迭代法中压缩对角存储的应用框架

在许多有限元、有限差分的应用中,待解方程组的系数矩阵是大型稀疏带状阵,方程组的求解一般使用迭代法.与其它存储方式相比,压缩对角存储由于不存矩阵元素的行列索引,对内存的使用最为节省.使用压缩对角存储,沿对角线操作可以完成高效的矩阵—向量乘.由于在以往的文献中,没有提及按行、列操作的算法,压缩对角存储的应用范围受到一定的限制.用行、列、对角版的矩阵—向量乘代表普通意义的行、列、对角方向操作模式,通过等价矩阵推导和伪代码,给出了一个包括按行、列操作算法在内的应用框架.这里运用C语言实现不完全Cholesky分解共轭梯度法解方程,阐述了如何在实际编程中使用这个算法框架.经理论与实验分析表明,对角压缩存储应用于框架中是高效的,因为与使用常用的一维行索引存储格式所编程序相比,同样迭代次数的耗时减少了约25％.     

有限元水流计算中内存和运行效率初探

有限元在非恒定流计算中耗内存大、耗机时多的问题一直困扰着工程师,限制了有限元的应用.采用分步有限元方法离散二维浅水方程,并初步探索了行指标矩阵压缩存储稀疏矩阵的方法和效率以及预条件双共扼梯度法在求解有限元方法中形成的大型线性方程组中的效率,取得了满意的结果.在一定程度上缓解了有限元在非恒定流计算中存在的耗内存大、耗时多的问题.     

大型对称变带宽方程组的Cholesky分解法

作者针对地球物理数值模拟中常碰到的大型稀疏变带宽方程组的求解问题,介绍了 大型稀疏变带宽矩阵的存储方法及Ｃｈｏｌｅｓｋｙ分解法,该方法的特点是用二个一维数组,其中一个输入时存储对称稀疏矩阵变带宽内的元素,输出时存储Ｃｈｌｏｅｓｋｙ下三角短阵带宽内的元素;另一个存储对称变带宽矩阵对角线元素在前一维数组中的位置,大大节约了所占的计算内存空间。     

双列块法——大型、稀疏、对称线代数方程组的一种有效解法

双列块法用于有限元分析计算中求解大型线代数方程组。目前在有限元计算中最通常使用的求解大型线代数方程组的方法是分块的三角分解法。由于这种方法对方程组系数矩阵的分块受带宽的限制‘以至目前一般计算机的内存贮量限制了大带宽问题的求解,使一些大型的有限元课题,特别是三维问题的解算难以实现。双列块法解决了这个西难。双列块法对方程组系数矩阵实行按计算机许可的容量划分列块,按列分解,可以完全不受带宽的限制。方法是成功的、有效的。用双列块法在PE-3220小型机上仅用686K字节的内存解算了最大半带宽为1746,系数矩阵存贮量为5000K以上字节的三维(124个20节点等参元,8个16节点等参节理元、831个节点)有限元课题,这种方法使小型和高档微机用于大型有限元的解算成为可能。     

LANCZOS迭代算法及其在三维地电场数值模拟计算中的应用研究

在三维电阻率的正演计算中往往涉及到快速、准确求解大型线性方程纽Ax=b的问题。通过采用有限差分法来构造出求解点电源三维地电场的大型稀疏对称线性方程组。并引入Lanczos迭代技术，构造出三对角阵方程组，然后采用正交分解法进行求解，它是Krylov子空间方法中的一种。与传统迭代算法相比，它占用内存少，收敛速度快且稳定。针对大型稀疏矩阵及MATLAB语言的特点，采用简单记录矩阵的非零元素值及其所在行、列值的方法存储大型稀疏矩阵，可大大节省机器内存，提高运算速度。理论分析和计算实例显示，此算法是地电三维正演计算的有效方法，为下一步的反演计算打好基础。     

三维电阻率正演计算中的Lanczos迭代算法

在三维电阻率的正反演计算中,快速、准确的正演计算是反演的关键。而正演计算往往涉及到求解大型线性方程组Ax=b的问题,通过Lanczos迭代构造出对称三对角阵方程组,并采用正交分解法进行求解,与传统算法相比,此算法占用内存少、收敛速度快、且稳定;针对大型稀疏矩阵的特点,采用简单地记录矩阵的非零元素值及其所在行、列值的方法,来存储大型稀疏矩阵,可大大节省机器内存,提高运算速度。通过理论分析和点电源三维地电场计算实例,阐述该法是地电三维正演计算的有效方法。     

井地直流电法三维数值模拟中若干问题研究

讨论了地下垂直线源分段计算和场叠加的方法,并实现了在套管上供直流电的三维数值模拟。讨论了大型容量矩阵的压缩存储方式,采用数组和结构体相结合的方法实现容量矩阵的一维链表式压缩存储。在求解超大型稀疏线形方程组时引入不完全Cholesky分解稳定化的双共轭梯度算法(ICBG),通过与均匀半空间垂直线源解析解的对比,证明了该算法是准确可靠的。     

稀疏矩阵快速回代的Cholesky分解法

采用一维压缩存储正演计算中的对称稀疏矩阵,进行Cholesky分解,利用分解后二个矩阵的对称性和稀疏性,对占用时间较多的回代过程采用先消去列的方法,实现快速回代.算例表明,采用该方法,对于点源场的求解与传统顺代回代求解法对比可以提高五倍的速度,对于大地电磁的正演问题,提高了二倍的速度.     

矩阵相乘的压缩存储算法

介绍了对稀疏矩阵进行压缩存储时,稀疏矩阵相乘运算的基本思想和算法.在此基础上,探讨了避免矩阵中零元素相乘的无效操作,奠定了该算法的矩阵变换基础.     

基于有限单元法的二维／三维大地电磁正演模拟策略

对于二维和三维大地电磁正演问题,有限单元法最后形成了一个线性方程组KX=p。方程组中的K是大型稀疏的带状对称复系数矩阵,其条件数远大于1,为严重病态矩阵,求解其对应方程组会遇到很多困难。不完全LU分解处理的BICGSTAB算法,可用于该线性方程组的求解,并且具有速度快,精度高,稳定性好等优点。为了模拟无穷远边界及满足计算机的内存需求,在保证计算精度的情况下,设计了非均匀网格剖分。在程序编制中,因只存储有限元系数矩阵的非零元素,大大减少了正演计算的时间。通过对二维模型和三维模型电磁响应的计算,验证了该算法的正确性。     

基于曲波稀疏变换的拉伸校正方法

动校正是地震数据处理中的重要步骤,但它在校正过程中会产生子波拉伸畸变效应,随着偏移距的增大,会出现主频降低、振幅扩大的现象。由于存在拉伸畸变,同相轴未被拉平,导致非同相叠加,会引起水平叠加剖面的频率失真和分辨率下降,因此,拉伸校正是提高水平叠加剖面分辨率的关键。子波拉伸畸变在曲波稀疏域中是不相干的,可以将拉伸校正视为是一个非线性优化过程。通过度量稀疏域中数据的稀疏性,使用一种快速有效的算法,来优化子波拉伸畸变生成的非线性问题,最终实现消除子波拉伸畸变的目的。曲波稀疏变换拉伸校正方法能够消除由动校正带来的子波拉伸畸变,恢复远偏移距处的高频信息,校平同相轴。综合模型数据和实际资料处理,曲波稀疏拉伸校正方法能够显著提高水平叠加剖面的分辨率。     

基于曲波稀疏变换的拉伸校正方法

动校正是地震数据处理中的重要步骤,但它在校正过程中会产生子波拉伸畸变效应,随着偏移距的增大,会出现主频降低、振幅扩大的现象。由于存在拉伸畸变,同相轴未被拉平,导致非同相叠加,会引起水平叠加剖面的频率失真和分辨率下降,因此,拉伸校正是提高水平叠加剖面分辨率的关键。子波拉伸畸变在曲波稀疏域中是不相干的,可以将拉伸校正视为是一个非线性优化过程。通过度量稀疏域中数据的稀疏性,使用一种快速有效的算法,来优化子波拉伸畸变生成的非线性问题,最终实现消除子波拉伸畸变的目的。曲波稀疏变换拉伸校正方法能够消除由动校正带来的子波拉伸畸变,恢复远偏移距处的高频信息,校平同相轴。综合模型数据和实际资料处理,曲波稀疏拉伸校正方法能够显著提高水平叠加剖面的分辨率。     

Automatic extraction of sparse trees from high-resolution ortho-images

Obtaining information about tree species distribution in agricultural lands is a topic of interest for various applications, such as tree inventory, forest management, agricultural land management, crop estimation, etc. This information can be derived from images obtained from modern remote sensing technology, which is the most economical way as compare to field surveys covering large geographic areas. Therefore, in this study, a new method is proposed for extraction and counting of sparse and regular distributed individual pistachio trees from agricultural areas on large scale from high-resolution digital ortho-photo maps, which were obtained using an airborne sensor (Ultracam-X). The input images were first smoothed by applying Gaussian filter to reduce the impact of noise. Normalized difference vegetation indices (NDVI) were then derived to obtain vegetation areas followed by Otsu’s global thresholding algorithm to obtain candidate tree areas. Further, connected component (CC) analysis was applied to segregate each object. Morphological processing was performed to fill holes within tree objects and get smooth contours, which were obtained by using the Moore-neighbor tracing method (MNTM) for each CC, while geometrical constraints were applied to undermine possible non-tree elements from output image. To further improve the segmentation results for sparse trees, a new method was applied, called quadratic local analysis (QLA). QLA helped to segment the trees, which were missed by the Otsu method due to low contrast and resulted in improved accuracy (3–6%). The obtained results were compared with well-known support vector machine (SVM) classifier. Proposed method produced slightly better results (1–5%) than SVM for extraction of pistachio trees and obtained accuracy for QLA and SVM were 96 and 91% for region 1, while 91 and 90% for region 2 respectively.     

Decoding earth's plate tectonic history using sparse geochemical data

Accurately mapping plate boundary types and locations through time is essential for understanding the evolution of the plate-mantle system and the exchange of material between the solid Earth and surface environments.However,the complexity of the Earth system and the cryptic nature of the geological record make it difficult to discriminate tectonic environments through deep time.Here we present a new method for identifying tectonic paleo-environments on Earth through a data mining approach using global geochemical data.We first fingerprint a variety of present-day tectonic environments utilising up to 136 geochemical data attributes in any available combination.A total of 38301 geochemical analyses from basalts aged from 5-0 Ma together with a well-established plate reconstruction model are used to construct a suite of discriminatory models for the first order tectonic environments of subduction and mid-ocean ridge as distinct from intraplate hotspot oceanic environments,identifying 41,35,and 39 key discriminatory geochemical attributes,respectively.After training and validation,our model is applied to a global geochemical database of 1547 basalt samples of unknown tectonic origin aged between 1000-410 Ma,a relatively ill-constrained period of Earth’s evolution following the breakup of the Rodinia supercontinent,producing 56 unique global tectonic environment predictions throughout the Neoproterozoic and Early Paleozoic.Predictions are used to discriminate between three alternative published Rodinia configuration models,identifying the model demonstrating the closest spatio-temporal consistency with the basalt record,and emphasizing the importance of integrating geochemical data into plate reconstructions.Our approach offers an extensible framework for constructing full-plate,deeptime reconstructions capable of assimilating a broad range of geochemical and geological observations,enabling next generation Earth system models.     

约束稀疏脉冲波阻抗反演在精细油藏描述中的应用

综合研究区地质、地震、测井、录井等各类信息,从测井约束稀疏脉冲波阻抗的反演技术的基本原理出发,探讨反演过程中测井资料的标准化处理、地震子波的提取、时深关系的转化,以及初始波阻抗模型的建立等主要的技术环节。综合分析了研究区双阳组二段重点圈闭区块砂体的发育和分布情况,并探讨在同一构造圈闭上不同井位失利的原因,为精细的油气储层研究提供了可靠的信息。     

基于联合求解法的疏桩地基沉降计算方法研究

疏桩基础作为一种工期短、效果好的软土地基处理方式,在工程中的应用越来越广泛。考虑带桩帽的PTC（预应力混凝薄壁管桩）刚性桩桩侧摩阻力分布规律,将桩侧摩阻力假定为2个三角形拼合的分布形式。联合应用Mindlin-Geddes解答及Boussinesq解答,推导出了疏桩补偿地基中的附加应力的计算公式。结合具体算例,计算复合地基的沉降变形量。研究表明,该联合方法的沉降计算结果比传统方法偏小,与实测数据较为吻合。当桩间距大于8倍桩径时,随着桩间距的增加,疏桩补偿地基的附加应力场基本不变,但沉降量相应增大。对于桩间距较大的疏桩补偿地基,采用长、短桩组合形式较为合理。通过设置深层水泥土搅拌桩来加固软土路堤,能有效控制沉降量。     

高层建筑疏桩筏板基础现场实测与分析

桩基础设计时如何考虑桩间土的承载能力,目前还是一个难题,通过对南京大学MBA大楼疏桩筏板基础的原位测试,得到了高层建筑疏桩筏板基础的沉降特性、桩顶压力分布、桩间土压力分布、筏板内钢筋轴力的分布,分析了桩与桩间土承担竖向荷载的比例,肯定了高层建筑应用疏桩基础的可能性,其现场实测结果可供高层建筑基础设计及理论研究作参考。     

有色反演技术在少井区岩性体预测中的应用

阐述了有色反演的基本原理,并给出了反演流程。通过模型试算,明确有色反演关键参数的物理意义及取值范围,并在孤南洼陷实际工区应用,较好地刻画出沙三下早期低位扇体的横向展布范围。与常规地震属性相比,反演结果更加符合沉积规律,与实钻井岩性分布情况吻合程度高。表明有色反演在保留地震数据原始现象的基础上,分辨率明显提高,适合无井或少井区的地层或岩性解释。     

A sequential sparse polynomial chaos expansion using Bayesian regression for geotechnical reliability estimations

Polynomial chaos expansions (PCEs) have been widely employed to estimate failure probabilities in geotechnical engineering. However, PCEs suffer from two deficiencies: (a) PCE coefficients are solved by the least-square minimization method which easily causes overfitting issues; (b) building a high order PCE is often computationally expensive. In order to overcome the aforementioned drawbacks, the Bayesian regression technique is employed to evaluate PCE coefficients, which not only provides a sparse solution but also avoids overfitting. With the aid of the predictive means and variances given by Bayesian analysis, a learning function is proposed to sequentially select the most informative samples that are critical to build a PCE. This sequential learning scheme can highly enhance the computational efficiency of PCEs. Besides, importance sampling (IS) is incorporated into the sequential learning (SL)-PCEs to deal with geotechnical problems with small failure probabilities. The proposed method of SL-PCE-IS is applied to three illustrative examples, which shows that the improved PCE method is more effective and efficient than the common PCEs method, leading to accurate estimations of small failure probabilities using fewer training samples.     

An approach for estimating sustainable yield of karst water in data sparse regions

This study presents an approach for transferring the qualitative analysis of groundwater sustainability for development to quantitative evaluation by an analogy of two similar regions. A concept of groundwater exploitation sustainability (GES), which is an evaluation index based on water supply capability, eco-geo-environment maintaining capability and the harmony between water and society, is put forward. The fuzzy analytic hierarchy process method is applied to calculate the GES for the Xiangshan and Dianchang karst groundwater sources in the Huaibei city, Anhui Province, China. The GES of the Xiangshan karst system was calculated to be 0.53 and represents medium exploitation sustainability, while that for the Dianchang is relatively high with a value of 0.70. These two karst systems are separate units but have similar hydrogeological conditions. The Dianchang area had limited groundwater observation data, while the Xiangshan area had long series of observation data, which enabled the computation of the sustainable yield. The sustainable yield of the Xiangshan karst area was used to calibrate the GES, and develop a linear equation between the GES and sustainable yield, which was used to calculate the sustainable yield of the Diangchang karst area as 40.4 million m³.