# Life reliability assessment of twin-web disk using the active learning kriging model

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## Abstract

Compared with the traditional single turbine disk, the novel twin-web turbine disk (TWD) has a bright future in the application of the aero high-pressure disk due to its advantages in weight loss and heat transfer. With the strong coupling of multiple disciplines and the uncertain factors during the manufacturing process, it is necessary to analyze the multidisciplinary reliability of its fatigue life cycles in an efficient way. In this paper, based on the stratified sampling, a new sampling method called modified quadrangular grid (MQG) method, which has better efficiency and stability of sampling, is applied with the active learning Kriging (ALK) surrogate model and the Monte Carlo simulation. The distance based on sampling efficiency (DBSE) and information entropy are proposed in this paper as the criteria to evaluate the current sampling methods. A platform is then built for analyzing its fluid characteristic and structural strength performance. And the reliability of low-cycle fatigue (LCF) life is analyzed by Monte Carlo simulation with ALK model (ALK-MC). Results show the failure probability of current design is higher than the criterion which needs further reliability-based optimization design.

## Keywords

Twin-web turbine Fatigue life Reliability analysis Sampling method Active learning Kriging surrogate model## Notes

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

## References

- Brujic D, Ristic M, Mattone M, Maggiore P, De Poli GP (2010) CAD based shape optimization for gas turbine component design. Struct Multidiscip Optim 41:647–659. https://doi.org/10.1007/s00158-009-0442-9 CrossRefGoogle Scholar
- Cairo RR, Sargent KA (2002) Twin web disk: a step beyond convention. J Eng Gas Turbines Power 124:298–302. https://doi.org/10.1115/1.1445440 CrossRefGoogle Scholar
- Chaudhuri S, Das G, Narasayya V (2007) Optimized stratified sampling for approximate query processing. Acm T Database Syst 32:9CrossRefGoogle Scholar
- Chen Z, Qiu H, Gao L, Li X, Li P (2014) A local adaptive sampling method for reliability-based design optimization using kriging model. Struct Multidiscip Optim 49:401–416. https://doi.org/10.1007/s00158-013-0988-4 MathSciNetCrossRefGoogle Scholar
- Cioppa TM, Lucas TW (2007) Efficient nearly orthogonal and space-filling Latin hypercubes. Technometrics 49:45–55. https://doi.org/10.1198/004017006000000453 MathSciNetCrossRefGoogle Scholar
- Echard B, Gayton N, Lemaire M (2011) AK-MCS: an active learning reliability method combining kriging and Monte Carlo simulation. Struct Saf 33:145–154. https://doi.org/10.1016/j.strusafe.2011.01.002 CrossRefGoogle Scholar
- Force UA (1984) MIL-STD-1783 engine structural integrity program (ENSIP). Washington: US Air Force, 1984: 1–59,Google Scholar
- Gao Y, Wang X (2008) An effective warpage optimization method in injection molding based on the kriging model. Int J Adv Manuf Technol 37:953–960. https://doi.org/10.1007/s00170-007-1044-6 CrossRefGoogle Scholar
- He W, Liu J, Xie D (2015) Probabilistic life assessment on fatigue crack growth in mixed-mode by coupling of kriging model and finite element analysis. Eng Fract Mech 139:56–77. https://doi.org/10.1016/j.engfracmech.2015.03.040 CrossRefGoogle Scholar
- Hong WS, Collopy PD (2005) Technology for jet engines: case study in science and technology development. J Propuls Power 21:769–777CrossRefGoogle Scholar
- Hu D, Wang R, Tao Z (2011) Probabilistic design for turbine disk at high temperature. Aircr Eng Aerosp Technol 83:199–207CrossRefGoogle Scholar
- Huang Z, Wang C, Chen J, Tian H (2011) Optimal design of aeroengine turbine disc based on kriging surrogate models. Comput Struct 89:27–37. https://doi.org/10.1016/j.compstruc.2010.07.010 CrossRefGoogle Scholar
- Hudak Jr S, Lanning B, Light G, Major J, Enright M, McClung R, Millwater H (2004) The influence of uncertainty in usage and fatigue damage sensing on turbine engine prognosis. In: Proceedings of the minerals, metals, and materials society materials science and technology symposium on materials damage prognosisGoogle Scholar
- Javiya U, Chew J, Hills N, Scanlon T (2015) Coupled FE–CFD thermal analysis for a cooled turbine disk. P I Mech Eng C-J Mec 229:3417–3432. https://doi.org/10.1177/0954406215572430 Google Scholar
- Kaymaz I (2005) Application of kriging method to structural reliability problems. Struct Saf 27:133–151. https://doi.org/10.1016/j.strusafe.2004.09.001 CrossRefGoogle Scholar
- Kim JB, Hwang KY, Kwon BI (2011) Optimization of two-phase in-wheel IPMSM for wide speed range by using the kriging model based on Latin hypercube sampling. Ieee T Magn 47:1078–1081. https://doi.org/10.1109/TMAG.2010.2096409 CrossRefGoogle Scholar
- Li G, Ding S, Bao M, Sun H (2017) Effect of actively managed thermal-loading in optimal design of an aeroengine turbine disk. Int Commun Heat Mass 81:257–268. https://doi.org/10.1016/j.icheatmasstransfer.2016.12.024 CrossRefGoogle Scholar
- Liu S, Liu C, Hu Y, Gao S, Wang Y, Zhang H (2016) Fatigue life assessment of centrifugal compressor impeller based on FEA. Eng Fail Anal 60:383–390. https://doi.org/10.1016/j.engfailanal.2015.11.035 CrossRefGoogle Scholar
- Melis ME, Zaretsky EV, August R (1999) Probabilistic analysis of aircraft gas turbine disk life and reliability. J Propuls Power 15:658–666. https://doi.org/10.2514/2.5490 CrossRefGoogle Scholar
- Raju PR, Satyanarayana B, Ramji K, Babu KS (2007) Evaluation of fatigue life of aluminum alloy wheels under radial loads. Eng Fail Anal 14:791–800CrossRefGoogle Scholar
- Shen X, Dong S, Chen Z (2014) Research of an advanced turbine disk for high thrust-weight ratio engine. Paper presented at the ASME Turbo expo 2014: turbine technical conference and exposition, Düsseldorf, Germany, 16–20 June 2014Google Scholar
- Shu Z, Jirutitijaroen P (2011) Latin hypercube sampling techniques for power systems reliability analysis with renewable energy sources. IEEE T Power Syst 26:2066–2073. https://doi.org/10.1109/TPWRS.2011.2113380 CrossRefGoogle Scholar
- Simpson TW, Mauery TM, Korte JJ, Mistree F (2001) Kriging models for global approximation in simulation-based multidisciplinary design optimization. AIAA J 39:2233–2241. https://doi.org/10.2514/2.1234 CrossRefGoogle Scholar
- Tryon RG, Cruse TA, Mahadevan S (1996) Development of a reliability-based fatigue life model for gas turbine engine structures. Eng Fract Mech 53:807–828CrossRefGoogle Scholar
- Vasilyev B, Salnikov A, Semenov A, Magerramova L (2018) Twin-web turbine discs: part 1 — design and analysis of their efficiency. Paper presented at the ASME Turbo expo 2018: turbomachinery technical conference and exposition, Oslo, Norway, 11–15 June 2018Google Scholar
- Weidemann HL, Stear EB (1969) Entropy analysis of parameter estimation. Inf Control 14:493–506. https://doi.org/10.1016/S0019-9958(69)90279-4 MathSciNetCrossRefzbMATHGoogle Scholar
- Witek L (2006) Failure analysis of turbine disc of an aero engine. Eng Fail Anal 13:9–17. https://doi.org/10.1016/j.engfailanal.2004.12.028 CrossRefGoogle Scholar
- Yang X, Liu Y, Gao Y, Zhang Y, Gao Z (2015a) An active learning kriging model for hybrid reliability analysis with both random and interval variables. Struct Multidiscip Optim 51:1003–1016. https://doi.org/10.1007/s00158-014-1189-5 MathSciNetCrossRefGoogle Scholar
- Yang X, Liu Y, Mi C, Tang C (2018) System reliability analysis through active learning kriging model with truncated candidate region. Reliab Eng Syst Saf 169:235–241. https://doi.org/10.1016/j.ress.2017.08.016 CrossRefGoogle Scholar
- Yang X, Liu Y, Zhang Y, Yue Z (2015b) Probability and convex set hybrid reliability analysis based on active learning kriging model. Appl Math Model 39:3954–3971. https://doi.org/10.1016/j.apm.2014.12.012 MathSciNetCrossRefGoogle Scholar
- Zhang M, Gou W, Li L, Wang X, Yue Z (2016) Multidisciplinary design and optimization of the twin-web turbine disk. Struct Multidiscip Optim 53(5):1129–1141. https://doi.org/10.1007/s00158-015-1373-2 CrossRefGoogle Scholar
- Zhang M, Gou W, Yao Q (2016) Reliability-based multidisciplinary design and optimization for twin-web disk using adaptive kriging surrogate model. Adv Mech Eng 8:1687814016671448. https://doi.org/10.1177/1687814016671448 CrossRefGoogle Scholar
- Zhu S-P, Huang H-Z, Peng W, Wang H-K, Mahadevan S (2016) Probabilistic physics of failure-based framework for fatigue life prediction of aircraft gas turbine discs under uncertainty. Reliab Eng Syst Saf 146:1–12. https://doi.org/10.1016/j.ress.2015.10.002855
- Zhu S-P, Liu Q, Lei Q, Wang Q (2018) Probabilistic fatigue life prediction and reliability assessment of a high pressure turbine disc considering load variations. Int J Damage Mech 27:1569–1588. https://doi.org/10.1177/1056789517737132 CrossRefGoogle Scholar