def perturb_rot(rpath, wpath, dth):
# dht - amount to rotate blade
cdim, sdim, x, y, z = read_blade.read_coords(rpath)
# split the blade
xu,yu,zu,xl,yl,zl = read_blade.split_blade(cdim,sdim,x,y,z)
xle = xu[0,0]; yle = yu[0,0]
xte = xu[-1,0]; yte = yu[-1,0]
th = arctan2(y-yle,x-xle)
r = sqrt((x-xle)**2 + (y-yle)**2)
xp = xle + r*cos(th+dth)
yp = yle + r*sin(th+dth)
zp = copy(z)
pylab.plot(x[:,0],y[:,0])
pylab.plot(xp[:,0],yp[:,0])
pylab.axis('Equal')
pylab.show()
# write out the blade surface
f = open(wpath,'w')
f.write('CDIM: %d\n' % cdim)
f.write('SDIM: %d\n' % sdim)
for i in arange(cdim):
for j in arange(sdim):
f.write('%20.8E' * 3 % (xp[i,j],yp[i,j],zp[i,j]))
f.write('\n')
f.close()
# write out to tecplot format
write_tecplot.write_blade_surf(xp,yp,zp,'tec_blade.dat')
def perturb(rpath, wpath, kl_path, Z_path, dth_path, nkl):
# inputs
# Z_path : where to write out the sample normal
# dth_path : where to write out the random rotation
# nkl : where to truncate the K-L expansion
cdim, sdim, x, y, z = read_blade.read_coords(rpath)
# translate blade random amount (rotate about x axis)
random.seed()
dth = random.randn(1)*pi/180*0.1/3.0
for i in range(cdim):
for j in range(sdim):
r = sqrt(y[i,j]**2 + z[i,j]**2)
th = math.atan2(z[i,j],y[i,j])
y[i,j] = r*cos(th+dth)
z[i,j] = r*sin(th+dth)
# write out dth
f = open(dth_path,'w')
f.write('%e\n' % dth)
f.close()
# generate and write out the Z for this mesh
random.seed()
Z = random.randn(nkl) # normal distribution vector
f = open(Z_path,'w')
for i in range(nkl):
f.write('%e\n' % Z[i])
f.close()
# read in PCA modes and singular values
lines = file(kl_path+'S.dat').readlines()
S = array([line.strip().split()[0] for line in lines], float).T
n_modes = len(S)
fp = zeros((cdim,sdim))
for i in range(nkl):
cdim,sdim,V = read_blade.read_mode(kl_path+'V'+str(i+1)+'.dat')
fp += Z[i]*sqrt(S[i])*V
np = read_blade.calcNormals(x,y,z)
xp = x + np[:,:,0]*fp
yp = y + np[:,:,1]*fp
zp = z + np[:,:,2]*fp
# write out the blade surface
f = open(wpath,'w')
f.write('CDIM: %d\n' % cdim)
f.write('SDIM: %d\n' % sdim)
for i in arange(cdim):
for j in arange(sdim):
f.write('%20.8E' * 3 % (xp[i,j],yp[i,j],zp[i,j]))
f.write('\n')
f.close()
# write out to tecplot format
write_tecplot.write_blade_surf(xp,yp,zp,fp,'blade.dat')
def perturb_chev(rpath, wpath, M):
# M - amplitudes of the Chevyshev modes
cdim, sdim, x, y, z = read_blade.read_coords(rpath)
# split the blade
xu,yu,zu,xl,yl,zl = read_blade.split_blade(cdim,sdim,x,y,z)
# compute the s coordinates
tck, su = splprep([xu[:,0],yu[:,0]],s=0)
tck, sl = splprep([xl[:,0],yl[:,0]],s=0)
# form the modes
nmodes = len(M)
cheb = zeros((nmodes,x.shape[0],x.shape[1]))
for i in arange(nmodes):
n = i + 1
if mod(n,2) == 0:
gu = (1-2*su-cos((n+1)*arccos(1-2*su)))/(n+1.)
gl = -(1-2*sl-cos((n+1)*arccos(1-2*sl)))/(n+1.)
cheb[i,:,:] = tile(hstack((gu,gl[::-1][1:])),(sdim,1)).T
else:
gu = (1-cos((n+1)*arccos(1-2*su)))/(n+1.)
gl = -(1-cos((n+1)*arccos(1-2*sl)))/(n+1.)
cheb[i,:,:] = tile(hstack((gu,gl[::-1][1:])),(sdim,1)).T
np = read_blade.calcNormals(x,y,z)
for i in arange(nmodes):
xp = x + np[:,:,0]*cheb[i,:,:]*M[i]
yp = y + np[:,:,1]*cheb[i,:,:]*M[i]
zp = z + np[:,:,2]*cheb[i,:,:]*M[i]
pylab.plot(x[:,0],y[:,0])
pylab.plot(xp[:,0],yp[:,0])
pylab.axis('Equal')
pylab.show()
# write out the blade surface
f = open(wpath,'w')
f.write('CDIM: %d\n' % cdim)
f.write('SDIM: %d\n' % sdim)
for i in arange(cdim):
for j in arange(sdim):
f.write('%20.8E' * 3 % (xp[i,j],yp[i,j],zp[i,j]))
f.write('\n')
f.close()
# write out to tecplot format
write_tecplot.write_blade_surf(xp,yp,zp,'tec_blade.dat')
def perturb_chev(rpath, wpath, M):
# M - amplitudes of the Chevyshev modes
cdim, sdim, x, y, z = read_blade.read_coords(rpath)
# split the blade
xu, yu, zu, xl, yl, zl = read_blade.split_blade(cdim, sdim, x, y, z)
# compute the s coordinates
tck, su = splprep([xu[:, 0], yu[:, 0]], s=0)
tck, sl = splprep([xl[:, 0], yl[:, 0]], s=0)
# form the modes
nmodes = len(M)
cheb = zeros((nmodes, x.shape[0], x.shape[1]))
for i in arange(nmodes):
n = i + 1
if mod(n, 2) == 0:
gu = (1 - 2 * su - cos((n + 1) * arccos(1 - 2 * su))) / (n + 1.)
gl = -(1 - 2 * sl - cos((n + 1) * arccos(1 - 2 * sl))) / (n + 1.)
cheb[i, :, :] = tile(hstack((gu, gl[::-1][1:])), (sdim, 1)).T
else:
gu = (1 - cos((n + 1) * arccos(1 - 2 * su))) / (n + 1.)
gl = -(1 - cos((n + 1) * arccos(1 - 2 * sl))) / (n + 1.)
cheb[i, :, :] = tile(hstack((gu, gl[::-1][1:])), (sdim, 1)).T
np = read_blade.calcNormals(x, y, z)
for i in arange(nmodes):
xp = x + np[:, :, 0] * cheb[i, :, :] * M[i]
yp = y + np[:, :, 1] * cheb[i, :, :] * M[i]
zp = z + np[:, :, 2] * cheb[i, :, :] * M[i]
pylab.plot(x[:, 0], y[:, 0])
pylab.plot(xp[:, 0], yp[:, 0])
pylab.axis('Equal')
pylab.show()
# write out the blade surface
f = open(wpath, 'w')
f.write('CDIM: %d\n' % cdim)
f.write('SDIM: %d\n' % sdim)
for i in arange(cdim):
for j in arange(sdim):
f.write('%20.8E' * 3 % (xp[i, j], yp[i, j], zp[i, j]))
f.write('\n')
f.close()
# write out to tecplot format
write_tecplot.write_blade_surf(xp, yp, zp, 'tec_blade.dat')
def perturb_rot(rpath, wpath, dth):
# dht - amount to rotate blade
cdim, sdim, x, y, z = read_blade.read_coords(rpath)
# split the blade
xu, yu, zu, xl, yl, zl = read_blade.split_blade(cdim, sdim, x, y, z)
xle = xu[0, 0]
yle = yu[0, 0]
xte = xu[-1, 0]
yte = yu[-1, 0]
th = arctan2(y - yle, x - xle)
r = sqrt((x - xle)**2 + (y - yle)**2)
xp = xle + r * cos(th + dth)
yp = yle + r * sin(th + dth)
zp = copy(z)
pylab.plot(x[:, 0], y[:, 0])
pylab.plot(xp[:, 0], yp[:, 0])
pylab.axis('Equal')
pylab.show()
# write out the blade surface
f = open(wpath, 'w')
f.write('CDIM: %d\n' % cdim)
f.write('SDIM: %d\n' % sdim)
for i in arange(cdim):
for j in arange(sdim):
f.write('%20.8E' * 3 % (xp[i, j], yp[i, j], zp[i, j]))
f.write('\n')
f.close()
# write out to tecplot format
write_tecplot.write_blade_surf(xp, yp, zp, 'tec_blade.dat')
fname = 'Z_blade'+str(n+1)+'.dat'
f = open(data_dir+fname,'w')
for i in arange(Z.shape[1]):
f.write('%e\n' % Z[n,i])
f.close()
# mesh surface file for interpolating modes to
mesh_path = '/home/ericdow/code/blade_pca/blade_surf.dat'
# read the surface mesh
xyz_mesh = read_mesh_surf(mesh_path)
xmesh = xyz_mesh[:,:,0]
ymesh = xyz_mesh[:,:,1]
zmesh = xyz_mesh[:,:,2]
write_tecplot.write_blade_surf(xmesh,ymesh,zmesh,V,'pca_modes_r37.dat')
'''
# plot the scatter fraction
pylab.figure()
pylab.semilogy(arange(S.shape[0]-1)+1,S[:-1]**2,'*')
pylab.grid(True)
pylab.xlabel('PCA Mode Index')
pylab.ylabel('PCA Eigenvalue')
pylab.figure()
# pylab.plot(arange(S.shape[0]),0.99*ones((S.shape[0])),'r--')
sf = cumsum(S**2)/sum(S**2)
nn = 10
ind = arange(nn)+1
V2 = transform_mode(xyzn,xe,xyz_mesh,ntip)
xe_r37[i,:,:] = V2
fname = 'blade'+str(i+1)+'.dat'
f = open(data_dir+fname,'w')
f.write('CDIM: %d\n' % V2.shape[1])
f.write('SDIM: %d\n' % V2.shape[0])
for i in arange(V2.shape[1]):
for j in arange(V2.shape[0]):
f.write('%e\n' % V2[j,i])
f.close()
xnom = zeros((npps+1,nsec))
ynom = zeros((npps+1,nsec))
znom = zeros((npps+1,nsec))
xnom[:-1,:] = xyzn[:,:,0].T
ynom[:-1,:] = xyzn[:,:,1].T
znom[:-1,:] = xyzn[:,:,2].T
xnom[-1,:] = xnom[0,:]
ynom[-1,:] = ynom[0,:]
znom[-1,:] = znom[0,:]
Vp = zeros((n,npps+1,nsec))
for i in range(n):
Vp[i,:-1,:] = xe_r5[i,:,:].T
Vp[:,-1,:] = Vp[:,0,:]
write_tecplot.write_blade_surf(xnom,ynom,znom,Vp,'errors_r5.dat')
xmesh = xyz_mesh[:,:,0]
ymesh = xyz_mesh[:,:,1]
zmesh = xyz_mesh[:,:,2]
write_tecplot.write_blade_surf(xmesh,ymesh,zmesh,xe_r37,'errors_r37.dat')
n = max_error.shape[0]
xnom = zeros((npps+1,nsec))
ynom = zeros((npps+1,nsec))
znom = zeros((npps+1,nsec))
xnom[:-1,:] = xyzn[:,:,0].T
ynom[:-1,:] = xyzn[:,:,1].T
znom[:-1,:] = xyzn[:,:,2].T
xnom[-1,:] = xnom[0,:]
ynom[-1,:] = ynom[0,:]
znom[-1,:] = znom[0,:]
Vp = zeros((n,npps+1,nsec))
for i in range(n):
Vp[i,:-1,:] = V[i,:,:].T
Vp[:,-1,:] = Vp[:,0,:]
write_tecplot.write_blade_surf(xnom,ynom,znom,Vp,'pca_modes_r5.dat')
'''
n = max_error.shape[0]
# find max error over all blades and plot
max_error = (max_error[:,:,0]).max(0)
# determine how many modes are needed
e_thresh = 5.0e-4
nmodes = nonzero((max_error - e_thresh) <= 0.0)[0][0]+1
print 'Total modes required: ', nmodes
pylab.semilogy(arange(max_error.shape[0])+1,max_error,'*')
pylab.ylim([1.0e-5,2.0*max(max_error)])
pylab.grid(True)
pylab.xlabel('Number of modes in reconstruction')
for j in arange(sdim):
f.write('%e\n' % V_trans[imode,i,j])
f.close()
# write out the transformed amplitudes
Cov_trans = dot(UT,dot(S_pca**2*eye(NZ),UT.T))
f = open('ob_modes/S.dat','w')
for i in arange(NZ):
f.write('%e\n' % sqrt(Cov_trans[i,i]))
f.close()
s, t = read_blade.xyz2st(x,y,z)
s /= s[-1]
# tecplot file with ob modes
write_tecplot.write_blade_surf(x,y,z,V_trans,'ob_modes_r37.dat')
# plot the transformed modes
# make sure they match up with the PCA modes
ls = len(s)+mod(len(s),2)
V_trans_tmp = zeros(V_trans.shape)
V_trans_tmp[:,:ls/2,:] = V_trans[:,ls/2-1:,:]
V_trans_tmp[:,ls/2-1:,:] = V_trans[:,:ls/2,:]
for i in range(4):
pylab.figure()
pylab.contourf(s,t,V_trans_tmp[i,:,:].T,50)
pylab.title('Output-based mode '+str(i+1))
pylab.xlabel('Chordwise location')
pylab.ylabel('Spanwise Coordinate')
pylab.text(0.03,t[0]-0.07,'LE')
pylab.text(0.5,t[0]-0.07,'TE')
eigs_1d = reshape(eigs,ns*nt,1)
ind = flipud(argsort(eigs_1d)[-nkl:])
ind_2d = zeros((nkl,2))
for i in range(nkl):
ind_2d[i,:] = unravel_index(ind[i],(nt,ns))
ind_2d = fliplr(ind_2d)
# write out the K-L modes/eigenvalues
f = open('kl_modes/S.dat','w')
for n in range(nkl):
f.write('%e\n' % eigs_1d[ind[n]])
f.close()
for n in range(nkl):
imode = ind_2d[n,0]
jmode = ind_2d[n,1]
V = outer(UX[:,imode],UY[:,jmode])
# project K-L mode onto mesh geometry
sABCD = array([0.05, 0.45, 0.55, 0.95])
slope = 0.1 # how much stuff is pushed towards hub/shroud
V_proj = project_GP.project(s,t,sABCD,V,x,y,z,slope)
f = open('kl_modes/V'+str(n+1)+'.dat','w')
f.write('CDIM: %d\n' % cdim)
f.write('SDIM: %d\n' % sdim)
for i in arange(cdim):
for j in arange(sdim):
f.write('%e\n' % V_proj[i,j])
f.close()
write_tecplot.write_blade_surf(x,y,z,V_proj,'blade.dat')
'''
# write out PCA singular values
'''
f = open(data_dir+'S.dat','w')
for s in S:
f.write('%e\n' % s)
f.close()
'''
# write out the first pca mode to tecplot format
xmesh = xyz_mesh[:,:,0]
ymesh = xyz_mesh[:,:,1]
zmesh = xyz_mesh[:,:,2]
V2 = transform_mode(xyzn,V[0,:,:],xyz_mesh,ntip)
write_tecplot.write_blade_surf(xmesh,ymesh,zmesh,V2,'pca_mode1_r37.dat')
xnom = zeros((npps+1,nsec))
ynom = zeros((npps+1,nsec))
znom = zeros((npps+1,nsec))
xnom[:-1,:] = xyzn[:,:,0].T
ynom[:-1,:] = xyzn[:,:,1].T
znom[:-1,:] = xyzn[:,:,2].T
xnom[-1,:] = xnom[0,:]
ynom[-1,:] = ynom[0,:]
znom[-1,:] = znom[0,:]
Vp = zeros((npps+1,nsec))
Vp[:-1,:] = V[0,:,:].T
Vp[-1,:] = Vp[0,:]
write_tecplot.write_blade_surf(xnom,ynom,znom,Vp,'pca_mode1_meas.dat')