基于最大似然多项式回归的鲁棒语音识别

本文针对最大似然线性回归算法线性假设的缺点,将多项式回归方法用于模型自适应,构建了基于最大似然多项式回归的非线性模型自适应算法。该算法在对数谱域用多项式回归方法,逼近每个Mel子带上识别环境模型均值与训练环境模型均值之间的非线性关系。多项式系数通过EM算法和最大似然准则从识别环境下的少量自适应数据中估计。实验结果表明,二阶多项式就可以较好地逼近模型均值的非线性环境变换关系。在噪声补偿和说话人自适应实验中,最大似然多项式回归算法的误识率都明显低于最大似然线性回归算法。本文算法较好地克服了线性模型自适应算法线性假设的缺陷,可同时减小噪声,和说话人的改变或其它因素对语音识别系统的影响,尤其适合说话人和噪声的联合自适应。      

Maximum likelihood subband polynomial regression for robust speech recognition

In this paper, we propose a model adaptation algorithm based on maximum likelihood subband polynomial regression (MLSPR) for robust speech recognition. In this algorithm, the cepstral mean vectors of prior trained hidden Markov models (HMMs) are converted to the log-spectral domain by the inverse discrete cosine transform (DCT) and each log-spectral mean vector is divided into several subband vectors. The relationship between the training and testing subband vectors is approximated by a polynomial function. The polynomial coefficients are estimated from adaptation data using the expectation–maximization (EM) algorithm under the maximum likelihood (ML) criterion. The experimental results show that the proposed MLSPR algorithm is superior to both the maximum likelihood linear regression (MLLR) adaptation and maximum likelihood subband weighting (MLSW) approach. In the MLSPR adaptation, only a very small amount of adaptation data is required and therefore it is more useful for fast model adaptation.     

Maximum likelihood estimator of operational modal analysis for linear time-varying structures in time–frequency domain

This paper investigates the problem of modal parameter estimation of time-varying structures under unknown excitation. A time–frequency-domain maximum likelihood estimator of modal parameters for linear time-varying structures is presented by adapting the frequency-domain maximum likelihood estimator to the time–frequency domain. The proposed estimator is parametric, that is, the linear time-varying structures are represented by a time-dependent common-denominator model. To adapt the existing frequency-domain estimator for time-invariant structures to the time–frequency methods for time-varying cases, an orthogonal polynomial and z-domain mapping hybrid basis function is presented, which has the advantageous numerical condition and with which it is convenient to calculate the modal parameters. A series of numerical examples have evaluated and illustrated the performance of the proposed maximum likelihood estimator, and a group of laboratory experiments has further validated the proposed estimator.     

On the Regression Model for Generalized Normal Distributions

The traditional linear regression model that assumes normal residuals is applied extensively in engineering and science. However, the normality assumption of the model residuals is often ineffective. This drawback can be overcome by using a generalized normal regression model that assumes a non-normal response. In this paper, we propose regression models based on generalizations of the normal distribution. The proposed regression models can be used effectively in modeling data with a highly skewed response. Furthermore, we study in some details the structural properties of the proposed generalizations of the normal distribution. The maximum likelihood method is used for estimating the parameters of the proposed method. The performance of the maximum likelihood estimators in estimating the distributional parameters is assessed through a small simulation study. Applications to two real datasets are given to illustrate the flexibility and the usefulness of the proposed distributions and their regression models.     

Research on application of polynomial fitting technique in rotary kiln infrared temperature measurement system

Aiming at the linear temperature compensation algorithm’s disadvantage of temperature measurement error in rotary kiln infrared scanning temperature measurement process, this paper proposes a precise nonlinear cubic polynomial fitting temperature compensation algorithm. The proposed algorithm compensates the temperature values of scanning points on rotary kiln surface by following steps: Calculating temperature difference between the real temperature value of rotary kiln and temperature value measured by infrared scanning temperature measurement system; Fitting the temperature difference data with cubic polynomial; Using the obtained function to compensate temperature. Experimental result shows that compared with the usual linear temperature compensation algorithm, the accuracy of proposed algorithm has raised about 2.25 times when cubic polynomial is used.     

Effect of nonlinear chirped Gaussian laser pulse parameters on the electron acceleration

One-dimensional analysis of electron acceleration by a nonlinear chirped Gaussian laser pulse was investigated numerically. Two main nonlinear chirped pulses, polynomial and periodical were used. The maximum energy of electron in nonlinear chirped is approximately three times more than that of linear chirped. In the case of first order nonlinear polynomial chirp, Ω(ξ) = 1 + aξ + bξ ², the electron can be accelerated up to 5.3 GeV. Indeed, the analysis of the electron trajectory in x-z plane showed that the electron in the field of the nonlinear chirped pulse has a much smaller divergence than that of linear chirped pulse.     

Adaptive and efficient nonlinear channel equalization for underwater acoustic communication

We investigate underwater acoustic (UWA) channel equalization and introduce hierarchical and adaptive nonlinear (piecewise linear) channel equalization algorithms that are highly efficient and provide significantly improved bit error rate (BER) performance. Due to the high complexity of conventional nonlinear equalizers and poor performance of linear ones, to equalize highly difficult underwater acoustic channels, we employ piecewise linear equalizers. However, in order to achieve the performance of the best piecewise linear model, we use a tree structure to hierarchically partition the space of the received signal. Furthermore, the equalization algorithm should be completely adaptive, since due to the highly non-stationary nature of the underwater medium, the optimal mean squared error (MSE) equalizer as well as the best piecewise linear equalizer changes in time. To this end, we introduce an adaptive piecewise linear equalization algorithm that not only adapts the linear equalizer at each region but also learns the complete hierarchical structure with a computational complexity only polynomial in the number of nodes of the tree. Furthermore, our algorithm is constructed to directly minimize the final squared error without introducing any ad-hoc parameters. We demonstrate the performance of our algorithms through highly realistic experiments performed on practical field data as well as accurately simulated underwater acoustic channels.     

Adaptation of homotopy-perturbation method for numeric-analytic solution of system of ODEs

A new reliable algorithm based on an adaptation of the standard Homotopy-Perturbation Method (HPM) is presented. The HPM is treated, for the first time, as an algorithm in a sequence of intervals (i.e., time step) for finding accurate approximate solutions of linear and nonlinear systems of ODEs. Numerical comparisons between the Multistage Homotopy-Perturbation Method (MHPM) and the available exact solution and the classical fourth-order Runge-Kutta (RK4) method reveal that the new technique is a promising tool for linear and nonlinear systems of ODEs.     

改进S/B算法的近红外光谱模型转移

针对模型转移中S/B算法对于非线性问题的局限性,在传统S/B算法进行线性拟合、偏最小二乘法求参数的基础上加以改进,提出了引入变量的高次幂、使用Lagrange插值法与Newton插值法求待定系数和插值多项式来解决两组数据的非线性问题。为了验证改进算法的有效性,先对主机样品建模并分别预测主机和子机样品,然后通过实验数据和评价指标,筛选出最佳函数关系进行子机模型校正,并分别用改进的S/B算法和传统的S/B算法对子机未知样本进行预测。实验结果表明：直接用主机原模型对子机预测的值与真实值差距较大,利用改进的S/B算法(H-S/B)比传统的S/B算法预测值更接近真实值。改进的S/B算法提高了预测值的准确性,解决了传统S/B算法的非线性问题,实现了更好的模型转移效果,增强了网络化模型应用的通用性。     

一种成像测量图像径向几何畸变的校正方法

通过对具有径向畸变的摄像机模型的分析,设计了一套求解图像径向几何畸变中心和畸变多项式系数的方案。首先,依据校正样板曲线的弯曲程度应用一元线性回归法和逐次逼近法求取光学图像的几何畸变中心,然后应用递推最小二乘法求解径向几何畸变的多项式系数,最后根据所得到的畸变中心和畸变多项式系数对图像进行校正得到满足要求的图像。仿真试验证明:该方法可以通过一次采集单幅图像对成像系统进行高精度标定,能够对成像测量系统的径向几何畸变进行一定精度的校正。实践证明:该方法通过图像处理的方法提高成像测量系统的精度,降低了系统的设计成本,可以作为成像测量系统中单独标定摄像机畸变参数的一种简单有效的方法。     

Application of piecewise linear regression twice to inspect the defective regions on thin film transistor liquid crystal display panels

Detecting defects in thin film transistor liquid crystal display (TFT-LCD) panels can be difficult due to non-uniform background brightness and slightly different brightness levels between the defective regions and the background. One well-known method is to inspect the defects of TFT-LCD panels using the polynomial approximation method. However, there are some problems such as determination of the polynomial degree and ghost objects. In this paper, to overcome these problems, we propose a new algorithm using the piecewise linear regression twice and Niblack’s method which do not require to determine the polynomial degree for the approximation. Our algorithm effectively removed ghost objects. The experimental results show that our proposed method performed well and was good enough to substitute the polynomial approximation method.     

基于SVR的多股簧机床张力控制

针对多股螺旋弹簧加工机床张力控制系统的非线性特性及存在干扰的问题,提出了基于支持向量回归(Support Vector Regression, 简称SVR)的有效抑制噪声的控制算法;即在基于SVR的逆动力学建模中采取非线性松弛因子替代线性松弛因子,抑制噪声在建模过程中的影响,提高建模精度;把系统逆模型作为前馈控制器,构成伪线性系统,PID控制器作为反馈控制,组成有效抑制噪声的复合控制算法;实验结果表明,这种改进基于SVR的复合控制方式在多股螺旋弹簧张力控制系统中具有较好的控制精度和鲁棒性。     

Predicting thermal displacements in modular tool systems

In the last decade, there has been an increasing interest in compensating thermally induced errors to improve the manufacturing accuracy of modular tool systems. These modular tool systems are interfaces between spindle and workpiece and consist of several complicatedly formed parts. Their thermal behavior is dominated by nonlinearities, delay and hysteresis effects even in tools with simpler geometry and it is difficult to describe it theoretically. Due to the dominant nonlinear nature of this behavior the so far used linear regression between the temperatures and the displacements is insufficient. Therefore, in this study we test the hypothesis whether we can reliably predict such thermal displacements via nonlinear temperature-displacement regression functions. These functions are estimated first from learning measurements using the alternating conditional expectation (ACE) algorithm and then tested on independent data sets. First, we analyze data that were generated by a finite element spindle model. We find that our approach is a powerful tool to describe the relation between temperatures and displacements for simulated data. Next, we analyze the temperature-displacement relationship in a silent real experimental setup, where the tool system is thermally forced. Again, the ACE algorithm is powerful to estimate the deformation with high precision. The corresponding errors obtained by using the nonlinear regression approach are 10-fold lower in comparison to multiple linear regression analysis. Finally, we investigate the thermal behavior of a modular tool system in a working milling machine and again get promising results. The thermally induced errors can be estimated with 1-2 microm accuracy using this nonlinear regression analysis. Therefore, this approach seems to be very useful for the development of new modular tool systems.     

Color reproduction method by support vector regression for color computer vision

In the color computer vision system, the nonlinearity of the camera and computer screen may result in different colors between the screen and the actual color of objects, which requires for color calibration. In this paper, support vector regression (SVR) method was introduced to reproduce the colors of the nonlinear imaging system. Firstly, successive 3σ method was used to eliminate the large errors found in the color measurement. Then, based on the training set measured in advance, SVR model of RBF kernel was applied to map the nonlinear imaging system. In this step, two important parameters (C, γ) were optimized by the Least Mean Squared Validating Errors algorithm to get the best SVR model. Finally, this optimized model could predict the real values displayed on the screen. Compared with quadratic polynomial regression, BP neural network and relevance vector machine, the optimized SVR model has better ability in color reproduction performance and generalization.     

A gradient-free adaptation method for nonlinear active noise control

Active Noise Control (ANC) problems are often affected by nonlinear effects, such as saturation and distortion of microphones and loudspeakers. Nonlinear models and specific adaptation algorithms must be employed to properly account for these effects. The nonlinear structure of the problem complicates the application of gradient-based Least Mean Squares (LMS) algorithms, due to the fact that exact gradient calculation requires executing nonlinear recursive filtering operations, which pose computational and stability issues. One favored solution to this problem consists in neglecting recursive terms in the gradient calculation, an approximation which is not always without consequences on the convergence performance. Besides, an efficient application of nonlinear models cannot avoid some form of model structure selection, to avoid the well-known effects of overparametrization and to reduce the computational load on-line. Unfortunately, the standard ANC setting configures an indirect identification problem, due to the presence of the secondary path in the control loop. In the nonlinear case, this destroys the linear regression structure of the problem even if the control filter is linear-in-the-parameters, thereby making it impossible to apply the many existing model selection methods for linear regression problems. A simple and computationally wise low demanding approach is here proposed for parameter estimation and model structure selection that provides an answer to the mentioned issues. The proposed method avoids altogether the use of the error gradient and relies on direct cost function evaluations. A virtualization scheme is used to assess the accuracy improvements when the model is subject to parametric or structural modifications, without directly affecting the control performance. Several simulation examples are discussed to show the effectiveness of the proposed algorithms.     

基于小波核偏最小二乘回归方法的混沌系统建模研究

基于核学习的强大非线性映射能力,结合用于回归建模的线性偏最小二乘(PLS)算法,提出一种小波核偏最小二乘(WKPLS)回归方法. 该方法基于支持向量机使用的经典核函数技巧,将输入映射到高维非线性的特征空间,在特征空间中,构造线性的PLS回归模型. PLS方法利用输入与输出变量之间的协方差信息提取潜在特征,而可允许的小波核函数具有近似正交以及适用于信号局部分析的特性. 因此,结合它们优点的WKPLS方法显示了更好的非线性建模性能. 将WKPLS方法应用在非线性混沌动力系统建模上,并与基于高斯核的核偏最小二乘 关键词： 小波核 偏最小二乘回归 混沌系统 建模     

物理实验数据的线性与非线性拟合

Origin是一款制图和数据处理功能强大的应用软件。本文结合大学物理实验,以实例详细介绍如何利用Origin进行实验数据的拟合分析。包括线性回归拟合、多项式拟合和非线性拟合中的一阶指数衰减拟合。实践证明,利用Origin软件对实验数据进行曲线拟合和分析能够显著提高数据处理效率。     

非线性动力系统分岔图中的暗线

基于非线性动力系统混沌运动的回归特性，构造了一种对分岔图中穿过混沌区的暗线进行研究的数值回归算法。运用该算法求得抛物线映射的暗线，并与通过暗线方程精确求得的暗线进行比较，验证了算法的有效性。对Brussel振子系统和分段线性单级齿轮动力系统的暗线进行了研究。通过对非线性动力系统分岔图中暗线的研究，由其切点可以得到嵌在混沌区中的周期窗口，由其交点可以得到混沌吸引子的激变点。研究结果表明该算法有助于分析系统的动力学行为和控制混沌运动。     

电磁脉冲测试系统的非线性辨识建模与性能补偿

给出了准阶跃信号激励下电磁脉冲测试系统非线性模型参数在连续域的直接辨识算法。结合实际研制的光纤传输式脉冲电压测试系统及其时域动态校准数据,建立了由4阶多项式非线性环节和3阶传递函数线性环节组成的测试系统Hammerstein模型,实测结果验证了辨识模型的准确性。在此基础上,构建了由动态线性补偿滤波器和静态非线性校正器组成的补偿环节,将测试系统的下限截止频率由数十kHz拓展至直流,稳态响应时间由s级降至ns级,有效改善了系统的动态性能,实测脉冲波形的重建结果验证了补偿环节设计的有效性。