时变偏微分方程的贝叶斯稀疏识别方法

在数据驱动的建模中,通过测量或模拟得到时空数据,我们发现基于拉普拉斯先验的贝叶斯稀疏识别方法能有效地恢复时变偏微分方程的稀疏系数.本文将贝叶斯稀疏识别方法运用于各种时变偏微分方程模型(KdV方程、Burgers方程、Kuramoto-Sivashinsky方程、反应-扩散方程、非线性薛定谔方程和纳维-斯托克斯方程)的方...     

结合残差U-Net神经网络和DIP的PET图像降噪

由于正电子发射型计算机断层显像(PET)噪声较大,现有图像降噪效果不理想,提出了一种结合残差U-Net神经网络和深度图像先验(DIP)的PET图像降噪.在U-Net网络中引入残差学习,提高网络表达能力和收敛速度;提出一种无训练数据的DIP算法,将神经网络解释为图像的参数化,利用图像噪声参数化后呈现高阻抗的特性将其去除,...     

PCA-BP模型在判别基于LIF技术煤矿突水水源的应用

防治煤矿突水时需迅速精准地判别突水水源,激光诱导荧光(LIF)光谱技术具有灵敏度高、快速准确监测特点,为检测突水水源提供了一种新的方法。该研究引入该技术以获取突水荧光光谱数据。采用卷积(SG)平滑和多元散射校正(MSC)方法对光谱图进行预处理,以消除光谱采集过程中噪声干扰。采用主成分分析(PCA)方法提取特征信息,针对SG预处理后的数据,当主成分个数为3时,累积贡献率可达到99.76%,已基本保留原数据的全信息。选择3层结构BP神经网络建立分类判别模型,通过不同方式构造训练集和测试集,SG预处理数据构建的分类模型可以达到精准判别,而对于MSC预处理和原始数据出现很少的误判。实验结果表明SG预处理结果要优于MSC预处理。研究结果表明,将PCA和BP神经网络结合建立分类模型,能有效判别煤矿突水水源,且具有较强的自组织、自学习能力。     

PCA-BP模型在判别基于LIF技术煤矿突水水源的应用（英文）

防治煤矿突水时需迅速精准地判别突水水源,激光诱导荧光(LIF)光谱技术具有灵敏度高、快速准确监测特点,为检测突水水源提供了一种新的方法。该研究引入该技术以获取突水荧光光谱数据。采用卷积(SG)平滑和多元散射校正(MSC)方法对光谱图进行预处理,以消除光谱采集过程中噪声干扰。采用主成分分析(PCA)方法提取特征信息,针对SG预处理后的数据,当主成分个数为3时,累积贡献率可达到99.76%,已基本保留原数据的全信息。选择3层结构BP神经网络建立分类判别模型,通过不同方式构造训练集和测试集,SG预处理数据构建的分类模型可以达到精准判别,而对于MSC预处理和原始数据出现很少的误判。实验结果表明SG预处理结果要优于MSC预处理。研究结果表明,将PCA和BP神经网络结合建立分类模型,能有效判别煤矿突水水源,且具有较强的自组织、自学习能力。     

基于噪声水平估计的多孔准直X射线荧光CT去噪算法

X射线荧光CT(XFCT)是X射线CT与X射线荧光分析相结合的新型成像方式,可用于探测被修饰后的纳米金颗粒在肿瘤内部的分布及质量分数,在早期癌症诊疗方面具有较好的应用潜力。如何抑制XFCT成像的康普顿散射噪声是当前的热点问题。本文基于深度学习方法,通过卷积神经网络学习图像中的噪声分布规律,从而抑制噪声。基于此,提出了一种基于噪声水平估计和卷积神经网络的XFCT去噪网络（NeCNN）算法,该算法运用噪声估计子网络及去噪主网络进行去噪。估计子网络通过去噪卷积神经网络（DnCNN）估计噪声水平并初步降噪,随后将估计结果输入去噪主网络——全卷积神经网络（FCN）用于学习康普顿散射的分布规律,同时为兼顾局部与全局最优解采用均方误差（MSE）及结构相似度（SSIM）作为损失函数。数据集通过Geant4软件模拟扫描填充各种金属纳米颗粒（Au、Bi、Ru、Gd）的空气模体及聚甲基丙烯酸甲酯（PMMA）模体来获取,且设置不同入射X射线的强度,以此模拟不同噪声水平,增强模型泛化能力。实验结果表明,与三维块匹配滤波（BM3D）及DnCNN算法相比,NeCNN算法的去噪结果最优,其SSIM为0.95066,峰...     

稀疏降噪自编码算法用于近红外光谱鉴别真假药的研究

近红外光谱分析技术作为一种快速、无损检测技术十分适用于真假药品现场鉴别。自编码网络作为当前机器学习领域研究的热点受到广泛关注,自编码网络是一种典型的深度学习网络模型,它比传统的潜层学习方法具有更强的模型表示能力。自编码网络使用贪婪逐层预训练算法,通过最小化各层网络的重构误差,依次训练网络的每一层,进而训练整个网络。通过对数据进行白化预处理并使用无监督算法对输入数据进行逐层重构,使网络更有效的学习到数据的内部结构特征。之后使用带标签数据通过监督学习算法对整个网络进行调优。首先对真假琥乙红霉素片的近红外光谱数据进行预处理以及白化预处理,通过白化处理降低数据特征之间的相关性,使数据各特征具有相同的方差。数据处理之后利用稀疏降噪自编码网络针对真假药品光谱数据建立分类模型,并将稀疏降噪自编码网络模型与BP神经网络以及SVM算法在分类准确率及算法稳定性方面进行对比。结果表明对光谱数据进行白化预处理能有效提升稀疏降噪自编码网络的分类准确率。并且自编码网络分类准确率在不同训练样本数量下均高于BP神经网络,SVM算法在少量训练样本的情况下更有优势,但在训练数据集样本数达到一定数量后,自编码网络的分类准确率将优于SVM算法。在算法稳定性方面,自编码网络较之BP神经网络和SVM算法也更稳定。使用稀疏降噪自编码网络对真假药品近红外光谱数据进行建模,能对真假药品进行有效的鉴别。     

一个新的对比饱和蒸气压方程

一、前言 目前,大多数饱和蒸气压方程都是在克拉贝隆-克劳修斯方程的基础上,假定△H_v和△Z_v随温度呈一定的变化关系并加以修正再进行积分得出的,例如Riedel方程、Miller方程、Thek-Stiel方程、Gomez Nieto-Thodos方程和徐忠方程等。本文在总结前人工作的基础上,从统计力学的角度,对分子结构及分子间作用力进行适当简化,先用分析的方法导出饱和压力随温度变化关系的基本函数形式,再用最小二乘回归的方法拟合出一套系数,从而得到纯流体从三相点到临界点的饱和蒸气压方程。     

基于卷积神经网络和近红外光谱的酒醅酸度分析方法研究

快速、准确检测酒醅酸度,可显著提高白酒出酒率和成品酒品质。近红外光谱(NIR)提供了分子的倍频和合频,即有机物中含氢基团(C—H、 N—H、 O—H)的振动信息,通常用于样品中含氢化合物的定性和定量分析。采用NIR能简单、迅速的测定酒醅酸度,克服了传统化学分析方法检测周期长、试剂消耗大、人为误差等不足。由于NIR是一种间接分析技术,如何建立校正模型是准确检测酒醅酸度的关键。作为深度学习中的典型模型,卷积神经网络(CNN)具有局部区域连接,分享权值等优点,不仅能从复杂的光谱数据中提取关键特征,还能减少网络模型的复杂度。因此,提出基于CNN和NIR的酒醅酸度定量分析方法,以某酒企生产线中采集的545个酒醅样本光谱数据作为研究对象,采用标准正态变换(SNV)、 Savitzky-Golay (SG)滤波和一阶求导(1^stD)三种算法相结合对原始光谱进行预处理;利用无信息变量消除法(UVE)选择光谱数据的特征波长;使用CNN建立酒醅酸度模型。结果表明：(1)对光谱数据进行预处理后,消除了原始光谱中的基线偏移,噪声等问题;经过预处理后的光谱数据模型相较于原始光谱建模,预测集...     

混合算法优化的乘用车舱内噪声感知烦恼度神经网络建模

针对传统乘用车舱内噪声感知烦恼度量化模型精度低的问题,提出了一种利用混合算法优化的神经网络模型预测舱内噪声感知烦恼度的评价方法。此混合算法融合麻雀搜索算法(SSA)和遗传算法(GA),对反向传播(BP)神经网络进行优化,根据声品质主客观评价数据,建立SSA-GA-BP网络的乘用车舱内噪声感知烦恼度客观量化模型,与BP模型、GA-BP模型、SSA-BP模型进行对比分析。结果表明, SSA-GA-BP模型能够实现更高的预测精度,更接近主观评价数值,泛化能力更强,可替代传统的声品质主观评价实验。     

基于XRF-CNN土壤重金属Zn元素含量预测模型研究

结合X射线荧光光谱法,针对土壤中重金属元素Zn含量的预测问题,提出基于深度卷积神经网络回归预测模型。对原始土壤进行相关预处理,用粉末压片法制作土壤压片,采用X射线荧光光谱法(X-Ray-fluorescence,XRF)获取土壤光谱,相比于传统检测方式,XRF法具有检测速度快、精度高、操作简单、不破坏样品属性并且可实现多种重金属元素同时检测等优点,故将XRF与深度卷积神经网络相结合,实现对土壤中重金属Zn元素含量的精确预测。采用箱型图来剔除X射线荧光光谱中的异常数据,采用熵权法结合多元散射校正来对样品盒数据进行校正,采用Savitzky-Golay平滑去噪法以及线性本底法对光谱数据进行预处理,可以有效地解决由外界环境和人为因素产生的噪声及基线漂移等问题。针对卷积神经网络结构的特殊性,将获取的一维光谱数据向量,采用构建光谱数据矩阵的方式来进行处理,将同一浓度、同一含水率下5组平行光谱数据向量转化为二维光谱信息矩阵,以该矩阵作为深度卷积神经网络预测模型的输入,以适应卷积层的操作要求,利用深度卷积神经网络特殊的结构模式,能有效提取土壤光谱数据特征,提高了深度卷积神经网络预测模型的学习能力,降低模型的训练难度。深度卷积神经网络预测模型采用3层卷积层搭建,使用ReLU激活函数激活,采用最大池化方式,减少数据的维度,增加Dropout层,防止过拟合,使用ADAM优化器对预测模型进行优化。实验以平均相对误差(mean relative error, MRE)、损失函数(LOSS)、平均绝对误差(mean absolute error, MAE)确定了模型的最优学习率为10-3以及最优迭代次数为3000,并将深度卷积神经网络预测模型与BP预测模型、ELM预测模型、PLS预测模型进行对比,以均方误差(mean square error, MSE)、均方根误差(root mean square error, RMSE)、以及拟合系数R2来分析比较预测模型的好坏,结果表明,基于深度卷积神经网络预测模型在对土壤中重金属Zn元素含量预测方面优于BP,ELM,PLS三种预测模型,提高了预测精度。     

A deep learning method for solving third-order nonlinear evolution equations

It has still been difficult to solve nonlinear evolution equations analytically. In this paper, we present a deep learning method for recovering the intrinsic nonlinear dynamics from spatiotemporal data directly. Specifically, the model uses a deep neural network constrained with given governing equations to try to learn all optimal parameters. In particular, numerical experiments on several third-order nonlinear evolution equations, including the Korteweg–de Vries (KdV) equation, modified KdV equation, KdV–Burgers equation and Sharma–Tasso–Olver equation, demonstrate that the presented method is able to uncover the solitons and their interaction behaviors fairly well.     

Effects of viscous dissipation and radiation on the thermal boundary layer over a nonlinearly stretching sheet

This Letter endeavours to complete an earlier numerical analysis for flow and heat transfer in a viscous fluid over a sheet nonlinearly stretched by extending the investigation in two directions. On one side, the effects of thermal radiation are included in the energy equation, and, on the other hand, the prescribed wall heat flux case (PHF case) is also analyzed. The governing partial differential equations are converted into nonlinear ordinary differential equations by a similarity transformation. The variations of dimensionless surface temperature as well as flow and heat-transfer characteristics with the governing dimensionless parameters of the problem, which include a nonlinearly stretching sheet, thermal radiation, viscous dissipation and power-law index of the wall temperature parameters, are graphed and tabulated.     

A Front-Tracking Method for Motion by Mean Curvature with Surfactant

In this paper, we present a finite difference method to track a network of curves whose motion is determined by mean curvature. To study the effect of inhomogeneous surface tension on the evolution of the network of curves, we include surfactant which can diffuse along the curves. The governing equations consist of one parabolic equation for the curve motion coupled with a convection-diffusion equation for the surfactant concentration along each curve. Our numerical method is based on a direct discretization of the governing equations which conserves the total surfactant mass in the curve network. Numerical experiments are carried out to examine the effects of inhomogeneous surface tension on the motion of the network, including the von Neumann law for cell growth in two space dimensions.     

On radially symmetric vibrations of orthotropic non-uniform disks including shear deformation

This paper deals with the free axisymmetric vibrations of orthotropic circular plates with linear variation in thickness. The analysis is based on a set of two differential equations derived by an extension of Mindlin's shear theory for plates. On simplification and algebraic manipulation, one of the dependent variables is eliminated from the governing equations of motion, giving rise to a fourth order linear differential equation with variable coefficients. The resulting differential equation is solved numerically by the Chebyshev collocation technique. Frequencies and mode shapes for the first five modes of vibration are computed for different plates.     

Reconstruction of non-linear time delay models from data by the use of optimal transformations

We propose a new technique for the numerical reconstruction of non-linear delay differential equations from time series by applying the method of optimal transformations, a concept of multiple non-linear regression analysis. By constructing a generalized correlation function, this method allows for testing time series for delay-induced dynamics. Also, the delay times and the governing differential equations are estimated with good numerical accuracy. We present several examples which show that this method is useful also for the analysis of short and noisy time series.     

Lienard Equation and Exact Solutions for Some Soliton-Producing Nonlinear Equations

In this paper, we first consider exact solutions for Lienard equation with nonlinear terms of any order. Then, explicit exact bell and kink profile solitary-wave solutions for many nonlinear evolution equations are obtained by means of results of the Lienard equation and proper deductions, which transform original partial differential equations into the Lienard one. These nonlinear equations include compound KdV, compound KdV-Burgers, generalized Boussinesq, generalized KP and Ginzburg-Landau equation. Some new solitary-wave solutions are found.     

A Hopf-like equation and perturbation theory for differential delay equations

We extend techniques developed for the study of turbulent fluid flows to the statistical study of the dynamics of differential delay equations. Because the phase spaces of differential delay equations are infinite dimensional, phase-space densities for these systems are functionals. We derive a Hopf-like functional differential equation governing the evolution of these densities. The functional differential equation is reduced to an infinite chain of linear partial differential equations using perturbation theory. A necessary condition for a measure to be invariant under the action of a nonlinear differential delay equation is given. Finally, we show that the evolution equation for the density functional is the Fourier transform of the infinite-dimensional version of the Kramers-Moyal expansion.     

Axisymmetric wave propagation of thermoelastic transversely isotropic half-space under buried loading using potential functions

By virtue of a new scalar potential function and Hankel integral transforms, the wave propagation analysis of a thermoelastic transversely isotropic half-space is presented under buried loading and heat flux. The governing equations of the problem are the differential equations of motion and the energy equation of the coupled thermoelasticity theory. Using a scalar potential function, these coupled equations have been uncoupled and a six-order partial differential equation governing the potential function is received. The displacements, temperature, and stress components are obtained in terms of this potential function in cylindrical coordinate system. Applying the Hankel integral transform to suppress the radial variable, the governing equation for potential function is reduced to a six-order ordinary differential equation with respect to z. Solving that equation, the potential function and therefore displacements, temperature, and stresses are derived in the Hankel transformed domain for two regions. Using inversion of Hankel transform, these functions can be obtained in the real domain. The integrals of inversion Hankel transform are calculated numerically via Mathematica software. Our numerical results for displacement and temperature are calculated for surface excitations and compared with the results reported in the literature and a very good agreement is achieved.