Medium term load forecasting in distribution systems based on multi linear regression & principal component analysis: A novel approach

This article discusses the methodology and theory of principal component analysis (PCA) for functional data. It first provides an overview of PCA in the context of finite-dimensional data and infinite-dimensional data, focusing on functional linear regression, before considering the applications of PCA for functional data analysis, principally in cases of dimension reduction. It then describes adaptive methods for prediction and weighted least squares in functional linear regression. It also examines the role of principal components in the assessment of density for functional data, showing how principal component functions are linked to the amount of probability mass contained in a small ball around a given, fixed function, and how this property can be used to define a simple, easily estimable density surrogate. The article concludes by explaining the use of PCA for estimating log-density.

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Evaluating the Performance Degradation of Centrifugal Pumps Using the Principal Component Analysis

Journal of Pressure Vessel Technology ◽

10.1115/1.4052522 ◽

2021 ◽

Author(s):

Andrew Eaton ◽

Wael Ahmed ◽

Marwan A. Hassan

Keyword(s):

Principal Component Analysis ◽

Distribution Systems ◽

Water Distribution ◽

Principal Component ◽

Component Analysis ◽

Performance Degradation ◽

Centrifugal Pumps ◽

Pump Performance ◽

Hydraulic Machines ◽

Wide Range

Abstract Centrifugal pumps are used in a variety of engineering applications, such as power production, heating, cooling, and water distribution systems. Although centrifugal pumps are considered to be highly reliable hydraulic machines, they are susceptible to a wide range of damage due to several degradation mechanisms, which make them operate away from their best efficiency range. Therefore, evaluating the energy efficiency and performance degradation of pumps is an important consideration to the operation of these systems. In the present study, the hydraulic performance along with the vibration response of an industrial scale centrifugal pump (7.5KW) subjected to different levels of impeller unbalance were experimentally investigated. Extensive testing of pump performance along with vibration measurements were carried. Both time and frequency domain techniques coupled with principal component analysis (PCA) were used in this evaluation. The effect of unbalance on the pump performance was found to be mainly on the shaft power, while no change in the flow rate and the pump head were observed. As the level of unbalance increased, the power required to operate the pump at the designated speed increased by as much as 12%. The PCA found to be a useful tool in comparing the pump vibrations in the field in order to determine the presence of unbalance as well as the degree of damage. The results of this work can be used to evaluate and monitor pump performance under prescribed degradation in order to enhance preventative maintenance programs.

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Online Monitoring of Water-Quality Anomaly in Water Distribution Systems Based on Probabilistic Principal Component Analysis by UV-Vis Absorption Spectroscopy

Journal of Spectroscopy ◽

10.1155/2014/150636 ◽

2014 ◽

Vol 2014 ◽

pp. 1-9 ◽

Cited By ~ 14

Author(s):

Dibo Hou ◽

Shu Liu ◽

Jian Zhang ◽

Fang Chen ◽

Pingjie Huang ◽

...

Keyword(s):

Water Quality ◽

Principal Component Analysis ◽

Water Contamination ◽

Distribution Systems ◽

Water Distribution ◽

Online Monitoring ◽

Principal Component ◽

Component Analysis ◽

Probabilistic Principal Component Analysis ◽

Contamination Events

This study proposes a probabilistic principal component analysis- (PPCA-) based method for online monitoring of water-quality contaminant events by UV-Vis (ultraviolet-visible) spectroscopy. The purpose of this method is to achieve fast and sound protection against accidental and intentional contaminate injection into the water distribution system. The method is achieved first by properly imposing a sliding window onto simultaneously updated online monitoring data collected by the automated spectrometer. The PPCA algorithm is then executed to simplify the large amount of spectrum data while maintaining the necessary spectral information to the largest extent. Finally, a monitoring chart extensively employed in fault diagnosis field methods is used here to search for potential anomaly events and to determine whether the current water-quality is normal or abnormal. A small-scale water-pipe distribution network is tested to detect water contamination events. The tests demonstrate that the PPCA-based online monitoring model can achieve satisfactory results under the ROC curve, which denotes a low false alarm rate and high probability of detecting water contamination events.

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