Estimación Espectral de Series de Tiempo de Absorbancia Uv-Vis para el Monitoreo de Calidad de Aguas

Context: Signals recorded as multivariate time series by UV-Vis absorbance captors installed in urban sewer systems, can be non-stationary, yielding complications in the analysis of water quality monitoring. This work proposes to perform spectral estimation using the Box-Cox transformation and differentiation in order to obtain stationary multivariate time series in a wide sense. Additionally, Principal Component Analysis (PCA) is applied to reduce their dimensionality.Method: Three different UV-Vis absorbance time series for different Colombian locations were studied: (i) El-Salitre Wastewater Treatment Plant (WWTP) in Bogotá; (ii) Gibraltar Pumping Station (GPS) in Bogotá; and (iii) San-Fernando WWTP in Itagüí. Each UV-Vis absorbance time series had equal sample number (5705). The esti-mation of the spectral power density is obtained using the average of modified periodograms with rectangular window and an overlap of 50%, with the 20 most important harmonics from the Discrete Fourier Transform (DFT) and Inverse Fast Fourier Transform (IFFT).Results: Absorbance time series dimensionality reduction using PCA, resulted in 6, 8 and 7 principal components for each study site respectively, altogether explaining more than 97% of their variability. Values of differences below 30% for the UV range were obtained for the three study sites, while for the visible range the maximum differences obtained were: (i) 35% for El-Salitre WWTP; (ii) 61% for GPS; and (iii) 75% for San-Fernando WWTP.Conclusions: The Box-Cox transformation and the differentiation process applied to the UV-Vis absorbance time series for the study sites (El-Salitre, GPS and San-Fernando), allowed to reduce variance and to eliminate ten-dency of the time series. A pre-processing of UV-Vis absorbance time series is recommended to detect and remove outliers and then apply the proposed process for spectral estimation.Language: Spanish.

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Comparison of discrete Fourier transform (DFT) and principal component analysis/DFT as forecasting tools for absorbance time series received by UV-visible probes installed in urban sewer systems

Water Science & Technology ◽

10.2166/wst.2014.011 ◽

2014 ◽

Vol 69 (5) ◽

pp. 1101-1107 ◽

Cited By ~ 2

Author(s):

Leonardo Plazas-Nossa ◽

Andrés Torres

Keyword(s):

Principal Component Analysis ◽

Time Series ◽

Fourier Transform ◽

Discrete Fourier Transform ◽

Treatment Plant ◽

Water System ◽

Principal Component ◽

Component Analysis ◽

Visible Range ◽

General Terms

The objective of this work is to introduce a forecasting method for UV-Vis spectrometry time series that combines principal component analysis (PCA) and discrete Fourier transform (DFT), and to compare the results obtained with those obtained by using DFT. Three time series for three different study sites were used: (i) Salitre wastewater treatment plant (WWTP) in Bogotá; (ii) Gibraltar pumping station in Bogotá; and (iii) San Fernando WWTP in Itagüí (in the south part of Medellín). Each of these time series had an equal number of samples (1051). In general terms, the results obtained are hardly generalizable, as they seem to be highly dependent on specific water system dynamics; however, some trends can be outlined: (i) for UV range, DFT and PCA/DFT forecasting accuracy were almost the same; (ii) for visible range, the PCA/DFT forecasting procedure proposed gives systematically lower forecasting errors and variability than those obtained with the DFT procedure; and (iii) for short forecasting times the PCA/DFT procedure proposed is more suitable than the DFT procedure, according to processing times obtained.

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Detection of Outliers and Imputing of Missing Values for Water Quality UV-VIS Absorbance Time Series

Ingeniería ◽

10.14483/udistrital.jour.reving.2017.1.a01 ◽

2017 ◽

Vol 22 (1) ◽

pp. 09

Author(s):

Leonardo Plazas-Nossa ◽

Miguel Antonio Ávila Angulo ◽

Andres Torres

Keyword(s):

Water Quality ◽

Time Series ◽

Fourier Transform ◽

Missing Values ◽

Waste Water Treatment ◽

Treatment Plant ◽

Water Treatment Plant ◽

Waste Water Treatment Plant ◽

Testing Time ◽

Hydrologic Time Series

Context: The UV-Vis absorbance collection using online optical captors for water quality detection may yield outliers and/or missing values. Therefore, data pre-processing is a necessary pre-requisite to monitoring data processing. Thus, the aim of this study is to propose a method that detects and removes outliers as well as fills gaps in time series.Method: Outliers are detected using Winsorising procedure and the application of the Discrete Fourier Transform (DFT) and the Inverse of Fast Fourier Transform (IFFT) to complete the time series. Together, these tools were used to analyse a case study comprising three sites in Colombia ((i) Bogotá D.C. Salitre-WWTP (Waste Water Treatment Plant), influent; (ii) Bogotá D.C. Gibraltar Pumping Station (GPS); and, (iii) Itagüí, San Fernando-WWTP, influent (Medellín metropolitan area)) analysed via UV-Vis (Ultraviolet and Visible) spectra.Results: Outlier detection with the proposed method obtained promising results when window parameter values are small and self-similar, despite that the three time series exhibited different sizes and behaviours. The DFT allowed to process different length gaps having missing values. To assess the validity of the proposed method, continuous subsets (a section) of the absorbance time series without outlier or missing values were removed from the original time series obtaining an average 12% error rate in the three testing time series.Conclusions: The application of the DFT and the IFFT, using the 10% most important harmonics of useful values, can be useful for its later use in different applications, specifically for time series of water quality and quantity in urban sewer systems. One potential application would be the analysis of dry weather interesting to rain events, a feat achieved by detecting values that correspond to unusual behaviour in a time series. Additionally, the result hints at the potential of the method in correcting other hydrologic time series.

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Nonstationary Stochastic Modelling of Multivariate Long-Term Wind and Wave Data

24th International Conference on Offshore Mechanics and Arctic Engineering: Volume 2 ◽

10.1115/omae2005-67461 ◽

2005 ◽

Cited By ~ 6

Author(s):

Christos N. Stefanakos ◽

Konstandinos A. Belibassakis

Keyword(s):

Time Series ◽

Standard Deviation ◽

Multivariate Time Series ◽

Stochastic Modelling ◽

Mean Value ◽

Wave Data ◽

Available Information ◽

Periodic Components ◽

Box Cox Transformation

In the present work, a nonstationary stochastic model, which is suitable for the analysis and simulation of multivariate time series of wind and wave data, is being presented and validated. This model belongs to the class of periodically correlated stochastic processes with yearly periodic mean value and standard deviation (periodically correlated or cyclostationary stochastic process). First, the time series is appropriately transformed to become Gaussian using the Box-Cox transformation. Then, the series is decomposed, using an appropriate seasonal standardization procedure, to a periodic (deterministic) mean value and a (stochastic) residual time series multiplied by a periodic (deterministic) standard deviation. The periodic components are estimated using appropriate time series of monthly data. The residual stochastic part, which is proved to be stationary, is modelled as a VARMA process. This way the initial process can be given the structure of a multivariate periodically correlated process. The present methodology permits a reliable reproduction of available information about wind and wave conditions, which is required for a number of applications.

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