Resolution of overlapping signals in spectrometry using a wavelet packet transform and an Elman recurrent neural network

A novel method named a wavelet packet transform based Elman recurrent neural network (WPTERNN) was proposed for the simultaneous UV–visible spectrometric determination of Cu(II), Cd(II) and Zn(II). This method combined wavelet packet denoising with an Elman recurrent neural network. A wavelet packet transform was applied to perform data compression, to extract relevant information, and to eliminate noise and collinearity. An Elman recurrent network was applied for nonlinear multivariate calibration. In this case, using trials, the kind of wavelet function, the decomposition level, and the number of hidden nodes for the WPTERNN method were selected as Daubechies 14, 3, and 8, respectively. A program (PWPTERNN) was designed that could perform the simultaneous determination of Cu(II), Cd(II) and Zn(II). The relative standard errors of prediction (RSEP) obtained for all components using WPTERNN, a Elman recurrent neural network (ERNN), partial least squares (PLS), principal component regression (PCR), Fourier transform based PCR (FTPCR), and multivariate linear regression (MLR) were compared. Experimental results demonstrated that the WPTERRN method was successful even where there was severe overlap of spectra. The results obtained from an additional test case also demonstrated that the WPTERNN method performed very well. Figure The part of WP coefficients obtained by wavelet packet transforms     

小波包压缩-RBF网络同时测定润滑油中铁、铜、锌

将小波包压缩-RBF网络方法用于润滑油中铁铜锌三组分分光光度同时测定该方法采用小波包函数对光谱数据进行压缩处理,用较大的小波色系数构成新的校正集和预测集代替原始的校正集和预测集,然后用RBF网络进行数据解析。研究表明,用bior2．4小波包处理原始测定数据,最佳小波基用logenerge熵标准,选择适当阈值将变量数由46个压缩成25个（压缩比为0．54）,整体预测效果最好。将此方法用于合成样预测．预测结果与实际浓度的相对误差绝对值在2．50％～9．40％之间;用于实际润滑油样品中铁、铜和锌的同时测定,解析值与原子吸收法（AAS）的测定值的相对误差绝对值作3．55％～7．86％之间。应用结果令人满意。     

小波包变换潜变量回归同时测定三组分混合物

采用小波包变换潜变量回归 (WPLVR)方法 ,同时测定水杨酸甲酯(MSA)、邻苯二甲酸二丁酯 (DBP)和邻苯二甲酸氢钾 (PHP)。该法结合小波包变换和潜变量回归改进除噪质量。通过最佳化 ,选择了小波函数及小波包分解水平 (L)。编制了两个程序 (PWPLVR)和 (PFTLVR)进行WPLVR和付立叶变换潜变量回归 (FTLVR)法计算。实验结果表明WPLVR法是成功的且优于FTLVR法。     

Simultaneous kinetic spectrophotometric analysis of five synthetic food colorants with the aid of chemometrics

This paper describes a simple and sensitive kinetic spectrophotometric method for the simultaneous determination of Amaranth, Ponceau 4R, Sunset Yellow, Tartrazine and Brilliant Blue in mixtures with the aid of chemometrics. The method involved two coupled reactions, viz. the reduction of iron(III) by the analytes to iron(II) in sodium acetate/hydrochloric acid solution (pH 1.71) and the chromogenic reaction between iron(II) and hexacyanoferrate(III) ions to yield a Prussian blue peak at 760 nm. The spectral data were recorded over the 500-1000 nm wavelength range every 2 s for 600 s. The kinetic data were collected at 760 nm and 600 s, and linear calibration models were satisfactorily constructed for each of the dyes with detection limits in the range of 0.04-0.50 mg L⁻¹. Multivariate calibration models for kinetic data were established and verified for methods such as the Iterative target transform factor analysis (ITTFA), principal component regression (PCR), partial least squares (PLS), and principal component-radial basis function-artificial neural network (PC-RBF-ANN) with and without wavelet packet transform (WPT) pre-treatment. The PC-RBF-ANN with WPT calibration performed somewhat better than others on the basis of the %RPE_T (∼9) and %Recovery parameters (∼108), although the effect of the WPT pre-treatment was marginal (∼0.5% RPE_T). The proposed method was applied for the simultaneous determination of the five colorants in foodstuff samples, and the results were comparable with those from a reference HPLC method.     

Combining orthogonal signal correction and wavelet packet transform with partial least squares to analyze overlapping spectra of three kinds of metal ions

A novel method named OSC-WPT-PLS approach based on partial least squares (PLS) regression with orthogonal signal correction (OSC) and wavelet packet transform (WPT) as pre-processed tools was proposed for the simultaneous spectrophotometric determination of Al(III), Mn(II) and Co(II). This method combines the ideas of OSC and WPT with PLS regression for enhancing the ability of extracting characteristic information and the quality of regression. OSC is used to remove information in the response matrix D by subtracting the structured noise that is orthogonal to the concentration matrix C. Wavelet packet transform was applied to perform data compression, to extract relevant information, and to eliminate noise and collinearity. PLS was applied for multivariate calibration and noise reduction by eliminating the less important latent variables. In this case, using trials, the kind of wavelet function, the decomposition level, the number of OSC components and the number of PLS factors for the OSC-WPT-PLS method were selected as Daubechies 4, 3, 2 and 3, respectively. A program (POSCWPTPLS) was designed to perform the simultaneous spectrophotometric determination of Al(III), Mn(II) and Co(II). The relative standard errors of prediction (RSEP) obtained for total elements using OSC-WPT-PLS, WPT-PLS and PLS were compared. Experimental results demonstrated that the OSC-WPT-PLS method had the best performance among the three methods and was successful even when there was severe overlap of spectra.     

小波包变换潜变量回归分辨重叠的紫外光谱

采用小波包变换潜变量回归(WPLVR)方法,同时测定联苯、苯酚和邻苯二酚。该法结合小波包变换和潜变量回归改进除噪质量。通过最佳化,选择了小波函数及小波包分解水平(L)。编制了两个程序PWPLVR和PFTLVR进行WPLVR和付立叶变换潜变量回归(FTLVR)法计算。试验结果表明WPLVR法是成功的且优于FTLVR法。     

Simultaneous determination of rifampicin and isoniazid by continuous-flow chemiluminescence with artificial neural network calibration

In this paper a continuous-flow chemiluminescence (CL) system with artificial neural network calibration is proposed for simultaneous determination of rifampicin and isoniazid. This method is based on the different kinetic spectra of the analytes in their CL reaction with alkaline N-bromosuccinimide as oxidant. The CL intensity was measured and recorded every second from 1 to 300 s. The data obtained were processed chemometrically by use of an artificial neural network. The experimental calibration set was 20 sample solutions. The relative standard errors of prediction for both analytes were approximately 5%. The proposed method was successfully applied to the simultaneous determination of rifampicin and isoniazid in a combined pharmaceutical formulation.     

Rapid Determination of Enantiomeric Excess of Tert-Butoxycarbonyl (BOC-Protected) Amino Acids Based on Infrared Spectra Technique with Optimal Wavelet Packet Transform Decomposition Frequency Band

A method was employed to determine enantiomeric excess (ee) value of chiral tert-butoxycarbonyl (Boc-protected) amino acids in a rapid way by using an infrared spectroscopy technique combined with wavelet packet transform (WPT) and least squares support vector machines (LS-SVM). Infrared spectral data were decomposed by using WPT algorithm. Simulated annealing (SA) algorithm was then used to search the optimal decomposed frequency band that had the greatest contribution to the quantitative analysis of ee values. As a result, the band (7, 34) with 34 variables and the band (5, 1) with 116 variables were determined as the optimal ones for the determination of Boc-protected proline and alanine, respectively. The selected variables in the optimal band were used as the inputs of LS-SVM models. The spectral variables selected by the WPT-SA method had lower predicting errors than full range spectra and the spectral variables selected by some traditional variable selection methods. Reasonable good results with root mean-square error of prediction (RMSEP) of 7.51 and 3.80 were obtained for the determination of ee values of two Boc-protected amino acids, showing that it is possible to rapidly determine ee values of amino acids by using IR spectroscopy rapidly.     

Identification of epilepsy from intracranial EEG signals by using different neural network models

In this work, a framework is provided for identifying intracranial electroencephalography (iEEG) seizures based on discrete wavelet transform (DWT) analysis of iEEG signals using forward propagation and feedback neural networks. The performance of 5 different data sets combination classifications is studied using the probabilistic neural network (PNN), learning vector quantization neural network (LVQ) and Elman neural network (ENN). Different feature combinations serve as the input vectors of the classifiers to obtain the best outcomes. It has been found that PNN has less running time and provides better classification accuracy (CA) than ENN and LVQ classifiers for all 5 classification problems. It is worth noticing that the CA for the C-D classification task, which shows the status of pre-ictal versus post-ictal, has been greatly improved, and reached 83.13%. Hence, the epilepsy iEEG signals pattern recognition based on DWT statistical features using the PNN classifier is more suitable for forming a reliable, automatic classification system in order to assist doctors in diagnosis.     

人工神经网络阻抑动力学光度法同时测定邻苯二酚和间苯二胺

在硫酸性介质中,Fe(Ⅲ)能够催化H2O2氧化中性红褪色反应,邻苯二酚和间苯二胺都能阻抑该催化氧化褪色反应的速度,研究发现：两者对Fe(Ⅲ)催化H2O2氧化中性红褪色反应阻抑作用不具有加和性,根据这一现象,用人工神经网络处理非线性体系的优势进行数据处理,从而建立了一种新的测定邻苯二酚和间苯二胺混合物的人工神经网络阻抑动力学光度法。对5组混合样品进行测定,回收率均在95%-105%之间。     

荧光光度法同时测定邻苯二酚、间苯二酚与对苯二酚

将一种直接信号校正(DOSC)-小波包变换(WPT)-偏最小二乘法(PLS)(DOSC-WPT-PLS)新方法用于解析荧光光谱严重重叠的邻苯二酚?间苯二酚和对苯二酚混合物,并对其进行测定。该法将DOSC、WPT及PLS 3种方法结合从而提高了获取特征信息的能力和回归质量。DOSC方法用于除去与浓度无关的结构噪音。利用WPT的时域和频域局部化的特点改进了除噪质量和数据压缩及信息提取能力。PLS方法用于多变量校准和噪音消除。处理该3种组分的荧光光谱数据,并实现了3种化合物的同时测定。设计了PDOSCWPTPLS程序执行相关计算,并对以上3种化学计量学方法进行了比较,其总体相对预测标准偏差分别为4.3%、7.7%、11.5%,结果表明DOSC-WPT-PLS法优于WPT-PLS法和PLS法。将该法用于测定自来水中邻苯二酚?间苯二酚和对苯二酚的含量,其回收率分别为99%~110%?95%~108%和98%~104%,结果满意。     

Application of silver nanoparticles and principal component-artificial neural network models for simultaneous determination of levodopa and benserazide hydrochloride by a kinetic spectrophotometric method

A multicomponent analysis method based on principal component analysis-artificial neural network model (PC-ANN) is proposed for the simultaneous determination of levodopa (LD) and benserazide hydrochloride (BH). The method is based on the reaction of levodopa and benserazide hydrochloride with silver nitrate as an oxidizing agent in the presence of PVP and formation of silver nanoparticles. The reaction monitored at analytical wavelength 440 nm related to surface plasmon resonance band of silver nanoparticles. Differences in the kinetic behavior of the levodopa and benserazide hydrochloride were exploited by using principal component analysis, an artificial neural network (PC-ANN) to resolve concentration of analytes in their mixture. After reducing the number of kinetic data using principal component analysis, an artificial neural network consisting of three layers of nodes was trained by applying a back-propagation learning rule. The optimized ANN allows the simultaneous determination of analytes in mixtures with relative standard errors of prediction in the region of 4.5 and 6.3 for levodopa and benserazide hydrochloride respectively. The results show that this method is an efficient method for prediction of these analytes.     

Simultaneous determination of iron and aluminium by differential kinetic spectrophotometric method and chemometrics

A differential kinetic spectrophotometric method was researched and developed for the simultaneous determination of iron and aluminium in food samples. It was based on the direct reaction kinetics and spectrophotometry of these two metal ions with Chrome Azurol S (CAS) in ethylenediamine-hydrochloric acid buffer (pH 6.3). The results were interpreted with the use of chemometrics. The kinetic runs and the visible spectra of the complex formation reaction were studied between 540 and 750 nm every 30 s over a total period of 285 s. A set of synthetic metal mixture samples was used to build calibrations models. These were based on the spectral and kinetic two-way data matrices, which were processed separately by the radial basis function-artificial neural network (global RBF-ANN) method. The prediction performance of these models was poorer than that from the combined kinetic-spectral three-way array, which was similarly processed by the same method (% relative prediction error (RPE_T) = 5.6). These results demonstrate that improved predictions can be obtained from the data array, which has more information, and that appropriate chemometrics methods can enhance analytical performance of simple techniques such as spectrophotometry.Other chemometrics models were then applied: N-way partial least squares (NPLS), parallel factor analysis (PARAFAC), back propagation-artificial neural network (BP-ANN), single radial basis function-artificial neural network (RBF-ANN), and principal component neural network (PC-RBF-ANN). There was no substantial difference between the methods with the overall %RPE_T range being 5.0-5.8. These two values corresponded to the NPLS and BP-ANN models, respectively. The proposed method was applied for the determination of iron and aluminium in some commercial food samples with satisfactory results.     

Determination of bismuth and copper using adsorptive stripping voltammetry couple with continuous wavelet transform

A new method is proposed for the determination of bismuth and copper in the presence of each other based on adsorptive stripping voltammetry of complexes of Bi(III)-chromazorul-S and Cu(II)-chromazorul-S at a hanging mercury drop electrode (HMDE). Copper is an interfering element for the determination of Bi(III) because, the voltammograms of Bi(III) and Cu(II) overlapped with each other. Continuous wavelet transform (CWT) was applied to separate the voltammograms. In this regards, wavelet filter, resolution of the peaks and the fitness were optimized to obtain minimum detection limit for the elements. Through continuous wavelet transform Symlet4 (Sym4) wavelet filter at dilation 6, quantitative and qualitative analysis the mixture solutions of bismuth and copper was performed. It was also realized that copper imposes a matrix effect on the determination of Bi(III) and the standard addition method was able to cope with this effect. Bismuth does not have matrix effect on copper determination, therefore, the calibration curve using wavelet coefficients of CWT was used for determination of Cu(II) in the presence of Bi(III). The detection limits were 0.10 and 0.05 ng ml⁻¹ for bismuth and copper, respectively. The linear dynamic range of 0.1-30.0 and 0.1-32.0 ng ml⁻¹ were obtained for determination of bismuth in the presence of 24.0 ng ml⁻¹ of copper and copper in the presence of 24.0 ng ml⁻¹ of bismuth, respectively. The method was used for determination of these two cations in water and human hair samples. The results indicate the ability of method for the determination of these two elements in real samples.     

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.     

Protein Secondary Structure Prediction with Partially Recurrent Neural Networks

Abstract

Partially recurrent neural networks with different topologies are applied for secondary structure prediction of proteins. The state of some activations in the network is available after a pattern presentation via feedback connections as additional input during the processing of the next pattern in a sequence. A reference data set containing 91 proteins in the training set and 15 non-homologous proteins in the test set is used for training and testing a network with a modified, hierarchical Elman architecture. The network predicts the secondary structures α-helix, β-sheet, and “coil” for each amino acid. The percentage of correctly classified amino acids is 67.83% on the training set and 63.98% on the test set. The best performance of a three-layer feedforward network is 62.7% on the same test set. A cascaded network, where the outputs of the recurrent network are processed by a second net with 13 × 3 inputs, four hidden and three output units has a predictive performance of 64.49%. The best corresponding feedforward net has a performance of 64.3%.     

基于独立分量和神经网络的近红外多组分分析方法

采用小波变换对光谱数据进行压缩,用独立分量分析(ICA)方法提取近红外光谱数据矩阵的独立成分和相应的混合矩阵,再用BP神经网络对混合矩阵和实测浓度矩阵进行建模,提出了基于独立分量分析-神经网络回归(ICA-NNR)的近红外分析建模方法。进一步研究了独立分量数和网络中间隐层的神经元数对模型性能的影响,经优化后的ICA-NNR模型在相关系数与均方根误差两个指标上均优于直接用光谱矩阵作为输入所建立的模型。本方法用于玉米中水分、淀粉、蛋白质3种主要成分含量的同时测定,检验样品集的化学检测值与近红外预测值的相关系数分别达到:淀粉r=0.971,蛋白质r=0.976,水分r=0.975。     

Sensitive flow-injection amperometric detection of iodide using Mn3+ and As3+.

A rapid, selective, and sensitive kinetic flow-injection method for iodide content determination with amperometric detection on a platinum electrode was developed. The method is based on the catalytic effect of iodide on the Mn3+ reaction with As3+ in the presence of sulfuric acid. The calibration curve was linear in the concentration range from 5.0 x 10(-7) to 1.0 x 10(-4) mol/L iodide. The limit of detection (LOD) was found to be 5.0 x 10(-9) mol/L iodide. The relative standard deviations (RSD) were 1.68% and 3.03% for 1.0 x 10(-3) mol/L standard and 1.0 x 10(-6) mol/L iodide solution (n = 6), respectively. The method has been successfully applied for determination of iodide in waters, table salts, fodder, organic substances and human blood sera. The results were compared with those obtained by a standard AOAC (Association of Official Analytical Chemists) method, as well as with those obtained by a kinetic spectrophotometric procedure for determination of iodide.