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

2014 ◽  
Vol 69 (5) ◽  
pp. 1101-1107 ◽  
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.

scholarly journals Forecasting of UV-Vis absorbance time series using artificial neural networks combined with principal component analysis

2016 ◽  
Vol 75 (4) ◽  
pp. 765-774
Author(s):  
Leonardo Plazas-Nossa ◽  
Thomas Hofer ◽  
Günter Gruber ◽  
Andres Torres
Keyword(s):  
Neural Networks ◽  
Principal Component Analysis ◽  
Time Series ◽  
Artificial Neural Networks ◽  
Principal Component ◽  
Component Analysis ◽  
Series Data ◽  
Visible Range ◽  
Artificial Neural ◽  
Uv Range

This work proposes a methodology for the forecasting of online water quality data provided by UV-Vis spectrometry. Therefore, a combination of principal component analysis (PCA) to reduce the dimensionality of a data set and artificial neural networks (ANNs) for forecasting purposes was used. The results obtained were compared with those obtained by using discrete Fourier transform (DFT). The proposed methodology was applied to four absorbance time series data sets composed by a total number of 5705 UV-Vis spectra. Absolute percentage errors obtained by applying the proposed PCA/ANN methodology vary between 10% and 13% for all four study sites. In general terms, the results obtained were hardly generalizable, as they appeared to be highly dependent on specific dynamics of the water system; however, some trends can be outlined. PCA/ANN methodology gives better results than PCA/DFT forecasting procedure by using a specific spectra range for the following conditions: (i) for Salitre wastewater treatment plant (WWTP) (first hour) and Graz West R05 (first 18 min), from the last part of UV range to all visible range; (ii) for Gibraltar pumping station (first 6 min) for all UV-Vis absorbance spectra; and (iii) for San Fernando WWTP (first 24 min) for all of UV range to middle part of visible range.

scholarly journals Detection of Lethal Bronzing Disease in Cabbage Palms (Sabal palmetto) Using a Low-Cost Electronic Nose

Biosensors ◽  
2020 ◽  
Vol 10 (11) ◽  
pp. 188
Author(s):  
Martin J. Oates ◽  
Nawaf Abu-Khalaf ◽  
Carlos Molina-Cabrera ◽  
Antonio Ruiz-Canales ◽  
Jose Ramos ◽  
...  
Keyword(s):  
Principal Component Analysis ◽  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Electronic Nose ◽  
Low Cost ◽  
Harmonic Component ◽  
Principal Component ◽  
Component Analysis ◽  
Sabal Palmetto ◽  
Cabbage Palm

Lethal Bronzing Disease (LB) is a disease of palms caused by the 16SrIV-D phytoplasma. A low-cost electronic nose (eNose) prototype was trialed for its detection. It includes an array of eight Taguchi-type (MQ) sensors (MQ135, MQ2, MQ3, MQ4, MQ5, MQ9, MQ7, and MQ8) controlled by an Arduino NANO® microcontroller, using heater voltages that vary sinusoidally over a 2.5 min cycle. Samples of uninfected, early symptomatic, moderate symptomatic, and late symptomatic infected palm leaves of the cabbage palm were processed and analyzed. MQ sensor responses were subjected to a 256 element discrete Fourier transform (DFT), and harmonic component amplitudes were reviewed by principal component analysis (PCA). The experiment was repeated three times, each showing clear evidence of differences in sensor responses between the samples of uninfected leaves and those in the early stages of infection. Within each experiment, four groups of responses were identified, demonstrating the ability of the unit to repeatedly distinguish healthy leaves from diseased ones; however, detection of the severity of infection has not been demonstrated. By selecting appropriate coefficients (here demonstrated with plots of MQ5 Cos1 vs. MQ8 Sin3), it should be possible to build a ruleset classifier to identify healthy and unhealthy samples.

scholarly journals PCA/DFT como herramienta de pronóstico para series temporales de absorbancia registradas mediante captores UV-Vis en sistemas de saneamiento urbano

Tecnura ◽  
2015 ◽  
Vol 19 (44) ◽  
pp. 47
Author(s):  
Leonardo Plazas Nossa ◽  
Andrés Torres
Keyword(s):  
Principal Component Analysis ◽  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Discrete Fourier Transform ◽  
Principal Component ◽  
Component Analysis ◽  
Inverse Fast Fourier Transform ◽  
San Fernando

El objetivo de este trabajo es presentar un método de pronóstico para series de tiempo de espectrometría UV-Vis, combinando el análisis de componentes principales PCA (Principal Component Analysis), la transformada discreta de Fourier, DFT (Discrete Fourier Transform) y la transformada inversa de Fourier, IFFT (Inverse Fast Fourier Transform). Se utilizaron las correspondientes series de tiempo de absorbancia para tres diferentes sitios de estudio: (i) Planta de tratamiento de aguas residuales Salitre (PTAR) en Bogotá; (ii) Estación elevadora de Gibraltar en Bogotá; y (iii) Planta de tratamiento de aguas residuales San Fernando (PTAR) en Itagüí (parte sur de Medellín). Cada una de las series de tiempo tiene igual número de muestras (5705). Al reducir la dimensionalidad de las series de tiempo de absorbancia con PCA, se utilizan para cada sitio de estudio 3, 5 y 6 componentes principales, respectivamente; explicando en conjunto más de 97% de la variabilidad. Se utiliza en el procedimiento DFT e IFFT el armónico más importante y se remueven desde uno hasta la mitad de los valores de la longitud total de las series de tiempo. Por consiguiente, los errores de pronóstico para los tres sitios de estudio y para tres rangos de longitudes de onda propuestos (UV, Vis y UV-Vis) están comprendidos entre 0,01% y 34% para 95% de los casos. Sin embargo, para 100% de los casos los errores son inferiores a 37%, independientemente de la longitud de onda y del tiempo de pronóstico.

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

Ingeniería ◽  
2017 ◽  
Vol 22 (2) ◽  
pp. 211
Author(s):  
Leonardo Plazas-Nossa ◽  
Miguel Antonio Ávila Angulo ◽  
Andres Torres
Keyword(s):  
Time Series ◽  
Fourier Transform ◽  
Multivariate Time Series ◽  
Treatment Plant ◽  
Visible Range ◽  
Wide Sense ◽  
Sample Number ◽  
San Fernando ◽  
Study Sites ◽  
Box Cox Transformation

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.

scholarly journals Optimal Vehicle Pose Estimation Network Based on Time Series and Spatial Tightness with 3D LiDARs

2021 ◽  
Vol 13 (20) ◽  
pp. 4123
Author(s):  
Hanqi Wang ◽  
Zhiling Wang ◽  
Linglong Lin ◽  
Fengyu Xu ◽  
Jie Yu ◽  
...  
Keyword(s):  
Principal Component Analysis ◽  
Time Series ◽  
Pose Estimation ◽  
Point Cloud ◽  
Principal Component ◽  
Component Analysis ◽  
Evaluation Index ◽  
Evaluation Indexes ◽  
Learning Network ◽  
Estimation Algorithms

Vehicle pose estimation is essential in autonomous vehicle (AV) perception technology. However, due to the different density distributions of the point cloud, it is challenging to achieve sensitive direction extraction based on 3D LiDAR by using the existing pose estimation methods. In this paper, an optimal vehicle pose estimation network based on time series and spatial tightness (TS-OVPE) is proposed. This network uses five pose estimation algorithms proposed as candidate solutions to select each obstacle vehicle's optimal pose estimation result. Among these pose estimation algorithms, we first propose the Basic Line algorithm, which uses the road direction as the prior knowledge. Secondly, we propose improving principal component analysis based on point cloud distribution to conduct rotating principal component analysis (RPCA) and diagonal principal component analysis (DPCA) algorithms. Finally, we propose two global algorithms independent of the prior direction. We provided four evaluation indexes to transform each algorithm into a unified dimension. These evaluation indexes’ results were input into the ensemble learning network to obtain the optimal pose estimation results from the five proposed algorithms. The spatial dimension evaluation indexes reflected the tightness of the bounding box and the time dimension evaluation index reflected the coherence of the direction estimation. Since the network was indirectly trained through the evaluation index, it could be directly used on untrained LiDAR and showed a good pose estimation performance. Our approach was verified on the SemanticKITTI dataset and our urban environment dataset. Compared with the two mainstream algorithms, the polygon intersection over union (P-IoU) average increased by about 5.25% and 9.67%, the average heading error decreased by about 29.49% and 44.11%, and the average speed direction error decreased by about 3.85% and 46.70%. The experiment results showed that the ensemble learning network could effectively select the optimal pose estimation from the five abovementioned algorithms, making pose estimation more accurate.

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