pith. sign in

arxiv: 2604.23068 · v1 · submitted 2026-04-24 · 📡 eess.SY · cs.CE· cs.NA· cs.SY· math.NA

Probabilistic Hazard Analysis Framework with Stochastic Optimal Control for Deteriorating Civil Infrastructure Systems

Sudhir P. Jodha , Konstantinos G. Papakonstantinou This is my paper

Pith reviewed 2026-05-08 10:21 UTC · model grok-4.3

classification 📡 eess.SY cs.CEcs.NAcs.SYmath.NA
keywords probabilistic hazard analysisstochastic optimal controldeteriorating civil infrastructureMarkov decision processKronecker producttensor decompositionlife-cycle optimizationseismic loss estimation
0
0 comments X

The pith

A tensor-based method with Kronecker-factored transition dynamics solves exact optimal maintenance for multi-component infrastructure systems at linear complexity.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a framework for life-cycle cost optimization of civil infrastructure under hazard risks and deterioration by modeling it as a Markov decision process. Transition matrices are derived to capture time-variant deterioration, hazards, and fragilities. The key innovation is a tensor method that factors these transitions using Kronecker products, allowing the dynamic programming solution to scale linearly rather than exponentially with the number of system components. A sympathetic reader would care because this makes it feasible to compute optimal, adaptive maintenance strategies for realistic large-scale infrastructure without losing optimality.

Core claim

The paper claims that exploiting Kronecker-factored transition dynamics in a tensor-based formulation reduces the computational complexity of solving the system-level Markov decision process from exponential to linear in the number of components, while preserving exact, global dynamic programming solutions for probabilistic hazard and deterioration management.

What carries the argument

Kronecker-factored transition dynamics in tensor decomposition of the MDP transition kernel, which enables the factoring of the multi-dimensional state space and value function updates.

If this is right

  • Optimal policies for maintenance and repair can be obtained exactly for systems with many components.
  • The approach integrates PBEE with stochastic control for nonstationary processes.
  • Decision-makers gain a practical tool for cost-effective risk mitigation across various hazard types.
  • The framework remains versatile for different infrastructure types and hazard models.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar Kronecker methods could apply to other large-scale stochastic control problems in networked systems like power grids or transportation networks.
  • Combining this with real-time data assimilation from structural health monitoring could lead to online adaptive policies.
  • Verification on benchmark systems with known small-scale solutions would confirm the exactness for larger cases.

Load-bearing premise

The derived transition matrices accurately capture the combined effects of time-variant deterioration, hazard risks, and state-dependent fragility, and the MDP formulation sufficiently represents the real-world decision dynamics.

What would settle it

For a small number of components where full dynamic programming is tractable, compare the optimal value functions and policies from the tensor method against those from standard enumeration of the joint state space; any discrepancy would falsify the exactness claim.

Figures

Figures reproduced from arXiv: 2604.23068 by Konstantinos G. Papakonstantinou, Sudhir P. Jodha.

Figure 1
Figure 1. Figure 1: Conceptual illustration of risk evolution under three hazard analysis and maintenance view at source ↗
Figure 2
Figure 2. Figure 2: Seismic hazard curve for a specific site, based on data from the U.S. Geological Survey view at source ↗
Figure 3
Figure 3. Figure 3: Simulated trajectories of the nonstationary gamma process for section loss due to corrosion. view at source ↗
Figure 4
Figure 4. Figure 4: Flowchart of the structural simulation workflow for comprehensive performance assessment. view at source ↗
Figure 5
Figure 5. Figure 5: Dynamic Bayesian Network (DBN) for the state-dependent generalized fragility model. view at source ↗
Figure 6
Figure 6. Figure 6: Computational complexity comparison for a homogeneous system with view at source ↗
Figure 7
Figure 7. Figure 7: Location and dependency of three infrastructure nodes. (a) The geographical location of view at source ↗
Figure 8
Figure 8. Figure 8: IM-conditional state transition probability matrix showing the probability of transitioning view at source ↗
Figure 9
Figure 9. Figure 9: State-dependent fragility plots for a component with initial corrosion damage state view at source ↗
Figure 10
Figure 10. Figure 10: Sample life-cycle realizations showing maintenance actions, CDS, and SDS over 50 years view at source ↗
Figure 11
Figure 11. Figure 11: Variation of probability of failure over time for all nodes. The red curves represent the view at source ↗
Figure 12
Figure 12. Figure 12: Sample trajectories of system-level risk evolution over 50 years under the optimal policy. view at source ↗
Figure 13
Figure 13. Figure 13: Annual exceedance probability (AEP) vs. economic loss for different management policies. view at source ↗
Figure 14
Figure 14. Figure 14: Comparison of total life-cycle costs, including maintenance/repair (M/R) costs and risk view at source ↗
read the original abstract

The safety and resilience of civil infrastructure systems are increasingly threatened by compounded risks from various hazard events and structural deterioration due to environmental stressors. This study presents a comprehensive risk-informed, life-cycle optimization framework that extends the Performance-Based Earthquake Engineering (PBEE) and probabilistic seismic loss estimation paradigms by combining hazard uncertainties, nonstationary deterioration, structural damage accumulation, and state-dependent fragility assessments, with optimal, adaptive maintenance strategies in time. The life-cycle cost optimization is formulated in this work as a Markov Decision Process (MDP) problem, utilizing derived, transition matrices reflecting time-variant deterioration effects and hazard risks. To mitigate the curse of dimensionality in system-level optimization, a novel tensor-based method exploiting Kronecker-factored transition dynamics is introduced, reducing complexity from exponential to linear in the number of components while still preserving exact, global dynamic programming solutions. Overall, the framework is general and versatile, able to accommodate various hazard types. A seismic hazard application is, however, demonstrated and explained in detail in this work. The developed methodology eventually provides decision-makers with a practical, data-driven tool toward cost effective risk mitigation of civil infrastructure systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The paper proposes a comprehensive risk-informed life-cycle optimization framework for deteriorating civil infrastructure systems. It extends Performance-Based Earthquake Engineering (PBEE) by incorporating nonstationary deterioration, hazard uncertainties, state-dependent fragility, and formulates optimal adaptive maintenance as a Markov Decision Process (MDP) using derived transition matrices. A novel tensor-based method is introduced that exploits Kronecker-factored transition dynamics to reduce complexity from exponential to linear in the number of components while claiming to preserve exact, global dynamic programming solutions. The framework is presented as general for various hazards, with a detailed seismic application.

Significance. If the exactness of the Kronecker factorization is rigorously shown to hold, the work would offer a valuable advance in scalable exact optimization for multi-component infrastructure systems, where standard MDP approaches are intractable. The integration of time-variant deterioration with adaptive strategies under probabilistic hazards addresses a practical gap in resilience planning and could support data-driven decision tools.

major comments (1)
  1. [Tensor-based method and transition dynamics description] The load-bearing claim is that the joint transition matrix exactly equals the Kronecker product of per-component matrices (P = P1 ⊗ P2 ⊗ … ⊗ Pn), enabling exact DP in linear time. Shared hazards and state-dependent fragility induce simultaneous correlated damage across components, so the joint probabilities are not separable. The manuscript must explicitly derive (in the tensor-based method section) how the common hazard random variable is absorbed into the factorization or whether the state is augmented to restore exact separability; absent this, the 'exact' guarantee and complexity reduction become approximate rather than exact.
minor comments (1)
  1. [Abstract] The abstract asserts 'exact, global dynamic programming solutions' and 'linear scaling' without referencing any numerical validation, error bounds, or comparison to brute-force DP on small systems; adding a brief statement on these in the abstract or introduction would improve clarity.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed and constructive review. The major comment identifies a key point requiring greater mathematical clarity in the tensor-based method. We address this below and will revise the manuscript to include an explicit derivation.

read point-by-point responses

  1. Referee: The load-bearing claim is that the joint transition matrix exactly equals the Kronecker product of per-component matrices (P = P1 ⊗ P2 ⊗ … ⊗ Pn), enabling exact DP in linear time. Shared hazards and state-dependent fragility induce simultaneous correlated damage across components, so the joint probabilities are not separable. The manuscript must explicitly derive (in the tensor-based method section) how the common hazard random variable is absorbed into the factorization or whether the state is augmented to restore exact separability; absent this, the 'exact' guarantee and complexity reduction become approximate rather than exact.

    Authors: We appreciate the referee drawing attention to this foundational aspect of the method. The per-component transition matrices are defined conditionally on a realized hazard intensity. Given the hazard, component damages are conditionally independent, so the conditional joint transition matrix is exactly the Kronecker product of the individual conditional matrices. The unconditional joint transition is therefore the expectation (integral or finite sum over a discretized hazard measure) of this Kronecker product. Because the Kronecker product is multilinear, the expectation yields a finite sum of Kronecker products, each weighted by the hazard probability mass. This representation is exact—no approximation is introduced—and permits the Bellman operator to be applied via tensor contractions whose cost scales linearly with the number of components (plus a small constant factor equal to the number of hazard bins). The common hazard is thereby absorbed through the outer expectation rather than by state augmentation. We acknowledge that the manuscript did not present this derivation with sufficient explicitness in the tensor-based method section. In the revision we will add a dedicated subsection containing the full mathematical steps, including the interchange of expectation and Kronecker product and the resulting complexity analysis, to make the exactness transparent. revision: yes

Circularity Check

0 steps flagged

No circularity in derivation chain

full rationale

The paper formulates life-cycle optimization as an MDP using derived transition matrices that incorporate time-variant deterioration, hazard risks, and state-dependent fragility, then introduces a tensor-based Kronecker factorization to reduce complexity while claiming exact global DP solutions. No load-bearing step reduces by construction to its own inputs: the transition matrices are presented as derived from the combined effects rather than fitted or renamed from the target result, the factorization is introduced as a novel computational device without self-definitional equivalence, and no self-citation chain is invoked to justify uniqueness or the exactness guarantee. The approach extends established PBEE and MDP concepts with an independent algorithmic contribution, remaining self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Review based solely on abstract; full paper would be needed to audit exact parameters and assumptions. The framework rests on standard MDP and deterioration modeling assumptions.

free parameters (1)
  • deterioration rates and fragility parameters
    These are typically estimated from data or models but not specified in the abstract.
axioms (1)
  • domain assumption The infrastructure system dynamics satisfy the Markov property and can be represented via time-variant transition matrices
    Invoked when formulating the life-cycle optimization as an MDP problem.

pith-pipeline@v0.9.0 · 5518 in / 1235 out tokens · 48802 ms · 2026-05-08T10:21:07.150051+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

98 extracted references · 73 canonical work pages

  1. [1]

    rep., American Society of Civil Engineers, Reston, VA (2025)

    American Society of Civil Engineers, 2025 report card for America’s infrastructure, Tech. rep., American Society of Civil Engineers, Reston, VA (2025). URLhttps://infrastructurereportcard.org/

    2025

  2. [2]

    rep., ASCE, Reston, VA (2021)

    American Society of Civil Engineers, A comprehensive assessment of America’s infrastructure, Tech. rep., ASCE, Reston, VA (2021)

    2021

  3. [3]

    rep., ASCE, Reston, VA (2021)

    American Society of Civil Engineers, Failure to act: Economic impacts of status quo investment across infrastructure systems, Tech. rep., ASCE, Reston, VA (2021)

    2021

  4. [4]

    P. C. Milly, J. Betancourt, M. Falkenmark, R. M. Hirsch, Z. W. Kundzewicz, D. P. Lettenmaier, R. J. Stouffer, Stationarity is dead: Whither water management?, Science 319 (5863) (2008) 573–574. doi:10.1126/science. 1151915

    work page doi:10.1126/science 2008

  5. [5]

    Bender, D

    R. Bender, D. F´ eron, D. Mills, S. Ritter, R. B¨ aßler, D. Bettge, I. De Graeve, A. Dugstad, S. Grassini, T. Hack, Corrosion challenges towards a sustainable society, Materials and Corrosion 73 (11) (2022) 1730–1751. doi:10.1002/maco.202213140

    work page doi:10.1002/maco.202213140 2022

  6. [6]

    X. Wang, M. G. Stewart, M. Nguyen, Impact of climate change on corrosion and damage to concrete infrastructure in Australia, Climatic Change 110 (3) (2012) 941–957.doi:10.1007/s10584-011-0124-7

    work page doi:10.1007/s10584-011-0124-7 2012

  7. [7]

    M. G. Stewart, X. Wang, M. N. Nguyen, Climate change impact and risks of concrete infrastructure deterioration, Engineering Structures 33 (4) (2011) 1326–1337.doi:10.1016/j.engstruct.2011.01.010

    work page doi:10.1016/j.engstruct.2011.01.010 2011

  8. [8]

    M. N. Nguyen, X. Wang, R. Leicester, An assessment of climate change effects on atmospheric corrosion rates of steel structures, Corrosion Engineering, Science and Technology 48 (5) (2013) 359–369. doi:10.1179/ 1743278213Y.0000000087

    2013

  9. [9]

    M. L. Sousa, Expected implications of climate change on the corrosion of structures, Ph.D. thesis, Joint Research Centre, Ispra, Italy (2020).doi:10.2760/05229. 26

    work page doi:10.2760/05229 2020

  10. [10]

    M. A. Bender, T. R. Knutson, R. E. Tuleya, J. J. Sirutis, G. A. Vecchi, S. T. Garner, I. M. Held, Modeled impact of anthropogenic warming on the frequency of intense Atlantic hurricanes, Science 327 (5964) (2010) 454–458.doi:10.1126/science.1180568

    work page doi:10.1126/science.1180568 2010

  11. [12]

    Barone, D

    G. Barone, D. M. Frangopol, M. Soliman, Optimization of life-cycle maintenance of deteriorating bridges with respect to expected annual system failure rate and expected cumulative cost, Journal of Structural Engineering 140 (2) (2014) 04013043.doi:10.1061/(ASCE)ST.1943-541X.0000812

    work page doi:10.1061/(asce)st.1943-541x.0000812 2014

  12. [13]

    V. H. S. de Abreu, A. S. Santos, T. G. M. Monteiro, Climate change impacts on the road transport infrastructure: A systematic review on adaptation measures, Sustainability 14 (14) (2022) 8864.doi:10.3390/su14148864

    work page doi:10.3390/su14148864 2022

  13. [14]

    D. M. Frangopol, M. Liu, M. Akiyama, D. Y. Yang, K. G. Papakonstantinou, K. Hass, M. G. Stewart, F. Biondini, M. Ghosn, S. Bianchi, G. Fiorillo, A. S. Kiremidjian, J. Y. Lee, A. Shafieezadeh, P. G. Morato, Life-cycle risk-based decision-making in a changing climate, in: F. Biondini, Z. Lounis, M. Ghosn (Eds.), Effects of Climate Change on Life-Cycle Perfo...

    work page doi:10.1061/9780784485804.ch4 2024

  14. [15]

    Moehle, G

    J. Moehle, G. G. Deierlein, A framework methodology for performance-based earthquake engineering, in: Proceedings of the 13th World Conference on Earthquake Engineering, Vol. 679, IAEE, Vancouver, Canada, 2004, p. 12

    2004

  15. [16]

    Krawinkler, Van Nuys hotel building testbed report: Exercising seismic performance assessment, Tech

    H. Krawinkler, Van Nuys hotel building testbed report: Exercising seismic performance assessment, Tech. Rep. PEER 2005/11, Pacific Earthquake Engineering Research (PEER) Center, Berkeley, CA (2005)

    2005

  16. [17]

    K. A. Porter, An overview of PEER’s performance-based earthquake engineering methodology, in: Proceedings of the 9th International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP9), San Francisco, CA, 2003, pp. 3729–3735

    2003

  17. [18]

    G¨ unay, K

    S. G¨ unay, K. M. Mosalam, PEER performance-based earthquake engineering methodology, revisited, Journal of Earthquake Engineering 17 (6) (2013) 829–858.doi:10.1080/13632469.2013.787377

    work page doi:10.1080/13632469.2013.787377 2013

  18. [19]

    T. Yang, J. Moehle, B. Stojadinovic, A. Der Kiureghian, Seismic performance evaluation of facilities: Methodology and implementation, Journal of Structural Engineering 135 (10) (2009) 1146–1154. doi:10.1061/(ASCE) 0733-9445(2009)135:10(1146)

    work page doi:10.1061/(asce 2009

  19. [20]

    Gardoni, A

    P. Gardoni, A. Der Kiureghian, K. M. Mosalam, Probabilistic capacity models and fragility estimates for reinforced concrete columns based on experimental observations, Journal of Engineering Mechanics 128 (10) (2002) 1024–1038.doi:10.1061/(ASCE)0733-9399(2002)128:10(1024)

    work page doi:10.1061/(asce)0733-9399(2002)128:10(1024 2002

  20. [21]

    J. G. S. Castillo, M. Bruneau, N. Elhami-Khorasani, Functionality measures for quantification of building seismic resilience index, Engineering Structures 253 (2022) 113800.doi:10.1016/j.engstruct.2021.113800

    work page doi:10.1016/j.engstruct.2021.113800 2022

  21. [22]

    URLhttps://ascelibrary.org/doi/book/10.1061/9780784485804

    Task Group 2 on Reliability-Based Performance Indicators for Structural Systems, Effects of Climate Change on Life-Cycle Performance of Structures and Infrastructure Systems: Safety, Reliability, and Risk, American Society of Civil Engineers, Reston, VA, 2024.doi:10.1061/9780784485804. URLhttps://ascelibrary.org/doi/book/10.1061/9780784485804

    work page doi:10.1061/9780784485804 2024

  22. [23]

    T. J. Sullivan, D. P. Welch, G. M. Calvi, Simplified seismic performance assessment and implications for seismic design, Earthquake Engineering and Engineering Vibration 13 (Suppl 1) (2014) 95–122. doi:10.1007/ s11803-014-0242-0

    2014

  23. [24]

    Krawinkler, E

    H. Krawinkler, E. Miranda, A perspective of performance-based earthquake engineering, in: Y. Bozorgnia, V. Bertero (Eds.), Earthquake Engineering: From Engineering Seismology to Performance-Based Engineering, CRC Press, Boca Raton, FL, 2004, Ch. 9, p. 87.doi:10.1201/9780203486245

    work page doi:10.1201/9780203486245 2004

  24. [25]

    Ramirez, A

    C. Ramirez, A. Liel, J. Mitrani-Reiser, C. Haselton, A. Spear, J. Steiner, G. Deierlein, E. Miranda, Expected earthquake damage and repair costs in reinforced concrete frame buildings, Earthquake Engineering & Structural Dynamics 41 (11) (2012) 1455–1475.doi:10.1002/eqe.2216

    work page doi:10.1002/eqe.2216 2012

  25. [26]

    Y. Mori, B. R. Ellingwood, Maintaining reliability of concrete structures. I: Role of inspection/repair, Journal of Structural Engineering 120 (3) (1994) 824–845.doi:10.1061/(ASCE)0733-9445(1994)120:3(824)

    work page doi:10.1061/(asce)0733-9445(1994)120:3(824 1994

  26. [27]

    Sanchez-Silva, G.-A

    M. Sanchez-Silva, G.-A. Klutke, D. V. Rosowsky, Life-cycle performance of structures subject to multiple deterioration mechanisms, Structural Safety 33 (3) (2011) 206–217.doi:10.1016/j.strusafe.2011.03.003

    work page doi:10.1016/j.strusafe.2011.03.003 2011

  27. [28]

    Ghosh, J

    J. Ghosh, J. E. Padgett, Aging considerations in the development of time-dependent seismic fragility curves, Journal of Structural Engineering 136 (12) (2010) 1497–1511.doi:10.1061/(ASCE)ST.1943-541X.0000260

    work page doi:10.1061/(asce)st.1943-541x.0000260 2010

  28. [29]

    D. M. Frangopol, Life-cycle performance, management, and optimisation of structural systems under uncertainty: Accomplishments and challenges, Structure and Infrastructure Engineering 7 (6) (2011) 389–413. doi:10.1080/ 15732471003594427

    2011

  29. [30]

    S´ anchez-Silva, D

    M. S´ anchez-Silva, D. M. Frangopol, J. Padgett, M. Soliman, Maintenance and operation of infrastructure systems, Journal of Structural Engineering 142 (9) (2016) F4016004.doi:10.1061/(ASCE)ST.1943-541X.0001543. 27

    work page doi:10.1061/(asce)st.1943-541x.0001543 2016

  30. [31]

    Biondini and D

    F. Biondini, D. M. Frangopol, Life-cycle performance of deteriorating structural systems under uncertainty, Journal of Structural Engineering 142 (9) (2016) F4016001.doi:10.1061/(ASCE)ST.1943-541X.0001544

    work page doi:10.1061/(asce)st.1943-541x.0001544 2016

  31. [32]

    Baker, B

    J. Baker, B. Bradley, P. Stafford, Seismic Hazard and Risk Analysis, Cambridge University Press, 2021. doi:10.1017/9781108425056

    work page doi:10.1017/9781108425056 2021

  32. [33]

    R. K. McGuire, Seismic Hazard and Risk Analysis, Earthquake Engineering Research Institute, Oakland, CA, 2004

    2004

  33. [34]

    Coburn, R

    A. Coburn, R. Spence, Earthquake Protection, 2nd Edition, John Wiley & Sons, Chichester, UK, 2002. doi:10.1002/0470855185

    work page doi:10.1002/0470855185 2002

  34. [35]

    Heresi, E

    P. Heresi, E. Miranda, RPBEE: Performance-based earthquake engineering on a regional scale, Earthquake Spectra 39 (3) (2023) 1328–1351.doi:10.1177/87552930231179491

    work page doi:10.1177/87552930231179491 2023

  35. [36]

    T. La, M. Schoettler, Adaptation of the PBEE Framework: A building block for community resilience models, in: Proceedings of the 17th World Conference on Earthquake Engineering (17WCEE), Sendai, Japan, 2020

    2020

  36. [37]

    G. A. Anwar, M. Z. Akber, H. A. Ahmed, M. Hussain, M. Nawaz, J. Anwar, W.-K. Chan, H.-H. Lee, Life-cycle performance modeling for sustainable and resilient structures under structural degradation: A systematic review, Buildings 14 (10) (2024) 3053.doi:10.3390/buildings14103053

    work page doi:10.3390/buildings14103053 2024

  37. [38]

    B. R. Ellingwood, Y. Mori, Reliability-based service life assessment of concrete structures in nuclear power plants: Optimum inspection and repair, Nuclear Engineering and Design 175 (3) (1997) 247–258. doi: 10.1016/S0029-5493(97)00042-3

    work page doi:10.1016/s0029-5493(97)00042-3 1997

  38. [39]

    G. Jia, P. Gardoni, Stochastic life-cycle analysis and performance optimization of deteriorating engineering systems using state-dependent deterioration stochastic models, in: Routledge Handbook of Sustainable and Resilient Infrastructure, Routledge, 2018, pp. 580–602.doi:10.4324/9781315142074-30

    work page doi:10.4324/9781315142074-30 2018

  39. [40]

    J. M. Van Noortwijk, A survey of the application of Gamma processes in maintenance, Reliability Engineering & System Safety 94 (1) (2009) 2–21.doi:10.1016/j.ress.2007.03.019

    work page doi:10.1016/j.ress.2007.03.019 2009

  40. [41]

    K. G. Papakonstantinou, M. Shinozuka, Probabilistic model for steel corrosion in reinforced concrete structures of large dimensions considering crack effects, Engineering Structures 57 (2013) 306–326. doi:10.1016/j.engstruct. 2013.06.038

    work page doi:10.1016/j.engstruct 2013

  41. [42]

    N. L. Dehghani, E. Fereshtehnejad, A. Shafieezadeh, A Markovian approach to infrastructure life-cycle analysis: Modeling the interplay of hazard effects and recovery, Earthquake Engineering & Structural Dynamics 50 (3) (2021) 736–755.doi:10.1002/eqe.3359

    work page doi:10.1002/eqe.3359 2021

  42. [43]

    Lin, X.-X

    P. Lin, X.-X. Yuan, E. Tovilla, Integrative modeling of performance deterioration and maintenance effectiveness for infrastructure assets with missing condition data, Computer-Aided Civil and Infrastructure Engineering 34 (8) (2019) 677–695.doi:10.1111/mice.12452

    work page doi:10.1111/mice.12452 2019

  43. [44]

    Saydam, P

    D. Saydam, P. Bocchini, D. M. Frangopol, Time-dependent risk associated with deterioration of highway bridge networks, Engineering Structures 54 (2013) 221–233.doi:10.1016/j.engstruct.2013.04.009

    work page doi:10.1016/j.engstruct.2013.04.009 2013

  44. [45]

    D.-E. Choe, P. Gardoni, D. Rosowsky, T. Haukaas, Seismic fragility estimates for reinforced concrete bridges subject to corrosion, Structural Safety 31 (4) (2009) 275–283.doi:10.1016/j.strusafe.2008.10.001

    work page doi:10.1016/j.strusafe.2008.10.001 2009

  45. [46]

    Esteva, O

    L. Esteva, O. J. D´ ıaz-L´ opez, A. V´ asquez, J. A. Le´ on, Structural damage accumulation and control for life cycle optimum seismic performance of buildings, Structure and Infrastructure Engineering 12 (7) (2016) 848–860. doi:10.1080/15732479.2015.1064967

    work page doi:10.1080/15732479.2015.1064967 2016

  46. [47]

    Iervolino, M

    I. Iervolino, M. Giorgio, E. Chioccarelli, Markovian modeling of seismic damage accumulation, Earthquake Engineering & Structural Dynamics 45 (3) (2016) 441–461

    2016

  47. [48]

    C. P. Andriotis, K. G. Papakonstantinou, Extended and generalized fragility functions, Journal of Engineering Mechanics 144 (9) (2018) 04018087.doi:10.1061/(ASCE)EM.1943-7889.0001478

    work page doi:10.1061/(asce)em.1943-7889.0001478 2018

  48. [49]

    Nardin, S

    C. Nardin, S. Marelli, O. S. Bursi, B. Sudret, M. Broccardo, UQ state-dependent framework for seismic fragility assessment of industrial components, Reliability Engineering & System Safety 261 (2025) 111067. doi:10.1016/j.ress.2025.111067

    work page doi:10.1016/j.ress.2025.111067 2025

  49. [51]

    Molaioni, C

    F. Molaioni, C. P. Andriotis, Z. Rinaldi, Life-cycle fragility analysis of aging reinforced concrete bridges: A dynamic Bayesian network approach, Structural Safety (2025) 102654doi:10.1016/j.strusafe.2025.102654

    work page doi:10.1016/j.strusafe.2025.102654 2025

  50. [52]

    Ot´ arola, L

    K. Ot´ arola, L. Iannacone, R. Gentile, C. Galasso, Multi-hazard life-cycle consequence analysis of deteriorating engineering systems, Structural Safety 111 (2024) 102515

    2024

  51. [53]

    Sabatino, D

    S. Sabatino, D. M. Frangopol, Y. Dong, Sustainability-informed maintenance optimization of highway bridges considering multi-attribute utility and risk attitude, Engineering Structures 102 (2015) 310–321. doi:10.1016/ j.engstruct.2015.07.030

    2015

  52. [54]

    Madanat, S

    S. Madanat, S. Park, K. Kuhn, Adaptive optimization and systematic probing of infrastructure system maintenance policies under model uncertainty, Journal of Infrastructure Systems 12 (3) (2006) 192–198. doi:10.1061/(ASCE)1076-0342(2006)12:3(192). 28

    work page doi:10.1061/(asce)1076-0342(2006)12:3(192 2006

  53. [55]

    K. G. Papakonstantinou, M. Shinozuka, Planning structural inspection and maintenance policies via dynamic programming and Markov processes. Part I: Theory, Reliability Engineering & System Safety 130 (2014) 202–213. doi:10.1016/j.ress.2014.04.005

    work page doi:10.1016/j.ress.2014.04.005 2014

  54. [56]

    P. G. Morato, K. G. Papakonstantinou, C. P. Andriotis, J. S. Nielsen, P. Rigo, Optimal inspection and maintenance planning for deteriorating structural components through dynamic Bayesian networks and Markov decision processes, Structural Safety 94 (2022) 102140.doi:10.1016/j.strusafe.2021.102140

    work page doi:10.1016/j.strusafe.2021.102140 2022

  55. [57]

    Luque, D

    J. Luque, D. Straub, Risk-based optimal inspection strategies for structural systems using dynamic Bayesian networks, Structural Safety 76 (2019) 68–80.doi:10.1016/j.strusafe.2018.08.002

    work page doi:10.1016/j.strusafe.2018.08.002 2019

  56. [58]

    Bismut, D

    E. Bismut, D. Straub, Optimal adaptive inspection and maintenance planning for deteriorating structural systems, Structural Safety 93 (2021) 102120.doi:10.1016/j.ress.2021.107891

    work page doi:10.1016/j.ress.2021.107891 2021

  57. [59]

    C. P. Andriotis, K. G. Papakonstantinou, Managing engineering systems with large state and action spaces through deep reinforcement learning, Reliability Engineering & System Safety 191 (2019) 106483. doi:10.1016/ j.ress.2019.04.036

    2019

  58. [60]

    C. P. Andriotis, K. G. Papakonstantinou, Deep reinforcement learning driven inspection and maintenance planning under incomplete information and constraints, Reliability Engineering & System Safety 212 (2021) 107551.doi:10.1016/j.ress.2021.107551

    work page doi:10.1016/j.ress.2021.107551 2021

  59. [61]

    X. Fan, X. Zhang, X. Wang, X. Yu, A deep reinforcement learning model for resilient road network recovery under earthquake or flooding hazards, Journal of Infrastructure Preservation and Resilience 4 (1) (2023) 8. doi:10.1186/s43065-023-00072-x

    work page doi:10.1186/s43065-023-00072-x 2023

  60. [62]

    Saifullah, C

    M. Saifullah, C. P. Andriotis, K. G. Papakonstantinou, S. M. Stoffels, Deep reinforcement learning-based life-cycle management of deteriorating transportation systems, in: Bridge Safety, Maintenance, Management, Life-Cycle, Resilience and Sustainability, CRC Press, 2022, pp. 293–301.doi:10.1201/9781003322641

    work page doi:10.1201/9781003322641 2022

  61. [63]

    arXiv preprint arXiv:2401.12455 , year=

    M. Saifullah, K. G. Papakonstantinou, A. Bhattacharya, S. M. Stoffels, C. P. Andriotis, Multi-agent deep reinforcement learning with centralized training and decentralized execution for transportation infrastructure management, arXiv preprint arXiv:2401.12455 (2026).doi:10.48550/arXiv.2401.12455

    work page doi:10.48550/arxiv.2401.12455 2026

  62. [64]

    P. G. Morato, C. P. Andriotis, K. G. Papakonstantinou, P. Rigo, Inference and dynamic decision-making for deteriorating systems with probabilistic dependencies through Bayesian networks and deep reinforcement learning, Reliability Engineering & System Safety 235 (2023) 109144.doi:10.1016/j.ress.2023.109144

    work page doi:10.1016/j.ress.2023.109144 2023

  63. [65]

    Metwally, C

    Z. Metwally, C. Andriotis, F. Molaioni, Managing aging bridges under seismic hazards through deep reinforcement learning, in: Bridge Maintenance, Safety, Management, Digitalization and Sustainability, CRC Press, 2024, pp. 3405–3413.doi:10.1201/9781003483755

    work page doi:10.1201/9781003483755 2024

  64. [66]

    J. W. Baker, An introduction to probabilistic seismic hazard analysis (PSHA), White paper, Stanford University (2008)

    2008

  65. [67]

    Geological Survey, U.S

    U.S. Geological Survey, U.S. seismic hazard maps and site-specific hazard curves, accessed: April 2026 (2025). URLhttps://earthquake.usgs.gov/hazards/

    2026

  66. [68]

    B. S. Clayton, USGS earthquake hazard toolbox: nshmp-apps (2023).doi:10.5066/P9UAIISF. URLhttps://earthquake.usgs.gov/nshmp/

    work page doi:10.5066/p9uaiisf 2023

  67. [69]

    Goda, H.-P

    K. Goda, H.-P. Hong, Spatial correlation of peak ground motions and response spectra, Bulletin of the Seismological Society of America 98 (1) (2008) 354–365.doi:10.1785/0120070078

    work page doi:10.1785/0120070078 2008

  68. [70]

    Jayaram, J

    N. Jayaram, J. W. Baker, Correlation model for spatially distributed ground-motion intensities, Earthquake Engineering & Structural Dynamics 38 (15) (2009) 1687–1708.doi:10.1002/eqe.922

    work page doi:10.1002/eqe.922 2009

  69. [71]

    Der Kiureghian, P.-L

    A. Der Kiureghian, P.-L. Liu, Structural Reliability under Incomplete Probability Information, Journal of Engineering Mechanics 112 (1) (1986) 85–104.doi:10.1061/(ASCE)0733-9399(1986)112:1(85)

    work page doi:10.1061/(asce)0733-9399(1986)112:1(85 1986

  70. [72]

    Vlachos, K

    C. Vlachos, K. G. Papakonstantinou, G. Deodatis, Predictive model for site specific simulation of ground motions based on earthquake scenarios, Earthquake Engineering & Structural Dynamics 47 (1) (2018) 195–218. doi:10.1002/eqe.2948

    work page doi:10.1002/eqe.2948 2018

  71. [73]

    Mahmoodian, A

    M. Mahmoodian, A. Alani, Modeling deterioration in concrete pipes as a stochastic Gamma process for time- dependent reliability analysis, Journal of Pipeline Systems Engineering and Practice 5 (1) (2014) 04013008. doi:10.1061/(ASCE)PS.1949-1204.0000145

    work page doi:10.1061/(asce)ps.1949-1204.0000145 2014

  72. [74]

    Nettis, A

    A. Nettis, A. Nettis, S. Ruggieri, G. Uva, Corrosion-induced fragility of existing prestressed concrete girder bridges under traffic loads, Engineering Structures 314 (2024) 118302. doi:10.1016/j.engstruct.2024.118302

    work page doi:10.1016/j.engstruct.2024.118302 2024

  73. [75]

    Mazzoni, F

    S. Mazzoni, F. McKenna, M. H. Scott, G. L. Fenves, OpenSees command language manual, Tech. Rep. 264, Pacific Earthquake Engineering Research (PEER) Center, Berkeley, CA (2006)

    2006

  74. [76]

    L. F. Ibarra, R. A. Medina, H. Krawinkler, Hysteretic models that incorporate strength and stiffness deterioration, Earthquake Engineering & Structural Dynamics 34 (12) (2005) 1489–1511.doi:10.1002/eqe.495

    work page doi:10.1002/eqe.495 2005

  75. [77]

    Y.-J. Park, A. H.-S. Ang, Y. K. Wen, Seismic damage analysis of reinforced concrete buildings, Journal of Structural Engineering 111 (4) (1985) 740–757.doi:10.1061/(ASCE)0733-9445(1985)111:4(740)

    work page doi:10.1061/(asce)0733-9445(1985)111:4(740 1985

  76. [78]

    Y. Ma, Y. Che, J. Gong, Behavior of corrosion damaged circular reinforced concrete columns under cyclic loading, Construction and Building Materials 29 (2012) 548–556.doi:10.1016/j.conbuildmat.2011.11.002. 29

    work page doi:10.1016/j.conbuildmat.2011.11.002 2012

  77. [79]

    K. P. Murphy, Dynamic Bayesian networks, in: M. I. Jordan (Ed.), Probabilistic Graphical Models, MIT Press, 2002, pp. 431–458

    2002

  78. [80]

    M. L. Puterman, Markov Decision Processes: Discrete Stochastic Dynamic Programming, John Wiley & Sons, 2014.doi:10.1002/9780470316887

    work page doi:10.1002/9780470316887 2014

  79. [81]

    R. S. Sutton, A. G. Barto, Reinforcement Learning: An Introduction, Vol. 1, MIT Press, Cambridge, MA, 1998

    1998

  80. [82]

    J. W. Baker, Efficient analytical fragility function fitting using dynamic structural analysis, Earthquake Spectra 31 (1) (2015) 579–599.doi:10.1193/021113EQS025M

    work page doi:10.1193/021113eqs025m 2015

Showing first 80 references.