An Efficient Procedure for Identifying the Prediction Model Between Residual Stress and Barkhausen Noise

Residual stress of case-hardened steel samples is predicted in this paper with the linear multivariable regression model. The development of the prediction model is based on the huge set of features calculated from the Barkhausen noise measurement signal among which the most suitable ones are chosen. The selection uses a genetic algorithm with leave-multiple-out cross-validation in the objective function. The original feature set contains collinear features that make the selection task even more complex. Thus a feature elimination procedure based on the successive projections algorithm is studied in this paper. Also the standard genetic algorithm is slightly modified to better serve the feature selection task. The obtained results are good showing that the proposed procedures suit well for residual stress predictions. Also the applied feature elimination procedure is applicable and can be safely used to reduce the dimensionality of the selection problem.     

Optimization of informative spectral variables for the quantification of EGCG in green tea using Fourier transform near-infrared (FT-NIR) spectroscopy and multivariate calibration

Epigallocatechin-3-gallate (EGCG) is credited with the majority of the health benefits associated with green tea consumption. It has a high economic and medicinal value. The feasibility of using different variable selection approaches in Fourier transform near-infrared (FT-NIR) spectroscopy for a rapid and conclusive quantitative determination of EGCG in green tea was investigated. Graphically oriented multivariate calibration modeling procedures such as interval partial least squares (iPLS), synergy interval partial least squares (siPLS), and genetic algorithm optimization combined with siPLS (siPLS-GA) were applied to select the most efficient spectral variables that provided the lowest prediction error. The performance of the final model was evaluated according to the root mean square error of prediction (RMSEP) and coefficient of determination (R(2)) for the prediction set. Experimental results showed that the siPLS-GA model obtained the best results in comparison to other models. The optimal models were achieved with R(2)(p) = 0.97 and RMSEP = 0.32. The model can be obtained with only 36 variables retained and it provides a robust model with good estimation accuracy. This demonstrates the potential of NIR spectroscopy with multivariate calibration methods to quickly detect the bioactive component in green tea.     

A variable selection procedure for X-ray diffraction phase analysis

The X-ray diffraction method has been widely used for qualitative and quantitative phase abundance analysis of crystalline materials. We propose the use of partial least squares when building the calibration model for a quantitative phase analysis based on X-ray diffraction spectra. We also propose a variable selection procedure to reduce the measurement points in terms of angles as an alternative to using the whole pattern. The proposed method is based on the variable importance in projection derived from the partial least squares and it considers some practical issues regarding the angle measurement. The method was particularly applied to the simultaneous determination of weight fractions of some iron oxides. It was found that the number of measurement points can be reduced to 30 percent of the total number of points with a small sacrifice in prediction error.     

Effects of nonlinearities and uncorrelated or correlated errors in realistic simulated data on the prediction abilities of augmented classical least squares and partial least squares

Comparisons of prediction models from the new augmented classical least squares (ACLS) and partial least squares (PLS) multivariate spectral analysis methods were conducted using simulated data containing deviations from the idealized model. The simulated data were based on pure spectral components derived from real near-infrared spectra of multicomponent dilute aqueous solutions. Simulated uncorrelated concentration errors, uncorrelated and correlated spectral noise, and nonlinear spectral responses were included to evaluate the methods on situations representative of experimental data. The statistical significance of differences in prediction ability was evaluated using the Wilcoxon signed rank test. The prediction differences were found to be dependent on the type of noise added, the numbers of calibration samples, and the component being predicted. For analyses applied to simulated spectra with noise-free nonlinear response, PLS was shown to be statistically superior to ACLS for most of the cases. With added uncorrelated spectral noise, both methods performed comparably. Using 50 calibration samples with simulated correlated spectral noise, PLS showed an advantage in 3 out of 9 cases, but the advantage dropped to 1 out of 9 cases with 25 calibration samples. For cases with different noise distributions between calibration and validation, ACLS predictions were statistically better than PLS for two of the four components. Also, when experimentally derived correlated spectral error was added, ACLS gave better predictions that were statistically significant in 15 out of 24 cases simulated. On data sets with nonuniform noise, neither method was statistically better, although ACLS usually had smaller standard errors of prediction (SEPs). The varying results emphasize the need to use realistic simulations when making comparisons between various multivariate calibration methods. Even when the differences between the standard error of predictions were statistically significant, in most cases the differences in SEP were small. This study demonstrated that unlike CLS, ACLS is competitive with PLS in modeling nonlinearities in spectra without knowledge of all the component concentrations. This competitiveness is important when maintaining and transferring models for system drift, spectrometer differences, and unmodeled components, since ACLS models can be rapidly updated during prediction when used in conjunction with the prediction augmented classical least squares (PACLS) method, while PLS requires full recalibration.     

Cyclic subspace regression with analysis of the hat matrix

Cyclic subspace regression (CSR) is a new approach to the complex multivariate calibration problem. The simple algorithm produces solutions for principal component regression (PCR), partial least squares (PLS), least squares (LS), and other related intermediate regressions. This paper describes further analysis of CSR and shows that by using hat matrices, CSR regression vectors are formed from a summation of weighted eigenvectors where weights are determined from the hat matrix, singular values, and sample space eigenvectors. Examination of CSR weights for PCR and PLS further documents differences and similarities and provides information to assist in determining prediction rank for PCR and PLS. By redefining CSR in terms of weighted eigenvectors, it can be shown when PLS and PCR produce essentially the same results where minor differences stem from overfitting by PLS. Additionally, weights derived from the hat matrix show when PCR and PLS generate different results and why. Equations are shown for the sample space that reveal PLS to be a method based on oblique projections while PCR uses orthogonal projections. The optimal intermediate CSR model can be identified as well. A near infrared data set is studied and illustrates principles involved.     

一种基于图像特征提取的浮选回收率预测算法

针对矿物浮选过程中的一类回收率预测问题,提出了一种基于泡沫图像特征提取的预测算法.该算法采用最小二乘支持向量机(LSSVM)建立预测模型,通过施密特正交化对核矩阵进行简约,利用核偏最小二乘方法(KPLS)进行LSSVM参数辨识,以此构造具有稀疏性的LSSVM,有效地减小了算法的计算复杂度.为检验模型泛化及预测能力,为多个泡沫特征信息引入预测模型,采用泡沫图像特征提取方法提取泡沫颜色、速度、尺寸、承载量及破碎率特征.实验结果表明,该预测算法对浮选回收率具有良好预测效果.     

时延系统中T-LSSVR动态软测量建模方法研究

针对工业过程中由于系统存在延时导致软测量模型难以建立、模型精度偏低等问题,提出将系统延时(T)与最小二乘支持向量回归机(LSSVR)相结合,构建一种基于T-LSSVR的动态软测量建模方法;该方法在建模过程中利用互相关函数与一阶广义差分算法辨识得到“静态响应延时”和“动态响应延时”,通过软测量手段对变量进行预测以实现辅助变量对主导变量的最佳估计。对某化工企业具有此类双延时性质的系统进行实验,实验结果表明该建模方法在动态和稳态数据预测方面都有良好的预测效果。     

基于改进偏最小二乘的CMM动态误差混合建模分析

三坐标测量机(CMM)动态误差源错综复杂,并且相互影响,因此很难建立一个通过误差源分析误差的准确预测模型.本文以空间测量位置的三维坐标值和测量机测量时的计算机直接控制(DCC)参数,包括移动速度、逼近距离和触测速度作为CMM动态测量误差模型的原始自变量,并通过3B样条变换获得各原始自变量与动态测量误差的非线性关系函数,再利用正交投影法把解释矩阵中与因变量无关的成分扣除掉,得到新的解释矩阵后再用偏最小二乘(PLS)回归进行降维和参数估计,从而得到CMM动态测量误差模型,即基于3B样条-正交投影偏最小二乘(3BS-OPPLS)模型.这样既避免了分析错综复杂的误差源及其相互影响,又能够捕捉各自变量对动态测量误差的非线性影响,并能克服因解释变量过多而产生的多重共线性问题.实验结果表明建立的3BS-OPPLS模型的预测效果优于未经正交投影的3B样条-偏最小二乘(3BS-PLS)模型,模型的预测精度得到显著提高.     

Comparison of linear and nonlinear calibration models based on near infrared (NIR) spectroscopy data for gasoline properties prediction

Six popular approaches of «NIR spectrum–property» calibration model building are compared in this work on the basis of a gasoline spectral data. These approaches are: multiple linear regression (MLR), principal component regression (PCR), linear partial least squares regression (PLS), polynomial partial least squares regression (Poly-PLS), spline partial least squares regression (Spline-PLS) and artificial neural networks (ANN). The best preprocessing technique is found for each method. Optimal calibration parameters (number of principal components, ANN structure, etc.) are also found. Accuracy, computational complexity and application simplicity of different methods are compared on an example of prediction of six important gasoline properties (density and fractional composition). Errors of calibration using different approaches are found. An advantage of neural network approach to solution of «NIR spectrum–gasoline property» problem is illustrated. An effective model for gasoline properties prediction based on NIR data is built.     

基于电磁检测的火车车轮残余应力定量预测

目的 为了突破火车车轮残余应力有损测试的局限性、实现车轮残余应力的准确定量预测,研究电磁参量特征值的遴选过程并建立相关模型。方法 对比分析单一电磁参量(磁巴克豪森噪声或增量磁导率)和电磁参量融合(磁巴克豪森噪声和增量磁导率)的检测方法,通过逐步回归对电磁参量的特征值进行遴选,利用多元线性回归方法构建残余应力的定量预测模型。结果 基于单一电磁参量建立的应力预测模型,其残余应力预测值与实际值的偏差超过±15 MPa的允差范围;基于电磁参量融合建立的应力预测模型,其残余应力预测值与实际值的偏差均在±15 MPa的允差范围之内。结论 采用电磁融合方法建立的多元线性模型,可以有效提高模型精度、实现火车车轮残余应力的定量预测。     

Blank augmentation protocol for improving the robustness of multivariate calibrations

An updating procedure is described for improving the robustness of multivariate calibration models based on near-infrared spectroscopy. Employing a single blank sample containing no analyte, repeated spectra are acquired during the instrumental warm-up period. These spectra are used to capture the instrumental profile on the analysis day in a way that can be used to update a previously computed calibration model. By augmenting the original spectra of the calibration samples with a group of spectra collected from the blank sample, an updated model can be computed that incorporates any instrumental drift that has occurred. This protocol is evaluated in the context of an analysis of physiological levels of glucose in a simulated biological matrix designed to mimic blood plasma. Employing data of calibration and prediction samples acquired over approximately six months, procedures are studied for implementing the algorithm in conjunction with calibration models based on partial least squares (PLS) regression. Over the range of 1-20 mM glucose, the final algorithm achieves a standard error of prediction (SEP) of 0.79 mM when the augmented PLS model is applied to data collected 176 days after the collection of the calibration spectra. Without updating, the original PLS model produces a seriously degraded SEP of 13.4 mM.     

Cyclic subspace regression with analysis of wavelength-selection criteria

Common methods of building linear calibration models are principal component regression (PCR), partial least squares (PLS), and least squares (LS). Recently, the method of cyclic subspace regression (CSR) has been presented and shown to provide PCR, PLS, LS and other related intermediate regressions with one algorithm. When forming a linear model with spectral data for quantitative analysis, prediction results can be adversely affected by responses that do not conform well to the linear model proposed. Wavelength selection can be used to eliminate wavelengths where such problem responses occur. It has recently been reported that CSR regression vectors can be formed by summing weighted eigenvectors where weights are determined from the hat matrix, singular values, and eigenvectors characterizing the sample space. Investigation of these weights shows that wavelength selection based on loading vectors can be misleading. Specifically, by using CSR it is shown that a small weight for an eigenvector can annihilate a large peak in a loading vector. In this study, correlograms are used with CSR regression vectors and eigenvector weights as wavelength-selection criteria. It is demonstrated that even though a model generated by LS for a wavelength subset produces substantially reduced prediction errors relative to PCR and PLS, CSR weight plots show that the LS model overfits and should not be used. Simulated situations containing spectral regions with excess noise or nonlinear responses are examined to study the effectiveness of wavelength selection based on the previously listed criteria. Near infrared spectra of gasoline samples with several known properties are also studied.     

Elastic net grouping variable selection combined with partial least squares regression (EN-PLSR) for the analysis of strongly multi-collinear spectroscopic data

In this paper a novel wavelength region selection algorithm, called elastic net grouping variable selection combined with partial least squares regression (EN-PLSR), is proposed for multi-component spectral data analysis. The EN-PLSR algorithm can automatically select successive strongly correlated prediction variable groups related to the response variable using two steps. First, a portion of the correlated predictors are selected and divided into subgroups by means of the grouping effect of elastic net estimation. Then, a recursive leave-one-group-out strategy is employed to further shrink the variable groups in terms of the root mean square error of cross-validation (RMSECV) criterion. The performance of the algorithm with real near-infrared (NIR) spectroscopic data sets shows that the EN-PLSR algorithm is competitive with full-spectrum PLS and moving window partial least squares (MWPLS) regression methods and it is suitable for use with strongly correlated spectroscopic data.     

Analysis of Barkhausen noise using wavelet-based fractal signal processing for fatigue crack detection

The paper presents new approach to Barkhausen noise signal processing for detection of fatigue crack. Barkhausen noise signal from mild steel samples under axial fatigue is investigated using fractal signal processing, particularly wavelet variance method. Based on repeatability analysis new algorithm is developed and applied to acquired signals. The influence of fatigue on fractal characteristics of Barkhausen noise is analyzed. Signal analysis reveals significant and repeatable changes in wavelet variance, spectral parameter and estimated Hurst exponent just after crack initiation. The results demonstrate high potential of fractal analysis of Surface Barkhausen noise applied to fatigue crack initiation detection.     

近红外光谱小波投影寻踪回归定量分析方法研究

为改进近红外光谱结构特征与定量回归模型的非线性拟合度和充分利用光谱中的非线性特征,提出了一种光谱小波投影寻踪定量分析方法。该方法对光谱进行小波分解后,用高斯混合模型噪声估计法降噪,对降噪后的小波系数向最优投影方向降维,用多项式岭函数拟合定量回归关系。建立黄酒近红外光谱快速预测酒精度小波投影寻踪回归模型,其相关系数R2和交叉检验标准差RMSECV分别为0.957和0.37838,该法比分析多元线性回归和偏最小二乘回归定量分析2种常规定量分析方法具有更优的预测效果,能更为有效地应用于近红外光谱快速定量分析检测。     

Extracting coal ash content from laser-induced breakdown spectroscopy (LIBS) spectra by multivariate analysis

Laser-induced breakdown spectroscopy (LIBS) combined with partial least squares (PLS) analysis has been applied for the quantitative analysis of the ash content of coal in this paper. The multivariate analysis method was employed to extract coal ash content information from LIBS spectra rather than from the concentrations of the main ash-forming elements. In order to construct a rigorous partial least squares regression model and reduce the calculation time, different spectral range data were used to construct partial least squares regression models, and then the performances of these models were compared in terms of the correlation coefficients of calibration and validation and the root mean square errors of calibration and cross-validation. Afterwards, the prediction accuracy, reproducibility, and the limit of detection of the partial least squares regression model were validated with independent laser-induced breakdown spectroscopy measurements of four unknown samples. The results show that a good agreement is observed between the ash content provided by thermo-gravimetric analyzer and the LIBS measurements coupled to the PLS regression model for the unknown samples. The feasibility of extracting coal ash content from LIBS spectra is approved. It is also confirmed that this technique has good potential for quantitative analysis of the ash content of coal.     

NNPLS方法在顾客满意度测评中的应用

分析了顾客满意度测评模型中各变量间存在的非线性关系,将神经网络偏最小二乘法(NNPLS)应用到顾客满意度测评中.算例的计算结果表明,与传统顾客满意度测评模型所采用的偏最小二乘法,以及神经网络的方法相比,NNPLS具有更高的拟合精度和较低的预测误差.因此NNPLS在顾客满意、顾客忠诚与其影响因素之间建立了一个稳健的模型,并为顾客满意度测评提供一种新的思路.     

Application of Vis–NIR hyperspectral imaging in classification between fresh and frozen-thawed pork Longissimus Dorsi muscles

Fresh and frozen-thawed (F-T) pork meats were classified by Vis–NIR hyperspectral imaging. Eight optimal wavelengths (624, 673, 460, 588, 583, 448, 552 and 609 nm) were selected by successive projections algorithm (SPA). The first three principal components (PCs) obtained by principal component analysis (PCA) accounted for over 99.98% of variance. Gray-level-gradient co-occurrence matrix (GLGCM) was applied to extract 45 textural features from the PC images. The correct classification rate (CCR) was employed to evaluate the performance of the partial least squares-discriminate analysis (PLS-DA) models, by using (A) the reflected spectra at full wavelengths and (B) those at the optimal wavelengths, (C) the extracted textures based on the PC images, and (D) the fused variables combining spectra at the optimal wavelengths and textures. The results showed that the best CCR of 97.73% was achieved by applying (D), confirming the high potential of textures for fresh and F-T meat discrimination.     

A new array decomposition method for multiway data analysis

In chemometrics, two-way singular value decomposition (SVD), CANDECOMP-PARAFAC decomposition (PARAFAC), and Tucker decomposition (TUKER) are three main array decomposition methods. There are disadvantages with the three methods. If multiway data are indeed multilinear, PARAFAC and TUCKER can provide more robust and interpretable models compared to two-way SVD. However, PARAFAC is sometimes numerically unstable, and TUCKER cannot guarantee the uniqueness of an approximate solution. This paper proposes a new array decomposition model with multiple bilinear structure. Then, utilizing this model, a new method, called multiple bilinear decomposition (MBD), is proposed as a generalization of two-way SVD. An algorithm is established to successively decompose an array without a full decomposition, which is not based on alternating least squares. Theoretically, the proposed method has an advantage over PARAFAC and TUCKER in its three important properties, including orthonormality of loading vectors, closed-form decomposition, and successive decomposition of variation. The simulation results based on orthogonal PARAFAC models show that the proposed method outperforms PARAFAC with respect to accuracy and robustness of loading estimate and data-fitting of model, even though the former does not use the priori information of multilinear structure. And, especially in the simulation under no noise, the equivalence of loading estimates indicates that as a successive decomposition, MBD is a superior alternative to PARAFAC.     

Discordance between net analyte signal theory and practical multivariate calibration

Lorber's concept of net analyte signal is reviewed in the context of classical and inverse least-squares approaches to multivariate calibration. It is shown that, in the presence of device measurement error, the classical and inverse calibration procedures have radically different theoretical prediction objectives, and the assertion that the popular inverse least-squares procedures (including partial least squares, principal components regression) approximate Lorber's net analyte signal vector in the limit is disproved. Exact theoretical expressions for the prediction error bias, variance, and mean-squared error are given under general measurement error conditions, which reinforce the very discrepant behavior between these two predictive approaches, and Lorber's net analyte signal theory. Implications for multivariate figures of merit and numerous recently proposed preprocessing treatments involving orthogonal projections are also discussed.