An expectation operator for belief functions in the Dempster–Shafer theory*

ABSTRACT

The main contribution of this paper is a new definition of expected value of belief functions in the Dempster–Shafer (D–S) theory of evidence. Our definition shares many of the properties of the expectation operator in probability theory. Also, for Bayesian belief functions, our definition provides the same expected value as the probabilistic expectation operator. A traditional method of computing expected of real-valued functions is to first transform a D–S belief function to a corresponding probability mass function, and then use the expectation operator for probability mass functions. Transforming a belief function to a probability function involves loss of information. Our expectation operator works directly with D–S belief functions. Another definition is using Choquet integration, which assumes belief functions are credal sets, i.e. convex sets of probability mass functions. Credal sets semantics are incompatible with Dempster's combination rule, the center-piece of the D–S theory. In general, our definition provides different expected values than, e.g. if we use probabilistic expectation using the pignistic transform or the plausibility transform of a belief function. Using our definition of expectation, we provide new definitions of variance, covariance, correlation, and other higher moments and describe their properties.     

Data envelopment analysis based on team reasoning

Existing approaches to data envelopment analysis focus mainly on the derivation of the efficiency of the individual decision‐making unit (DMU) or on the calculation of the weights of multiple inputs or outputs, but pay little attention to the team interest of all the DMUs. Motivated by the idea of team reasoning, in which the benefit of the team is of higher importance than that of each individual, this paper considers all the DMUs as a team and introduces the team indexes including the overall efficiencies, variance, boundaries of all the DMUs, and relationships between DMUs. Several models are first developed to estimate values of the team indexes based on which decision makers can provide their preferences regarding them. Then, models are established to obtain the interval efficiencies of individual DMUs under the condition that the team indexes are satisfied. Several examples are given to illustrate the proposed approaches and verify their applicability.     

双盘式磁力耦合器振动噪声分析与实验研究

为了在双盘式磁力耦合器设计阶段分析振动噪声特性,优化双盘式磁力耦合器设计,提出了一种利用模态叠加原理来分析其振动噪声的方法。双盘式磁力耦合器具有高转矩密度与高效率等优势,因此逐渐发展成为煤矿机械柔性传动装置。由于双盘式磁力耦合内部的转子磁场非正弦分布以及涡电流谐波等因素影响,双盘式磁力耦合器输出转矩中不可避免的存在波动。若根据计算得出的双盘式磁力耦合器的电磁振动噪声特点,在设计时选取振动噪声小的参数进行优化组合,可在实际中降低其电磁振动及噪声,有利于减少制造成本。本文结合双盘式磁力耦合器的结构特征,提出了一种模态叠加响应法计算电磁振动噪声,建立了其电磁径向力的解析模型,并在多物理场耦合作用下分析主要电磁径向力波在工作频率内的谐波响应,最后在额定功率为55 kW双盘式磁力耦合器实验台上进行试验验证。基于麦克斯韦张量法,建立了双盘式磁力耦合器的径向电磁力解析模型,并得出0阶与10阶电磁径向力波是产生振动噪声的最主要原因;利用多物理场耦合分析法进行谐波响应NVH特性分析,结果显示0阶力波的振动加速度与形变量均大于10阶力波的振动加速度与形变量,因此双盘式磁力耦合器的电磁振动主要来源于0阶力波;在额定功率为55 kW,最高转速为1 500 r/min的双盘式磁力耦合器实验台进行振动测试,试验结果显示在1 500 r/min时,试验得出的最大振动峰值及频率约为35 m/s^2和4 950 Hz,与有限元仿真结果的误差对应为6.3%和1.1%;而当变频电机的输入转速依次增大时,振动加速度的理论值、仿真值与试验值的曲线形态较为接近,误差较小;噪声估计值与实测值的最大误差仅为8.9%,基本验证了本文所提出模态叠加法的正确性。     

A new linearly constrained minimum variance beamformer for reconstructing EEG sparse sources

Brain source imaging based on EEG aims to reconstruct the neural activities producing the scalp potentials. This includes solving the forward and inverse problems. The aim of the inverse problem is to estimate the activity of the brain sources based on the measured data and leadfield matrix computed in the forward step. Spatial filtering, also known as beamforming, is an inverse method that reconstructs the time course of the source at a particular location by weighting and linearly combining the sensor data. In this paper, we considered a temporal assumption related to the time course of the source, namely sparsity, in the Linearly Constrained Minimum Variance (LCMV) beamformer. This assumption sounds reasonable since not all brain sources are active all the time such as epileptic spikes and also some experimental protocols such as electrical stimulations of a peripheral nerve can be sparse in time. Developing the sparse beamformer is done by incorporating L1-norm regularization of the beamformer output in the relevant cost function while obtaining the filter weights. We called this new beamformer SParse LCMV (SP-LCMV). We compared the performance of the SP-LCMV with that of LCMV for both superficial and deep sources with different amplitudes using synthetic EEG signals. Also, we compared them in localization and reconstruction of sources underlying electric median nerve stimulation. Results show that the proposed sparse beamformer can enhance reconstruction of sparse sources especially in the case of sources with high amplitude spikes.     

Visually deficient working conditions and reduced work performance in office workers: Is it mediated by visual discomfort?

IntroductionThe main purpose of this cross-sectional study was to investigate whether visual discomfort acts as a mediating factor between perceived visual ergonomic working conditions and self-rated visual performance among office workers who carry out administrative tasks and computer-based work at the Swedish Tax Agency.MethodsA questionnaire was sent to 94 office workers addressing: 1) perceived visual quality of the visual display units; 2) prevalence of eye symptoms; and 3) self-rated visual performance. Eighty-six persons (54 women (63%), 31 men (36%), and 1 of unspecified sex) answered the questionnaire. Multiple regression analysis investigated the association between visual ergonomic working conditions and visual performance, both with and without visual discomfort as a mediator.ResultsThe group mean of the Indexed survey questions indicated a reasonably good quality of visual ergonomic working conditions, a relative absence of eye symptoms, and acceptable self-rated visual performance. Results from multiple regression analysis showed a significant association between perceived visual ergonomic working conditions and self-rated visual performance (r² = 0.30, β = 0.327, p < 0.01). When visual discomfort was used as a mediator, the association between perceived visual ergonomic working conditions and self-rated visual performance remained the same (r² = 0.32, β = 0.315, p < 0.01).DiscussionIt was remarkable to discover that self-rated visual performance was independent of visual discomfort. Possible explanations include exposure factors not included in the current study, such as dry air and sensory irritation in the eyes, psychosocial stress, time spent performing near work activities, or time exposed to visually deficient working conditions.Relevance to industryThe strong connection between satisfaction with visual ergonomic working conditions and productivity in this study has implications for workplace profitability and staff satisfaction. If productivity is enhanced by better visual ergonomic working conditions, then managers of workplaces may be able to improve work outcomes by optimizing the physical work environment.     

A side-sensitive synthetic coefficient of variation chart

Control charts for monitoring the coefficient of variation (γ) are useful for processes with an inconsistent mean (μ) and a standard deviation (σ) which changes with μ, by monitoring the consistency in the ratio σ over μ. The synthetic-γ chart is one of the charts proposed to monitor γ, and its attractiveness lie in waiting until a second point to fall outside the control limits before a decision is made. However, existing synthetic-γ charts do not differentiate between the points falling outside the upper control limit (UCL) and lower control limit (LCL). Hence, this paper proposes a side-sensitive synthetic-γ chart, where successive nonconforming samples must either fall above the UCL or below the LCL. Formulae to compute the average run length (ARL), the standard deviation of the run length (SDRL) and expected average run length (EARL) are derived using the Markov chain approach, and the algorithms to obtain the optimal charting parameters are proposed. Subsequently, the optimal charting parameters, ARL, SDRL and EARL values for various numerical examples are shown. Comparisons show that the side-sensitive synthetic-γ chart consistently outperforms the existing synthetic-γ chart, especially for small shifts. The proposed chart also consistently outperforms the Shewhart-γ chart, while showing comparable or better performance than the Exponentially Weighted Moving Average (EWMA) chart for most shift sizes, except for very small shifts. Finally, this paper shows the implementation of the proposed chart on an industrial example.     

基于GA-BP的汽车风振噪声声品质预测模型

目前对于汽车风振噪声的优化研究主要以声压级（Sound pressure level，SPL）作为单一评价指标，既不能全面反映噪声的物理属性，也无法考虑人耳对噪声的主观认知过程。为准确评价风振噪声，引入声品质，运用大涡模拟（Large eddy simulation，LES）对风振噪声进行数值仿真，根据实车道路试验判断仿真的准确性；对仿真结果进行声品质客观评价与主观评价，综合声品质客观评价参数与声品质主观评价试验结果建立BP神经网络预测模型；利用遗传算法（Genetic algorithm，GA），进一步对BP神经网络的结构参数进行优化，建立GA-BP声品质预测模型。研究结果表明，GA-BP声品质预测模型在训练速度和预测精度上都优于BP神经网络预测模型。预测模型基于声品质主客观评价结果，其预测值可以代替传统的声压级评价指标，为风振噪声提供更为准确合理的评价。     

A hybrid homogeneously weighted moving average control chart for process monitoring: Discussion

The sensitivity of a monitoring scheme depends on many factors including the variance of the charting statistic which is very important in the computation of the control limits. This paper discusses the computation of the variance of the recently proposed hybrid homogeneously weighted moving average (HHWMA) $\overline{X}$ scheme which was based on an incorrect assumption. The correct variance is used to evaluate the run-length characteristics of the HHWMA $\overline{X}$ scheme. It is observed that the incorrect variance has a significant impact on the sensitivity (or performance) of the HHWMA $\overline{X}$ scheme.