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。     

Improving accuracy of automatic optical inspection with machine learning

Electronic devices require the printed circuit board(PCB)to support the whole structure,but the assembly of PCBs suffers from welding problem of the electronic components such as surface mounted devices(SMDs)resistors.The automated optical inspection(AOI)machine,widely used in industrial production,can take the image of PCBs and examine the welding issue.However,the AOI machine could commit false negative errors and dedicated technicians have to be employed to pick out those misjudged PCBs.This paper proposes a machine learning based method to improve the accuracy of AOI.In particular,we propose an adjacent pixel RGB value based method to pre-process the image from the AOI machine and build a customized deep learning model to classify the image.We present a practical scheme including two machine learning procedures to mitigate AOI errors.We conduct experiments with the real dataset from a production line for three months,the experimental results show that our method can reduce the rate of misjudgment from 0.3%–0.5%to 0.02%–0.03%,which is meaningful for thousands of PCBs each containing thousands of electronic components in practice.     

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.     

关于提升装载机电子秤检定结果测量准确度的探讨

装载机电子秤广泛应用于货场、建筑工地,如何使检定结果准确可靠,本文对自动衡器检定装置标准器量值的管理方法进行了一些探讨。     

Correlation of the leakage flow rate with pressure changes in a clearance-sealed piston prover

Leakage flow rate is one of the most important contributions to the measurement uncertainty when measuring small gas flow rates with a clearance-sealed piston prover. Our previous study has shown that the systematic effects related to the change of the gas viscosity can be successfully corrected, whereas the effects related to the reproducibility of the leakage flow rate are poorly understood. This paper focuses on the interpretation and correction of the reproducibility related effects by analysing experimentally identified variations of the leakage flow rate and the gas pressure in the inclined piston prover. Small changes of the leakage flow in the inclined piston prover indicate that the position of the piston relative to the cylinder remains approximately the same. The obtained relationship between the leakage flow rate and the gas pressure below the piston led to the pressure-based correction of the leakage flow rate.