Bayesian networks inference algorithm to implement Dempster Shafer theory in reliability analysis

This paper deals with the use of Bayesian networks to compute system reliability. The reliability analysis problem is described and the usual methods for quantitative reliability analysis are presented within a case study. Some drawbacks that justify the use of Bayesian networks are identified. The basic concepts of the Bayesian networks application to reliability analysis are introduced and a model to compute the reliability for the case study is presented. Dempster Shafer theory to treat epistemic uncertainty in reliability analysis is then discussed and its basic concepts that can be applied thanks to the Bayesian network inference algorithm are introduced. Finally, it is shown, with a numerical example, how Bayesian networks’ inference algorithms compute complex system reliability and what the Dempster Shafer theory can provide to reliability analysis.     

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.     

一种基于Seth应变张量的超弹性模型

为精确表征橡胶类材料在大变形范围内的力学行为,基于Seth应变张量不变量提出了一种适用于橡胶类材料的不可压缩各向同性超弹性模型。为考察其预测能力,分别利用Treloar经典试验数据和某型炭黑填充橡胶试验数据对该模型、Yeoh模型和二阶多项式模型进行了参数识别。结果表明,在同时使用单轴拉伸和等双轴拉伸试验数据情况下,相较于其他两种常用模型,该模型能够更准确地拟合两种橡胶材料的试验数据,并较好地预测纯剪切(或平面拉伸)试验数据。最后,分别基于前述三种超弹性模型对橡胶衬套进行了静刚度仿真计算和试验验证。结果表明,基于所提出的超弹性模型得到的径向刚度和轴向刚度仿真误差分别为6.61%和9.72%,显著小于基于其他两种模型得到的仿真误差。因此,提出的模型在一定误差范围内能够有效适用于橡胶产品的性能分析。该模型仅含4个材料参数,对不同的橡胶材料有较好地适用性,具有良好的工程应用价值。     

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.     

Surrogate-assisted Bayesian inference inverse material identification method and application to advanced high strength steel

Proper definition of certain material properties is a paramount issue for accurate simulation. However, the values of a material parameter are commonly uncertain due to multiple factors in practice. To obtain reliable material parameters, parameter identification via Bayesian theory has become an attractive framework and received more attention recently. Based on this frame, the determination of likelihood function is critical for posterior probability. Unfortunately, it is commonly difficult to be determined directly, especially for complex engineering problems. In this study, Bayesian formulas for material parameter identification are given. To make it feasible for real engineering problems, the least square-support vector regression surrogate and Monte Carlo Simulation are integrated to obtain the maximum likelihood estimation of likelihood function. The uncertainty of parameter identification is quantified via the Bayesian method. In two benchmarks, two cases with single and multiple uncertainty sources are used to propagate and quantify uncertainties in material parameters based on Bayesian approach. Moreover, the proposed method is used to identify the material parameters of advanced high strength steel used in vehicle successfully.     

An analytic model for situation assessment of nuclear power plant operators based on Bayesian inference

Simulation-based human reliability analysis (HRA) methods such as IDAC seem to provide a new direction for the development of advanced HRA methods. In such simulation-based HRA methods, the simulation model for the situation assessment of nuclear power plant (NPP) operators is essential, especially for addressing the issue of errors-of-commission (EOCs). Therefore, we propose an analytic model for the situation assessment of NPP operators based on Bayesian inference. The proposed model is found to be able to address several important features of the situation assessment of NPP operators, and is expected to provide good approximations to some parts of the situation assessment. A comparison with an existing model and identification of several other features of the situation assessment of NPP operators that should be further addressed are also provided.     

Bayesian network modelling for supply chain risk propagation

Supply chain risk propagation is a cascading effect of risks on global supply chain networks. The paper attempts to measure the behaviour of risks following the assessment of supply chain risk propagation. Bayesian network theory is used to analyse the multi-echelon network faced with simultaneous disruptions. The ripple effect of node disruption is evaluated using metrics like fragility, service level, inventory cost and lost sales. Developed risk exposure and resilience indices support in assessing the vulnerability and adaptability of each node in the supply chain network. The research provides a holistic measurement approach for predicting the complex behaviour of risk propagation for improved supply chain risk management.     

A novel Bayesian approach to reliability modeling: The benefits of uncertainty evaluation in the model selection procedure

This paper proposes a different likelihood formulation within the Bayesian paradigm for parameter estimation of reliability models. Moreover, the assessment of the uncertainties associated with parameters, the goodness of fit, and the model prediction of reliability are included in a systematic framework for better aiding the model selection procedure. Two case studies are appraised to highlight the contributions of the proposed method and demonstrate the differences between the proposed Bayesian formulation and an existing Bayesian formulation.     

A Bayesian model for measurements on a set of instruments

A Bayesian model is proposed based on randomizing the systematic errors of the instruments. Conditions are identified under which the randomization reduces the expected bias in estimating a measured quantity. __________ Translated from Izmeritel’naya Tekhnika, No. 3, pp. 22–25, March, 2007.     

A Cauchy‐stress based solution for a necking elastic constitutive model under large deformation

A finite element based method for solution of large‐deformation hyperelastic constitutive models is developed, which solves the Cauchy‐stress balance equation using a single rotation of stress from principal directions to a fixed co‐ordinate system. Features of the method include stress computation by central differencing of the hyperelastic energy function, mixed integration‐order incompressibility enforcement, and an iterative solution method that employs notional ‘small strain’ stiffness. The method is applied to an interesting and difficult elastic model that replicates polymer ‘necking’; the method is shown to give good agreement with published results from a well‐established finite element package, and with published experimental results. It is shown that details of the manner in which incompressibility is enforced affects whether key experimental phenomena are clearly resolved. Copyright © 2005 John Wiley & Sons, Ltd.     

贝叶斯网络推理在信息系统安全风险评估中的应用

提出了一种基于贝叶斯网络推理的安全风险评估方法。从实际出发建立信息系统的贝叶斯网络模型，根据专家给出的先验信息，结合获得的证据信息，运用Pearl方法完成对模型的评估，给出在特定条件下模型的计算——线性推理算法。最后，以实例分析信息系统安全评估的实现过程，结果表明，该方法可行、有效。     

A novel Bayesian strategy for the identification of spatially varying material properties and model validation: an application to static elastography

The present paper proposes a novel Bayesian, a computational strategy in the context of model‐based inverse problems in elastostatics. On one hand, we attempt to provide probabilistic estimates of the material properties and their spatial variability that account for the various sources of uncertainty. On the other hand, we attempt to address the question of model fidelity in relation to the experimental reality and particularly in the context of the material constitutive law adopted. This is especially important in biomedical settings when the inferred material properties will be used to make decisions/diagnoses. We propose an expanded parametrization that enables the quantification of model discrepancies in addition to the constitutive parameters. We propose scalable computational strategies for carrying out inference and learning tasks and demonstrate their effectiveness in numerical examples with noiseless and noisy synthetic data. Copyright © 2012 John Wiley & Sons, Ltd.     

Sensibility of Bayesian inference methods for reliability prediction of ageing systems,case of Diesel locomotives

This paper addresses the problem of reliability analysis of in-service identical systems when a limited number of lifetime data is available compared to censored ones. Lifetime (resp. censored) data characterise the life of failed (resp. non-failed) systems in the sample. Because, censored data induce biassed estimators of reliability model parameters, a methodology approach is proposed to overcome this inconvenience and improve the accuracy of the parameter estimation based on Bayesian inference methods. These methods combine, in an effective way, system’s life data and expert opinions learned from failure diagnosis of similar systems. Three Bayesian inference methods are considered: Classical Bayesian, Extended Bayesian and Bayesian Restoration Maximisation methods. Given a sample of lifetime data, simulated according to prior opinions of maintenance expert, a sensibility analysis of each Bayesian method is performed. Reliability analysis of critical subsystems of Diesel locomotives is established under the proposed methodology approach. The relevance of each Bayesian inference methods with respect to collected reliability data of critical subsystems and expert opinions is discussed.     

Parameter inference in a computational model of haemodynamics in pulmonary hypertension

Pulmonary hypertension (PH), defined by a mean pulmonary arterial pressure (mPAP) greater than 20 mmHg, is characterized by increased pulmonary vascular resistance and decreased pulmonary arterial compliance. There are few measurable biomarkers of PH progression, but a conclusive diagnosis of the disease requires invasive right heart catheterization (RHC). Patient-specific cardiovascular systems-level computational models provide a potential non-invasive tool for determining additional indicators of disease severity. Using computational modelling, this study quantifies physiological parameters indicative of disease severity in nine PH patients. The model includes all four heart chambers, the pulmonary and systemic circulations. We consider two sets of calibration data: static (systolic and diastolic values) RHC data and a combination of static and continuous, time-series waveform data. We determine a subset of identifiable parameters for model calibration using sensitivity analyses and multi-start inference and perform posterior uncertainty quantification. Results show that additional waveform data enables accurate calibration of the right atrial reservoir and pump function across the PH cohort. Model outcomes, including stroke work and pulmonary resistance-compliance relations, reflect typical right heart dynamics in PH phenotypes. Lastly, we show that estimated parameters agree with previous, non-modelling studies, supporting this type of analysis in translational PH research.     

Large deformation response of a hyperelastic fibre reinforced composite: Theoretical model and numerical validation

The mechanical behaviour of an incompressible neo-Hookean material directionally reinforced with a generalised neo-Hookean fibre is examined in the finite deformation regime. To consider the interaction between the fibre and the matrix, we use a composite model for this transversely isotropic material based on a multiplicative decomposition of deformation, which decouples the uniaxial deformation along the fibre direction from the remaining shear deformation. The model is then verified numerically by a unit cell model with periodic boundary conditions. The strain energy stored in the unit cell is compared with the energy predicted by the proposed theoretical model and excellent agreement is reported.     

一种基于Bayes方法的随机模型修正方法

提出了一种随机模型的修正方法用以估计结构参数的统计特性.基于Bayes方法的参数估计原理,将需要修正的结构参数的均值和方差看作符合一定先验概率分布的随机变量,根据核密度估计原理构建得到似然函数,进而使用基于差分进化的MCMC方法估计参数的后验概率密度,并根据最大后验概率密度准则估计结构参数的均值和方差.同时使用Kriging方法建立了结构输入和输出之间的代理模型,保证计算精度的同时极大地节约了计算时间.数值算例验证了本方法的可行性.     

Ti-50．75at％Ni形状记忆合金绞线超弹性试验研究

为了在常温条件下更充分地利用TiNi形状记忆合金绞线的超弹性性能，以Ti-50．75％（原子分数）Ni形状记忆合金（SMA）丝和绞线两种形式试件进行了室温条件下，加载速率、应变幅值及循环次数等因素对SMA丝和SMA绞线超弹性性能影响的试验。试验表明SMA以绞线的形式使用时能够大幅度提高其极限应变能力，相对SMA丝来说更适合应用于大变形时提供足够的恢复力；SMA绞线相对SMA丝具有更强大的超弹性性能；SMA绞线的残余应变量要比SMA丝的小得多，这也是使它具有较高的超弹性性能的主要因素之一．从而验证了SMA以绞线形式使用可以提供更强的超弹性性能．     

Transport Map sampling with PGD model reduction for fast dynamical Bayesian data assimilation

The motivation of this work is to address real-time sequential inference of parameters with a full Bayesian formulation. First, the proper generalized decomposition (PGD) is used to reduce the computational evaluation of the posterior density in the online phase. Second, Transport Map sampling is used to build a deterministic coupling between a reference measure and the posterior measure. The determination of the transport maps involves the solution of a minimization problem. As the PGD model is quasi-analytical and under a variable separation form, the use of gradient and Hessian information speeds up the minimization algorithm. Eventually, uncertainty quantification on outputs of interest of the model can be easily performed due to the global feature of the PGD solution over all coordinate domains. Numerical examples highlight the performance of the method.     

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.