Probability Analysis of Static Frequency and Dynamic Frequency of Steam Turbine Blade Based on RBF Neural Network and Monte Carlo Simulation

Abstract

Dynamic stress of steam turbine blade has great influence on its reliability and fatigue life. In order to decrease the magnitude of dynamic stress, frequency modulation method is often used to avoid resonance, which implies the frequency of active force must be kept away from the inherent vibration frequency of blade. At present, many models of calculating inherent vibration frequency of blade are deterministic, which didn't consider the randomness of many parameters (such as loading parameters, geometric parameters, material parameters) in practical operation. So, in this paper, an equal cross-section blade is investigated and a finite element model is built parametrically. Geometrical parameters (such as length, width and thickness), material parameters (such as young's modulus and density) and rotation speed of blade are treated as input random variables while the static frequencies and dynamic frequencies are treated as output random variables. The radial basis function (RBF) neural network is adopted to model and approximate the implicit function between the inherent frequencies and input random variables. The RBF technique uses a small set of the actual data which are obtained from calling the finite element solver several times and are used to develop a trained RBF algorithm. Then a large number of function values can be obtained from the established and successfully trained RBF network and are applied by Monte Carlo simulation to obtain the statistical characteristics and cumulative distribution functions of static frequencies and dynamic frequencies of the blade. The results demonstrate that the FEM-RBF-Monte Carlo method is an optional approach for the dynamic strength reliability design of the blade as RBF network has high regression precision and rapid calculation.