Effect of classification by competitive neural network on reconstruction of reflectance spectra using principal component analysis

The best way to describe a color is to study its reflectance spectrum, which provide the most useful information. Different methods were purposed for reflectance spectra reconstruction from CIE tristimulus values such as principal components analysis. In this study, the training samples were first divided into 3, 6, 9, and 12 subgroups by creating a competitive neural network. To do that, L*a*b*, L*C*h or L*a*b*C*h were introduced to neural network as input elements. In order to investigate the performance of reflectance spectra reconstruction, the color difference and RMS between actual and reconstructed data were obtained. The reconstruction of reflectance spectra were improved by using a six or nine‐neuron layer with L*a*b* input elements. © 2016 Wiley Periodicals, Inc. Col Res Appl, 42, 182–188, 2017     

基于加权互信息主元分析算法的质量相关故障检测

质量相关的故障检测已成为近几年研究热点,它的目标是在过程监测中,对质量相关的故障检测率更高,对质量无关的故障少报警或不报警。传统主元分析算法的故障检测会对所有故障均报警,不能达到上述要求。另外,在实际工业生产中,质量变量通常难以实时获得,需要后续分析或延时得到。为此,提出一种融合贝叶斯推断与互信息的加权互信息主元分析算法。首先利用贝叶斯推断的加权方法将度量过程变量和质量变量之间相关关系的互信息进行融合,选出包含质量变量信息量最大的一组过程变量。然后对过程变量利用主元分析（principal component analysis,PCA）进行统计建模,再次根据加权互信息选出包含质量变量信息量最大的主元,建立统计量进行故障检测。最后,通过实验验证该方法的可行性和有效性。     

Prediction of emission spectra of fluorescence materials using principal component analysis

Fluorescent materials are now a critical field of research due to their unique excitation and emission properties that can be tailored to specific fluorescence detection technologies. In this work, a procedure is described to approximate the emission spectral data of fluorescent materials of different types from their excitation spectral data using principal component analysis (PCA) technique. First, PCA as a statistical and mathematical method was used to reconstruct the excitation and emission spectra of training dataset and then, the approximation was accomplished by multiple linear regression (MLR).The performance of obtained function was examined on testing dataset. Afterward, CIE tristimulus values of the fluorescent samples were calculated based on ASTM, E2152–12 standard test method. The colorimetric accuracy was then evaluated by calculating the geometric differences in CIE tristimulus values X, Y, and Z for the 1964 standard colorimetric observer under illuminant D65. The obtained results show a good curve fit between the actual emission spectra and recovered emission spectra. In addition, based on cumulative variance and root mean square (RMS), eight principal components were selected as optimum number of principal components for prediction of emission spectra data. © 2015 Wiley Periodicals, Inc. Col Res Appl, 41, 16–21, 2016     

A hybrid adaptation strategy for reconstruction reflectance based on the given tristimulus values

Recently, Cao et al proposed an adaptive weighting method for the training samples for reflectance reconstruction according to both colorimetric and spectral reflectance similarities for a given vector defined by tristimulus values. It was shown the Cao et al method outperforms the other methods including the regression estimation method in terms of multiple evaluation criteria. In this article, motivated by the work of Cao et al, a hybrid weight is introduced, which results in the size of the training samples selected is half of that used by the Cao et al method. Simulation results showed that the proposed method performs equally well as or slightly better than the Cao et al method, but uses less central processing unit time than that used by the Cao et al method. It was also found that about 100 training samples selected is good enough for the proposed method.     

A review of principal component analysis and its applications to color technology

Principal component analysis, abbreviated PCA, has been an important and useful mathematical tool in color technology since the 1960s. Its uses have included defining tolerance intervals and ellipsoidal regions, estimating colorant spectral properties from mixtures, deriving CIE daylight, data reduction for large ensembles of spectra, and spectral imaging. Although PCA is a common topic in many engineering disciplines, statistics, and mathematics, many color‐technology professionals and color‐science students come from disciplines where this technique is not part of their curricula. It is from this perspective that this review publication was written. The purpose of this publication is to describe PCA and present examples in its use for colorant estimation, spectral data reduction, and defining multidimensional confidence regions for colorimetric scatter data. © 2005 Wiley Periodicals, Inc. Col Res Appl, 30, 84–98, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20086     

变量加权型主元分析算法及其在故障检测中的应用

传统主成分分析（PCA）算法旨在挖掘训练数据各变量间的相关性特征,已在数据驱动的故障检测领域得到了广泛的研究与应用。然而,传统PCA方法在建模过程中通常认为各个测量变量的重要性是一致的,因此不能有效而全面地描述出变量间相关性的差异。为此,提出一种变量加权型PCA（VWPCA）算法并将之应用于故障检测。首先,通过对训练数据进行加权处理,使处理后的数据能够充分体现出变量间相关性的差异。然后,在此基础上建立分布式的PCA故障检测模型。在线实施故障检测时,则通过贝叶斯准则将多组监测结果融合为一组概率指标。VWPCA方法通过相关性大小为各变量赋予不同的权值,从而将相关性差异考虑进了PCA的建模过程中,相应模型对训练数据特征的描述也就更全面。最后,通过在TE过程上的测试验证VWPCA方法用于故障检测的优越性。     

Reconstruction of reflectance data by modification of Berns' Gaussian method

Berns' method for the synthesis of spectral reflectance curve from the tristimulus color coordinates is modified. Firstly, the Gaussian bell shape red primary is replaced with a sigmoidal one to solve the dissimilarity between the spectral curves at the end region of spectrum. Secondly, three predetermined Gaussian primaries used in the original Berns' method are replaced by the adaptive ones which their half‐height bandwidths vary with the tristimulus values of the desired color. The mentioned modifications are applied for the recovery of the reflectance curves of 1409 surface colors (including 1269 Munsell color chips and 140 samples of Colorchecker SG) and also 204 textile samples. Results of recovery are evaluated by the mean and the maximum color difference values under other standard light sources. The mean as well as the maximum of root mean squares between the reconstructed and the actual spectra are also calculated. The modifications are compared with the common principal component analysis (PCA) as well as Hawkyard's methods for recovery of reflectance factor. Although the PCA leads to the best results, the modifications significantly improve the recovery outcomes in comparison with the original Berns method. © 2008 Wiley Periodicals, Inc. Col Res Appl, 34, 26–32, 2009.     

Performance of neural networks for predicting yarn properties using principal component analysis

In recent years, neural networks have been used as a tool for modeling an industrial process. An improvement in their performance may be expected either by divining more efficient training algorithms or by intelligently manipulating the data set. The second method is examined. The problem chosen is one of predicting the properties of cotton yarn from the fiber properties. When the input data are known to correlate with each other, principal component analysis can be used to improve the performance of neural networks. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 91: 1746–1751, 2004     

Improving the Hawkyard method for generating reflectance functions

An iterative method was developed by Hawkyard in 1993 for generating reflectance functions, based on a given set of tristimulus values. In a recent article by Dupont (Col Res Appl 2002;27:88–99), many methods for generating reflectance functions were compared, and it was shown that the Hawkyard method is one of the best methods. However, one of the weak points of the Hawkyard method is its iterative nature. In addition, one important issue for the Hawkyard method is its convergence, which has not been addressed. In this article, this issue is examined. The necessary and sufficient condition to achieve convergence, using the Hawkyard method, is given. The method is then modified to make it an analytical method. © 2005 Wiley Periodicals, Inc. Col Res Appl, 30, 283–287, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20126     

Nonlinear process monitoring using kernel principal component analysis

In this paper, a new nonlinear process monitoring technique based on kernel principal component analysis (KPCA) is developed. KPCA has emerged in recent years as a promising method for tackling nonlinear systems. KPCA can efficiently compute principal components in high-dimensional feature spaces by means of integral operators and nonlinear kernel functions. The basic idea of KPCA is to first map the input space into a feature space via nonlinear mapping and then to compute the principal components in that feature space. In comparison to other nonlinear principal component analysis (PCA) techniques, KPCA requires only the solution of an eigenvalue problem and does not entail any nonlinear optimization. In addition, the number of principal components need not be specified prior to modeling. In this paper, a simple approach to calculating the squared prediction error (SPE) in the feature space is also suggested. Based on T² and SPE charts in the feature space, KPCA was applied to fault detection in two example systems: a simple multivariate process and the simulation benchmark of the biological wastewater treatment process. The proposed approach effectively captured the nonlinear relationship in the process variables and showed superior process monitoring performance compared to linear PCA.     

Applying metamer sets to investigate data dependency of principal component analysis method in recovery of spectral data

Principal component analysis (PCA) has been widely studied for reconstruction of spectral reflectance of a color sample from its tristimulus values. One of the most important factors that influences the recovery performance is the characteristic of the data set used for obtaining principal vectors. In this article, we investigated the influence of color similarities or color differences between the recovered and principal component (PC) data sets on the reconstruction error. For this purpose, two metamer sets that have similar color differences with the recovered samples, are used. The results show that two metamer sets can make completely different performance in recovery of specific color samples. It was shown that the most important factor that influences the recovery of spectral reflectance by PCA method is the characteristics of the data set used for obtaining PC vectors independent of the recovered samples. Another factor that influences the performance of PCA for spectral recovery is the characteristic of the sample that would be recovered. Some spectral data cannot be recovered precisely even applying different PC data sets. © 2010 Wiley Periodicals, Inc. Col Res Appl, 2011     

Analysis of rat haunch odor using dynamic solvent effect and principal component analysis

We used the dynamic solvent effect to sample rat haunch odor, which we then analyzed using principal component analysis. PCA, based on 22 volatile components, indicated that one axis clearly separated rat haunch odor samples according to sex and female reproductive condition (estrus and diestrus), explaining 79.5% of the variation in proportional peak area. We have therefore been able to separate odors along biologically meaningful lines.     

A novel method for determination of compatibility of dyes by means of principal component analysis

A novel method for determination of the compatibility of dyes in mixtures based on the application of principal component analysis is presented. The well known dip‐test method is used to dye samples in different binary combinations of cationic dyestuffs. The spectral reflectance of different samples of each mixture that dyed with a given set of dyestuffs by dip‐test method has been measured and the corresponding K/S values are calculated. The actual dimensional properties of each mixture are evaluated by using principal component analysis technique and determination of cumulative percentage variance of the eigenvalues of proposed datasets. Ideally, the K/S spectral data of fully compatible pairs scatter around one dimension, while proportional to the degree of incompatibility of dyes in the mixture, other dimensions should be taken into account and cannot be ignored. Strong correlations are found between the calculated percentage variance and the traditional compatibility values of dyes shown by K value for cationic dyestuffs. The validity of suggested technique is also reconfirmed by normalization of spectral K/S data obtained from different dye sets. © 2010 Wiley Periodicals, Inc. Col Res Appl, 2010     

主元空间中的故障分离与识别方法

主元分析 (PCA)作为数据驱动的一种统计建模方法,在化工产品质量控制与故障诊断方面得到广泛研究和应用.在故障重构技术的基础上,研究了基于T²统计量的故障分离和识别问题,分别获得了主元空间中故障可分离和识别的理论条件.以双效蒸发过程为例,对该生产过程中的10种不同故障进行仿真监测分析,证实了所获理论结果的有效性.     

Fault identification for process monitoring using kernel principal component analysis

In this research, we develop a new fault identification method for kernel principal component analysis (kernel PCA). Although it has been proved that kernel PCA is superior to linear PCA for fault detection, the fault identification method theoretically derived from the kernel PCA has not been found anywhere. Using the gradient of kernel function, we define two new statistics which represent the contribution of each variable to the monitoring statistics, Hotelling's T²and squared prediction error (SPE) of kernel PCA, respectively. The proposed statistics which have similar concept to contributions in linear PCA are directly derived from the mathematical formulation of kernel PCA and thus they are straightforward to understand. The main contribution of this work is that we firstly suggest a fault identification method especially applicable to process monitoring using kernel PCA. To demonstrate the performance, the proposed method is applied to two simulated processes, one is a simple nonlinear process and the other is a non-isothermal CSTR process. The simulation results show that the proposed method effectively identifies the source of various types of faults.     

Using weighted pseudo‐inverse method for reconstruction of reflectance spectra and analyzing the dataset in terms of normality

Most of spectral estimation methods are based on improving the learning‐based procedures which mainly modify the training sets used by the basic methods. In this article, a new method is developed for analyzing of superiority of these modified processes to the basic methods in terms of normality of datasets. Hence, two qualitative terms, named generality and similarity are introduced to interpret the recovery achievements of different databases and their roles as training and testing sets. Also, a simple technique based on dataset modification of pseudo‐inverse method is introduced for the recovery of reflectance spectra of samples from their corresponding colorimetric data. The method modifies the training dataset according to the color specifications of test sample. In fact, different weighting matrices are employed as dynamic modifiers to improve the pseudo‐inverse estimation as a simple recovery method. The employed datasets are examined in the self as well as cross test conditions and the results are spectrally and colorimetrically evaluated. The root mean square errors between the reconstructed and actual spectra along with the corresponding color difference values under different illuminants decrease by employing the suggested modification method in comparison to classical pseudo‐inverse technique as well as the recently improved version named optimized adaptive Wiener method. © 2010 Wiley Periodicals, Inc. Col Res Appl, 2010     

Detection of olive oil adulteration using principal component analysis applied on total and regio FA content

Principal component analysis (PCA) has been used to establish a new method for the detection of olive oil adulteration. The data set, composed of values obtained from the determination of the mole percentage of total FA and their regiospecific distribution in positions 1 and 3 in TG of oils (pure or mixtures) by GC analysis, was subjected to PCA. 3-D scatter plots showed clearly that it is possible to distinguish the pure oils from the mixtures. Moreover it is possible to discriminate the different types of seed oil used for the adulteration.     

Ultraviolet‐induced crosslinking of poly(vinyl alcohol) evaluated by principal component analysis of FTIR spectra

The crosslinking of poly(vinyl alcohol) (PVA) films under ultraviolet irradiation for between 1 and 4 h was studied in air at 25 °C in the presence of sodium benzoate by Fourier‐transform infrared spectroscopy (FTIR) using the attenuated total reflectance technique (ATR). Principal component analysis (PCA) is a mathematical procedure that allows treatment of the entire infrared spectrum and is very appropriate for analysing the chemical modifications initiated by sodium benzoate which occur in PVA upon UV irradiation. By PCA it was possible to clarify the mechanism of crosslinking of PVA. From this FTIR–PCA study, it is suggested that a free radical arising from the photolysis of sensitizer would abstract a tertiary hydrogen atom from the polymer chain to yield a polymeric radical. This radical reacts with O? H groups, leading to the formation of ether bonds between the polymeric chains and hence to crosslinking and insolubilization of the PVA. © 2001 Society of Chemical Industry     

On-line batch process monitoring using a consecutively updated multiway principal component analysis model

Batch processes lie at the heart of many industries; hence the effective monitoring and control of batch processes is crucial to the production of high-quality materials. Multiway principal component analysis (MPCA) has been widely used for batch monitoring and has proved to be an effective method for monitoring many industrial batch processes. However, because MPCA is a fixed-model monitoring technique, it gives false alarms when it is used to monitor real processes whose normal operation involves slow changes. In this paper, we propose a simple on-line batch monitoring method that uses a consecutively updated MPCA model. The key to the proposed approach is that whenever a batch successfully remains within the bounds of normal operation, its batch data are added to the historical database of normal data and a new MPCA model is developed based on the revised database. The proposed method was applied to monitoring fed-batch penicillin production, and the results were compared with those obtained using conventional MPCA. The simulation results clearly show that the ability of the proposed method to adapt to new normal operating conditions eliminates the many false alarms generated by the fixed model and provides a reliable monitoring chart.     

Molecular reconstruction of complex hydrocarbon mixtures: An application of principal component analysis

Three methods for reconstruction of the detailed molecular composition of complex hydrocarbon mixtures, based on their global properties, are compared: a method based on the Shannon entropy criterion, an artificial neural network and a multiple linear regression model. In spite of the broad range of naphthas included in the training set, the application range of the last two methods proved to be limited. Principal component analysis allowed to identify their three‐dimensional ellipsoidal application range. In this subspace, the artificial neural network is more accurate than the multiple linear regression model and the Shannon entropy method. However, outside its application range, the performance of the neural network, as well as the regression model, decreases drastically. In contrast, the performance of the Shannon entropy method is not influenced by the characteristics of the considered naphtha, but rather depends on the number of available commercial indices. The Shannon entropy method yields comparable results to the artificial neural network, provided that a sufficient amount of distillation data is available to supply information on the carbon number distribution. Combining the reconstruction methods with a fundamental simulation model illustrates the necessity of having accurate feedstock reconstruction methods since they allow to capture the full power of fundamental simulation models for the simulation of industrial processes. © 2010 American Institute of Chemical Engineers AIChE J, 2010