A stochastic restricted ridge regression estimator

Groß [J. Groß, Restricted ridge estimation, Statistics & Probability Letters 65 (2003) 57–64] proposed a restricted ridge regression estimator when exact restrictions are assumed to hold. When there are stochastic linear restrictions on the parameter vector, we introduce a new estimator by combining ideas underlying the mixed and the ridge regression estimators under the assumption that the errors are not independent and identically distributed. Apart from [J. Groß, Restricted ridge estimation, Statistics & Probability Letters 65 (2003) 57–64], we call this new estimator as the stochastic restricted ridge regression (SRRR) estimator. The performance of the SRRR estimator over the mixed estimator in respect of the variance and the mean square error matrices is examined. We also illustrate our findings with a numerical example. The shrinkage generalized least squares (GLS) and the stochastic restricted shrinkage GLS estimators are proposed.     

回归系数的广义岭型主相关估计及其优良性

在回归系数的主相关估计基础上提出一种新的降维估计——广义岭型主相关估计,并讨论它的优良性.     

Determination of α-linolenic acid and linoleic acid in edible oils using near-infrared spectroscopy improved by wavelet transform and uninformative variable elimination

This paper proposes an analytical method for simultaneous near-infrared (NIR) spectrometric determination of α-linolenic and linoleic acid in eight types of edible vegetable oils and their blending. For this purpose, a combination of spectral wavelength selection by wavelet transform (WT) and elimination of uninformative variables (UVE) was proposed to obtain simple partial least square (PLS) models based on a small subset of wavelengths. WT was firstly utilized to compress full NIR spectra which contain 1413 redundant variables, and 42 wavelet approximate coefficients were obtained. UVE was then carried out to further select the informative variables. Finally, 27 and 19 wavelet approximate coefficients were selected by UVE for α-linolenic and linoleic acid, respectively. The selected variables were used as inputs of PLS model. Due to original spectra were compressed, and irrelevant variables were eliminated, more parsimonious and efficient model based on WT-UVE was obtained compared with the conventional PLS model with full spectra data. The coefficient of determination (r²) and root mean square error prediction set (RMSEP) for prediction set were 0.9345 and 0.0123 for α-linolenic acid prediction by WT-UVE-PLS model. The r² and RMSEP were 0.9054, 0.0437 for linoleic acid prediction. The good performance showed a potential application using WT-UVE to select NIR effective variables. WT-UVE can both speed up the calculation and improve the predicted results. The results indicated that it was feasible to fast determine α-linolenic acid and linoleic acid content in edible oils using NIR spectroscopy.     

Two-dimensional wavelet analysis based classification of gas chromatogram differential mobility spectrometry signals

This study introduces two-dimensional (2-D) wavelet analysis to the classification of gas chromatogram differential mobility spectrometry (GC/DMS) data which are composed of retention time, compensation voltage, and corresponding intensities. One reported method to process such large data sets is to convert 2-D signals to 1-D signals by summing intensities either across retention time or compensation voltage, but it can lose important signal information in one data dimension. A 2-D wavelet analysis approach keeps the 2-D structure of original signals, while significantly reducing data size. We applied this feature extraction method to 2-D GC/DMS signals measured from control and disordered fruit and then employed two typical classification algorithms to testify the effects of the resultant features on chemical pattern recognition. Yielding a 93.3% accuracy of separating data from control and disordered fruit samples, 2-D wavelet analysis not only proves its feasibility to extract feature from original 2-D signals but also shows its superiority over the conventional feature extraction methods including converting 2-D to 1-D and selecting distinguishable pixels from training set. Furthermore, this process does not require coupling with specific pattern recognition methods, which may help ensure wide applications of this method to 2-D spectrometry data.     

Application of continuous wavelet transformation to the simultaneous kinetic determination of binary mixtures

Wavelet transformation of kinetic profiles as a new and simple method was developed for the simultaneous determination of binary mixtures without prior separation steps. The mathematical explanation of the procedure is illustrated. Daubechies (db), symlet (sym) and discrete meyer wavelet (meyr) from the family of wavelet transforms were selected and applied under the optimal conditions for the resolution of binary mixtures. A model data as well as experimental data were tested. The results from the experimental data relating to the simultaneous spectrophotometric determination of phosphate and silicate based on the formation of phospho- and silico-molybdenum blue complexes in the presence of ascorbic acid, and also simultaneous determination of Co²⁺ and Ni²⁺ based on their complexation reactions with 1-(2-pyridylazo)-2-naphthol (PAN) in micellar media at pH 6.0 were presented as real models. The proposed method was validated by simultaneous determination of phosphate and silicate in detergent and tap water and also Co²⁺ and Ni²⁺ in tap water samples.     

Wavelet optimized finite difference method using interpolating wavelets for self-adjoint singularly perturbed problems

We design a wavelet optimized finite difference (WOFD) scheme for solving self-adjoint singularly perturbed boundary value problems. The method is based on an interpolating wavelet transform using polynomial interpolation on dyadic grids. Small dissipation of the solution is captured significantly using an adaptive grid. The adaptive feature is performed automatically by thresholding the wavelet coefficients. Numerical examples have been solved and compared with non-standard finite difference schemes in [J.M.S. Lubuma, K.C. Patidar, Uniformly convergent non-standard finite difference methods for self-adjoint singular perturbation problems, J. Comput. Appl. Math. 191 (2006) 228–238]. The proposed method outperforms the non-standard finite difference for studying singular perturbation problems for small dissipations (very small ) and effective grid generation. Therefore, the proposed method is better for studying the more challenging cases of singularly perturbed problems.     

基于差分吸收光谱技术监测苯-甲苯-二甲苯的实验研究

苯-甲苯-二甲苯(BTX)是大气挥发性有机物(VOCs）的重要组成成份,人类长期暴露在苯系物的环境中致癌风险将极大提高。利用BTX在紫外波段有明显的光谱吸收特征,选取250～275 nm作为研究波段,该波段可将BTX的主要特征吸收包含在内。设计了一套由标准BTX液体制备标准气态BTX的装置,采用连续紫外光源和差分吸收光谱技术分别对单组分苯与BTX混合气体进行连续监测研究。为最大程度去除外界噪声干扰,分别采用小波变换滤波和多项式平滑滤波法,并对两种方法的去噪效果进行评价。研究表明尽管传统处理吸收光谱噪声的方法常采用多项式平滑滤波,但该方法会使吸收截面上的细节信息或高频分量丢失。而小波变换滤波具有良好的时频局域化特性,能通过伸缩和平移对信号进行多分辨率分析并可聚焦到信号的任意细节,更能保持光谱谱线的特征结构且信噪比优于多项式平滑滤波。通过实验获得了BTX的吸收截面并与HITRAN数据库吸收截面对比,发现若直接采用HITRAN数据库中吸收截面值将造成由于温度与压强变化导致的浓度反演误差。为了能够与实际监测环境相符合,采用实验室获取的吸收截面作为标准吸收截面。对单组分苯浓度的反演分别采用积分面积法和最小二乘法,研究表明两种方法的测量精度均能满足环保监测法规要求,且最小二乘法更加稳定、精度更高。针对BTX混合气体的测量,采用通过浓度值反演差分吸光度的方法进而逐一反演苯-甲苯-二甲苯的浓度值。研究发现对BTX混合物的浓度反演时二甲苯测量误差均在2%以下,但对甲苯和苯的测量误差逐渐增大,苯浓度的反演最大误差达到了9.07%,苯的测量精度受到了二甲苯、甲苯测量精度以及苯光谱特征吸收波段的影响。     

Active learning for spectroscopic data regression

In this work, we introduce an active learning approach for the estimation of chemical concentrations from spectroscopic data. Its main objective is to opportunely collect training samples in such a way as to minimize the error of the regression process while minimizing the number of training samples used, and thus to reduce the costs related to training sample collection. In particular, we propose two different active learning strategies developed for regression approaches based on partial least squares regression, ridge regression, kernel ridge regression, and support vector regression. The first strategy uses a pool of regressors in order to select the samples with the greatest disagreements among the different regressors of the pool, while the second one is based on adding samples that are distant from the current training samples in the feature space. For support vector regression, a specific strategy based on the selection of the samples distant from the support vectors is proposed. Experimental results on three different real data sets are reported and discussed. Copyright © 2012 John Wiley & Sons, Ltd.     

混合误差下回归函数小波估计的一致收敛速度

该文构造了回归函数的一类小波估计，在误差序列为ψ 混合或φ 混合下得到了小波估计的强一致收敛速度和狉阶矩一致收敛速度．     

Fracture complexity of pressure vessel steels

Abstract

Significant volume of literatures are already available in the published domain reporting the mechanical and fracture behaviour of different pressure vessel steels under various testing conditions and other potential circumstances. There have been limited researches available in the open domain to correlate the tensile properties of these steels with their corresponding fracture features at various testing temperatures, which are primarily aimed at in the current investigation. A comprehensive literature review has been performed to realise this fact critically. There has been high probability that fracture features are the signature of the entire deformation history which was operated in the material. In order to understand this hypothesis, many tensile experiments are carried out at a constant strain rate by systematic variation in temperature of a reactor pressure vessel steel. The initial inclusion content and their distribution pattern are kept unaltered for all the specimens before tests, and temperatures are varied methodically to vary the nucleation sites of micro-voids (i.e. carbides, phase interfaces, etc.) which result in change of ductile fracture features. Conventional metallographic technique has been employed to characterise the microstructures at various temperatures. Fractographic characterisation of all broken tensile specimens is done to measure the two-dimensional fracture features (i.e. dimple geometry, extent of tearing ridge pattern and dimple number density) under secondary mode of imaging in scanning electron microscope. Quantitative fractography and image processing have been extensively employed to measure the two-dimensional fractographic features. An excellent correlation has been drawn between the ductile fractographic features, microstructures and corresponding tensile properties of the material as a function of test temperature. This study brings to the fore that from the systematic fractographic features, it is possible to determine reasonably the mechanical and fracture properties of a material, when the microstructure is known.