一类分数阶微积分的中值定理及应用

Riemann-Liouville分数阶微积分算子是一类带有一个函数的分数阶微积分算子的特殊情形，以Riemann-Liouville分数阶微积分算子的积分中值定理和微分中值定理为基础，我们得到了一类带有一个函数的分数阶微积分算子的积分中值定理和微分中值定理，并给出其在计算方面的一些应用。     

一种跨公司航天软件缺陷预测方法

为提高航天软件测试的效率和质量，针对同公司航天软件数量少、研制周期长的特点，提出了一种跨公司航天软件缺陷预测方法。从航天软件背景信息复杂、规模大、功能独立等特征出发，提出基于静态分类缺陷预测的模型构建思想。引入迁移学习方法，利用最近邻分类器和数据引力模型，对训练数据的分布特征进行修正，提高训练数据与目标数据的相似性；为提高模型的泛化能力以适应目标数据的多样性，提出在训练数据中加入少量目标数据用于模型训练。将该方法在实际工程中进行应用，实验结果表明，与已有软件缺陷预测方法相比，该方法在保持较低误报率（不高于0.3）的情况下可有效提高召回率（接近0.6），整体可信度得到有效增强（G- measure超过0.6），方法稳定度高，泛化能力较强；本方法在实际工程中对测试规模影响可控，测试效率得到提高。     

Study of planar structure applying reciprocity technique combined with MGEC and analysis of discontinuity

The 3D structure electromagnetic computation presents several difficulties related to the volume mesh. In fact, the entire volume space must be taken into account even the smallest details. In this article, we propose a formulation based on the reciprocity theorem combined with the generalized equivalent circuit method to model a planar 3D structure with both coaxial and planar excitation. The major advantage of this formulation is the fact to reduce the computational volume into 2D ones in the discontinuity plane. In addition, we focused on the calculation of the discontinuity between the excitation source and the planar structure to determine the exact behavior of the electric coaxial excitation model. The obtained current density, electric field distributions, and the input impedance are presented and discussed in the following sections. An approximately good agreement of input impedance with those obtained by the simulator and measurement is shown.     

Weighted preliminary-summation-based principal component analysis for non-Gaussian processes

For industrial chemical process, preliminary-summation-based principal component analysis (PS-PCA), an amended PCA method was recently provided for coping with both Gaussian and non-Gaussian characteristics. By summing the training and monitoring data respectively, PS-PCA is capable of resolving the issue of non-Gaussian processes and achieves higher fault detection rate than the traditional PCA. However, in the PS-PCA summation operation, all data samples are regarded as the same weight, which results in the fault information of newly-samples may be diluted, leading to significant detection delays. To address this challenge, in this paper, we propose a novel weighted PS-PCA (WPS-PCA) method that employs an exponential weighting scheme to put more emphasis on recent information. Subsequently, a mathematical argument demonstrates that when the number of variables is enough plentiful, the obtained summation combined with the generalized central limit theorem conforms to approximately a Gaussian distribution. The kurtosis relationships indicate this conversion will bring out well-pleasing feasibility for conventional PCA. Ultimately, the proposed technique verifies detection performance using the Tennessee Eastman process, which is compared with the existing PCA and PS-PCA schemes, in terms of the fault detection time and fault detection rate. The simulation studies reveal that the proposed method is efficient and superior.     

一类Hilfer型分数阶微分方程解的存在和唯一性

用Banach不动点定理和上下解方法研究了α(1<α <2)阶数和β(0≤β ≤1)类型Hilfer分数阶微分方程的解,给出了方程解的存在和唯一性,并通过例证验证了本文所得结果的有效性.     

Beta-Binomial删除信道中的喷泉码文件传输协议

由于命名数据网络(NDN,Named-Data Networking)无环路、逐包、逐跳转发的特点,使得数据包回传成功率降低,而传统的TCP/IP协议中的ARQ和ACK机制对于多播会话不再适用.由于NDN中的传输信道可以等效为二进制删除信道,因此可以通过应用层编码来实现文件的可靠传输.传统的信道编码技术如卷积码、级联码和RS码等复杂度较高,而将NDN与低复杂度的喷泉码的结合可以实现分布式的存储架构,因而可通过喷泉编码在应用层协议中实现可靠的纠删机制,保证整体文件的传输可靠性.以往的研究一般是基于确定的删除概率信道模型,但是由于网络的异构性和信道噪声等因素影响,可能会造成信道丢包概率呈随机性分布.因此,本文在Beta-Binomial分布模型的前提下,根据贝叶斯统计的先验信息和中心极限定理,对随机概率下的纠删信道的文件可靠传输协议进行了数学建模和理论推导.仿真结果显示此模型更具有普适性,此传输协议可在信道状况未知的前提下从理论上求出最小发包数,减少冗余编码包,提高文件整体的投递成功率,在保证传输可靠性的同时有效提升协议传输效率.     

基于概率分析的核电传热管降质失效评估方法研究

发展核电是国家能源安全战略的重要组成部分，核电安全是对核电事业发展的最基本要求。依据核电传热管的检测历史数据和专家数据，利用全概率理论和Bayes公式提出了对传热管降质完整性评估的概率计算方法。通过对应力腐蚀、疲劳损伤等影响因素的分析，实现了在不同应力腐蚀和疲劳损伤条件下对传热管降质分布的概率计算。该评估方法可以将多个影响因素共同作用的复杂问题，简化为单个影响因素的逐一修正问题，简化了计算和处理方法。该方法可为核电蒸汽发生器传热管的降质概率评估提供借鉴。