Modular Bayesian uncertainty assessment for Structural Health Monitoring

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uncertainty assessment for Structural Health Monitoring Warwick Centre for Predictive Modelling André Jesus a.jesus@warwick.ac.uk June 26, 2017 Thesis advisor: Irwanda Laory & Peter Brommer

Structural Health Monitoring The BIG picture probabilities Civil and mechanical engineering; Signal processing; Machine learning; Electronics; Information theory; Computer science... André Jesus uncertainty assessment for Structural Health Monitoring 2/14

Tasks/Approach/Challenges probabilities Tasks Measurement system design; Damage detection; Structural identification; Data interpretation; Approach Data-driven; Model-based; Challenges Complexity: structure; monitoring; model! uncertainties; Decision-makers need to know how good the model predictions are Model predictions should be accompanied by quantification of uncertainty; André Jesus uncertainty assessment for Structural Health Monitoring 3/14

probabilities André Jesus uncertainty assessment for Structural Health Monitoring 4/14

Multiple response (mrgp) Workframe for UQ; Reduced computational effort; mrgp: Dataset(X, Y )! non-parametric probabilistic model probabilities Simulations Measurements André Jesus uncertainty assessment for Structural Health Monitoring 5/14

Uncertainty quantification probabilities Sources of uncertainty Experimental: Noise; Residual variations Prediction: Parametric; Model discrepancy; Interpolations Bayes Theorem posterior = likelihood prior marginal likelihood specific p( D) = generic p(d )p( ) R p(d )p( )d Y e (X) =Y m (X, ) André Jesus uncertainty assessment for Structural Health Monitoring 6/14

Uncertainty quantification André Jesus uncertainty assessment for Structural Health Monitoring 6/14 probabilities Sources of uncertainty Experimental: Noise; Residual variations Prediction: Parametric; Model discrepancy; Interpolations Bayes Theorem posterior = likelihood prior marginal likelihood Measurements Simulations p( D) = Y e (X) =Y m (X, )+ (X)+" Structural Parameters p(d )p( ) R p(d )p( )d Prior information Model Noise Discrepancy Multiple parameters: Markov Chain Monte Carlo methods

Setup Experiment TD TC SJ SH, SI, SK SF,SG TB TA, SA SC, SE SB, SD SF 604 TA TC TD SH SI SJ SK SG SA TB SB SC SD 2032 SE 382 probabilities Model André Jesus 18.9 25.4 cross section 406 uncertainty assessment for Structural Health Monitoring [mm] 7/14

Results probabilities Strain (µ" B ) Strain (µ" G ) 9 8 7 6 5 4 3 2 Probability density 0.03 0.02 0.01 Prior Likelihood Posterior True 0 300 400 500 600 700 800 900 K (N/mm) Strain (µ" B ) RMSE (µ") 30 20 10 Det. MBA True 0 300 400 500 600 700 800 900 K (N/mm) -2-4 -10-8 -6 PI 95% Prediction -12-14 -16-18 -20-22 290 295 300 305 310 315 320 Temperature (K) -1-2 PI 95% Prediction -3 Strain (µ" G ) Strain (µ" B ) 0-2 -4-6 -8-10 -12-14 Strain (µ" G ) PI 95% Prediction true -1 01-16 -18 290 295 300 305 310 315 320 290 295 300 305 310 315 320 Temperature (K) Temperature (K) 5 5 0 0 PI 95% Prediction -5-5 Measured -10-10 -4-15 -15-20 -5-20 -25-6 -25-30 -7-30 295 300 305 310 315 320 295 300 305 310 315 320 295 300 305 310 315 320 Temperature (K) Temperature (K) Temperature (K) André Jesus uncertainty assessment for Structural Health Monitoring 8/14

Setup André Jesus uncertainty assessment for Structural Health Monitoring 9/14 probabilities Experiment Measurements during a one year span X Temperature; traffic Y Natural frequencies; Mid-span displacement; Model Expansion gap k Side Cables Main Cable Prestress " i SALTASH PLYMOUTH

Results probabilities Forces (kn) Year Main cable Side cable Method 1961 20296 20597 iterative shape finding 2001 20296 20597 iterative shape finding 2009 23564 25985 modular A 13% increase in the cables forces was identified André Jesus uncertainty assessment for Structural Health Monitoring 10/14

probabilities Credibility of modelling should always be assessed by uncertainty quantification (UQ); Sufficiently informative responses improve UQ of the ; Methodology was applied in reduced and full-scale examples of Structural Health Monitoring, allowing identification of critical parameters; Enhancement of the methodology for multiple parameter identification; Acknowledgementes: EPSRC funding; supervisors & colleagues; Exeter research group; André Jesus uncertainty assessment for Structural Health Monitoring 11/14

Thank you for your attention. Questions? André Jesus

Workflow André Jesus uncertainty assessment for Structural Health Monitoring 13/14 probabilities 1 Fit model with mrgp Y m (X m, m ) mrgp m 2 Fit discrepancy function with mrgp Z Y e (X e ) mrgp m (X e, )p( )d mrgp 3 Bayes theorem p( D) = p(d )p( ) R p(d )p( )d 4 Predictions with updated metamodel Y e mrgp m +mrgp

probabilities André Jesus uncertainty assessment for Structural Health Monitoring 14/14

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