一种用于多码CP-DS-CDMA系统的混合时频域均衡器

提出了一种新的用于基于循环前缀的多码直接序列扩频码分多址接入(CP-DS-CDMA)系统的混合时频域均衡器.该均衡器包括一个前向频域线性均衡器(FDLE)和一个反向时域线性预测器(TDLP).依据最小均方误差(MMSE)准则导出了该均衡器的最优系数,并证明了前向频域均衡器系数与反向时域线性预测器阶数无关,因此只需改变反向线性预测器的结构就可以灵活地调整系统性能.通过结合块交织处理,该均衡器能利用解扩后在符号级的判决结果,来增强反馈信号的可靠性.计算机仿真结果表明在多码CP-DS-CDMA系统中该均衡器比现有的频域线性均衡器有3dB的性能提高.     

On Inverse Estimation in Linear Regression

A procedure suggested by Krutchkoff (1967) f or inverse estimation in linear regression is compared with the classical procedure from other points of view than that taken by Krutchkoff, i.e. comparative mean square error. In particular, comparisons are made on the basis of “closeness” in estimation (Pitman, 1937), consistency (in a setting where this concept is relevant), and mean square error of the relevant asymptotic distributions. It is found that, for large samples, Krutchkoff's estimate is superior in the sense of “closeness” if values of the independent variable are restricted to a certain closed interval around the mean of the independent variates in the experiment and inferior elsewhere. However, the width of this interval varies inversely as the product of the absolute value of the standardized slope (i.e. scaled by the error standard deviation) and the standard deviation of the independent variables used in the experiment. As a practical matter the parameter tends to be large so that the interval where the Krutchkoff estimate is superior will be trivially small. In addition large values of this product parameter imply that the two estimates being compared are virtually indistinguishable. Coupling these latter remarks with the fact that the classical procedure allows an exact confidence interval for the parameter under estimate while the Krutchkoff procedure does not, suggests the classical estimate is to be preferred using the “closeness” criterion. If one uses the criterion of mean square error applied to the relevant asymptotic distribution, one reaches conclusions similar to the above, except that the interval of superiority of the Krutchkoff estimate is no longer trivially small even at best. However, the mean square error criterion fails to take into account the fact that the estimates are correlated and so should be considered an intrinsically less appropriate criterion than closeness. We also find that, in circumstances where the concept is applicable, Krutchkoff's estimate is not consistent whereas the classical estimate is; Krutchkoff's estimate can be trivially modified so that it is consistent but will then tend to never be better in the sense of closeness than the classical estimate.     

The Effect of the Image Local Mean on the Two-dimensional Least Mean Square Algorithm Weight Convergence

Abstract

This paper discusses the effect of an image's non-zero local mean value on the mean square estimation error (MSEE) and the steady-state weights of the two-dimensional least mean square (TDLMS) algorithm [1] when used in image processing. It shows that the local mean causes an increase in the MSEE which is proportional to the square of the image's local mean value. This causes the filter to converge to non-optimum weights and the shift from the optimum values is proportional to the square of the image's local mean value. It is shown that this effect can be reduced by normalizing the filter's weights to unity.     

Least squares finite element analysis of laminar boundary layer flows

Based on the least squares error criterion, a class of finite element is formulated for the numerical analysis of steady state viscous boundary layer flow problems. The method is essentially a discrete element-wise minimization of square and weighted residuals which arise from the attempts in approximately satisfying boundary layer equations. An iterative linearization scheme is developed to circumvent the mathematical difficulties posed by the non-linear boundary layer equations. It results in a process of successive least squares minimizations of residual errors arising from satisfying a set of linear differential equations. A mathematical justification for the method is presented. A major feature of the method lies in the linearization approach which renders non-linear differential equations amenable to linear least squares finite element analysis. Another important feature rests on the proposed finite element formulation which preserves the symmetric nature of finite element matrix equations through the use of the least squares error criterion. Numerical examples of viscous flow along a flat plate are presented to demonstrate the applicability of the method as well as to illuminate discussions on the theoretical aspects of the method.     

A combined method using modified routh stability array and MSE criterion for the reduction of discrete‐time systems

Abstract

A new mixed method using modified stability array and mean‐square error (MSE) criterion is proposed for deriving reduced‐order 2‐transfer functions for discrete‐time systems. More precisely, the modified Routh stability array is used to obtain the reduced‐order denominator, thus ensuring stability preservation, while the numerator is obtained by minimizing the mean‐square error between the unit step responses of the original system and reduced model. The main feature of the method is that it does not actually evaluate the system and model responses in the step of minimizing mean‐square error.     

A new method for the 3D regression of the experimental data of radiation receivers

A new method of calculating the calibration surface of pyrometer systems based on linearization of the experimental relations is proposed. It is shown that the method has a root mean square calibration error not exceeding ±1.5% over a range of measured temperatures from −40°C to +150°C at an ambient temperature of ±60°C.     

基于小波系数非线性连续函数衰减的脑电信号去噪

环境噪声和工频噪声的干扰对脑电信号(EEG)的进一步处理和分析带来极为不利的影响。针对传统小波系数软阈值消噪方法去噪后产生的波形失真和硬阈值消噪方法去噪后产生的振荡现象,提出了一种新的小波系数非线性连续函数衰减处理算法。通过小波系数的非线性衰减处理,使低值端小波系数连续函数的变化介于硬软阈值函数之间,有效避免了处理后的波形失真和振荡。通过实验数据比较,证明处理后的脑电信号信噪比和均方误差均优于传统的小波去噪处理方法。     

一种基于小波变换的多聚焦图像融合方法

提出了一种基于低频系数局部区域梯度信息的多分辨率图像融合方法。根据局部梯度信息对源图像的小波低频系数进行选择,获取融合图像的对应低频系数。依照平均误差、峰值信噪比、均方根误差以及偏差度、熵等评价标准,将该方法的多聚焦图像融合效果与其他三种常用低频系数融合方法的效果进行了比较。实验结果表明,该方法获得的大部分评价指标都优于其他三种方法,且其最佳小波分解层数为2层,而其他三种方法的最佳小波分解层数为5层。最佳小波分解层数越少,图像融合的计算量越小。该方法在减少计算量的同时,提高了融合质量。     

Wiener filter in the gyrator domain

The Wiener filter is the optimal filter according to the minimal mean square error criterion. For data distorted by noise with given spectral density, the Wiener filter is the optimal filter for restoring the noisy image. In this paper we will define a gyrator convolution operator and its optical implementation. The new generalized gyrator Wiener filter was defined using the new operator. The new filter was compared to the conventional Wiener filter and showed improved performance. An improvement of up to 40?dB in the mean square error at the optimal rotation angle in comparison to the conventional Wiener filter is demonstrated.     

Multiresponse Optimization and Pareto Frontiers

Methods that can capture evenly distributed solutions along the Pareto frontier are useful for multiresponse optimization problems because they provide a large variety of alternative solutions to the decision maker from among a set of nondominated solutions. However, methods often used for optimizing dual and multiple dual response problems have been rarely evaluated in terms of their ability to capture those solutions. This article provides this information by evaluating a global criterion–based method and the popular weighted mean square error method. Convex and nonconvex response surfaces were considered, and results of the methods were compared with those of a lexicographic approach on the basis of two examples from the literature. Regarding the results, it is shown that the user can be successful in capturing Pareto solutions in convex and nonconvex regions using the global criterion–based method. Moreover, it is shown that the starting point affects the distribution of solutions along the Pareto frontier but is not pivotal to obtain a complete representation of the Pareto frontier. For this purpose, it is necessary to decrease the weight increment and to compute for more solutions. Copyright © 2011 John Wiley & Sons, Ltd.     

约束条件下的线性贝叶斯估计

本文提出等式约束下线性模型中回归参数的线性贝叶斯估计,证明其在均方误差矩阵准则下相对于约束最小二乘估计的优越性,并采用蒙特卡洛模拟和数值算例验证其优越性．     

Assessment of pareto calibration, stability, and wavelength selection

Recent work has shown that ridge regression (RR) is Pareto to partial least squares (PLS) and principal component regression (PCR) when the variance indicator Euclidian norm of the regression coefficients, //p//, is plotted against the bias indicator root mean square error of calibration (RMSEC). Simplex optimization demonstrates that RR is Pareto for several other spectral data sets when //p// is used with RMSEC and the root mean square error of evaluation (RMSEE) as optimization criteria. From this investigation, it was observed that while RR is Pareto optimal, PLS and PCR harmonious models are near equivalent to harmonious RR models. Additionally, it was found that RR is Pareto robust, i.e., models formed at one temperature were then used to predict samples at another temperature. Wavelength selection is commonly performed to improve analysis results such that bias indicators RMSEC, RMSEE, root mean square error of validation, or root mean square error of cross-validation decrease using a subset of wavelengths. Just as critical to an analysis of selected wavelengths is an assessment of variance. Using wavelengths deemed optimal in a previous study, this paper reports on the variance/bias tradeoff. An approach that forms the Pareto model with a Pareto wavelength subset is suggested.     

The Bayes estimator in a misspecified linear regression model

Summary The paper presents an optimal Bayes estimator in the linear regression model under misspecification. This estimator is compared with the ordinary least squares estimator in terms of the matrix mean square error criterion. Some results on admissibility and prediction are also derived.     

求解混凝土等效断裂韧度的小波基无单元方法

考虑混凝土主裂缝亚临界扩展长度及虚拟裂缝区粘聚力,利用,积分与应力强度因子的解析关系,建立基于小波基无单元方法求解混凝土等效断裂韧度的数值方法,研究不同基底小波分辨率对混凝土等效断裂韧度计算值的影响。对8个带裂缝试件的混凝土等效断裂韧度的计算结果表明:在相同小波基分辨率下,4根体积系列试件的计算值的均方差和变异系数分别小于0.0244和0.0231,4根高度系列试件的计算值的均方差和变异系数分别小于0.0384和0.0362,计算结果的一致性好;与解析解相比,8个试件的计算值的最大相对误差均在5%左右,计算结果的精度高;且不同小波基分辨率对计算结果影响不大。由此得出结论,小波基无单元方法是求解混凝土等效断裂韧度的一种可靠的高精度数值方法,可以作为混凝土断裂力学的一种有力的计算工具。     

Computer and Information Sciences-II

A simple non-iterative procedure is described for obtaining missing value estimates by solving a set of simultaneous linear equations that can be written directly. The method is derived for the two-way crossed classification and results for the P-way crossed classification are also given. Following the procedure of Yates (1933), estimates of the missing values are obtained such that their residuals are zero, thereby minimizing the error mean square. For the P-way crossed classifications the error mean square may be a pooled mean square of higher ordered interactions. The procedure is applicable to other designs as well.     

Response analysis of Van der Pol oscillator subjected to harmonic and random excitations

The response of the Van der Pol oscillator subjected to combined harmonic and random excitations is investigated by a technique combining two excellent methods, namely the stochastic averaging method and the equivalent linearization method. The original equation is averaged by the stochastic averaging method at first. Then the resulting nonlinear averaged equations are linearized by the equivalent linearization method so that the equations obtained can be solved exactly by the technique of auxiliary function. The mean square response of the Van der Pol oscillator is computed algebraically and compared to the ones obtained by numerical simulation and by technique combining methods of stochastic averaging and equivalent non-linearization. The results show that the proposed technique gives a good prediction on mean square responses of the Van der Pol oscillator. In addition, the proposed technique can be applied to other nonlinear systems for it does not require any special conditions, and it can be improved by advanced optimization criteria of the equivalent linearization method.     

EMD与SLS法在爆破振动加速度信号时域积分中的应用

实测差异分析表明,速度振幅峰值分布受外界因素影响更具规律性,加速度信号主频分布比速度信号更分散。提出一种加速度信号时域积分算法,先基于经验模态分解法对信号进行趋势项剔除、去均值化和高频降噪,再对存在漂移现象的各固有模态函数分量时域积分速度分量进行最小二乘法处理。研究表明:各固有模态函数分量在处理过程中应分别对待;为达到较好降噪效果,阈值修正系数k应不断调整;分段最小二乘法对漂移现象的消除能力优于单段最小二乘法和经验模态分解法。最后,通过本文定义的全局参量和局部参量验证算法的优越性。     

SYNTHESIS OF OPTIMUM FIRST ORDER FILTERS FOR FLAT SPECTRA COMMAND AND NOISE SIGNALS∗

Command and noise signals expected to operate on specific control systems are often only scantily known at the design stage. This paper considers some of the problems which may arise in choosing a system transfer function when supplied with such inadequate information. A first order linear filter has been considered, and for synthesis purposes both command and noise signals have been represented by flat power spectra. The total power content and bandwidth of both signals have been varied, and the optimum transfer function for the various combinations determined by using the mean square error criterion.

With the above assumptions, it is shown that under the circumstances most likely to be met in practice, and in the absence of more specific information, a time constant of one-quarter of the inverse of the expected command signal bandwidth will yield reasonable mean square error performance.     

Optimal training design for linearly time-varying MIMO/OFDM channels modelled by a complex exponential basis expansion

Time- and frequency-selective fading of propagating channels degrades the performance of multiple-input multiple-output/orthogonal frequency-division multiplexing (MIMO/OFDM) systems extensively by introducing double convolutions in both time-domain and frequency- domain. The author addresses the problem of linearly time-varying (LTV) channel estimation of MIMO/OFDM systems. First, the time-varying coefficients of the LTV channel are modelled by complex exponential basis expansions. Secondly, the LTV channel is estimated and the optimal pilot symbols are derived following the minimum mean square error criterion. It is shown that the optimal pilot strategy is to group consecutive pilot tones together as a pilot cluster and to distribute uniformly all pilot clusters in frequency-domain. In addition, the LTV channel estimation is further improved by imposing a window function on received signals. Finally, through simulations, it is shown that the new channel estimator can provide a considerable performance improvement in estimating MIMO-LTV channels, especially for the rapidly time-varying channel of a large Doppler frequency.     

A new method of calibrating strain release coefficients in measuring welding stresses

The measured values of welding residual stresses often exceed material yield strength (σ_y) or tensile strength (σ_t), in measuring welding residual stresses in the welded joints of low carbon steel or stainless steel by drilling a blind hole. It is quite evident that measured values do not represent reality. Local plastic strain caused by residual stress concentrations round the blind hole has a main effect on the measuring error of welding residual stresses. This article presents a new method of calibrating strain coefficients A and B for eliminating influence of local plastic strain. In calibrating strain release coefficients A and B, calibrating stresses applied on the specimen were increased so that material round the blind hole produced local plastic deformation, ie coefficients A and B contained a component of the plastic strain. Numerial values of coefficients A and B were classified into four grades. Every grade coefficient contained a different quantity of the plastic strain for offseting the influence of the plastic strain round the blind hole. Test results have proved that by adopting these coefficients more satisfactory values for residual stresses can be obtained in practical engineering. The measuring average error in stainless steel (1Cr18Ni9Ti) reduces from 109% to 1.52%. The measuring average error in low carbon steel reduces from 54.69% to 3.21%.