Uncertainty quantification and model validation of fatigue crack growth prediction

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.     

Validation of reliability computational models using Bayes networks

This paper proposes a methodology based on Bayesian statistics to assess the validity of reliability computational models when full-scale testing is not possible. Sub-module validation results are used to derive a validation measure for the overall reliability estimate. Bayes networks are used for the propagation and updating of validation information from the sub-modules to the overall model prediction. The methodology includes uncertainty in the experimental measurement, and the posterior and prior distributions of the model output are used to compute a validation metric based on Bayesian hypothesis testing. Validation of a reliability prediction model for an engine blade under high-cycle fatigue is illustrated using the proposed methodology.     

线加速度计模型方程系数的测量不确定度

阐述了线加速度计静态数学模型方程的精密离心校准方法，利用最小二乘原理推导了实验数据处理方法，并分析了线加速度计模型方程系数的测量不确定度计算方法。     

Computational methods for model reliability assessment

This paper investigates various statistical approaches for the validation of computational models when both model prediction and experimental observation have uncertainties, and proposes two new methods for this purpose. The first method utilizes hypothesis testing to accept or reject a model at a desired significance level. Interval-based hypothesis testing is found to be more practically useful for model validation than the commonly used point null hypothesis testing. Both classical and Bayesian approaches are investigated. The second and more direct method formulates model validation as a limit state-based reliability estimation problem. Both simulation-based and analytical methods are presented to compute the model reliability for single or multiple comparisons of the model output and observed data. The proposed methods are illustrated and compared using numerical examples.     

Comments on generalised likelihood uncertainty estimation

The paper presents an application of the generalised likelihood uncertainty estimation methodology to the problem of estimating the uncertainty of predictions produced by environmental models. The methodology is placed in a wider context of different approaches to inverse modelling and, in particular, a comparison is made with Bayesian estimation techniques based on explicit structural assumptions about model error. Using a simple example of a rainfall-flow model, different evaluation measures and their influence on the prediction uncertainty and credibility intervals are demonstrated.     

新安江模型参数有效优化及不确定性评估

应用新安江模型进行水文模拟时,由于模型本身的不足及参数多、信息量少等原因,会出现率定的最优参数组不唯一、不稳定等问题。考虑到以往的参数优选,都只得出一个参数组,不能反映出其不确定性状况。提出应用基于马尔可夫链蒙特卡罗(MCMC)理论的SCEM-UA算法,通过双牌流域以1 h为时段间隔的36场典型洪水数据对新安江模型参数进行优选和不确定性评估。结果表明,该算法能很好地推出新安江模型参数的后验概率分布;率定和检验结果分析也表明,应用SCEM-UA算法对新安江模型进行优选和不确定评估是有效和可行的。     

Bayesian methodology for reliability model acceptance

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.     

A Resource Allocation Framework for Experiment-Based Validation of Numerical Models

In experiment-based validation, uncertainties and systematic biases in model predictions are reduced by either increasing the amount of experimental evidence available for model calibration—thereby mitigating prediction uncertainty—or increasing the rigor in the definition of physics and/or engineering principles—thereby mitigating prediction bias. Hence, decision makers must regularly choose between either allocating resources for experimentation or further code development. The authors propose a decision-making framework to assist in resource allocation strictly from the perspective of predictive maturity and demonstrate the application of this framework on a nontrivial problem of predicting the plastic deformation of polycrystals.     

计量中回归模型参数值及其不确定度评估

针对计量领域中广泛应用的数据回归处理方法,阐述了在基于正态分布噪声条件下,最小二乘法与贝叶斯推断法用于回归模型参数估计以及相应不确定度评估的过程。GUM系列不确定度评估准则中没有明确指出如何对回归参数进行不确定度评估,同时有些回归模型也无法唯一地转化为相应的测量方程。通过计量校准的实例说明了如何处理相应参数的确定等问题,以此说明2种方法的相同与不同之处。最小二乘方法计算简单直接且便于使用;而基于贝叶斯推断的方法则能充分利用计量校准中的经验和历史数据等信息,但由于其参数后验分布计算通常较为复杂,需采用马尔科夫链-蒙特卡罗(MCMC)法通过数值计算得到关注参数的结果。     

Surface roughness predictive modeling: neural networks versus regression

Surface roughness plays an important role in product quality and manufacturing process planning. This research focuses on developing an empirical model for surface roughness prediction in finish turning. The model considers the following working parameters: work-piece hardness (material), feed, cutter nose radius, spindle speed and depth of cut. Two competing data mining techniques, nonlinear regression analysis and computational neural networks, are applied in developing the empirical models. The values of surface roughness predicted by these models are then compared with those from some of the representative models in the literature. Metal cutting experiments and tests of hypothesis demonstrate that the models developed in this research have a satisfactory goodness of fit. It has also presented a rigorous procedure for model validation and model comparison. In addition, some future research directions are outlined.     

Calibration of adhesion models based on Bayesian inference

The use of composite materials in a myriad of applications fostered the development of reliable procedures to connect components with adhesives. This led to a demand for reliable adhesion models to be used in engineering designs that are based on computer simulations. This paper presents a strategy to be used for calibration of adhesion models. The proposed methodology is built on the formalism of Statistical Inverse Problems. Uncertainties about the unknowns are inferred using Population-Based Markov Chain Monte Carlo and Adaptive Metropolis. It is proposed to perform model assessments based on the analysis of a validation metric. Realizations of the validation metric are computed with the posterior densities of model parameters that are provided by the calibration process. The analysis of the validation metric allows for model selection to be performed. Some numerical experiments are presented with noise-contaminated data. The calibration strategy proved effective when dealing with both the nonlinearity and nondifferentiability of the adhesion constitutive equation.     

On the model building for transmission line cables: a Bayesian approach

This work is aimed at building models to predict the bending vibrations of stranded cables used in high-voltage transmission lines. The present approach encompasses model calibration, validation and selection based on a statistical framework. Model calibration is tackled using a Bayesian framework and the Delayed Rejection Adaptive Metropolis (DRAM) sampling algorithm is employed to explore the posterior probability of the unknown model parameters. Two model classes are proposed to predict the bending vibrations of a typical high-voltage stranded cable. Both model classes account for the aerodynamic damping with the surrounding medium and the bending stiffness of the cable. The difference between the two relies on the damping model chosen to quantify the energy dissipation due to friction among the constituent wires of the cable. Model ranking is rigorously quantified by means of a Bayesian model class selection approach, in which both the data-fitting capability and complexity of each model class are simultaneously taken into account. Experimental tests are performed on a laboratory span with a typical high-voltage stranded cable. The measured frequency response functions are the observable quantities employed in the Bayesian model updating for the two model classes proposed. Both model classes provide comparable and accurate predictions for the cable’s frequency response functions within the range [5, 25] Hz, with the fractional derivative-based model class providing the most accurate predictions. Nonetheless, both model classes failed to accurately reproduce the measured cable’s dynamic response within the frequency range [25, 30] Hz.     

Development of regression equations for local calibration of rutting and IRI as predicted by the MEPDG models for flexible pavements using Ontario's long-term PMS data

Local calibration is an important step before a transportation agency adopts the American Association of State Highway and Transportation Officials' (AASHTO) mechanistic-empirical pavement design guide (MEPDG). This paper presents the challenges of and findings from the local calibration of flexible pavements in provincial highways under the jurisdiction of the Ministry of Transportation of Ontario (MTO). A calibration database was developed that involved a hierarchical framework of the input parameters required for AASHTOWare Pavement ME (the MEPDG software) and the historical field performance data based on the MTO's second-generation pavement management system. A regression analysis is carried out for preliminary calibration of rutting and international roughness index (IRI) models by comparing the predicted distress to observed distress. The analysis suggested that whereas the MEPDG provided fairly unbiased prediction of the IRI value, it often over-predicted the total rutting. Calibrated predicted IRI and rut depth are found for Ontario's local conditions from MEPDG distress prediction models. A further clustering analysis based on Functional Class and geographical zone for the rutting and IRI, respectively, improved the precision of the locally calibrated models.     

A stochastic framework for hydraulic performance assessment of complex water distribution networks: Application to connectivity detection problems

This paper is concerned with the hydraulic performance assessment of large scale water distribution networks in presence of uncertainty. In particular, the associate connectivity detection problem is examined in detail. For this purpose, a Bayesian system identification methodology is combined with an efficient hydraulic simulation model. A number of hydraulic model classes are defined as potential connectivity events. Based on information from flow rates in the pipes, the proposed updating technique provides estimates of the most probable connectivity scenarios. Such scenarios correspond to the model classes that maximize their evidences or posterior probabilities. The effectiveness of the proposed identification framework is illustrated by applying the connectivity detection approach to a real water distribution system.     

A cement Vertical Roller Mill modeling based on the number of breakages

This study investigated a mathematical model for an industrial-scale vertical roller mill(VRM) at the Ilam Cement Plant in Iran. The model was calibrated using the initial survey's data, and the breakage rates of clinker were then back-calculated. The modeling and validation results demonstrated that according to the bed-breakage mechanism in VRM, clinker particles only stay in the VRM for a short time. Particles in the VRM haven't a 1 to 3 times greater chance of breaking due to their brief time in the VRM. Matrix model's results model provides a more robust prediction based on the number of 2-times clinker breakage in VRMs (R² = 0.9916, MSE = 5.3526, accuracy = 94.6474). Also shown by the results of the matrix modeling, the S increased with decreasing the particle size. In contrast, the population balance model increased with increased particle size.     

Combining the cost of reducing uncertainty with the selection of risk assessment models for remediation decision of site contamination

The decision as to whether a contaminated site poses a threat to human health and should be cleaned up relies increasingly upon the use of risk assessment models. However, the more sophisticated risk assessment models become, the greater the concern with the uncertainty in, and thus the credibility of, risk assessment. In particular, when there are several equally plausible models, decision makers are confused by model uncertainty and perplexed as to which model should be chosen for making decisions objectively. When the correctness of different models is not easily judged after objective analysis has been conducted, the cost incurred during the processes of risk assessment has to be considered in order to make an efficient decision. In order to support an efficient and objective remediation decision, this study develops a methodology to cost the least required reduction of uncertainty and to use the cost measure in the selection of candidate models. The focus is on identifying the efforts involved in reducing the input uncertainty to the point at which the uncertainty would not hinder the decision in each equally plausible model. First, this methodology combines a nested Monte Carlo simulation, rank correlation coefficients, and explicit decision criteria to identify key uncertain inputs that would influence the decision in order to reduce input uncertainty. This methodology then calculates the cost of required reduction of input uncertainty in each model by convergence ratio, which measures the needed convergence level of each key input's spread. Finally, the most appropriate model can be selected based on the convergence ratio and cost. A case of a contaminated site is used to demonstrate the methodology.     

Bayesian inference on a microstructural,hyperelastic model of tendon deformation

Microstructural models of soft-tissue deformation are important in applications including artificial tissue design and surgical planning. The basis of these models, and their advantage over their phenomenological counterparts, is that they incorporate parameters that are directly linked to the tissue’s microscale structure and constitutive behaviour and can therefore be used to predict the effects of structural changes to the tissue. Although studies have attempted to determine such parameters using diverse, state-of-the-art, experimental techniques, values ranging over several orders of magnitude have been reported, leading to uncertainty in the true parameter values and creating a need for models that can handle such uncertainty. We derive a new microstructural, hyperelastic model for transversely isotropic soft tissues and use it to model the mechanical behaviour of tendons. To account for parameter uncertainty, we employ a Bayesian approach and apply an adaptive Markov chain Monte Carlo algorithm to determine posterior probability distributions for the model parameters. The obtained posterior distributions are consistent with parameter measurements previously reported and enable us to quantify the uncertainty in their values for each tendon sample that was modelled. This approach could serve as a prototype for quantifying parameter uncertainty in other soft tissues.     

ICP-OES不确定度评定模型的探讨

不确定度的大小是评定一种测量方法能力优劣的指征。等离子发射光谱(ICP—OES)在化学计量领域和分析测试领域均有广泛的应用,对于申请CNAL认证认可的实验室而言．校准实验室和检测实验室在不确定度评定的模型选用原则上存在很大的区别,本文采用国家一级或二级标准物质对仪器进行校准和检测试验,并根据需要拟订出校准实验室的检出限不确定度评定模型和检测实验室中检测结果不确定度评定模型。经过对大量数据的统计分析给出输入量的A类或B类不确定度评定实例．并按照国际通行方法进行不确定度的合成与扩展,最终得到ICP-OES在2种实验室中不确定度的判断。     

Practical Case Application for Stress Model Validation and Enhancement by Means of Metrological Tools

Models consider ideal and simplified situations that will never be met in the real case. The process of comparing model predictions and experimental observation is in the basis of scientific research. This comparison is however complicated because of the uncertainties of the model input data and the difficulty to control the accuracy of the tests and to obtain a significant statistical sampling. Moreover, there isn't yet a consensus on a validation parameter. This paper presents a three‐step validation procedure that allows quantifying the application limits of a two‐dimensional stress model in a three‐dimensional situation. A global uncertainty model is calculated comprising the uncertainty of the model and also the uncertainty coming from the experimental results. The E_N number, a statistical magnitude for interlaboratory comparisons, is used to analyse the compatibility between the experimental and theoretical results. Finally, a bootstrapping method is proposed to calculate the coverage interval of the sampling and determine if new experiments should be carried out. Numerical results of this new validation procedure are provided for the case under study. It is also demonstrated that the computed uncertainty budget can be a useful tool to enhance the two‐dimensional model by enlarging its uncertainty limits.     

Validating behavioral models for reuse

When using a model to predict the behavior of a physical system of interest, engineers must be confident that, under the conditions of interest, the model is an adequate representation of the system. The process of building this confidence is called model validation. It requires that engineers have knowledge about the system and conditions of interest, properties of the model and their own tolerance for uncertainty in the predictions. To reduce time and costs, engineers often reuse preexisting models that other engineers have developed. However, if the user lacks critical parts of this knowledge, model validation can be as time consuming and costly as developing a similar model from scratch. In this article, we describe a general process for performing model validation for reused behavioral models that overcomes this problem by relying on the formalization and exchange of knowledge. We identify the critical elements of this knowledge, discuss how to represent it and demonstrate the overall process on a simple engineering example.