PSI - Issue 80

Mengke Zhuang et al. / Procedia Structural Integrity 80 (2026) 299–309 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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4. Conclusion The current study adopted the active learning function GEALF for strategically selecting high-fidelity and low fidelity evaluation points in multi-fidelity reliability analysis. Failure probabilities were estimated using a multi fidelity Kriging surrogate combined with importance sampling, significantly reducing computational costs while maintaining accuracy. The method was demonstrated through a two-dimensional analytical example and validated against Monte Carlo simulation. A shallow shell structure was then analysed as a numerical example, with results compared to Kriging based MCS. The findings showed very close agreement, with the multi-fidelity approach requiring only ~100 function evaluations compared to millions for MCS. As expected, relative errors increased for small failure probabilities (below 10 −5 ), though the method remained effective for practical reliability assessment in aerospace applications. Future work could focus on improving the accuracy for rare event estimation through enhanced learning functions or more advanced adaptive fidelity selection strategies. Additionally, extending the framework to time dependent reliability problems and incorporating multiple failure modes would expand its applicability to complex This paper presents work undertaken as part of the “Advanced Landing Gear” project supported by Safran Landing Systems. The research was funded through the Aerospace Technology Institute (ATI), under application number: 10079975, as part of the ATI programme: Batch 40 research projects. References Lee, I., Lee, U., Ramu, P., Yadav, D., Bayrak, G., Acar, E., 2022. Small Failure Probability: Principles, Progress and Perspectives. Structural and Multidisciplinary Optimization 65, 326. Su, M., Xue, G., Wang, D., Zhang, Y., Zhu, Y., 2020. A Novel Active Learning Reliability Method Combining Adaptive Kriging and Spherical Decomposition-MCS (AK-SDMCS) for Small Failure Probabilities. Structural and Multidisciplinary Optimization 62, 3165 – 3187. Ditlevsen, O., Madsen, H.O., 1996. Structural Reliability Methods. Wiley, New York. Lemaire, M., 2013. Structural Reliability. John Wiley & Sons, Chichester. Teixeira, R., Nogal, M., O'Connor, A., 2021. Adaptive Approaches in Metamodel-based Reliability Analysis: A Review. Structural Safety 89, 102019. Hoole, J., Sartor, P., Booker, J.D., Cooper, J.E., Gogouvitis, X., Schmidt, R.K., 2020. Comparison of Surrogate Modeling Methods for Finite Element Analysis of Landing Gear Loads. In: AIAA Scitech 2020 Forum. AIAA, p. 0681. Kaymaz, I., 2005. Application of Kriging Method to Structural Reliability Problems. Structural Safety 27, 133 – 151. Echard, B., Gayton, N., Lemaire, M., 2011. AK-MCS: An Active Learning Reliability Method Combining Kriging and Monte Carlo Simulation. Structural Safety 33, 145 – 154. Echard, B., Gayton, N., Lemaire, M., Relun, N., 2013. A Combined Importance Sampling and Kriging Reliability Method for Small Failure Probabilities with Time-demanding Numerical Models. Reliability Engineering & System Safety 111, 232 – 240. Moustapha, M., Marelli, S., Sudret, B., 2022. Active Learning for Structural Reliability: Survey, General Framework and Benchmark. Structural Safety 96, 102174. Dai, H., Li, D., Beer, M., 2025. Adaptive Kriging-assisted Multi-fidelity Subset Simulation for Reliability Analysis. Computer Methods in Applied Mechanics and Engineering 436, 117705. Chaudhuri, A., Marques, A., Willcox, K., 2021. mfEGRA: Multifidelity Efficient Global Reliability Analysis through Active Learning for Failure Boundary Location. Structural and Multidisciplinary Optimization 64, 797 – 811. Bichon, B., Eldred, M., Swiler, L., Mahadevan, S., McFarland, J., 2008. Efficient Global Reliability Analysis for Nonlinear Implicit Performance Functions. AIAA Journal 46, 2459 – 2468. Bichon, B.J., McFarland, J.M., Mahadevan, S., 2011. Efficient Surrogate Models for Reliability Analysis of Systems with Multiple Failure Modes. Reliability Engineering & System Safety 96, 1386 – 1395. Zhang, C., Song, C., Shafieezadeh, A., 2022. Adaptive Reliability Analysis for Multi-fidelity Models Using a Collective Learning Strategy. Structural Safety 94, 102141. Lu, N., Li, Y.-F., Mi, J., Huang, H.-Z., 2024. AMFGP: An Active Learning Reliability Analysis Method Based on Multi-fidelity Gaussian Process Surrogate Model. Reliability Engineering & System Safety 246, 110020. aerospace structures. Acknowledgements