Bayesian and Dempster-Shafer fusion

The Kalman Filter is traditionally viewed as a prediction-correction filtering algorithm. In this work we show that it can be viewed as a Bayesian fusion algorithm and derive it using Bayesian arguments. We begin with an outline of Bayes theory, using it to discuss well-known quantities such as priors, likelihood and posteriors, and we provide the basic Bayesian fusion equation. We derive the Kalman Filter from this equation using a novel method to evaluate the Chapman-Kolmogorov prediction integral. We then use the theory to fuse data from multiple sensors. Vying with this approach is the Dempster-Shafer theory, which deals with measures of “belief”, and is based on the nonclassical idea of “mass” as opposed to probability. Although these two measures look very similar, there are some differences. We point them out through outlining the ideas of the Dempster-Shafer theory and presenting the basic Dempster-Shafer fusion equation. Finally we compare the two methods, and discuss the relative merits and demerits using an illustrative example.     

Dempster-Shafer theory-based hierarchical saliency detection

This article presents a new saliency detection method based on a hierarchical structure. In order to better capture the key elements in an image, we first construct a three-layer structure by applying a merging strategy to the image. For different layers, we exploit different methods to detect salient regions. After obtaining initial saliency maps of five layers, we construct a Dempster-Shafer model to fuse and refine these saliency maps. In the Dempster-Shafer model, the saliency value of upper layers can provide guidance for saliency detection of lower layers. Finally, we fuse the saliency map of each layer to obtain the final result. Abundant experimental results on two benchmark data sets demonstrate that our method outperforms most of 12 state-of-the-art methods in terms of three popular evaluation criteria, that is, the P-R curve, the F-measure, and the mean absolute error.     

Multisource classification using ICM and Dempster-Shafer theory

We propose to use evidential reasoning in order to relax Bayesian decisions given by a Markovian classification algorithm, the multiscale iterated conditional mode (ICM) algorithm. The Dempster-Shafer rule of combination enables us to fuse decisions in a local spatial neighborhood which we further extend to be multisource. This approach enables us to more directly fuse information. Application to the classification of very noisy images produces interesting results     

贝叶斯估计动态汽车衡分时段数据融合研究

数据融合是一个多级、多层面的数据处理过程,主要完成对来自多个信息源的数据进行自动检测、关联、相关、估计及组合等处理。该文通过分析动态汽车衡的称重原理,对两路称重传感器不同时段的输出数据进行分析,提出基于贝叶斯估计的数据融合方法。实验检定表明:采用这种融合方法的动态汽车衡称重误差小,克服了动态汽车衡由于车辆振动、路面不平和传感器灵敏度分散性、传感器线性度误差等因素对称量结果的影响,准确度高。     

基于BP神经网络的D-S证据理论及其应用

命题基本概率分配（BPA）的确定是D-S证据理论得以广泛应用的关键之一。目前，大部分确定方法受专家知识偏好影响较大，难以反映客观情况。将BP网络运用到基本概率分配的确定过程中，使得BP网络和D-S证据理论两者有机地联合应用，这样既可利用D-S证据理论来表达和处理不确定信息，又可以充分发挥BP网络的自学习、自适应和容错能力。文中建立了基于BP网络的D-S证据理论的故障诊断模型，并给出了证据的融合算法。仿真实验表明，该模型可行。     

Crack localization in stepped rotors based on Bayesian fusion of multiscale superharmonic characteristic deflection shapes

A crack is one of the most dangerous faults in rotors of key rotating machinery. In order to make reasonable maintenance, crack localization for rotors under operational conditions is very important and full of challenges. Focusing on crack localization in rotating rotors, a new crack localization method for stepped rotors based on Bayesian fusion of multiscale superharmonic characteristic deflection shapes (SCDSs) is proposed. The non‐linearity induced by cracks is utilized to eliminate the interference of stiffness reduction by steps in the rotor, and the noise‐robustness issue is tackled by casting the SCDSs into multiscale SCDSs with multiscale space theory. Moreover, Bayesian fusion is applied to the multiscale SCDSs to derive a new damage index to localize cracks. Numerical and experimental investigations are conducted to validate the proposed method. The results indicate that the proposed method is effective, accurate and robust for single or multiple crack localization in stepped rotors, and thus, it has a great potential in practical applications.     

Application of Dempster-Shafer Theory in Aircraft Maintenance Time Assessment: A Case Study

Abstract:

The goal of this case study is to demonstrate the use of the Dempster-Shafer Theory of Evidence as a decision aid to predict aircraft maintenance times during Turkish Air Force wartime tactical operations. A questionnaire was administered to aircraft maintenance experts to investigate maintenance times of major aircraft failure modes (ignition, fuel, and electrical). An example examining jet engine aircraft failure is presented to demonstrate use of the developed approach. The results of this methodology provide a useful and specific application area for the Dempster-Shafer Theory to aid a decision maker in making wartime tactical decisions.     

Learning Likelihood-Equivalence Bayesian Networks Using an Empirical Bayesian Approach

Behaviormetrika - Many studies on learning Bayesian networks have used the Dirichlet prior score metric (DPSM). Although they assume different optimum hyper-parameter values for DPSM, few studies...     

Bayesian Reliability Demonstration

A Bayesian approach to reliability demonstration testing is described and differences between the Bayesian viewpoint and the commonly employed classical approach are highlighted. A procedure for selecting a specific inverted gamma probability density to characterize the prior distribution of the MTBF of electronic hardware is developed and a table of Bayesian demonstration plans for a practical range of input parameters is provided. In addition, procedures for the implementation of the plans and two illustrative examples are given. Finally, two commonly employed classical plans are compared to a Bayesian plan illustrating the efficiency of the latter in terms of demonstration test time requirements.     

Approximate Bayesian methods

Summary This paper develops asymptotic expansions for the ratios of integrals that occur in Bayesian analysis: for example, the posterior mean. The first term omitted isO(n ⁻²) and it is shown how the termO(n ⁻¹) can be of importance.     

Bayesian Local Kriging

We consider the problem of constructing metamodels for computationally expensive simulation codes; that is, we construct interpolators/predictors of functions values (responses) from a finite collection of evaluations (observations). We use Gaussian process (GP) modeling and kriging, and combine a Bayesian approach, based on a finite set GP models, with the use of localized covariances indexed by the point where the prediction is made. Our approach is not based on postulating a generative model for the unknown function, but by letting the covariance functions depend on the prediction site, it provides enough flexibility to accommodate arbitrary nonstationary observations. Contrary to kriging prediction with plug-in parameter estimates, the resulting Bayesian predictor is constructed explicitly, without requiring any numerical optimization, and locally adjusts the weights given to the different models according to the data variability in each neighborhood. The predictor inherits the smoothness properties of the covariance functions that are used and its superiority over plug-in kriging, sometimes also called empirical-best-linear-unbiased predictor, is illustrated on various examples, including the reconstruction of an oceanographic field over a large region from a small number of observations. Supplementary materials for this article are available online.