Two-dimensional extreme distribution for estimating mechanism reliability under large variance

Abstract

The effective estimation of the operational reliability of mechanism is a significant challenge in engineering practices, especially when the variance of uncertain factors becomes large. Addressing this challenge, a novel mechanism reliability method via a two-dimensional extreme distribution is investigated in the paper. The time-variant reliability problem for the mechanism is first transformed to the time-invariant system reliability problem by constructing the two-dimensional extreme distribution. The joint probability density functions (JPDFs), including random expansion points and extreme motion errors, are then obtained by combining the kernel density estimation (KDE) method and the copula function. Finally, a multidimensional integration is performed to calculate the system time-invariant reliability. Two cases are investigated to demonstrate the effectiveness of the presented method.

Keywords

Time-variant reliability / Great variance / Two-dimensional / Extreme distribution / Kernel density estimation (KDE) / Multidimensional / Integration

References

[1] Giuseppe M, Roberta S, Alba S. Reliability analysis of structures with interval uncertainties under stationary stochastic excitations. Comput Methods Appl Mech Eng, 2016, 300: 47-69.

[2] Wang Z, Liu J, Yu S. Time-variant reliability prediction for dynamic systems using partial information. Reliab Eng Syst Saf, 2019.

[3] Yu S, Wang Z. A general decoupling approach for time- and space-variant system reliability-based design optimization. Comput Methods Appl Mech Eng, 2019, 357: 112608.

[4] Zhang J, Du X. Time-dependent reliability analysis for function generation mechanisms with random joint clearances. Mech Mach Theory, 2015, 92: 184-199.

[5] Zhang D, Han X. Kinematic reliability analysis of robotic manipulator. J Mech Des, 2020, 142(4): 044502.

[6] Wang Z, Cheng X, Liu J. Time-variant concurrent reliability-based design optimization integrating experiment-based model validation. Struct Multidiscip Optim, 2018, 57(4): 1523-1531.

[7] Shi Y, Lu Z, Xu L, et al. An adaptive multiple-kriging-surrogate method for time-dependent reliability analysis. Appl Math Modell, 2019, 70: 545-571.

[8] Yu S, Wang Z. A novel time-variant reliability analysis method based on failure processes decomposition for dynamic uncertain structures. J Mech Des, 2018, 140(5): 051401.

[9] Wang J, Zhang J, Du X. Hybrid dimension reduction for mechanism reliability analysis with random joint clearances. Mech Mach Theory, 2011, 46(10): 1396-1410.

[10] Zhao Y, Ono T. Moment methods for structural reliability. Struct Saf, 2001, 23(1): 47-75.

[11] Beck A, Melchers R. On the ensemble crossing rate approach to time-variant reliability analysis of uncertain structures. Probab Eng Mech, 2004, 19(1/2): 9-19.

[12] Wang ZL, Wang ZH, Yu S, et al. Time-dependent concurrent reliability-based design optimization integrating the time-variant B-distance index. J Mech Des, 2019, 141(9): 091403.

[13] Rice S. Mathematical analysis of random noise. Bell Syst Tech J, 1944, 23(3): 282-332.

[14] Andrieu-Renaud C, Sudret B, Lemaire M. The PHI2 method: a way to compute time-variant reliability. Reliab Eng Syst Saf, 2004, 84(1): 75-86.

[15] Hu Z, Du XP. Time-variant reliability analysis with joint up crossing rates. Struct Multidiscip Optim, 2013, 48(5): 893-907.

[16] Li J, Chen JB, Fan W. The equivalent extreme-value event and evaluation of the structural system reliability. Struct Saf, 2007, 29: 112-131.

[17] Hu Z, Du XP. A sampling approach to extreme value distribution for time-variant reliability analysis. J Mech Des, 2013, 135(7): 071003.

[18] Du XP. Time-dependent mechanism reliability analysis with envelope functions and first-order approximation. J Mech Des, 2014, 136(8): 081010.

[19] Gholaminezhad I, Jamali A, Assimi H. Multi-objective reliability-based robust design optimization of robot gripper mechanism with probabilistically uncertain parameters. Neural Comput Appl, 2017, 28(1): 659-670.

[20] Yu S, Wang Z, Meng D. Time-variant reliability assessment for multiple failure modes and temporal parameters. Struct Multidiscip Optim, 2018, 58(4): 1705-1717.

[21] Moon MY, Choi KK, Cho H, et al. Reliability-based design optimization using confidence-based model validation for insufficient experimental data. J Mech Des, 2017, 139(3): 031404.

[22] Yang X, Liu Y, Mi C, et al. Active learning kriging model combining with kernel-density-estimation-based importance sampling method for the estimation of low failure probability. J Mech Des, 2018, 140(5): 051402.

[23] Yu S, Wang Z, Zhang K. Sequential time-variant reliability analysis for the lower extremity exoskeleton under uncertainty. Reliab Eng Syst Saf, 2018, 170: 45-52.

[24] Aas K, Czado C, Frigessi A, et al. Pair-copula constructions of multiple dependence. Insur Math Econ, 2009, 44(2): 182-198.

[25] Papaefthymiou G, Kurowicka D. Using copulas for modeling stochastic dependence in power system uncertainty analysis. IEEE Trans Power Syst, 2009, 4(1): 40-49.

[26] Sklar A. Random variables, joint distribution functions, and copulas. Kybernetika, 1973, 9(6): 449-460.

[27] Wang Z, Wang Z, Yu S, et al. Time-dependent mechanism reliability analysis based on envelope function and vine-copula function. Mech Mach Theory, 2019, 134: 667-684.

[28] Zhang X, Wilson A. System reliability and component importance under dependence: a copula approach. Technometrics, 2017, 59(2): 215-224.

Funding

National Key R&D Program of China(2017YFB1302301)

Fundamental Research Funds for Central Universities(ZYGX2019J043)