Ruoxue Zhang

Model uncertainty and Bayesian updating in reliability-based inspection

In this paper, a Bayesian procedure is proposed to quantify the modeling uncertainty, including the uncertainty in mechanical and statistical model selection and the uncertainty in distribution parameters. The procedure is developed first using a simple example and then is applied to a fatigue reliability problem, with the combination of two competing crack growth models and considering the uncertainty in the statistical distribution parameters for each model. This Bayesian failure probability analysis can be incorporated with information from nondestructive inspections performed on the structure to derive more realistic reliability estimates. The procedure for updating the mechanical model, probabilistic model, distribution parameter statistics and reliability is illustrated for the fatigue reliability problem.

Bayesian networks for system reliability reassessment

Abstract This paper proposes a methodology to apply Bayesian networks to structural system reliability reassessment, with the incorporation of two important features of large structures: (1) multiple failure sequences, and (2) correlations between component-level limit states. The proposed method is validated by analytical comparison with the traditional reliability analysis methods for series and parallel systems. The Bayesian network approach is combined with the branch-and-bound method to improve its efficiency and to facilitate its application to large structures. A framed structure with multiple potential locations of plastic hinges and multiple failure sequences is analyzed to illustrate the proposed method.

Bayesian methodology for reliability model acceptance

Abstract This paper develops a methodology to assess the reliability computation model validity using the concept of Bayesian hypothesis testing, by comparing the model prediction and experimental observation, when there is only one computational model available to evaluate system behavior. Time-independent and time-dependent problems are investigated, with consideration of both cases: with and without statistical uncertainty in the model. The case of time-independent failure probability prediction with no statistical uncertainty is a straightforward application of Bayesian hypothesis testing. However, for the life prediction (time-dependent reliability) problem, a new methodology is developed in this paper to make the same Bayesian hypothesis testing concept applicable. With the existence of statistical uncertainty in the model, in addition to the application of a predictor estimator of the Bayes factor, the uncertainty in the Bayes factor is explicitly quantified through treating it as a random variable and calculating the probability that it exceeds a specified value. The developed method provides a rational criterion to decision-makers for the acceptance or rejection of the computational model.

Reliability-based reassessment of corrosion fatigue life

Abstract A reliability-based evaluation approach for pitting corrosion fatigue damage which combines analytical estimation and nondestructive inspection is developed in this paper. First, a mechanics-based probabilistic life model for the corrosion fatigue on the surface of a lap sheet is established and then a reassessment approach is developed after in-service inspection. The reliability of the NDI technique is quantified through a probabilistic description of its detectability and accuracy. The reassessment approach incorporates the reliability of the NDI technique, inspection data and prior prediction in a probabilistic framework for decisions regarding maintenance or repair. The methodology is illustrated through a numerical example and the effect of the reliability of the NDI technique on reassessment results is investigated.

Integration of computation and testing for reliability estimation

Abstract This paper develops a methodology to integrate reliability testing and computational reliability analysis for product development. The presence of information uncertainty such as statistical uncertainty and modeling error is incorporated. The integration of testing and computation leads to a more cost-efficient estimation of failure probability and life distribution than the tests-only approach currently followed by the industry. A Bayesian procedure is proposed to quantify the modeling uncertainty using random parameters, including the uncertainty in mechanical and statistical model selection and the uncertainty in distribution parameters. An adaptive method is developed to determine the number of tests needed to achieve a desired confidence level in the reliability estimates, by combining prior computational prediction and test data. Two kinds of tests — failure probability estimation and life estimation — are considered. The prior distribution and confidence interval of failure probability in both cases are estimated using computational reliability methods, and are updated using the results of tests performed during the product development phase.

Fatigue test planning using reliability and confidence simulation

This paper develops a methodology for reliability test planning using computational reliability methods. Empirical methods of reliability estimation are based on tests on actual components and the use of classical statistics. Computational methods of reliability analysis propagate the uncertainty information about primitive variables through the system computational model to estimate the reliability. This paper combines the two approaches for cost-effective reliability testing. The proposed method also includes the uncertainties due to limitations and bias in data and the computational model. An adaptive method is developed to determine the number of tests needed to achieve a desired confidence level in the reliability estimate, by combining computational prediction and test data. The proposed approach is applied to the probabilistic life prediction of a composite helicopter rotor hub under fatigue loading, based on the delamination failure analysis of composite laminates.

Validation of Reliability Prediction Models

This paper proposes new methods to assess the validity of reliability prediction models through a Bayesian approach. The concept of Bayesian hypothesis testing is extended to system-level problems where full-scale testingis impossible. Component-level validation results are used to derive a system-level validation measure. This derivation depends on the knowledge of interrelationships between component modules. Bayes networks are used for the propagation of validation information from the component-level to system-level. Validation of reliability prediction model for a single degree of freedom oscillator under high-cycle fatigue and fatigue life prediction of a helicopter rotor hub is illustrated for this purpose.