Journal of the Korea institute for structural maintenance and inspection (한국구조물진단유지관리공학회 논문집)

Korea Institute for Structural Maintenance Inspection (한국구조물진단유지관리공학회)
권호 표지
DOI QR코드

DOI QR Code

The Risk Assessment and Prediction for the Mixed Deterioration in Cable Bridges Using a Stochastic Bayesian Modeling

확률론적 베이지언 모델링에 의한 케이블 교량의 복합열화 리스크 평가 및 예측시스템

  • Received : 2012.04.03
  • Accepted : 2012.06.14
  • Published : 2012.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

The main objective is to predict the future degradation and maintenance budget for a suspension bridge system. Bayesian inference is applied to find the posterior probability density function of the source parameters (damage indices and serviceability), given ten years of maintenance data. The posterior distribution of the parameters is sampled using a Markov chain Monte Carlo method. The simulated risk prediction for decreased serviceability conditions are posterior distributions based on prior distribution and likelihood of data updated from annual maintenance tasks. Compared with conventional linear prediction model, the proposed quadratic model provides highly improved convergence and closeness to measured data in terms of serviceability, risky factors, and maintenance budget for bridge components, which allows forecasting a future performance and financial management of complex infrastructures based on the proposed quadratic stochastic regression model.

상관관계가 높은 복합열화의 완벽한 개별예측모델의 개발은 매우 어려운 문제로, 본 논문에서는 현수교 시스템의 미래열화와 유지 예산을 예측하기 위하여, 10년간의 유지 데이터가 주어진 매개변수(파손지표와 사용성)의 사후 확률 밀도함수를 찾기 위해 베이지언 추론을 적용하였다. 마르코프 연쇄 몬테카를로법을 이용하여 매개변수의 사후 분포를 조사하였다. 감소한 사용성의 모의위험예측은 사전분포와 연간유지 업무에서 업데이트한 데이터의 가능성에 따라 작성한 사후 분포이다. 기존의 선형 예측 모델과 비교하면, 제안된 2차 모델은 교량부품의 사용성, 위험요소, 그리고 유지 예산의 측정 데이터에 대하여 매우 개선된 수렴성과 근접성을 제공한다. 따라서 제안된 2차 추계학적 회귀 모델을 기반으로 복잡한 사회간접설비의 미래 성능과 유지관리예산을 예측하고 제어할 수 있는 기회를 제공할 것으로 기대한다.

Keywords

References

  1. Andrew Gelman, John B. Carlin, Hal S. Stern, Donald B., "Rubin. Bayesian Data Analysis", Second Edition, Chapman & Hall/CRC, 2003, pp.275-298.
  2. Andrew Keats, Eugene Yee, Fue-Sang Liena., "Bayesian inference for source determination with applications to a complex urban environment", Atmospheric Environment, vol. 41, 2007, pp.465-479. https://doi.org/10.1016/j.atmosenv.2006.08.044
  3. Cho, T., Kim, T., LEE, D., HAN, S., Chol, J., "Reliability Analysis of a Suspension Bridge Affected by Hydrogen Induced Cracking Based upon Response Surface Method", ISIJ International [J], 2009, vol. 49, No. 9, pp.1414-1423. https://doi.org/10.2355/isijinternational.49.1414
  4. Cho, T., Song, M., Lee, D., "Reliability analysis for the uncertainties in vehicle and high-speed railway bridge system based on an improved response surface method for nonlinear limit states", Nonlinear Dyn, 2010, pp.1-17.
  5. Gelfand, A., Smith, A. and Lee, T.-M., "Bayesian analysis of constrained parameter and truncated data problems using Gibbs sampling", Journal of the American Statistical Association, vol. 87, 1992, pp.523-532. https://doi.org/10.1080/01621459.1992.10475235
  6. Gelfand, A. and Smith, A., "Sampling-based approaches to calculating marginal densities", Journal of the American Statistical Association, vol. 85, 1990, pp.398-409. https://doi.org/10.1080/01621459.1990.10476213
  7. Geman, S. and Geman, D., "Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images", IEEE Transactions on Pattern Analysis and Machine intelligence 6, vol. 72, 1984, pp.1-741.
  8. Hastings, W., "Monte Carlo sampling methods using Markov chains and their applications", Biometrika, vol. 57, l970, pp.97-109. https://doi.org/10.1093/biomet/57.1.97
  9. LaFrance-Linden D., Watson, S., Haines, MJ., "Threat assessment of hazardous materials transportation in aircraft cargo compartments", Transportation research record 1763, TRB. Washington (DC), National Research Council, 2001, pp.130-137.
  10. Metropolis, N., Rosenbluth, A. W., Rosenbluth M. N., A. H. Teller, E. Teller, "Equation of State Calculations by Fast Computing Machines", Chem. Phys., vol. 21, No. 6, 1953, pp.1087-1092.
  11. Nowak, A. S., Cho, T., "Prediction of the combination of failure modes for an arch bridge system", Journal of Constructional Steel Research, vol. 63, 2007. pp.1561- 1569. https://doi.org/10.1016/j.jcsr.2007.05.004
  12. Schafer, J. L. and Olsen, M. K., "Multiple imputation for multivariate missing data problems: A data analyst's perspective", Multivariate Behavioral Research, vol. 33, 1998, pp.545-571. https://doi.org/10.1207/s15327906mbr3304_5
  13. Siu, Nathan O., Kelly, Dana L., "Bayesian parameter estimation in probabilistic risk assessment", Reliab. Eng. Syst. Saf., 1998, pp.89-116.
  14. Sundararajan, C., Probabilistic structural mechanics handbook, Chapman & Hall, 1994. pp.102-111.
  15. Tanner, M. and Wong, W., "The calculation of the posterior distributions by data augmentation", Journal of the American Statistical Association, vol. 82, 1987, pp.528-549. https://doi.org/10.1080/01621459.1987.10478458