271 lines
8.5 KiB
Python
271 lines
8.5 KiB
Python
import csv
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import matplotlib.pyplot as plt
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import os
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import math
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import sys
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import numpy as np
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from matplotlib import animation
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import cmath
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from scipy.fft import fft
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def newtonpplus(f, h, u):
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# calcul de k:
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g = 9.81
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kh = 0.5
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x = 0.001
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u = -u
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while abs((kh - x) / x) > 0.00000001:
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x = kh
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fx = x * math.tanh(x) - (h / g) * (2 * math.pi * f - (u / h) * x) * (
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2 * math.pi * f - (u / h) * x
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)
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fprimx = (
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math.tanh(x)
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+ x * (1 - (math.tanh(x)) ** 2)
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+ (2 * u / g) * (2 * math.pi * f - (u / h) * x)
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)
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kh = x - (fx / fprimx)
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k = kh / h
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return k
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def newtonpmoins(f, h, u0):
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# calcul de k:
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g = 9.81
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kh = 0.5
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x = 0.01
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x = 6 * h
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while np.abs((kh - x) / x) > 0.00000001:
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x = kh
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fx = x * math.tanh(x) - (h / g) * (2 * math.pi * f - (u0 / h) * x) * (
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2 * math.pi * f - (u0 / h) * x
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)
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fprimx = (
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math.tanh(x)
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+ x * (1 - (math.tanh(x)) ** 2)
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+ (2 * u0 / g) * (2 * math.pi * f - (u0 / h) * x)
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)
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kh = x - (fx / fprimx)
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k = kh / h
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return k
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# Calcul du vecteur d'onde a partir de la frÈquence
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# kh : vecteur d'onde * profondeur d'eau
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def newtonpropa(hi, f):
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# calcul de k:
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g = 9.81
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si = (2 * math.pi * f) ** 2 / g
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kh = 0.5
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x = 0.001
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while np.abs((kh - x) / x) > 0.00000001:
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x = kh
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fx = x * math.tanh(x) - si * hi
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fprimx = math.tanh(x) + x * (1 - (math.tanh(x)) ** 2)
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kh = x - (fx / fprimx)
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kpropa = kh / hi
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return kpropa
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def reflex3S(x1, x2, x3, xs1, xs2, xs3, h, mean_freq, fmin, fmax):
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# Analyse avec transformee de fourier d un signal en sinus
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# calcul du coefficient de reflexion en presence d un courant u
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# tinit : temps initial
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# tfinal : temps final
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# deltat : pas de temps
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# fech= 1/deltat : frequence d echantillonnage
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# T : periode de la houle
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# nbrepoints : nombre de points
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# fmin : frequence minimale de recherche des maxima du signal de fourier
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# fmax : frequence maximale de recherche des maxima du signal de fourier
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# ampliseuil : amplitude minimale des maxima recherches
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# valeur du courant (u > 0 correspond a un courant dans le sens
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# des x croissants)
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# u=0;
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# h profondeur d'eau
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# hold on;
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# fech=16;
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# fmin=0.1;fmax=4;ampliseuil=0.005;
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# nbrepoints=fech*T*1000;
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# deltat=1./fech;
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# tinit=0;tfinal=tinit+deltat*(nbrepoints-1);
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# aitheo=1;artheo=0.4;
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# h=3;
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# T=1.33;
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# ftheo=1/T;
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# fech=16;
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# fmin=0.1;fmax=4;ampliseuil=0.005;
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# nbrepoints=fech*T*1000;
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# deltat=1./fech;
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# tinit=0;tfinal=tinit+deltat*(nbrepoints-1);
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# t = [tinit:deltat:tfinal];
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# ktheo = newtonpropa(ftheo,h);
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# Positions respectives sondes amonts entr'elles et sondes aval
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# entr'elles
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# xs1=0;xs2=0.80;xs3=1.30;
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# ENTREES DONNEES DES 3 SONDES AMONT et des 2 SONDES AVAL
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ampliseuil = 0.005
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#'check'
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# pause
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# PAS DE TEMPS
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deltat1 = 1 / mean_freq
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deltat2 = 1 / mean_freq
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deltat3 = 1 / mean_freq
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# transformees de Fourier
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Y1 = fft(x1, len(x1))
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N1 = len(Y1)
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Y2 = fft(x2, len(x2))
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N2 = len(Y2)
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Y3 = fft(x3, len(x3))
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N3 = len(Y3)
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# amplitudes normalisees, soit coef de fourier
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amplitude1 = np.abs(Y1[1 : N1 // 2]) / (N1 // 2)
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nyquist = 1 / 2
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freq1 = (np.arange(1, (N1 // 2) + 1, 1) - 1) / (N1 // 2) / deltat1 * nyquist
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amplitude2 = np.abs(Y2[1 : N2 // 2]) / (N2 // 2)
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nyquist = 1 / 2
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freq2 = (np.arange(1, (N2 // 2) + 1, 1) - 1) / (N2 // 2) / deltat2 * nyquist
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amplitude3 = np.abs(Y3[1 : N3 // 2]) / (N3 // 2)
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nyquist = 1 / 2
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freq3 = (np.arange(1, (N3 // 2) + 1, 1) - 1) / (N3 // 2) / deltat3 * nyquist
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# recherche de la phase
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theta1 = np.angle(Y1[1 : N1 // 2])
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theta2 = np.angle(Y2[1 : N2 // 2])
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theta3 = np.angle(Y3[1 : N3 // 2])
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# pas de frequence deltaf
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deltaf = 1 / (N1 // 2) / deltat1 * nyquist
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nbrefreq = len(freq1)
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# Caracteristiques fondamentaux,sondes canaux 1 et 3
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# distances entre les sondes
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x12 = xs2 - xs1
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x13 = xs3 - xs1
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x23 = xs3 - xs2
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# Debut calcul des coefficients de reflexion
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indmin = np.min(np.where(freq1 > 0.02))
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indfmin = np.min(np.where(freq1 > fmin))
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indfmax = np.max(np.where(freq1 < fmax))
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T = []
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fre = []
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aincident12 = []
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aincident23 = []
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aincident13 = []
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areflechi12 = []
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areflechi23 = []
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areflechi13 = []
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r13 = []
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ai = []
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ar = []
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Eincident123 = []
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Ereflechi123 = []
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count = 0
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for jj in np.arange(indfmin, indfmax, 1):
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f = freq1[jj]
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# periode
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T.append(1 / f)
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fre.append(f)
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# calcul des vecteurs d'onde
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kplus = newtonpplus(f, h, 0)
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kmoins = newtonpmoins(f, h, 0)
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k = newtonpropa(h, f)
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deltaku = k - (kmoins + kplus) / 2
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# amplitude des signaux pour la frequence f:
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a1 = amplitude1[jj]
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a2 = amplitude2[jj]
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a3 = amplitude3[jj]
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# dephasages entre les signaux experimentaux des 3 sondes amont
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phi1 = theta1[jj]
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phi2 = theta2[jj]
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phi3 = theta3[jj]
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phi12 = phi2 - phi1
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phi13 = phi3 - phi1
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phi23 = phi3 - phi2
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# evolution theorique entre les sondes de la phase pour une onde progressive
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delta12p = -kplus * x12
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delta13p = -kplus * x13
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delta23p = -kplus * x23
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delta12m = -kmoins * x12
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delta13m = -kmoins * x13
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delta23m = -kmoins * x23
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# calcul du coefficient de reflexion a partir des sondes 1 et 2
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aincident12.append(
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math.sqrt(a1 * a1 + a2 * a2 - 2 * a1 * a2 * math.cos(phi12 + delta12p))
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/ (2 * np.abs(math.sin((delta12p + delta12m) / 2)))
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)
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areflechi12.append(
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math.sqrt(a1 * a1 + a2 * a2 - 2 * a1 * a2 * math.cos(phi12 - delta12m))
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/ (2 * np.abs(math.sin((delta12p + delta12m) / 2)))
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)
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# r12(jj)=areflechi12(jj)/aincident12(jj);
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# calcul du coefficient de reflexion a partir des sondes 2 et 3
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aincident23.append(
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math.sqrt(a2 * a2 + a3 * a3 - 2 * a2 * a3 * math.cos(phi23 + delta23p))
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/ (2 * np.abs(math.sin((delta23p + delta23m) / 2)))
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)
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areflechi23.append(
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math.sqrt(a2 * a2 + a3 * a3 - 2 * a2 * a3 * math.cos(phi23 - delta23m))
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/ (2 * np.abs(math.sin((delta23p + delta23m) / 2)))
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)
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# r23(jj)=areflechi23(jj)/aincident23(jj);
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# calcul du coefficient de reflexion a partir des sondes 1 et 3
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aincident13.append(
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math.sqrt(a1 * a1 + a3 * a3 - 2 * a1 * a3 * math.cos(phi13 + delta13p))
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/ (2 * np.abs(math.sin((delta13p + delta13m) / 2)))
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)
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areflechi13.append(
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math.sqrt(a1 * a1 + a3 * a3 - 2 * a1 * a3 * math.cos(phi13 - delta13m))
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/ (2 * np.abs(math.sin((delta13p + delta13m) / 2)))
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)
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# r13.append(areflechi13[jj]/aincident13[jj])
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# calcul du coefficient de reflexion par methode des 3 sondesavec moindres carres
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delta1m = 0
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delta2m = delta12m
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delta3m = delta13m
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delta1p = 0
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delta2p = delta12p
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delta3p = delta13p
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s1 = (
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cmath.exp(-1j * 2 * delta1m)
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+ cmath.exp(-1j * 2 * delta2m)
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+ cmath.exp(-1j * 2 * delta3m)
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)
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s2 = (
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cmath.exp(+1j * 2 * delta1p)
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+ cmath.exp(+1j * 2 * delta2p)
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+ cmath.exp(+1j * 2 * delta3p)
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)
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s12 = (
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cmath.exp(1j * (delta1p - delta1m))
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+ cmath.exp(1j * (delta2p - delta2m))
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+ cmath.exp(1j * (delta3p - delta3m))
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)
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s3 = (
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a1 * cmath.exp(-1j * (phi1 + delta1m))
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+ a2 * cmath.exp(-1j * (phi2 + delta2m))
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+ a3 * cmath.exp(-1j * (phi3 + delta3m))
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)
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s4 = (
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a1 * cmath.exp(-1j * (phi1 - delta1p))
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+ a2 * cmath.exp(-1j * (phi2 - delta2p))
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+ a3 * cmath.exp(-1j * (phi3 - delta3p))
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)
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s5 = s1 * s2 - s12 * s12
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ai.append(abs((s2 * s3 - s12 * s4) / s5))
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ar.append(abs((s1 * s4 - s12 * s3) / s5))
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# refl[jj]=ar[jj]/ai[jj];
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# Calcul de l'energie, on divise par le pas de frequence deltaf
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# calcul de l'energie incidente sans ponderation avec les voisins
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Eincident123.append(0.5 * ai[count] * ai[count] / deltaf)
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Ereflechi123.append(0.5 * ar[count] * ar[count] / deltaf)
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count += 1
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return ai, ar, Eincident123, Ereflechi123, indfmin, indfmax, fre
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