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

2022 ◽  
Vol 155 ◽  
pp. 111712
Author(s):  
Donglin Yan ◽  
Yang Zheng ◽  
Wanying Liu ◽  
Tianya Chen ◽  
Qijuan Chen
2020 ◽  
Vol 37 (9) ◽  
pp. 2983-2998
Author(s):  
Lei Wang ◽  
Chuang Xiong ◽  
Qinghe Shi

Purpose Considering that uncertain factors widely exist in engineering practice, an adaptive collocation method (ACM) is developed for the structural fuzzy uncertainty analysis. Design/methodology/approach ACM arranges points in the axis of the membership adaptively. Through the adaptive collocation procedure, ACM can arrange more points in the axis of the membership where the membership function changes sharply and fewer points in the axis of the membership where the membership function changes slowly. At each point arranged in the axis of the membership, the level-cut strategy is used to obtain the cut-level interval of the uncertain variables; besides, the vertex method and the Chebyshev interval uncertainty analysis method are used to conduct the cut-level interval uncertainty analysis. Findings The proposed ACM has a high accuracy without too much additional computational efforts. Originality/value A novel ACM is developed for the structural fuzzy uncertainty analysis.


Materials ◽  
2021 ◽  
Vol 14 (17) ◽  
pp. 5033
Author(s):  
Yi Cai ◽  
Zi-Feng Liu ◽  
Tian-Yu Zhao ◽  
Jie Yang

This paper conducts a parameter interval uncertainty analysis of the internal resonance of a rotating porous shaft–disk–blade assembly reinforced by graphene nanoplatelets (GPLs). The nanocomposite rotating assembly is considered to be composed of a porous metal matrix and graphene nanoplatelet (GPL) reinforcement material. Effective material properties are obtained by using the rule of mixture and the Halpin–Tsai micromechanical model. The modeling and internal resonance analysis of a rotating shaft–disk–blade assembly are carried out based on the finite element method. Moreover, based on the Chebyshev polynomial approximation method, the parameter interval uncertainty analysis of the rotating assembly is conducted. The effects of the uncertainties of the GPL length-to-width ratio, porosity coefficient and GPL length-to-thickness ratio are investigated in detail. The present analysis procedure can give an interval estimation of the vibration behavior of porous shaft–disk–blade rotors reinforced with graphene nanoplatelets (GPLs).


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Chengcheng Xu ◽  
Chuiyu Lu ◽  
Jianhua Wang

AbstractWater inflow forecast is influenced by many factors and yields uncertain results. To more accurately predict the magnitude of water inflow and quantitatively define the corresponding response in the parameter change interval, this study combined a non-probabilistic set theory and uncertainty analysis to derive an equation for the confined water inflow. Using mining area data and comparing the calculation of upper and lower boundary limits obtained by a Monte Carlo method, results of the confined water inflow equation were calculated with relative errors of 5% and 10%. When corresponding to the rate of change of the variable parameter, the results showed that under the same error conditions, the allowable rate of change when calculating the minimum value using Eq. A was greater than when using Eq. B, and the maximum value using Eq. B yielded a greater allowable rate of change than the maximum value calculated by Eq. A. Thus, the obtained rate of change for Eq. A is indicative of the lower limit, and Eq. B is conducive to the calculation of the upper limit of mine water inflow.


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