As a heat-end core component of an aeroengine, a turbine blisk endures complex alternating loads due to operation in a severe environment with high temperatures and high rotation speeds. In this case, it is easy to produce large plastic deformation for blisk and to induce the low cycle fatigue (LCF) failure of blisk [1
]. Most of the parameters that significantly effect blisk LCF failure have some randomness [3
]. To improve the safety and reliability of a turbine blisk to ensure the high performance of an aeroengine, it is important to study blisk LCF life reliability from a probabilistic perspective [4
The LCF life of structures has been widely investigated. Sun et al. established a nonlinear model for LCF life of a steam turbine rotor under a temperature-stress coupling field by considering the relationship between cyclic stress and strain and validated the model to be accurate and reasonable in describing damage accumulation [9
]. Letcher et al. proposed an energy-based critical fatigue life prediction approach, which derived the approximate failure cycle index from the ratio of the total accumulation of energy in the fracture process to the one-cycle strain energy [10
]. Bargmann et al. discussed the full-probability quick integral algorithm based on the Coffin-Manson-Neuber local strain-fatigue theory [11
]. Zhu et al. discussed the probabilistic LCF life prediction of a turbine disk under uncertainties [12
]. Viadro et al. studied the reliability of stiffened bending plates [14
]. Repetto et al. discussed the role of parameter uncertainty in the damage prediction of the alongwind-induced fatigue and long term simulation of wind-induced fatigue loadings [15
]. Most of the above work was conducted based on numerical simulation methods (or-called direct simulation methods) with Monte Carlo (MC) simulation [15
]. Generally, the direct simulation methods are powerful for the deterministic analyses of component LCF life. However, for the probabilistic analyses of component LCF life with thousands of iterations and MC simulations, it is unbelievable to efficiently perform blisk fatigue life analysis owing to excess computational burden (loads) and unacceptable computational efficiency; although this method has satisfactory computing precision against engineering practice. Therefore, it is urgent to seek an alternative effective method for direct methods to address this issue.
In respect of the in-depth investigation of structural fatigue probabilistic analyses, the response surface method (RSM, also called surrogate model method) is indeed an alternative method to direct simulation methods [21
]. With the development of structural reliability theory and methods, various surrogate methods have emerged [27
]. To improve the computational efficiency and accuracy of RSM for complex structural reliability analysis, Bai et al. proposed a distributed collaborative response surface method for the mechanical dynamic assemble reliability analysis of aeroengine high pressure turbine blade-tip clearance [30
]. Hurtado et al. proposed a highly efficient surrogate method, a support vector machine, for structural reliability analysis with small samples [31
]. Zhang et al. developed an extremum response surface method (ERSM) in respect of the extreme thought, to address the transient problem in the dynamic reliability analysis of a flexible mechanism and validated the ERSM to be precise for the reliability analysis of a flexible manipulator [32
]. Lu et al. developed an improved Kriging method by integrating the Kriging algorithm and ERSM for the reliability and sensitivity analyses of a compressor blisk regarding multiple failure (deformation failure, stress failure and strain failure) modes [33
]. From the efforts in References [32
], it can be seen that ERSM has the potential to handle the transient problem in structural dynamic probabilistic analyses with a high simulation accuracy and efficiency, which provides useful insight into the process of the reliability analysis of blisk LCF life with the consideration of aeroengine operating conditions. For another, the developed ERSM does not satisfy the requirement of engineering in computing precision, derived from the weakness in processing the involved nonlinear probabilistic analyses.
With the development of neural network technology recently, the nonlinear problem was skillfully addressed by developing a generalized regression neural network (GRNN) due to the strong nonlinear mapping capability and robustness [34
]. Zhao et al. established an all-purpose regression neural network model based on a freight volume condition and validated the effectiveness of this model in freight volume prediction by modeling adaptive training and extrapolation evaluation in terms of historical statistical data of freight volume and related samples and economic indicators [35
]. Li et al. fused the drosophila optimization algorithm and GRNN to build the prediction model of power loads for power load prediction and this model had a strong nonlinear fitting ability [36
]. Sun et al. compared the GRNN model with the back propagation neural network (BPNN) model based on air quality prediction and the GRNN method needed less training time and had better stability, a higher fitting precision as well, compared to the BPNN model [37
]. Wang et al. validated the strengths of the GRNN method again by waveguide orientation [38
]. Therefore, the GRNN method has been comprehensively verified to be highly computationally precise and efficient.
To effectively perform the reliability and sensitivity analyses of a turbine blsik LCF life, the generalized regression extremum neural network (GRENN) method is proposed in this paper; by integrating the transient procession ability of ERSM and the nonlinear mapping and small samples of GRNN, to collectively ensure and improve computing precision and efficiency. The reliability analysis of a turbine blisk LCF life was implemented based on the the developed GRENN, by considering random input variables of temperature, rotation speed, material parameters (density, Poisson’s ratio and elastic modulus) and fatigue performance parameters (fatigue ductility coefficient, fatigue strength coefficient and fatigue ductility index and fatigue strength index) as well as the output response of the minimum fatigue life. The developed GRENN method was validated by comparison with the MC method and ERSM.
The aim of this paper was to propose a new reliability analysis method, i.e., the generalized regression extreme neural network (GRENN) method, for the reliability analysis of blisk LCF life, to improve the life and performance of turbine blisks. The developed GRENN absorbed the strengths of a generalized regression neural network (GRNN) in nonlinear mapping and small sample-based modeling, and the extremum response surface method (ERSM) for handling the transient problem of the dynamic reliability analysis of blisk LCF life. Through this study, some conclusions are summarized as follows:
The reliability degree of blisk LCF life was 0.99848 when the life allowable value was 6000 cycles. Relative to 4450 cycles acquired from the deterministic analysis after considering the double coefficient of a safe life, the LCF (6000 cycles to ensure a reliability degree of 0.99848) of the blisk obtained from the reliability design had enough life margin (about 1550 cycles) to ensure the operation of the blisk structure.
From the sensitivity analysis of a blisk, the fatigue ductility index c and gas temperature T played key roles in blisk LCF life evaluation and design. T and c were positively and negatively correlated with blisk life, respectively. The conclusions can significantly guide the optimization and design of blisk LCF life.
Through the comparison of the methods, it is demonstrated that the developed GRENN method is far better than ERSM in modeling precision and computing efficiency and is basically consistent with the MC method. Moreover, the strengths of the GRENN method become more obvious with the increasing number of simulations. It is fully supported that the proposed GRENN method is a high-accuracy and high-efficiency method to address the key questions of nonlinearity, transients and large sample-based modeling.
In summary, the efforts of this paper provide a promising method (GRENN method) for the nonlinear dynamic reliability analysis of complex structures and enrich and develop mechanical reliability theory.