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베이지안 접근법 기반 시뮬레이션 방법을 이용한 입력변수 및 근사모델 불확실성 하에서의 신뢰성 분석
안다운(Dawn An),원준호(Junho Won),김은정(Eunjeong Kim),최주호(Jooho Choi) 대한기계학회 2009 대한기계학회 춘추학술대회 Vol.2009 No.5
Reliability analysis is of great importance in product and process design. For this purpose, uncertainty analysis is needed, there are two types of uncertainties classification - according to amount of data, aleatory and epistemic uncertainty; - according to the subject, input variable and metamodel uncertainty. Aleatory uncertainty is irreducible and related with inherent physical randomness that is completely described by a suitable probability model. Epistemic uncertainty, on the other hand, results from the lack of knowledge such as insufficient data, and can be reduced by collecting more information. Input variable uncertainty is due to the uncertainty of needed variable for design, such as dimension tolerance, material propertyㆍload uncertainty. And lastly, the model uncertainty is due to the simplifying assumptions of response function. For practical reliability based design optimization, integration of input variable and metamodel uncertainty is required. This paper addresses Bayesian framework for the reliability analysis which can take account of both the input variable and metamodel uncertainties. Markov Chain Monte Carlo (MCMC) method is employed as a means for the simulation of posterior distribution. A couple of mathematical and engineering examples are used to demonstrate the proposed method.
베이지안 접근법을 이용한 입력변수 및 근사모델 불확실성 하에서의 신뢰성 분석
안다운(Dawn An),원준호(Junho Won),김은정(Eunjeong Kim),최주호(Jooho Choi) 대한기계학회 2009 大韓機械學會論文集A Vol.33 No.10
Reliability analysis is of great importance in the advanced product design, which is to evaluate reliability due to the associated uncertainties. There are three types of uncertainties: the first is the aleatory uncertainty which is related with inherent physical randomness that is completely described by a suitable probability model. The second is the epistemic uncertainty, which results from the lack of knowledge due to the insufficient data. These two uncertainties are encountered in the input variables such as dimensional tolerances, material properties and loading conditions. The third is the metamodel uncertainty which arises from the approximation of the response function. In this study, an integrated method for the reliability analysis is proposed that can address all these uncertainties in a single Bayesian framework. Markov Chain Monte Carlo (MCMC) method is employed to facilitate the simulation of the posterior distribution. Mathematical and engineering examples are used to demonstrate the proposed method.
Bayesian approach for reliability analysis of side load spring design problem
안다운(Dawn An),최주호(Jooho Choi),원준호(Junho Won) 대한기계학회 2008 대한기계학회 춘추학술대회 Vol.2008 No.5
Bayesian approach for the structural reliability analysis is proposed, which can deal with the epistemic uncertainty arising due to the limited number of data. Until recently, the conventional reliability analysis mostly dealt with the aleatory uncertainty in which the statistical properties are completely known. In practice, however, this is not the case due to the insufficient data for estimating the statistical information, which makes the existing methods less useful. In the Bayesian approach, the probability itself is a random variable conditioned by the observed data, and is represented by a PDF, which is obtained by conducting a double loop of reliability analyses. KDRM is employed for the efficient implementation of the reliability analysis, which can construct the PDF of the limit state function with favorable accuracy under a small number of analyses Mathematical examples are used to verify the proposed method. A reliability problem of a side load spring is solved as an example for practical application.
피로시험 데이터의 산포를 고려한 스프링의 신뢰성 최적설계
안다운(Dawn An),원준호(Junho Won),최주호(Jooho Choi) 대한기계학회 2008 대한기계학회 춘추학술대회 Vol.2008 No.11
Fatigue reliability problems are nowadays actively considered in the design of mechanical components. Recently, Dimension Reduction Method using Kriging approximation (KDRM) was proposed by the authors to efficiently calculate statistical moments of the response function. This method, which is more tractable for its sensitivity-free nature and providing the response PDF in a few number of analyses, is adopted in this study for the reliability analysis. Before applying this method to the practical fatigue problems, accuracies are studied in terms of parameters of the KDRM through a number of numerical examples, from which best set of parameters are suggested. In the fatigue reliability problems, good number of experimental data are necessary to get the statistical distribution of the S-N parameters. The information, however, are not always available due to the limited expense and time. In this case, a family of curves with prediction interval, called P-S-N curve, is constructed from regression analysis. Using the KDRM, once a set of responses are available at the sample points at the mean, all the reliability analyses for each P-S-N curve can be efficiently studied without additional response evaluations. The method is applied to a spring design problem as an illustration of practical applications, in which reliability-based design optimization (RBDO) is conducted by employing stochastic response surface method which includes probabilistic constraints in itself. Resulting information is of great practical value and will be very helpful for making trade-off decision during the fatigue design.
안다운(Dawn An),최주호(Jooho Choi),김남호(Nam H. Kim),Pattabhiraman Sriram 대한기계학회 2009 대한기계학회 춘추학술대회 Vol.2009 No.11
In the design considering fatigue life of mechanical components, uncertainties arising from the materials and manufacturing processes should be taken into account for ensuring reliability. Common practice in the design is to apply safety factor in conjunction with the numerical codes for evaluating the lifetime. This approach. however, most likely relies on the designer's experience. Besides, the predictions often are not in agreement with the real observations during the actual use. In this paper, a more dependable approach based on the Bayesian technique is proposed, which incorporates the field failure data with the prior knowledge to obtain the posterior distribution of the unknown parameters of the fatigue life. Posterior predictive distributions and associated values are estimated afterwards. which represents the degree of our belief of the life conditional on the observed data. As more data are provided, the values will be updated to more confident information. The results can be used in various needs such as a risk analysis, reliability based design optimization. maintenance scheduling. or validation of reliability analysis codes. In order to obtain the posterior distribution. Markov Chain Monte Carlo (MCMC) technique is employed, which is a modern statistical computational method which draws effectively the samples of the given distribution. Field data of turbine components are exploited to illustrate om approach. which counts as a regular inspection the number of failed blades in a turbine disk.