Results 1 - 10 of 35
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[en] This paper presents a model selection methodology for maximizing the accuracy in the predicted distribution of a stochastic output of interest subject to an available computational budget. Model choices of different resolutions/fidelities such as coarse vs. fine mesh and linear vs. nonlinear material model are considered. The proposed approach makes use of efficient simulation techniques and mathematical surrogate models to develop a model selection framework. The model decision is made by considering the expected (or estimated) discrepancy between model prediction and the best available information about the quantity of interest, as well as the simulation effort required for the particular model choice. The form of the best available information may be the result of a maximum fidelity simulation, a physical experiment, or expert opinion. Several different situations corresponding to the type and amount of data are considered for a Monte Carlo simulation over the input space. The proposed methods are illustrated for a crack growth simulation problem in which model choices must be made for each cycle or cycle block even within one input sample
[en] 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
[en] 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
[en] This paper develops a damage tolerance reliability analysis methodology for automotive spot-welded joints under multi-axial and variable amplitude loading history. The total fatigue life of a spot weld is divided into two parts, crack initiation and crack propagation. The multi-axial loading history is obtained from transient response finite element analysis of a vehicle model. A three-dimensional finite element model of a simplified joint with four spot welds is developed for static stress/strain analysis. A probabilistic Miner's rule is combined with a randomized strain-life curve family and the stress/strain analysis result to develop a strain-based probabilistic fatigue crack initiation life prediction for spot welds. Afterwards, the fatigue crack inside the base material sheet is modeled as a surface crack. Then a probabilistic crack growth model is combined with the stress analysis result to develop a probabilistic fatigue crack growth life prediction for spot welds. Both methods are implemented with MSC/NASTRAN and MSC/FATIGUE software, and are useful for reliability assessment of automotive spot-welded joints against fatigue and fracture
[en] Calibration of model parameters is an essential step in predicting the response of a complicated system, but the lack of data at the system level makes it impossible to conduct this quantification directly. In such a situation, system model parameters are estimated using tests at lower levels of complexity which share the same model parameters with the system. For such a multi-level problem, this paper proposes a methodology to quantify the uncertainty in the system level prediction by integrating calibration, validation and sensitivity analysis at different levels. The proposed approach considers the validity of the models used for parameter estimation at lower levels, as well as the relevance at the lower level to the prediction at the system level. The model validity is evaluated using a model reliability metric, and models with multivariate output are considered. The relevance is quantified by comparing Sobol indices at the lower level and system level, thus measuring the extent to which a lower level test represents the characteristics of the system so that the calibration results can be reliably used in the system level. Finally the results of calibration, validation and relevance analysis are integrated in a roll-up method to predict the system output. - Highlights: • Relevance analysis to quantify the closeness of two models. • Stochastic model reliability metric to integrate multiple validation experiments. • Extend the model reliability metric to deal with multivariate output. • Roll-up formula to integrate calibration, validation, and relevance.
[en] Sobol' index is a prominent methodology in global sensitivity analysis. This paper aims to directly estimate the Sobol' index based only on available input–output samples, even if the underlying model is unavailable. For this purpose, a new method to calculate the first-order Sobol' index is proposed. The innovation is that the conditional variance and mean in the formula of the first-order index are calculated at an unknown but existing location of model inputs, instead of an explicit user-defined location. The proposed method is modularized in two aspects: 1) index calculations for different model inputs are separate and use the same set of samples; and 2) model input sampling, model evaluation, and index calculation are separate. Due to this modularization, the proposed method is capable to compute the first-order index if only input–output samples are available but the underlying model is unavailable, and its computational cost is not proportional to the dimension of the model inputs. In addition, the proposed method can also estimate the first-order index with correlated model inputs. Considering that the first-order index is a desired metric to rank model inputs but current methods can only handle independent model inputs, the proposed method contributes to fill this gap. - Highlights: • An efficient method to estimate the first-order Sobol' index. • Estimate the index from input–output samples directly. • Computational cost is not proportional to the number of model inputs. • Handle both uncorrelated and correlated model inputs.
[en] This paper proposes a probabilistic framework to include both aleatory and epistemic uncertainty within model-based reliability estimation of engineering systems for individual limit states. Epistemic uncertainty is considered due to both data and model sources. Sparse point and/or interval data regarding the input random variables leads to uncertainty regarding their distribution types, distribution parameters, and correlations; this statistical uncertainty is included in the reliability analysis through a combination of likelihood-based representation, Bayesian hypothesis testing, and Bayesian model averaging techniques. Model errors, which include numerical solution errors and model form errors, are quantified through Gaussian process models and included in the reliability analysis. The probability integral transform is used to develop an auxiliary variable approach that facilitates a single-level representation of both aleatory and epistemic uncertainty. This strategy results in an efficient single-loop implementation of Monte Carlo simulation (MCS) and FORM/SORM techniques for reliability estimation under both aleatory and epistemic uncertainty. Two engineering examples are used to demonstrate the proposed methodology. - Highlights: • Epistemic uncertainty due to data and model included in reliability analysis. • A novel FORM-based approach proposed to include aleatory and epistemic uncertainty. • A single-loop Monte Carlo approach proposed to include both types of uncertainties. • Two engineering examples used for illustration.
[en] This paper develops a probabilistic approach that could use empirical data to derive values of performance shaping factor (PSF) multipliers for use in quantitative human reliability analysis (HRA). The proposed approach is illustrated with data on sleep deprivation effects on performance. A review of existing HRA methods reveals that sleep deprivation is not explicitly included at present, and expert opinion is frequently used to inform HRA model multipliers. In this paper, quantitative data from empirical studies regarding the effect of continuous hours of wakefulness on performance measures (reaction time, accuracy, and number of lapses) are used to develop a method to derive PSF multiplier values for sleep deprivation, in the context of the SPAR-H model. Data is extracted from the identified studies according to the meta-analysis research synthesis method and used to investigate performance trends and error probabilities. The error probabilities in test and control conditions are compared, and the resulting probability ratios are suggested for use in informing the selection of PSF multipliers in HRA methods. Although illustrated for sleep deprivation, the proposed methodology is general, and can be applied to other performance shaping factors. - Highlights: • Method proposed to derive performance shaping factor multipliers from empirical data. • Studies reporting the effect of sleep deprivation on performance are analyzed. • Test data using psychomotor vigilance tasks are analyzed. • Error probability multipliers computed for reaction time, lapses, and accuracy measures.
[en] The effect of fatigue on human performance has been observed to be an important factor in many industrial accidents. However, defining and measuring fatigue is not easily accomplished. This creates difficulties in including fatigue effects in probabilistic risk assessments (PRA) of complex engineering systems that seek to include human reliability analysis (HRA). Thus the objectives of this paper are to discuss (1) the importance of the effects of fatigue on performance, (2) the difficulties associated with defining and measuring fatigue, (3) the current status of inclusion of fatigue in HRA methods, and (4) the future directions and challenges for the inclusion of fatigue, specifically sleep deprivation, in HRA. - Highlights: →We highlight the need for fatigue and sleep deprivation effects on performance to be included in human reliability analysis (HRA) methods. Current methods do not explicitly include sleep deprivation effects. → We discuss the difficulties in defining and measuring fatigue. → We review sleep deprivation research, and discuss the limitations and future needs of the current HRA methods.
[en] In this paper, we propose a probabilistic approach to represent interval data for input variables in reliability and uncertainty analysis problems, using flexible families of continuous Johnson distributions. Such a probabilistic representation of interval data facilitates a unified framework for handling aleatory and epistemic uncertainty. For fitting probability distributions, methods such as moment matching are commonly used in the literature. However, unlike point data where single estimates for the moments of data can be calculated, moments of interval data can only be computed in terms of upper and lower bounds. Finding bounds on the moments of interval data has been generally considered an NP-hard problem because it includes a search among the combinations of multiple values of the variables, including interval endpoints. In this paper, we present efficient algorithms based on continuous optimization to find the bounds on second and higher moments of interval data. With numerical examples, we show that the proposed bounding algorithms are scalable in polynomial time with respect to increasing number of intervals. Using the bounds on moments computed using the proposed approach, we fit a family of Johnson distributions to interval data. Furthermore, using an optimization approach based on percentiles, we find the bounding envelopes of the family of distributions, termed as a Johnson p-box. The idea of bounding envelopes for the family of Johnson distributions is analogous to the notion of empirical p-box in the literature. Several sets of interval data with different numbers of intervals and type of overlap are presented to demonstrate the proposed methods. As against the computationally expensive nested analysis that is typically required in the presence of interval variables, the proposed probabilistic representation enables inexpensive optimization-based strategies to estimate bounds on an output quantity of interest.