- Volume 37 Issue 7
DOI QR Code
Comparative Study of Reliability Analysis Methods for Discrete Bimodal Information
바이모달 이산정보에 대한 신뢰성해석 기법 비교
- Lim, Woochul (Dept. of Automotive Engineering, College of Engineering, Hanyang Univ.) ;
- Jang, Junyong (Dept. of Automotive Engineering, College of Engineering, Hanyang Univ.) ;
- Lee, Tae Hee (Dept. of Automotive Engineering, College of Engineering, Hanyang Univ.)
- Received : 2012.12.28
- Accepted : 2013.05.29
- Published : 2013.07.01
The distribution of a response usually depends on the distribution of a variable. When the distribution of a variable has two different modes, the response also follows a distribution with two different modes. In most reliability analysis methods, the number of modes is irrelevant, but not the type of distribution. However, in actual problems, because information is often provided with two or more modes, it is important to estimate the distributions with two or more modes. Recently, some reliability analysis methods have been suggested for bimodal distributions. In this paper, we review some methods such as the Akaike information criterion (AIC) and maximum entropy principle (MEP) and compare them with the Monte Carlo simulation (MCS) using mathematical examples with two different modes.
Reliability Analysis;Akaike Information Criterion(AIC);Finite Mixture Model(FMM);Maximum Entropy Principle;Monte Carlo Simulation(MCS);Bimodal Distribution
Supported by : 한국연구재단
- Buslenko, N.P., Golenko, D.I., Shreider, Y.A., Sobol, I.M. and Sragowich, V.G., 1994, The Monte Carlo Method, Pergamon Press.
- Cornell, C.A., 1969, "A Probability-based Structural Code," Journal of the American Concrete Institute, Vol.66, No.12, pp.974-985.
- Breitung, K., 1984, "Asymptotic Approximations for Multinormal Integrals," Journal of Engineering Mechanics Division, ASCE, Vol. 110, No. 3, pp. 357-366. https://doi.org/10.1061/(ASCE)0733-9399(1984)110:3(357)
- Rahman, S. and Xu, H., 2004, "A Univariate Dimension-Reduction Method for Multi-Dimensional Integration in Stochastic Mechanics," Probabilistic Engineering Mechanics, Vol. 19, No. 4, pp. 393-408. https://doi.org/10.1016/j.probengmech.2004.04.003
- Jung, J. J., 2007, Multiplicative Decomposition Method for Accurate Moment-Based Reliability Analysis, Ph.D. thesis, Hanyang University.
- Choi, J., Hong, S., Chi, S., Lee, H., Park, C., Kim, H., Yeu, T. and Lee, T. H., 2011, "Probability Distribution for the Shear Strength of Seafloor Sediment in the KR5 Area for the Development of Manganese Nodule Miner," Ocean Engineering, Vol. 38, pp. 2033-2041. https://doi.org/10.1016/j.oceaneng.2011.09.011
- Kim, S., Jun, S., Kang H., Park Y., and Lee D., 2011, "Reliability Based Optimal Design of a Helicopter Considering Annual Variation of Atmospheric Temperature," Journal of Mechanical Science and Technology, Vol. 25, pp. 1095-1104. https://doi.org/10.1007/s12206-011-0303-5
- Fu, G. and Moses, F., 1993, "Multimodal Simulation Method for System Reliability Analysis," Journal of Engineering Mechanics, Vol. 119, No. 6, pp. 1173-1179. https://doi.org/10.1061/(ASCE)0733-9399(1993)119:6(1173)
- Lim, W. and Lee, T. H., 2012, "Reliability-based Design Optimization Using Akaike Information Criterion for Discrete Information," Trans. Korean Soc. Mech. Eng. A, Vol. 36, No. 6, pp. 921-927. https://doi.org/10.3795/KSME-A.2012.36.8.921
- Xi, Z., Hu, C. and Youn B. D., 2012, "A Comparative Study of Probability Estimation Methods for Reliability Analysis," Struct. Multidisc. Optim., Vol. 45, pp. 33-52. https://doi.org/10.1007/s00158-011-0656-5
- Lim, W. and Lee, T. H., 2012, Akaike Information Criterion-based Reliability Analysis for Bimodal Discrete Information, Trans. Korean Soc. Mech. Eng. A, Vol. 36, No. 12. https://doi.org/10.3795/KSME-A.2012.36.12.1605
- Johnson, N. L., Kotz, S. and Balakrishnan, L., 1994, Continuous univariate distributions, Vol. 1, Wiley-Interscience.
- Akaike, H., 1973, "Information theory and an extension of the maximum likelihood principle," Proceedings of the Second International Symposium on Information Theory, pp. 267-281.
- Hurvich, C. M., Simonoff, J. S. and Tsai, C. L., 1998, "Smoothing Parameter Selection in Nonparametric Regression using an Improved Akaike Informaion Criterion," Journal of the Royal Statistical Society Series B-Statistical Methodology, Vol.60, pp. 271-293. https://doi.org/10.1111/1467-9868.00125
- Spendelow, J. A., Nichols, J. D., Nisbet, I. C. T., Hays, H., Cormons, G. D., Burger, J., Safina, C., Hines, J. E. and Gochfeld, M., 1995, "Estimating Annual Survival and Movement Rates of Adults within a Metapopulation of Roseate Terns," Ecology, Vol. 76, No. 8, pp. 2415-2428. https://doi.org/10.2307/2265817
- Go, S. J., Lee, M. C. and Park, M. K., 2001, "Fuzzy Sliding Mode Control of a Polishing Robot based on Genetic Algorithm," Journal of Mechanical Science and Technology, Vol. 15, No. 5, pp. 580-591.
- Sakamoto, Y., Ishiguro, M. and Kitagawa, G., 1986, Akaike Information Criterion Statistics, KTK Scientific Publishers.
- Jaynes, E. T., 1957, "Information Theory and Statistical Mechanics," Physical Review, Vol. 106, No. 4, pp. 620-630. https://doi.org/10.1103/PhysRev.106.620
- Mead, L. R. and Papanicolaou, N., 1984, "Maximum Entropy in the Problem of Moments," Journal of Mathematical Physics, Vol. 25, pp.2404-2417. https://doi.org/10.1063/1.526446
- Neal, M. R., 2003, "Slice Sampling," The Annals of Statistics, Vol. 31, No. 3, pp. 705-767. https://doi.org/10.1214/aos/1056562461