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Reducing Uncertainty in Structural Safety
Special Session SS6
Ghent, Belgium
28-31 October 2018
Franck Schoefs, Thierry Yalamas, Barbara Heitner,
Eugene OBrien, Guillaume Causse
Scope
Introduction
Multi-step Bayesian updating
Example application
Results and conclusions
Introduction
Problems of ageing bridges
How to estimate the level of safety of these bridges?
How to plan inspection/maint...
Introduction
Problems of ageing bridges
How to estimate the level of safety of these bridges?
How to plan inspection/maint...
Introduction
Problems of ageing bridges
How to estimate the level of safety of these bridges?
How to plan inspection/maint...
Introduction
Problems of ageing bridges
How to estimate the level of safety of these bridges?
How to plan inspection/maint...
Introduction
Corrosion is one of the most common and dangerous
phenomena related to the deterioration of RC bridges
Loss o...
Introduction
Corrosion is one of the most common and dangerous
phenomena related to the deterioration of RC bridges
Loss o...
Multi-step Bayesian updating
Estimating the value
of interest*
Developing the
physical model of
deterioration at t = 0
Est...
Multi-step Bayesian updating
Estimating the value
of interest*
Collecting relevant
data at time t = xi
Developing the
phys...
Multi-step Bayesian updating
Estimating the value
of interest*
Collecting relevant
data at time t = xi
Estimating the
dete...
Multi-step Bayesian updating
Estimating the value
of interest*
Collecting relevant
data at time t = xi
Estimating the
dete...
Multi-step Bayesian updating
Estimating the value
of interest*
Collecting relevant
data at time t = xi
Estimating the
dete...
Multi-step Bayesian updating
Some ideas about what is
going on
Physical model can be built
High level of uncertainty
Envir...
Multi-step Bayesian updating
Some ideas about what is
going on
Physical model can be built
High level of uncertainty
Envir...
Multi-step Bayesian updating
Some ideas about what is
going on
Physical model can be built
High level of uncertainty
Envir...
Example application
Corrosion model prior knowledge
To calculate the residual reinforcement area
5.13
27
c
fc
w
th
corr
c
...
Example application
Corrosion model prior knowledge
2D histogram of reinforcement area loss
(RAL) based on 100 000 sample ...
Example application
Corrosion model prior knowledge
2D histogram of reinforcement area loss
(RAL) based on 100 000 sample ...
Example application
Bayesian updating of LN distribution
At a given time RAL can be modelled using Log-Normal distribution...
Example application
Bayesian updating of LN distribution
At a given time RAL can be modelled using Log-Normal distribution...
Example application
Bayesian updating of LN distribution
At a given time RAL can be modelled using Log-Normal distribution...
Example application
Measurement scenarios
Obtaining new data
at t = 20 years
at t = 40 years
9 different cases:
no. of mea...
Example application
Measurement scenarios
Obtaining new data
at t = 20 years
at t = 40 years
9 different cases:
no. of mea...
Example application
Measurement scenarios
Obtaining new data
at t = 20 years
at t = 40 years
9 different cases:
no. of mea...
10 20 50
0.2
0.1
0.05
Results and conclusions
10 20 50
0.2
0.1
0.05
Results and conclusions
Results and conclusions
Number of data: 50
CoV of data: 0.05
Results and conclusions
Comparing the results based on
One updating at t = 20 years (blue)
Involving a second updating at ...
Results and conclusions
A methodology is presented for better estimating reinforcement
loss due to corrosion in RC structu...
Results and conclusions
A methodology is presented for better estimating reinforcement
loss due to corrosion in RC structu...
Results and conclusions
A methodology is presented for better estimating reinforcement
loss due to corrosion in RC structu...
Results and conclusions
A methodology is presented for better estimating reinforcement
loss due to corrosion in RC structu...
The TRUSS ITN project (http://trussitn.eu) has
received funding from the European
Horizon 2020 research and innovation
pro...
MCMC
Sample size of each posterior: 2000
Hyper-priors are normally distributed (truncated at 0) with
CoV = 0.5
Burn-in per...
MCMC
Example for the posterior distribution random walk samples for the
three hyper-prior
�log log
MCMC
Results of MCMC for all 9 scenarios
Mean and SD for the 3 hyper prior parameters
�log log
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"Using step-by-step Bayesian updating to better estimate the reinforcement loss due to corrosion in reinforced concrete structures" presented at IALCCE2018 by Barbara Heitner

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Probabilistic assessment of ageing structures has become an important research area as it attracts the interest from not only researchers but also investors, municipalities, and governments. The most commonly used material for many important structures and infrastructure is reinforced concrete. Various degradations of such structures are manifest in the form of direct loss of reinforcement area. In this study, a time-dependent stochastic model of the reinforcement loss (in [%]) due to corrosion is presented, which has a crucial role in the estimation of the lifetime and the time-dependent health state of the structure. Bayesian updating is applied in multiple steps during the lifetime of the structure in order to improve the estimate of the reinforcement loss. An example application is shown where updating is applied in two steps.

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"Using step-by-step Bayesian updating to better estimate the reinforcement loss due to corrosion in reinforced concrete structures" presented at IALCCE2018 by Barbara Heitner

  1. 1. Reducing Uncertainty in Structural Safety Special Session SS6 Ghent, Belgium 28-31 October 2018
  2. 2. Franck Schoefs, Thierry Yalamas, Barbara Heitner, Eugene OBrien, Guillaume Causse
  3. 3. Scope Introduction Multi-step Bayesian updating Example application Results and conclusions
  4. 4. Introduction Problems of ageing bridges How to estimate the level of safety of these bridges? How to plan inspection/maintenance?
  5. 5. Introduction Problems of ageing bridges How to estimate the level of safety of these bridges? How to plan inspection/maintenance? Different approaches/models exist Involving stochastic parameters (e.g. Monte Carlo, FORM, SORM) Incorporating measurement data (e.g. FE model calibration, Bayesian updating) Bayesian Networks Stochastic processes etc.
  6. 6. Introduction Problems of ageing bridges How to estimate the level of safety of these bridges? How to plan inspection/maintenance? Different approaches/models exist Involving stochastic parameters (e.g. Monte Carlo, FORM, SORM) Incorporating measurement data (e.g. FE model calibration, Bayesian updating) Bayesian Networks Stochastic processes etc. Crucial to estimate/model as good as possible The original geometrical/material/structural properties The loading (history) The level of deterioration/ health state
  7. 7. Introduction Problems of ageing bridges How to estimate the level of safety of these bridges? How to plan inspection/maintenance? Different approaches/models exist Involving stochastic parameters (e.g. Monte Carlo, FORM, SORM) Incorporating measurement data (e.g. FE model calibration, Bayesian updating) Bayesian Networks Stochastic processes etc. Crucial to estimate/model as good as possible The original geometrical/material/structural properties The loading (history) The level of deterioration/ health state
  8. 8. Introduction Corrosion is one of the most common and dangerous phenomena related to the deterioration of RC bridges Loss of capacity Loss of elasticity Increased deformations Cracking Spalling Aesthetical aspects
  9. 9. Introduction Corrosion is one of the most common and dangerous phenomena related to the deterioration of RC bridges Loss of capacity Loss of elasticity Increased deformations Cracking Spalling Aesthetical aspects In this work Corrosion is modelled in a simplified context Bayesian updating is applied on the distribution of reinforcement area loss due to corrosion at different points in time Parametric study is conducted based on: The quality of measurement data and The number of data available
  10. 10. Multi-step Bayesian updating Estimating the value of interest* Developing the physical model of deterioration at t = 0 Estimating the deterioration level until t = service life * Can be inspection/maintenance planning, probability of failure, remaining service life etc.
  11. 11. Multi-step Bayesian updating Estimating the value of interest* Collecting relevant data at time t = xi Developing the physical model of deterioration at t = 0 Estimating the deterioration level until t = service life * Can be inspection/maintenance planning, probability of failure, remaining service life etc.
  12. 12. Multi-step Bayesian updating Estimating the value of interest* Collecting relevant data at time t = xi Estimating the deterioration level at t = xi Developing the physical model of deterioration at t = 0 Estimating the deterioration level until t = service life i = 1 * Can be inspection/maintenance planning, probability of failure, remaining service life etc.
  13. 13. Multi-step Bayesian updating Estimating the value of interest* Collecting relevant data at time t = xi Estimating the deterioration level at t = xi Developing the physical model of deterioration at t = 0 Estimating the deterioration level until t = service life Updating the deterioration level at t = xi i = 1 * Can be inspection/maintenance planning, probability of failure, remaining service life etc.
  14. 14. Multi-step Bayesian updating Estimating the value of interest* Collecting relevant data at time t = xi Estimating the deterioration level at t = xi Developing the physical model of deterioration at t = 0 Estimating the deterioration level until t = service life Updating the deterioration level at t = xi Updated estimation of the deterioration level until t = service life i = i+1 i = 1 * Can be inspection/maintenance planning, probability of failure, remaining service life etc.
  15. 15. Multi-step Bayesian updating Some ideas about what is going on Physical model can be built High level of uncertainty Environmental conditions Material and geometrical imperfections etc. Why Bayesian updating?
  16. 16. Multi-step Bayesian updating Some ideas about what is going on Physical model can be built High level of uncertainty Environmental conditions Material and geometrical imperfections etc. Monitoring bridges has become commonplace periodical inspections (visual inspections, NDT) SHM systems Valuable new information BUT Limit on the amount of data High level of uncertainty Indirectly related data Why Bayesian updating?
  17. 17. Multi-step Bayesian updating Some ideas about what is going on Physical model can be built High level of uncertainty Environmental conditions Material and geometrical imperfections etc. Bayesian inference: prior hypothesis + new evidence/information Why Bayesian updating? Monitoring bridges has become commonplace periodical inspections (visual inspections, NDT) SHM systems Valuable new information BUT Limit on the amount of data High level of uncertainty Indirectly related data
  18. 18. Example application Corrosion model prior knowledge To calculate the residual reinforcement area 5.13 27 c fc w th corr c c w Tti 64.1 1 )1(378 )( 29.0 11 85.0)()( pcorrpcorr tTtitTti ptT T corr dttiDtD 1 1 )(232.0)( 0 For one reinforcing bar Where: w/c : water cement ration of concrete fc : compressive strength of concrete in [N/mm2] icorr(t) : corrosion rate in [�A/cm2] at time t t : time in [year] Cth : cover thickness in [cm] T1 : corrosion time initiation (=0) tp : time since T1 in [year] D0 : initial reinforcing bar diameter in [mm] D(t) : reinforcing bar diameter in [mm] at time t
  19. 19. Example application Corrosion model prior knowledge 2D histogram of reinforcement area loss (RAL) based on 100 000 sample size (Monte Carlo simulation)
  20. 20. Example application Corrosion model prior knowledge 2D histogram of reinforcement area loss (RAL) based on 100 000 sample size (Monte Carlo simulation) Mean, SD and 95% CI
  21. 21. Example application Bayesian updating of LN distribution At a given time RAL can be modelled using Log-Normal distribution 3 hyper parameters to update: �log log
  22. 22. Example application Bayesian updating of LN distribution At a given time RAL can be modelled using Log-Normal distribution 3 hyper parameters to update: �log log
  23. 23. Example application Bayesian updating of LN distribution At a given time RAL can be modelled using Log-Normal distribution 3 hyper parameters to update: �log log Markov Chain Monte Carlo (MCMC) method Numerical method Sampling directly from the posterior distribution using Metropolis- Hastings algorithm Convergence has to be ensured The mean values of the posterior distribution of hyper parameters are chosen to define the posterior LN distribution
  24. 24. Example application Measurement scenarios Obtaining new data at t = 20 years at t = 40 years 9 different cases: no. of measurements: 10,20 or 50 (Coefficient of variation of the measurement data / damage indicator): 0.05, 0.1 or 0.2
  25. 25. Example application Measurement scenarios Obtaining new data at t = 20 years at t = 40 years 9 different cases: no. of measurements: 10,20 or 50 (Coefficient of variation of the measurement data / damage indicator): 0.05, 0.1 or 0.2 A realization is randomly chosen in order to simulate the measurements
  26. 26. Example application Measurement scenarios Obtaining new data at t = 20 years at t = 40 years 9 different cases: no. of measurements: 10,20 or 50 (Coefficient of variation of the measurement data / damage indicator): 0.05, 0.1 or 0.2 t = 20 years A realization is randomly chosen in order to simulate the measurements
  27. 27. 10 20 50 0.2 0.1 0.05 Results and conclusions
  28. 28. 10 20 50 0.2 0.1 0.05 Results and conclusions
  29. 29. Results and conclusions Number of data: 50 CoV of data: 0.05
  30. 30. Results and conclusions Comparing the results based on One updating at t = 20 years (blue) Involving a second updating at t = 40 years (red)
  31. 31. Results and conclusions A methodology is presented for better estimating reinforcement loss due to corrosion in RC structures based on periodically collected data relatively simple, low computational cost requires limited workforce and traffic disruption can be used in case of any other deterioration process, where relevant data can be collected from time to time
  32. 32. Results and conclusions A methodology is presented for better estimating reinforcement loss due to corrosion in RC structures based on periodically collected data relatively simple, low computational cost requires limited workforce and traffic disruption can be used in case of any other deterioration process, where relevant data can be collected from time to time In all the studied cases it is possible to improve the estimation of the reinforcement loss
  33. 33. Results and conclusions A methodology is presented for better estimating reinforcement loss due to corrosion in RC structures based on periodically collected data relatively simple, low computational cost requires limited workforce and traffic disruption can be used in case of any other deterioration process, where relevant data can be collected from time to time In all the studied cases it is possible to improve the estimation of the reinforcement loss More measurements or better quality of measurements both significant
  34. 34. Results and conclusions A methodology is presented for better estimating reinforcement loss due to corrosion in RC structures based on periodically collected data relatively simple, low computational cost requires limited workforce and traffic disruption can be used in case of any other deterioration process, where relevant data can be collected from time to time In all the studied cases it is possible to improve the estimation of the reinforcement loss More measurements or better quality of measurements both significant Collecting less data multiple times leads to higher rate of improvement than collecting more data at a single point in time
  35. 35. The TRUSS ITN project (http://trussitn.eu) has received funding from the European Horizon 2020 research and innovation programme under the Marie -Curie grant agreement No. 642453
  36. 36. MCMC Sample size of each posterior: 2000 Hyper-priors are normally distributed (truncated at 0) with CoV = 0.5 Burn-in period: 100 Thinning: 20 Acceptance rate: 0.15 - 0.25 For each case measurement data sampling and updating have been done 100 times to have some statistical understanding of the results
  37. 37. MCMC Example for the posterior distribution random walk samples for the three hyper-prior �log log
  38. 38. MCMC Results of MCMC for all 9 scenarios Mean and SD for the 3 hyper prior parameters �log log

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