Q estimation using multifrequency point average method based on the Taylor series expansion with a different order

The quality factor Q is an important parameter because it can refl ect the reservoir attenuated features and can be used for inverse-Q filtering to compensate for the seismic wave energy.The accuracy of the Q estimation is greatly significant for improving the precision of the reservoir prediction and the resolution of seismic data.In this paper,the Q estimation formulas of the single-frequency point are derived on the basis of a diff erent-order Taylor series expansion of the amplitude attenuated factor.Moreover,the multifrequency point average(MFPA)method is introduced to obtain a stable Q estimation.The model tests demonstrate that the MFPA method is less aff ected by the frequency band,travel time diff erence,time window width,and noise interference than the logical spectrum ratio(LSR)method and the energy ratio(ER)method and has a higher Q estimation accuracy.In addition,the proposed method can be applied to post-stack seismic data and obtain eff ective Q values of complex models.When the MFPA method was applied to real marine seismic data,the Q values estimated by the MFPA method with the 1st–4th order showed good consistency with each other.In contrast,the Q values obtained by the ER method were larger than those of the proposed method,while those estimated by the LSR method signifi cantly deviated from the average values.In conclusion,the MFPA method has superior stability and practicability for the Q estimation.

Numerical Solution of Differential Equations by Direct Taylor Expansion

A variation of the direct Taylor expansion algorithm is suggested and applied to several linear and nonlinear differential equations of interest in physics and engineering, and the results are compared with those obtained from other algorithms. It is shown that the suggested algorithm competes strongly with other existing algorithms, both in accuracy and ease of application, while demanding a shorter computation time.

Comparative Studies between Picard’s and Taylor’s Methods of Numerical Solutions of First Ordinary Order Differential Equations Arising from Real-Life Problems

To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’s and Taylor’s series methods. We have carried out a descriptive analysis using the MATLAB software. Picard’s and Taylor’s techniques for deriving numerical solutions are both strong mathematical instruments that behave similarly. All first-order differential equations in standard form that have a constant function on the right-hand side share this similarity. As a result, we can conclude that Taylor’s approach is simpler to use, more effective, and more accurate. We will contrast Rung Kutta and Taylor’s methods in more detail in the following section.

基于Chan氏算法和Taylor级数展开法的协同定位方法

该文分析讨论了Chan和泰勒两种TDOA定位算法的优缺点,并在此基础上提出了基于 Chan氏算法(1994)和Taylor级数展开法(1976)的协同定位方法。通过在不同信道环境下对协同定位 方法进行仿真,表明该方法在信道环境恶劣时能够有效地提高定位精度。

Taylor级数展开法定位及其性能分析

讨论适合于TDOA定位的信道模型,分析1种典型TDOA定位算法———Taylor级数展开法,并针对其收敛问题提出改进方法。结合不同信道环境和蜂窝基站位置分布,对Taylor级数展开法的性能进行仿真,并就各种环境参数对算法性能的影响,与其它算法进行分析比较。

Taylor级数法动态潮流计算

提出采用Ｔａｙｌｏｒ级数展开技术求解电力系统动态潮流的方法，以曲线拟合方式获取节点注入功率的时间函数，论证并推导了节点电压各阶导数的递推算式。分析和计算结果表明，本方法能直接得到节点电压的时间函数，计算速度快。

用Taylor展开最小二乘法反演水文地质参数

采用Taylor展开最小二乘法 ,对有解析解的水文地质问题进行参数反演 ,不仅计算速度快 ,而且计算准确 。

基于Taylor-Edgeworth级数的结构可靠性分析

为了解决工程实际中高维非线性或功能函数为隐式的情况给结构数值分析带来的困难,文中提出了一种新型结构可靠性直接分析方法.首先利用降维算法将维函数展开为个一维函数的形式,再将各一维函数中的变量运用变量转换方法进行变换,并结合Gauss-Hermite数值积分方法,计算得到个一维函数的原点矩及中心矩,将所得矩信息与Taylor展开计算出的结构功能函数的中心矩结合,再借助Edgeworth级数法推导出结构功能函数的累积分布函数表达式,并运用结构可靠性理论计算得到结构功能函数的失效概率.该方法在计算过程中无需进行多重积分计算功能函数的统计矩.数值算例结果表明该方法正确可行.

基于Taylor级数展开定理的高阶FDTD的色散分析

时域有限差分法(FDTD)是计算电磁领域中的一类非常重要的研究工具。而 Taylor 级数展开定理是构造差分格式的一种重要方法,例如 Yee 格式采用二阶 Taylor 格式,Fang 格式采用四阶 Taylor 格式。本文借助于采样定理,详细分析了不同阶 Taylor 中心差分格式的谱特性以及计算误差,并将任意阶 Taylor 中心差分格式用于数值求解麦克斯韦方程中,严格导出了稳定性条件和数值色散关系的表达式,引入了新的误差定义来衡量算法的好坏。详细地研究了 Courant 数、网格分辨率 CPW 和网格长度比率等因素对于数值色散误差的影响,为基于 Taylor 差分格式的 FDTD 算法的研究提供了有用的参考。

Taylor级数多极边界元法及其在轧制工程中的应用

通过基本解的多极展开与边界元线性方程组的隐式求解方法(GMRES)相结合,开发出了快速多极边界元法。Taylor级数多极边界元法更新了传统边界元法的求解模式,大大提高了计算效率,扩大了边界元法的求解规模。介绍了Taylor级数多极边界元法的发展历史和现状,给出了Taylor级数多极边界元法的基本思想、基本原理和分类,给出了基本解的Taylor展开方法和边界积分的基本实现步骤。将该方法应用于轧制工程中,通过轧辊弹性变形和HC轧机辊系接触和变形的数值解析,说明了Taylor级数多极边界元法适合于大规模轧制工程问题的解析。

地下水水质模型的 Taylor 展开随机模拟方法

地下水水质模型是由水流问题和水动力弥散问题耦合而成。本文从Ｔａｙ－ｌｏｒ展开式入手，结合有限元等方法，直接推导某节点浓度的均值和方差、协方差的表达式，把水流问题和水动力弥散问题统一进行考虑，避免了计算过程中随机变量的增加，提高了计算效率，为地下水水质模型的随机模拟提供了新的计算方法。

Taylor级数多极边界元法远场影响的误差估计(英文)

快速多极方法能够有效地提高边界元法的计算效率.求解的计算量和内存量与问题的自由度数N成正比.求解的精度与传统边界元法相比有所下降.分析了Taylor级数多极边界元法的计算精度和远场影响系数的误差.研究了核函数r的Taylor级数展开性质,推导了三维弹性问题基本解的误差估计公式.说明了影响多极边界元法计算精度的因素.数值算例显示了误差估计公式的正确性和有效性.

向量函数的Taylor展开式探讨

主要剖析教材[2]和[3]中关于向量函数的Taylor展开式与收敛问题,指出一些存在问题,并提出利于教与学的见解.

Taylor幂级数直接展开的新方法

从函数可积分性质与基本积分法出发,导出了Taylor公式的新证法,打破了几百年来Cauchy繁琐的证法,并定义了积分型余项,进而加以推广和应用,得到了Taylor幂级数直接展开的新方法。

地下水随机规划模型的Taylor展开解法

讨论了将线性随机约束地下水规划模型转化为与之等价的确定性约束地下水规划模型的方法，并以地下水优化疏干规划模型为例，推导了转化后的非线性约束地下水管理模型的Ｔａｙｌｏｒ展开解法，并通过对一假设模型的计算分析，证实了该求解方法的有效性。

改进的Taylor-Chan算法的多点定位精度研究

多点定位系统因其具有高精度、建站灵活和安装简便等优点,已经被广泛应用于民航监视系统中,目的是减少雷达覆盖盲区,改善天气状况对空管监视数据的影响,增加对目标定位的精度,加强对机场的安全监控,提出了一种改进的Taylor-Chan算法计算航空器的位置,算法的初始值是基于Taylor运行结果的初始值,并通过迭代Chan算法。在假定的理想条件下,对算法进行仿真,其结果表明,与Chan、Taylor、Chan-Taylor三种算法相比较,改进的Taylor-Chan算法的结果模型简单并且精度较高。

地下水水流模型的Taylor展开随机有限元法

从Ｔａｙｌｏｒ展开式入手，结合有限元法，直接推导某节点水头的均值、方差和协方差的表达式，特别对输入随机变量较少的非稳定地下水流问题，不会引起随机变量的增加，使Ｔａｙ－ｌｏｒ展开随机有限元法在地下水中的应用得到发展．同时选取二维承压地下水水流问题（有解析解）作为例子，进行了随机数值模拟实验，以检验方法的有效性和局限性．

Accelerating spectral digital image correlation computation with Taylor series image reconstruction

In this paper,we introduce an accelerating algorithm based on the Taylor series for reconstructing target images in the spectral digital image correlation method(SDIC).The Taylor series image reconstruction method is employed instead of the previous direct Fourier transform(DFT)image reconstruction method,which consumes the majority of the computational time for target image reconstruction.The partial derivatives in the Taylor series are computed using the fast Fourier transform(FFT)of the entire image,following the principles of Fourier transform theory.To examine the impact of different orders of Taylor series expansion on accuracy and efficiency,we employ third-and fourth-order Taylor series image reconstruction methods and compare them with the DFT image reconstruction method through simulated experiments.As a result of these enhancements,the computational efficiency using the third-and fourth-order Taylor series improves by factors of 57 and 46,respectively,compared to the previous method.In terms of analysis accuracy,within a strain range of 0–0.1 and without the addition of image noise,the accuracy of the proposed method increases with higher expansion orders,surpassing that of the DFT image reconstruction method when the fourth order is utilized.However,when different levels of Gaussian noise are applied to simulated images individually,the accuracy of the third-or fourth-order Taylor series expansion method is superior to that of the DFT reconstruction method.Finally,we present the analyzed experimental results of a silicone rubber plate specimen with bilateral cracks under uniaxial tension.

基于多元变量Taylor级数展开模型的定位算法

为了进一步提高无线传感器网络的定位精度,通过考虑未知传感器之间的距离信息,构建了多元变量Taylor级数展开的定位模型。在对该模型求解过程中,首先利用三边测距法得到未知传感器的初始位置,再采用加权最小二乘法计算其最优值作为未知传感器的估计位置。为评价该算法的性能,推导了定位结果的Cramer-Rao下界(CRLB)。仿真测试了不同距离测量误差和已知传感器数目对定位误差的影响,以及算法的累积分布函数(CDF)。仿真结果表明,该算法有效地提高了定位精度,且定位误差非常接近CRLB。

函数Riemann和式的类Taylor级数展开式

如果一元解析函数f(x)无f限阶可导,其Taylor级数展开式f(x)=f(0)+f'(0)x+f″(0)/2!x^2+…+f^((k))(0)/k!x^k+…=∞∑k=0f^((k))(0)/k!x^k.本文讨论将一元无限阶可导函数f(x)在区间[a,b]上的Riemann和式b-a/nn∑k=1f(a+k/n(b-a))展开成1/n的级数:b-a/nn∑k=1f(a+k/n(b-a))=A_0+A_1·1/n+A_2/2!·(1/n)~2+···+A_i/i!·(1/n)~i+···可以看到,这个展开式在形式上与函数的Taylor级数展开式非常相似.