ETH Chair Of Structural Mechanics Structural Identification & Health .

ETH Chair of Structural MechanicsStructural Identification & Health MonitoringLecture 18: Structural Health MonitoringDr. V.K. Dertimanis & Prof. Dr. E.N. Chatzi

OutlineIntroductionDamage-Sensitive FeaturesStatistical Methods for SHMFurther ReadingAcknowledgementsETH Chair of Structural Mechanics20.05.20202

IntroductionThe conceptThe four SHM levels- Level I SHM damage detection (presence of damage)- Level II SHM damage localization (location of damage)- Level III SHM damage identification (type and size of damage)- Level IV SHM damage prognosis (remaining life estimation)ETH Chair of Structural Mechanics20.05.20203

IntroductionThe conceptTypical applications- Bridge and buildings under earthquake excitation- Railway bridge monitoring- Monitoring of large industrial structures- Surface vehicle monitoring- Underwater, sea vessel, off-shore platform monitoring- In-flight aircraft monitoringETH Chair of Structural Mechanics20.05.20204

Damage-Sensitive FeaturesReceptance matrixStructural equation Mẍ Cẋ Kx fFrequency domain Z(ω)X(ω) F(ω)Receptance matrixZ(ω) ω 2 M iωC K,i 1Damage shifted natural frequencies change in Z[Z(ω) Z(ω)]X(ω) F(ω) Z(ω) effect of damageETH Chair of Structural Mechanics20.05.20205

Damage-Sensitive FeaturesReceptance matrix“Damage vector”dω F(ω) Z(ω) · X(w) Z(ω)X(ω)F from measured inputsX from measured responsesZ from system identification of the undamaged structureRemarks- Inspecting d(ω) can give information on DOFs affected by damage- 0 j -th row of Z(ω) 0 j -th element of d(ω)- Noisy data a perfect zero/non-zero patterns rarely occurETH Chair of Structural Mechanics20.05.20206

Damage-Sensitive FeaturesFlexibility matrixFlexibility matrixF K 1 ΦΩ 2 ΦT nX1i 1ωi2Φi ΦTiDamaged structure:F Φ Ω 2 Φ TMeasure of damage F F F Damage localization largest values in columns of FETH Chair of Structural Mechanics20.05.20207

Damage-Sensitive FeaturesStiffness matrixEigenvalue problem of the undamaged structure(λi M K)φi 0Eigenvalue problem of the damaged structure(λ i [M Md ] [K Kd ])Φ i 0 Md , Kd perturbations from healthy stateETH Chair of Structural Mechanics20.05.20208

Damage-Sensitive FeaturesStiffness matrixReformDi (λ i M K)φ i (λ i Md Kd )φ iUsually Md 0 Di Kd φ iRemarks- K w - Early stages of damage evolution oftentimes not apparent in DiETH Chair of Structural Mechanics20.05.20209

Damage-Sensitive FeaturesLoad surface curvaturei-th column of the flexibility matrix F deflected shape due to a unitload applied at the i-th DOFSum of all columns deflection due to a uniform load UniformLoad SurfaceMeasure of flexibility change/damage:00 F F 00 F00 00F second derivative more “sensitive” to changes00The F vector can indicate damage at location iETH Chair of Structural Mechanics20.05.202010

Damage-Sensitive FeaturesStrain EnergyRationale changes in F, K, φ, λ are not apparent unless the level ofdamage is significantDerivatives more sensitiveBeam element strain energy due to bending1dU M dθ2M EIw00 (x) moment (w00 : curvature)dθ R1 dx w00 dx angleETH Chair of Structural Mechanics20.05.202011

Damage-Sensitive FeaturesStrain EnergyRHence U (w00 (x))2 dxStrain energy for mode iUi Z L0(φ00i (x))2 dxDamage index for mode i at location jR b 00 2RLβij R L 00 200 2a φi dx 0 φi dx) 0 φi dxR 00RR0000( αb φi 2 dx 0L φi 2 dx) 0L φi 2 dx([a, b] interval around location j damaged quantitiesETH Chair of Structural Mechanics20.05.202012

Damage-Sensitive FeaturesMode shape curvaturesBeam under bending momentM (x) EIw00 (x)Stiffness reduction curvature increaseK EI w00 Damaged region larger differences between undamaged anddamaged mode shape curvaturesETH Chair of Structural Mechanics20.05.202013

Statistical Methods for SHMThe conceptThe statistical SHM Problem- Given random vibration data, solve the Level I SHM problem.- If damaged, proceed in solving Level II-IV SHM problems.ETH Chair of Structural Mechanics20.05.202014

Statistical Methods for SHMThe conceptStructure either in healthy (So ), or in faulty (S̄o ) stateInspection structure in unknown state (Su )Inspection If damaged, it will belong to a specific damage typeA, . . . , D (SA , . . . , SD )ETH Chair of Structural Mechanics20.05.202015

Statistical Methods for SHMThe conceptETH Chair of Structural Mechanics20.05.202016

Statistical Methods for SHMOverall properties“Global” methods working at a “system level”Time and cost effective“Automation” capabilityNo visual inspectionAdaptable to on-line useNo need for special experimental conditions/proceduresLess sensitive than certain “local” methodsETH Chair of Structural Mechanics20.05.202017

Statistical Methods for SHMAdvantages and pitfalls[ ] Inherently optimal accounting of uncertainty and random vibration[ ] Accounting for exogenous uncertainties[ ] No requirement for physical or finite element models[ ] No requirement for complete models (partial models may be used)[ ] Optimal statistical decision making under uncertainty[ ] May locate damage only to the extent allowed by the model type used[ ] Baseline phase requires groundwork under various damage typesETH Chair of Structural Mechanics20.05.202018

Statistical Methods for SHMMethodsETH Chair of Structural Mechanics20.05.202019

Statistical Methods for SHMMethodsPros and consMethodsNon-parametricParametricPros simplicity computational efficiency some user expertise required improved parsimony potentially increased accuracyCons- potentially reduced accuracy- increased complexity- computationally intensive- increased user expertise requiredETH Chair of Structural Mechanics20.05.202020

Statistical Methods for SHMPSD-based SHMIdea damage is associated with changes in the power spectrumStatistical quantity processed:Q Syy (f ) S(f )ETH Chair of Structural Mechanics20.05.202021

Statistical Methods for SHMPSD-based SHMIdea damage is associated with changes in the power spectrumDamage detection hypothesis testing problemHo :H1 :Su (f ) So (f )Su (f ) 6 So (f )(null hypothesis – healthy structure)(alternative hypothesis – faulty structure)ETH Chair of Structural Mechanics20.05.202022

Statistical Methods for SHMPSD-based SHMIdea damage is associated with changes in the power spectrumHo F belongs to (central) F distribution with 2K, 2K DOFF Sbo (f )Sbu (f ) F(2K, 2K)ETH Chair of Structural Mechanics20.05.202023

Statistical Methods for SHMPSD-based SHMDecision making Ho is accepted with risk level1 α1Risk level: the probability of accepting H1 although Ho is true – false alarmETH Chair of Structural Mechanics20.05.202024

Statistical Methods for SHMPSD-based SHMRemarks- Level II-IV SHM similar procedure- Signals should be scaled to account for different excitation levels- Environmental conditions should be constantETH Chair of Structural Mechanics20.05.202025

Statistical Methods for SHMModel parameter-based SHMIdea Level I-IV SHM is associated with changes in the parameter vector θ ofa suitable parametric modelStatistical quantity processed:Q g(θ)ETH Chair of Structural Mechanics20.05.202026

Statistical Methods for SHMModel parameter-based SHMDamage detection hypothesis testing problemHo :H1 : δθ θ o θ u 0 δθ θ o θ u 6 0(null hypothesis – healthy structure)(alternative hypothesis – faulty structure)Ho Q belongs to (central) χ2 distribution with d DOFTQ δ θ̂ · δ(2Γo ) 1 · δ θ̂ χ2 (d)d the size of the parameter vectorETH Chair of Structural Mechanics20.05.202027

Statistical Methods for SHMModel parameter-based SHMDecision making Ho is accepted with risk level αETH Chair of Structural Mechanics20.05.202028

Statistical Methods for SHMResidual-based SHMIdea Level I-IV SHM is associated with changes in the residual sequencesobtained by driving the current signals through predetermined parametricmodels.Statistical quantity processed:Q g(e[k])ETH Chair of Structural Mechanics20.05.202029

Statistical Methods for SHMResidual-based SHMETH Chair of Structural Mechanics20.05.202030

Further Reading1. Farrar, C.R. and Worden, K. (2013), Structural Health Monitoring: A MachineLearning Perspective, John Wiley & Sons Ltd, Chichester, UK2. Wenzel, H. (2009), Health monitoring of bridges, John Wiley & Sons Ltd,Chichester, UKETH Chair of Structural Mechanics20.05.202031

AcknowledgementsProf. Fotis Kopsaftopoulos, Rensselaer Polytechnic InstituteProf. Spilios Fassois, Stochastic Mechanical Systems & Automation LaboratoryETH Chair of Structural Mechanics20.05.202032

Structural Identification & Health Monitoring Lecture 18: Structural Health Monitoring Dr. V.K. Dertimanis & Prof. Dr. E.N. Chatzi. Outline Introduction Damage-Sensitive Features Statistical Methods for SHM Further Reading Acknowledgements ETH Chair of Structural Mechanics 20.05.2020 2.