrid beam with shear flexibility
  • Hybrid beam with both shear and flexural
  • flexibilities
  • Decomposition of system matrices
  • The generic element
  • The eigen-decomposition
  • Super-element
  • Beam element with semi-rigid joints
  • The Tsing Ma bridge deck
  • Concrete beam with flexural crack and debonding at the steel and concrete interface
  • Beam with unbonded pre-stress tendon
  • Pre-stressed concrete box-girder with bonded tendon
  • Models with thin plate
  • Anisotropic model of elliptical crack with strain energy equivalence
  • Thin plates with anisotropic crack from dynamic characteristic equivalence
  • Model with thick plate
  • Thick plate with anisotropic crack model
  • Model of thick plate reinforced with Fibre-Reinforced-Plastic
  • Damage-detection-oriented model of delamination of fibre-reinforced plastic and thick plate
  • Conclusions

4. Model reduction

  • Introduction
  • Static condensation
  • Dynamic condensation
  • Iterative condensation
  • Moving force identification using the improved reduced system
  • Theory of moving force identification
  • Numerical example
  • Structural damage detection using incomplete modal data
  • Mode shape expansion
  • Application
  • Remarks on more recent developments

5. Damage detection from static measurement

  • Introduction
  • Constrained minimization
  • Output error function
  • Displacement output error function
  • Strain output error function
  • Damage detection from the static response changes
  • Damage detection from combined static and dynamic measurements
  • Variation of static deflection profile with damage
  • The static deflection profile
  • Spatial wavelet transform
  • Application
  • Damage assessment of concrete beams
  • Effect of measurement noise
  • Damage identification
  • Damage evolution under load
  • Damage identification – Simulating practical assessment
  • Assessment of bonding condition in reinforced concrete beams
  • Local beam damage identification
  • Identification of local bonding
  • Simultaneous identification of local bonding and beam damages
  • Limitations with static measurements
  • Conclusions

6. Damage detection in the frequency domain

  • Introduction
  • Spatial distributed system
  • The eigenvalue problem
  • Sensitivity of eigenvalues and eigenvectors
  • System with close or repeated eigenvalues
  • Localization and quantification of damage
  • Finite element model updating
  • Higher order modal parameters and their sensitivity
  • Elemental modal strain energy
  • Model strain energy change sensitivity
  • Modal flexibility
  • Model flexibility sensitivity
  • Unit load surface
  • The curvatures
  • Mode shape curvature
  • Modal flexibility curvature
  • Unit load surface curvature
  • Chebyshev polynomial approximation
  • The gap-smoothing technique
  • The uniform load surface curvature sensitivity
  • Numerical examples of damage localization
  • Simply supported plate
  • Study on truncation effect
  • Comparison of curvature methods
  • Resolution of damage localization
  • Cantilever plate
  • Effect of sensor sparsity
  • Effect of measurement noise
  • When the damage changes the boundary condition of the structure
  • Conclusions

7. System identification based on response sensitivity

  • Time-domain methods
  • The response sensitivity
  • The computational approach
  • The analytical formulation
  • Main features of the response sensitivity
  • Applications in system identification
  • Excitation force identification
  • The response sensitivity
  • Experimental verification
  • Condition assessment from output only
  • Algorithm of iteration
  • Experimental verification
  • Removal of the temperature effect
  • Identification with coupled system parameters
  • Condition assessment of structural parameters having a wide range of sensitivities
  • Condition assessment of load resistance of isotropic structural components
  • Dynamic test for model updating
  • Damage scenarios
  • Dynamic test for damage detection
  • Damage scenario E1
  • Damage scenario E2
  • Damage scenario E3
  • The false positives in the identified results
  • System identification under operational loads
  • Existing approaches
  • The equation of motion
  • Damage detection from displacement measurement
  • The generalized orthogonal function expansion
  • Application to a bridge-vehicle system
  • The vehicle and bridge system
  • The residual pre-stress identification
  • Conclusions

8. System identification with wavelet

  • Introduction
  • The wavelets
  • The wavelet packets
  • Identification of crack in beam under operating load
  • Dynamic behaviour of the cracked beam subject to moving load
  • The crack model
  • Crack identification using continuous wavelet transform
  • Numerical study
  • Experimental verification
  • The sensitivity approach
  • The wavelet packet component energy sensitivity and the solution algorithm
  • The solution algorithm
  • The wavelet sensitivity and the solution algorithm
  • Analytical approach
  • Computational approach
  • The solution algorithm
  • The wavelet packet transform sensitivity
  • Damage information from different wavelet bandwidths
  • Damage scenarios and their detection
  • Effect of measurement noise and model error
  • Damage information from different wavelet coefficients
  • Frequency and energy content of wavelet coefficients
  • Comparison with response sensitivity
  • Damage identification
  • Effect of model error
  • Noise effect
  • Approaches that are independent of input excitation
  • The unit impulse response function sensitivity
  • Wavelet-based unit impulse response
  • Impulse response function via discrete wavelet transform
  • Solution algorithm
  • Simulation study
  • Damage identification with model error and noise effect
  • Discussions
  • The covariance sensitivity
  • Covariance of measured responses
  • When under single random excitation
  • When under multiple random excitations
  • Sensitivity of the cross-correlation function
  • Condition assessment including the load environment
  • Sources of external excitation
  • Under earthquake loading or ground-borne excitation
  • Simulation studies
  • The sensitivities
  • Damage identification from WPT sensitivity and response sensitivity
  • Effect of model error and noise
  • Performance from a subset of the measured response
  • Under normal random support excitation
  • Damage localization based on mode shape changes
  • Laboratory experiment
  • Modelling of the structure
  • Ambient vibration test for damage detection
  • Damage scenarios
  • Model improvement for damage detection
  • Conclusions

9. Uncertainty analysis

  • Introduction
  • System uncertainties
  • Modelling uncertainty
  • Parameter uncertainty
  • Measurement and environmental uncertainty
  • System identification with parameter uncertainty
  • Monte Carlo simulation
  • Integrated perturbed and Bayesian method
  • Modelling the uncertainty
  • Propagation of uncertainties in the condition assessment process
  • Theoretical formulation
  • Uncertainties of the system
  • Derivatives of local damage with respect to the uncertainties
  • Uncertainty in the system parameter
  • Uncertainty in the exciting force
  • Uncertainty in the structural response
  • Statistical characteristics of the damage vector
  • Statistical analysis in damage identification
  • Numerical example
  • The structure
  • Uncertainty with the mass density
  • Uncertainty with the elastic modulus of material
  • Uncertainty with the excitation force and measured response
  • Discussions
  • Integration of system uncertainties with the reliability analysis of a box-section bridge deck structure
  • Numerical example
  • Condition assessment
  • Reliability analysis
  • Conclusions

References

Subject Index

Author Bio

Siu-Seong Law is is an Associate Professor with the Civil and Structural Engineering Department of the Hong Kong Polytechnic University, prior to which he spent several years in the civil engineering industry with especial experience with long-span bridges.

Name: Damage Models and Algorithms for Assessment of Structures under Operating Conditions: Structures and Infrastructures Book Series, Vol. 5 (Hardback)CRC Press 
Description: By Siu-Seong Law, Xin-Qun ZhuSeries Editor: Dan M. Frangopol. Extensive amounts of operational data are generated over time by the health monitoring system of a structure’s management system, yet there are few analysis algorithms which can tell the exact working state of the structure on-line. Good...
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