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Research Papers: Design Automation

Uncertainty Analysis for Time- and Space-Dependent Responses With Random Variables

[+] Author and Article Information
Xinpeng Wei

Department of Mechanical and
Aerospace Engineering,
Missouri University of Science and Technology,
258A Toomey Hall 400 West 13th Street,
Rolla, MO 65409-0500
e-mail: weixinp@mst.edu

Xiaoping Du

Professor
Department of Mechanical and
Aerospace Engineering,
Missouri University of Science and Technology,
272 Toomey Hall, 400 West 13th Street,
Rolla, MO 65409-0500
e-mail: dux@mst.edu

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received June 25, 2018; final manuscript received August 31, 2018; published online December 20, 2018. Assoc. Editor: Nam H. Kim.

J. Mech. Des 141(2), 021402 (Dec 20, 2018) (6 pages) Paper No: MD-18-1486; doi: 10.1115/1.4041429 History: Received June 25, 2018; Revised August 31, 2018

The performance of a product varies with respect to time and space if the associated limit-state function involves time and space. This study develops an uncertainty analysis method that quantifies the effect of random input variables on the performance (response) over time and space. The combination of the first order reliability method (FORM) and the second-order reliability method (SORM) is used to approximate the extreme value of the response with respect to space at discretized instants of time. Then the response becomes a Gaussian stochastic process that is fully defined by the mean, variance, and autocorrelation functions obtained from FORM and SORM, and a sequential single loop procedure is performed for spatial and random variables. The method is successfully applied to the reliability analysis of a crank-slider mechanism, which operates in a specified period of time and space.

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References

Du, X. , 2015, “ Development of Engineering Uncertainty Repository,” ASME Paper No. DETC2015-46172.
Du, X. , and Chen, W. , 2001, “ A Most Probable Point-Based Method for Efficient Uncertainty Analysis,” J. Des. Manuf. Autom., 4(1–2), pp. 47–66.
Hu, Z. , and Du, X. , 2012, “ Reliability Analysis for Hydrokinetic Turbine Blades,” Renewable Energy, 48, pp. 251–262. [CrossRef]
Hu, Z. , and Du, X. , 2014, “ Lifetime Cost Optimization With Time-Dependent Reliability,” Eng. Optim., 46(10), pp. 1389–1410. [CrossRef]
Hu, Z. , Li, H. , Du, X. , and Chandrashekhara, K. , 2013, “ Simulation-Based Time-Dependent Reliability Analysis for Composite Hydrokinetic Turbine Blades,” Struct. Multidiscip. Optim., 47(5), pp. 765–781. [CrossRef]
Choi, S. K. , Canfield, R. A. , and Grandhi, R. V. , 2007, Reliability-Based Structural Design, Springer, London.
Du, X. , Sudjianto, A. , and Huang, B. , 2005, “ Reliability-Based Design With the Mixture of Random and Interval Variables,” ASME J. Mech. Des., 127(6), pp. 1068–1076. [CrossRef]
Huang, B. , and Du, X. , 2008, “ Probabilistic Uncertainty Analysis by Mean-Value First Order Saddlepoint Approximation,” Reliab. Eng. Syst. Saf., 93(2), pp. 325–336. [CrossRef]
Zhang, J. , and Du, X. , 2010, “ A Second-Order Reliability Method With First-Order Efficiency,” ASME J. Mech. Des., 132(10), p. 101006. [CrossRef]
Madsen, H. O. , Krenk, S. , and Lind, N. C. , 1985, “ Methods of Structural Safety,” Prentice Hall, Englewood Cliffs, NJ.
Banerjee, B. , and Smith, B. G. , 2011, “ Reliability Analysis for Inserts in Sandwich Composites,” Proc. Adv. Mater. Res., 275, pp. 234–238. [CrossRef]
Kim, D.-W. , Jung, S.-S. , Sung, Y.-H. , and Kim, D.-H. , 2011, “ Optimization of SMES Windings Utilizing the First-Order Reliability Method,” Trans. Korean Inst. Electr. Eng., 60(7), pp. 1354–1359. [CrossRef]
Huang, B. , and Du, X. , 2006, “ Uncertainty Analysis by Dimension Reduction Integration and Saddlepoint Approximations,” ASME J. Mech. Des., 128(1), pp. 26–33. [CrossRef]
Jin, R. , Du, X. , and Chen, W. , 2003, “ The Use of Metamodeling Techniques for Optimization Under Uncertainty,” Struct. Multidiscip. Optim., 25(2), pp. 99–116. [CrossRef]
Isukapalli, S. , Roy, A. , and Georgopoulos, P. , 1998, “ Stochastic Response Surface Methods (SRSMs) for Uncertainty Propagation: Application to Environmental and Biological Systems,” Risk Anal., 18(3), pp. 351–363. [CrossRef] [PubMed]
Zhu, Z. , and Du, X. , 2016, “ Reliability Analysis With Monte Carlo Simulation and Dependent Kriging Predictions,” ASME J. Mech. Des., 138(12), p. 121403. [CrossRef]
Xiong, F. , Xiong, Y. , Greene, S. , Chen, W. , and Yang, S. , 2010, “ A New Sparse Grid Based Method for Uncertainty Propagation,” Struct. Multidiscip. Optim., 41(3), pp. 335–349. [CrossRef]
Ditlevsen, O. , and Madsen, H. O. , 1996, Structural Reliability Methods, Wiley, New York.
Soboĺ, I. , 1990, “ Quasi-Monte Carlo Methods,” Prog. Nucl. Energy, 24(1–3), pp. 55–61. [CrossRef]
Dey, A. , and Mahadevan, S. , 1998, “ Ductile Structural System Reliability Analysis Using Adaptive Importance Sampling,” Struct. Saf., 20(2), pp. 137–154. [CrossRef]
Au, S.-K. , and Beck, J. L. , 2001, “ Estimation of Small Failure Probabilities in High Dimensions by Subset Simulation,” Probab. Eng. Mech., 16(4), pp. 263–277. [CrossRef]
Der Kiureghian, A. , and Ke, J.-B. , 1988, “ The Stochastic Finite Element Method in Structural Reliability,” Probab. Eng. Mech., 3(2), pp. 83–91. [CrossRef]
Ghanem, R. G. , and Spanos, P. D. , 1991, “ Stochastic Finite Element Method: Response Statistics,” Stochastic Finite Elements: A Spectral Approach, Springer, New York, pp. 101–119.
Andrieu-Renaud, C. , Sudret, B. , and Lemaire, M. , 2004, “ The PHI2 Method: A Way to Compute Time-Variant Reliability,” Reliab. Eng. Syst. Saf., 84(1), pp. 75–86. [CrossRef]
Hu, Z. , and Du, X. , 2013, “ Time-Dependent Reliability Analysis With Joint Upcrossing Rates,” Struct. Multidiscip. Optim., 48(5), pp. 893–907. [CrossRef]
Jiang, C. , Wei, X. P. , Huang, Z. L. , and Liu, J. , 2017, “ An Outcrossing Rate Model and Its Efficient Calculation for Time-Dependent System Reliability Analysis,” ASME J. Mech. Des., 139(4), p. 041402. [CrossRef]
Hu, Z. , and Du, X. , 2015, “ Mixed Efficient Global Optimization for Time-Dependent Reliability Analysis,” ASME J. Mech. Des., 137(5), p. 051401. [CrossRef]
Hu, Z. , and Mahadevan, S. , 2016, “ A Single-Loop Kriging Surrogate Modeling for Time-Dependent Reliability Analysis,” ASME J. Mech. Des., 138(6), p. 061406. [CrossRef]
Wang, Z. , and Chen, W. , 2016, “ Time-Variant Reliability Assessment Through Equivalent Stochastic Process Transformation,” Reliab. Eng. Syst. Saf., 152, pp. 166–175. [CrossRef]
Wang, Z. , and Wang, P. , 2012, “ A Nested Extreme Response Surface Approach for Time-Dependent Reliability-Based Design Optimization,” ASME J. Mech. Des., 134(12), p. 121007. [CrossRef]
Wang, Z. , Mourelatos, Z. P. , Li, J. , Baseski, I. , and Singh, A. , 2014, “ Time-Dependent Reliability of Dynamic Systems Using Subset Simulation With Splitting Over a Series of Correlated Time Intervals,” ASME J. Mech. Des., 136(6), p. 061008. [CrossRef]
Singh, A. , Mourelatos, Z. , and Nikolaidis, E. , 2011, “ Time-Dependent Reliability of Random Dynamic Systems Using Time-Series Modeling and Importance Sampling,” SAE Int. J. Mater. Manuf., 4(1), pp. 929–946. [CrossRef]
Chen, J.-B. , and Li, J. , 2005, “ Dynamic Response and Reliability Analysis of Non-Linear Stochastic Structures,” Probab. Eng. Mech., 20(1), pp. 33–44. [CrossRef]
Du, X. , 2014, “ Time-Dependent Mechanism Reliability Analysis With Envelope Functions and First-Order Approximation,” ASME J. Mech. Des., 136(8), p. 081010. [CrossRef]
Yu, S. , and Wang, Z. , 2018, “ A Novel Time-Variant Reliability Analysis Method Based on Failure Processes Decomposition for Dynamic Uncertain Structures,” ASME J. Mech. Des., 140(5), p. 051401. [CrossRef]
Yu, S. , Wang, Z. , and Meng, D. , 2018, “ Time-Variant Reliability Assessment for Multiple Failure Modes and Temporal Parameters,” Struct. Multidiscip. Optim., 58(4), pp. 1705–1717.
Hu, Z. , and Mahadevan, S. , 2018, “ Reliability Analysis of Multidisciplinary System With Spatio-Temporal Response Using Adaptive Surrogate Modeling,” AIAA Paper No. AIAA 2018-1934.
Hu, Z. , and Mahadevan, S. , 2017, “ A Surrogate Modeling Approach for Reliability Analysis of a Multidisciplinary System With Spatio-Temporal Output,” Struct. Multidiscip. Optim., 56(3), pp. 553–569. [CrossRef]
Shi, Y. , Lu, Z. , Cheng, K. , and Zhou, Y. , 2017, “ Temporal and Spatial Multi-Parameter Dynamic Reliability and Global Reliability Sensitivity Analysis Based on the Extreme Value Moments,” Struct. Multidiscip. Optim., 56(1), pp. 117–129. [CrossRef]
Shi, Y. , Lu, Z. , Zhang, K. , and Wei, Y. , 2017, “ Reliability Analysis for Structures With Multiple Temporal and Spatial Parameters Based on the Effective First-Crossing Point,” ASME J. Mech. Des., 139(12), p. 121403. [CrossRef]
Hu, Z. , and Du, X. , 2015, “ A Random Field Approach to Reliability Analysis With Random and Interval Variables,” ASCE-ASME J. Risk Uncertainty Eng. Syst., Part B: Mech. Eng., 1(4), p. 041005. [CrossRef]
Hu, Z. , and Du, X. , 2016, “ A Random Field Method for Time-Dependent Reliability Analysis With Random and Interval Variables,” ASME Paper No. DETC2016-59031.
Guo, J. , and Du, X. , 2010, “ Reliability Analysis for Multidisciplinary Systems With Random and Interval Variables,” AIAA J., 48(1), pp. 82–91. [CrossRef]
Lophaven, S. N. , Nielsen, H. B. , and Søndergaard, J. , 2002, DACE: A Matlab Kriging Toolbox, Technical University of Denmark, Kgs. Lyngby, Denmark.
Hu, Z. , and Du, X. , 2015, “ First Order Reliability Method for Time-Variant Problems Using Series Expansions,” Struct. Multidiscip. Optim., 51(1), pp. 1–21. [CrossRef]
Jiang, C. , Lu, G. , Han, X. , and Liu, L. , 2012, “ A New Reliability Analysis Method for Uncertain Structures With Random and Interval Variables,” Int. J. Mech. Mater. Des., 8(2), pp. 169–182. [CrossRef]

Figures

Grahic Jump Location
Fig. 2

The procedure of updating β(t) using SORM

Grahic Jump Location
Fig. 3

Flow chart of the complete procedure

Grahic Jump Location
Fig. 4

Probability of failure over different time intervals

Grahic Jump Location
Fig. 5

A slider mechanism

Grahic Jump Location
Fig. 6

Probability of failure over different time intervals

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