Blind spatial signature estimation using time-varying user power loading and parallel factor analysis

In order to solve the identification problem of oil pollutants containing micro content, the fluorescence characteristics of oil samples were studied using fluorescence excitation emission matrix spectra (EEMs) combined with parallel factor (PARAFAC) analysis. According to the conventional standard of oil content in water, simulated the component of oil pollution in I-V water was simulated by preparing samples of CCL4 with oil content. Firstly, measured the EEMs of 97# gasoline, 0# diesel, kerosene and CCL4 were measured individually, then the EEMs of 97# gasoline, 0# diesel, and kerosene in CCL4 were measured, and finally, the EEMs of the composite sample with all three oil contents in CCL4 were measured. The EEMs of the composite sample were superimposed by the EEMs of all its different components. It is therefore difficult to analyze the fluorescence component by chemical separation or simple fluorescence analysis. Since the EEMs of each oil component are already measured, we used the PARAFAC analysis to decompose the EEMs of the composite sample, and then extract the concentration ratio of each component. In this work, we solved the problem of identifying and quantifying the main micro-content petroleum pollutant in composite oil samples using EEMs and PARAFAC analysis.

Parallel factor analysis (PARAFAC) is a branch of multi-way signal processing that has received increased attention recently. This is due to the large class of applications as well as the milestone identifiability results demonstrating the superiority to matrix (two-way) analysis approaches. A significant amount of research was dedicated to iterative methods to estimate the factors from noisy data. In many situations these require many iterations and are not guaranteed to converge to the global optimum. Therefore, suboptimal closed-form solutions were proposed as initializations. In this contribution we derive a closed-form solution to completely replace the iterative approach by transforming PARAFAC into several joint diagonalization problems. Thereby, we obtain several estimates for each of the factors and present a new matching scheme to select the best estimate for each factor. In contrast to the techniques known from the literature, our closed-form solution can efficiently exploit symmetric as well as Hermitian symmetric models and solve the underdetermined case, if there are at least two modes that are non-degenerate and full rank. This closed-form solution achieves approximately the same performance as previously proposed iterative solutions and even outperforms them in critical scenarios.

<strong class="journal-contentHeaderColor">Abstract.</strong> The optical properties, chemical composition, and potential chromophores of brown carbon (BrC) aerosol particles were studied during typical summertime and wintertime at a kerbside in downtown Karlsruhe, a city in central Europe. The average absorption coefficient and mass absorption efficiency at 365 nm (Abs<span class="inline-formula">₃₆₅</span> and MAE<span class="inline-formula">₃₆₅</span>) of methanol-soluble BrC (MS-BrC) were lower in the summer period (1.6 <span class="inline-formula">±</span> 0.5 Mm<span class="inline-formula">⁻¹</span>, 0.5 <span class="inline-formula">±</span> 0.2 m<span class="inline-formula">²</span> g<span class="inline-formula">⁻¹</span>) than in the winter period (2.8 <span class="inline-formula">±</span> 1.9 Mm<span class="inline-formula">⁻¹</span>, 1.1 <span class="inline-formula">±</span> 0.3 m<span class="inline-formula">²</span> g<span class="inline-formula">⁻¹</span>). Using a parallel factor (PARAFAC) analysis to identify chromophores, two different groups of highly oxygenated humic-like substances (HO-HULIS) dominated in summer and contributed 96 <span class="inline-formula">±</span> 6 % of the total fluorescence intensity. In contrast, less-oxygenated HULIS (LO-HULIS) dominated the total fluorescence intensity in winter with 57 <span class="inline-formula">±</span> 12 %, followed by HO-HULIS with 31 <span class="inline-formula">±</span> 18 %. Positive matrix factorization (PMF) analysis of organic compounds detected in real time by an online aerosol mass spectrometer (AMS) led to five characteristic organic compound classes. The statistical analysis of PARAFAC components and PMF factors showed that LO-HULIS chromophores were most likely emitted from biomass burning in winter. HO-HULIS chromophores could be low-volatility oxygenated organic aerosol from regional transport and oxidation of biogenic volatile organic compounds (VOCs) in summer. Five nitro-aromatic compounds (NACs) were identified by a chemical ionization mass spectrometer (C<span class="inline-formula">₇</span>H<span class="inline-formula">₇</span>O<span class="inline-formula">₃</span>N, C<span class="inline-formula">₇</span>H<span class="inline-formula">₇</span>O<span class="inline-formula">₄</span>N, C<span class="inline-formula">₆</span>H<span class="inline-formula">₅</span>O<span class="inline-formula">₅</span>N, C<span class="inline-formula">₆</span>H<span class="inline-formula">₅</span>O<span class="inline-formula">₄</span>N, and C<span class="inline-formula">₆</span>H<span class="inline-formula">₅</span>O<span class="inline-formula">₃</span>N), which contributed 0.03 <span class="inline-formula">±</span> 0.01 % to the total organic mass but can explain 0.3 <span class="inline-formula">±</span> 0.1 % of the total absorption of MS-BrC at 365 nm in winter. Furthermore, we identified 316 potential brown carbon molecules which accounted for 2.5 <span class="inline-formula">±</span> 0.6 % of the organic aerosol mass. Using an average mass absorption efficiency (MAE<span class="inline-formula">₃₆₅</span>) of 9.5 m<span class="inline-formula">²</span>g<span class="inline-formula">⁻¹</span> for these compounds, we can estimate their mean light absorption to be 1.2 <span class="inline-formula">±</span> 0.2 Mm<span class="inline-formula">⁻¹</span>, accounting for 32 <span class="inline-formula">±</span> 15 % of the total absorption of MS-BrC at 365 nm. This indicates that a small fraction of brown carbon molecules dominates the overall absorption. The potential BrC molecules assigned to the LO-HULIS component had a higher average molecular weight (265 <span class="inline-formula">±</span> 2 Da) and more nitrogen-containing molecules (62 <span class="inline-formula">±</span> 1 %) than the molecules assigned to the HO-HULIS components. Our analysis shows that the LO-HULIS, with a high contribution of nitrogen-containing molecules originating from biomass burning, dominates aerosol fluorescence in winter, and HO-HULIS, with fewer nitrogen-containing molecules as low-volatility oxygenated organic aerosol from regional transport and oxidation of biogenic volatile organic compounds (VOC), dominates in summer.

Characterizing the interaction between uranyl ion and soil fulvic acid using parallel factor analysis and a two-site fluorescence quenching model

In autumn, the dissolved organic matter (DOM) contribution of leaf litter leachate to streams in forested watersheds changes as trees undergo resorption, senescence, and leaf abscission. Despite its biogeochemical importance, little work has investigated how leaf litter leachate DOM changes throughout autumn and how any changes might differ interspecifically and intraspecifically. Since climate change is expected to cause vegetation migration, it is necessary to learn how changes in forest composition could affect DOM inputs via leaf litter leachate. We examined changes in leaf litter leachate fluorescent DOM (FDOM) from American beech (Fagus grandifolia Ehrh.) leaves in Maryland, Rhode Island, Vermont, and North Carolina and from yellow poplar (Liriodendron tulipifera L.) leaves from Maryland. FDOM in leachate samples was characterized by excitation‐emission matrices (EEMs). A six‐component parallel factor analysis (PARAFAC) model was created to identify components that accounted for the majority of the variation in the data set. Self‐organizing maps (SOM) compared the PARAFAC component proportions of leachate samples. Phenophase and species exerted much stronger influence on the determination of a sample's SOM placement than geographic origin. As expected, FDOM from all trees transitioned from more protein‐like components to more humic‐like components with senescence. Percent greenness of sampled leaves and the proportion of tyrosine‐like component 1 were found to be significantly different between the two genetic beech clusters, suggesting differences in photosynthesis and resorption. Our results highlight the need to account for interspecific and intraspecific variations in leaf litter leachate FDOM throughout autumn when examining the influence of allochthonous inputs to streams.

Data collected for the spectral study of time series can be presented as a three-way array in which the three modes are the batches, time and wavelengths. The parallel factor analysis (PARAFAC) model is relevant for the analysis of three-way data tables, while the malting process consists of the time transformation of barley into malt. Furthermore, samples were collected on each day of an industrial malting process and their near infrared spectra were recorded in diffuse reflectance mode from 1100 to 2500 nm. The time and the wavelength modes associated with the first component showed that the spectra intensities allowed the classification of samples according to time. A study of the other loading vectors weighted by their coefficients on the time-mode explain some phenomena taking place during malting [the appearance of soluble substances (1950 nm), β-glucan degradation (2240–2360 nm), moisture modification (1450 and 1950 nm)…]. PARAFAC allowed us to separate batches according to the malting process to which they were submitted. Batches were also differentiated according to the chemical modification rate that occurred as expressed by the biochemical analyses results of the final malts. This work shows that PARAFAC can be a useful tool in the study of time series.

Lakes are areas of ecological significance that host a wide range of living species. Therefore, monitoring changes in lake surfaces is critical for ecosystem preservation. Since conventional methods based on one-dimensional data analysis have limited capacity to analyze complex systems, they may not always produce the desired results in examining surface change. In this regard, a novel approach based on a three-way analysis model of a multi-temporal dataset was improved for the first time to monitor surface changes in Lake Burdur between 2014 and 2023 in terms of latitude, longitude, and year modes. The newly proposed approach, based on the deconvolution of a multi-temporal data series, provided a new way and an alternative approach with a three-dimensional perspective for the simultaneous prediction of changes in latitude, longitude, and relative quantity profiles of Lake Burdur between 2014 and 2023. The proposed approach is based on the parallel factor analysis (PARAFAC) modeling of the multi-temporal datasets. The change in the lake surface as water levels were monitored from latitudinal and longitudinal profiles was obtained by applying the PARAFAC model to the multi-temporal data array. In the same model, the change in lake water surface over the years was determined from the relative quantity profile. The results obtained from the three-way analysis model were compared with the results provided by the conventional method. It was concluded that the findings of this study could provide valuable information to researchers and policymakers in developing effective strategies to analyze changes in lake surfaces in future studies.

Objective Although widely used, the validity of the Coping Ways Checklist (WCC) is a persistent problem. Methods By studying a sample (n=285) obtained from a population that had experienced the same traumatic event (an earthquake), using with parallel factor analysis and exploratory structure model (ESEM), a scale of 46 items was obtained: Ways of the Coping Checklist after a disaster (WCC-D). Results The results indicate a valid model of six dimensions and two dimensions correlated with the post-traumatic stress scale used as criterion. Discussion The good properties of the WCC-D and its relationship to posttraumatic stress were discussed. The WCC-D is made available in a format ready to be applied and reviewed by health personnel.

Organic matter (OM) plays a significant role in biogeochemical processes in soil and water systems. Water-soluble organic matter (WSOM) leached from soil samples is often analyzed as representative of potentially mobile OM. However, there are many WSOM extraction methods in the literature with no clear guidelines for method selection. In this study, four common leaching solutions (0.5 M K2SO4, 0.01 M CaCl2, 2 M KCl, and H2O) were used to extract WSOM from various locations within a forested catchment. Fluorescence spectroscopy was used to analyze the impact of extraction method on WSOM chemistry. While all four methods consistently identified chemical differences between WSOM from a north-facing slope, south-facing slope, and riparian zone, there were clear differences in fluorescence signals between the leaching methods. All three salt solutions contained WSOM with a higher fluorescence index and humification index than WSOM leached with H2O, suggesting the presence of salts releases different fractions of the soil organic matter. A parallel factor analysis (PARAFAC) model developed from the leachates identified a distinctive soil humic fluorophore observed in all samples and fluorescent artifacts present in H2O-leached samples.

Composition analysis of colored dissolved organic matter in Taihu Lake based on three dimension excitation-emission fluorescence matrix and PARAFAC model, and the potential application in water quality monitoring

The widely used fluoroquinolone (FQ) antibiotics have become emerging contaminants due to their unconstrained usage. A prompt, straightforward, précised, and advanced technique named fluorescence spectroscopy was applied to characterize and semi-quantify FQs. However, excitation wavelengths on the comparable ranges of FQs and ubiquitous humic substance (HS) complicate their identification in the mixture. This study develops a simple spectral technique that affirms the individual identification of FQs and HS in the natural environment. The following characteristics and methods can demonstrate the traces of FQs in the environment-•Presence of fluorophore at Excitation/Emission = 225-230/285-295 nm wavelength in excitation-emission matrix (EEM) and parallel factor analysis (PARAFAC) models.•FQs and HS have fluorophores at excitation wavelengths of 275 nm and 325 nm in PARAFAC analysis. Unlike HS, the notable spectral presence in <350 nm emission during 275 nm excitation in FQs ensures their distinct identification in the mixture.•FQ affirming component intensity at Excitation/Emission = 225-230/285-295 nm and the intensity <350 nm emission during 275 nm excitation are considered in conjunction to quantify the amount of least FQ in any environmental sample.

The spatial information of the signal is neglected by the conventional frequency/time decompositions such as the fast Fourier transformation, principal component analysis, and independent component analysis. Framing of the data being as a three-way array indexed by channel, frequency, and time allows the application of parallel factor analysis, which is known as a unique multi-way decomposition. The parallel factor analysis was used to decompose the wavelet transformed ongoing diagnostic channel–frequency–time signal and each atom is trilinearly decomposed into spatial, spectral, and temporal signature. The time–frequency–space characteristics of the single-source fault signal was extracted from the multi-source dynamic feature recognition of mechanical nonlinear multi-failure mode and the corresponding relationship between the nonlinear variable, multi-fault mode, and multi-source fault features in time, frequency, and space was obtained. In this article, a new method for the multi-fault condition monitoring of slurry pump based on parallel factor analysis and continuous wavelet transform was developed to meet the requirements of automatic monitoring and fault diagnosis of industrial process production lines. The multi-scale parallel factorization theory was studied and a three-dimensional time–frequency–space model reconstruction algorithm for multi-source feature factors that improves the accuracy of mechanical fault detection and intelligent levels was proposed.

A 2(3) factorial design has been used to analyze the effect of pH, the nature of the catalyst, and the concentration of the substrate on the rate constant of the photodegradation reaction of phenol. The main effects of the considered variables and their interaction are discussed. The significance of the effects has been corroborated using an ANOVA test. The values of phenol concentrations, used to calculate the rate constant, and the concentrations of intermediates were obtained by applying parallel factor (PARAFAC) analysis to the data obtained from monitoring the process by means of excitation-emission fluorescence (EEM). The proposed methodology, which combines experimental design and multivariate techniques, is a rapid alternative for study of chemical kinetics.

Passive localization of nonstationary sources in the spherical coordinates (azimuth, elevation, and range) is considered, and a parallel factor analysis based method is addressed for the near-field parameter estimation problem. In this scheme, a parallel factor analysis model is firstly constructed by computing five time-frequency distribution matrices of the properly chosen observation data. In addition, the uniqueness of the constructed model is proved, and both the two-dimensional (2D) direction-of-arrival (DOA) and range can be jointly obtained via trilinear alternating least squares regression (TALS). The investigated algorithm is well suitable for near-field nonstationary source localization and does not require parameter-pairing or multidimensional search. Several simulation examples confirm the effectiveness of the proposed algorithm.

The Mississippi River high water levels in 2011 and 2016 resulted in the opening of the Bonnet Carré Spillway (BCS), introducing nutrients and terrestrial sourced dissolved organic matter (DOM) into Lake Pontchartrain Estuary. The resulting dynamic change in concentration and composition of the DOM was measured using ultraviolet visible (A254, A350, SUVA254, and S275-295) and fluorescence spectroscopy (excitation emission matrices and fluorescence and biological indices). Additionally, the analysis was enhanced and individual fluorophores of DOM were determined using multi-way parallel factor analysis (PARAFAC). Through comparing the results of the 2011 dataset and 2016 dataset, similarities in the DOM composition during diversions were determined and variations of the overall DOM composition were identified and predicted to be the result in variations of temperature, sunlight, and rain fall.