Arabian Journal for Science and Engineering

, Volume 44, Issue 2, pp 971–979 | Cite as

Parameter Sensitivity Analysis and Probabilistic Optimal Design for the Main-Shaft Device of a Mine Hoist

  • Hao LuEmail author
  • Yuxing Peng
  • Shuang Cao
  • Zhencai Zhu
Research Article - Mechanical Engineering


As a key component of a mine hoist system, the main-shaft device bears most of the bending moment and torque. Thus, it is important to quantify the performance of the main-shaft device and ensure the reliability of the device. The paper aims to investigate the impact of uncertain structural parameters on the reliability of the main-shaft device. The probabilistic optimal design is performed based on the parameter sensitivity results. First, the design of experiments is adopted to realize the stochastic response analysis of the main-shaft device. Second, the moment-based saddlepoint approximation method is used to evaluate the strength reliability of the device considering uncertain parameters. Next, the reliability-based sensitivity is derived to investigate the parametric significance of random input variables. Finally, the probabilistic optimal design involving the reliability sensitivity is conducted. The results of the sensitivity indicate that the torque and the contact length of left bearing have relatively greater impact on the structural reliability than other variables of the main-shaft device.


Sensitivity analysis Reliability Main-shaft device Optimization Saddlepoint approximation 

List of symbols


Cumulant generating function


Diameter of the left bearing


Diameter of the sleeve


Diameter of the right bearing


Bending moment


Approximated CGF

\(K^{{\prime }{\prime }}_{Zs}\)

Second derivation of the approximated CGF


Latin hypercube sampling


Contact length of the left bearing


Contact length of the right bearing


Strength degradation function


Initial strength




Robust design optimization


Reliability-based design optimization


Reliability-based robust design optimization


Target reliability of the ith reliability constraints


Stress response function




Strength attenuation coefficient


Basic random variable vector


Design variable vector


Lower bounds of Y


Upper bounds of Y


Performance function


Standardized variable

\(\beta \)

Reliability index

\(\mu \)\(_{Z}\)

Mean of the standardized variable

\(\sigma _{Z}\)

Standard deviation of the standardized variable

\(\gamma _{G}\)

Skewness of X

\({\varvec{\Phi }}\)

Standard normal cumulative distribution Function

\({\varvec{\theta }}\)


\(\xi \)

Dimensionless index of sensitivity

\(\omega _{i}\)

Weighting coefficients


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Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  1. 1.College of Mechanical and Electrical EngineeringChina University of Mining and TechnologyXuzhouChina
  2. 2.Jiangsu Key Laboratory of Mine Mechanical and Electrical EquipmentChina University of Mining and TechnologyXuzhouChina

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