def testBladeOuterScalar():
# scalar to blade/ scalar to scalar
B1 = Blade(np.eye(2))
B2 = Blade(1, s=2)
result1 = bd.outer(B1, B2)
print 'B1 outer B2 s: ', result1.s
assert np.allclose(2, result1.s), 'value'
assert result1.blade.shape == (2, 2), 'shape'
result2 = bd.outer(B2, B1)
print 'B2 outer B1 s: ', result2.s
assert np.allclose(2, result2.s), 'value'
assert result2.blade.shape == (2, 2), 'shape'
result3 = bd.outer(B2, B2)
print 'B2 outer B2 s: ', result3.s
assert np.allclose(result3.s, 4)
B1 = Blade(1, s=2)
B2 = Blade(1, s=-.5)
result1 = bd.outer(B1, B2)
print 'B1 outer B2 s: ', result1.s
assert np.allclose(-1, result1.s), 'value'
assert result1.blade.shape == (1, 0), 'shape'
def testBladeOuterScaleMultplicative():
# multiplicative scaling
B1 = Blade(np.array([2, 0]))
B2 = Blade(np.array([0, 1]))
result1 = bd.outer(B1, B2)
print 'B1 outer B2 s: ', result1.s
print 'B1 outer B2 blade: ', result1.blade
assert la.det(result1.blade) > 0, la.det(result1.blade)
assert result1.blade.shape == (2, 2), result1.blade.shape
assert np.allclose(np.eye(2), np.dot(result1.blade.T, result1.blade))
assert np.allclose(bd.inner(result1, result1).s,
-4), bd.inner(result1, result1).s
result2 = bd.outer(B2, B1)
print 'B2 outer B1 s: ', result2.s
print 'B2 outer B1 blade: ', result2.blade
assert la.det(result2.blade) < 0, la.det(result2.blade)
assert result2.blade.shape == (2, 2), result2.blade.shape
assert np.allclose(np.eye(2), np.dot(result2.blade.T, result2.blade))
assert np.allclose(bd.inner(result2, result2).s,
-4), bd.inner(result2, result2).s
# result1 == inverse(result2)
assert np.allclose(bd.inner(result1, result2).s,
4), bd.inner(result1, result2).s
def testBladeInitScalar():
" Testing scalar blade "
B = Blade(1)
assert B.blade.shape == (1, 0)
assert np.allclose(B.s, 1)
assert B.k == 0
B = Blade(1, s=2)
assert B.blade.shape == (1, 0)
assert np.allclose(B.s, 2)
assert B.k == 0
B = Blade(2)
assert B.blade.shape == (1, 0)
assert np.allclose(B.s, 2)
assert B.k == 0
B = Blade(2, s=2)
assert B.blade.shape == (1, 0)
assert np.allclose(B.s, 4)
assert B.k == 0
B = Blade(1, s=0)
assert B.blade.shape == (1, 0)
assert np.allclose(B.s, 0)
assert B.k == 0
def testBladeDualEuclidean():
# s=0
B = Blade(0)
try:
D = bd.dual(B)
except AttributeError as err:
assert err[0] == 'Not dualizable, s=0'
except:
assert False, err
# scalar, expect a 2-blade
A = Blade(2)
D = bd.dual(A, n=2)
revPseudo = bd.outer(bd.inverse(A), D)
shouldBeOne = bd.inner(revPseudo, bd.pseudoScalar(2))
assert np.allclose(shouldBeOne.s, 1.0), (shouldBeOne.blade, shouldBeOne.s)
# 1-blade, expect 1-blade back
A = Blade(np.array([1, 0]))
D = bd.dual(A)
revPseudo = bd.outer(bd.inverse(A), D)
shouldBeOne = bd.inner(revPseudo, bd.pseudoScalar(2))
assert np.allclose(shouldBeOne.s, 1.0), (shouldBeOne.blade, shouldBeOne.s)
# 2-blade, expect 0-blade back
A = Blade(np.eye(2))
D = bd.dual(A)
revPseudo = bd.outer(bd.inverse(A), D)
shouldBeOne = bd.inner(revPseudo, bd.pseudoScalar(2))
assert np.allclose(shouldBeOne.s, 1.0), (shouldBeOne.blade, shouldBeOne.s)
def testBladeUnDualEuclidean():
# s=0
B = Blade(0)
try:
D = bd.undual(B)
except AttributeError as err:
assert err[0] == 'Not dualizable, s=0'
except:
assert False, err
# scalar, expect a 2-blade
A = Blade(2)
Aprime = bd.dual(bd.undual(A, n=2), n=2)
print 'A: ', A.blade, A.s
print 'APrimeInv: ', bd.inverse(Aprime).blade, bd.inverse(Aprime).s
shouldBeOne = bd.outer(A, bd.inverse(Aprime))
print 'shouldBeOne: ', shouldBeOne.blade, shouldBeOne.s
assert np.allclose(shouldBeOne.s, 1.0), (shouldBeOne.blade, shouldBeOne.s)
# 1-blade, expect 1-blade back
A = Blade(np.array([1, 0]))
Aprime = bd.undual(bd.dual(A, n=2), n=2)
shouldBeOne = bd.inner(A, bd.inverse(Aprime))
assert np.allclose(shouldBeOne.s, 1.0), (shouldBeOne.blade, shouldBeOne.s)
# 2-blade, expect 0-blade back
A = Blade(np.eye(2))
Aprime = bd.undual(bd.dual(A, n=2), n=2)
print 'A: ', A.blade, A.s
print 'APrimeInv: ', bd.inverse(Aprime).blade, bd.inverse(Aprime).s
shouldBeOne = bd.inner(A, bd.inverse(Aprime))
print 'shouldBeOne: ', shouldBeOne.blade, shouldBeOne.s
assert np.allclose(shouldBeOne.s, 1.0), (shouldBeOne.blade, shouldBeOne.s)
def testBladeCopy():
B1 = Blade(np.eye(2))
B2 = bd.copy(B1)
assert np.allclose(B1.blade, B2.blade)
assert np.allclose(B1.s, B2.s)
B1.blade[1, 1] = 2
assert not np.allclose(B1.blade, B2.blade)
def testBladeEqualityNotSameSubspace():
# 45-degree rotation in plane x-y
A = Blade(np.array([[1, 0], [0, 1], [1, 0]]))
B = Blade(np.array([[1, 1], [-1, 1], [0, 0]]))
print 'join dim: ', bd.join(A, B).k
print 'equal: ', bd.equality(A, B)
assert not bd.subSpaceEquality(A, B)
assert not bd.equality(A, B)
def testBladeCopy():
B1 = Blade(np.eye(2))
B2 = bd.copy(B1)
assert np.allclose(B1.blade, B2.blade)
assert np.allclose(B1.s, B2.s)
B1.blade[1, 1] = 2
assert not np.allclose(B1.blade, B2.blade)
def testBladeLeftContractOrthoProj():
# orthogonal projection
A = Blade(np.array([1, 1, 0]))
B = Blade(np.array([[2, 0], [0, 0], [0, 2]]))
Aproj = bd.leftContract(bd.leftContract(A, B), bd.inverse(B))
assert (np.allclose(Aproj.blade, np.array([[1], [0], [0]])) and \
np.allclose(Aproj.s * la.norm(np.array([1, 1, 0])), A.s)) or \
(np.allclose(-Aproj.blade, np.array([[-1], [0], [0]])) and \
np.allclose(-Aproj.s * la.norm(np.array([1, 1, 0])), A.s))
def testBladeInnerCommutativity():
# commutative
for i in range(1, 5):
B1 = Blade(np.eye(i, i))
B2 = Blade(-np.eye(i, i))
firstOrdering = bd.inner(B1, B2)
secondOrdering = bd.inner(B2, B1)
assert np.allclose(firstOrdering.s,
secondOrdering.s), (firstOrdering.s,
secondOrdering.s)
def testBladeLeftContractBasic():
# basic usage
A = Blade(np.array([1, 0]))
B = Blade(np.array([[1, 0], [0, 1]]))
lc = bd.leftContract(A, B)
assert np.allclose(lc.s, 1.0), (lc.blade, lc.s)
assert (np.allclose(lc.blade, np.array([[0], [1]])) and \
np.allclose(lc.s, 1)) or \
(np.allclose(lc.blade, np.array([[0], [-1]])) and \
np.allclose(lc.s, -1)), (lc.blade, lc.s)
def testBladeInitQrScaling():
# testing qr scaling
A = np.array([[2, 0], [0, 1], [0, 0]])
B = Blade(A)
assert np.allclose(np.dot(B.blade.T, B.blade), np.eye(2))
assert np.allclose(B.s, 2.0)
B = Blade(A, s=2.0)
assert np.allclose(np.dot(B.blade.T, B.blade), np.eye(2))
assert np.allclose(B.s, 4.0)
def testBladeJoinBasic():
# two bases
A = Blade(np.array([1, 0, 0]))
B = Blade(np.array([0, 1, 0]))
J = bd.join(A, B)
assert J.blade.shape == (3, 2)
assert J.s == 1
# add a third
C = Blade(np.array([0, 0, 1]))
J2 = bd.join(J, C)
assert J2.blade.shape == (3, 3)
assert J2.s == 1
# linearly dependent
A = Blade(np.array([1, 0, 0]))
B = Blade(np.array([1, 0, 0]))
J = bd.join(A, B)
assert J.blade.shape == (3, 1)
assert J.s == 1
# linearly dependent
A = Blade(np.array([1, 0, 0]))
B = Blade(np.array([0, 1, 0]))
J = bd.join(A, B)
C = Blade(np.array([1, 1, 0]))
D = Blade(np.array([1, -1, 2]))
J2 = bd.join(C, D)
J3 = bd.join(J, J2)
assert J3.blade.shape == (3, 3)
assert J3.s == 1
def testBladeInitNull():
" Testing null blade "
B = Blade()
assert B.blade.shape == (1, 0)
assert np.allclose(B.s, 0)
assert B.k == 0
B = Blade(s=0)
assert B.blade.shape == (1, 0)
assert np.allclose(B.s, 0)
assert B.k == 0
def testBladeInitQr():
" Testing qr "
# testing qr
A = np.array([[1, 0], [0, 1], [0, 0]])
B = Blade(A)
print 'B.blade: ', B.blade
assert np.allclose(np.dot(B.blade.T, B.blade), np.eye(2))
assert np.allclose(B.s, 1)
B = Blade(A, s=2.0)
assert np.allclose(np.dot(B.blade.T, B.blade), np.eye(2))
assert np.allclose(B.s, 2.0)
def testBladeInvolutio():
# sign
B = Blade(1)
assert np.allclose(B.s, (-1)**B.k * bd.involution(B).s)
assert np.allclose(B.s, (-1)**B.k * bd.involutionScaling(B))
assert B.k == 0
for i in range(1, 5):
B = Blade(np.eye(i))
assert np.allclose(B.s, (-1)**B.k * bd.involution(B).s)
assert np.allclose(B.s, (-1)**B.k * bd.involutionScaling(B))
assert B.k == i
def testBladeEqualityAndSubEqualSelf():
# self equal
A = Blade(np.array([[1, 2], [2, 3], [0, 0]]))
B = Blade(np.array([[1, 2], [2, 3], [0, 0]]))
assert bd.subSpaceEquality(A, B)
assert bd.equality(A, B)
# self equal
A = Blade(np.array([[1, 2], [2, 3], [0, 0]]))
B = Blade(2 * np.array([[1, 2], [2, 3], [0, 0]]), s=.25)
assert bd.subSpaceEquality(A, B)
assert bd.equality(A, B)
def testBladeEqualityRotation():
# 90-degree rotation in plane x-y
A = Blade(np.array([[1, 0], [0, 1], [0, 0]]))
B = Blade(np.array([[0, 1], [-1, 0], [0, 0]]))
assert bd.subSpaceEquality(A, B)
assert bd.equality(A, B)
# with scaling now
A = Blade(np.array([[1, 0], [0, 1], [0, 0]]))
B = Blade(np.array([[0, 1], [-1, 0], [0, 0]]), s=2)
assert bd.subSpaceEquality(A, B)
assert not bd.equality(A, B)
def testBladeOuterSameSubspace():
B1 = Blade(np.eye(2))
B2 = Blade(np.eye(2)[:, 0])
result = bd.outer(B1, B2)
print 'B1 outer B2: ', result.s
assert np.allclose(0, result.s)
B1 = Blade(np.eye(2))
B2 = Blade(np.eye(2))
result = bd.outer(B1, B2)
print 'B1 outer B2: ', result.s
assert np.allclose(0, result.s)
def testBladeReverse():
# sign
B = Blade(1)
assert np.allclose(B.s, (-1)**(B.k * (B.k - 1) / 2) * bd.reverse(B).s)
assert np.allclose(B.s, (-1)**(B.k * (B.k - 1) / 2) * bd.reverseScaling(B))
assert B.k == 0
for i in range(1, 5):
B = Blade(np.eye(i))
assert np.allclose(B.s, (-1)**(B.k * (B.k - 1) / 2) * bd.reverse(B).s)
assert np.allclose(B.s,
(-1)**(B.k * (B.k - 1) / 2) * bd.reverseScaling(B))
assert B.k == i
def testBladeInnerScale():
# scale
A = np.array([[2, 0], [0, 1]])
print 'A.T A : ', np.dot(A.T, A)
B = Blade(A)
print 'B inner B: ', bd.inner(B, B).s
assert np.allclose(-4, bd.inner(B, B).s)
A = np.array([[-2, 0], [0, 1]])
print 'A.T A : ', np.dot(A.T, A)
B = Blade(A)
print 'B inner B: ', bd.inner(B, B).s
assert np.allclose(-4, bd.inner(B, B).s)
def testBladeInitOneIndexVector():
# testing one-index (row-ish) vector
c = np.array([2, 0, 0])
B = Blade(c)
assert np.allclose(np.dot(B.blade.T, B.blade), np.eye(1))
assert np.allclose(B.s, 2.0)
assert B.k == 1
def testBladeInitOrthonormal():
" Testing orthonormal "
# testing orthonormal
A = np.array([[1, 0], [0, 1], [0, 0]])
B = Blade(A, orthonormal=True)
assert np.allclose(B.blade, A)
assert np.allclose(B.s, 1.0)
B = Blade(A, orthonormal=True, s=2.0)
assert np.allclose(B.blade, A)
assert np.allclose(B.s, 2.0)
B = Blade(A, orthonormal=True, s=0.0)
assert B.blade.shape == (1, 0)
assert np.allclose(B.s, 0)
assert B.k == 0
def testBladeInitColumnVector():
# testing column vector
c = np.array([[2], [0], [0]])
B = Blade(c)
print 's: ', B.s
print 'blade: ', B.blade
assert np.allclose(np.dot(B.blade.T, B.blade), np.eye(1))
assert np.allclose(B.s, 2.0)
assert B.k == 1
B = Blade(c, s=2.0)
print 's: ', B.s
print 'blade: ', B.blade
assert np.allclose(np.dot(B.blade.T, B.blade), np.eye(1))
assert np.allclose(B.s, 4.0)
assert B.k == 1
def start(self):
logger.info("Starting Tryptofan...")
self.opc_client = opc.Client('localhost:7890')
apps = [
(r'/ws', handlers.ControllerHandler, {
'tryptofan': self
}),
(r'/(.*)', handlers.IndexStaticFileHandler, {
'path': settings.WEBROOT
}),
]
application = Application(apps)
self.http_server = HTTPServer(application)
self.updater = PeriodicCallback(self.update, 1000 / settings.FRAMERATE)
for i in range(settings.BLADES):
blade = Blade(self.pixels, i * settings.BLADE_PIXELS,
self.state[i][0], self.state[i][1], self.state[i][2])
self.blades.append(blade)
self.http_server.listen(settings.HTTP_PORT)
self.updater.start()
IOLoop.instance().start()
def testBladeLinearTransformScale():
# scale
B = Blade(np.eye(2), s=2)
T = np.array([[2, 0], [0, .75]])
result = bd.applyLinearTransform(T, B)
assert result.k == 2, (result.blade, result.s)
assert result.s == 3, (result.blade, result.s)
def testBladeLinearTransformUnit():
# unit transform
B = Blade(np.eye(2), s=2)
T = np.array([[1, 0], [0, 1]])
result = bd.applyLinearTransform(T, B)
assert result.k == 2, (result.blade, result.s)
assert result.s == 2, (result.blade, result.s)
def testBladeInnerSign():
# sign
for i in range(1, 5):
B = Blade(np.eye(i, i))
print 'B inner B: ', bd.inner(B, B).s
assert np.allclose((-1)**((i * (i - 1)) / 2),
bd.inner(B, B).s), 'value'
assert bd.inner(B, B).blade.shape == (1, 0), 'shape'
def testBladeJoinScalar():
# scalars
A = Blade(1, s=2)
B = Blade(1, s=4)
J = bd.join(A, B)
assert J.blade.shape == (1, 0)
assert J.s == 1
# scalar/blade
B = Blade(np.array([1, 0, 1]))
J = bd.join(A, B)
assert J.blade.shape == (3, 1)
assert J.s == 1
B = Blade(np.array([1, 0, 1]))
J = bd.join(B, A)
assert J.blade.shape == (3, 1)
assert J.s == 1
def __init__(self, bladed_file, root_length=0, rigid=False):
# Modal element using data from Bladed model
print "Loading modes from '%s'..." % bladed_file
self.blade = Blade(bladed_file)
self.tower = Tower(bladed_file)
self.modes = self.blade.modal_rep()
#self.tmodes = self.tower.modal_rep()
Ry = rotmat_y(-pi/2)
Rhb1 = rotmat_x(0 * 2*pi/3)
Rhb2 = rotmat_x(1 * 2*pi/3)
Rhb3 = rotmat_x(2 * 2*pi/3)
self.base = FreeJoint('base')
self.towerlink = RigidConnection('tower', [0,0,self.tower.hubheight])
self.bearing = Hinge('bearing', [1,0,0])
root1 = RigidConnection('root1', root_length*np.dot(Rhb1,[0,0,1]), dot(Rhb1,Ry))
root2 = RigidConnection('root2', root_length*np.dot(Rhb2,[0,0,1]), dot(Rhb2,Ry))
root3 = RigidConnection('root3', root_length*np.dot(Rhb3,[0,0,1]), dot(Rhb3,Ry))
self.blade1 = ModalElement('blade1', self.modes)
self.blade2 = ModalElement('blade2', self.modes)
self.blade3 = ModalElement('blade3', self.modes)
self.base.add_leaf(self.towerlink)
self.towerlink.add_leaf(self.bearing)
self.bearing.add_leaf(root1)
self.bearing.add_leaf(root2)
self.bearing.add_leaf(root3)
root1.add_leaf(self.blade1)
root2.add_leaf(self.blade2)
root3.add_leaf(self.blade3)
self.system = System(self.base)
# Prescribed DOF accelerations - constant rotor speed
self.base_motion = None
self.base_motion_amp = 0
self.system.prescribe(self.bearing, vel=0)
self.system.prescribe(self.base, vel=0)
if rigid:
for b in (self.blade1, self.blade2, self.blade3):
self.system.prescribe(b, vel=0)
# setup integrator
self.integ = Integrator(self.system, ('pos','vel','acc'))
self.integ.add_output(dynamics.LoadOutput(self.base.iprox))
self.integ.add_output(dynamics.LoadOutput(self.towerlink.iprox))
self.integ.add_output(dynamics.LoadOutput(self.bearing.iprox))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(dynamics.LoadOutput(b.iprox, local=True))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(b.output_deflections())
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(b.output_positions())
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(dynamics.NodeOutput(b.iprox, local=True, deriv=2))
def testBladeInitRankDeficient():
# testing rank deficient
A = np.array([[1, 0], [1, 0], [0, 0]])
B = Blade(A)
print B.blade.shape
assert B.blade.shape == (1, 0)
assert np.allclose(B.s, 0)
assert B.k == 0
B = Blade(A, s=2.0)
assert B.blade.shape == (1, 0)
assert np.allclose(B.s, 0)
assert B.k == 0
# too many columns
C = np.array([[1, 0, 1], [0, 1, 0]])
B2 = Blade(C)
assert B2.blade.shape == (1, 0)
assert np.allclose(B2.s, 0)
assert B2.k == 0
def testBladeDualEuclideanRegression():
# regression test -- tests a bunch of functions and they all have to work
# for many input dimensions for this to succeed fully
for n in range(1, 10):
for k in range(0, n + 1):
if k == 0:
blade = Blade(1, s=float(rn.rand(1)[0]))
else:
blade = Blade(rn.randn(n, k))
print 'blade n, k: ', blade.n, blade.k
if np.allclose(blade.s, 0): # just skip this one for now...
continue # measure 0 event but could happen
D = bd.dual(blade, n=n)
print 'D n, k: ', D.n, D.k
revPseudo = bd.outer(bd.inverse(blade), D)
print 'n, k: ', n, k
print 'revPseudo blade, s: ', revPseudo.blade, revPseudo.s
shouldBeOne = bd.inner(revPseudo, bd.pseudoScalar(n))
assert np.allclose(shouldBeOne.s,
1.0), (shouldBeOne.blade, shouldBeOne.s)
def __init__(self, mode_source_file, root_length=0, wind_table=None):
# Modal element using data from Bladed model
print "Loading modes from '%s'..." % mode_source_file
self.blade = Blade(mode_source_file)
self.modes = self.blade.modal_rep()
if wind_table is not None:
loading = BladeLoading(self.blade, wind_table, None)
else:
loading = None
Ry = rotmat_y(-pi/2)
Rhb1 = rotmat_x(0 * 2*pi/3)
Rhb2 = rotmat_x(1 * 2*pi/3)
Rhb3 = rotmat_x(2 * 2*pi/3)
self.bearing = Hinge('bearing', [1,0,0])
root1 = RigidConnection('root1', root_length*np.dot(Rhb1,[0,0,1]), dot(Rhb1,Ry))
root2 = RigidConnection('root2', root_length*np.dot(Rhb2,[0,0,1]), dot(Rhb2,Ry))
root3 = RigidConnection('root3', root_length*np.dot(Rhb3,[0,0,1]), dot(Rhb3,Ry))
self.blade1 = ModalElement('blade1', self.modes, loading)
self.blade2 = ModalElement('blade2', self.modes)
self.blade3 = ModalElement('blade3', self.modes)
self.bearing.add_leaf(root1)
self.bearing.add_leaf(root2)
self.bearing.add_leaf(root3)
root1.add_leaf(self.blade1)
root2.add_leaf(self.blade2)
root3.add_leaf(self.blade3)
self.system = System(self.bearing)
# Prescribed DOF accelerations - constant rotor speed
self.system.prescribe(self.bearing, vel=0.0, acc=0.0)
# setup integrator
self.integ = Integrator(self.system, ('pos','vel'))
self.integ.add_output(dynamics.LoadOutput(self.bearing.iprox))
self.integ.add_output(dynamics.LoadOutput(self.blade1.iprox, local=True))
self.integ.add_output(self.blade1.output_deflections())
self.integ.add_output(self.blade1.output_positions())
class Rotor(object):
def __init__(self, mode_source_file, root_length=0):
# Modal element using data from Bladed model
print "Loading modes from '%s'..." % mode_source_file
self.blade = Blade(mode_source_file)
self.modes = self.blade.modal_rep()
Ry = rotmat_y(-pi/2)
Rhb1 = rotmat_x(0 * 2*pi/3)
Rhb2 = rotmat_x(1 * 2*pi/3)
Rhb3 = rotmat_x(2 * 2*pi/3)
self.bearing = Hinge('bearing', [1,0,0])
root1 = RigidConnection('root1', root_length*np.dot(Rhb1,[0,0,1]), dot(Rhb1,Ry))
root2 = RigidConnection('root2', root_length*np.dot(Rhb2,[0,0,1]), dot(Rhb2,Ry))
root3 = RigidConnection('root3', root_length*np.dot(Rhb3,[0,0,1]), dot(Rhb3,Ry))
self.blade1 = ModalElement('blade1', self.modes)
self.blade2 = ModalElement('blade2', self.modes)
self.blade3 = ModalElement('blade3', self.modes)
self.bearing.add_leaf(root1)
self.bearing.add_leaf(root2)
self.bearing.add_leaf(root3)
root1.add_leaf(self.blade1)
root2.add_leaf(self.blade2)
root3.add_leaf(self.blade3)
self.system = System(self.bearing)
# Prescribed DOF accelerations - constant rotor speed
self.system.prescribe(self.bearing, acc=0.0)
# setup integrator
self.integ = Integrator(self.system, ('pos','vel'))
self.integ.add_output(dynamics.LoadOutput(self.bearing.iprox))
self.integ.add_output(dynamics.LoadOutput(self.blade1.iprox, local=True))
self.integ.add_output(self.blade1.output_deflections())
self.integ.add_output(self.blade1.output_positions())
def simulate(self, qm0=None, spin=10.0, t1=1.5, dt=0.01):
# reset
self.system.q [:] = 0.0
self.system.qd[:] = 0.0
# initial conditions
if qm0 is not None: # initial modal amplitudes
self.system.q[self.blade1.istrain] = qm0
self.system.q[self.blade2.istrain] = qm0
self.system.q[self.blade3.istrain] = qm0
self.system.qd[self.bearing.istrain][0] = spin
# simulate
self.t,self.y = self.integ.integrate(t1, dt)
for i,lab in enumerate(self.integ.labels()):
print "%2d %s" % (i,lab)
return self.t, self.y
def lin(self, qm0=None, spin=10.0):
# reset
self.system.q [:] = 0.0
self.system.qd[:] = 0.0
# initial conditions
if qm0 is not None: # initial modal amplitudes
self.system.q[self.blade1.istrain] = qm0
self.system.q[self.blade2.istrain] = qm0
self.system.q[self.blade3.istrain] = qm0
else:
qm0 = np.zeros(self.blade1._nstrain * 3)
self.system.prescribe(self.bearing, vel=spin, acc=0.0)
self.system.qd[self.bearing.istrain][0] = spin
linsys = linearisation.LinearisedSystem(self.system, qm0)
return linsys
def ani(self, t=None, y=None, planview=True):
if t is None: t = self.t
if y is None: y = self.y
l = 40
if planview:
return dynvis.anim(self.system, t, y, (1,2), (-l,l), (-l,l))
else:
return dynvis.anim(self.system, t, y, (0,1), (-l,l), (-5,5))
class Turbine(object):
def __init__(self, bladed_file, root_length=0, rigid=False):
# Modal element using data from Bladed model
print "Loading modes from '%s'..." % bladed_file
self.blade = Blade(bladed_file)
self.tower = Tower(bladed_file)
self.modes = self.blade.modal_rep()
#self.tmodes = self.tower.modal_rep()
Ry = rotmat_y(-pi/2)
Rhb1 = rotmat_x(0 * 2*pi/3)
Rhb2 = rotmat_x(1 * 2*pi/3)
Rhb3 = rotmat_x(2 * 2*pi/3)
self.base = FreeJoint('base')
self.towerlink = RigidConnection('tower', [0,0,self.tower.hubheight])
self.bearing = Hinge('bearing', [1,0,0])
root1 = RigidConnection('root1', root_length*np.dot(Rhb1,[0,0,1]), dot(Rhb1,Ry))
root2 = RigidConnection('root2', root_length*np.dot(Rhb2,[0,0,1]), dot(Rhb2,Ry))
root3 = RigidConnection('root3', root_length*np.dot(Rhb3,[0,0,1]), dot(Rhb3,Ry))
self.blade1 = ModalElement('blade1', self.modes)
self.blade2 = ModalElement('blade2', self.modes)
self.blade3 = ModalElement('blade3', self.modes)
self.base.add_leaf(self.towerlink)
self.towerlink.add_leaf(self.bearing)
self.bearing.add_leaf(root1)
self.bearing.add_leaf(root2)
self.bearing.add_leaf(root3)
root1.add_leaf(self.blade1)
root2.add_leaf(self.blade2)
root3.add_leaf(self.blade3)
self.system = System(self.base)
# Prescribed DOF accelerations - constant rotor speed
self.base_motion = None
self.base_motion_amp = 0
self.system.prescribe(self.bearing, vel=0)
self.system.prescribe(self.base, vel=0)
if rigid:
for b in (self.blade1, self.blade2, self.blade3):
self.system.prescribe(b, vel=0)
# setup integrator
self.integ = Integrator(self.system, ('pos','vel','acc'))
self.integ.add_output(dynamics.LoadOutput(self.base.iprox))
self.integ.add_output(dynamics.LoadOutput(self.towerlink.iprox))
self.integ.add_output(dynamics.LoadOutput(self.bearing.iprox))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(dynamics.LoadOutput(b.iprox, local=True))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(b.output_deflections())
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(b.output_positions())
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(dynamics.NodeOutput(b.iprox, local=True, deriv=2))
@property
def mass(self):
"""Total mass of turbine"""
return self.tower.total_mass + self.modes.mass * 3
@property
def inertia(self):
"""Total rotational inertia of turbine about base"""
inertia = self.tower.total_inertia
inertia[(0,1),(0,1)] = self.modes.mass * 3 * self.tower.hubheight
return inertia
# XXX neglecting rotor rotational inertia
def set_base_motion(self, dof, w, amp):
self.base_motion = dof
self.base_motion_amp = amp
self.system.prescribe(self.base, part=dof,
vel=lambda t: -w *amp*np.sin(w*t),
acc=lambda t: -w**2*amp*np.cos(w*t))
def set_initial_conditions(self, qm0=None, az0=None, rotor_speed=None):
# initial conditions
if qm0 is not None: # initial modal amplitudes
self.system.q[self.blade1.istrain] = qm0
self.system.q[self.blade2.istrain] = qm0
self.system.q[self.blade3.istrain] = qm0
if az0 is not None:
self.system.q[self.bearing.istrain][0] = az0
if self.base_motion is not None:
self.system.q[self.base.istrain][self.base_motion] = self.base_motion_amp
if rotor_speed is not None:
self.system.prescribe(self.bearing, vel=rotor_speed)
def simulate(self, qm0=None, az0=0.0, rotor_speed=10.0, t1=None,
dt=0.01, t0=0.0, init=False):
# reset
self.system.q [:] = 0.0
self.system.qd[:] = 0.0
self.set_initial_conditions(qm0, az0, rotor_speed)
if t1 is None:
t1 = 4*pi/rotor_speed if (rotor_speed != 0.0) else 2
if init:
self.system.find_equilibrium()
# simulate
self.t,self.y = self.integ.integrate(t1, dt, t0)
for i,lab in enumerate(self.integ.labels()):
print "%2d %s" % (i,lab)
return self.t, self.y
def lin(self, qm0=None, az0=None, rotor_speed=None, init=False):
# reset
self.system.q [:] = 0.0
self.system.qd[:] = 0.0
self.set_initial_conditions(qm0, az0, rotor_speed)
if init:
self.system.find_equilibrium()
linsys = linearisation.LinearisedSystem(self.system)
return linsys
def ani(self, vs=(0,1), t=None, y=None):
if t is None: t = self.t
if y is None: y = self.y
limits = [(-10,10), (-42,42), (-5,110)]
return dynvis.anim(self.system, t, y, vs, limits[vs[0]], limits[vs[1]])
class Turbine(object):
def __init__(self, bladed_file, root_length=0, rigid=False):
# Modal element using data from Bladed model
print "Loading modes from '%s'..." % bladed_file
self.blade = Blade(bladed_file)
self.tower = Tower(bladed_file)
self.modes = self.blade.modal_rep()
Ry = rotmat_y(-pi/2)
Rhb1 = rotmat_x(0 * 2*pi/3)
Rhb2 = rotmat_x(1 * 2*pi/3)
Rhb3 = rotmat_x(2 * 2*pi/3)
self.base = FreeJoint('base')
self.towerlink = RigidConnection('tower', [0,0,self.tower.hubheight])
self.bearing = Hinge('bearing', [1,0,0])
root1 = RigidConnection('root1', root_length*np.dot(Rhb1,[0,0,1]), dot(Rhb1,Ry))
root2 = RigidConnection('root2', root_length*np.dot(Rhb2,[0,0,1]), dot(Rhb2,Ry))
root3 = RigidConnection('root3', root_length*np.dot(Rhb3,[0,0,1]), dot(Rhb3,Ry))
self.blade1 = ModalElement('blade1', self.modes)
self.blade2 = ModalElement('blade2', self.modes)
self.blade3 = ModalElement('blade3', self.modes)
self.base.add_leaf(self.towerlink)
self.towerlink.add_leaf(self.bearing)
self.bearing.add_leaf(root1)
self.bearing.add_leaf(root2)
self.bearing.add_leaf(root3)
root1.add_leaf(self.blade1)
root2.add_leaf(self.blade2)
root3.add_leaf(self.blade3)
self.system = System(self.base)
# Prescribed DOF accelerations - constant rotor speed
self.base_motion = None
self.base_motion_amp = 0
self.system.prescribe(self.bearing, vel=0)
self.system.prescribe(self.base, vel=0)
if rigid:
for b in (self.blade1, self.blade2, self.blade3):
self.system.prescribe(b, vel=0)
# setup integrator
self.integ = Integrator(self.system, ('pos','vel','acc'))
self.integ.add_output(dynamics.LoadOutput(self.base.iprox))
self.integ.add_output(dynamics.LoadOutput(self.towerlink.iprox))
self.integ.add_output(dynamics.LoadOutput(self.bearing.iprox, local=True))
self.integ.add_output(dynamics.LoadOutput(self.bearing.idist[0], local=True))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(dynamics.LoadOutput(b.iprox, local=True))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(b.output_deflections())
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(b.output_positions())
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(dynamics.NodeOutput(b.iprox, local=True, deriv=2))
def set_base_motion(self, dof, w, amp):
self.base_motion = dof
self.base_motion_amp = amp
self.system.prescribe(self.base, part=dof,
vel=lambda t: -w *amp*np.sin(w*t),
acc=lambda t: -w**2*amp*np.cos(w*t))
def set_initial_conditions(self, qm0=None, az0=None, rotor_speed=None):
# initial conditions
if qm0 is not None: # initial modal amplitudes
self.system.q[self.blade1.istrain] = qm0
self.system.q[self.blade2.istrain] = qm0
self.system.q[self.blade3.istrain] = qm0
if az0 is not None:
self.system.q[self.bearing.istrain][0] = az0
if self.base_motion is not None:
self.system.q[self.base.istrain][self.base_motion] = self.base_motion_amp
if rotor_speed is not None:
self.system.prescribe(self.bearing, vel=rotor_speed)
def simulate(self, qm0=None, az0=0.0, rotor_speed=10.0, t1=None,
dt=0.01, t0=0.0, init=False):
# reset
self.system.q [:] = 0.0
self.system.qd[:] = 0.0
self.set_initial_conditions(qm0, az0, rotor_speed)
if t1 is None:
t1 = 4*pi/rotor_speed if (rotor_speed != 0.0) else 2
if init:
self.system.find_equilibrium()
# simulate
t,y = self.integ.integrate(t1, dt, t0)
#for i,lab in enumerate(self.integ.labels):
# print "%2d %s" % (i,lab)
#return self.t, self.y
# Build results structure
results = TurbineResults(t, y, self.modes.mode_names)
return results
def lin(self, qm0=None, az0=None, rotor_speed=None, init=False):
# reset
self.system.q [:] = 0.0
self.system.qd[:] = 0.0
self.set_initial_conditions(qm0, az0, rotor_speed)
if init:
self.system.find_equilibrium()
# need initial amplitudes for linearisation point
if qm0 is None:
qm0 = self.system.q[self.blade1.istrain]
linsys = linearisation.LinearisedSystem(self.system, np.tile(qm0, 3))
return linsys
def ani(self, results, x=0, y=1):
H = self.tower.hubheight + self.blade.radii[-1]
limits = [(-H,H), (-H,H), (-5,H+5)]
return dynvis.anim(self.system, results.t, results.strains.as_matrix(),
(x, y), limits[x], limits[y])
def __init__(self, bladed_file, root_length=0):
# Load modes but use a simple flapped blade
print "Loading modes from '%s'..." % bladed_file
self.blade = Blade(bladed_file)
self.tower = Tower(bladed_file)
self.modes = self.blade.modal_rep()
# Calculate equivalent blade properties
I1 = self.modes.I0[0]
I2 = self.modes.J0[0,0]
print I1, I2
wflap = self.modes.freqs[0]
bmass = self.modes.mass
inertia = self.modes.inertia_tensor(np.zeros(len(self.modes.freqs)))
Xc = [I1 / bmass, 0, 0]
kflap = I2 * wflap**2
Ry = rotmat_y(-pi/2)
Rhb1 = rotmat_x(0 * 2*pi/3)
Rhb2 = rotmat_x(1 * 2*pi/3)
Rhb3 = rotmat_x(2 * 2*pi/3)
self.base = FreeJoint('base')
self.towerlink = RigidConnection('tower', [0,0,self.tower.hubheight])
self.bearing = Hinge('bearing', [1,0,0])
root1 = RigidConnection('root1', root_length*np.dot(Rhb1,[0,0,1]), dot(Rhb1,Ry))
root2 = RigidConnection('root2', root_length*np.dot(Rhb2,[0,0,1]), dot(Rhb2,Ry))
root3 = RigidConnection('root3', root_length*np.dot(Rhb3,[0,0,1]), dot(Rhb3,Ry))
self.flap1 = Hinge('flap1', [0,1,0])
self.flap2 = Hinge('flap2', [0,1,0])
self.flap3 = Hinge('flap3', [0,1,0])
self.blade1 = RigidBody('blade1', bmass, inertia, Xc)
self.blade2 = RigidBody('blade2', bmass, inertia, Xc)
self.blade3 = RigidBody('blade3', bmass, inertia, Xc)
self.flap1.stiffness = self.flap2.stiffness = self.flap3.stiffness = kflap
self.base.add_leaf(self.towerlink)
self.towerlink.add_leaf(self.bearing)
self.bearing.add_leaf(root1)
self.bearing.add_leaf(root2)
self.bearing.add_leaf(root3)
root1.add_leaf(self.flap1)
root2.add_leaf(self.flap2)
root3.add_leaf(self.flap3)
self.flap1.add_leaf(self.blade1)
self.flap2.add_leaf(self.blade2)
self.flap3.add_leaf(self.blade3)
self.system = System(self.base)
# Prescribed DOF accelerations - constant rotor speed
self.base_motion = None
self.base_motion_amp = 0
self.system.prescribe(self.bearing, vel=0)
self.system.prescribe(self.base, vel=0)
# setup integrator
self.integ = Integrator(self.system, ('pos','vel','acc'))
self.integ.add_output(dynamics.LoadOutput(self.base.iprox))
self.integ.add_output(dynamics.LoadOutput(self.towerlink.iprox))
self.integ.add_output(dynamics.LoadOutput(self.bearing.iprox, local=True))
self.integ.add_output(dynamics.LoadOutput(self.bearing.idist[0], local=True))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(dynamics.LoadOutput(b.iprox, local=True))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(dynamics.NodeOutput(b.iprox, local=True, deriv=2))
class FlappedBladeTurbine(object):
def __init__(self, bladed_file, root_length=0):
# Load modes but use a simple flapped blade
print "Loading modes from '%s'..." % bladed_file
self.blade = Blade(bladed_file)
self.tower = Tower(bladed_file)
self.modes = self.blade.modal_rep()
# Calculate equivalent blade properties
I1 = self.modes.I0[0]
I2 = self.modes.J0[0,0]
print I1, I2
wflap = self.modes.freqs[0]
bmass = self.modes.mass
inertia = self.modes.inertia_tensor(np.zeros(len(self.modes.freqs)))
Xc = [I1 / bmass, 0, 0]
kflap = I2 * wflap**2
Ry = rotmat_y(-pi/2)
Rhb1 = rotmat_x(0 * 2*pi/3)
Rhb2 = rotmat_x(1 * 2*pi/3)
Rhb3 = rotmat_x(2 * 2*pi/3)
self.base = FreeJoint('base')
self.towerlink = RigidConnection('tower', [0,0,self.tower.hubheight])
self.bearing = Hinge('bearing', [1,0,0])
root1 = RigidConnection('root1', root_length*np.dot(Rhb1,[0,0,1]), dot(Rhb1,Ry))
root2 = RigidConnection('root2', root_length*np.dot(Rhb2,[0,0,1]), dot(Rhb2,Ry))
root3 = RigidConnection('root3', root_length*np.dot(Rhb3,[0,0,1]), dot(Rhb3,Ry))
self.flap1 = Hinge('flap1', [0,1,0])
self.flap2 = Hinge('flap2', [0,1,0])
self.flap3 = Hinge('flap3', [0,1,0])
self.blade1 = RigidBody('blade1', bmass, inertia, Xc)
self.blade2 = RigidBody('blade2', bmass, inertia, Xc)
self.blade3 = RigidBody('blade3', bmass, inertia, Xc)
self.flap1.stiffness = self.flap2.stiffness = self.flap3.stiffness = kflap
self.base.add_leaf(self.towerlink)
self.towerlink.add_leaf(self.bearing)
self.bearing.add_leaf(root1)
self.bearing.add_leaf(root2)
self.bearing.add_leaf(root3)
root1.add_leaf(self.flap1)
root2.add_leaf(self.flap2)
root3.add_leaf(self.flap3)
self.flap1.add_leaf(self.blade1)
self.flap2.add_leaf(self.blade2)
self.flap3.add_leaf(self.blade3)
self.system = System(self.base)
# Prescribed DOF accelerations - constant rotor speed
self.base_motion = None
self.base_motion_amp = 0
self.system.prescribe(self.bearing, vel=0)
self.system.prescribe(self.base, vel=0)
# setup integrator
self.integ = Integrator(self.system, ('pos','vel','acc'))
self.integ.add_output(dynamics.LoadOutput(self.base.iprox))
self.integ.add_output(dynamics.LoadOutput(self.towerlink.iprox))
self.integ.add_output(dynamics.LoadOutput(self.bearing.iprox, local=True))
self.integ.add_output(dynamics.LoadOutput(self.bearing.idist[0], local=True))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(dynamics.LoadOutput(b.iprox, local=True))
for b in (self.blade1, self.blade2, self.blade3):
self.integ.add_output(dynamics.NodeOutput(b.iprox, local=True, deriv=2))
def set_base_motion(self, dof, w, amp):
self.base_motion = dof
self.base_motion_amp = amp
self.system.prescribe(self.base, part=dof,
vel=lambda t: -w *amp*np.sin(w*t),
acc=lambda t: -w**2*amp*np.cos(w*t))
def set_initial_conditions(self, qm0=None, az0=None, rotor_speed=None):
# initial conditions
if qm0 is not None: # initial hinge angle
self.system.q[self.flap1.istrain][0] = qm0
self.system.q[self.flap2.istrain][0] = qm0
self.system.q[self.flap3.istrain][0] = qm0
if az0 is not None:
self.system.q[self.bearing.istrain][0] = az0
if self.base_motion is not None:
self.system.q[self.base.istrain][self.base_motion] = self.base_motion_amp
if rotor_speed is not None:
self.system.prescribe(self.bearing, vel=rotor_speed)
def simulate(self, qm0=None, az0=0.0, rotor_speed=10.0, t1=None,
dt=0.01, t0=0.0, init=False):
# reset
self.system.q [:] = 0.0
self.system.qd[:] = 0.0
self.set_initial_conditions(qm0, az0, rotor_speed)
if t1 is None:
t1 = 4*pi/rotor_speed if (rotor_speed != 0.0) else 2
if init:
self.system.find_equilibrium()
# simulate
t,y = self.integ.integrate(t1, dt, t0)
#for i,lab in enumerate(self.integ.labels):
# print "%2d %s" % (i,lab)
#return self.t, self.y
# Build results structure
results = FlappedTurbineResults(t, y)
return results
def lin(self, qm0=None, az0=None, rotor_speed=None, init=False):
# reset
self.system.q [:] = 0.0
self.system.qd[:] = 0.0
self.set_initial_conditions(qm0, az0, rotor_speed)
if init:
self.system.find_equilibrium()
# need initial amplitudes for linearisation point
if qm0 is None:
qm0 = self.system.q[self.blade1.istrain]
linsys = linearisation.LinearisedSystem(self.system, np.tile(qm0, 3))
return linsys
def ani(self, results, x=0, y=1):
H = self.tower.hubheight + self.blade.radii[-1]
limits = [(-H,H), (-H,H), (-5,H+5)]
return dynvis.anim(self.system, results.t, results.strains.as_matrix(),
(x, y), limits[x], limits[y])
import matplotlib.pyplot as plt
import matplotlib.gridspec as gridspec
import dynamics
from dynamics import System, ModalElement, Integrator, RigidConnection, rotmat_y
from blade import Blade
from loading import BladeLoading
import dynvis
dynamics.OPT_GRAVITY = False
bladed_path = '/bladed/blade_nrel/parked'
# Modal element using data from Bladed model
print "Loading blade from '%s'..." % bladed_path
blade = Blade(bladed_path+'.$pj')
modes = blade.modal_rep()
# Blade loading
wind_table = np.array([
[0, 1, 2, 10], # time
[0, 0, 20, 20], # x
[0, 0, 0, 0 ], # y
[0, 0, 0, 0 ], # z
])
loading = BladeLoading(blade, wind_table, None)
# Modal element
base = RigidConnection('base', rotation=rotmat_y(-np.pi/2))
el = ModalElement('el', modes, loading)
base.add_leaf(el)
