Parameter distribution characteristics of material fatigue life using improved bootstrap method

Abstract

The bootstrap method is mostly used to estimate statistical characteristics of small sample data. However, the limitations of the bootstrap method itself lead to a reduction in the reliability of small-sample estimates. In this article, an improved bootstrap method is developed to address this problem. In the statistically significant error range (the sample average error and the limit error of sampling) of the original single sample data, expanding the virtual test data that obey two distributions to overcome the limitations of the bootstrap method itself. This article compares and analyses these two methods through the case; the result indicates that the improved bootstrap method can enhance the reliability of the estimation results without changing its probability distribution. We also discussed how to reduce the fluctuation of the improved bootstrap method. And the effectiveness and feasibility of this improved method are discussed in the analysis of fatigue life test data.

Keywords

Distribution characteristics fatigue life error range bootstrap method small sample

Get full access to this article

View all access options for this article.

References

Bai

(2007) A New Resampling Method to Improve Quality Research with Small Samples, Cincinnati: University of Cincinnati.

Beran

(1992) The Bootstrap and Edgeworth Expansion by Peter Hall, New York: Springer-Verlag.

Bhachu KS, Haftka RT and Kim NH (2015) Using bootstrap to assess sampling uncertainty in fatigue crack growth life. In: 17th AIAA non-deterministic approaches conference. Kissimmee, Florida: American Institute of Aeronautics and Astronautics.

Chen

Zheng

Feng

(2017) Statistical dependency analysis of multiple competing failure causes of fuel cell engines. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability 231: 83–90.

Danielsson

de Haan

Peng

et al. (2001) Using a bootstrap method to choose the sample fraction in tail index estimation. Journal of multivariate analysis 76: 226–248.

Diaconis

Holmes

(1994) Gray codes for randomization procedures. Statistics and Computing 4: 287–302.

Dvison

Hinkley

Schechtman

(1986) Efficient bootstrap simulation. Biometrika 73: 555–566.

Efron

(1979) Bootstrap methods: Another look at the jackknife. The Annals of Statistics 7: 1–26.

Efron

(1997) Improvements on cross-validation: the 632+bootstrap method. Journal of the American Statistical Association 92: 548–560.

10.

Efron

Tibshirani

(1993) An Introduction to the Bootstrap, New York: Chapman & Hall.

11.

Fang

Zhang

(2013) A comparison of the analysis of simple mediating effect of the parametric and nonparametric bootstrap methods. Journal of Psychological Science 36: 722–727.

12.

Fisher

(1937) On a point raised by M.S.Bartlett on fiducial probability. Annals of Eugenics 7: 370–375.

13.

Haibach E (2003) Analytical Strength Assessment of Components in Mechanical Engineering (5th edition). Frank-furt: FKM Guideline.

14.

Ghosh

(2008) Analysis of the interpretation of yielding and strengthening behavior in small-size samples. Acta Materialia 56: 2353–2362.

15.

Graham

Hinkley

John

PWM

et al. (1990) Balanced design of bootstrap simulations. Journal of the Royal Statistical Society. Series B (Methodological) 52: 185–202.

16.

Hahn

Newey

(2004) Jackknife and analytical bias reduction for nonlinear panel models. Econometrica 72: 1295–1319.

17.

Hall

(1992) On bootstrap confidence intervals in nonparametric regression. The Annals of Statistics 20: 695–711.

18.

Joshi

Seidel-Morgenstern

Kremling

(2006) Exploiting the bootstrap method for quantifying parameter confidence intervals in dynamical systems. Metabolic Engineering 8: 447–455.

19.

Kijewski

Kareem

(2002) On the reliability of a class of system identification techniques: Insights from bootstrap theory. Structural Safety 24: 261–280.

20.

Konietschke

Bathke

Harrar

et al. (2015) Parametric and nonparametric bootstrap methods for general MANOVA. Journal of multivariate analysis 140: 291–301.

21.

Kreiss

J-P

Paparoditis

(2011) Bootstrap methods for dependent data: A review. Journal of the Korean Statistical Society 40: 357–378.

22.

Lahiri

(2003) Resampling Methods for Dependent Data, New York: Springer.

23.

Larsen

JEP

Lund

Nielsen

(2006) Improved method for predicting linear B-cell epitopes. Immunome Research 2: 2.

24.

Linton

Song

Whang

Y-J

(2010) An improved bootstrap test of stochastic dominance. Journal of Econometrics 154: 186–202.

25.

Chen

et al. (2016) Dispersion analysis of Lamb waves in composite laminates based on reverberation-ray matrix method. Composite Structures 136: 419–429.

26.

Mackinnon

Lockwood

Williams

(2004) Confidence limits for the indirect effect: Distribution of the product and resampling methods. Multivariate Behavioral Research 39: 99.

27.

Peters

Wüthrich

Shevchenko

(2010) Chain ladder method: Bayesian bootstrap versus classical bootstrap. Insurance Mathematics and Economics 47: 36–51.

28.

Pituch

Stapleton

(2008) The performance of methods to test upper-level mediation in the presence of nonnormal data. Multivariate Behavioral Research 43: 237–267.

29.

Sanderson

Wojciechowski

(2000) Improved bootstrap confidence limits in large-scale phylogenies, with an example from Neo-Astragalus (Leguminosae). Systematic Biology 49: 671–685.

30.

Särndal

Swensson

Wretman

(1992) Model Assisted Survey Sampling, New York: Springer-Verlag.

31.

Wen

Sun

et al. (2017) Rough set-support vector machine-based real-time monitoring model of safety status during dangerous dam reinforcement. International Journal of Damage Mechanics 26: 501–522.

32.

Troendle

Korn

McShane

(2004) An example of slow convergence of the bootstrap in high dimensions. The American statistician 58: 25–29.

33.

Uchida

Kojima

Iida

(1980) Determination of metals in small samples by atomic absorption and emission spectrometry with discrete nebulization. Analytica Chimica Acta 116: 205–210.

34.

van der Laarse

van Leuven

HCE

(1966) A rapid method for the simultaneous determination of total carbon and carbon-14 in small samples. Analytica Chimica Acta 34: 370–371.

35.

Veritas DN. (2011) Fatigue Design of Offshore Steel Structures, (DNV-RP-C203) 176.

36.

Wang

Xue

et al. (2017a) Bootstrap analysis of designed experiments for reliability improvement with a non-constant scale parameter. Reliability Engineering & System Safety 160: 114–121.

37.

Wang

Liu

Wang

et al. (2017b) Fatigue test analysis of automotive key parts based on censored data and small sample setting. Quality and Reliability Engineering International 33: 1031–1043.

38.

Wang

Liu

Wang

et al. (2018a) Probabilistic modeling of unified S-N curves for mechanical parts. International Journal of Damage Mechanics 27: 979–999.

39.

Wang

Liu

Wang

et al. (2018b) Research on load-spectrum construction of automobile key parts based on Monte Carlo sampling. Journal of Testing & Evaluation 46: 1099–1110.

40.

Wang

Sun

et al. (2014) Gray bootstrap method for estimating frequency-varying random vibration signals with small samples. Chinese Journal of Aeronautics 27: 383–389.

41.

Wormsen

Avice

Fjeldstad

et al. (2015) Base material fatigue data for low alloy forged steels used in the subsea industry. Part 1: In air S–N data. International Journal of Fatigue 80: 477–495.

42.

(2017) Elastoplastic damage micromechanics for continuous fiber-reinforced ductile matrix composites with progressive fiber breakage. International Journal of Damage Mechanics 26: 4–28.

43.

Yan

Xie

et al. (2012) Reliability apportionment approach for spacecraft solar array using fuzzy reasoning Petri net and fuzzy comprehensive evaluation. Acta Astronautica 76: 136–144.

44.

Yan

Zuo

(2016) Evaluating the reliability of multi-body mechanisms: A method considering the uncertainties of dynamic performance. Reliability Engineering & System Safety 149: 96–106.

45.

Xie

Liao

Jin

(2014) Maximizing system availability through joint decision on component redundancy and spares inventory. European Journal of Operational Research 237: 164–176.

46.

Yaghoubi

Vakilzadeh

Abrahamsson

TJS

(2018) Automated modal parameter estimation using correlation analysis and bootstrap sampling. Mechanical Systems and Signal Processing 100: 289–310.

47.

Young Min

Yongku

(2017) Bootstrap methods for long-memory processes: a review. Communications for Statistical Applications and Methods 24: 1–13.

48.

Yang

Song

et al. (2016) An improved model-free sampling technique based on bootstrap methods. ASME International Mechanical Engineering Congress and Exposition 14: V014T14A007, DOI: 10.1115/IMECE2016-66404.

49.

Zar

(2007) Biostatistical Analysis, 5th ed. New Jersey: Prentice-Hall, Inc.

50.

Zhang

Chu

et al. (2014) Uncertainty analysis of hydrological model parameters based on the bootstrap method: A case study of the SWAT model applied to the Dongliao River Watershed, Jilin Province, Northeastern China. Science China Technological Sciences 57: 219–229.

51.

Zhou

Zhu

et al. (2017) Modeling microcapsule-enabled self-healing cementitious composite materials using discrete element method. International Journal of Damage Mechanics 26: 340–357.

52.

Zhu

S-P

Huang

H-Z

Wang

Z-L

(2011) Fatigue life estimation considering damaging and strengthening of low amplitude loads under different load sequences using fuzzy sets approach. International Journal of Damage Mechanics 20: 876–899.