Damage Models and Algorithms for Assessment of Structures Under Operation Conditions: Damage Models and Algorithms

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.

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.

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