Uncertainty analysis of rock tunnel based on fractional moment and dimensional reduction method

2021 ◽  
Vol 139 ◽  
pp. 104656
Author(s):  
Hongbo Zhao ◽  
Shaojun Li ◽  
Changxing Zhu
Keyword(s):  
Uncertainty Analysis ◽  
Dimensional Reduction ◽  
Reduction Method ◽  
Fractional Moment ◽  
Dimensional Reduction Method ◽  
Rock Tunnel

Computationally Efficient Reliability Analysis of Mechanisms Based on a Multiplicative Dimensional Reduction Method

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
Xufang Zhang ◽  
Mahesh D. Pandey ◽  
Yimin Zhang
Keyword(s):  
Reliability Analysis ◽  
Dimensional Reduction ◽  
System Reliability ◽  
Reduction Method ◽  
Maximum Output ◽  
Computationally Efficient ◽  
Output Error ◽  
System Reliability Analysis ◽  
Dimensional Reduction Method ◽  
Fractional Moments

The paper presents a computationally efficient method for system reliability analysis of mechanisms. The reliability is defined as the probability that the output error remains within a specified limit in the entire target trajectory of the mechanism. This mechanism reliability problem is formulated as a series system reliability analysis that can be solved using the distribution of maximum output error. The extreme event distribution is derived using the principle maximum entropy (MaxEnt) along with the constraints specified in terms of fractional moments. To optimize the computation of fractional moments of a multivariate response function, a multiplicative form of dimensional reduction method (M-DRM) is developed. The main benefit of the proposed approach is that it provides full probability distribution of the maximal output error from a very few evaluations of the trajectory of mechanism. The proposed method is illustrated by analyzing the system reliability analysis of two planar mechanisms. Examples presented in the paper show that the results of the proposed method are fairly accurate as compared with the benchmark results obtained from the Monte Carlo simulations.

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