Steel bridge structures are the fundamental of transport infrastructure. In nature, steel bridge structures’ performance will decrease over time by many reasons. Bridge maintenance is essential requirement. The life extension of the bridges not only makes the large economic profit but also relieves the financial issue on asset management. Bridge maintenance is carried out to extend the life of the structure and to ensure that it functions as designed. One of challenges in bridge maintenance comes from uncertainty factors which make it difficult to get an accurate prediction of bridge behavior and performance of bridge structures. Therefore, the time-variant reliability model in bridge maintenance is needed. There are several techniques to penetrate the time-variant reliability such as iterative procedure; sampling techniques or Monte Carlo Simulation… This research presents another method called probability density evolution method (PDEM) to solve this issue. PDEM has been researched and developed recently, started with the idea of physical stochastic systems. In general, time-variant reliability model could be treated as a stochastic system. From application of PDEM in generic stochastic system, the probability density function of time-variant reliability in reliability model will be captured. A case study is considered to apply PDEM. Lastly, to fulfillment the problem Stochastic Optimization (PDEM combines with Particle Swarm Optimization algorithm) with uncertainties is used to optimize the maintenance cost by using the result from time-variant reliability as a constraint.

Steel bridge structures are the fundamental of transport infrastructure. In nature, steel bridge structures’ performance will decrease over time by many reasons. Bridge maintenance is essential requirement. The life extension of the bridges not only makes the large economic profit but also relieves the financial issue on asset management. Bridge maintenance is carried out to extend the life of the structure and to ensure that it functions as designed. One of challenges in bridge maintenance comes from uncertainty factors which make it difficult to get an accurate prediction of bridge behavior and performance of bridge structures. Therefore, the time-variant reliability model in bridge maintenance is needed. There are several techniques to penetrate the time-variant reliability such as iterative procedure; sampling techniques or Monte Carlo Simulation… This research presents another method called probability density evolution method (PDEM) to solve this issue. PDEM has been researched and developed recently, started with the idea of physical stochastic systems. In general, time-variant reliability model could be treated as a stochastic system. From application of PDEM in generic stochastic system, the probability density function of time-variant reliability in reliability model will be captured. A case study is considered to apply PDEM. Lastly, to fulfillment the problem Stochastic Optimization (PDEM combines with Particle Swarm Optimization algorithm) with uncertainties is used to optimize the maintenance cost by using the result from time-variant reliability as a constraint.

AASHTO (2010). "LRFD Bridge Design Specifications " American Association of Satate Highway and Transportation Officials (AASHTO) Fifth Edition.
Abdelaziz, F. B. (2012). "Solution approaches for the multiobjective stochastic programming." European Journal of Operational Research 216(1): 1-16.
Ahmed, S., A. J. King, et al. (2003). "A Multi-Stage Stochastic Integer Programming Approach for Capacity Expansion under Uncertainty." J. of Global Optimization 26(1): 3-24.
Chen, J.-B., R. Ghanem, et al. (2009). "Partition of the probability-assigned space in probability density evolution analysis of nonlinear stochastic structures." Probabilistic Engineering Mechanics 24(1): 27-42.
Chen, J.-B. and J. Li (2008). "Strategy for selecting representative points via tangent spheres in the probability density evolution method." International Journal for Numerical Methods in Engineering 74(13): 1988-2014.
Christian, J. and G. Baecher (1999). "Point-Estimate Method as Numerical Quadrature." Journal of Geotechnical and Geoenvironmental Engineering 125(9): 779-786.
Czarnecki, A. A. and A. S. Nowak (2008). "Time-variant reliability profiles for steel girder bridges." Structural Safety 30(1): 49-64.
Diwekar, U. M. R., Edward S.; Frey, H.Christopher (1997). "Optimal design of advanced power systems under uncertainty." Energy conversion and management Vol. 38.
Enright, M. P. and D. M. Frangopol (1998). "Probabilistic analysis of resistance degradation of reinforced concrete bridge beams under corrosion." Engineering Structures 20(11): 960-971.
Estes, A. (1997). "A system reliability approach to the lifetime optimization of inspection and repair of highway bridges."
Estes, A. and D. Frangopol (1999). "Repair Optimization of Highway Bridges Using System Reliability Approach." Journal of Structural Engineering 125(7): 766-775.
Estes, A. and D. Frangopol (2003). "Updating Bridge Reliability Based on Bridge Management Systems Visual Inspection Results." Journal of Bridge Engineering 8(6): 374-382.
Ghosn, M. and F. Moses (1986). "RELIABILITY CALIBRATION OF BRIDGE DESIGN CODE." Journal of structural engineering New York, N.Y. 112(4): 745-763.
Kayser, J. R. and A. S. Nowak (1989). "Reliability of corroded steel girder bridges." Structural Safety 6(1): 53-63.
Li, J. and J.-B. Chen (2006). "The dimension-reduction strategy via mapping for probability density evolution analysis of nonlinear stochastic systems." Probabilistic Engineering Mechanics 21(4): 442-453.
Li, J. and J.-B. Chen (2006). "The probability density evolution method for dynamic response analysis of non-linear stochastic structures." International Journal for Numerical Methods in Engineering 65(6): 882-903.
Li, J., J.-b. Chen, et al. (2007). "The equivalent extreme-value event and evaluation of the structural system reliability." Structural Safety 29(2): 112-131.
Li, J. and J. Chen (2008). "The principle of preservation of probability and the generalized density evolution equation." Structural Safety 30(1): 65-77.
Li, J., J. Chen, et al. (2012). "Advances of the probability density evolution method for nonlinear stochastic systems." Probabilistic Engineering Mechanics 28(0): 132-142.
Li, J. and J. B. Chen (2004). "Probability density evolution method for dynamic response analysis of structures with uncertain parameters." Computational Mechanics 34(5): 400-409.
Li J, C. J. (2009). "Stochastic dynamics of structures.".
Naeemi, P. A. A. H. (1984). "Performance of Weathering Steel in Bridges." National Cooperative Highway Research Program Report 272.
Nowak, A. S. (1993). "Live load model for highway bridges." Structural Safety 13(1–2): 53-66.
Nowak, A. S. a. K. R. C. (2000). "Reliability of Structures."
Rockafellar, R. T. and R. J.-B. Wets (1991). "Scenarios and policy aggregation in optimization under uncertainty." Math. Oper. Res. 16(1): 119-147.
Ruszczyński, A. and A. Shapiro (2003). Stochastic Programming Models. Handbooks in Operations Research and Management Science. A. Ruszczynski and A. Shapiro, Elsevier. Volume 10: 1-64.
Shapiro, A. and T. Homem-de-Mello (1998). "A simulation-based approach to two-stage stochastic programming with recourse." Math. Program. 81(3): 301-325.
Shapiro, A. and Y. Wardi (1996). "Convergence analysis of gradient descent stochastic algorithms." Journal of Optimization Theory and Applications 91(2): 439-454.
So, K. K. L., M. M. S. Cheung, et al. (2012). "Life-Cycle Management Strategy on Steel Girders in Bridges." Advances in Civil Engineering 2012: 14.
Szerszen, M. M., A. S. Nowak, et al. (1999). "Fatigue reliability of steel bridges." Journal of Constructional Steel Research 52(1): 83-92.
Tabsh, S. and A. Nowak (1991). "Reliability of Highway Girder Bridges." Journal of Structural Engineering 117(8): 2372-2388.
Wang, J.-P. and D. Huang (2012). "RosenPoint: A Microsoft Excel-based program for the Rosenblueth point estimate method and an application in slope stability analysis." Computers & Geosciences 48(0): 239-243.