基于贝叶斯网络模型的电子装备故障诊断研究

针对电子装备故障的层次性、相关性、不确定性特点,结合贝叶斯网络在处理不确定性问题上的优点,提出了电子装备故障诊断的贝叶斯网络方法;研究了基于故障树分析和故障模式、影响、危害度信息的贝叶斯网络模型建立方法,分析了贝叶斯网络的故障预测和推理原理,确立了各底事件对故障诊断的重要度,形成了故障诊断的合理顺序,通过实例验证了上述方法的可行性和有效性;研究成果对复杂电子装备的故障诊断有借鉴意义。     

SEDRET—an intelligent system for the diagnosis and prediction of events in power plants

Artificial Intelligence applications in large-scale industry, such as fossil power plants, require the ability to manage uncertainty and time. In this paper, we present an intelligent system to assist an operator of a power plant. This system, called SEDRET, is based on a novel knowledge representation of uncertainty and time, called Temporal Nodes Bayesian Networks (TNBN), a type of Probabilistic Temporal Network. A set of temporal nodes and a set of edge define a TNBN, each temporal node is defined by a value of a variable and a time interval associate to the change of variable value. A TNBN generates a formal and systematic structure for modeling the temporal evolution of a process under uncertainty. The inference mechanism is based on probabilistic reasoning. A TNBN can be used to recognize events and state variables with respect to current plant conditions and predict the future propagation of disturbances. SEDRET was validated with the diagnosis and prediction of events in a steam generator with a power plant training simulator. The results performed in this work indicate that SEDRET can potentially improve plant availability through early diagnosis and prediction of disturbances that could lead to plant shutdown.     

The effect of ambiguous prior knowledge on Bayesian model parameter inference and prediction

Environmental modeling often requires combining prior knowledge with information obtained from data. The robust Bayesian approach makes it possible to consider ambiguity in this prior knowledge. Describing such ambiguity using sets of probability distributions defined by the Density Ratio Class has important conceptual advantages over alternative robust formulations. Earlier studies showed that the Density Ratio Class is invariant under Bayesian inference and marginalization. We prove that (i) the Density Ratio Class is also invariant under propagation through deterministic models, whereas (ii) predictions of a stochastic model with parameters defined by a Density Ratio Class are embedded in a Density Ratio Class. These invariance properties make it possible to describe sequential learning and prediction under a unified framework. We developed numerical algorithms to minimize the additional computational burden relative to the use of single priors. Practical feasibility of these methods is demonstrated by their application to a simple ecological model.     

Sensitivity analysis and variance reduction in a stochastic non-destructive testing problem

In this paper, we present a framework to deal with uncertainty quantification in case where the ranges of variability of the random parameters are ill-known. Namely the physical properties of the corrosion product (magnetite) which frequently clogs the tube support plate of steam generator, which is inaccessible in nuclear power plants. The methodology is based on polynomial chaos (PC) for the direct approach and on Bayesian inference for the inverse approach. The direct non-intrusive spectral projection (NISP) method is first employed by considering prior probability densities and therefore constructing a PC surrogate model of the large-scale non-destructive testing finite element model. To face the prohibitive computational cost underlying the high-dimensional random space, an adaptive sparse grid technique is applied on NISP resulting in drastic time reduction. The PC surrogate model, with reduced dimensionality, is used as a forward model in the Bayesian procedure. The posterior probability densities are then identified by inferring from few noisy experimental data. We demonstrate effectiveness of the approach by identifying the most influential parameter in the clogging detection as well as a variability range reduction.     

基于t分布的贝叶斯深度学习模型及其应用

贝叶斯深度学习(BDL)融合了贝叶斯方法与深度学习(DL)的互补优势, 成为复杂问题中不确定性建模与推断的强大工具. 本文构建了基于t 分布和循环随机梯度汉密尔顿蒙特卡罗采样算法的BDL框架, 并基于数据不确定性和模型定不确定性给出了不确定性的度量. 为了验证模型框架的有效性和适用性, 我们分别基于人工神经网络(ANN)、卷积神经网络(CNN) 和循环神经网络(RNN)构建了相应的BDL模型, 并将模型应用于全球15个股票指数预测, 实证结果显示: 1)该框架在ANN、CNN和RNN 下均适用, 对全部指数的预测效果均很出色; 2) 在预测精度和通用性方面, 基于t分布BDL的模型比基于正态分布的BDL模型具有显著优越性; 3)在给定不确定性阈值之下的预测MAE 比初始MAE显著提升, 表明文中定义的不确定性是有效的, 对不确定性建模具有重要意义. 鉴于该BDL框架在预测精度、易于拓展和具备提供预测不确定性度量的优势, 其在金融和其他具有复杂数据特征的领域均有广阔的应用前景.     

Efficient Bayesian spatial prediction with mobile sensor networks using Gaussian Markov random fields

In this paper, we consider the problem of predicting a large scale spatial field using successive noisy measurements obtained by mobile sensing agents. The physical spatial field of interest is discretized and modeled by a Gaussian Markov random field (GMRF) with uncertain hyperparameters. From a Bayesian perspective, we design a sequential prediction algorithm to exactly compute the predictive inference of the random field. The main advantages of the proposed algorithm are: (1) the computational efficiency due to the sparse structure of the precision matrix, and (2) the scalability as the number of measurements increases. Thus, the prediction algorithm correctly takes into account the uncertainty in hyperparameters in a Bayesian way and is also scalable to be usable for mobile sensor networks with limited resources. We also present a distributed version of the prediction algorithm for a special case. An adaptive sampling strategy is presented for mobile sensing agents to find the most informative locations in taking future measurements in order to minimize the prediction error and the uncertainty in hyperparameters simultaneously. The effectiveness of the proposed algorithms is illustrated by numerical experiments.     

贝叶斯网络在汽轮机故障诊断中的应用

针对在汽轮发电机组振动故障诊断中的不确定性问题，提出了应用贝叶斯网络对其进行推理和诊断。本文介绍了贝叶斯网络的建模方法与推理机制，并通过专家系统的建模过程与诊断实例，证明了应用贝叶斯网络对汽轮发电机组进行故障诊断所具有的独特优点。     

A bivariate frailty model for events with a permanent survivor fraction and non-monotonic hazards; with an application to age at first maternity

For certain life cycle events a non-susceptible fraction of subjects will never undergo the event. In demographic applications, examples are provided by marriage and age at first maternity. A model for survival data allowing a permanent survival fraction, non-monotonic failure rates and unobserved frailty is considered here. Regressions are used to explain both the failure time and permanent survival mechanisms and additive correlated errors are included in the general linear models defining these regressions. A hierarchical Bayesian approach is adopted with likelihood conditional on the random frailty effects and a second stage prior defining the bivariate density of those effects. The gain in model fit, and potential effects on inference, from adding frailty is demonstrated in a case study application to age at first maternity in Germany.     

Use of freely available datasets and machine learning methods in predicting deforestation

The range and quality of freely available geo-referenced datasets is increasing. We evaluate the usefulness of free datasets for deforestation prediction by comparing generalised linear models and generalised linear mixed models (GLMMs) with a variety of machine learning models (Bayesian networks, artificial neural networks and Gaussian processes) across two study regions. Freely available datasets were able to generate plausible risk maps of deforestation using all techniques for study zones in both Mexico and Madagascar. Artificial neural networks outperformed GLMMs in the Madagascan (average AUC 0.83 vs 0.80), but not the Mexican study zone (average AUC 0.81 vs 0.89). In Mexico and Madagascar, Gaussian processes (average AUC 0.89, 0.85) and structured Bayesian networks (average AUC 0.88, 0.82) performed at least as well as GLMMs (average AUC 0.89, 0.80). Bayesian networks produced more stable results across different sampling methods. Gaussian processes performed well (average AUC 0.85) with fewer predictor variables.     

STATISTICAL INFERENCES BASED ON A SECOND-ORDER POSSIBILITY DISTRIBUTION

Abstract

A new, general method of statistical inference is proposed. It encompasses all the coherent forms of statistical inference that can be derived from a Bayesian prior distribution, Bayesian sensitivity analysis or upper and lower prior probabilities. The method is to model prior uncertainty about statistical parameters in terms of a second-order possibility distribution (a special type of upper probability) which measures the plausibility of each conceivable prior probability distribution. This defines an imprecise hierarchical model. Two,applications are studied: the problem of robustifying Bayesian analyses by forming a neighbourhood of a Bayesian prior distribution, and the problem of combining prior opinions from different sources.     

Multivariate Bayesian modeling of known and unknown causes of events--an application to biosurveillance

This paper investigates Bayesian modeling of known and unknown causes of events in the context of disease-outbreak detection. We introduce a multivariate Bayesian approach that models multiple evidential features of every person in the population. This approach models and detects (1) known diseases (e.g., influenza and anthrax) by using informative prior probabilities and (2) unknown diseases (e.g., a new, highly contagious respiratory virus that has never been seen before) by using relatively non-informative prior probabilities. We report the results of simulation experiments which support that this modeling method can improve the detection of new disease outbreaks in a population. A contribution of this paper is that it introduces a multivariate Bayesian approach for jointly modeling both known and unknown causes of events. Such modeling has general applicability in domains where the space of known causes is incomplete.     

输入不确定BELM在发酵过程软测量中的应用

为复杂的发酵过程建立软测量模型要求模型最好能够给出预测值的置信区间,以便技术人员对发酵过程的真实状况和模型的可靠性进行评估。贝叶斯极限学习机能够在实现预测的同时一并给出预测值的置信区间,因此将其用于发酵过程的软测量建模。然而,实际发酵过程中的输入数据往往带有噪声,贝叶斯极限学习机仅能处理输出含噪声的情况。针对这个问题,提出了输入不确定贝叶斯极限学习机。在原有的贝叶斯推理过程中引入输入不确定性,得到了综合考虑输入输出噪声的模型参数和预测置信区间。最后利用青霉素发酵过程进行仿真验证,建立了产物质量浓度的软测量模型,结果表明该方法预测精度高,得到的预测置信区间包含了所有真实值。     

Weak approximation of transformed stochastic gradient MCMC

Stochastic gradient Langevin dynamics (SGLD) is a computationally efficient sampler for Bayesian posterior inference given a large scale dataset and a complex model. Although SGLD is designed for unbounded random variables, practical models often incorporate variables within a bounded domain, such as non-negative or a finite interval. The use of variable transformation is a typical way to handle such a bounded variable. This paper reveals that several mapping approaches commonly used in the literature produce erroneous samples from theoretical and empirical perspectives. We show that the change of random variable in discretization using an invertible Lipschitz mapping function overcomes the pitfall as well as attains the weak convergence, while the other methods are numerically unstable or cannot be justified theoretically. Experiments demonstrate its efficacy for widely-used models with bounded latent variables, including Bayesian non-negative matrix factorization and binary neural networks.

     

Varying-coefficient models for geospatial transfer learning

We study prediction problems in which the conditional distribution of the output given the input varies as a function of task variables which, in our applications, represent space and time. In varying-coefficient models, the coefficients of this conditional are allowed to change smoothly in space and time; the strength of the correlations between neighboring points is determined by the data. This is achieved by placing a Gaussian process (GP) prior on the coefficients. Bayesian inference in varying-coefficient models is generally intractable. We show that with an isotropic GP prior, inference in varying-coefficient models resolves to standard inference for a GP that can be solved efficiently. MAP inference in this model resolves to multitask learning using task and instance kernels. We clarify the relationship between varying-coefficient models and the hierarchical Bayesian multitask model and show that inference for hierarchical Bayesian multitask models can be carried out efficiently using graph-Laplacian kernels. We explore the model empirically for the problems of predicting rent and real-estate prices, and predicting the ground motion during seismic events. We find that varying-coefficient models with GP priors excel at predicting rents and real-estate prices. The ground-motion model predicts seismic hazards in the State of California more accurately than the previous state of the art.     

贝叶斯网络扩展研究综述

贝叶斯网络是一种能够对复杂不确定系统进行推理和建模的有效工具,广泛用于不确定决策、数据分析以及智能推理等领域.由于理论和实际的需要,贝叶斯网络不断扩展,出现了各种模型和研究方法.为此,综述了贝叶斯网络在不同领域的扩展模型以及在不同理论框架下的进展,并展望了未来的几个发展方向.     

Sensor planning for mobile robot localization using Bayesian network inference

We propose a new method of sensor planning for mobile robot localization using Bayesian network inference. Since we can model causal relations between situations of the robot's behavior and sensing events as nodes of a Bayesian network, we can use the inference of the network for dealing with uncertainty in sensor planning and thus derive appropriate sensing actions. In this system we employ a multi-layered-behavior architecture for navigation and localization. This architecture effectively combines mapping of local sensor information and the inference via a Bayesian network for sensor planning. The mobile robot recognizes the local sensor patterns for localization and navigation using a learned regression function. Since the environment may change during the navigation and the sensor capability has limitations in the real world, the mobile robot actively gathers sensor information to construct and reconstruct a Bayesian network, and then derives an appropriate sensing action which maximizes a utility function based on inference of the reconstructed network. The utility function takes into account belief of the localization and the sensing cost. We have conducted some simulation and real robot experiments to validate the sensor planning system.     

Bayesian parameter inference for individual-based models using a Particle Markov Chain Monte Carlo method

Parameter estimation for agent-based and individual-based models (ABMs/IBMs) is often performed by manual tuning and model uncertainty assessment is often ignored. Bayesian inference can jointly address these issues. However, due to high computational requirements of these models and technical difficulties in applying Bayesian inference to stochastic models, the exploration of its application to ABMs/IBMs has just started. We demonstrate the feasibility of Bayesian inference for ABMs/IBMs with a Particle Markov Chain Monte Carlo (PMCMC) algorithm developed for state-space models. The algorithm profits from the model's hidden Markov structure by jointly estimating system states and the marginal likelihood of the parameters using time-series observations. The PMCMC algorithm performed well when tested on a simple predator-prey IBM using artificial observation data. Hence, it offers the possibility for Bayesian inference for ABMs/IBMs. This can yield additional insights into model behaviour and uncertainty and extend the usefulness of ABMs/IBMs in ecological and environmental research.     

Statistical performance evaluation of biometric authentication systems using random effects models

As biometric authentication systems become more prevalent, it is becoming increasingly important to evaluate their performance. This paper introduces a novel statistical method of performance evaluation for these systems. Given a database of authentication results from an existing system, the method uses a hierarchical random effects model, along with Bayesian inference techniques yielding posterior predictive distributions, to predict performance in terms of error rates using various explanatory variables. By incorporating explanatory variables as well as random effects, the method allows for prediction of error rates when the authentication system is applied to potentially larger and/or different groups of subjects than those originally documented in the database. We also extend the model to allow for prediction of the probability of a false alarm on a "watch-list" as a function of the list size. We consider application of our methodology to three different face authentication systems: a filter-based system, a Gaussian mixture model (GMM)-based system, and a system based on frequency domain representation of facial asymmetry