Turbine blisk low cycle fatigue (LCF) is affected by various factors such as heat load, structural load, operation parameters and material parameters; it seriously influences the reliability and performance of the blisk and aeroengine. To study the influence of thermal-structural coupling on the reliability of blisk LCF life, the generalized regression extreme neural network (GRENN) method was proposed by integrating the basic thoughts of generalized regression neural network (GRNN) and the extreme response surface method (ERSM). The mathematical model of the developed GRENN method was first established in respect of the LCF life model and the ERSM model. The method and procedure for reliability and sensitivity analysis based on the GRENN model were discussed. Next, the reliability and sensitivity analyses of blisk LCF life were performed utilizing the GRENN method under a thermal-structural interaction by regarding the randomness of gas temperature, rotation speed, material parameters, LCF performance parameters and the minimum fatigue life point of the objective of study. The analytical results reveal that the reliability degree was 0.99848 and the fatigue life is 9419 cycles for blisk LCF life when the allowable value is 6000 cycles so that the blisk has some life margin relative to 4500 cycles in the deterministic analysis. In comparison with ERSM, the computing time and precision of the proposed GRENN under 10,000 simulations is 1.311 s and 99.95%. This is improved by 15.18% in computational efficiency and 1.39% in accuracy, respectively. Moreover, high efficiency and high precision of the developed GRENN become more obvious with the increasing number of simulations. In light of the sensitivity analysis, the fatigue ductility index and temperature are the key factors of determining blisk LCF life because their effect probabilities reach 41% and 26%, respectively. Material density, rotor speed, the fatigue ductility coefficient, the fatigue strength coefficient and the fatigue ductility index are also significant parameters for LCF life. Poisson’s ratio and elastic modulus of materials have little effect. The efforts of this paper validate the feasibility and validity of GRENN in the reliability analysis of blisk LCF life and give the influence degrees of various random parameters on blisk LCF life, which are promising to provide useful insights for the probabilistic optimization of turbine blisk LCF life.

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Abstract. To more accurately calculate the dynamic reliability for the center gear of power assisting cycle with various failure modes, the multi-extremum response surface method is adopted. The first, the gear's torque, material density, elastic modulus and poisson's ratio are sampled in small batches as the random input samples, the dynamic extremum of deformation, stress and strain are obtained as output response by finite element model. Then, the multiextremum response surface equation is established. Finally, multitudinous sample points are obtained by using Monte Carlo method and linkage sampling to multi-extremum response surface equation, which can used to calculate the reliability of the deformation, stress and strain of the gear in the comprehensive failure mode. The results show that the comprehensive reliability degree of gear is 0.9949 when the allowable deformation, stress and strain are 0.47 mm, 540 Mpa and 0.003 , respectively. IntroductionThe gears support complex loads during the operation of the power assisting cycle operation. Once the gears fail, the energy stored in the spring can't be released and the whole system does not run. So, the structural reliability analysis of gear is very necessary. In recent years, a structural analysis method considering the tooth contact of internal gear system is introduced through the comparison with the simplified gear system model and applied to the structural analysis of a 2-stage differential-type gearbox for wind turbine by Cho et al [1]. The key meshing states of the gear pair for the contact fatigue and the bending fatigue was investigated based on the cumulative fatigue criterion and the stress-life equation by Deng et al [2]. Although the problem of gear contact was studied in different degrees, they were based on deterministic analysis method, and it is not discussed further from the angle of probability. Currently, scientists have presented a lot of research on the gear reliability analysis method, response surface method is the most widely used [3][4][5][6]. The reliability analysis method based on response surface and the Markov chain Monte Carlo (MCMC) were proposed to improve the precision of the response function, and the dependability sensitivity analysis was conducted to quantify the effects of assembly errors, machining errors and stochastic external loads on gear transmission reliability by Tong et al [7], then the reliability was calculated using the founded mathematical model by Monte Carlo method (MCM). However, these methods only consider the reliability of single failure mode analysis without considering the failure correlation of dynamic reliability problems. In order to solve the problem of multiple failure mode correlation, the multi-extremum response surface method was introduced in the reliability analysis of gear. The gear's torque, material density,

In order to more reasonable analyze the dynamic reliability of aero-engine blade with coupling failure mode. A fuzzy intelligent multiple extremum response surface method (FIMERSM) was proposed. Considering the coupling effect of temperature load and centrifugal load, the maximum stress point, the maximum strain point and the minimum life point on blade were found by deterministic analysis. Then, the density of blade, rotor speed, elastic modulus, blade-tip temperature, blade-root temperature, fatigue strength coefficient, fatigue strength exponent, fatigue ductility coefficient, fatigue ductility exponent, blade width, blade thickness, blade torsion angle, and blade height as input random variables. By using Latin hypercube sampling technique, the sample values of the input random variables were acquired and finite element basic equation was calculated for each samples which obtained the corresponding dynamic output response of their stress, strain, and low cycle fatigue life within the analysis time domain. By taking the entire maximum values of the dynamic output response in the analysis time domain as new output response, the fuzzy intelligent multiple extremum response surface function (FIMERSF) was established. Finally, the dynamic reliability of the blade structure were obtained by using the Monte Carlo method (MCM) large amount linkage sampling of the input random variables and take it into the FIMERSF to calculate the output response. The results imply that the comprehensive reliability of blade is 99.46%. Through the comparison of MCM, Multiple extremum response surface method (MERSM) and FIMERSM, the computational results show that the FIMERSM has high computational precision and computational efficiency.