To improve the efficiency and accuracy of reliability assessment for structures with small failure probability and time-consuming simulation, a new structural reliability analysis method (RCA-PCK) is proposed, which combines PC-Kriging model and radial centralized adaptive sampling strategy. Firstly, the PC-Kriging model is constructed by improving the basis function of Kriging model with sparse polynomials. Then, the sampling region which contributes a great impact on the failure probability is constructed by combining the radial concentration and important sampling technology. Subsequently, the k-means++ clustering technology and learning function LIF are adopted to select new training samples from each subdomains in each iteration. To avoid the sampling distance in one subdomain or the distance between the new training samples in two subdomains being too small, we construct a screening mechanism to ensure that the selected new training samples are evenly distributed in the limit state. In addition, a new convergence criterion is derived based on the relative error estimation of failure probability. Four benchmark examples are given to illustrate the convergence process, accuracy and stability of the proposed method. Finally, the transmission error reliability analysis of thermal-elastic coupled gears is carried out to prove the applicability of the proposed method RCA-PCK to the structures with strong nonlinearity and time-consuming simulation.
ZhaoYGOnoT.A general procedure for first/second-order reliability method (FORM/SORM). Struct Saf1999;
21: 95–112.
2.
ZhangHMullenRLMuhannaRL.Interval monte carlo methods for structural reliability. Struct Saf2010;
32: 183–190.
3.
RackwitzR.Reliability analysis—a review and some perspectives. Struct Saf2001;
23: 365–395.
4.
AuSKBeckJL.Estimation of small failure probabilities in high dimensions by subset simulation. Probab Eng Mech2001;
16: 263–277.
5.
KoutsourelakisPSPradlwarterHJSchuëllerGI.Reliability of structures in high dimensions, part I: algorithms and applications. Probab Eng Mech2004;
19: 409–417.
6.
BongTSonY.A stochastic dual response surface method for reliability analysis considering the spatial variability. KSCE J Civ Eng2018;
22: 3524–3533.
7.
ZertiAYalleseMAZertiO, et al.
Prediction of machining performance using RSM and ANN models in hard turning of martensitic stainless steel AISI 420. Proc IMechE, Part C: J Mechanical Engineering Science2019;
233: 4439–4462.
8.
PatelCDasSNarayananRG.CAFE modeling, neural network modeling, and experimental investigation of friction stir welding. Proc IMechE, Part C: J Mechanical Engineering Science2013;
227: 1164–1176.
9.
SwainADasMK.Artificial intelligence approach for the prediction of heat transfer coefficient in boiling over tube bundles. Proc IMechE, Part C: J Mechanical Engineering Science2014;
228: 1680–1688.
10.
AlibrandiUAlaniAMRicciardiG.A new sampling strategy for SVM-based response surface for structural reliability analysis. Probab Eng Mech2015;
41: 1–12.
11.
YuYLiJ.Residuals-based deep least square support vector machine with redundancy test based model selection to predict time series. Tinshhua Sci Technol2019;
24: 706–715.
12.
GaoYZhangFLiY.Reliability optimization design of a planar multi-body system with two clearance joints based on reliability sensitivity analysis. Proc IMechE, Part C: J Mechanical Engineering Science2019;
233: 1369–1382.
13.
JiluFZhiliSHongzheS.Optimization of structure parameters for angular contact ball bearings based on Kriging model and particle swarm optimization algorithm. Proc IMechE, Part C: J Mechanical Engineering Science2017;
231: 4298–4308.
QiuYSBaiJQ.Stationary flow fields prediction of variable physical domain based on proper orthogonal decomposition and Kriging surrogate model. Chin J Aeronaut2015;
28: 44–56.
16.
MorrisMDMitchellTJYlvisakerD.Bayesian design and analysis of computer experiments: use of derivatives in surface prediction. Technometrics1993;
35: 243–255.
17.
HanZHZhangYSongCX, et al.
Weighted gradient-enhanced Kriging for high-dimensional surrogate modeling and design optimization. AIAA J2017;
55: 4330–4346.
18.
GasparBTeixeiraAPSoaresCG.Assessment of the efficiency of Kriging surrogate models for structural reliability analysis. Probabilist Eng Mech2014;
37: 24–34.
19.
SchobiRSudretBWiartJ.Polynomial-chaos-based Kriging. Int J Uncertaintyquantification2015;
5: 171–193.
20.
DuttaSGhoshSInamdarMM.Optimisation of tensile membrane structures under uncertain wind loads using PCE and Kriging based metamodels. Struct Multidisc Optim2018;
57: 1149–1161.
21.
WeinmeisterJGaoXRoyS.Analysis of a polynomial Chaos-Kriging metamodel for uncertainty quantification in aerodynamics. AIAA J2019;
57: 2280–2296.
22.
BichonBJEldredMSSwilerLP, et al.
Efficient global reliability analysis for nonlinear implicit performance functions. AIAA J2008;
46: 2459–2468.
23.
EchardBGaytonNLemaireM.AK-MCS: an active learning reliability method combining Kriging and Monte Carlo simulation. Struct Saf2011;
33: 145–154.
24.
EchardBGaytonNLemaireM, et al.
A combined importance sampling and Kriging reliability method for small failure probabilities with time-demanding numerical models. Reliab Eng Syst Saf2013;
111: 232–240.
25.
TongCSunZZhaoQ, et al.
A hybrid algorithm for reliability analysis combining Kriging and subset simulation importance sampling. J Mech Sci Technol2015;
29: 3183–3193.
26.
LvZLuZWangP.A new learning function for Kriging and its applications to solve reliability problems in engineering. Comput Math Appl2015;
70: 1182–1197.
27.
YangXLiuYGaoY, et al.
An active learning Kriging model for hybrid reliability analysis with both random and interval variables. Struct Multidisc Optim2015;
51: 1003–1016.
28.
SunZWangJLiR, et al.
LIF: a new Kriging based learning function and its application to structural reliability analysis. Reliab Eng Syst Saf2017;
157: 152–165.
29.
LiYZhangQWuY, et al.
A sequential Kriging method assisted by trust region strategy for proxy cache size optimization of the streaming media video data due to fragment popularity distribution. Multimed Tools Appl2019;
78: 28737–28756.
30.
WangYHongDMaX, et al.
A radial-based centralized Kriging method for system reliability assessment. J Mech Des2018;
140: 403–414.
31.
TibshiraniRJohnstoneIHastieT, et al.
Least angle regression. Ann Statist2004;
32: 407–451.
32.
ArnoldTW.Uninformative parameters and model selection using Akaike’s information criterion. J Wildl Manage2010;
74: 1175–1178.
33.
WangZShafieezadehA.ESC: an efficient error-based stopping criterion for Kriging-based reliability analysis methods. Struct Multidisc Optim2019;
59: 1621–1637.
34.
ZhangYSunZYanY, et al.
An efficient adaptive reliability analysis method based on Kriging and weighted average misclassification rate improvement. IEEE Access2019;
7: 94954–94965.
35.
Kouhi EsfahaniRShahbaziFAkbarzadehM.Three-phase classification of an uninterrupted traffic flow: a k-means clustering study. Transp B Transp Dyn2019;
7: 546–558.
36.
GuanWDongLCaiY, et al.
Sparse component analysis with optimized clustering for underdetermined blind modal identification. Meas Sci Technol2019;
30: 125011–125141.
37.
YuZSunZWangJ, et al.
A new Kriging-based DoE strategy and its application to structural reliability analysis. Adv Mech Eng2018;
10: 168781401876768–168781401876713.
38.
LiXGongCGuL, et al.
A sequential surrogate method for reliability analysis based on radial basis function. Struct Saf2018;
73: 42–53.
39.
DubourgVSudretBDeheegerF.Metamodel-based importance sampling for structural reliability analysis. Probab Eng Mech2013;
33: 47–57.
40.
CadiniFSantosFZioE.An improved adaptive Kriging based importance technique for sampling multiple failure regions of low probability. Reliab Eng Syst Saf2014;
131: 109–117.
41.
WangZWangP.Accelerated failure identification sampling for probability analysis of rare events. Struct Multidisc Optim2016;
54: 137–149.
42.
JingZChenJLiX.RBF-GA: an adaptive radial basis function metamodeling with genetic algorithm for structural reliability analysis. Reliab Eng Syst Saf2019;
189: 42–57.
43.
YounBDChoiKKYangRJ, et al.
Reliability-based design optimization for crashworthiness of vehicle side impact. Struct Multidisc Optim2004;
26: 272–283.
44.
GuoJDuXP.Reliability sensitivity analysis with random and interval variables. Int J Numer Meth Eng2009;
78: 1585–1617.
45.
WenZPeiHLiuH, et al.
A sequential Kriging reliability analysis method with characteristics of adaptive sampling regions and parallelizability. Reliab Eng Syst Saf2016;
153: 170–179.
46.
ShiJLMaXGXuCL, et al.
Meshing stiffness analysis of gear using the Ishikawa method. Appl Mech Mater2013;
401–403: 203–206.
