Search

Abstract: This paper presents a Bayesian probabilistic methodology to integrate model-based fatigue damage prognosis (FDP) with online and offline structural health monitoring (SHM) data. The prognosis uses fracture mechanics-based fatigue crack growth modeling, along with quantification of various sources of uncertainty, including natural variability, data uncertainty and model errors. These uncertainty sources are connected using a Bayesian network and a probabilistic sensitivity analysis is performed to assess the uncertainty contributions from these sources. The cycle-by-cycle simulation of fatigue crack growth is expedited via the use of a surrogate modeling technique (Gaussian process model) to replace computationally expensive finite element analysis. Real-time monitoring data of external variable amplitude loading history is used to construct a Bayesian autoregressive integrated moving average (ARIMA) model to predict and update the loading. On-ground crack inspection data is used to quantify the uncertainty in the initial and current size of an existing crack, using the Bayesian approach. Three possible cases of inspection results are considered: (1) crack is not detected; (2) crack is detected but not measured; (3) crack is detected and measured. Different scenarios of data availability (load monitoring data and inspection data) are considered for the prognosis of an individual component in a fleet. A numerical example, surface cracking in a rotorcraft mast under service loading, is implemented to illustrate the proposed methodology. The results of prognosis are validated using Bayesian hypothesis testing. [Copyright &y& Elsevier]

Abstract: This paper presents a methodology for uncertainty quantification and model validation in fatigue crack growth analysis. Several models – finite element model, crack growth model, surrogate model, etc. – are connected through a Bayes network that aids in model calibration, uncertainty quantification, and model validation. Three types of uncertainty are included in both uncertainty quantification and model validation: (1) natural variability in loading and material properties; (2) data uncertainty due to measurement errors, sparse data, and different inspection results (crack not detected, crack detected but size not measured, and crack detected with size measurement); and (3) modeling uncertainty and errors during crack growth analysis, numerical approximations, and finite element discretization. Global sensitivity analysis is used to quantify the contribution of each source of uncertainty to the overall prediction uncertainty and to identify the important parameters that need to be calibrated. Bayesian hypothesis testing is used for model validation and the Bayes factor metric is used to quantify the confidence in the model prediction. The proposed methodology is illustrated using a numerical example of surface cracking in a cylindrical component. [Copyright &y& Elsevier]

Abstract: A probabilistic methodology is proposed in this paper to estimate the equivalent initial flaw size (EIFS) distribution accounting for various sources of variability, uncertainty and error, for mechanical components with complicated geometry and multi-axial variable amplitude loading conditions. A Bayesian approach is used to calibrate the distribution of EIFS, where the likelihood function is constructed from model-based fatigue crack growth analysis and inspection results. The variability, uncertainties and errors in the above procedures are quantified, and the distribution of EIFS is calibrated by explicitly accounting for the various sources of uncertainty. Three types of uncertainty are considered: (1) natural variability in loading and material properties; (2) data uncertainty, due to crack detection uncertainty, measurement errors, and sparse data; (3) modeling uncertainty and errors during crack growth analysis, numerical approximations, and finite element discretization. A Monte Carlo simulation-based approach is developed for uncertainty quantification in the crack growth analysis and for constructing the likelihood function of EIFS. The proposed methodology is illustrated by a numerical example. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents several efficient statistical inference techniques to calibrate the equivalent initial flaw size (EIFS) of fatigue cracks for mechanical components with complicated geometry and multi-axial, variable amplitude loading. Finite element analysis is used to address the complicated geometry and calculate the stress intensity factors. Multi-modal stress intensity factors due to multi-axial loading are combined to calculate an equivalent stress intensity factor using a characteristic plane approach. During cycle-by-cycle integration of the crack growth law, a Gaussian process surrogate model is used to replace the expensive finite element analysis, resulting in rapid computation. Experimental data (crack size after a particular number of loading cycles) and statistical methods are used to calibrate the EIFS. The methods of least squares and maximum likelihood method are extended to evaluate the entire probability distribution of EIFS. Bayesian techniques are also implemented for this purpose. A fast numerical integration technique is developed as an efficient alternative to the expensive Markov Chain Monte Carlo sampling approach in the Bayesian analysis. An application problem of cracking in a cylindrical structure is used to illustrate the proposed methods. [Copyright &y& Elsevier]