221 lines
7.4 KiB
Python
221 lines
7.4 KiB
Python
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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 imageio
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import cmath
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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)*(2*math.pi*f-(u/h)*x)
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fprimx = math.tanh(x) + x*(1- (math.tanh(x))**2)+(2*u/g)*(2*math.pi*f-(u/h)*x)
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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)*(2*math.pi*f-(u0/h)*x);
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fprimx = math.tanh(x) + x*(1- (math.tanh(x))**2)+(2*u0/g)*(2*math.pi*f-(u0/h)*x);
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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(math.sqrt(a1*a1+a2*a2-2*a1*a2*math.cos(phi12+delta12p))/(2*np.abs(math.sin((delta12p+delta12m)/2))))
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areflechi12.append(math.sqrt(a1*a1+a2*a2-2*a1*a2*math.cos(phi12-delta12m))/(2*np.abs(math.sin((delta12p+delta12m)/2))))
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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(math.sqrt(a2*a2+a3*a3-2*a2*a3*math.cos(phi23+delta23p))/(2*np.abs(math.sin((delta23p+delta23m)/2))))
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areflechi23.append(math.sqrt(a2*a2+a3*a3-2*a2*a3*math.cos(phi23-delta23m))/(2*np.abs(math.sin((delta23p+delta23m)/2))))
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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(math.sqrt(a1*a1+a3*a3-2*a1*a3*math.cos(phi13+delta13p))/(2*np.abs(math.sin((delta13p+delta13m)/2))))
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areflechi13.append(math.sqrt(a1*a1+a3*a3-2*a1*a3*math.cos(phi13-delta13m))/(2*np.abs(math.sin((delta13p+delta13m)/2))))
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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=cmath.exp(-1j*2*delta1m)+cmath.exp(-1j*2*delta2m)+cmath.exp(-1j*2*delta3m)
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s2=cmath.exp(+1j*2*delta1p)+cmath.exp(+1j*2*delta2p)+cmath.exp(+1j*2*delta3p)
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s12=cmath.exp(1j*(delta1p-delta1m))+cmath.exp(1j*(delta2p-delta2m))+cmath.exp(1j*(delta3p-delta3m))
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s3=a1*cmath.exp(-1j*(phi1+delta1m))+a2*cmath.exp(-1j*(phi2+delta2m))+a3*cmath.exp(-1j*(phi3+delta3m))
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s4=a1*cmath.exp(-1j*(phi1-delta1p))+a2*cmath.exp(-1j*(phi2-delta2p))+a3*cmath.exp(-1j*(phi3-delta3p))
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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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