Characterisation of Organic Matter and Its Transformation Processes in On-Site Wastewater Effluent Percolating through Soil Using Fluorescence Spectroscopic Methods and Parallel Factor Analysis (PARAFAC)

This research has used fluorescence spectroscopy and parallel factor analysis (PARAFAC) in order to characterize dissolved organic matter in septic tank effluent, as it passes through the biomat/biozone, infiltrating into the unsaturated zone beneath domestic wastewater treatment systems (DWWTSs). Septic tank effluent and soil moisture samples from the percolation areas of two DWWTSs have been analyzed using fluorescence excitation–emission spectroscopy. Using PARAFAC analysis, a six-component model was obtained whereby individual model components could be assigned to humified organic matter, fluorescent whitening compounds (FWCs), and protein-like compounds. This has shown that fluorescent dissolved organic matter (FDOM) in domestic wastewater was dominated by protein-like compounds and FWCs and that, with treatment in the percolation area, protein-like compounds and FWCs are removed and contributions from terrestrially derived (soil) organic decomposition compounds increase, leading to a higher degree of humification and aromaticity. The results also suggest that the biomat is the most important element determining FDOM removal and consequently affecting DOM composition. Furthermore, no significant difference was found in the FDOM composition of samples from the percolation area irrespective of whether they received primary or secondary effluent. Overall, the tested fluorometric methods were shown to provide information about structural and functional properties of organic matter which can be useful for further studies concerning bacterial and/or virus transport from DWWTSs.

A New Algorithm for Computing Disjoint Orthogonal Components in the Parallel Factor Analysis Model with Simulations and Applications to Real-World Data

In this paper, we extend the use of disjoint orthogonal components to three-way table analysis with the parallel factor analysis model. Traditional methods, such as scaling, orthogonality constraints, non-negativity constraints, and sparse techniques, do not guarantee that interpretable loading matrices are obtained in this model. We propose a novel heuristic algorithm that allows simple structure loading matrices to be obtained by calculating disjoint orthogonal components. This algorithm is also an alternative approach for solving the well-known degeneracy problem. We carry out computational experiments by utilizing simulated and real-world data to illustrate the benefits of the proposed algorithm.

Multi-source and multi-fault condition monitoring based on parallel factor analysis and sequential probability ratio test

The monitoring of mechanical equipment systems contains an increasing number of complex content, expanding from traditional time, and frequency information to three-dimensional data of the time, space, and frequency information, and even higher-dimensional data containing subjects, experimental conditions. For high-dimensional data analysis, traditional decomposition methods such as Hilbert transform, fast Fourier transformation, and Gabor transformation not only lose the integrity of the data, but also increase the amount of calculation and introduce a lot of redundant information. The phenomenon of feature coupling, aliasing, and redundancy between the mechanical multi-source data signals will cause the inaccuracy of the evaluation, diagnosis, and prediction of industrial production operation status. The analysis of the three-way tensor composed of channel, frequency, and time is called parallel factor analysis (PARAFAC). The properties between the parallel factor analysis results and the input signals are studied through simulation experiments. Parallel factor analysis is used to decompose the third-order tensor composed of channel-time-frequency after continuous wavelet transformation of vibration signal into channel, time, and frequency characteristics. Multi-scale parallel factor analysis successfully extracted non-linear multi-dimensional dynamic fault characteristics by generating the spatial, spectral, time-domain signal loading value and three-dimensional fault characteristic expression. In order to verify the effectiveness of the space, frequency, and time domain signal loading values of the fault characteristic factors generated by the centrifugal pump system after parallel factor analysis, the characteristic factors obtained after parallel factor analysis are used as the SPRT test sequence for identification and verification. The results indicate that the method proposed in this article improves the measurement accuracy and intelligence of mechanical fault detection.