Prediction of constrained modulus for granular soil using 3D discrete element method and convolutional neural networks

To efficiently predict the mechanical parameters of granular soil based on its random micro-structure,this study proposed a novel approach combining numerical simulation and machine learning algorithms.Initially,3500 simulations of one-dimensional compression tests on coarse-grained sand using the three-dimensional(3D)discrete element method(DEM)were conducted to construct a database.In this process,the positions of the particles were randomly altered,and the particle assemblages changed.Interestingly,besides confirming the influence of particle size distribution parameters,the stress-strain curves differed despite an identical gradation size statistic when the particle position varied.Subsequently,the obtained data were partitioned into training,validation,and testing datasets at a 7:2:1 ratio.To convert the DEM model into a multi-dimensional matrix that computers can recognize,the 3D DEM models were first sliced to extract multi-layer two-dimensional(2D)cross-sectional data.Redundant information was then eliminated via gray processing,and the data were stacked to form a new 3D matrix representing the granular soil’s fabric.Subsequently,utilizing the Python language and Pytorch framework,a 3D convolutional neural networks(CNNs)model was developed to establish the relationship between the constrained modulus obtained from DEM simulations and the soil’s fabric.The mean squared error(MSE)function was utilized to assess the loss value during the training process.When the learning rate(LR)fell within the range of 10-5e10-1,and the batch sizes(BSs)were 4,8,16,32,and 64,the loss value stabilized after 100 training epochs in the training and validation dataset.For BS?32 and LR?10-3,the loss reached a minimum.In the testing set,a comparative evaluation of the predicted constrained modulus from the 3D CNNs versus the simulated modulus obtained via DEM reveals a minimum mean absolute percentage error(MAPE)of 4.43%under the optimized condition,demonstrating the accuracy of this approach.Thus,by combining DEM and CNNs,the variation of soil’s mechanical characteristics related to its random fabric would be efficiently evaluated by directly tracking the particle assemblages.

Discrete Singular Convolution Method for Numerical Solutions of Fifth Order Korteweg-De Vries Equations

A new computational method for solving the fifth order Korteweg-de Vries (fKdV) equation is proposed. The nonlinear partial differential equation is discretized in space using the discrete singular convolution (DSC) scheme and an exponential time integration scheme combined with the best rational approximations based on the Carathéodory-Fejér procedure for time discretization. We check several numerical results of our approach against available analytical solutions. In addition, we computed the conservation laws of the fKdV equation. We find that the DSC approach is a very accurate, efficient and reliable method for solving nonlinear partial differential equations.

Discrete Convolution Associated with Fractional Cosine and Sine Series

Fractional sine series(FRSS)and fractional cosine series(FRCS)are the discrete form of the fractional cosine transform(FRCT)and fractional sine transform(FRST).The recent stud-ies have shown that discrete convolution is widely used in optics,signal processing and applied mathematics.In this paper,firstly,the definitions of fractional sine series(FRSS)and fractional co-sine series(FRCS)are presented.Secondly,the discrete convolution operations and convolution theorems for fractional sine and cosine series are given.The relationship of two convolution opera-tions is presented.Lastly,the discrete Young’s type inequality is established.The proposed theory plays an important role in digital filtering and the solution of differential and integral equations.

DISCRETE SINGULAR CONVOLUTION METHOD WITH PERFECTLY MATCHED ABSORBING LAYERS FOR THE WAVE SCATTERING BY PERIODIC STRUCTURES

A new computational algorithm is introduced for solving scattering problem in periodic structure. The PML technique is used to deal with the difficulty on truncating the unbounded domain while the DSC algorithm is utilized for the spatial discretization. The present study reveals that the method is efficient for solving the problem.

Uniform stable conformal convolutional perfectly matched layer for enlarged cell technique conformal finite-difference time-domain method

Based on conformal construction of physical model in a three-dimensional Cartesian grid,an integral-based conformal convolutional perfectly matched layer（CPML） is given for solving the truncation problem of the open port when the enlarged cell technique conformal finite-difference time-domain（ECT-CFDTD） method is used to simulate the wave propagation inside a perfect electric conductor（PEC） waveguide.The algorithm has the same numerical stability as the ECT-CFDTD method.For the long-time propagation problems of an evanescent wave in a waveguide,several numerical simulations are performed to analyze the reflection error by sweeping the constitutive parameters of the integral-based conformal CPML.Our numerical results show that the integral-based conformal CPML can be used to efficiently truncate the open port of the waveguide.

A WEIGHTED GENERAL DISCRETE FOURIER TRANSFORM FOR THE FREQUENCY-DOMAIN BLIND SOURCE SEPARATION OF CONVOLUTIVE MIXTURES

This letter deals with the frequency domain Blind Source Separation of Convolutive Mixtures (CMBSS). From the frequency representation of the "overlap and save", a Weighted General Discrete Fourier Transform (WGDFT) is derived to replace the traditional Discrete Fourier Transform (DFT). The mixing matrix on each frequency bin could be estimated more precisely from WGDFT coefficients than from DFT coefficients, which improves separation performance. Simulation results verify the validity of WGDFT for frequency domain blind source separation of convolutive mixtures.

Borehole-GPR numerical simulation of full wave field based on convolutional perfect matched layer boundary

The absorbing boundary is the key in numerical simulation of borehole radar.Perfect match layer(PML) was chosen as the absorbing boundary in numerical simulation of GPR.But CPML(convolutional perfect match layer) approach that we have chosen has the advantage of being media independent.Beginning with the Maxwell equations in a two-dimensional structure,numerical formulas of finite-difference time-domain(FDTD) method with CPML boundary condition for transverse electric(TE) or transverse magnetic(TM) wave are presented in details.Also,there are three models for borehole-GPR simulation.By analyzing the simulation results,the features of targets in GPR are obtained,which can provide a better interpretation of real radar data.The results show that CPML is well suited for the simulation of borehole-GPR.

A Revised Piecewise Linear Recursive Convolution FDTD Method for Magnetized Plasmas

The piecewise linear recursive convolution （PLRC） finite-different time-domain （FDTD） method improves accuracy over the original recursive convolution （RC） FDTD approach and current density convolution （JEC） but retains their advantages in speed and efficiency. This paper describes a revised piecewise linear recursive convolution PLRC-FDTD formulation for magnetized plasma which incorporates both anisotropy and frequency dispersion at the same time, enabling the transient analysis of magnetized plasma media. The technique is illustrated by numerical simulations of the reflection and transmission coefficients through a magnetized plasma layer. The results show that the revised PLRC-FDTD method has improved the accuracy over the original RC FDTD method and JEC FDTD method.

Scheme for Designing the 1-D Convolution Window of Gabor Filter

A scheme for designing one-dimensional (1-D) convolution window of the circularly symmetric Gabor filter which is directly obtained from frequency domain is proposed. This scheme avoids the problem of choosing the sampling frequency in the spatial domain, or the sampling frequency must be determined when the window data is obtained by means of sampling the Gabor function, the impulse response of the Gabor filter. In this scheme, the discrete Fourier transform of the Gabor function is obtained by discretizing its Fourier transform. The window data can be derived by minimizing the sums of the squares of the complex magnitudes of difference between its discrete Fourier transform and the Gabor function's discrete Fourier transform. Not only the full description of this scheme but also its application to fabric defect detection are given in this paper. Experimental results show that the 1-D convolution windows can be used to significantly reduce computational cost and greatly ensure the quality of the Gabor filters. So this scheme can be used in some real-time processing systems.

Numerical Methods for Discrete Double Barrier Option Pricing Based on Merton Jump Diffusion Model

As a kind of weak-path dependent options, barrier options are an important kind of exotic options. Because the pricing formula for pricing barrier options with discrete observations cannot avoid computing a high dimensional integral, numerical calculation is time-consuming. In the current studies, some scholars just obtained theoretical derivation, or gave some simulation calculations. Others impose underlying assets on some strong assumptions, for example, a lot of calculations are based on the Black-Scholes model. This thesis considers Merton jump diffusion model as the basic model to derive the pricing formula of discrete double barrier option;numerical calculation method is used to approximate the continuous convolution by calculating discrete convolution. Then we compare the results of theoretical calculation with simulation results by Monte Carlo method, to verify their efficiency and accuracy. By comparing the results of degeneration constant parameter model with the results of previous models we verified the calculation method is correct indirectly. Compared with the Monte Carlo simulation method, the numerical results are stable. Even if we assume the simulation results are accurate, the time consumed by the numerical method to achieve the same accuracy is much less than the Monte Carlo simulation method.

Learning to sample initial solution for solving 0-1 discrete optimization problem by local search

Local search methods are convenient alternatives for solving discrete optimization problems(DOPs).These easy-to-implement methods are able to find approximate optimal solutions within a tolerable time limit.It is known that the quality of the initial solution greatly affects the quality of the approximated solution found by a local search method.In this paper,we propose to take the initial solution as a random variable and learn its preferable probability distribution.The aim is to sample a good initial solution from the learned distribution so that the local search can find a high-quality solution.We develop two different deep network models to deal with DOPs established on set(the knapsack problem)and graph(the maximum clique problem),respectively.The deep neural network learns the representation of an optimization problem instance and transforms the representation to its probability vector.Experimental results show that given the initial solution sampled from the learned probability distribution,a local search method can acquire much better approximate solutions than the randomly-sampled initial solution on the synthesized knapsack instances and the Erd?s-Rényi random graph instances.Furthermore,with sampled initial solutions,a classical genetic algorithm can achieve better solutions than a random initialized population in solving the maximum clique problems on DIMACS instances.Particularly,we emphasize that the developed models can generalize in dimensions and across graphs with various densities,which is an important advantage on generalizing deep-learning-based optimization algorithms.

An Intelligent Sensor Data Preprocessing Method for OCT Fundus Image Watermarking Using an RCNN

Watermarks can provide reliable and secure copyright protection for optical coherence tomography(OCT)fundus images.The effective image segmentation is helpful for promoting OCT image watermarking.However,OCT images have a large amount of low-quality data,which seriously affects the performance of segmentationmethods.Therefore,this paper proposes an effective segmentation method for OCT fundus image watermarking using a rough convolutional neural network(RCNN).First,the rough-set-based feature discretization module is designed to preprocess the input data.Second,a dual attention mechanism for feature channels and spatial regions in the CNN is added to enable the model to adaptively select important information for fusion.Finally,the refinement module for enhancing the extraction power of multi-scale information is added to improve the edge accuracy in segmentation.RCNN is compared with CE-Net and MultiResUNet on 83 gold standard 3D retinal OCT data samples.The average dice similarly coefficient(DSC)obtained by RCNN is 6%higher than that of CE-Net.The average 95 percent Hausdorff distance(95HD)and average symmetric surface distance(ASD)obtained by RCNN are 32.4%and 33.3%lower than those of MultiResUNet,respectively.We also evaluate the effect of feature discretization,as well as analyze the initial learning rate of RCNN and conduct ablation experiments with the four different models.The experimental results indicate that our method can improve the segmentation accuracy of OCT fundus images,providing strong support for its application in medical image watermarking.

基于图卷积的一维平流方程空间离散化数值求解加速方法

本文提出了一种基于图卷积神经网络的偏微分方程空间离散化数值求解加速方法,并将该方法应用于求解一维平流方程的研究中,实现了一维平流方程的加速求解。并设计了基于图卷积的一维平流方程空间离散化神经网络模型(GCPNN),其在物理先验知识指导下基于图模型利用空间图结构特征进行一维平流方程空间离散化求解加速方案建模,在构建图结构关系过程中,基于物理先验知识建立邻接矩阵,利用邻接矩阵融合了全局信息,从而实现了一维平流方程的加速求解。并且通过设计对比实验和消融实验验证了基于GCPNN的求解器相较于基线求解器和CNN求解器在求解精度和计算成本方面的优势,且验证了加入物理先验知识指导及全局信息融合的有效性。

基于DFT与ECA的滚动轴承故障诊断

针对滚动轴承故障诊断中传统卷积神经网络(convolutional neural networks,简称CNN)提取特征的感受野受限于卷积核大小的问题,提出了一种结合离散傅里叶变换(discrete Fourier transform,简称DFT)和高效通道注意力(efficient channel attention,简称ECA)的卷积神经网络模型(convolutional neural network combining discrete Fourier transform and efficient channel attention,简称DFT-ECANet)。首先,将原始振动信号通过DFT变换到频域,在频域上经卷积和离散傅里叶逆变换(inverse discrete Fourier transform,简称IDFT)转换到时域,使信号在时域上具有全局的感受野;其次,将该信号与经过卷积的数据在通道维度上进行拼接,通过ECA为各通道数据分配权重,并关注诊断性能高的特征;最后,通过多个卷积-池化层进一步提取模型深层特征,结合池化层和全连接层诊断轴承故障。实验结果表明:DFT-ECANet在原始振动数据集上具有较高的诊断精度和较好的泛化性能,通过T分布随机近邻嵌入(T-distributed stochastic neighbor embedding,简称T-SNE)可降维可视化模型的诊断过程;在强噪声干扰下仍能保持较高的精度,具备较强的鲁棒性和抗噪性能。

融合小波域信息的语义分割疫苗玻璃试管缺陷检测算法

针对疫苗玻璃试管缺陷检测中遇到的缺陷形态不规则以及缺陷类间相似度高的问题,提出了一种融合小波域信息的语义分割网络。该网络通过引入离散小波变换分支,实现了小波域信息与卷积主干网络特征图的有效融合,从而提高了对不规则缺陷的分割完整度。在主干网络设计中,加入了动态蛇形卷积,以提升对不规则缺陷分割的细腻度。同时,对主干网络结构进行优化,降低了对计算资源的依赖同时提升了分割精度。通过构建专用的疫苗玻璃试管缺陷分割数据集,与现有的几种卷积语义分割网络和视觉Transformer网络进行了一系列对比实验。实验结果显示,该方法在精度、完整度及细腻度方面均优于所对比的网络,证实了该方法在疫苗玻璃缺陷检测任务中的有效性。

多分辨率多粒度时空特征提取的轨道交通短时OD客流预测方法

面对大规模的路网OD客流分布的“长尾效应”,提出一种多分辨率多粒度时空特征提取的短时客流预测模型,以解决稀疏OD矩阵中不同量级OD客流预测精度不高的问题。将离散小波变换引入OD矩阵特征提取,结合CNN获取多分辨率下空间特征;构建多粒度历史OD客流矩阵序列,利用ConvLSTM网络提取OD矩阵长期的周期依赖性及短时的相邻时段依赖性。以北京地铁为例,分析结果表明:该模型在整体预测精度方面较其他基线模型的均方根误差RMSE提升7.4%以上;模型内部消融实验证明,多分辨率多粒度的结构对高、中、低3种量级的OD预测均有提升作用,且对高量级OD预测的RMSE提升12.5%以上。以杭州地铁为例对模型进行稳定性验证,结果表明:该模型在不同数据集下的预测结果明显优于其他基线模型;在工作日/非工作日、高低峰/平峰等场景下的适用性分析均能取得稳定的预测效果。

用于热成像数据的卷积神经网络特征图筛选方法

红外热成像数据可以有效辅助可见光图像数据,弥补其在天气和光照条件上的不足。现有的研究往往借助域适应将基于可见光图像数据训练得到的卷积神经网络用于处理热成像数据,以弥补热成像数据缺少大量标注训练集的不足,但是这类方法仍无法避免一定程度的训练。而一些研究者发现,图像在频域上呈现域不变成分和随域改变成分的分离现象。受这一现象的启发,提出一种基于离散余弦变换和卡方独立性分数的卷积神经网络特征图筛选方法。利用频域分离域不变成分和随域改变成分,借鉴卡方独立性检验的思想提出基于频段分量的独立性分数,用于度量特征图的差异度,使用聚类将特征图分类,保留主要包含域不变成分的特征图分支,得到适用于热成像数据的网络。实验结果表明,该方法可以充分利用预训练卷积神经网络的潜在预测能力,且不需要重新训练模型。预训练网络无法预测热成像数据,而筛选后的网络前5位预测结果与目标相关的比例最高可达90%。

Positive definiteness of real quadratic forms resulting from the variable-step L1-type approximations of convolution operators

The positive definiteness of real quadratic forms with convolution structures plays an important rolein stability analysis for time-stepping schemes for nonlocal operators. In this work, we present a novel analysistool to handle discrete convolution kernels resulting from variable-step approximations for convolution operators.More precisely, for a class of discrete convolution kernels relevant to variable-step L1-type time discretizations, weshow that the associated quadratic form is positive definite under some easy-to-check algebraic conditions. Ourproof is based on an elementary constructing strategy by using the properties of discrete orthogonal convolutionkernels and discrete complementary convolution kernels. To our knowledge, this is the first general result onsimple algebraic conditions for the positive definiteness of variable-step discrete convolution kernels. Using theunified theory, we obtain the stability for some simple nonuniform time-stepping schemes straightforwardly.

A robust discretization method of factor screening for landslide susceptibility mapping using convolution neural network,random forest,and logistic regression models

The selection of discretization criteria and interval numbers of landslide-related environmental factors generally fails to quantitatively determine orfilter,resulting in uncertainties and limitations in the performance of machine learning(ML)methods for landslide susceptibility mapping(LSM).The aim of this study is to propose a robust discretization criterion(RDC)to quantify and explore the uncertainty and subjectivity of different discretization methods.The RDC consists of two steps:raw classification dataset generation and optimal dataset extraction.To evaluate the robustness of the proposed RDC method,Lushan County of Sichuan Province in China was chosen as the study area to generate the LSM based on three datasets(optimal dataset,original dataset with continuous values,and statistical dataset)using three popular ML methods,namely,convolution neural network,random forest,and logistic regression.The results show that the areas under the receiver operating characteristic curve(AUCs)of the optimal dataset for the abovementioned ML models are 0.963,0.961,and 0.930 which are higher than those of the original dataset(0.938,0.947,and 0.900)and statistical dataset(0.948,0.954,and 0.897).In conclusion,the RDC method can extract the more representative features from environmental factors and outperform the other conventional discretization methods.

基于小波集成一维卷积神经网络的抗噪声聚变电源故障诊断方法研究

数据驱动的电源故障诊断方法高度依赖于电源传感器的信号数据质量,托卡马克聚变装置中的电源系统往往在复杂电磁场耦合的环境下运行,导致其采集到的具有物理特征的信号常与大量无法解耦的噪声混合。为了抑制噪声对最终诊断结果的影响,提出了一种利用抗噪声小波增强一维卷积神经网络的多分支降噪网络(Hierarchy Branch Denoising Convolutional Neural Network,HBD-CNN),以完成噪声干扰下的电源系统故障诊断任务。具体而言,本研究将离散小波变换(Discrete Wavelet Transform,DWT)的信号分解功能植入CNN的网络层中,结合对噪声更加鲁棒的指数线性激活单元(Exponentially Linear Unit,ELU),对传统1D-CNN网络结构进行深度优化。此外,根据先验知识构建起的数据多层级结构,搭配网络中分层级的分类模块,提高了HBDCNN的泛化能力。最后,基于仿真电源数据集开展了对本模型架构的初步验证,当信噪比为10 dB时,对电源变换器的故障诊断准确率可达98.31%;当信噪比为2 dB时,准确率仍能保持92%以上。实验结果表明,HBDCNN在噪声工况下具有良好的故障诊断性能。