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.     

双离心机法线加速度计动态校准中三参数余弦算法实现及应用

在双离心机的线加速度计动态校准中,三参数余弦算法贯穿在幅频特性、相频特性以及幅值线性度的整个测试中。本文详细描述了三参数余弦算法的概念和推导过程,以及在双离心机线加速度计动态校准数据处理过程中三参数余弦算法的程序实现;介绍了在幅频特性和相频特性中关于采集点的选取方式,降低由于采集点选择方式不同对数据拟合精度造成的影响。选取某型线加速度计为例,利用双离心机进行动态校准,对采集得到的数据点进行曲线拟合并得到测试结果,验证了所编写的三参数余弦算法程序的可行性。     

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.     

Spectral variable selection for partial least squares calibration applied to authentication and quantification of extra virgin olive oils using Fourier transform Raman spectroscopy

The limits of quantitative multivariate assays for the analysis of extra virgin olive oil samples from various Greek sites adulterated by sunflower oil have been evaluated based on their Fourier transform (FT) Raman spectra. Different strategies for wavelength selection were tested for calculating optimal partial least squares (PLS) models. Compared to the full spectrum methods previously applied, the optimum standard error of prediction (SEP) for the sunflower oil concentrations in spiked olive oil samples could be significantly reduced. One efficient approach (PMMS, pair-wise minima and maxima selection) used a special variable selection strategy based on a pair-wise consideration of significant respective minima and maxima of PLS regression vectors, calculated for broad spectral intervals and a low number of PLS factors. PMMS provided robust calibration models with a small number of variables. On the other hand, the Tabu search strategy recently published (search process guided by restrictions leading to Tabu list) achieved lower SEP values but at the cost of extensive computing time when searching for a global minimum and less robust calibration models. Robustness was tested by using packages of ten and twenty randomly selected samples within cross-validation for calculating independent prediction values. The best SEP values for a one year's harvest with a total number of 66 Cretian samples were obtained by such spectral variable optimized PLS calibration models using leave-20-out cross-validation (values between 0.5 and 0.7% by weight). For the more complex population of olive oil samples from all over Greece (total number of 92 samples), results were between 0.7 and 0.9% by weight with a cross-validation sample package size of 20. Notably, the calibration method with Tabu variable selection has been shown to be a valid chemometric approach by which a single model can be applied with a low SEP of 1.4% for olive oil samples across three different harvest years.     

Effect on the partial least-squares prediction of yarn properties combining raman and infrared measurements and applying wavelength selection

The combination of Raman and infrared spectroscopy on the one hand and wavelength selection on the other hand is used to improve the partial least-squares (PLS) prediction of seven selected yarn properties. These properties are important for on-line quality control during production. From 71 yarn samples, the Raman and infrared spectra are measured and reference methods are used to determine the selected properties. Making separate PLS models for all yarn properties using the Raman and infrared spectra, prior to wavelength selection, reveals that Raman spectroscopy outperforms infrared spectroscopy. If wavelength selection is applied, the PLS prediction error decreases and the correlation coefficient increases for all properties. However, a substantial wavelength selection effect is present for the infrared spectra compared to the Raman spectra. For the infrared spectra, wavelength selection results in PLS prediction errors comparable with the prediction performance of the Raman spectra prior to wavelength selection. Concatenating the Raman and infrared spectra does not enhance the PLS prediction performance, not even after wavelength selection. It is concluded that an infrared spectrometer, combined with a wavelength selection procedure, can be used if no (suitable) Raman instrument is available.     

Pure component selectivity analysis of multivariate calibration models from near-infrared spectra

A novel procedure is proposed as a method to characterize the chemical basis of selectivity for multivariate calibration models. This procedure involves submitting pure component spectra of both the target analyte and suspected interferences to the calibration model in question. The resulting model output is analyzed and interpreted in terms of the relative contribution of each component to the predicted analyte concentration. The utility of this method is illustrated by an analysis of calibration models for glucose, sucrose, and maltose. Near-infrared spectra are collected over the 5000-4000-cm(-)(1) spectral range for a set of ternary mixtures of these sugars. Partial least-squares (PLS) calibration models are generated for each component, and these models provide selective responses for the targeted analytes with standard errors of prediction ranging from 0.2 to 0.7 mM over the concentration range of 0.5-50 mM. The concept of the proposed pure component selectivity analysis is illustrated with these models. Results indicate that the net analyte signal is solely responsible for the selectivity of each individual model. Despite strong spectral overlap for these simple carbohydrates, calibration models based on the PLS algorithm provide sufficient selectivity to distinguish these commonly used sugars. The proposed procedure demonstrates conclusively that no component of the sucrose or maltose spectrum contributes to the selective measurement of glucose. Analogous conclusions are possible for the sucrose and maltose calibration models.     

矢量水听器低频绝对校准装置研究

提出了矢量水听器低频绝对校准装置。首先给出了矢量水听器绝对校准的原理,通过测量声源辐射面的加速度,利用驻波管中平面驻波声场中的声压、质点振速和质点加速度在垂直方向上的分布规律,得出了校准计算公式;之后对校准装置中平面驻波场在垂直方向上的分布规律进行了测量验证,并对测量用加速度计进行了校准;最后对待校矢量水听器的灵敏度和指向性进行了测试。结果表明:在10~315 Hz频带内,矢量水听器低频绝对校准装置在±1 d B误差允许范围内,可用于矢量水听器的绝对校准。     

加速度冲击校准研究

文章将加速度冲击校准分为绝对法、相对法和比较法进行介绍,并给出了几种半正弦冲击脉冲激励装置的激励范围及校准装置的测量范围和测量不确定度。所提出的加速度类比法系冲击校准新方法,是相对法和比较法的结合,能对冲击加速度传感器灵敏度、幅值线性度与频率响应等进行较为准确的检定与校准。     

高g值加速计和压电式力传感器的动态校准

本提出一种高g值加速度计的动态校准方法和装置,其最大加速度峰值超过100000g。这套装置还可以对压电式力传感器进行动态校准。中给出两个加速度计加速度峰值的二十余次实验结果,以及加速度计与力传感器的冲击响应实验曲线。同时,还求出它们的动态数学模型（包括差分模型、传递函数、频率特性）和动态性能指标。此外,还讨论了本的4个创新点。     

A novel approach for development of a multivariate calibration model using a Doehlert experimental design: Application for prediction of key gasoline properties by Near-infrared Spectroscopy

Alternative methods for quality control in the petroleum industry have been obtained using Near-infrared Spectroscopy (NIRS) combined with multivariate techniques such as PLS (Partial Least-Square). The process of development and refinement of PLS models usually follows a nonsystematic and univariate procedure. The Standard Error of Cross Validation (SECV), the Standard Error of Prediction (SEP) and the determination coefficient (r²_regr.) are usually the only guides used in pursuit of the best model. In the present work, a novel approach was proposed using a Doehlert experimental design with three input variables (wavenumber range, preprocessing technique and regression/validation technique) varied at 5, 7 and 3 levels, respectively. Besides SECV, SEP and r²_regr., some additional response variables, such as the slope, r² and p_value from the external validation, as well as the number of PLS factors, were simultaneously assessed to find the optimum conditions for PLS modeling. The optimum setting for each input variable was simultaneously defined through a multivariate approach using a desirability function. With the proposed approach, the main and interaction effects could also be investigated. The methodology was successfully applied to obtain PLS models to monitor the gasoline quality through the process of product loading in trucks. To prevent product contamination or adulteration, fast prediction of key properties was obtained from FT-NIR spectra within the 7300-3900 cm^− 1 region with SECV in the range 0.04-0.63% w/w for composition (Aromatics, Saturates, Olefins and Benzene) and 0.0008 for Relative Density 20/4 °C. Each optimized PLS model was obtained with less than 40 modeling runs, demonstrating the efficiency of the proposed approach.     

Forensic application of gas chromatography-differential mobility spectrometry with two-way classification of ignitable liquids from fire debris

With respect to the emerging role of forensic science for arson investigation, a low cost and promising onsite detection method for ignitable liquids is desirable. Gas chromatography-differential mobility spectrometry (GC-DMS) was investigated as a tool for analysis of ignitable liquids from fire debris. Headspace solid-phase microextraction (SPME) was applied as the preconcentration and sampling method. The combined information afforded by gas chromatography and differential mobility spectrometry provided unique two-way patterns for each sample of ignitable liquid. Two-way GC-DMS data were classified into one of seven ignitable liquids using a fuzzy rule-building expert system (FuRES). The performance of the classifier was validated using bootstrap Latin partitions (BLPs) and also compared to optimized partial least-squares (PLS) classifiers. Better prediction results can be obtained by using two-way GC-DMS data than only using one-way total ion chromatograms or integrated differential mobility spectra. FuRES models constructed with the neat ignitable liquids identified the spiked samples from simulated fire debris with 99.07 +/- 0.04% accuracy.     

Influence of temperature on vibrational spectra and consequences for the predictive ability of multivariate models

Temperature, pressure, viscosity, and other process variables fluctuate during an industrial process. When vibrational spectra are measured on- or in-line for process analytical and control purposes, the fluctuations influence the shape of the spectra in a nonlinear manner. The influence of these temperature-induced spectral variations on the predictive ability of multivariate calibration model is assessed. Short-wave NIR spectra of ethanol/water/2-propanol mixtures are taken at different temperatures, and different local and global partial least-squares calibration strategies are applied. The resulting prediction errors and sensitivity vectors of a test set are compared. For data with no temperature variation, the local models perform best with high sensitivity but the knowledge of the temperature for prediction measurements cannot aid in the improvement of local model predictions when temperature variation is introduced. The prediction errors of global models are considerably lower when temperature variation is present in the data set but at the expense of sensitivity. To be able to build temperature-stable calibration models with high sensitivity, a way of explicitly modeling the temperature should be found.     

Increasing robustness against changes in the interferent structure by incorporating prior information in the augmented classical least-squares framework

A class of multivariate calibration methods called augmented classical least squares (ACLS) has been proposed which combines an explicit linear additive model with the predictive power of inverse models, such as principal component regression (PCR) and partial least squares (PLS). Because of its use of the explicit linear additive model, ACLS provides an interesting framework to incorporate different sources of prior information, such as measured pure component spectra, in the model. In this study, the predictive power of ACLS models incorporating different amounts of prior information has been compared to that of PCR and PLS using two examples, a designed experiment and one with biological samples. In both cases, the ACLS models showed predictive power comparable to PLS under idealized validation conditions. When a different interferent structure was present in the validation samples, the predictive power of the inverse models (PCR and PLS) dramatically decreased, with an increase in root-mean-squared error of prediction by a factor of 3.5 for the first example and a factor of 2 in the second example. The incorporation of prior information in the ACLS framework was found to considerably reduce or even completely remove these dramatic effects, especially when the pure component contributions for the interferents were taken into account.     

Application of Fourier transform Raman spectroscopy for prediction of bitterness of peptides

The potential application of Fourier transform (FT) Raman spectroscopy to predict the bitterness of peptides was investigated. FT-Raman spectra were measured for the amino acid Phe and 9 synthetic di-, tri-, and tetra peptides composed of Phe, Gly, and Pro. Partial least squares regression (PLS)-1 analysis was applied to correlate the FT-Raman spectra with bitterness intensity values (R(caf) and log 1/T) reported in the literature. Using full cross-validation, Model 1 based on the single spectral data set for the nine peptides yielded a high correlation coefficient for calibration (R = 0.99), but a low correlation coefficient for prediction (R = 0.56). Two models were constructed using the data sets including replicate spectra for the calibrations and were validated using full cross-validation. Using leave-one-sample-set-out calibrations, Model 2, which was developed with the data for the peptides as well as Phe, yielded a low correlation coefficient (R = 0.533) for the prediction of the bitterness, while Model 3 developed with only the peptide data provided better correlation coefficients (R = 0.807 and 0.724 for R(caf) and log 1/T values, respectively). The correlation coefficients for prediction were 0.975 (R(caf) values) and 0.874 (log 1/T values) for Model 4, which was developed using subtracted spectral data (spectra of peptides with higher R(caf) values minus spectra of peptides with lower R(caf) values). Examination of the PLS regression coefficients at wavenumbers most highly correlated with bitterness revealed the importance of hydrophobicity and peptide length on bitterness. This study indicates the potential of FT-Raman spectroscopy as a useful tool for predicting bitterness of peptides and amino acids.     

A new boundary element method for resonance of an acoustic enclosure

Abstract

This paper presents a new boundary element formulation in which the eigenvalue appears outside the integral operator, which distinguishes it from the Helmholtz integral equation. Thus, the formation of global matrices need only be assembled once. Since the kernel of the operator used in the new formulation is real‐valued, all calculations can be carried out in a much simpler way in the real domain. The complex acoustic pressure amplitude is considered herein to deivate by a certain amount from a harmonic function. It is an important contribution that an exact relation between the deviator and the complex acoustic pressure amplitude is constructed locally and thus no more approximations are introduced except conventional boundary discretizations. Several examples are given to illustrate the feasibility of an accurate, effective prediction of resonance.     

绿茶汤中茶多酚近红外定量分析的光程选择

研究了光程对近红外定量分析绿茶汤中茶多酚的影响.以不同光程(1 mm,2 mm,5 mm)的样品池采集50个绿茶汤样品的近红外透射光谱.采用偏最小二乘法(PLS)建立茶汤中茶多酚的定量分析模型,并验证模型的准确度和精密度.结果表明,选择1 mm光程光谱建立的茶多酚定量分析模型最优,模型的校正集相关系数R2和内部交叉验证均方根RMSECV分别为91.08%和0.009 3%;检验集相关系数R2和预测标准差SEP为91.53%和0.008 5%;实际值与预测值配对t检验值为0.224 9,差异不显著.10次重复测量相对标准偏差RSD为0.008 7%,表明方法检测重复性好.     

A variable selection method based on uninformative variable elimination for multivariate calibration of near-infrared spectra

Variable (or wavelength) selection plays an important role in the quantitative analysis of near-infrared (NIR) spectra. A modified method of uninformative variable elimination (UVE) was proposed for variable selection in NIR spectral modeling based on the principle of Monte Carlo (MC) and UVE. The method builds a large number of models with randomly selected calibration samples at first, and then each variable is evaluated with a stability of the corresponding coefficients in these models. Variables with poor stability are known as uninformative variable and eliminated. The performance of the proposed method is compared with UVE-PLS and conventional PLS for modeling the NIR data sets of tobacco samples. Results show that the proposed method is able to select important wavelengths from the NIR spectra, and makes the prediction more robust and accurate in quantitative analysis. Furthermore, if wavelet compression is combined with the method, more parsimonious and efficient model can be obtained.     

Hemoglobin correction for near-infrared pH determination in lysed blood solutions

The near-infrared (NIR) measurement of blood pH relies on the spectral signature of histidine residing on the hemoglobin molecule. If the amount of hemoglobin in solution varies, the size of the histidine signal can vary depending on changes in either the pH or hemoglobin concentration. Multivariate calibration models developed using the NIR spectra collected from blood at a single hemoglobin concentration are shown to predict data from different hemoglobin levels with a bias and slope. A simple, scalar path length correction of the spectral data does not correct this problem. However, global partial least-square (PLS) models built with data encompassing a range of hemoglobin concentration have a cross-validated standard error of prediction (CVSEP) similar to the CVSEP of data obtained from a single hemoglobin level. It will be shown that the prediction of pH of an unknown sample using a global PLS model requires that the unknown have a hemoglobin concentration falling within the range encompassed by the global model. An alternative method for correcting the predicted pH for hemoglobin levels is also presented. The alternative method updates the single-hemoglobin-level models with slope and intercept estimates from the pH predictions of data collected at alternate hemoglobin levels. The slope and intercept correction method gave SEP values averaging to 0.034 pH units. Since both methods require some knowledge of the hemoglobin concentration in order for a pH prediction to be made, a model for hemoglobin concentration is developed using spectral data and is used for pH correction.     

Experimental measurements of the flow resistance and inductance of inertance tubes at high acoustic amplitudes

We measured the flow resistance and flow inductance of inertance tubes at high acoustic amplitudes for four different inner diameters of 0.6, 1.0, 1.5 and 2.0 mm at various tube length ranging from 100 to 1500 mm, at frequencies of 30, 40, 50, 60 and 70 Hz. The experiments were carried out under system mean pressure of 20 bar at room temperature. The experimental data were compared with the explicit solution to the linear momentum equation for small acoustic amplitudes and were fitted with the modification coefficients in terms of the operating frequency and Reynolds numbers characterized by the amplitude of gas velocities.