Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

"Comparative study on Bayesian updating of bridge safety model" presented at ESREL2017 by Barbara Heitner

256 views

Published on

Abstract: Probabilistic assessment of ageing bridges has become an important research area as it interests not only researchers but investors, municipalities and even governments. In this paper a simple bridge model is presented in a probabilistic context. A comparative study is carried out involving damage indicators and Bayesian updating. Bayesian updating is a powerful tool, which has been used in various research areas. However, using it for approximating the safety level of a bridge is challenging due to the various sources of uncertainties that may affect the performance of a measurement based damage indicator. The effects of different factors involved in the updating are examined in this paper and compared.

Published in: Engineering
  • Be the first to comment

  • Be the first to like this

"Comparative study on Bayesian updating of bridge safety model" presented at ESREL2017 by Barbara Heitner

  1. 1. … solutions for robust engineering This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 642453 Comparative study on Bayesian updating of bridge safety model Barbara Heitner, Eugene OBrien, Thierry Yalamas, Franck Schoefs, Rodrigue Décatoire
  2. 2. ©PhimecaEngineering Scope Introduction Bridge safety model Bayesian updating Comparative study Results Conclusions ESREL 2017 - Portoroz, 21/06/2017
  3. 3. ©PhimecaEngineering Introduction Bridge safety assessment • Probability of failure (level of safety) • Advanced probabilistic theory • Methodology that is flexible, yet robust • Introduction of any deterioration process • Information about the existence of damage  increase the power of a bridge safety model Bayesian updating • Most important advantages:  Works even with poor initial assumptions  Works even with small number of or quite uncertain data available ESREL 2017 - Portoroz, 21/06/2017
  4. 4. ©PhimecaEngineering Introduction Questions • How effective an updating can be in case of bridge safety models? • How the available number of measurements influences the results in terms of probability of failure of the bridge? • How the reliability of the measurement data (Damage Indicator data) influences the results in terms of probability of failure of the bridge? ESREL 2017 - Portoroz, 21/06/2017
  5. 5. ©PhimecaEngineering Scope Introduction Bridge safety model Bayesian updating Comparative study Results Conclusions ESREL 2017 - Portoroz, 21/06/2017
  6. 6. ©PhimecaEngineering Bridge safety model The scheme of the bridge safety model ESREL 2017 - Portoroz, 21/06/2017
  7. 7. ©PhimecaEngineering Bridge safety model Resistance and dead load models • Reinforced concrete slab bridge • Modelled as simply supported beam • A localized damage is introduced • Resistance = Bending moment capacity • Deterministic and stochastic variables for geometrical and material properties of the structure • Moment capacity and dead load are slightly correlated through the common geometrical stochastic variables Localized damage ESREL 2017 - Portoroz, 21/06/2017
  8. 8. ©PhimecaEngineering Bridge safety model Traffic load • Weigh-in-Motion database • Extract daily maximum bending moment values segment-wise • Generalized Extreme Value (GEV) distribution fitted to the tail                                /1 1exp),,;( x xGEV 1 2 3 … ESREL 2017 - Portoroz, 21/06/2017
  9. 9. ©PhimecaEngineering Bridge safety model Monte Carlo simulation • Probability of failure: where Nsim is the total number of simulations and where C is the capacity Ed is the load effect from dead load Et is the load effect from traffic load i=1…k and k is the number of segment      ij Et ij Ed ij C j G min sim N j j N I sim MC Pf    1      otherwise j Gif j I ,0 0,1 ESREL 2017 - Portoroz, 21/06/2017
  10. 10. ©PhimecaEngineering Scope Introduction Bridge safety model Bayesian updating Comparative study Results Conclusions ESREL 2017 - Portoroz, 21/06/2017
  11. 11. ©PhimecaEngineering Bayesian updating Model deterioration process in probabilistic context  Prior knowledge Conduct real time measurement, which has to: • Be easy and fast; • Lead to no restriction on the traffic flow; • Give relevant information about possible damage extent; • And damage location. Establish a damage indicator (DI) based on the measurement Identify the connection between the damage indicator and the possible deterioration  ‘Measurement data’ for updating ESREL 2017 - Portoroz, 21/06/2017
  12. 12. ©PhimecaEngineering Scope Introduction Bridge safety model Bayesian updating Comparative study Results Conclusions ESREL 2017 - Portoroz, 21/06/2017
  13. 13. ©PhimecaEngineering Resistance and dead load • Stochastic variables of the model: Comparative study Parameter (Distribution) Nominal value Unit Mean value STD* / CoV** Slab depth (Normal) 1000 [mm] + 0.8 3.6 Concrete cover (N) 50 [mm] + 6 11.5 Concrete compressive strength (N) 45 [N/mm2] + 7.4 6 Steel yield strength (LogNormal) 400 [N/mm2] +36 21.3 Unit weight of concrete (N) 23.68 [kN/m3] x 1.05 x 0.11 Unit weight of asphalt (N) 22.73 [kN/m3] x 1.0 x 0.25 Thickness of asphalt (N) 80 [mm] + 0 40 Bar area loss (Gamma) [%] Shape: k=1.5 Scale: λ=8.9 *Standard deviation **Coefficient of Variation ESREL 2017 - Portoroz, 21/06/2017
  14. 14. ©PhimecaEngineering Comparative study Traffic load • One lane traffic • 1 year Weigh-in-Motion (WIM) database from a site in Illinois (2011) Daily maximum bending moments Parameter Unit Mean CI95%- CI95%+ Speed [km/h] 105.95 94.94 117.47 GVW* [tons] 22.93 3.81 35.88 Length [m] 19.84 6.1 24.10 No. of axles [-] 4.57 2 5 Wheel base [m] 16.10 3.60 20.86 Gap behind [sec] 37.00 1.41 106.6 *Gross Vehicle Weight ESREL 2017 - Portoroz, 21/06/2017
  15. 15. ©PhimecaEngineering Comparative study Bayesian updating • Prior distribution  Parameter of ‘bar area loss’ for the damaged segment (from literature)  Gamma distribution (k=1.5; λ=8.9) • Updating the two parameters (shape and scale) of ‘bar area loss’ initial distribution using different levels of ‘measured’ damage • Markov Chain Monte Carlo method is applied using the Metropolis- Hastings algorithm Measurement scenarios • Related uncertainties of a DI may depend on:  The accuracy and resolution of the applied sensor;  The relevance of the human factor;  The sensitivity to environmental conditions;  The sensitivity to traffic conditions. ESREL 2017 - Portoroz, 21/06/2017
  16. 16. ©PhimecaEngineering Comparative study • These uncertainties influence the quality of DI, or with the other words the ‘DI’s reliability’ The variance (or standard deviation) of the measured DI values at a given bridge state • The number of measurements possible (no. of data available for updating) can also be an important burden • Applied scenarios in the comparative study: Number of measurements Standard deviation of DI 1.0 2.0 3.0 4.0 5 SC1 SC2 SC3 SC4 10 SC5 SC6 SC7 SC8 20 SC9 SC10 SC11 SC12 50 SC13 SC14 SC15 SC16 ESREL 2017 - Portoroz, 21/06/2017
  17. 17. ©PhimecaEngineering Comparative study Prior and (example) posterior gamma distributions Real value is 5% Real value is 20% ESREL 2017 - Portoroz, 21/06/2017
  18. 18. ©PhimecaEngineering Scope Introduction Bridge safety model Bayesian updating Comparative study Results Conclusions ESREL 2017 - Portoroz, 21/06/2017
  19. 19. ©PhimecaEngineering Results Results of the Bayesian updating regarding the bar area loss distribution • When the prior is poor (20% case) the updating shows clearer trends with increasing no. of measurements regarding both hyperparameters • When the prior is good (5% case) the shape (k) of the distribution changes less, while the scale (𝜆) changes more 5 measurement data 10 measurement data 20 measurement data 50 measurement data Triangle: STD=4 Star: STD=3 Diamond: STD=2 Circle: STD=1 Sample size for each case = 10 ESREL 2017 - Portoroz, 21/06/2017
  20. 20. ©PhimecaEngineering Results Results regarding the probability of failure – Real value = 5% • For all the case is possible to improve the prior assumption • For STD=1 or 2 the trend of getting better results with increasing no. of measurements is clear • The uncertainty can be visibly decreased by increasing the no. of measurements except for STD=4 Pf using the prior distribution is 0.07 ESREL 2017 - Portoroz, 21/06/2017
  21. 21. ©PhimecaEngineering Results Results regarding the probability of failure – Real value = 20% • For any STD only for the 50 measurement case is possible to improve the prior assumption • Only for STD=1 the trend of getting better results with increasing no. of measurements is clear • The uncertainty can be visibly decreased by increasing the no. of measurements for STD=1 or 2 Pf using the prior distribution is 0.023 ESREL 2017 - Portoroz, 21/06/2017
  22. 22. ©PhimecaEngineering Scope Introduction Bridge safety model Bayesian updating Comparative study Results Conclusions ESREL 2017 - Portoroz, 21/06/2017
  23. 23. ©PhimecaEngineering Conclusions Bayesian updating can give significantly different results depending on the quality and number of measurement (or DI) data as well as on the prior assumption Overall improvement of the bar area loss parameter does not necessarily lead to improvement of the estimation on the probability of failure It is also important to acknowledge the effect of the order of magnitude of the probability of failure and the type of distribution defined Wisely updating the bar area loss parameter according to the different scenarios can lead to significant enhancement of the safety model ESREL 2017 - Portoroz, 21/06/2017
  24. 24. … solutions for robust engineering This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 642453 Thank you for your kind attention! Any questions?

×