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).     

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.     

改进的IRS辅助毫米波MIMO级联信道估计

为改善智能反射表面（Intelligent reflective surface,IRS）辅助的毫米波多输入多输出（Multiple-input multiple-output,MIMO）级联信道的估计精度和收敛速度,基于平行因子（Parallel factor,PARAFAC）分解模型,把常规的双线性交替最小二乘（Bilinear alternating least squares,BALS）算法改进为带松弛因子的ω-BALS算法和正则化的T-BALS,加快了收敛速度和算法稳定性。当基站、IRS元件或用户侧的阵列天线数目较大时,提出改进的奇异值（Singular value decomposition,svd）-BALS算法。该算法通过奇异值分解压缩张量,再利用低维度的核心张量来重构模式n矩阵。仿真结果表明,该算法的归一化均方误差性能有所提高,并且加快了收敛速度。     

Novel insights into sludge dewaterability by fluorescence excitation-emission matrix combined with parallel factor analysis

Sludge dewatering is of major interest in sludge volume reduction and handling properties improvement. Here we report an approach of fluorescence excitation-emission matrix (EEM) combined with parallel factor (PARAFAC) analysis to elucidate the factors that influence sludge dewaterability. Sludge flocs from 11 full-scale wastewater treatment plants were collected to stratify into different extracellular polymeric substances (EPS) fractions and then to characterize their fluorescence EEMs. Both the normalized capillary suction time (CST) and specific resistance to filtration (SRF) were applied to determine sludge dewaterability. The results showed that fluorescence EEMs of tightly bound fractions were not affected by the wastewater sources. In contrast, fluorescence EEMs of loosely bound fractions were affected by the wastewater sources. All the fluorescence EEMs could be successfully decomposed into a six-component model by PARAFAC analysis. Both normalized CST and SRF were significantly correlated with component 1 [excitation/emission (Ex/Em) = (220, 275)/350] in the supernatant fraction, with components 5 [Ex/Em = (230, 280)/430] and 6 [Ex/Em = (250, 360)/460] in the slime and LB-EPS fraction. These results reveal that except for proteins-like substances (component 1), sludge dewaterability is also affected by humic acid-like and fulvic acid-like substances (components 5 and 6) in the slime and LB-EPS fractions. Furthermore, this paper presents a promising and facile approach (i.e., EEM-PARAFAC) for investigating sludge dewaterability.     

Application of multi-way models to the time-resolved fluorescence of polycyclic aromatic hydrocarbons mixtures in water

The time-resolved laser-induced fluorescence of a series of polycyclic aromatic compounds (PAHs) and mixtures of these latter in aqueous solution was measured by means of an apparatus equipped with optical fibers, which allows their real time in situ monitoring. The potential of such spectroscopic technique, yielding 4-way fluorescence data arrays, together with the application of multi-way models to the matricized data, was tested for the resolution of complex aqueous mixtures containing low concentrations of PAHs, as typical fluorescent pollutants in aquatic systems. PARAllel FACtors analysis was employed for the qualitative resolution of PAHs mixtures and for calculating the fluorescence lifetimes of single PAHs; n-way partial least squares analysis was applied for evaluating the concentration of the single PAHs in the aqueous mixtures.     

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.     

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.     

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.     

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.