Analyse en ondelettes de fluctuations de débit en réseau de distribution d’eau potable

Abstract

Ce travail évalue la pertinence d’une analyse en ondelettes appliquée à la consommation en eau potable, afin d’établir les habitudes de consommation des usagers et de détecter des changements. Cette démonstration exploite une série d’observations de débit au pas de temps horaire, couvrant une période de dix semaines dont le congé des Fêtes de fin d’année, tirée du réseau de distribution d’eau potable de la ville de Québec, Canada. Les résultats confirment la non-stationnarité du débit pour la gamme de périodes à l’étude, soit de 2 à 256 heures. Le principal cycle, qui explique la moitié de la variance naturelle de la série, possède une période de 24 heures dont l’intensité non stationnaire décrit un cycle de sept jours avec des pointes le dimanche matin et des creux au coeur de la semaine de travail. Le second cycle, responsable de plus du tiers de la variance, possède une période de 12 heures dont l’intensité suit également (mais un peu moins clairement) un cycle de sept jours avec des pointes la semaine et des creux le week-end. Ce comportement diffère pendant le congé des Fêtes de fin d’année, lorsque presque toute la variance naturelle est expliquée par la composante 24 heures de la série.This study evaluates the relevance of wavelet analysis applied to water consumption in order to detect habits and changes in these habits. The demonstration is based on a series of one-hour flow observations from Quebec City’s water distribution flowmeter network for a 10-week period, which includes Christmas and the New Year holidays. Results confirm the non-stationarity of the flow data for all studied periods, which range from 2 to 256 h. The main cycle, which accounts for half of the natural variance of the series, has a period of 24 h, with a non-stationary intensity varying over 7 d, peaking on Sunday mornings and with lows during the work week. The second cycle, responsible for a third of the variance, has a period of 12 h, with an intensity which follows (although not as strongly as the previous cycle) a 7-d cycle, peaking during the week and with lows during the weekend. This behaviour differs during the Holidays, when most of the natural variance is explained by the 24-h component of the series

A new regionalization of rainfall patterns based on wavelet transform information and hierarchical cluster analysis in northeastern Algeria

“…According to Anctil and Pelletier (2011), calculating an average power spectrum using bands of periods allows the clear illustration of the differences in the frequency distribution and temporal evolution of the variance. The spectrum for a selected band consists of the weighted sum of the power spectrum between two scales, s1 and s2, defined by the user (Torrence and Compo, 1998;Santos et al, 2001;Grinsted et al, 2004;Santos et al, 2013).…”

Wavelet Analysis of the Interconnection between Atmospheric Aerosol Types and Direct Irradiation over Cameroon

“…Many wavelet functions are available in the literature. In this study, Morlet's function [53,54] is used because of its ability to detect specific periodic behaviors in a signal [55]. In addition, it consists of both real and imaginary parts that enable investigating a signal's coherence and phase angle [22,33,35].…”

“…Coherence analysis, cospectral power, and wavelet phase coherence are often used to identify the degree of correlation between two signals. e wavelet coherence expressed in (7) enables highlighting relations of influence between two signals at different frequencies (scales) as a function of time [36,37,53,57]. Its values range between 0 and 1.…”