Jun-Ho Won

Bayesian Approach for Structural Reliability Analysis and Optimization Using the Kriging Dimension Reduction Method

An efficient method for a structural reliability analysis is proposed under the Bayesian framework, which can deal with the epistemic uncertainty arising from a limited amount of data. Until recently, conventional reliability analyses dealt mostly with the aleatory uncertainty, which is related to the inherent physical randomness and its statistical properties are completely known. In reality, however, epistemic uncertainties are prevalent, which makes the existing methods less useful. In the Bayesian approach, the probability itself is treated as a random variable of a beta distribution conditional on the provided data, which is determined by conducting a double loop of reliability analyses. The Kriging dimension reduction method is employed to promote efficient implementation of the reliability analysis, which can construct the PDF of the limit state function with favorable accuracy using a small number of analyses. Mathematical examples are used to demonstrate the proposed method. An engineering design problem is also addressed, which is to find an optimum design of a pigtail spring in a vehicle suspension, taking material uncertainty due to limited test data into account.

Reliability Analysis Under Input Variable and Metamodel Uncertainty Using Simulation Method Based on Bayesian Approach

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.

Dynamic Property Identification of Structural Systems with Hinge Joint Using Equivalent Stiffness

. Abstract: The identification of the dynamic properties of structural joints is important for predicting the dynamic behavior of assembled systems. However, the identification of the properties using analytical or experimental approaches is extremely difficult or even impossible. Several studies have proposed hybrid or synthesis methods that simultaneously used analytical and experimental approaches to identify the dynamic properties of a joint. However, among the many types of joints, only the bolt joint was treated as a practical example in these studies. In this study, for a simple assembly system comprising two plates and one hinge joint, a simple methodology involving the use of the static-based subpart analysis method to identify the dynamic properties is proposed. Finally, the proposed method is applied to a glove box in a passenger vehicle that includes hinge joints.

Integrated Bayesian Reliability Analysis under Input Variable and Metamodel Uncertainties

Reliability analysis is recently gaining more importance in the structural design process, which is to evaluate reliability due to the associated uncertainties. There are three types of uncertainties: first is the aleatory uncertainty which is irreducible and related with inherent physical randomness that is completely described by a suitable probability model. The second is the statistical uncertainty or the epistemic uncertainty, which results from the lack of knowledge due to the insufficient data, and can be reduced by collecting more information. 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, which is often required in the case of costly computation such as finite element model. 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, which is a modern computational method to draw random sequence of parameters that samples the given distribution. Mathematical and engineering examples are used to demonstrate the proposed method.

Inverse Estimation of Fatigue Life Parameters of Springs Based on the Bayesian Approach

In this study, a procedure for the inverse estimation of the fatigue life parameters of springs which utilize the field fatigue life test data is proposed to replace real test with the FEA on fatigue life prediction. The Bayesian approach is employed, in which the posterior distributions of the parameters are determined conditional on the accumulated life data that are routinely obtained from the regular tests. In order to obtain the accurate samples from the distributions, the Markov chain Monte Carlo (MCMC) technique is employed. The distributions of the parameters are used in the FEA for predicting the fatigue life in the form of a predictive interval. The results show that the actual fatigue life data are found well within the posterior predictive distributions.

Reliability Analysis under Integrated Input Variable and Metamodel Uncertainty Based on Bayesian Approach

A reliability analysis procedure is proposed based on a Bayesian framework, which can address the uncertainty in the input variables and the metamodel uncertainty of the response function in an integrated manner. The input uncertainty includes the statistical uncertainty due to the lack of knowledge or insufficient data, which is often the case in the design practice. A method of posterior prediction is used to evaluate the influence of this uncertainty. The metamodel uncertainty is accounted for, which arises due to the surrogate approximation to reduce the costly computation of the response function. Gaussian process model, also known as Kriging model, is employed to assess the associated uncertainty in the form of prediction band. Posterior distributions are obtained by Markov Chain Monte Carlo (MCMC) method, which is an efficient simulation method to draw random sequence of parameters that samples the given distribution. Mathematical and engineering examples are used to demonstrate the proposed method.