def execute(self):
# water depth
d = self.z_surface - self.z_floor
# design wave height
h = 1.1 * self.hs
# circular frequency
omega = 2.0 * math.pi / self.T
# compute wave number from dispersion relationship
k = brentq(lambda k: omega**2 - self.g * k * math.tanh(d * k), 0,
10 * omega**2 / self.g)
# zero at surface
z_rel = self.z - self.z_surface
# maximum velocity
self.U = h / 2.0 * omega * np.cosh(k * (z_rel + d)) / math.sinh(
k * d) + self.Uc
self.U0 = h / 2.0 * omega * np.cosh(k * (0. + d)) / math.sinh(
k * d) + self.Uc
# check heights
self.U[np.logical_or(self.z < self.z_floor,
self.z > self.z_surface)] = 0.
# acceleration
self.A = self.U * omega
self.A0 = self.U0 * omega
# angles
self.beta = self.betaWave * np.ones_like(self.z)
self.beta0 = self.betaWave
# derivatives
dU_dz = h / 2.0 * omega * np.sinh(k *
(z_rel + d)) / math.sinh(k * d) * k
dU_dUc = np.ones_like(self.z)
idx = np.logical_or(self.z < self.z_floor, self.z > self.z_surface)
dU_dz[idx] = 0.0
dU_dUc[idx] = 0.0
dA_dz = omega * dU_dz
dA_dUc = omega * dU_dUc
self.J = vstack([
hstack([np.diag(dU_dz), dU_dUc]),
hstack([np.diag(dA_dz), dA_dUc])
])
def provideJ(self):
# rename
z = self.z
zref = self.zref
z0 = self.z0
z_roughness = self.z_roughness/1e3
Uref = self.Uref
n = len(z)
dU_dUref = np.zeros(n)
dU_dz_diag = np.zeros(n)
dU_dzref = np.zeros(n)
idx = [z - z0 > z_roughness]
lt = np.log((z[idx] - z0)/z_roughness)
lb = math.log((zref - z0)/z_roughness)
dU_dUref[idx] = lt/lb
dU_dz_diag[idx] = Uref/lb / (z[idx] - z0)
dU_dzref[idx] = -Uref*lt / math.log((zref - z0)/z_roughness)**2 / (zref - z0)
J = hstack([dU_dUref, np.diag(dU_dz_diag), dU_dzref])
return J
def provideJ(self):
# rename
z = self.z
zref = self.zref
z0 = self.z0
z_roughness = self.z_roughness / 1e3
Uref = self.Uref
n = len(z)
dU_dUref = np.zeros(n)
dU_dz_diag = np.zeros(n)
dU_dzref = np.zeros(n)
idx = [z - z0 > z_roughness]
lt = np.log((z[idx] - z0) / z_roughness)
lb = math.log((zref - z0) / z_roughness)
dU_dUref[idx] = lt / lb
dU_dz_diag[idx] = Uref / lb / (z[idx] - z0)
dU_dzref[idx] = -Uref * lt / math.log(
(zref - z0) / z_roughness)**2 / (zref - z0)
J = hstack([dU_dUref, np.diag(dU_dz_diag), dU_dzref])
return J
def execute(self):
# water depth
#CJB z_surface = wdepth+z_floor, so d = wdepth
d = self.z_surface - self.z_floor
# design wave height
h = self.hmax
# circular frequency
omega = 2.0*math.pi/self.T
# compute wave number from dispersion relationship
k = brentq(lambda k: omega**2 - self.g*k*math.tanh(d*k), 0, 10*omega**2/self.g)
# zero at surface
z_rel = self.z - self.z_surface
# maximum velocity
self.U = h/2.0*omega*np.cosh(k*(z_rel + d))/math.sinh(k*d) + self.Uc
self.U0 = h/2.0*omega*np.cosh(k*(0. + d))/math.sinh(k*d) + self.Uc
# check heights
self.U[np.logical_or(self.z < self.z_floor, self.z > self.z_surface)] = 0.
# acceleration
self.A = self.U * omega
self.A0 = self.U0 * omega
# angles
self.beta = self.betaWave*np.ones_like(self.z)
self.beta0 =self.betaWave
# derivatives
dU_dz = h/2.0*omega*np.sinh(k*(z_rel + d))/math.sinh(k*d)*k
dU_dUc = np.ones_like(self.z)
idx = np.logical_or(self.z < self.z_floor, self.z > self.z_surface)
dU_dz[idx] = 0.0
dU_dUc[idx] = 0.0
dA_dz = omega*dU_dz
dA_dUc = omega*dU_dUc
dU0 = np.zeros(len(self.z) + 1)
dU0[-1] = 1.0
dA0 = omega * dU0
self.J = vstack([hstack([np.diag(dU_dz), dU_dUc]), hstack([np.diag(dA_dz), dA_dUc]), np.transpose(dU0), np.transpose(dA0)])
def provideJ(self):
G = self.G
nu = self.nu
h = self.depth
r0 = self.r0
# vertical
eta = 1.0 + 0.6 * (1.0 - nu) * h / r0
deta_dr0 = -0.6 * (1.0 - nu) * h / r0**2
dkz_dr0 = 4 * G / (1.0 - nu) * (eta + r0 * deta_dr0)
deta_dh = 0.6 * (1.0 - nu) / r0
dkz_dh = 4 * G * r0 / (1.0 - nu) * deta_dh
# horizontal
eta = 1.0 + 0.55 * (2.0 - nu) * h / r0
deta_dr0 = -0.55 * (2.0 - nu) * h / r0**2
dkx_dr0 = 32.0 * (1.0 - nu) * G / (7.0 - 8.0 * nu) * (eta +
r0 * deta_dr0)
deta_dh = 0.55 * (2.0 - nu) / r0
dkx_dh = 32.0 * (1.0 - nu) * G * r0 / (7.0 - 8.0 * nu) * deta_dh
# rocking
eta = 1.0 + 1.2 * (1.0 - nu) * h / r0 + 0.2 * (2.0 - nu) * (h / r0)**3
deta_dr0 = -1.2 * (1.0 - nu) * h / r0**2 - 3 * 0.2 * (2.0 - nu) * (
h / r0)**3 / r0
dkthetax_dr0 = 8.0 * G / (3.0 * (1.0 - nu)) * (3 * r0**2 * eta +
r0**3 * deta_dr0)
deta_dh = 1.2 * (1.0 - nu) / r0 + 3 * 0.2 * (2.0 - nu) * (1.0 /
r0)**3 * h**2
dkthetax_dh = 8.0 * G * r0**3 / (3.0 * (1.0 - nu)) * deta_dh
# torsional
dkphi_dr0 = 16.0 * G * 3 * r0**2 / 3.0
dkphi_dh = 0.0
dk_dr0 = np.array(
[dkx_dr0, dkthetax_dr0, dkx_dr0, dkthetax_dr0, dkz_dr0, dkphi_dr0])
dk_dr0[self.rigid] = 0.0
dk_dh = np.array(
[dkx_dh, dkthetax_dh, dkx_dh, dkthetax_dh, dkz_dh, dkphi_dh])
dk_dh[self.rigid] = 0.0
J = hstack((dk_dr0, dk_dh))
return J
def provideJ(self):
# gradients
dPbar_dPa = dPbar_dPbar1 * dPbar1_dPbar0 / rated_power
dPbar_dPr = -dPbar_dPbar1 * dPbar1_dPbar0 * aero_power / rated_power**2
deff_dPa = dPbar_dPa * (constant / Pbar**2 - quadratic)
deff_dPr = dPbar_dPr * (constant / Pbar**2 - quadratic)
dP_dPa = eff + aero_power * deff_dPa
dP_dPr = aero_power * deff_dPr
self.J = hstack([np.diag(dP_dPa), dP_dPr])
return self.J
def provideJ(self):
G = self.G
nu = self.nu
h = self.depth
r0 = self.r0
# vertical
eta = 1.0 + 0.6*(1.0-nu)*h/r0
deta_dr0 = -0.6*(1.0-nu)*h/r0**2
dkz_dr0 = 4*G/(1.0-nu)*(eta + r0*deta_dr0)
deta_dh = 0.6*(1.0-nu)/r0
dkz_dh = 4*G*r0/(1.0-nu)*deta_dh
# horizontal
eta = 1.0 + 0.55*(2.0-nu)*h/r0
deta_dr0 = -0.55*(2.0-nu)*h/r0**2
dkx_dr0 = 32.0*(1.0-nu)*G/(7.0-8.0*nu)*(eta + r0*deta_dr0)
deta_dh = 0.55*(2.0-nu)/r0
dkx_dh = 32.0*(1.0-nu)*G*r0/(7.0-8.0*nu)*deta_dh
# rocking
eta = 1.0 + 1.2*(1.0-nu)*h/r0 + 0.2*(2.0-nu)*(h/r0)**3
deta_dr0 = -1.2*(1.0-nu)*h/r0**2 - 3*0.2*(2.0-nu)*(h/r0)**3/r0
dkthetax_dr0 = 8.0*G/(3.0*(1.0-nu))*(3*r0**2*eta + r0**3*deta_dr0)
deta_dh = 1.2*(1.0-nu)/r0 + 3*0.2*(2.0-nu)*(1.0/r0)**3*h**2
dkthetax_dh = 8.0*G*r0**3/(3.0*(1.0-nu))*deta_dh
# torsional
dkphi_dr0 = 16.0*G*3*r0**2/3.0
dkphi_dh = 0.0
dk_dr0 = np.array([dkx_dr0, dkthetax_dr0, dkx_dr0, dkthetax_dr0, dkz_dr0, dkphi_dr0])
dk_dr0[self.rigid] = 0.0
dk_dh = np.array([dkx_dh, dkthetax_dh, dkx_dh, dkthetax_dh, dkz_dh, dkphi_dh])
dk_dh[self.rigid] = 0.0
J = hstack((dk_dr0, dk_dh))
return J
def provideJ(self):
# rename
z = self.z
zref = self.zref
z0 = self.z0
shearExp = self.shearExp
U = self.U
Uref = self.Uref
# gradients
n = len(z)
dU_dUref = np.zeros(n)
dU_dz = np.zeros(n)
dU_dzref = np.zeros(n)
idx = z > z0
dU_dUref[idx] = U[idx]/Uref
dU_dz[idx] = U[idx]*shearExp/(z[idx] - z0)
dU_dzref[idx] = -U[idx]*shearExp/(zref - z0)
# # cubic spline region
# idx = np.logical_and(z > z0, z < zsmall)
# # d w.r.t z
# dU_dz[idx] = self.spline.eval_deriv(z[idx])
# # d w.r.t. Uref
# df2_dUref = k**shearExp
# dg2_dUref = k**shearExp*shearExp/(zsmall - z0)
# dU_dUref[idx] = self.spline.eval_deriv_params(z[idx], 0.0, 0.0, 0.0, df2_dUref, 0.0, dg2_dUref)
# # d w.r.t. zref
# dx2_dzref = k
# dg2_dzref = -Uref*k**shearExp*shearExp/k/(zref - z0)**2
# dU_dzref[idx] = self.spline.eval_deriv_params(z[idx], 0.0, dx2_dzref, 0.0, 0.0, 0.0, dg2_dzref)
J = hstack([dU_dUref, np.diag(dU_dz), dU_dzref])
return J
def provideJ(self):
# rename
z = self.z
zref = self.zref
z0 = self.z0
shearExp = self.shearExp
U = self.U
Uref = self.Uref
# gradients
n = len(z)
dU_dUref = np.zeros(n)
dU_dz = np.zeros(n)
dU_dzref = np.zeros(n)
idx = z > z0
dU_dUref[idx] = U[idx] / Uref
dU_dz[idx] = U[idx] * shearExp / (z[idx] - z0)
dU_dzref[idx] = -U[idx] * shearExp / (zref - z0)
# # cubic spline region
# idx = np.logical_and(z > z0, z < zsmall)
# # d w.r.t z
# dU_dz[idx] = self.spline.eval_deriv(z[idx])
# # d w.r.t. Uref
# df2_dUref = k**shearExp
# dg2_dUref = k**shearExp*shearExp/(zsmall - z0)
# dU_dUref[idx] = self.spline.eval_deriv_params(z[idx], 0.0, 0.0, 0.0, df2_dUref, 0.0, dg2_dUref)
# # d w.r.t. zref
# dx2_dzref = k
# dg2_dzref = -Uref*k**shearExp*shearExp/k/(zref - z0)**2
# dU_dzref[idx] = self.spline.eval_deriv_params(z[idx], 0.0, dx2_dzref, 0.0, 0.0, 0.0, dg2_dzref)
J = hstack([dU_dUref, np.diag(dU_dz), dU_dzref])
return J
