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Risk & reliability assessment

Deterioration and other sources of changing operating conditions make systems reliability evolve over time and efficient approaches for describing this evolution are indispensable. Methods particular to learning multi-event reliability in the context of fragility analysis are discussed here. Beyond learning, in the case of already learned models, parametric and state updates need to also be possible based on new information. For this problem, two basic mathematical components are required: a model describing the dynamics of system states and parameters in time, and a model describing the way we can access these dynamics.


Based on these two components, as new measurements and observations are collected (e.g. from inspections and monitoring), the knowledge about the reliability of the system can be updated through a model-based prediction of the probabilistic system configuration at the next step (prediction step), followed by a likelihood-weighted adjustment of that prediction based on the received observation (estimation step). The two steps can be efficiently accounted for through filtering of Dynamic Bayesian Networks (DBNs).

Leveraging the Markovian (in-time) properties of a DBN, allows us to recursively perform the above computations. As discussed in the projects related to decision-making optimization, DBNs form the core around which global decision optimization formulations such as partially observable Markov decision processes can be wrapped to apply control.

Deterioration DBN.png

Excluding the control part, below is shown the reliability evolution of a steel truss structure subject to corrosion. Corrosion inflicts section losses to the truss members and is governed by a gamma process. The shape-related parameters of the gamma process as well as the actual section losses of individual members are hidden, and are only accessible through observations with 7% noise (e.g. reflecting the imprecision expected by typically used ultra-sonic thickness measurements for this structure). Measurements are taken according to a known plan of inspection visits at different time steps.

The quantities inferred by the collected observations over the course of the system operating horizon are the section losses of the members, the structural system reliability, and the shared environment parameters of the gamma process. As expected, uncertainty around the estimated states drops at inspection steps, and the structural reliability is updated. It is also observed that, as more information is collected, the real environment parameters can be more accurately approximated.

Apart from corrosion, high-cycle fatigue is also an important deteriorating factor in various civil engineering structures. This type of degradation is particularly prominent in steel structures like the truss system shown above, with the most vulnerable links typically being located at the member connections (either welded or bolted). Below is shown the evolution of the probability of failure of such a structural member subject to fatigue deterioration. Failure probability is updated as a binary indicator is observed (detection, D, or no-detection, ND), given a known Probability of Detection (PoD) curve. 

parametric vs deterioration rate DBN.PNG
fatigue policy.PNG

The first plot (from left to right) shows a validation of the above described DBN, including a comparison of the predicted crack size evolution based on Paris' law, against Monte Carlo results and standard parametric DBNs. The other plots depict the probability of failure in time based on different detection outcomes, and the relevant PoD, respectively.  


  • Andriotis, C.P., and Papakonstantinou, K.G., “Deep reinforcement learning driven inspection and maintenance planning under incomplete information and constraints”, Reliability Engineering & System Safety (under review), arXiv preprint arXiv:2007.01380, 2020. [Link]


  • Morato, P.G., Papakonstantinou, K.G., Andriotis, C.P., Nielsen, J.S., and Rigo, P., “Optimal inspection and maintenance planning for deteriorating structures using dynamic Bayesian networks and Markov decision processes”, Structural Safety (under review), 2020. [Link]

  • Andriotis, C.P., and Papakonstantinou, K.G., “Managing engineering systems with large state and action spaces through deep reinforcement learning”, Reliability Engineering & System Safety, 191 (11), 106483, 2019. [Link]


  • Andriotis C.P., and Papakonstantinou, K.G., “Life-cycle policies for large engineering systems under complete and partial observability”, 13th International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP), Seoul, South Korea, 2019. [Link]



Data, Documentation, Presentations


Faculty of Architecture & the Built Environment

Delft University of Technology

Julianalaan 134, 2628 BL, Delft 

email: c.andriotis [at] tudelft [dot] nl

Copyright © 2020-21 by C.P. Andriotis

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