Efficient reliability analysis of complex systems
Final Report Abstract
The complexity and size of modern systems impose the hurdle of dimensionality on most types of analysis. However, through the survival signature the numerical effort can be diminished. Although the approach may be dynamic, versatile and efficient compared to previous analysis schemes, it is still slowed down due to the influence of exponential growth in computational effort. During the course of this project, efficient methods to calculate the survival signature representation were devised to compute the survival signature. Statistical methods were introduced by replacing the individual checking of all possible system states through the sampling of candidate configurations. A significant improvement for the calculation of the survival signature representation of a complex system could be achieved through this. Not just the reduction of numerical cost is possible, but also the precision of the results can be fine-tuned to any degree necessary previous and during the computations. The inherent imprecision through the statistical approach translates smoothly into the final results, giving a clear upper and lower boundary on the level of uncertainty gained through a given numerical effort due to sampling. Measures from graph theory were implemented into this framework to further aid the statistical methods. The shortest path and percolation threshold are easily obtained before the sampling process starts and significantly reduce the amount of calculations while maintaining a high level of precision under the reasonable condition of a coherent system structure. Advanced sampling as line sampling or subset simulation methods were so far not applicable as anticipated due to the discrete binary state-space of the system, but for large systems an approach was developed to estimate the survival signature entries to a predetermined precision. The successive decomposition of the network along minimal-cut-sets or –path-sets provides a lower and upper bound for each survival signature entry. Additionally, the sequential application of this algorithm leads to other possible graph-theory measures being computed during sequential runs of the method. The handling of the boundaries and uncertainties mentioned for all aspects above are easily and directly implemented in the reliability analysis of the system. For systems with more delicate failure mode behavior and interdependencies between components it was possible to develop a method to apply the survival signature efficiently. During this, implementation of imprecise copulas, probability boxes, and a Monte Carlo simulation algorithm with sampling for only nontrivial entries of the survival signature lead to a sound prediction of the system reliability for even very complex objects that otherwise would be hard to handle numerically.
Publications
- "A Novel Application of System Survival Signature in Reliability Assessment of Offshore Structures." In ICO 2018: Intelligent Computing & Optimization, by Pandian Vasant, Ivan Zelinka and Gerhard-Wilhelm Weber, 11-20. Springer, Cham, 2018
Regenhardt, Tobias-Emanuel, Md Samdani Azad, Wonsiri Punurai, and Michael Beer
(See online at https://doi.org/10.1007/978-3-030-00979-3_2) - "Applying Graph Theory and Lifeline Reliability to the System Survival Signature." Proc. of the 6th Intl. Symposium on Reliability Engineering and Risk Management (6ISRERM). Singapore: RPS, 2018. 681-686
Regenhardt, Tobias-Emanuel, Liu Wei, Matteo Broggi, and Michael Beer
(See online at https://doi.org/10.3850/978-981-11-2726-7_crr19) - "Efficient approximation of the survival signature for large systems." Proc. of the 6th Intl. Symposium on Reliability Engineering and Risk Management (6ISRERM). Singapore: RPS, 2018. 661-666
Behrensdorf, Jasper, Sebastian Brandt, Matteo Broggi, and Michael Beer
(See online at https://doi.org/10.3850/978-981-11-2726-7_crr14) - "Reliability Analysis of Networks Interconnected With Copulas." ASCE-ASME J Risk and Uncert in Engrg Sys Part B Mech Engrg 5(4): 041006, 2019
Behrensdorf, Jasper, Matteo Broggi, and Michael Beer
(See online at https://doi.org/10.1115/1.4044043)
