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Reliability analysis using bootstrap information criterion for small sample size response functions

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Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

Statistical model selection and evaluation methods like Akaike information criteria (AIC) and Monte Carlo simulation (MCS) have often established efficient output for reliability analysis with large sample size. Information criterion can provide better model selection and evaluation in small sample sizes setup by considering the well-known measure of bootstrap resampling. Our purpose is to utilize the capabilities of bootstrap resampling in information criterion to check for uncertainty arising from model selection as well as statistics of interest for small sample size using reliability analysis. In this study, therefore, a unique and efficient simulation scheme is proposed which contemplates the best model selection devised from efficient bootstrap simulation or variance reduced bootstrap information criterion to be combined with reliability analysis. It is beneficial to compute the spread of reliability values as against solitary fixed values with desirable statistics of interest for uncertainty analysis. The proposed simulation scheme is verified using a number of sample size focused response functions under repetitions-centred approach with AIC-based reliability analysis for comparison and MCS for accuracy. The results show that the proposed simulation scheme aids the statistics of interest by reducing the spread and hence the uncertainty in sample size-based reliability analysis when compared with conventional methods.

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References

  • Akaike H (1974) A new look at the statistical model identification. IEEE Trans Autom Control 19(6):716–723

    Article  MathSciNet  MATH  Google Scholar 

  • Burnham KP, Anderson DR (2002) Model selection and multi-model inference: a practical information-theoretic approach, 2nd edn. Springer, New York

    MATH  Google Scholar 

  • Burnham KP, Anderson DR (2004) Multimodel inference: understanding AIC and BIC in model selection. Sociol Methods Res 33(2):261–304

    Article  MathSciNet  Google Scholar 

  • Cavanaugh JE, Shumway RH (1997) A bootstrap variant of AIC for state-space model selection. Stat Sin 7(2):473–496

    MathSciNet  MATH  Google Scholar 

  • Chowdhury R, Rao BN, Prasad AM (2009) High-dimensional model representation for structural reliability analysis. Commun Numer Methods Eng 25(4):301–337

    Article  MathSciNet  MATH  Google Scholar 

  • Davison AC, Hinkley DV, Schechtman E (1986) Efficient bootstrap simulation. Biometrika 73(3):555–566

    Article  MathSciNet  MATH  Google Scholar 

  • Efron B (1979) Bootstrap methods: another look at the jackknife. Ann Stat 7(1):1–26

    Article  MathSciNet  MATH  Google Scholar 

  • Efron B, Tibshirani RJ (1994) An introduction to the bootstrap. CRC press

  • Fukuda K (2015) Determining co-integration rank via bootstrap-based information criterion. Ann Biom Biostat 2(2):1016

    Google Scholar 

  • Ishiguro M, Sakamoto Y, Kitagawa G (1997) Bootstrapping log likelihood and EIC. An extension of AIC. Ann Inst Stat Math 49(3):411–434

    Article  MathSciNet  MATH  Google Scholar 

  • Kim SH, Na SW (1997) Response surface method using vector projected sampling points. Struct Saf 19(1):3–19

    Article  Google Scholar 

  • Konishi S, Kitagawa G (2008) Information criteria and statistical modeling. Springer Science & Business Media

  • Lim W (2016) Reliability-based design optimization by considering correlated and multimodal limited data. Dissertation, Hanyang University

  • Lim W, Lee TH (2012) Reliability-based design optimization using Akaike information criterion for discrete information. Trans Korean Soc Mech Eng A 36(8):921–927

    Article  Google Scholar 

  • Lim W, Lee TH, Kang S, Cho S (2016) Estimation of body and tail distribution under extreme events for reliability analysis. Struct Multidiscip Optim 54:1631–1639

    Article  MathSciNet  Google Scholar 

  • Luo Z, Atamturktur S, Juang H (2013) Bootstrapping for characterizing the effect of uncertainty in sample statistics for braced excavations. J Geotech Geoenviron Eng 139(1):13–23

    Article  Google Scholar 

  • Morris TP, White IR, Crowther MJ (2019) Using simulation studies to evaluate statistical methods. Stat Med 38(11):2074–2102

    Article  MathSciNet  Google Scholar 

  • Pan W (1999) Bootstrapping likelihood for model selection with small samples. J Comput Graph Stat 8(4):687–698

    Google Scholar 

  • Picheny V, Kim NH, Haftka RT (2010) Application of bootstrap method in conservative estimation of reliability with limited samples. Struct Multidiscip Optim 41(2):205–217

    Article  MathSciNet  MATH  Google Scholar 

  • Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6(2):461–464

    Article  MathSciNet  MATH  Google Scholar 

  • Yafune A, Funatogawa T, Ishiguro M (2005) Extended information criterion (EIC) approach for linear mixed effects models under restricted maximum likelihood (REML) estimation. Stat Med 24(22):3417–3429

    Article  MathSciNet  Google Scholar 

  • Zhang Y, Kim NH, Palliyaguru UR, Schutte JF, Haftka RT (2020) Reduced allowable strength of composite laminate for unknown distribution due to limited tests. J Compos Mater 0021998320903781

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Funding

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2019R1A2C1007644).

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Authors and Affiliations

  1. Hanyang University, Seoul, South Korea

    Eshan Amalnerkar & Tae Hee Lee

  2. Mando Corporation, Seongnam, Gyeonggi-do, South Korea

    Woochul Lim

Authors
  1. Eshan Amalnerkar
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  2. Tae Hee Lee
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  3. Woochul Lim
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Corresponding author

Correspondence to Tae Hee Lee.

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On behalf of all authors, the corresponding author states that there is no conflict of interest.

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The pseudocode for the scheme has been provided in the supplementary material.

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Responsible Editor: Nam Ho Kim

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Highlights

• Simulation scheme proposed for using ordinary bootstrap resampling in variance reduced bootstrap information criterion (EIC) for reliability analysis.

• Simulation scheme compared with Akaike information criteria and Monte Carlo simulation-based reliability analysis for various response functions.

• Small sample-based analysis with repetitions to show the robustness of method.

• Uncertainty reduction by considering spread of reliability values and not a single fixed value.

• Using model occurrence number, mean, absolute percent error and standard deviation as statistics of interest for comparisons.

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Amalnerkar, E., Lee, T.H. & Lim, W. Reliability analysis using bootstrap information criterion for small sample size response functions. Struct Multidisc Optim 62, 2901–2913 (2020). https://doi.org/10.1007/s00158-020-02724-y

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  • DOI: https://doi.org/10.1007/s00158-020-02724-y

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