分数误差与波谱分析——信号、电路与系统理论在高校课程考试系统中的应用

考试系统与电路系统具有一定程度的相似性。本文结合高校课程考试的具体情况 ,就考试系统中的非线性、随机性与干扰进行了简要分析 ,提出了解决方法 ;针对一般统计分析方法于高校多专业分散课程分数小样本的不适应性 。

Stability of finite difference numerical simulations of acoustic logging-while-drilling with different perfectly matched layer schemes

In acoustic logging-while-drilling （ALWD） finite difference in time domain （FDTD） simulations, large drill collar occupies, most of the fluid-filled borehole and divides the borehole fluid into two thin fluid columns （radius -27 mm）. Fine grids and large computational models are required to model the thin fluid region between the tool and the formation. As a result, small time step and more iterations are needed, which increases the cumulative numerical error. Furthermore, due to high impedance contrast between the drill collar and fluid in the borehole （the difference is 〉30 times）, the stability and efficiency of the perfectly matched layer （PML） scheme is critical to simulate complicated wave modes accurately. In this paper, we compared four different PML implementations in a staggered grid finite difference in time domain （FDTD） in the ALWD simulation, including field-splitting PML （SPML）, multiaxial PML（M- PML）, non-splitting PML （NPML）, and complex frequency-shifted PML （CFS-PML）. The comparison indicated that NPML and CFS-PML can absorb the guided wave reflection from the computational boundaries more efficiently than SPML and M-PML. For large simulation time, SPML, M-PML, and NPML are numerically unstable. However, the stability of M-PML can be improved further to some extent. Based on the analysis, we proposed that the CFS-PML method is used in FDTD to eliminate the numerical instability and to improve the efficiency of absorption in the PML layers for LWD modeling. The optimal values of CFS-PML parameters in the LWD simulation were investigated based on thousands of 3D simulations. For typical LWD cases, the best maximum value of the quadratic damping profile was obtained using one do. The optimal parameter space for the maximum value of the linear frequency-shifted factor （a0） and the scaling factor （β0） depended on the thickness of the PML layer. For typical formations, if the PML thickness is 10 grid points, the global error can be reduced to 〈1% using the optimal PML parameters, and the error will decrease as the PML thickness increases.

Calculation of saturation in carbonate reservoirs based on electrical efficiency

We derived an equation for saturation in carbonate reservoirs based on the electrical efficiency model in the case of lacking core data. Owing to the complex pore structure and strong heterogeneity in carbonate reservoirs, the relation between electrical efficiency and water porosity is either complex or linear. We proposed an electrical efficiency equation that accounts for the relation between electrical efficiency and water porosity. We also proposed a power-law relation between electrical efficiency and deep-formation resistivity and analyzed the factors controlling the error in the water saturation computations. We concluded that the calculation accuracy of the electrical efficiency is critical to the application of the saturation equation. The saturation equation was applied to the carbonate reservoirs of three wells in Iraq and Indonesia. For relative rock electrical efficiency error below 0.1, the water saturation absolute error is also below 0.1. Therefore, we infer that the proposed saturation equation generally satisfies the evaluation criteria for carbonate reservoirs.

Data Analysis and Modeling of Fiber Optic Gyroscope Drift

A data gathering system is designed for the interferometric fiber optic gyroscope (IFOG) of land strapdown inertial system. IFOG is tested and the testing curve is given. The test data of IFOG are analyzed with Allan variance method and each error coefficient is identified. Furthermore, a random drift error model for IFOG is built by the method of time series analysis. The conclusion provides supports for improving IFOG design and compensating for errors of IFOG in practice.

Design of the Testing System for Jet Elements

To analyze the errors of processing data, the testing principle for jet elements is introduced and the property of testing system is theoretically and experimentally studied. On the basis of the above, the method of processing data is presented and the error formulae, which are the functions of the testing system property, are derived. Finally, the methods of reducing the errors are provided. The measured results are in correspondence with the theoretical conclusion.

标准化不等于科学化

笔者从报上看到一份来自澳大利亚的语文试卷，真有“柳暗花明又一村”的感觉。这份语文试卷有３张考卷共５道大题，分别是３道写作试题（看图作文，写一份告示，写生活短论：《学生打工的利与弊》）和两道阅读试题。读者面对这样一份“洋考卷”也许会大吃一惊吧。标准化考...

A New Class of Biased Linear Estimators in Deficient-rank Linear Models

In this paper, we define a new class of biased linear estimators of the vector of unknown parameters in the deficient_rank linear model based on the spectral decomposition expression of the best linear minimun bias estimator. Some important properties are discussed. By appropriate choices of bias parameters, we construct many interested and useful biased linear estimators, which are the extension of ordinary biased linear estimators in the full_rank linear model to the deficient_rank linear model. At last, we give a numerical example in geodetic adjustment.

2和3级静止式交流无功电度表(乏小时)(续)

仪表应能经受脉冲电压试验和5-4-6条中规定的交流电压试验。 4.5 电磁兼容性(EMC) 4.5.1 抗电磁干扰仪表的设计应能在传导和辐射电磁干扰以及静电放电时既不能使仪表损坏也不能有实质影响。注:考虑的干扰因素有: ——静电放电;——高频(HF)电磁场;——快速瞬变。

Rice condition numbers of QR and Cholesky factorizations

A condition number is an amplification coefficient due to errors in computing. Thus the theory of condition numbers plays an important role in error analysis. In this paper, following the approach of Rice, condition numbers are defined for factors of some matrix factorizations such as the Cholesky factorization of a symmetric positive definite matrix and QR factorization of a general matrix. The condition numbers are derived by a technique of analytic expansion of the factor dependent on one parameter and matrix-vector equation. Condition numbers of the Cholesky and QR factors are different from the ones previously introduced by other authors, but similar to Chang's results. In Cholesky factorization, corresponding with the condition number of the factor matrix L , K _L is a low bound of Stewart's condition number K .

3-D fracture network dynamic simulation based on error analysis in rock mass of dam foundation

Accurate 3-D fracture network model for rock mass in dam foundation is of vital importance for stability,grouting and seepage analysis of dam foundation.With the aim of reducing deviation between fracture network model and measured data,a 3-D fracture network dynamic modeling method based on error analysis was proposed.Firstly,errors of four fracture volume density estimation methods(proposed by ODA,KULATILAKE,MAULDON,and SONG)and that of four fracture size estimation methods(proposed by EINSTEIN,SONG and TONON)were respectively compared,and the optimal methods were determined.Additionally,error index representing the deviation between fracture network model and measured data was established with integrated use of fractal dimension and relative absolute error(RAE).On this basis,the downhill simplex method was used to build the dynamic modeling method,which takes the minimum of error index as objective function and dynamically adjusts the fracture density and size parameters to correct the error index.Finally,the 3-D fracture network model could be obtained which meets the requirements.The proposed method was applied for 3-D fractures simulation in Miao Wei hydropower project in China for feasibility verification and the error index reduced from 2.618 to 0.337.

高电压精密电压互感器的研制

研制了一种高电压精密电压互感器,可以用于高电压电压互感器误差校验及高电压的扩大量限高精度测量,文章具体阐述了精密电压互感器的结构原理、误差分析,提出了降低误差的技术措施。

Geometric Approximation Technique for Minimum Zone Sphericity Error

The mathematical modeling for evaluation of the sphericity error is proposed with minimum radial separation center. To obtain the minimum sphericity error from the form data, a geometric approximation technique was devised. The technique regarded the least square sphere center as the initial center of the concentric spheres containing all measurement points, and then the center was moved gradually to reduce the radial separation till the minimum radial separation center was got where the constructed concentric spheres conformed to the minimum zone condition. The method was modeled firstly, then the geometric approximation process was analyzed, and finally,the software for data processing was programmed. As evaluation example, five steel balls were measured and the measurement data were processed with the developed program. The average iteration times of the approximation technique is 4.2, and on average the obtained sphericity error is 0. 529μm smaller than the least square solution,with accuracy increased by 7. 696%.

WSN中利用XGBoost和加权自适应HFLMS的数据约减组合预测方法

针对无线传感器网络(WSN)中能量、带宽和内存等各种资源的限制问题,提出了一种XGBoost结合加权自适应分层分数最小均方误差(hierarchical fractional least-mean-square,HFLMS)的数据约减组合预测方法。首先,利用XGBoost方法对损失函数进行了二阶的泰勒展开,权衡模型的复杂度和损失函数的下降速度,实现了资源限制的稳定预测;然后提出自适应HFLMS滤波器实现WSN数据约简的传输,并基于误差估计来预测所感测的数据,有效降低了WSN中的能量约束;最后,利用两个评估参数(能量和预测误差)来验证所提组合预测方法的性能。实验结果表明,相比没有预测、近似最速下降算法和分层最小均方滤波技术,提出的预测方法获得的预测结果更好。

Improved Cotes Formula and Error Analysis

The truncation error of improved Cotes formula is presented in this paper. It also displays an analysis on convergence order of improved Cotes formula. Examples of numerical calculation is given in the end.

Quantifying the attribution of model bias in simulating summer hot days in China with IAP AGCM 4.1

Using lAP AGCM simulation results for the period 1961-2005, summer hot days in China were calculated and then compared with observations. Generally, the spatial pattern of hot days is reasonably reproduced, with more hot days found in northern China, the Yangtze and Huaihe River basin, the Chuan-Yu region, and southern Xinjiang. However, the model tends to overestimate the number of hot days in the above-mentioned regions, particularly in the Yangtze and Huaihe River basin where the simulated summer-mean hot days is 13 days more than observed when averaged over the whole region, and the maximum overestimation of hot days can reach 23 days in the region. Analysis of the probability distribution of daily maximum temperature （Trnax） suggests that the warm bias in the model-simulated Tmax contributes largely to the overestimation of hot days in the model. Furthermore, the discrepancy in the simulated variance of the Tmax distribution also plays a non- negligible role in the overestimation of hot days. Indeed, the latter can even account for 22% of the total bias of simulated hot days in August in the Yangtze and Huaihe River basin. The quantification of model bias from the mean value and variability can provide more information for further model improvement.

抗冲激噪声的核分式低次幂自适应滤波算法

文中提出了一种基于分数低阶统计误差准则的抗非高斯冲激噪声的核分式低次幂(KFLP)算法。在存在脉冲干扰的环境下,该算法利用权重更新公式中存在瞬时估计误差的倒数系数的有利特性,使得算法在瞬时估计误差突然增大时的权重向量自动停止更新,由此消除了脉冲干扰对权重向量的影响。仿真结果表明,在相同的冲激噪声环境下,随着代价函数的幂次逐渐趋近于1,核分式低次幂算法的稳定性将得到进一步的提高。另一方面,在非高斯脉冲环境下与采用传统的均方误差准则的核最小均方(Kernel Least-Mean-Square,KLMS)算法相比,所提算法的收敛曲线更加平滑,性能更加稳定。

Study on fast calibration of a ULA's gain and phase error

Array calibration is important in engineering practice. In this paper, fast calibration methods for a ULA's gain and phase errors both in far and near fields are proposed. In the far field, using a single sound source without exact orientation, this method horizontally rotates the array exactly once, performs eigen value decomposition for the covariance matrix of received data, then computes the gain and phase error according to the formulas. In the near field, using the same single sound source, it is necessary to rotate the array horizontally at most three times, build equations according to geometric relations, then solve them. Using the formula proposed in this paper, spherical waves are modified into plane waves. Then eigen values decomposition is performed. These two calibration methods were shown to be valid by simulation and are fast, accurate and easy to use. Finally, an analysis of factors influencing estimation precision is given.

A New Multi-sensor Data Fusion Algorithm Based on EMD-MMSE

A new multi-sensor data fusion algorithm based on EMD-MMSE was proposed.Empirical mode decomposition(EMD)is used to extract the noise of every time series for estimating the variance of the noise.Then minimum mean square error(MMSE)estimator is used to calculate the weights of the corresponding series.Finally,the fused signal is the weighted addition of all these series.The experiments in lab testified the efficiency of this method.In addition,the comparison in fusion time and fusion results with existing fusion method based on wavelet and average technique shows the advantage of this method greatly.

Error Analysis on Corrector Formula for Rectangular Rule

This paper presents truncation errors among Corrector Formula for left Rectangular rule and Corrector Formula for middle Rectangular rule respectively. It also displays an analysis on convergence order of compound corrector formulas for rectangular rule. Examples of numerical calculation have validated theoretical analysis.

The Convergence of 1-Periodic Branched Continued Fraction of the Special Form in Parabolic Regions

Branched continued fractions are one of the multidimensional generalization of the continued fractions. Branched continued fractions with not equivalent variables are an analog of the regular C-fractions for multiple power series. We consider 1-periodic branched continued fraction of the special form which is an analog fraction with not equivalent variables if the values of that variables are fixed. We establish an analog of the parabola theorem for that fraction and estimate truncation error bounds for that fractions at some restrictions. We also propose to use weight coefficients for obtaining different parabolic regions for the same fraction without any additional restriction for first element.