Use of Raman microscopy and band-target entropy minimization analysis to identify dyes in a commercial stamp. Implications for authentication and counterfeit detection

Raman microscopy was used in mapping mode to collect more than 1000 spectra in a 100 microm x 100 microm area from a commercial stamp. Band-target entropy minimization (BTEM) was then employed to unmix the mixture spectra in order to extract the pure component spectra of the samples. Three pure component spectral patterns with good signal-to-noise ratios were recovered, and their spatial distributions were determined. The three pure component spectral patterns were then identified as copper phthalocyanine blue, calcite-like material, and yellow organic dye material by comparison to known spectral libraries. The present investigation, consisting of (1) advanced curve resolution (blind-source separation) followed by (2) spectral data base matching, readily suggests extensions to authenticity and counterfeit studies of other types of commercial objects. The presence or absence of specific observable components form the basis for assessment. The present spectral analysis (BTEM) is applicable to highly overlapping spectral information. Since a priori information such as the number of components present and spectral libraries are not needed in BTEM, and since minor signals arising from trace components can be reconstructed, this analysis offers a robust approach to a wide variety of material problems involving authenticity and counterfeit issues.     

Band-target entropy minimization. A robust algorithm for pure component spectral recovery. Application to complex randomized mixtures of six components

A newly developed self-modeling curve resolution method, band-target entropy minimization (BTEM), is described. This method starts with the data decomposition of a set of spectroscopic mixture data using singular value decomposition. It is followed by the transformation of the orthonormal basis vectors/loading vectors into individual pure component spectra one at a time. The transformation is based in part on some seminal ideas borrowed from information entropy theory with the desire to maximize the simplicity of the recovered pure component spectrum. Thus, the proper estimate is obtained via minimization of the proposed information entropy function or via minimization of derivative and area of the spectral estimate. Nonnegativity constraints are also imposed on the recovered pure component spectral estimate and its corresponding concentrations. As its name suggests, in this method, one targets a spectral feature readily observed in loading vectors to retain, and then combinations of the loading vectors are searched to achieve the global minimum value of an appropriate objective function. The major advantage of this method is its one spectrum at a time approach and its capability of recovering minor components having low spectroscopic signals. To illustrate the application of BTEM, spectral resolution was performed on FT-IR measurements of very highly overlapping mixture spectra containing six organic species with a two-component background interference (air). BTEM estimates were also compared with the estimates obtained using other self-modeling curve resolution techniques, i.e., SIMPLISMA, IPCA, OPA-ALS, and SIMPLISMA-ALS.     

Constrained nonlinear method for estimating component spectra from multicomponent mixtures

A method is described for estimating the spectra of pure components from the spectra of unknown mixtures with various relative concentrations. This method is based on principal component analysis and a constrained nonlinear optimization technique and is applicable to qualitative analysis of mixtures of more than three components. The method gives two curves as the estimate of a component spectrum: one consists of the set of the maxima and the other consists of the set of the minima for all sampling points subject to a priori information. Experimental results of the estimation of the infrared absorption spectra of xylene-isomer mixtures are shown; the noise problem with this method is also discussed.     

Spectral pattern recognition of in situ FT-IR spectroscopic reaction data using minimization of entropy and spectral similarity (MESS): application to the homogeneous rhodium catalyzed hydroformylation of isoprene

An improved algorithm using minimization of entropy and spectral similarity (MESS) was tested to recover pure component spectra from in situ experimental Fourier transform infrared (FT-IR) reaction spectral data, which were collected from a homogeneous rhodium catalyzed hydroformylation of isoprene. The experimental spectra are complicated and highly overlapping because of the presence of multiple intermediate products in this reaction system. The traditional entropy minimization method fails to resolve real reaction mixture spectra, but MESS can successfully reconstruct pure component spectra of unknown intermediate products for real reaction systems by the addition of minimization of spectral similarity. The quantitative measure of spectral similarity between two spectra was given by their inner products. The results indicate that MESS is a stable and useful algorithm for spectral pattern recognition of highly overlapped experimental reaction spectra. Comparison is also made between MESS, entropy minimization, simple-to-use interactive self-modeling mixture analysis (SIMPLISMA), interactive principle component analysis (IPCA), and orthogonal projection approach-alternating least squares (OPA-ALS).     

Development of 2D band-target entropy minimization and application to the deconvolution of multicomponent 2D nuclear magnetic resonance spectra

Spectral reconstruction from multicomponent spectroscopic data is the frequent primary goal in chemical system identification and exploratory chemometric studies. Various methods and techniques have been reported in the literature. However, few algorithms/methods have been devised for spectral recovery without the use of any a priori information. In the present studies, a higher dimensional entropy minimization method based on the BTEM algorithm (Widjaja, E.; Li, C.; Garland, M. Organometallics 2002, 21, 1991-1997.) and related techniques were extended to large-scale arrays, namely, 2D NMR spectroscopy. The performance of this novel method had been successfully verified on various real experimental mixture spectra from a series of randomized 2D NMR mixtures (COSY NMR and HSQC NMR). With the new algorithm and raw multicomponent NMR alone, it was possible to reconstruct the pure spectroscopic patterns and calculate the relative concentration of each species without recourse to any libraries or any other a priori information. The potential advantages of this novel algorithm and its implications for general chemical system identification of unknown mixtures are discussed.     

Evaluation techniques for two-way data from in situ fourier transform mid-infrared reaction monitoring in aqueous solution

A model chemical reaction was monitored with in situ Fourier transform mid-infrared spectroscopy using an attenuated total reflectance probe. The evaluation of the IR spectra is complicated by the fact that the reaction runs in nonisothermal aqueous solution with large variations in pH. Despite this, it was possible to extract large amounts of useful information on the reaction after suitable pretreatment of the spectra. Alternating least-squares (ALS) multivariate curve resolution is shown to be a useful technique for obtaining pure component spectra and concentrations if suitable spectral regions are analyzed. Rank mapping methods are used as the basis for this sectioning into smaller regions. Techniques for finding and analyzing selective spectral regions are also shown to be applicable to this type of data. Partial least-squares (PLS) regression models based on spectral data were used to verify the results where possible. The correlation between the concentrations predicted from PLS and ALS is excellent.     

Identification of pure component spectra by independent component analysis in glucose prediction based on mid-infrared spectroscopy

We present a method for glucose prediction from mid-IR spectra by independent component analysis (ICA). This method is able to identify pure, or individual, absorption spectra of constituent components from the mixture spectra without a priori knowledge of the mixture. This method was tested with a two-component system consisting of an aqueous solution of both glucose and sucrose, which exhibit distinct but closely overlapped spectra. ICA combined with principal component analysis was able to identify a spectrum for each component, the correct number of components, and the concentrations of the components in the mixture. This method does not need a calibration process and is advantageous in noninvasive glucose monitoring since expensive and time-consuming clinical tests for data calibration are not required.     

基于形态分量分析的滚动轴承故障诊断方法

在改进形态分量分析阈值去噪方法的基础上,提出了基于形态分量分析的滚动轴承故障诊断方法。形态分量分析根据信号中各组成成分的形态差异,构建不同的稀疏表示字典对各组成成分进行分离。当轴承出现局部损伤时,其振动信号往往由以包含轴承自身振动的谐振分量、包含轴承故障信息的冲击分量及随机噪声分量构成。谐振分量表现为信号中的平滑部分,而冲击分量则表现为信号中的细节部分,因此,可根据谐振分量与冲击分量的形态差异,实现二者的分离。该方法利用形态分量分析对滚动轴承故障信号中的谐振分量、冲击分量和噪声分量进行分离,然后根据冲击分量中冲击之间的时间间隔诊断滚动轴承故障。算法仿真和应用实例表明,该方法能有效地提取滚动轴承故障振动信号中的故障冲击成分。     

Padé approximants and the modal connection: Towards increased robustness for fast parametric sweeps

To increase the robustness of a Padé‐based approximation of parametric solutions to finite element problems, an a priori estimate of the poles is proposed. The resulting original approach is shown to allow for a straightforward, efficient, subsequent Padé‐based expansion of the solution vector components, overcoming some of the current convergence and robustness limitations. In particular, this enables for the intervals of approximation to be chosen a priori in direct connection with a given choice of Padé approximants. The choice of these approximants, as shown in the present work, is theoretically supported by the Montessus de Ballore theorem, concerning the convergence of a series of approximants with fixed denominator degrees. Key features and originality of the proposed approach are (1) a component‐wise expansion which allows to specifically target subsets of the solution field and (2) the a priori, simultaneous choice of the Padé approximants and their associated interval of convergence for an effective and more robust approximation. An academic acoustic case study, a structural‐acoustic application, and a larger acoustic problem are presented to demonstrate the potential of the approach proposed.     

The multi-reconstruction entropy minimization method: unsupervised spectral reconstruction of pure components from mixture spectra, without the use of a priori information

The band-target entropy minimization method (BTEM) and its variant methods excel at reconstructing known/unknown pure spectra from mixtures without prior information. These mixtures may represent either non-reactive or even reactive systems. In this work, an unsupervised form of the entropy minimization curve resolution, namely, the multi-reconstruction entropy minimization method (MREM), is presented. MREM differs from BTEM by removing the need for band-targets and by introducing a multiple search routine to find multiple local entropy minima. This multiple search routine, which provides a rapid survey of spectral estimates, utilizes a localized form of Corona's simulated annealing method in the optimization. The objective functions and penalty functions of the BTEM type methods are essentially retained. Compared to BTEM type methods, MREM (1) searches for multiple local minima instead of a single global minimum and hence reconstructs many pure component spectra at once instead of one pure spectrum; and (2) utilizes a user-defined broad spectral range [v1, v2] for all searches instead of multiple user-defined narrow "targets" as in BTEM. The new MREM has been tested on four sets of real spectra using Fourier transform infrared spectroscopy (FT-IR), mass spectroscopy (MS), and ultraviolet-visible (UV-Vis) spectroscopy. The results show that MREM is computationally much faster than BTEM for finding the major components present. Also, because MREM does not rely on band targeting, it is very useful for spectra that have no localized features and are highly overlapping, such as UV-Vis.