Interval uncertainty analysis of vibration response of hydroelectric generating unit based on Chebyshev polynomial

Abstract

The uncertainty of the hydroelectric generating unit (HGU) is unavoidable in practical engineering. However, up to now, the research about influences of the uncertain parameters on the system responses is still very scarce, especially in the case that the probability distribution of the uncertain parameter is not clear. So, this paper will aim to study the influence of interval uncertain parameters on the vibration response characteristics of HGU. Firstly, a nonlinear mathematical model of rotor-shaft-bearing system of the HGU is established under the action of interval uncertain parameters. Then, based on Chebyshev polynomial and interval analysis theory, three feasible analysis methods of interval uncertainty for the HGU are proposed, which are also compared with the brute-force Monte Carlo Simulation (MCS) method. And it is proved the proposed Chebyshev-MCS method has higher accuracy and lower cost obtaining the vibration response boundary of the HGU. Next, using Chebyshev-MCS method, the uncertain response characteristics of the system under single parameter, multiple parameters and shock excitation are further analyzed, respectively. Meanwhile, the upper and lower boundaries of the vibration response under different degrees of uncertainty and rotational speeds are obtained. Besides, the coupling effects of several uncertain parameters on the vibration response under the rated rotational speed condition are also presented. And the influence of uncertain parameters on the transient characteristics of the system under shock excitation is also gotten. More importantly, the proposed method and obtained conclusions are helpful to the manufacture, installation, operation of the HGU.