Computational Techniques for Structural Health Monitoring (Springer Series in Reliability Engineering)

Computational Techniques for Structural Health Monitoring
Part I Introductory Concepts in Structural Health Monitoring
1 Introduction
1.1…Overview on Structural Health Monitoring
1.1.1 Why Do We Need Structural Health Monitoring?SHM!Need
1.1.2 Basic Elements of SHM SystemsSHM!Elements
1.1.3 Levels of Structural Health MonitoringSHM!Levels
1.1.4 State-of-Art and Technological Needs
1.1.4.1 On-Line SHMSHM!On-line
1.1.4.2 Off-Line SHMSHM!Off-line
1.2…Dynamics-Based Structural Health MonitoringSHM!Dynamics based
1.2.1 Passive SHMSHM!Passive and active
1.2.2 Classification of Inspection Techniques Based on Frequency Range of Analysis
1.2.3 Vibration-Based TechniquesSHM!Vibration based
1.2.4 Guided Waves InspectionGuided wave
1.2.5 Ultrasonics and Nonlinear Ultrasound
1.3…Sensing and Actuation Strategies
1.3.1 Piezoelectric Actuators and SensorsActive sensors!Piezoelectric
1.3.2 Fiber Optics Sensors
1.3.2.1 FOS Classification
1.3.2.2 Basic Components of a FOS
1.3.2.3 Principle of Operation
1.3.2.4 Fabry-Perot Interferometric FOS
1.3.2.5 Fiber Bragg Grating FOS
1.3.3 Laser Vibrometer
1.4…Modeling and Simulation Techniques for SHM
1.4.1 The Importance of Modeling in Structural Health Monitoring
1.4.2 Finite Difference TechniquesFinite difference
1.4.3 Finite Element Method
1.4.4 Boundary Element MethodBoundary element method
1.4.5 Spectral Finite Element Method
1.4.6 Perturbation Techniques
1.5…Organization of the Book
References
2 Fundamentals Concepts in Elasticity, Mechanics and Wave Propagation
2.1…Introduction
2.2…Basic Concepts in Elasticity
2.2.1 Description of Motion
2.2.2 Strain
2.2.3 Strain--Displacement Relations
2.2.4 Stress
2.2.5 Constitutive Relations
2.2.6 Elastic Symmetry
2.2.6.1 Monoclinic System: One Elastic Symmetric Plane
2.2.6.2 Orthotropic System: Three Orthogonal Planes of Symmetry
2.2.6.3 Isotropic System: Infinite Plane of Symmetry
2.3…Governing Equations of Motion and the Solution Methods
2.3.1 Solution Procedures in Linear Theory of Elasticity
2.3.1.1 Displacement Formulation: Navier’s Equation
2.3.1.2 Stress Formulation: Beltrami--Mitchell Equations
2.3.2 Plane Problems in Elasticity
2.4…Introduction to Theory of Composites
2.4.1 Theory of Laminated Composites
2.4.1.1 Micromechanical Analysis of a Lamina
2.4.1.2 Determination of Material Properties of a Lamina
2.4.1.3 Stress--Strain Relations for a Lamina
2.4.2 Stress--Strain Relation for a Lamina with Arbitrary Orientation of Fibers
2.5…Introduction to Wave Propagation in Structures
2.5.1 Spectral Analysis
2.6…Characteristics of Waves in Anisotropic Media
2.7…Governing Equations for Beams and Plates
2.7.1 Governing Equation for an Elementary Beam
2.7.2 Governing Differential Equation for a Higher Order Beam
2.7.3 Governing Equations for a Composite Plate
2.8…Spectrum and Dispersion Relations
2.8.1 Efficient Computation of the Wavenumber and Wave Amplitude
2.8.1.1 Method 1: The Companion Matrix and the SVD Technique
2.8.1.2 Method 2: Linearization of PEP
2.8.2 Spectrum and Dispersion Relation for an Elementary Beam
2.8.3 Spectrum and Dispersion Relation for a Higher Order Beam
2.8.4 Spectrum and Dispersion Relation for an Anisotropic Plate
References
3 Signal Processing Techniques
3.1…Integral Transforms
3.1.1 Fourier Transforms
3.1.1.1 Continuous Fourier Transforms
3.1.2 Fourier Series
3.1.3 Discrete Fourier Transform
3.1.4 Wavelet Transforms
3.1.5 Wavelet-Based Numerical Solutions of Wave Equations
3.1.6 Comparative Advantages and Disadvantages of Different Transforms
3.2…Signal Processing Issues
3.2.1 Wraparound Problems
3.2.2 Signal Processing of Sampled Waveforms
3.2.3 Artificial Dispersion in Wavelet Transform
3.2.3.1 Periodic Boundary Condition
3.2.3.2 Non-Periodic Boundary Condition
3.2.4 Excitation Signals and Wave Dispersion
3.3…Frequency/Wavenumber Analysis
3.3.1 Analysis of a One-Dimensional Propagating Wave
3.3.1.1 Incident Wave Removal
3.3.2 Analysis of 2D Wave Propagation
3.3.3 Numerical Examples: Wave Propagation in a Damaged Rod
3.3.4 Numerical Examples: Wave Propagation in a Homogeneous Medium
3.3.5 Frequency/Wavenumber Filtering for Mode Separation
References
Part II Computational Simulation Techniques for Structural Health Monitoring
4 Application of the Finite Element Method in SHM
4.1…Overview and Basic Principles
4.2…Modeling Issues in FEM
4.3…Damage Modeling Using FEM
4.3.1 Stiffness Reduction MethodStiffness Reduction Method
4.3.2 Duplicate Node MethodDuplicate Node Method
4.3.3 Kinematics Based MethodKinematics Based Method
4.3.3.1 Modeling of Horizontal Crack or DelaminationKinematics Based Method!Modeling of Delaminations
4.3.3.2 Modeling of Vertical Crack or Fibre BreakageKinematics based method!Modeling of fiber breakage
4.4…Numerical Examples
4.4.1 Static and Free Vibration Analysis of a Damaged Cantilever Beam Using DNM
4.4.2 Response Analysis of a Cantilever Composite Beam with Different Damage Types
4.5…Finite Element Modeling Suggestions
4.6…Modeling Pitfalls in FEM for SHM and Their RemediesFEM!Modeling pitfalls
References
5 Spectral Finite Element Method
5.1…The Need for Spectral FEM in SHMSpectral element!Need in SHM
5.1.1 General Formulation Procedure: Fourier Transform Based SFEMFSFEM!General procedure
5.1.2 General Formulation Procedure: Wavelet Transform Based SFEMSpectral element!WSFEM procedure
5.2…Spectral Elements for Rods and Beams
5.2.1 Non-dispersive Isotropic Rod: FFT Based Spectral Element FormulationSpectral element!FSFEM for isotropic rods
5.2.2 Non-dispersive Isotropic Rod: Wavelet Transform Based Spectral Element FormulationSpectral element!WSFEM isotropic rods
5.2.3 Dispersive Isotropic Timoshenko Beams-FFT Based Spectral Element FormulationSpectral element!FSFEM for isotropic beams
5.2.4 Composite Beams-FFT Based Spectral Element FormulationSpectral element!FSFEM for composite beams
5.2.4.1 Finite Length Element
5.2.4.2 Throw-Off ElementSpectral element!Beam throw-off element
5.2.5 Higher Order Composite Beam-FFT Based Spectral Element FormulationSpectral element!FSFEM for higher order beam
5.2.5.1 Finite Length Element
5.2.5.2 Throw-Off ElementSpectral element!Higher order beam throw-off element
5.3…Spectral Elements for 2D Composite Layers-FFT Based Spectral Element FormulationSpectral element!2-D Layer element
5.3.1 Finite Layer Element (FLE)
5.3.2 Infinite Layer (Throw-Off) Element (ILE)Spectral element!2-D layer throw-off element
5.3.3 Expressions for Stresses and Strains
5.3.4 Prescription of Force Boundary ConditionsForce boundary condition
5.3.5 Determination of Lamb Wave ModesLamb wave!Modes determination
5.4…Anisotropic Plate-FFT Based Spectral Element FormulationSpectral element!Anisotropic plate
5.4.1 Finite Plate Element
5.4.2 Semi-infinite or Throw-Off Plate ElementSpectral element!Anisotropic plate throw-off element
5.5…Numerical Examples
5.5.1 Wave Transmission and Scattering Through an Angle-JointWave propagation!Angled joint
5.5.2 Wave Propagation in 2D Portal FrameWave propagation!2-D portal frame
5.5.3 Propagation of Surface and Interfacial Waves in a Composite LayerWave propagation!2-D Composite layer medium
5.5.4 Propagation of Lamb WaveLamb wave!Propagation
5.5.5 Wave Propagation in a Composite Plate with Ply-DropWave propagation!Composite plate with ply-drop
5.6…Conclusions
References
6 Simplified Spectral Models for Damaged Waveguides
6.1…Need for Spectral Element Damage Models in Structural Health Monitoring
6.2…Review of Simplified Models for Structural Defects
6.3…Modeling of Single Delamination or Horizontal Cracks
6.3.1 Wave Scattering in a Delaminated Beam Using Wavelet Spectral Elements
6.3.2 Effect of Wave Scattering Due to Delamination at Ply-Drops
6.4…Modeling of Fiber Breakage and Vertical Cracks
6.4.1 Interface Equilibrium of Forces
6.4.2 Assembly of the Element Internal Waveguides
6.4.3 Modeling Dynamic Contact Between Crack Surfaces
6.4.4 Modeling of Surface Breaking Cracks
6.4.4.1 Super Element Level Condensation
6.4.5 Distributed Constraints at the Interfaces Between Sub-Laminates and Hanging Laminates
6.4.6 Wave Scattering Due to Transverse Cracks
6.4.7 Sensitivity of the Fiber Breakage Location and Configuration
6.5…Modeling of Structures with Multiple Horizontal Cracks or Delaminations
6.5.1 Wave Scattering from Delamination: Comparison with 2D FEM
6.5.2 Computational Efficiency of FSFEM Compared to FEM
6.6…Modeling of Corrosion Pits
6.6.1 Wave Propagation Response Due to Corrosion Pits
6.7…Modeling of Material Degradation
6.7.1 Experimental Degraded Model (EDM)
6.7.1.1 Wave Propagation in Degraded Composites Using ED Model
6.7.2 Average Degraded Model
6.7.3 Wave Scattering in a Degraded Composite Beam Using ADM
6.8…Modeling of Vertical Cracks in 2D Waveguides
6.8.1 Flexibility Along the Crack
6.8.2 Scattering Due to a Transverse Crack
6.9…Conclusions
References
7 Perturbation Methods for Damaged Structures
7.1…Perturbation Methods for Notched Structures
7.2…Modal Analysis of Damaged Plates
7.2.1 Governing Equations
7.2.2 Perturbation Solution
7.2.3 Fourier Series Solution of \varepsilon^1 Equations
7.2.4 Strain Energy Ratio for Damage Localization
7.2.5 Effect of Notch Damage on the Plate Modal Properties
7.2.6 Notch Damage Localization Through the Strain Energy Ratio
7.2.7 Effect of Line Damage on the Plate Modal Properties
7.3…Analysis of Wave Propagation in Notched Beams Through Spectral FE Solution
7.4…Governing Equations
7.4.1 Spectral Finite Element Discretization
7.5…Wave Propagation in Notched Beams: Numerical Examples
7.5.1 Technique Validation: FSFEM Versus FE Predictions
7.5.2 FSFEM and Modal Superposition Results
7.5.3 Time Domain Results
7.5.4 Frequency Domain Results
References
8 Bridging Scales Analysis of Wave Propagation in Heterogeneous Structures with Imperfections
8.1…Overview
8.2…Theoretical Background
8.2.1 Coarse and Fine Scale Discretization and Bridging Matrices
8.2.2 Multiscale Lagrangian
8.2.3 Reduction of the Degrees of Freedom
8.2.4 Time Domain Formulation
8.2.5 Frequency Domain Formulation
8.3…Results for Time-Domain Bridging
8.3.1 Application to a One-Dimensional Rod
8.3.2 Homogenized Bi-material Rod with Imperfections
8.3.3 Energy-Based Time Integration Scheme
8.3.4 Propagation of In-plane Waves in a 2D Elastic Domain
8.4…Results for Frequency-Domain Bridging
8.4.1 Time Domain Spectral Element Discretization
8.4.2 Rod
8.4.3 Damaged Timoshenko Beam
8.4.4 Two Dimensional Waveguides
8.5…Conclusions
References
9 Modeling of Actuators and Sensors for SHM
9.1…Introduction
9.2…Modeling of Lamb Wave Generation
9.2.1 Governing EquationsGoverning equation!Lamb wave modeling
9.2.2 Harmonic Far Field ResponseHarmonic far field response
9.2.3 Actuator DirectivityActuator!Directivity
9.2.4 Example: Circular ActuatorActuator!Circular
9.2.5 Experimental ValidationLamb wave!Experimental validation
9.2.6 Finite Element Evaluation of the Interface StressesFEM!Interface stresses evaluation
9.2.7 Example: Circular PatchActuator!Circular
9.2.8 Rectangular Isotropic Piezo PatchActuator!Rectangular
9.3…Beamforming Through One-Dimensional Phased Arrays: A Quick Overview
9.3.1 Response Due to a Single Component
9.3.2 Array Response
9.3.3 Beam Steering StrategiesBeam steering!Strategies
9.3.3.1 Strategy 1: Linear Phase DelayBeam steering!Linear phase delay
9.3.3.2 Strategy 2: Frequency Based SteeringBeam steering!Frequency based steering
9.4…Two Dimensional Arrays for Frequency Based Beam Steering
9.4.1 Application to SV Waves in a MembraneSV waves!Membrane
9.4.1.1 Rectangular Two Dimensional Periodic Array of Point SourcesPhased arrays!2D rectangular
9.4.1.2 Quadrilateral Array of Point SourcesPhased arrays!2D quadrilateral
9.4.2 Application to Guided Waves in Thin PlatesGuided wave!Thin plates
9.4.2.1 Plate and Array Configuration
9.4.2.2 Dispersion Analysis for Directional Excitation of Lamb WavesLamb wave!Directional excitation
9.4.2.3 Plate Response Due to the Actuator Array: Narrow Band Burst ExcitationActuator array!Plate responseLoading!Tone burst
9.5…Modeling of Lamb Wave Sensors
9.5.1 Plate Configuration and Piezoelectric Constitutive Relations
9.5.2 Voltage Generated by Piezo Sensors of Arbitrary Shape
9.5.3 Examples of Directivities for Simple Geometries
9.5.3.1 Circular Sensor
9.5.3.2 Rectangular Sensor
9.5.4 Frequency Steerable Acoustic Transducer Periodic Array
References
Part III Computational Methodologies for Damage Detection and Quantification
10 Computational Techniques for Damage Detection, Classification and Quantification
10.1…Overview
10.2…A General Introduction to Vibration-Based Techniques
10.2.1 Early Techniques Based on Natural Frequency Shifts
10.2.2 Mode Shape Analysis
10.2.3 Mode Shape Curvature Changes
10.3…Damage Measure Based on Energy Functional Distributions
10.3.1 Formulation for Beams and Plates
10.3.2 Spline Interpolation of Operational Deflection Shapes Spline interpolation
10.3.3 Numerical Results on Beams Strain energy ratio!Damage index-beams
10.3.4 Numerical Results on Plates
10.3.5 Experimental Results on Beams Strain energy ratio!Experiments on beam
10.3.6 Experimental Results on Plates Strain energy ratio!Experiments on plates
10.4…Wave Propagation Techniques: Time Domain Damage Measure Wave propagation technique!Time domain damage index
10.4.1 Theoretical Background Wave propagation technique!Damage index theoretical background
10.4.2 Numerical Examples: Wave Propagation in a Homogeneous Medium Wave propagation!Homogeneous medium
10.4.3 Experimental Results: Aluminum Plate
10.5…Phase Gradient and Conversion Coefficients Evaluation for Damage Localization and Quantification Damage localization!Phase gradient
10.5.1 Simplified Description of a Multi-Modal Wave
10.5.2 Phase Gradient for Damage Localization
10.5.3 Reflection, Transmission and Conversion Coefficients for Damage Quantification Lamb wave!Reflection/Conversion coefficients
10.5.4 Application to Simulated Data
10.5.4.1 Model Configuration
10.5.4.2 Damage Localization Through Phase Gradient Estimation Damage localization!Phase gradient
10.5.4.3 Numerical Estimation of Mode Conversion Mode conversion!Estimation
10.5.5 Application to Experimental Data
10.5.5.1 Set up
10.5.5.2 Damage Localization Damage localization
10.5.5.3 Mode Conversion Estimation Mode conversion!Estimation
10.6…Damage Force Indicator Technique
10.6.1 Identification of Single Delamination Through Damage Force Indicator Damage force indicator!single delamination detection
10.6.2 Identification of Multiple Delamination Through Damage Force Indicator Damage force indicator!Multiple delaminations detection
10.6.3 Sensitivity of Damage Force Indicator Due to Variation in Delamination Size Damage force indicator!Variation in delamination size
10.6.4 Sensitivity of Damage Force Indicator Due to Variation in Delamination Depth Damage force indicator!Variation in delamination depth
10.7…Summary
References
11 Use of Soft Computing Tools for Damage Detection
11.1…Genetic Algorithms
11.1.1 A Brief Introduction to Genetic Algorithms
11.1.2 Genetic Algorithm Process for Damage Detection and DefinitionsGA!Process
11.1.3 Objective Functions in GA for Delamination IdentificationObjective functions
11.1.3.1 Displacement Based FunctionsObjective functions!Displacement based
11.1.3.2 Power Based Objective FunctionsObjective functions!Power flow based
11.1.4 Case Studies with a Cantilever Beam
11.1.4.1 Identification of Delamination LocationGA!Damage location identification
11.1.4.2 Identification of Delamination SizeGA!Damage size identification
11.1.4.3 Identification of Delamination Location and SizeGA!Damage location & size identification
11.1.5 Identification of Delamination Location, Size and DepthGA!Damage location, size & depth identification
11.2…Artificial Neural Networks
11.2.1 Simple Model of NeuronNeuron!Simple model
11.2.2 Types of Activation FunctionActivation function!Types
11.2.3 Multilayer Feedforward NetworksANN!Multiple layer feed forward networks
11.2.4 Neural Network Integrated with SFEMMulti-layer perceptron
11.2.4.1 Feedforward Computation
11.2.4.2 Error Back PropagationANN!Back propagation error
11.2.5 Numerical Results and Discussion
11.2.5.1 Effect of NoiseANN!Effect of noise
11.3…Summary
References
Index