Advertisement

Correlated Maps for Regional Multi-Hazard Analysis: Ideas for a Novel Approach

  • Paolo Bocchini
  • Vasileios Christou
  • Manuel J. Miranda
Chapter

Abstract

The modeling of multiple hazards for regional risk assessment has attracted increasing interest during the last years, and several methods have been developed. Traditional hazard maps concisely present the probabilistic frequency and magnitude of natural hazards. However, these maps have been developed for the analysis of individual sites. Instead, the probabilistic risk assessment for spatially distributed systems is a much more complex problem, and it requires more information than what is provided by traditional hazard maps. Engineering problems dealing with interdependent systems, such as lifeline risk assessment or regional loss estimation, are highly coupled, and thus it is necessary to know the probability of having simultaneously certain values of the intensity measure (e.g., peak ground acceleration) at all locations of interest. Therefore, the problem of quantifying and modeling the spatial correlation between pairs of geographically distributed points has been addressed in several different ways. In this chapter, a brief review of some of these approaches is provided. Then, a new methodology is presented for the generation of an optimal set of maps, representing the intensity measure of a natural disaster over a region. This methodology treats the intensity measures as two-dimensional, non-homogeneous, non-Gaussian random fields. Thus, it can take advantage of probabilistic tools for the optimal sampling of multidimensional stochastic functions. Even with few sample maps generated in this way, it is possible to capture accurately the hazard at all individual sites, as well as the spatial correlation among the disaster intensities at the various locations. The framework of random field theory enables a very elegant formulation of the problem, which can be applied to all types of hazards with minimal adjustments. This makes the proposed methodology particularly appropriate for multi-hazard analysis.

Keywords

Spatial Correlation Peak Ground Acceleration Storm Surge Hazard Curve Functional Quantization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Abrahamson, N. A., & Silva, W. J. (1997). “Empirical response spectral attenuation relations for shallow crustal earthquakes.” Seismological Research Letters, 68(1), 94–127.CrossRefGoogle Scholar
  2. Apivatanagul, P., Davidson, R., Blanton, B., & Nozick, L. (2011). “Long-term regional hurricane hazard analysis for wind and storm surge.” Coastal Engineering, 58(6), 499–509.CrossRefGoogle Scholar
  3. Bocchini, P., Frangopol, D., Ummenhofer, T., & Zinke, T. (2014). “Resilience and sustainability of civil infrastructure: Toward a unified approach.” ASCE Journal of Infrastructure Systems, 20(2), 04014004.CrossRefGoogle Scholar
  4. Bocchini, P., & Frangopol, D. M. (2011a). “Generalized bridge network performance analysis with correlation and time-variant reliability.” Structural Safety, 33(2), 155–164.Google Scholar
  5. Bocchini, P., & Frangopol, D. M. (2011b). “A stochastic computational framework for the joint transportation network fragility analysis and traffic flow distribution under extreme events.” Probabilistic Engineering Mechanics, 26(2), 182–193.Google Scholar
  6. Bocchini, P., & Frangopol, D. M. (2012). “Restoration of bridge networks after an earthquake: multi-criteria intervention optimization.” Earthquake Spectra, 28(2), 426–455.CrossRefGoogle Scholar
  7. Bocchini, P., Miranda, M. J., & Christou, V. (2014). “Functional quantization of probabilistic life-cycle performance models.” In H. Furuta, D. M. Frangopol, & M. Akiyama (Eds.), Life-Cycle of Structural Systems: Design, Assessment, Maintenance and Management (pp. 816–823). Tokyo, Japan: Taylor and Francis.Google Scholar
  8. Boore, M. D., & Atkison, M., G. (2008). “Ground-motion prediction equations for the average horizontal component of PGA, PGV, and 5%-damped PSA at spectral periods between 0.01s and 10.0s.” Earthquake Spectra, 24(1), 99–138.Google Scholar
  9. Bucher, C. (2009). Computational Analysis of Randomness in Structural Mechanics. Balkema: CRC Press. Leiden, The Netherlands: Taylor & Francis.Google Scholar
  10. Campbell, K., & Seligson, H. (2003). “Quantitative method for developing hazard-consistent earthquake scenarios.” Advancing Mitigation Technologies and Disaster Response for Lifeline Systems, 829–838.Google Scholar
  11. Chang, E. S., Shinozuka, M., & Moore, E., J. (2000). “Probabilistic earthquake scenarios: Extending risk analysis methodologies to spatially distributed systems.” Earthquake Spectra, 16(3), 557–572.Google Scholar
  12. Christou, V., & Bocchini, P. (2015). “Efficient computational models for the optimal representation of correlated regional hazard.” In Proceedings of the 12th International Conference on Applications of Statistics and Probability in Civil Engineering (pp. 1–8), Vancouver, Canada, July 12–15.Google Scholar
  13. Christou, V., Bocchini, P., & Miranda, M. J. (2016). “Optimal representation of multi-dimensional random fields with a moderate number of samples: application to stochastic mechanics.” Probabilistic Engineering Mechanics, Elsevier, in press. DOI:  10.1016/j.probengmech.2015.09.016.
  14. Crowley, H., & Bommer, J. J. (2006). “Modelling seismic hazard in earthquake loss models with spatially distributed exposure.” Bulletin of Earthquake Engineering, 4, 249–273.CrossRefGoogle Scholar
  15. Decò, A., Bocchini, P., & Frangopol, D. M. (2013). “A probabilistic approach for the prediction of seismic resilience of bridges.” Earthquake Engineering & Structural Dynamics, 42(10), 1469–1487.CrossRefGoogle Scholar
  16. DHS. (2003). In HAZUS-MH MR4 Earthquake Model Technical Manual. Department of Homeland Security; Emergency Preparedness and Response Directorate; Whashington, D.C.: Federal Emergency Management Agency; Mitigation Division.Google Scholar
  17. Emanuel, K., Ravela, S., Vivant, E., & Risi, C. (2006). “A statistical deterministic approach to hurricane risk assessment.” Bulletin of the American Meteorological Society, 87(3), 299–314.CrossRefGoogle Scholar
  18. Gardoni, P., Mosalam, K., & Der Kiureghian, A. (2003). “Probabilistic seismic demand models and fragility estimates for rc bridges.” Journal of Earthquake Engineering, 7, 79–106.Google Scholar
  19. Ghanem, R., & Spanos, P. D. (2003). Stochastic finite elements: a spectral approach, revised edition. New York: Dover.Google Scholar
  20. Grigoriu, M. (2009). “Reduced order models for random functions. Application to stochastic problems.” Applied Mathematical Modelling, 33(1), 161–175.MathSciNetCrossRefzbMATHGoogle Scholar
  21. Han, Y., & Davidson, R. A. (2012). “Probabilistic seismic hazard analysis for spatially distributed infrastructure.” Earthquake Engineering & Structural Dynamics, 41, 2141–2158.Google Scholar
  22. Jayaram, N., & Baker, J. W. (2009). “Correlation model for spatially distributed ground-motion intensities.” Earthquake Engineering & Structural Dynamics, 38, 1687–1708.CrossRefGoogle Scholar
  23. Jayaram, N., & Baker, J. W. (2010). “Efficient sampling and data reduction techniques for probabilistic seismic lifeline risk assessment.” Earthquake Engineering & Structural Dynamics, 39, 1109–1131.Google Scholar
  24. Ju, L., Du, Q., & Gunzburger, M. (2002). “Probabilistic methods for centroidal Voronoi tessellations and their parallel implementations.” Parallel Computing, 28(10), 1477–1500.MathSciNetCrossRefzbMATHGoogle Scholar
  25. Kiremidjian, S. A., Stergiou, E., & Lee, R. (2007). “Issues in seismic risk assessment of transportation networks.” In K. D. Pitilakis (Ed.), Earthquake Geotechnical Engineering (pp. 461–480). Netherlands: Springer.CrossRefGoogle Scholar
  26. Lee, R. G., & Kiremidjian, A. S. (2007). “Uncertainty and correlation in seismic risk assessment of transportation systems.” Technical Report 2007/05, Pacific Earthquake Engineering Research Center (PEER).Google Scholar
  27. Legg, R. M., Nozick k. L., & Davidson, A. R. (2010). “Optimizing the selection of hazard-consistent probabilistic scenarios for long-term regional hurricane loss estimation.” Structural Safety, 32(1), 90–100.Google Scholar
  28. Luschgy, H., & Pagès, G. (2002). “Functional quantization of Gaussian processes.” Journal of Functional Analysis, 196(2), 486–531.MathSciNetCrossRefzbMATHGoogle Scholar
  29. Luschgy, H., & Pagès, G. (2004). “Sharp asymptotics of the functional quantization problem for Gaussian processes.” The Annals of Probability, 32(2), 1574–1599.MathSciNetCrossRefzbMATHGoogle Scholar
  30. McGuire, K. R. (2004). Seismic hazard and risk analysis. Oakland, CA: Earthquake Engineering Research Institute.Google Scholar
  31. Miranda, M., & Bocchini, P. (2012). “Mean square optimal approximation of random processes using functional quantization.” In Proceedings of the 2012 Joint Conference of the Engineering Mechanics Institute and the 11th ASCE Joint Specialty Conference on Probabilistic Mechanics and Structural Reliability. Notre Dame, IN, June 17–20, 2012.Google Scholar
  32. Miranda, M. J., & Bocchini, P. (2013). “Functional quantization of stationary gaussian and non-gaussian random processes.” In G. Deodatis, B. R. Ellingwood, & D. M. Frangopol (Eds.), Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures (pp. 2785–2792). New York, NY: Columbia University, CRC Press, Taylor and Francis Group.Google Scholar
  33. Miranda, M. J., & Bocchini, P. (2015). “A versatile technique for the optimal approximation of random processes by functional quantization.” Applied Mathematics and Computation, Elsevier, 271, 935–958.MathSciNetCrossRefGoogle Scholar
  34. Moghtaderi-Zadeh, M., & Kiureghian, A. D. (1983). “Reliability upgrading of lifeline networks for post-earthquake serviceability.” Earthquake Engineering & Structural Dynamics, 11, 557–566.CrossRefGoogle Scholar
  35. Saydam, D., Bocchini, P., & Frangopol, D. M. (2013). “Time-dependent risk associated with deterioration of highway bridge networks.” Engineering Structures, 54, 221–233.CrossRefGoogle Scholar
  36. Stefanou, G. (2009). “The stochastic finite element method: past, present and future.” Computer Methods in Applied Mechanics and Engineering, 198(9–12), 1031–1051.CrossRefzbMATHGoogle Scholar
  37. Vaziri, P., Davidson, R., Apivatanagul, P., & Nozick, L. (2012). “Identification of optimization-based probabilistic earthquake scenarios for regional loss estimation.” Journal of Earthquake Engineering, 16, 296–315.CrossRefGoogle Scholar
  38. Vickery, P., Masters, F., Powell, M., & Wadhera, D. (2009). “Hurricane hazard modeling: The past, present, and future.” Journal of Wind Engineering and Industrial Aerodynamics, 97, 392–405.CrossRefGoogle Scholar
  39. Vickery, P., & Twisdale, L. (1995a). “Prediction of hurricane wind speeds in the united states.” Journal of Structural Engineering, 121(11), 1691–1699.Google Scholar
  40. Vickery, P., & Twisdale, L. (1995b). “Wind-field and filling models for hurricane wind-speed predictions.” Journal of Structural Engineering, 121(11), 1700–1709.Google Scholar
  41. Vickery, P. J., & Blanton, B. O. (2008). “North carolina coastal flood analysis system hurricane parameter development.” Technical report, Renaissance Computing Technical Report TR-08-06. University of North Carolina at Chapel Hill, North Carolina.Google Scholar
  42. Vickery, P. J., Skerlj, P. F., Steckley, A. C., & Twisdale, L. A. (2000). “Hurricane wind field model for use in hurricane simulations.” Journal of Structural Engineering, 126(10), 1203–1221.CrossRefGoogle Scholar
  43. Vickery, P. J., Skerlj, P. F., & Twisdale, L. A. (2000). “Simulation of hurricane risk in the U.S. using empirical track model.” Journal of Structural Engineering, 126(10), 1222–1237.CrossRefGoogle Scholar
  44. Westerink, J. J., Luettich, R. A., Feyen, J. C., Atkinson, J. H., Dawson, C., Roberts, H. J., et al. (2008) “A basin- to channel-scale unstructured grid hurricane storm surge model applied to southern louisiana.” Monthly Weather Review, 136(10), 833–864.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Paolo Bocchini
    • 1
  • Vasileios Christou
    • 1
  • Manuel J. Miranda
    • 2
  1. 1.Advanced Technology for Large Structural Systems (ATLSS) Engineering Research Center, Department of Civil and Environmental EngineeringLehigh UniversityBethlehemUSA
  2. 2.Department of Engineering, 200D Weed HallHofstra UniversityHempsteadUSA

Personalised recommendations