Variational regularization method of solving the Cauchy problem for Laplace's equation: Innovation of the Grad–Shafranov(GS) reconstruction

The simplified linear model of Grad-Shafranov （GS） reconstruction can be reformulated into an inverse boundary value problem of Laplace＇s equation. Therefore, in this paper we focus on the method of solving the inverse boundary value problem of Laplace＇s equation. In the first place, the variational regularization method is used to deal with the ill- posedness of the Cauchy problem for Laplace＇s equation. Then, the ＇L-Curve＇ principle is suggested to be adopted in choosing the optimal regularization parameter. Finally, a numerical experiment is implemented with a section of Neumann and Dirichlet boundary conditions with observation errors. The results well converge to the exact solution of the problem, which proves the efficiency and robustness of the proposed method. When the order of observation error δ is 10-1, the order of the approximate result error can reach 10-3.

Image reconstruction based on total-variation minimization and alternating direction method in linear scan computed tomography

Linear scan computed tomography （LCT） is of great benefit to online industrial scanning and security inspection due to its characteristics of straight-line source trajectory and high scanning speed. However, in practical applications of LCT, there are challenges to image reconstruction due to limited-angle and insufficient data. In this paper, a new reconstruction algorithm based on total-variation （TV） minimization is developed to reconstruct images from limited-angle and insufficient data in LCT. The main idea of our approach is to reformulate a TV problem as a linear equality constrained problem where the objective function is separable, and then minimize its augmented Lagrangian function by using alternating direction method （ADM） to solve subproblems. The proposed method is robust and efficient in the task of reconstruction by showing the convergence of ADM. The numerical simulations and real data reconstructions show that the proposed reconstruction method brings reasonable performance and outperforms some previous ones when applied to an LCT imaging problem.

New Method of Reconstruction from Nonparallel Stereo and Application to Surgical Navigator

A new method to reconstruct 3D scene points from nonparallel stereo is proposed. From a pair of conjugate images in an arbitrarily configured stereo system that has been calibrated, coordinates of 3D scene points can be computed directly using the method, bypassing the process of rectifying images or iterative solution involved in existing methods. Experiment results from both simulated data and real images validate the method. Practical application to surgical navigator shows that the method has advantages to improve efficiency and accuracy of 3D reconstruction from nonparallel stereo system in comparison with the conventional method that employs algorithm for standard parallel axes stereo geometry.

An efficient source wavefield reconstruction scheme using single boundary layer values for the spectral element method

In the adjoint-state method, the forward-propagated source wavefield and the backward-propagated receiver wavefield must be available simultaneously either for seismic imaging in migration or for gradient calculation in inversion. A feasible way to avoid the excessive storage demand is to reconstruct the source wavefield backward in time by storing the entire history of the wavefield in perfectly matched layers. In this paper, we make full use of the elementwise global property of the Laplace operator of the spectral element method (SEM) and propose an efficient source wavefield reconstruction method at the cost of storing the wavefield history only at single boundary layer nodes. Numerical experiments indicate that the accuracy of the proposed method is identical to that of the conventional method and is independent of the order of the Lagrange polynomials, the element type, and the temporal discretization method. In contrast, the memory-saving ratios of the conventional method versus our method is at least N when using either quadrilateral or hexahedron elements, respectively, where N is the order of the Lagrange polynomials used in the SEM. A higher memorysaving ratio is achieved with triangular elements versus quadrilaterals. The new method is applied to reverse time migration by considering the Marmousi model as a benchmark. Numerical results demonstrate that the method is able to provide the same result as the conventional method but with about 1/25 times lower storage demand. With the proposed wavefield reconstruction method, the storage demand is dramatically reduced;therefore, in-core memory storage is feasible even for large-scale three-dimensional adjoint inversion problems.

Unhappy triad in limb reconstruction:Management by Ilizarov method

AIM To evaluate the results of the Ilizarov method in management of cases with bone loss, soft tissue loss and infection.METHODS Twenty eight patients with severe leg trauma complicated by bone loss, soft tissue loss and infection were managed by distraction osteogenesis in our institution. After radical debridement of all the infected and dead tissues the Ilizarov frame was applied, corticotomy was done and bone transport started. The wounds were left open to drain. Partial limb shortening was done in seven cases to reduce the size of both the skeletal and soft tissue defects. The average follow up period was 39 mo(range 27-56 mo). RESULTS The infection was eradicated in all cases. All the soft tissue defects healed during bone transport and plastic surgery was only required in 2 cases. Skeletal defects were treated in all cases. All patients required another surgery at the docking site to fashion the soft tissue and to cover the bone ends. The external fixation time ranged from 9 to 17 mo with an average of 13 mo. The complications included pin tract infection in 16 cases, wire breakage in 2 cases, unstable scar in 4 cases and chronic edema in 3 cases. According to the association for study and application of methods of Ilizarov score the bone results were excellent in 10, good in 16 and fair in 2 cases while the functional results were excellent in 8, good in 17 and fair in 3 cases. CONCLUSION Distraction osteogenesis is a good method that can treat the three problems of this triad simultaneously.

SPECTRAL/HP ELEMENT METHOD WITH HIERARCHICAL RECONSTRUCTION FOR SOLVING NONLINEAR HYPERBOLIC CONSERVATION LAWS

The hierarchical reconstruction （HR） [Liu, Shu, Tadmor and Zhang, SINUM ＇07] has been successfully applied to prevent oscillations in solutions computed by finite volume, Runge-Kutta discontinuous Galerkin, spectral volume schemes for solving hyperbolic conservation laws. In this paper, we demonstrate that HR can also be combined with spectral/hp element method for solving hyperbolic conservation laws. An orthogonal spectral basis written in terms of Jacobi polynomials is applied. High computational efficiency is obtained due to such matrix-free algorithm. The formulation is conservative, and essential nomoscillation is enforced by the HR limiter. We show that HR preserves the order of accuracy of the spectral/hp element method for smooth solution problems and generate essentially non-oscillatory solutions profiles for capturing discontinuous solutions without local characteristic decomposition. In addition, we introduce a postprocessing technique to improve HR for limiting high degree numerical solutions.

Preliminary analysis of reactivity reconstruction capability based on inverse kinetics method under different initial reactivity states

Online reactivity monitoring plays an important role in operation and safety analyses of fission reactor systems. The inverse kinetics method, which is based on a point kinetics model, is the most widely used method for reactivity reconstruction of critical water reactors. However, this method is seldom applied to the reactivity reconstruction of subcritical reactors. In this study, an inverse kinetics method was employed for the reactivity reconstruction of a lead-based reactor under different initial reactivity states(ρ_0= 0,-2786,-5486,-8367, and-12,371 pcm). The results showed that the deviation in the reactivity of the lead-based subcritical reactor was greater when ρ_0 became smaller. The reactivity reconstructed using the inverse kinetics method was globally underestimated. At a given reactivity perturbation, the relative and absolute errors increased with the decrease in the initial reactivity. At a given initial reactivity, with the increase in the reactivity perturbation, the absolute error increased, whereas the relative error remained the same.This deviation is due to the variation in the external neutron source, spatial-spectral effects, and sub-diffusive effects, which require further study.

TRACKING AND RECONSTRUCTION METHODS FOR MOVING-INTERFACES

A simple,efficient and accurate high resolution method to tracking moving-interfaces-the characteristic integral-averaging finite volume method on unstructured meshes is proposed. And some numerical tests and evaluation of six main efficient methods for interface reconstruction are made. Through strict numerical simulation,their characters,advantages and shortcomings are compared,analyzed and commended in particular.

关节腔内移植物长度测量在前交叉韧带全内重建的应用研究

目的:探讨关节镜下测量关节腔内移植物长度在前交叉韧带(anterior cruciate ligament,ACL)全内重建应用的临床疗效。方法:回顾性分析2020年1月至2022年1月收治的ACL损伤患者60例的资料,其中男37例,女23例,年龄22~44岁。按照手术方式的不同,分为传统手术组(常规组)和拉线测量组(测量组),每组各30例。常规组男20例,女10例,年龄(30.00±3.95)岁;身体质量指数(body mass index,BMI)为(22.58±1.41)kg·m^(-2);左侧9例,右侧21例;受伤至手术时间(3.00±1.35)d。测量组男17例,女13例,年龄(32.00±4.29)岁;BMI为(23.29±1.39)kg·m^(-2);左侧12例,右侧18例;受伤至手术时间(3.00±1.27)d。记录患者术前及术后6、12个月的临床资料。从术后视觉模拟评分法(visual analogue scale,VAS)、膝关节损伤与骨关节炎评分(knee injury and osteoarthritis outcome score,KOOS)、Lysholm评分、国际膝关节文献委员会(International Knee Documentation Committee,IKDC)膝关节评估表、膝关节稳定性(Lachman试验、前抽屉试验和轴移试验)、术后不同阶段CT测量骨隧道直径增宽程度和MRI评分系统等方面比较两种方法的临床疗效。结果:术后6个月两组VAS比较差异无统计学意义(P>0.05),术后12个月测量组VAS(2.23±1.01)分,低于常规组(3.30±1.02)分(P<0.001)。术后12个月,两组KOOS评分除症状评分差异无统计学意义(P=0.221),其余各项评分差异均有统计学意义(P<0.05)。术后6个月,测量组Lysholm总分和IKDC总分均高于常规组(P<0.05)。术后12个月,测量组Lachman试验、前抽屉试验和轴移试验和常规组比较,差异均无统计学意义(P>0.05);但是,整体膝关节不稳定性分析,测量组膝关节稳定性优于对照组(P=0.038)。术后2 d及术后6、12个月两组患者影像学评估结果显示,测量组股骨和胫骨的肌腱隧道直径增宽程度均较常规组术后减少(P<0.05);MRI评分测量组患者均高于常规组(P<0.05)。结论:关节镜下测量关节腔内移植物长度在全内技术ACL重建,肌腱利用率高,稳定性好,1年内膝关节功能恢复满意,疗效肯定。

Reconstruction method of differentiated backprojection-projection onto convex sets in the interior problem and design of bone-nail model

This work focuses on the application of the reconstruction method of differentiated backprojection （DBP）-projection onto convex sets （POCS） in the interior problem.First,we present the definition of the interior problem and real truncated Hilbert transform,and then outline the implementation steps of DBP-POCS.After that,we introduce the middle-part known condition for region of interest （ROI） accurate reconstruction and the unique condition of the interior problem,and verify the uniqueness and stability of the interior problem accurate reconstruction through numerical experiments,and then compare the results for the interior problem in reconstruction images using filtered backprojection （FBP）.In addition,the authors also design the application models of ROI reconstruction and make an initial attempt to the application of DBP-POCS method in the interior problem.

基于图拉普拉斯正则化的PET图像核重建方法

正电子发射断层成像(Positron Emission Tomography,PET)在很多疾病的早期诊断中有重要的作用,PET图像重建的难点之一是如何在保持重建图像中病灶边缘特性的同时具有良好的去噪性能.针对此问题,本文提出了一种结合图拉普拉斯正则化和深度图像先验的PET图像核重建方法 .设计了改进的U-net神经网络,将PET前向投影模型中的核系数表示为神经网络的输出;通过先验图像构建图拉普拉斯矩阵,重建问题被建模为基于神经网络的带图拉普拉斯正则化项的最大似然函数优化问题.利用优化转移方法导出了收敛的迭代重建算法,每一次迭代包括由核重建方法更新图像和利用神经网络更新核系数两个步骤.仿真和临床实验结果表明,本文提出的方法在不同的指标下都有更好的重建效果,优于已有核重建方法以及最新的基于深度系数先验的重建方法 .

深层超深层油气藏高应力下数字岩心构建方法

深层超深层油气藏由于埋藏深,其地应力达200 MPa,会显著改变储层岩石孔隙的微观结构。数字岩心是孔隙尺度数值模拟的重要载体,但是现有数字岩心重构方法是基于常温常压下岩心的扫描图像重构,不能反映高应力下的孔隙结构。为此,提出了一种基于离散元法考虑高应力影响的数字岩心重构方法。首先,采用分水岭算法分割CT图像,利用球面谐波分析方法建立轮廓数据库,并在PFC^(3D)中建立Clump(团簇)模板库;然后,根据孔隙度和粒径分布使用模板库中的Clump建立离散元模型,并用两点相关和线性路径相关函数曲线评价模型的准确性;随后,标定颗粒间微观力学参数,并加载应力模拟得到不同应力下的数字岩心;最后,分析了不同应力下数字岩心的孔隙几何拓扑结构,计算孔隙度和渗透率。以Bentheim砂岩为例,构建了其不同应力下的数字岩心,研究结果表明,应力增大,导致孔隙和喉道半径缩小、喉道伸长、连通性变差、孔隙度和渗透率减小。研究结果为深层超深层油气藏孔隙尺度模拟提供了技术途径。

基于微格重构的混合教学方式在医学院校计算机类课程中的应用

目的探讨基于微格重构的混合教学方式在医学院校计算机类课程中的应用。方法采用微格化重构策略,构建一种新的混合式教学方法,并将其应用于医学院校计算机类课程的教学实践中。对计算机类课程进行微格化处理,按照线上线下、理论实践等模式进行各门课程之间的微格化混合重构,构建计算机类课程教学效果评价的结构方程模型,以验证其实施效果。结果评价结果显示,微格化处理、混合模式重构,对于提升医学院校学生对计算机类课程的学习兴趣具有显著的正向影响,并间接起到了提高学生学习成绩的作用,结构方程路径系数为0.39。结论基于微格重构的混合教学方式在医学院校计算机类课程中的应用效果显著,可以在同类院校乃至更多高校中推广应用。

核酸检测的重排算法及其数值模拟

2022年春季上海遭受到奥密克戎变异株的侵袭,核酸检测是筛查新冠阳性病例的重要手段之一。目前社区常用核酸检测方式是10人/20人混合检测,重点人群单人单管复测。考虑到检测数量的庞大,二次复核易对非阳性人员造成恐慌,仿照CT成像原理,设计一种核酸检测重排方法,每人检测后将检测液分别随机置于多组不同试管中,根据不同组试管中的检测结果(投影数据),利用反投影方法,确定进入二次检测人员。计算机仿真结果表明,上述所设计的重排算法能够实现减少总检测数量和提高进入二次检测人员精度的目的。因此以上重排方法有望进一步应用到智能化的核酸采样机器人上,达到高效检测的目的。

基于小波与反褶积结合的薄互层岩性界面识别方法

准噶尔盆地莫西庄地区三工河组二段岩性复杂多样、变化快,单砂岩体中薄层岩性频繁互层,存在较强的岩性、物性、含油非均质性特征。精细划分薄互层岩性并识别其分层界面是开展储层识别、流体解释及有效储层厚度确立等重要的前提工作。为了精确地识别薄互层岩性的分层界面,从测井信息采集分辨率与信号分析角度出发,提出了基于小波与反褶积相结合的薄互层岩性分层界面识别方法。首先,利用小波变换多尺度分解和重构原理,对自然伽马测井曲线进行高、低频分解,提取出反映地层岩性变化的有效信号与高频噪声;然后,对有效信号进行重构,构建一条去除噪声能够表征更接近真实地层信息的自然伽马测井曲线;最后,利用反褶积方法对重构的自然伽马测井曲线进行高分辨率处理,很大程度上提高了自然伽马测井曲线响应薄层岩性的纵向分辨率。经实例井取心岩性资料验证,利用该方法处理得到高分辨率自然伽马测井曲线的形态与数值特征能够有效地提高单砂岩体中多套薄互层岩性分层界面识别的精度,为莫西庄三工河组二段储层有效性精细评价提供了依据。

基于NSGA-Ⅱ传感位置优化的曲面重构及误差补偿方法

通过优化光纤布拉格光栅形状传感技术中传感点位置和补偿重构结果来提高薄层合金板三维形状重构精度。通过ANSYS workbench建立合金板仿真模型,提取应变和位移模态振型,根据模态置信准则、转换矩阵稳定性和模态振型相似性分别设计了三个目标函数,采用快速和精英机制的多目标遗传算法优化传感器位置。将镍钛合金板弯曲成不同曲率半径的弧形,利用光纤布拉格光栅中心波长漂移量和线性插值算法计算得出不同形状下的结构应变,重构合金板形状,均方根误差和最大误差相较于单目标优化算法分别减小30%和15%。利用粒子群优化径向基函数神经网络算法拟合误差与位移的关系实现误差补偿,均方根误差和最大误差比无补偿时分别减小了90%和70%,最大相对百分比误差仅为5%,提高了三维形状重构算法精度。

应用生成对抗网络的地震数据重建和去噪一体化方法

在实际采集过程中,受地形条件和人为因素的影响,地震数据不仅在空间上会出现采样不足或不规则的情况,而且会混入噪声,不利于后续地震数据的处理和解释。通常将重建与去噪分为两个阶段处理,这样往往会引入额外的误差。为此,文中提出了一种基于条件韦氏生成对抗网络(cWGAN)的地震数据重建去噪一体化方法,该方法研究的重点是在缺失道和噪声的混合干扰下,准确提取地震数据的有效特征。首先,以U-Net模型为基本网络结构来构建生成器模型,分级提取地震数据同相轴特征;在判别器模型中引入条件约束,引导生成器优化梯度方向。其次,建立重建和去噪误差描述模型,该模型设计了一体化损失函数,可以兼顾重建与去噪两方面的处理任务。最后,经过合成数据和实际数据测试,证明文中所提的网络模型恢复的地震数据信噪比更高且具有较强鲁棒性。

改进的三频四步相移面结构光三维重建算法

针对面结构光中传统三频四步相移算法投影图片过多、效率较慢这一问题,提出了改进的三频四步相移面结构光重建算法。改进的算法需要3个高频率的正弦条纹图,但所需投影的条纹数量从传统算法的12张减少到了7张,最高频率的条纹图4张,次高频和最低条纹图分别为2张和1张,投影效率比传统算法提高了41.7%。介绍了改进算法的原理,将最高频率4张图所计算的包裹相位用来三维重建,其余两个频率条纹图计算的包裹相位用来进行相位展开,理论上该方法与传统算法精度一致。最后,通过实验验证了该算法的重建精度以及对具有复杂表面物体的三维重建能力。实验结果表明改进的面结构光算法在提高投影效率的同时与传统算法保持着一致的精度。

考古学如何重建上古史

中国考古学的古史重建主要采取“二重证据法”,用考古材料印证文献记载。考古学文化是用来分辨古代族群和政体的关键概念。就当代历史学和考古学的范式而言,这种将两类证据简单对应的做法已经难以胜任这项任务。考古学文化是整理材料的一种方法,而古史重建需要一套与之有别的方法。这是在社会科学理论指导下的多学科探索,以重建上古时期社会复杂化的过程。这种古史重建不再是编年史学的补充或延伸,而是像年鉴学派所倡导的那种整体史。秘鲁维鲁河谷聚落形态的国家探源,以及埃及统一的考古学探索两项经典案例,为我们提供可借鉴的他山之石。

近场声全息重建参数对隔声测量精度的影响

等效源法近场声全息可以开展建筑构件隔声测量的工作。采用近场声全息测量构件隔声量时,重建参数对声场重建结果影响显著。基于对等效源法近场声全息隔声测量理论的分析,利用传声器阵列测得构件表面的复声压信号,通过声场重建得到构件的隔声量和表面法向声强分布。为进一步探究重建参数对等效源法近场声全息隔声测量精度的影响,通过控制变量法在隔声室开展以传统声压法为对比的建筑构件隔声测量实验。结果表明:当等效源面位置从-2 cm变化至-5 cm时,表面法向声强的重建平均误差值由3.9 dB增大至5.6 dB,隔声量的重建平均误差值由5.2 dB增大至6.9 dB,测量误差随等效源面距离而增大,因此等效源面宜靠近声源面;当全息测量面距离为4、8和16 cm时,表面法向声强的重建平均误差值分别为0.6、1.9和5.5 dB,隔声量的重建平均误差值分别为0.9、1.4和4.6 dB,测量误差随全息测量面距离而增大,因此建议全息测量面距离保持在8 cm之内;当等效源点数目与全息面测点数目一致时,与传统声压法差异仅为0.84 dB,当二者数目不一致时,隔声量和表面法向声强平均误差值均增大至4.6~6.8 dB。通过对重建参数进行优选可以有效提高构件隔声测量精度,对实验室测量建筑构件隔声性能与方法有重要借鉴意义,同时在隔声测量技术的实际运用中有较高的参考价值。