Convergence analysis of the alternating RGLS algorithm for the identification of the reduced complexity Volterra model

In this paper we provide a convergence analysis of the alternating RGLS (Recursive Generalized Least Square) algorithm used for the identification of the reduced complexity Volterra model describing stochastic non-linear systems. The reduced Volterra model used is the 3rd order SVD-PARAFC-Volterra model provided using the Singular Value Decomposition (SVD) and the Parallel Factor (PARAFAC) tensor decomposition of the quadratic and the cubic kernels respectively of the classical Volterra model. The Alternating RGLS (ARGLS) algorithm consists on the execution of the classical RGLS algorithm in alternating way. The ARGLS convergence was proved using the Ordinary Differential Equation (ODE) method. It is noted that the algorithm convergence canno׳t be ensured when the disturbance acting on the system to be identified has specific features. The ARGLS algorithm is tested in simulations on a numerical example by satisfying the determined convergence conditions. To raise the elegies of the proposed algorithm, we proceed to its comparison with the classical Alternating Recursive Least Squares (ARLS) presented in the literature. The comparison has been built on a non-linear satellite channel and a benchmark system CSTR (Continuous Stirred Tank Reactor). Moreover the efficiency of the proposed identification approach is proved on an experimental Communicating Two Tank system (CTTS).     

EEM fluorescence spectroscopy as a fast method to assess the brine composition of salted herring

Ripening of barrel-salted herring (Clupea harengus) is evaluated by the use of fluorescence spectroscopy and protein determinations. During ripening, protein degradation takes place in the herring and protein is extracted into the brine. The present study aims at identifying parameters which are correlated to the ripening characteristics of barrel-salted herring and which can provide a better understanding of the ripening process. Front face fluorescence landscapes were obtained by measuring directly on the brine from barrel-salted herring. These data were analyzed by parallel factor analysis (PARAFAC), which revealed four fluorophores, tryptophan (two states), vitamin B6 and riboflavin. All four parameters showed an increase in concentration during the storage period corresponding to an increase in protein content that varied from 3 g/100 g at day 60 to 5 g/100 g after 277 days of storage. It was not possible to see a difference in the development of the four fluorophores during the ripening period. The protein content was predicted from the fluorescence landscapes by partial least squares (PLS). The use of unfolded fluorescence spectra gave an RMSECV of 0.26 g/100 g and a correlation between the measured protein content and the predicted values of 0.86.     

Assessment of water quality in the vicinity of peat extraction sites: The case of Pien‐Saimaa,Finland

Peatlands have an important global role as carbon sinks. Locally, however, peat bog extraction can cause pollution in nearby watercourses. The aim of this study is to investigate the application of multivariate methods in the renovation and protection of eutrophic lakes surrounded by agricultural and peat extraction areas. The analytical data used in the study originated from a national water quality database and the period studied was 2000–2013. Multivariate methods: Principal Component Analysis (PCA) and Parallel Factor Analysis (PARAFAC) were applied to solve interactions of variables and pollution sources in a complex water ecosystem. Leaching from the peat bog area was found to be the main source of iron, which has an important role as a precipitator of phosphorus in loose sediment and in water. Nutrient ratios had no direct correlation to algae blooms, but high ratios indicated an increased likelihood of an upcoming bloom.     

现代分析化学中的三线性成分模型

本文针对现代分析化学实际 ,有选择性地介绍了三相三道三线性成分模型 ,扼要地列举了其主要的三线性分解算法 ,讨论了立体阵的秩估计、三线性分解的唯一性等。     

用数据驱动实现的抗生素发酵过程监控软件

主要介绍了基于数据驱动的抗生素发酵过程监控软件的结构设计和具体实现方法,文章着重介绍了优化补料的方法,以及用多元统计过程控制在线监控发酵过程的方法,并给出了相应的实例。     

基于变分贝叶斯推断的半盲信道估计

现有MIMO中继通信系统中,基于张量分解的半盲信道估计不能有效地将信道先验信息引入估计过程中,为此提出一种基于变分贝叶斯推断的信道估计算法.该算法首先利用NP(Nested PARAFAC)张量模型,引入有效精度、噪声精度等隐性超参数,建立信道估计概率图模型;由于所求信道参数后验概率分布较为复杂,传统最大似然和最大后验等点估计方法难以实现,算法采用变分贝叶斯推断,推导出信道矩阵、有效精度及噪声精度的递推公式,使具有因子分解形式的q分布逼近所求信道参数的后验分布;并分析了模型证据的下界、模型的初始化及算法复杂度等.该算法能利用信道先验信息以提高信道估计性能,有效精度和噪声精度等参数可自动调节,且计算复杂度与数据的维度呈线性关系.仿真结果表明:在平稳瑞利衰落信道条件下,与基于交替最小二乘(Alternating Least Square,ALS)的半盲估计算法相比,算法的计算复杂度较低,收敛速度较快;与带监督序列的双线性最小二乘(Bilinear Alternating Least Square,BALS)非盲估计算法,基于ALS及非线性最小二乘(Nolinear Least Square,NLS)的半盲估计算法相比,算法具有较高的估计精度.     

On rotational ambiguity in parallel factor analysis

Although, in many cases parallel factor analysis (PARAFAC) resolves the trilinear data arrays to the true physical factors that form the data, i.e., unique solution can be found, the algorithm does not always converge to chemically meaningful solutions. Kiers and Smilde [J. Chemom. 1995; 9: 179-195] rigorously proved that unique decomposition does not hold in cases with ‘rank overlap’. They showed when PARAFAC is applied on a three-way data array which has rank overlap in one of its loading modes; the solution obtained is not unique and at best cannot be easily compared with the underlying physical factors owing to a rotational ambiguity.An aspect which is significantly less documented in the previous publications is the reliable detection of rotational ambiguities in multi-way methods. A few reported methods are based on bilinear models for calculating the feasible bands of three-way data. In this paper we propose a method to calculate feasible bands of resolved profiles of components in three-way methods and visualize the rotational ambiguity in three-way data in the results of the three-way methods. Most of discussion is in the PARAFAC algorithm. The principle behind the algorithm is described in detail and tested for simulated data set. Completely general and exhaustive results are presented for the two-component cases. In particular, the effect of the noise is investigated and a comparison is made between feasible solutions obtained from PARAFAC and matrix-augmented with trilinearity. It is shown that the results obtained from both methods are identical.     

Second order standard addition method and fluorescence spectroscopy in the quantification of ibuprofen enantiomers in biological fluids

The second order standard addition method and spectrofluorimetry were used for determination of ibuprofen enantiomers in human plasma and urine. The methodology was based on chiral recognition of ibuprofen by formation of an inclusion complex with a chiral auxiliary, β-cyclodextrin, in the presence of 1-butanol. The strategy combines the use of PARAFAC, for extraction of the pure analyte signal, with the standard addition method, for determinations in presence of a matrix effect. A specific PARAFAC model was built for each sample and the scores were related to (S)-ibuprofen concentration using a linear regression in the standard addition method. Feasible results were obtained for determinations in the molar fraction range from 50 to 80% of (S)-ibuprofen, providing absolute errors lowers than 4.0% for plasma and urine.     

PARAFAC modeling of three-way hyperspectral images: Endogenous fluorophores as health biomarkers in aquatic species

Demand for a renewable liquid-phase fuel has reinvigorated interest in the development of novel biofuels from algae. The effects of fluctuating nutrients, temperature, and predation which arise in algal aquaculture necessitate novel analytical methods to assess and optimize the health of these cultures. In this article we describe the use of trilinear modeling to these ends, using imaging data of endogenous fluorescence from the marine diatom, Thalassiosira pseudonana, collected on a hyperspectral fluorescence confocal microscope (HSF-CM). By combining the spatial and spectral data with the additional physical parameter introduced by the varying photobleach rates of endogenous fluorophores, we obtain a means for employing trilinear analysis in this system. In this case, analysis was implemented using the method of parallel factors analysis (PARAFAC) which alleviates the rotational ambiguities involved in multivariate analysis of 2-way data. By imposing a nutrient limitation in our diatom culture, and collecting single cell microscopy data at various time points during the nutritional stress, PARAFAC results reveal evolution of the spectral emission characteristics of six components and a background as a result of incremental photobleaching. Although the underlying mechanisms for these observations are not addressed, the differences observed between nutritively normal and nutritively stressed cells provide signatures for early detection of health deterioration in the algal culture. Finally, the combination of hyperspectral fluorescence microscopy with PARAFAC is generally applicable for the study of complex biological systems with endogenous fluorescence.     

Fast analysis of 4 phenolic acids in olive oil by HPLC-DAD and chemometrics

Polyphenols are important components of virgin olive oils, due to their antioxidant properties. Among the various analytical methods proposed for their determination, HPLC plays a dominant role, both coupled to UV-spectrophotometric and MS detection of the eluted component. However, the optimal time required for the full separation of all the components can be quite long. In this study, we investigated the possibility of reducing the analytical time of HPLC-DAD analysis of polyphenols by allowing the overlapping and coelution of some peaks, whose signals were separated off-column by two- and three-way resolution methods. In particular, we focused our attention on a peak where four phenolic acids (syringic acid, vanillic acid, p-hydroxybenzoic acid, and caffeic acid) coeluted. Both MCR-ALS and PARAFAC2 provided a good resolution of the peaks in the case of training and test samples, however the former technique provided the better results.