Fatigue reliability estimation framework for blade-disk based on improved constrained boundary sampling and dual-point enrichment active learning strategy
Restricted accessResearch articleFirst published online April, 2026
Fatigue reliability estimation framework for blade-disk based on improved constrained boundary sampling and dual-point enrichment active learning strategy
The fatigue reliability of blade-disk significantly impacts the performance and safety of heavy-duty gas turbines. To achieve higher computing precision and efficiency for blade-disk reliability estimation, an improved constrained boundary sampling and dual-point enrichment active learning strategy (DP-ACBS) is proposed. Two numerical examples are employed to verify the feasibility of the proposed strategy. Considering multi-uncertainty comprehensively, a framework of blade-disk fatigue reliability assessment is developed based on the DP-ACBS method. Low-cycle fatigue (LCF) reliability and sensitivity analyses on a typical compressor blade-disk are conducted. Variations in both environmental and design factors are considered. The results indicate that the proposed DP-ACBS algorithm achieves a superior balance between computational accuracy and efficiency on numerical examples. The dovetail is the crucial failure zone of the compressor blade-disk. Mortise and tenon fillet radius are the primary factors affecting LCF lifespan with an overall sensitivity index of 0.731. The failure probability of the compressor blade-disk is 2.11% at a safety lifetime of 15,500 cycles.
MadariagaAGarayAEsnaolaJA, et al. Effect of surface integrity generated by machining on isothermal low cycle fatigue performance of Inconel 718. Eng Fail Anal2022; 137: 106422.
2.
GaoHWangAZioE, et al. An integrated reliability approach with improved importance sampling for low-cycle fatigue damage prediction of turbine disks. Reliab Eng Syst Saf2020; 199: 106819.
3.
LuCLiHHanL, et al. Bi-iterative moving enhanced model for probability-based transient LCF life prediction of turbine blisk. Aerosp Sci Technol2023; 132: 107998.
4.
FengHWangYJiangX. Reliability estimation for low cycle fatigue life of a gas turbine disk. In: 17th AIAA/ISSMO multidisciplinary analysis and optimization conference. Washington, DC: American Institute of Aeronautics and Astronautics, 13–17 June 2016.
5.
YangFXuZ.Multidisciplinary reliability analysis of turbine blade with shape uncertainty by Kriging model and free-form deformation methods. Proc Inst Mech Eng Part O: J Risk Reliab2020; 234: 611–621.
6.
WangWMaYLiuB, et al. Reliability analysis of reusable turbine rotor blisk: an application of parametric modelling method under multi-field coupling. Eng Fail Anal2023; 152: 107511.
7.
LiX-QSongL-KBaiG-C.Recent advances in reliability analysis of aeroengine rotor system: a review. Int J Struct Integr2022; 13: 1–29.
8.
ZhangMLuS.A reliability model of blade to avoid resonance considering multiple fuzziness. Proc Inst Mech Eng Part O: J Risk Reliab2014; 228: 641–652.
9.
GaoH-FZioEGuoJ-J, et al. Dynamic probabilistic-based LCF damage assessment of turbine blades regarding time-varying multi-physical field loads. Eng Fail Anal2020; 108: 104193.
10.
SongL-KBaiG-CLiX-Q.A novel metamodeling approach for probabilistic LCF estimation of turbine disk. Eng Fail Anal2021; 120: 105074.
11.
HohenbichlerMRackwitzR.First-order concepts in system reliability. Struct Saf1982; 1: 177–188.
12.
HaldarAMahadevanS. First-order and second-order reliability methods. In: SundararajanC (ed.) Probabilistic structural mechanics handbook: theory and industrial applications. Springer, pp.27–52.
13.
MengDXieTWuP, et al. An uncertainty-based design optimization strategy with random and interval variables for multidisciplinary engineering systems. Structures2021; 32: 997–1004.
14.
MelchersRE.Importance sampling in structural systems. Struct Saf1989; 6: 3–10.
15.
AuS-KBeckJL.Estimation of small failure probabilities in high dimensions by subset simulation. Probabilistic Eng Mech2001; 16: 263–277.
16.
XiongYSampathS.A fast-convergence algorithm for reliability analysis based on the AK-MCS. Reliab Eng Syst Saf2021; 213: 107693.
17.
HeWLiuJXieD.Probabilistic life assessment on fatigue crack growth in mixed-mode by coupling of Kriging model and finite element analysis. Eng Fract Mech2015; 139: 56–77.
18.
SongL-KBaiG-CFeiC-W.Probabilistic LCF life assessment for turbine discs with DC strategy-based wavelet neural network regression. Int J Fatigue2019; 119: 204–219.
19.
EchardBGaytonNLemaireM.AK-MCS: an active learning reliability method combining Kriging and Monte Carlo Simulation. Struct Saf2011; 33: 145–154.
20.
WeiPTangCYangY.Structural reliability and reliability sensitivity analysis of extremely rare failure events by combining sampling and surrogate model methods. Proc Inst Mech Eng Part O: J Risk Reliab2019; 233: 943–957.
21.
ZhangHSongLBaiG.Active kriging-based adaptive importance sampling for reliability and sensitivity analyses of stator blade regulator. Comput Model Eng Sci2023; 134: 1871–1897.
22.
BichonBJEldredMSSwilerLP, et al. Efficient global reliability analysis for nonlinear implicit performance functions. AIAA J2008; 46: 2459–2468.
23.
LeeTHJungJJ.A sampling technique enhancing accuracy and efficiency of metamodel-based RBDO: constraint boundary sampling. Comput Struct2008; 86: 1463–1476.
24.
WangLChenY.An improved active Kriging method for reliability analysis combining expected improvement and U learning functions. Proc Inst Mech Eng Part O: J Risk Reliab2024; 238(4): 764–776.
25.
YangSLeeMJungY, et al. An effective active learning strategy for reliability-based design optimization under multiple simulation models. Struct Saf2024; 107: 102426.
26.
ZhouCLiuCYangT, et al. An adaptive Kriging-based structural reliability analysis method combing dichotomy and improved convergence criterion. Proc Inst Mech Eng Part O: J Risk Reliab2023; 237: 1114–1131.
27.
WangPZhangZHuangX, et al. An application of active learning Kriging for the failure probability and sensitivity functions of turbine disk with imprecise probability distributions. Eng Comput2022; 38: 3417–3437.
28.
ZhangMYaoQShengZ, et al. A sequential reliability assessment and optimization strategy for multidisciplinary problems with active learning kriging model. Struct Multidiscip Optim2020; 62: 2975–2994.
29.
TeixeiraRNogalMO’ConnorA.Adaptive approaches in metamodel-based reliability analysis: a review. Struct Saf2021; 89: 102019.
30.
WenZPeiHLiuH, et al. A Sequential Kriging reliability analysis method with characteristics of adaptive sampling regions and parallelizability. Reliab Eng Syst Saf2016; 153: 170–179.
31.
ZhangMZhangZXiaS, et al. An active learning strategy of reliability-based design and optimization by parallel adaptive sequential importance candidate region method. Struct Multidiscip Optim2024; 67: 14.
32.
WangJCaoZXuG, et al. An adaptive Kriging method based on K-means clustering and sampling in n-ball for structural reliability analysis. Eng Comput2023; 40: 378–410.
33.
ZhouTGuoTDangC, et al. Parallel active learning reliability analysis: a multi-point look-ahead paradigm. Comput Methods Appl Mech Eng2025; 434: 117524.
34.
ZhouTZhuXGuoT, et al. Multi-point Bayesian active learning reliability analysis. Struct Saf2025; 114: 102557.
WeiNLuZ.Sequential optimization method based on the adaptive Kriging model for the possibility-based design optimization. Aerosp Sci Technol2022; 130: 107939.
37.
ChenZPengSLiX, et al. An important boundary sampling method for reliability-based design optimization using kriging model. Struct Multidiscip Optim2015; 52: 55–70.
38.
BichonBEldredMSwilerL, et al. Multimodal reliability assessment for complex engineering applications using efficient global optimization. In: 48th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference. Washington, DC: American Institute of Aeronautics and Astronautics, 23–26 April 2007. Honolulu, Hawaii.
39.
YangSMengDWangH, et al. A novel learning function for adaptive surrogate-model-based reliability evaluation. Philos Trans R Soc Math Phys Eng Sci2024; 382: 20220395.
40.
ZhouCXiaoN-CZuoMJ, et al. AK-PDF: an active learning method combining kriging and probability density function for efficient reliability analysis. Proc Inst Mech Eng Part O: J Risk Reliab2020; 234: 536–549.
41.
AouesYChateauneufA.Benchmark study of numerical methods for reliability-based design optimization. Struct Multidiscip Optim2010; 41: 277–294.
42.
US Department of Defense. Military handbook: metallic materials and elements for aerospace vehicle structures. US Department of Defense, 1990.
43.
LiuJ.Fatigue life evaluation and system reliability study of aeroengine low pressure compressor blade-disk system. Dissertation, Northeastern University, 2022. (In Chinese)
BourgeoisJAMartinuzziRJSavoryE, et al. Assessment of turbulence model predictions for an aero-engine centrifugal compressor. J Turbomach2011; 133: 011025.
46.
SunW.Assessment of advanced RANS turbulence models for prediction of complex flows in compressors. Chin J Aeronaut2023; 36: 162–177.
47.
HuangRNiJWangQ, et al. Assessing the effects of computational model parameters on aerodynamic noise characteristics of a heavy-duty diesel engine turbocharger compressor at full operating conditions. SAE paper 2024-01-2352, 2024.
48.
LvZHuangH-ZWangH-K, et al. Determining the Walker exponent and developing a modified Smith-Watson-Topper parameter model. J Mech Sci Technol2016; 30: 1129–1137.
49.
ConcliFFraccaroliLNalliF, et al. High and low-cycle-fatigue properties of 17–4 PH manufactured via selective laser melting in as-built, machined and hipped conditions. Prog Addit Manuf2022; 7: 99–109.
50.
SobolIM.Sensitivity estimates for nonlinear mathematical models. Math Model Comput Exp1993; 1: 112–118.
51.
YangYLiuH.Sensitivity analysis of disease-information coupling propagation dynamics model parameters. PLOS ONE2022; 17: e0265273.
