def linearize(self, params, unknowns, resids):
# rename
rho = params['rho']
U = params['U']
d = params['d']
mu = params['mu']
beta = params['beta']
# dynamic pressure
q = 0.5*rho*U**2
# Reynolds number and drag
if params['cd_usr'] in [np.inf, -np.inf, None, np.nan]:
cd = params['cd_usr']
Re = 1.0
dcd_dRe = 0.0
else:
Re = rho*U*d/mu
cd, dcd_dRe = cylinderDrag(Re)
# derivatives
dq_dU = rho*U
const = (dq_dU*cd + q*dcd_dRe*rho*d/mu)*d
dPx_dU = const*cosd(beta)
dPy_dU = const*sind(beta)
const = (cd + dcd_dRe*Re)*q
dPx_dd = const*cosd(beta)
dPy_dd = const*sind(beta)
n = len(params['z'])
zeron = np.zeros((n, n))
J = {}
J['windLoads.Px', 'U'] = np.diag(dPx_dU)
J['windLoads.Px', 'z'] = zeron
J['windLoads.Px', 'd'] = np.diag(dPx_dd)
J['windLoads.Py', 'U'] = np.diag(dPy_dU)
J['windLoads.Py', 'z'] = zeron
J['windLoads.Py', 'd'] = np.diag(dPy_dd)
J['windLoads.Pz', 'U'] = zeron
J['windLoads.Pz', 'z'] = zeron
J['windLoads.Pz', 'd'] = zeron
J['windLoads.qdyn', 'U'] = np.diag(dq_dU)
J['windLoads.qdyn', 'z'] = zeron
J['windLoads.qdyn', 'd'] = zeron
J['windLoads.z', 'U'] = zeron
J['windLoads.z', 'z'] = np.eye(n)
J['windLoads.z', 'd'] = zeron
return J
def linearize(self, params, unknowns, resids):
# rename
rho = params['rho']
U = params['U']
d = params['d']
mu = params['mu']
beta = params['beta']
# dynamic pressure
q = 0.5*rho*U**2
# Reynolds number and drag
if params['cd_usr'] in [np.inf, -np.inf, None, np.nan]:
cd = params['cd_usr']
Re = 1.0
dcd_dRe = 0.0
else:
Re = rho*U*d/mu
cd, dcd_dRe = cylinderDrag(Re)
# derivatives
dq_dU = rho*U
const = (dq_dU*cd + q*dcd_dRe*rho*d/mu)*d
dPx_dU = const*cosd(beta)
dPy_dU = const*sind(beta)
const = (cd + dcd_dRe*Re)*q
dPx_dd = const*cosd(beta)
dPy_dd = const*sind(beta)
n = len(params['z'])
zeron = np.zeros((n, n))
J = {}
J['windLoads.Px', 'U'] = np.diag(dPx_dU)
J['windLoads.Px', 'z'] = zeron
J['windLoads.Px', 'd'] = np.diag(dPx_dd)
J['windLoads.Py', 'U'] = np.diag(dPy_dU)
J['windLoads.Py', 'z'] = zeron
J['windLoads.Py', 'd'] = np.diag(dPy_dd)
J['windLoads.Pz', 'U'] = zeron
J['windLoads.Pz', 'z'] = zeron
J['windLoads.Pz', 'd'] = zeron
J['windLoads.qdyn', 'U'] = np.diag(dq_dU)
J['windLoads.qdyn', 'z'] = zeron
J['windLoads.qdyn', 'd'] = zeron
J['windLoads.z', 'U'] = zeron
J['windLoads.z', 'z'] = np.eye(n)
J['windLoads.z', 'd'] = zeron
return J
def provideJ(self):
J = np.array([[
cosd(self.precone),
sind(self.precone),
(-self.Rtip * sind(self.precone) +
self.precurveTip * sind(self.precone)) * pi / 180.0
]])
return J
def solve_nonlinear(self, params, unknowns, resids):
rho = params['rho']
U = params['U']
d = params['d']
mu = params['mu']
beta = params['beta']
# dynamic pressure
q = 0.5*rho*U**2
# Reynolds number and drag
if params['cd_usr'] in [np.inf, -np.inf, None, np.nan]:
Re = rho*U*d/mu
cd, dcd_dRe = cylinderDrag(Re)
else:
cd = params['cd_usr']
Re = 1.0
dcd_dRe = 0.0
Fp = q*cd*d
# components of distributed loads
Px = Fp*cosd(beta)
Py = Fp*sind(beta)
Pz = 0*Fp
# pack data
unknowns['windLoads_Px'] = Px
unknowns['windLoads_Py'] = Py
unknowns['windLoads_Pz'] = Pz
unknowns['windLoads_qdyn'] = q
unknowns['windLoads_z'] = params['z']
unknowns['windLoads_beta'] = beta
def execute(self):
rho = self.rho
U = self.U
d = self.d
mu = self.mu
beta = self.beta
# dynamic pressure
q = 0.5*rho*U**2
# Reynolds number and drag
if self.cd_usr:
cd = self.cd_usr
Re = 1.0
dcd_dRe = 0.0
else:
Re = rho*U*d/mu
cd, dcd_dRe = cylinderDrag(Re)
Fp = q*cd*d
# components of distributed loads
Px = Fp*cosd(beta)
Py = Fp*sind(beta)
Pz = 0*Fp
print "CommonSE Px (Wind): ", Px
# pack data
self.windLoads.Px = Px
self.windLoads.Py = Py
self.windLoads.Pz = Pz
self.windLoads.qdyn = q
self.windLoads.z = self.z
self.windLoads.beta = beta
# derivatives
self.dq_dU = rho*U
const = (self.dq_dU*cd + q*dcd_dRe*rho*d/mu)*d
self.dPx_dU = const*cosd(beta)
self.dPy_dU = const*sind(beta)
const = (cd + dcd_dRe*Re)*q
self.dPx_dd = const*cosd(beta)
self.dPy_dd = const*sind(beta)
def execute(self):
rho = self.rho
U = self.U
d = self.d
mu = self.mu
beta = self.beta
# dynamic pressure
q = 0.5 * rho * U**2
# Reynolds number and drag
if self.cd_usr:
cd = self.cd_usr
Re = 1.0
dcd_dRe = 0.0
else:
Re = rho * U * d / mu
cd, dcd_dRe = cylinderDrag(Re)
Fp = q * cd * d
# components of distributed loads
Px = Fp * cosd(beta)
Py = Fp * sind(beta)
Pz = 0 * Fp
# pack data
self.windLoads.Px = Px
self.windLoads.Py = Py
self.windLoads.Pz = Pz
self.windLoads.qdyn = q
self.windLoads.z = self.z
self.windLoads.beta = beta
# derivatives
self.dq_dU = rho * U
const = (self.dq_dU * cd + q * dcd_dRe * rho * d / mu) * d
self.dPx_dU = const * cosd(beta)
self.dPy_dU = const * sind(beta)
const = (cd + dcd_dRe * Re) * q
self.dPx_dd = const * cosd(beta)
self.dPy_dd = const * sind(beta)
def solve_nonlinear(self, params, unknowns, resids):
rho = params['rho']
U = params['U']
d = params['d']
mu = params['mu']
beta = params['beta']
if not (params['rho'] == 0. or all(params['U'] == 0.) or params['mu'] == 0.):
# dynamic pressure
q = 0.5*rho*U**2
# Reynolds number and drag
if params['cd_usr'] in [np.inf, -np.inf, None, np.nan]:
Re = rho*U*d/mu
cd, dcd_dRe = cylinderDrag(Re)
else:
cd = params['cd_usr']
Re = 1.0
dcd_dRe = 0.0
Fp = q*cd*d
# components of distributed loads
Px = Fp*cosd(beta)
Py = Fp*sind(beta)
Pz = 0*Fp
# pack data
unknowns['windLoads_Px'] = Px
unknowns['windLoads_Py'] = Py
unknowns['windLoads_Pz'] = Pz
unknowns['windLoads_qdyn'] = q
unknowns['windLoads_beta'] = beta
unknowns['windLoads_z'] = params['z']
unknowns['windLoads_d'] = params['d']
def provideJ(self):
J = np.array([[cosd(self.precone), sind(self.precone),
(-self.Rtip*sind(self.precone) + self.precurveTip*sind(self.precone))*pi/180.0]])
return J
def execute(self):
self.R = self.Rtip*cosd(self.precone) + self.precurveTip*sind(self.precone)
def execute(self):
rho = self.rho
U = self.U
U0 = self.U0
d = self.d
zrel= self.z-self.wlevel
mu = self.mu
beta = self.beta
beta0= self.beta0
# dynamic pressure
q = 0.5*rho*U**2
q0= 0.5*rho*U0**2
# Reynolds number and drag
if self.cd_usr:
cd = self.cd_usr*np.ones_like(self.d)
Re = 1.0
dcd_dRe = 0.0
else:
Re = rho*U*d/mu
cd, dcd_dRe = cylinderDrag(Re)
d = self.d
mu = self.mu
beta = self.beta
# inertial and drag forces
Fi = rho*self.cm*math.pi/4.0*d**2*self.A # Morrison's equation
Fd = q*cd*d
Fp = Fi + Fd
#FORCES [N/m] AT z=0 m
idx0 = np.abs(zrel).argmin() # closest index to z=0, used to find d at z=0
d0 = d[idx0] # initialize
cd0 = cd[idx0] # initialize
if (zrel[idx0]<0.) and (idx0< (zrel.size-1)): # point below water
d0 = np.mean(d[idx0:idx0+2])
cd0 = np.mean(cd[idx0:idx0+2])
elif (zrel[idx0]>0.) and (idx0>0): # point above water
d0 = np.mean(d[idx0-1:idx0+1])
cd0 = np.mean(cd[idx0-1:idx0+1])
Fi0 = rho*self.cm*math.pi/4.0*d0**2*self.A0 # Morrison's equation
Fd0 = q0*cd0*d0
Fp0 = Fi0 + Fd0
# components of distributed loads
Px = Fp*cosd(beta)
Py = Fp*sind(beta)
Pz = 0.*Fp
Px0 = Fp0*cosd(beta0)
Py0 = Fp0*sind(beta0)
Pz0 = 0.*Fp0
#Store qties at z=0 MSL
self.waveLoads.Px0 = Px0
self.waveLoads.Py0 = Py0
self.waveLoads.Pz0 = Pz0
self.waveLoads.q0 = q0
self.waveLoads.beta0 = beta0
# pack data
self.waveLoads.Px = Px
self.waveLoads.Py = Py
self.waveLoads.Pz = Pz
self.waveLoads.qdyn = q
self.waveLoads.z = self.z
self.waveLoads.beta = beta
self.waveLoads.d = d
# derivatives
self.dq_dU = rho*U
const = (self.dq_dU*cd + q*dcd_dRe*rho*d/mu)*d
self.dPx_dU = const*cosd(beta)
self.dPy_dU = const*sind(beta)
const = (cd + dcd_dRe*Re)*q + rho*self.cm*math.pi/4.0*2*d*self.A
self.dPx_dd = const*cosd(beta)
self.dPy_dd = const*sind(beta)
const = rho*self.cm*math.pi/4.0*d**2
self.dPx_dA = const*cosd(beta)
self.dPy_dA = const*sind(beta)
def execute(self):
#simplify nomenclature
psi_wi=self.towerWindLoads.beta[0] #psi is stored in beta already, however for legs and piles it needs to be adjusted for psi
psi_wa=self.towerWaveLoads.beta[0]
twrZs=self.towerWindLoads.z
pillegZs=self.pileLegWaveLoads.z
pillegDs=self.pileLegWaveLoads.d
nlegs=self.nlegs
al_bat3D=self.al_bat3D
VPFlag=self.VPFlag
TwrRigidTop=(self.RNAinputs.CMoff[2] != 0.) and self.TwrRigidTop #This makes sure we do not have TwrRigidTop=True with CMzoff=0., no length segment that is.
pilendIDs=self.pilendIDs
legndIDs=self.legndIDs
twrndIDs=self.twrndIDs
wdepth=self.wdepth
#COSINE MATRIX FROM LOCAL TO GLOBAL COORDINATE SYSTEMS
DIRCOSwind=np.array([ [cosd(psi_wi) , -sind(psi_wi) ,0.],
[ sind(psi_wi) , cosd(psi_wi),0.],
[ 0., 0., 1.]])
DIRCOSwave=np.array([ [cosd(psi_wa) , -sind(psi_wa) ,0.],
[ sind(psi_wa) , cosd(psi_wa),0.],
[ 0., 0., 1.]])
#I need to get the right node IDs to be able to assign forces for Frame3DD
#Get the values of the loads at the nodes of pile and leg 1
#for the other legs, the wdrag is going to be the same
if nlegs== 4: #Diagonal loading condition ONLY for the time being
pileidx=np.array([]) #Initialize in case empty piles
if pilendIDs.size:
pileidx=pilendIDs[0:pilendIDs.size/nlegs] #np.arange(Pilemems[0,0],Pilemems[-1,1]/nlegs+1)-1 #indices of pile 1
legidx=legndIDs[0:legndIDs.size/nlegs] #legidx=np.arange(Legmems[0,0],Legmems[-1,1]/nlegs+1)-1 #indices of leg 1
deltaz=((np.roll(pillegZs,-1)-pillegZs)/2)[0:-1] #these are the appropriate 1/2 deltazs for the entire pile-leg assembly
deltaz=np.hstack((deltaz[0],(np.roll(deltaz,-1)+deltaz)[0:-1],deltaz[-1])) #This is the actual DeltaZ to be assigned at each node starting from the 2nd and ending at the one before last
#Correct the delta z for the node just below water to avoid jumps in loading - use refined mesh however
#idx_bw=np.nonzero(pillegZs<= wdepth)[0][-1] #CJB- Original code. Modified line below
idx_bw=np.nonzero(pillegZs<= 0)[0][-1] #CJBe THe MSL is now at z=0, not z=wdepth
#Also Attempt at using load at z=0
###Px0=self.pileLegWaveLoads.Px_i0overd2*pillegDs[idx_bw]**2+self.pileLegWaveLoads.Px_d0overd*pillegDs[idx_bw]
###Py0=self.pileLegWaveLoads.Py_i0overd2*pillegDs[idx_bw]**2+self.pileLegWaveLoads.Py_d0overd*pillegDs[idx_bw]
Px0=self.pileLegWaveLoads.Px0
Py0=self.pileLegWaveLoads.Py0
#deltaz0=(wdepth-pillegZs[idx_bw]) #CJB- Original code. Modified line below
deltaz0=np.abs(0-pillegZs[idx_bw]) #CJBe
#if (wdepth-pillegZs[idx_bw])> deltaz[idx_bw]/2.: #point with its deltaz entriely below surface #CJB- Original code. Modified line below
if np.abs(0-pillegZs[idx_bw])> np.abs(deltaz[idx_bw]/2.): #CJBe Remove wdepth
deltaz0 -= deltaz[idx_bw]/2. #note deltaz0 before deltaz as deltaz gets modified
#deltaz[idx_bw]=deltaz[idx_bw]/2. -(pillegZs[idx_bw]-wdepth)
else:
deltaz[idx_bw]=deltaz[idx_bw]/2.
waDrag0=np.sqrt(Px0**2.+Py0**2.)*deltaz0 #In case add this one to the original wDrag, or alternatively do awhat I do below, increasing Deltaz
waDrag=np.sqrt(self.pileLegWaveLoads.Px**2.+self.pileLegWaveLoads.Py**2.)*deltaz #[N] forces from waves, considered normal to the sloping 1 leg.
waDrag[idx_bw] += waDrag0
wiDrag=np.sqrt(self.pileLegWindLoads.Px**2.+self.pileLegWindLoads.Py**2.)*deltaz * (np.cos(al_bat3D))**2 #[N] forces from wind normal to the sloping 1 leg. Wind is horizontal, that's why cos^2
#Forces on legs 1 (and 3 though sign of Fz reversed)
junk=np.zeros(waDrag.size)
waDrag1_3= (np.dot(DIRCOSwave , np.vstack((waDrag*np.cos(al_bat3D),junk,waDrag*np.sin(al_bat3D))))).T #[n,3] [N] This is an approx for air drag, as it is not normal to the leg to begin with, but it makes it easier
wiDrag1_3= (np.dot(DIRCOSwind , np.vstack((wiDrag*np.cos(al_bat3D),junk,wiDrag*np.sin(al_bat3D))))).T #[n,3] [N]
#Forces on legs 2 (and 4), it is as if they were vertical
waDrag2_4= (np.dot(DIRCOSwave ,np.vstack((waDrag,junk, waDrag*0.)))).T #[n,3] [N]
wiDrag2_4= (np.dot(DIRCOSwind ,np.vstack((wiDrag,junk, wiDrag*0.)))).T #[n,3] [N]
#Add them together
wDrag1_3=waDrag1_3+wiDrag1_3 #[N]
wDrag2_4=waDrag2_4+wiDrag2_4 #[N]
wDrag=waDrag+wiDrag #[N]
wl_idx=np.nonzero(wDrag)[0] #indices of the pile-leg nodes where loading is applied--
if VPFlag and pileidx: #Need to account for the cos
#Forces on legs 1 (and 3 though sign of Fz reversed)
wDrag1_3[pileidx]=wDrag2_4[pileidx]
n_pillegLds=wl_idx.size
n_loads=n_pillegLds*nlegs #Total number of wave load nodes
pilleg_ndsfrc=np.zeros([n_loads,7])
nNodespile=pileidx.size #number of nodes in 1 pile
nNodesleg=legidx.size #number of nodes in 1 leg
for ii in range(0,nlegs): #Cycle through legs
idx0=nNodespile*ii #start index for pile IDs
idx1=idx0+nNodespile #stop index for pile IDs
idx2=nNodesleg*ii #start index for leg IDs
idx3=idx2+nNodesleg #stop index for leg IDs
nd_ids=np.vstack((self.pilendIDs[idx0:idx1],self.legndIDs[idx2:idx3]))[wl_idx]
if np.mod(ii,2)==0:
lds=wDrag2_4[wl_idx,:]
elif ii==1:
lds=np.hstack((wDrag1_3[wl_idx,0:2],-wDrag1_3[wl_idx,2].reshape(-1,1)))
else:
lds=wDrag1_3[wl_idx,:]
idx0=n_pillegLds*ii #start index in pilleg_ndsfrc
idx1=idx0+n_pillegLds #stop index in pilleg_ndsfrc
pilleg_ndsfrc[idx0:idx1,:-3]=np.hstack((nd_ids,lds))
#Store wave loads
self.Loadouts.wdrag1_3=wDrag1_3
self.Loadouts.wdrag2_4=wDrag2_4
else: #3legged jacket in progress
#TO DO THIS CASE
sys.exit("nlegs <>4 not implemented yet for loading")
#-----Need to add hydrostatic loading -BUOYANCY FORCE
#IT is a distributed force along the non-flooded members
#Still TO DO
#________________________________TOWER__________________________________#
#Now get the values of the loads at the nodes of Tower
junk=(np.roll(twrZs,-1)-np.roll(twrZs,1))[1:-1]/2.
deltaz=np.hstack(((twrZs[1]-twrZs[0])/2.,junk,(twrZs[-1]-twrZs[-2])/2.))#these are the appropriate deltazs
#just wind loading for tower but wtrload perhaps in the future for tripods
junk=(np.sqrt(self.towerWindLoads.Px**2+self.towerWindLoads.Py**2)*deltaz).reshape([-1,1]) #[N] forces
#decompose along local x,y and add z component
junk=np.hstack((junk,np.zeros([junk.size,2]))).T
self.Loadouts.twr_dragf=np.dot(DIRCOSwind , junk) #*np.sin(wind_dict['psi']), junk*0.])
#Tower Loads for Frame3DD
n_twrlds=(twrndIDs.shape[0]-TwrRigidTop)*(self.Loadouts.twr_dragf.any()) #distributed loads along tower+RNA node load
twr_ndsfrc=np.zeros([n_twrlds,7])
twr_ndsfrc[0:n_twrlds,:-3]=np.hstack((twrndIDs[0:len(twrndIDs)-TwrRigidTop].reshape([-1,1]),self.Loadouts.twr_dragf.T))
#____________ADD CONCENTRATED RNA FORCES________________________________#
#First account for moment transfer in global coordinate system as if yaw=0
RNAload=np.copy(self.RNA_F.reshape([2,3]).T)#RNAload: 1columns forces, 2nd column moments
#Store yaw-rotated forces and moments at the hub still [3,2]
self.Loadouts.RNAload=np.dot(DIRCOSwind,RNAload)
Deltax=self.RNAinputs.Thoff[0]-self.RNAinputs.CMoff[0]
Deltay=self.RNAinputs.Thoff[1]-self.RNAinputs.CMoff[1]
Deltaz=self.RNAinputs.Thoff[2]-self.RNAinputs.CMoff[2]
if not(TwrRigidTop):
Deltax=self.RNAinputs.Thoff[0]
Deltay=self.RNAinputs.Thoff[1]
Deltaz=self.RNAinputs.Thoff[2]
#Rotor Loads - no weight yet
RNAload[0,1] += -RNAload[1,0]*Deltaz + RNAload[2,0]*Deltay #Mxx=-Fy*Deltaz +Fz*deltay
RNAload[1,1] += RNAload[0,0]*Deltaz - RNAload[2,0]*Deltax #Myy= Fx*deltaz-Fz*deltax
RNAload[2,1] += -RNAload[0,0]*Deltay + RNAload[1,0]*Deltax #Mzz=-Fx*Deltay +Fy*deltax
#Then rotate them in the global coordinate system for PYFRAME to account for yaw
RNAload=np.dot(DIRCOSwind,RNAload) #Gravity is already accounted for by Frame3DD for concentrated masses: Jacket.Twr.RNAmass*aux['g_z'],np.zeros(3))) self.RNA_F.reshape([2,3]).T
if not(TwrRigidTop):
twr_ndsfrc[-1,1:] += RNAload.T.flatten()
else:
twr_ndsfrc = np.vstack(( twr_ndsfrc,np.hstack((twrndIDs[-1],RNAload.T.flatten())) ))
# If we apply this load at tower-top and not tower-top+CMzoff we need to account for different DeltaZ
## if not(TwrRigidTop):
## RNAload[0,1] -= RNAload[1,0]*ThOffset_z #*CMzoff #Mxx
## RNAload[1,1] += RNAload[0,0]*CMzoff #Myy
## twr_ndsfrc[-1,1:] += RNAload.T.flatten()
## else: #Put forces at the RNA.CM location
## RNAload[0,1] -= RNAload[1,0]*ThOffset_z #*CMzoff #Mxx
## RNAload[1,1] += RNAload[0,0]*CMzoff #Myy
##
## twr_ndsfrc[-1,:] += np.hstack((twrndIDs[-1],RNAload.T.flatten()))
#STACK ALLOF THEM TOGETHER
self.Loadouts.nds_frc=np.vstack((pilleg_ndsfrc, twr_ndsfrc)) #Concentrated loads
def execute(self):
rho = self.rho
U = self.U
U0 = self.U0
d = self.d
zrel = self.z - self.wlevel
mu = self.mu
beta = self.beta
beta0 = self.beta0
# dynamic pressure
q = 0.5 * rho * U**2
q0 = 0.5 * rho * U0**2
# Reynolds number and drag
if self.cd_usr:
cd = self.cd_usr * np.ones_like(self.d)
Re = 1.0
dcd_dRe = 0.0
else:
Re = rho * U * d / mu
cd, dcd_dRe = cylinderDrag(Re)
d = self.d
mu = self.mu
beta = self.beta
# inertial and drag forces
Fi = rho * self.cm * math.pi / 4.0 * d**2 * self.A # Morrison's equation
Fd = q * cd * d
Fp = Fi + Fd
#FORCES [N/m] AT z=0 m
idx0 = np.abs(
zrel).argmin() # closest index to z=0, used to find d at z=0
d0 = d[idx0] # initialize
cd0 = cd[idx0] # initialize
if (zrel[idx0] < 0.) and (idx0 < (zrel.size - 1)): # point below water
d0 = np.mean(d[idx0:idx0 + 2])
cd0 = np.mean(cd[idx0:idx0 + 2])
elif (zrel[idx0] > 0.) and (idx0 > 0): # point above water
d0 = np.mean(d[idx0 - 1:idx0 + 1])
cd0 = np.mean(cd[idx0 - 1:idx0 + 1])
Fi0 = rho * self.cm * math.pi / 4.0 * d0**2 * self.A0 # Morrison's equation
Fd0 = q0 * cd0 * d0
Fp0 = Fi0 + Fd0
# components of distributed loads
Px = Fp * cosd(beta)
Py = Fp * sind(beta)
Pz = 0. * Fp
Px0 = Fp0 * cosd(beta0)
Py0 = Fp0 * sind(beta0)
Pz0 = 0. * Fp0
#Store qties at z=0 MSL
self.waveLoads.Px0 = Px0
self.waveLoads.Py0 = Py0
self.waveLoads.Pz0 = Pz0
self.waveLoads.q0 = q0
self.waveLoads.beta0 = beta0
# pack data
self.waveLoads.Px = Px
self.waveLoads.Py = Py
self.waveLoads.Pz = Pz
self.waveLoads.qdyn = q
self.waveLoads.z = self.z
self.waveLoads.beta = beta
self.waveLoads.d = d
# derivatives
self.dq_dU = rho * U
const = (self.dq_dU * cd + q * dcd_dRe * rho * d / mu) * d
self.dPx_dU = const * cosd(beta)
self.dPy_dU = const * sind(beta)
const = (cd + dcd_dRe *
Re) * q + rho * self.cm * math.pi / 4.0 * 2 * d * self.A
self.dPx_dd = const * cosd(beta)
self.dPy_dd = const * sind(beta)
const = rho * self.cm * math.pi / 4.0 * d**2
self.dPx_dA = const * cosd(beta)
self.dPy_dA = const * sind(beta)
def provideJ(self):
J = np.array([[cosd(self.precone), -self.Rtip*sind(self.precone)*pi/180.0]])
return J
def solve_nonlinear(self, params, unknowns, resids):
#wlevel = params['wlevel']
#if wlevel > 0.0: wlevel *= -1.0
rho = params['rho']
U = params['U']
#U0 = params['U0']
d = params['d']
#zrel= params['z']-wlevel
mu = params['mu']
beta = params['beta']
#beta0 = params['beta0']
# dynamic pressure
q = 0.5*rho*U**2
#q0= 0.5*rho*U0**2
# Reynolds number and drag
if params['cd_usr'] in [np.inf, -np.inf, None, np.nan]:
Re = rho*U*d/mu
cd, dcd_dRe = cylinderDrag(Re)
else:
cd = params['cd_usr']*np.ones_like(d)
Re = 1.0
dcd_dRe = 0.0
# inertial and drag forces
Fi = rho*params['cm']*math.pi/4.0*d**2*params['A'] # Morrison's equation
Fd = q*cd*d
Fp = Fi + Fd
# components of distributed loads
Px = Fp*cosd(beta)
Py = Fp*sind(beta)
Pz = 0.*Fp
#FORCES [N/m] AT z=0 m
#idx0 = np.abs(zrel).argmin() # closest index to z=0, used to find d at z=0
#d0 = d[idx0] # initialize
#cd0 = cd[idx0] # initialize
#if (zrel[idx0]<0.) and (idx0< (zrel.size-1)): # point below water
# d0 = np.mean(d[idx0:idx0+2])
# cd0 = np.mean(cd[idx0:idx0+2])
#elif (zrel[idx0]>0.) and (idx0>0): # point above water
# d0 = np.mean(d[idx0-1:idx0+1])
# cd0 = np.mean(cd[idx0-1:idx0+1])
#Fi0 = rho*params['cm']*math.pi/4.0*d0**2*params['A0'] # Morrison's equation
#Fd0 = q0*cd0*d0
#Fp0 = Fi0 + Fd0
#Px0 = Fp0*cosd(beta0)
#Py0 = Fp0*sind(beta0)
#Pz0 = 0.*Fp0
#Store qties at z=0 MSL
#unknowns['waveLoads_Px0'] = Px0
#unknowns['waveLoads_Py0'] = Py0
#unknowns['waveLoads_Pz0'] = Pz0
#unknowns['waveLoads_qdyn0'] = q0
#unknowns['waveLoads_beta0'] = beta0
# pack data
unknowns['waveLoads_Px'] = Px
unknowns['waveLoads_Py'] = Py
unknowns['waveLoads_Pz'] = Pz
unknowns['waveLoads_qdyn'] = q
unknowns['waveLoads_pt'] = q + params['p']
unknowns['waveLoads_z'] = params['z']
unknowns['waveLoads_beta'] = beta
unknowns['waveLoads_d'] = d
def execute(self):
self.R = self.Rtip * cosd(self.precone) + self.precurveTip * sind(
self.precone)
def linearize(self, params, unknowns, resids):
#wlevel = params['wlevel']
#if wlevel > 0.0: wlevel *= -1.0
rho = params['rho']
U = params['U']
#U0 = params['U0']
d = params['d']
#zrel= params['z']-wlevel
mu = params['mu']
beta = params['beta']
#beta0 = params['beta0']
# dynamic pressure
q = 0.5*rho*U**2
#q0= 0.5*rho*U0**2
# Reynolds number and drag
if params['cd_usr'] in [np.inf, -np.inf, None, np.nan]:
cd = params['cd_usr']*np.ones_like(d)
Re = 1.0
dcd_dRe = 0.0
else:
Re = rho*U*d/mu
cd, dcd_dRe = cylinderDrag(Re)
# derivatives
dq_dU = rho*U
const = (dq_dU*cd + q*dcd_dRe*rho*d/mu)*d
dPx_dU = const*cosd(beta)
dPy_dU = const*sind(beta)
const = (cd + dcd_dRe*Re)*q + rho*params['cm']*math.pi/4.0*2*d*params['A']
dPx_dd = const*cosd(beta)
dPy_dd = const*sind(beta)
const = rho*params['cm']*math.pi/4.0*d**2
dPx_dA = const*cosd(beta)
dPy_dA = const*sind(beta)
n = len(params['z'])
zeron = np.zeros((n, n))
J = {}
J['waveLoads.Px', 'U'] = np.diag(dPx_dU)
J['waveLoads.Px', 'A'] = np.diag(dPx_dA)
J['waveLoads.Px', 'z'] = zeron
J['waveLoads.Px', 'd'] = np.diag(dPx_dd)
J['waveLoads.Px', 'p'] = zeron
J['waveLoads.Py', 'U'] = np.diag(dPy_dU)
J['waveLoads.Py', 'A'] = np.diag(dPy_dA)
J['waveLoads.Py', 'z'] = zeron
J['waveLoads.Py', 'd'] = np.diag(dPy_dd)
J['waveLoads.Py', 'p'] = zeron
J['waveLoads.Pz', 'U'] = zeron
J['waveLoads.Pz', 'A'] = zeron
J['waveLoads.Pz', 'z'] = zeron
J['waveLoads.Pz', 'd'] = zeron
J['waveLoads.Pz', 'p'] = zeron
J['waveLoads.qdyn', 'U'] = np.diag(dq_dU)
J['waveLoads.qdyn', 'A'] = zeron
J['waveLoads.qdyn', 'z'] = zeron
J['waveLoads.qdyn', 'd'] = zeron
J['waveLoads.qdyn', 'p'] = zeron
J['waveLoads.pt', 'U'] = np.diag(dq_dU)
J['waveLoads.pt', 'A'] = zeron
J['waveLoads.pt', 'z'] = zeron
J['waveLoads.pt', 'd'] = zeron
J['waveLoads.pt', 'p'] = 1.0
J['waveLoads.z', 'U'] = zeron
J['waveLoads.z', 'A'] = zeron
J['waveLoads.z', 'z'] = np.eye(n)
J['waveLoads.z', 'd'] = zeron
J['waveLoads.z', 'p'] = zeron
return J
def execute(self):
#simplify nomenclature
psi_wi = self.towerWindLoads.beta[
0] #psi is stored in beta already, however for legs and piles it needs to be adjusted for psi
psi_wa = self.towerWaveLoads.beta[0]
twrZs = self.towerWindLoads.z
pillegZs = self.pileLegWaveLoads.z
pillegDs = self.pileLegWaveLoads.d
nlegs = self.nlegs
al_bat3D = self.al_bat3D
VPFlag = self.VPFlag
TwrRigidTop = (
self.RNAinputs.CMoff[2] != 0.
) and self.TwrRigidTop #This makes sure we do not have TwrRigidTop=True with CMzoff=0., no length segment that is.
pilendIDs = self.pilendIDs
legndIDs = self.legndIDs
twrndIDs = self.twrndIDs
wdepth = self.wdepth
#COSINE MATRIX FROM LOCAL TO GLOBAL COORDINATE SYSTEMS
DIRCOSwind = np.array([[cosd(psi_wi), -sind(psi_wi), 0.],
[sind(psi_wi), cosd(psi_wi), 0.], [0., 0., 1.]])
DIRCOSwave = np.array([[cosd(psi_wa), -sind(psi_wa), 0.],
[sind(psi_wa), cosd(psi_wa), 0.], [0., 0., 1.]])
#I need to get the right node IDs to be able to assign forces for Frame3DD
#Get the values of the loads at the nodes of pile and leg 1
#for the other legs, the wdrag is going to be the same
if nlegs == 4: #Diagonal loading condition ONLY for the time being
pileidx = np.array([]) #Initialize in case empty piles
if pilendIDs.size:
pileidx = pilendIDs[
0:pilendIDs.size /
nlegs] #np.arange(Pilemems[0,0],Pilemems[-1,1]/nlegs+1)-1 #indices of pile 1
legidx = legndIDs[
0:legndIDs.size /
nlegs] #legidx=np.arange(Legmems[0,0],Legmems[-1,1]/nlegs+1)-1 #indices of leg 1
deltaz = (
(np.roll(pillegZs, -1) - pillegZs) / 2
)[0:
-1] #these are the appropriate 1/2 deltazs for the entire pile-leg assembly
deltaz = np.hstack(
(deltaz[0], (np.roll(deltaz, -1) + deltaz)[0:-1], deltaz[-1])
) #This is the actual DeltaZ to be assigned at each node starting from the 2nd and ending at the one before last
#Correct the delta z for the node just below water to avoid jumps in loading - use refined mesh however
#idx_bw=np.nonzero(pillegZs<= wdepth)[0][-1] #CJB- Original code. Modified line below
idx_bw = np.nonzero(pillegZs <= 0)[0][
-1] #CJBe THe MSL is now at z=0, not z=wdepth
#Also Attempt at using load at z=0
###Px0=self.pileLegWaveLoads.Px_i0overd2*pillegDs[idx_bw]**2+self.pileLegWaveLoads.Px_d0overd*pillegDs[idx_bw]
###Py0=self.pileLegWaveLoads.Py_i0overd2*pillegDs[idx_bw]**2+self.pileLegWaveLoads.Py_d0overd*pillegDs[idx_bw]
Px0 = self.pileLegWaveLoads.Px0
Py0 = self.pileLegWaveLoads.Py0
#deltaz0=(wdepth-pillegZs[idx_bw]) #CJB- Original code. Modified line below
deltaz0 = np.abs(0 - pillegZs[idx_bw]) #CJBe
#if (wdepth-pillegZs[idx_bw])> deltaz[idx_bw]/2.: #point with its deltaz entriely below surface #CJB- Original code. Modified line below
if np.abs(0 - pillegZs[idx_bw]) > np.abs(
deltaz[idx_bw] / 2.): #CJBe Remove wdepth
deltaz0 -= deltaz[
idx_bw] / 2. #note deltaz0 before deltaz as deltaz gets modified
#deltaz[idx_bw]=deltaz[idx_bw]/2. -(pillegZs[idx_bw]-wdepth)
else:
deltaz[idx_bw] = deltaz[idx_bw] / 2.
waDrag0 = np.sqrt(
Px0**2. + Py0**2.
) * deltaz0 #In case add this one to the original wDrag, or alternatively do awhat I do below, increasing Deltaz
waDrag = np.sqrt(
self.pileLegWaveLoads.Px**2. + self.pileLegWaveLoads.Py**2.
) * deltaz #[N] forces from waves, considered normal to the sloping 1 leg.
waDrag[idx_bw] += waDrag0
wiDrag = np.sqrt(
self.pileLegWindLoads.Px**2. + self.pileLegWindLoads.Py**2.
) * deltaz * (
np.cos(al_bat3D)
)**2 #[N] forces from wind normal to the sloping 1 leg. Wind is horizontal, that's why cos^2
#Forces on legs 1 (and 3 though sign of Fz reversed)
junk = np.zeros(waDrag.size)
waDrag1_3 = (
np.dot(
DIRCOSwave,
np.vstack((waDrag * np.cos(al_bat3D), junk,
waDrag * np.sin(al_bat3D))))
).T #[n,3] [N] This is an approx for air drag, as it is not normal to the leg to begin with, but it makes it easier
wiDrag1_3 = (np.dot(
DIRCOSwind,
np.vstack((wiDrag * np.cos(al_bat3D), junk,
wiDrag * np.sin(al_bat3D))))).T #[n,3] [N]
#Forces on legs 2 (and 4), it is as if they were vertical
waDrag2_4 = (np.dot(DIRCOSwave,
np.vstack((waDrag, junk,
waDrag * 0.)))).T #[n,3] [N]
wiDrag2_4 = (np.dot(DIRCOSwind,
np.vstack((wiDrag, junk,
wiDrag * 0.)))).T #[n,3] [N]
#Add them together
wDrag1_3 = waDrag1_3 + wiDrag1_3 #[N]
wDrag2_4 = waDrag2_4 + wiDrag2_4 #[N]
wDrag = waDrag + wiDrag #[N]
wl_idx = np.nonzero(wDrag)[
0] #indices of the pile-leg nodes where loading is applied--
if VPFlag and pileidx: #Need to account for the cos
#Forces on legs 1 (and 3 though sign of Fz reversed)
wDrag1_3[pileidx] = wDrag2_4[pileidx]
n_pillegLds = wl_idx.size
n_loads = n_pillegLds * nlegs #Total number of wave load nodes
pilleg_ndsfrc = np.zeros([n_loads, 7])
nNodespile = pileidx.size #number of nodes in 1 pile
nNodesleg = legidx.size #number of nodes in 1 leg
for ii in range(0, nlegs): #Cycle through legs
idx0 = nNodespile * ii #start index for pile IDs
idx1 = idx0 + nNodespile #stop index for pile IDs
idx2 = nNodesleg * ii #start index for leg IDs
idx3 = idx2 + nNodesleg #stop index for leg IDs
nd_ids = np.vstack((self.pilendIDs[idx0:idx1],
self.legndIDs[idx2:idx3]))[wl_idx]
if np.mod(ii, 2) == 0:
lds = wDrag2_4[wl_idx, :]
elif ii == 1:
lds = np.hstack(
(wDrag1_3[wl_idx,
0:2], -wDrag1_3[wl_idx, 2].reshape(-1, 1)))
else:
lds = wDrag1_3[wl_idx, :]
idx0 = n_pillegLds * ii #start index in pilleg_ndsfrc
idx1 = idx0 + n_pillegLds #stop index in pilleg_ndsfrc
pilleg_ndsfrc[idx0:idx1, :-3] = np.hstack((nd_ids, lds))
#Store wave loads
self.Loadouts.wdrag1_3 = wDrag1_3
self.Loadouts.wdrag2_4 = wDrag2_4
else: #3legged jacket in progress
#TO DO THIS CASE
sys.exit("nlegs <>4 not implemented yet for loading")
#-----Need to add hydrostatic loading -BUOYANCY FORCE
#IT is a distributed force along the non-flooded members
#Still TO DO
#________________________________TOWER__________________________________#
#Now get the values of the loads at the nodes of Tower
junk = (np.roll(twrZs, -1) - np.roll(twrZs, 1))[1:-1] / 2.
deltaz = np.hstack(
((twrZs[1] - twrZs[0]) / 2., junk,
(twrZs[-1] - twrZs[-2]) / 2.)) #these are the appropriate deltazs
#just wind loading for tower but wtrload perhaps in the future for tripods
junk = (
np.sqrt(self.towerWindLoads.Px**2 + self.towerWindLoads.Py**2) *
deltaz).reshape([-1, 1]) #[N] forces
#decompose along local x,y and add z component
junk = np.hstack((junk, np.zeros([junk.size, 2]))).T
self.Loadouts.twr_dragf = np.dot(
DIRCOSwind, junk) #*np.sin(wind_dict['psi']), junk*0.])
#Tower Loads for Frame3DD
n_twrlds = (twrndIDs.shape[0] - TwrRigidTop) * (
self.Loadouts.twr_dragf.any()
) #distributed loads along tower+RNA node load
twr_ndsfrc = np.zeros([n_twrlds, 7])
twr_ndsfrc[0:n_twrlds, :-3] = np.hstack(
(twrndIDs[0:len(twrndIDs) - TwrRigidTop].reshape([-1, 1]),
self.Loadouts.twr_dragf.T))
#____________ADD CONCENTRATED RNA FORCES________________________________#
#First account for moment transfer in global coordinate system as if yaw=0
RNAload = np.copy(self.RNA_F.reshape(
[2, 3]).T) #RNAload: 1columns forces, 2nd column moments
#Store yaw-rotated forces and moments at the hub still [3,2]
self.Loadouts.RNAload = np.dot(DIRCOSwind, RNAload)
Deltax = self.RNAinputs.Thoff[0] - self.RNAinputs.CMoff[0]
Deltay = self.RNAinputs.Thoff[1] - self.RNAinputs.CMoff[1]
Deltaz = self.RNAinputs.Thoff[2] - self.RNAinputs.CMoff[2]
if not (TwrRigidTop):
Deltax = self.RNAinputs.Thoff[0]
Deltay = self.RNAinputs.Thoff[1]
Deltaz = self.RNAinputs.Thoff[2]
#Rotor Loads - no weight yet
RNAload[0, 1] += -RNAload[1, 0] * Deltaz + RNAload[
2, 0] * Deltay #Mxx=-Fy*Deltaz +Fz*deltay
RNAload[1, 1] += RNAload[0, 0] * Deltaz - RNAload[
2, 0] * Deltax #Myy= Fx*deltaz-Fz*deltax
RNAload[2, 1] += -RNAload[0, 0] * Deltay + RNAload[
1, 0] * Deltax #Mzz=-Fx*Deltay +Fy*deltax
#Then rotate them in the global coordinate system for PYFRAME to account for yaw
RNAload = np.dot(
DIRCOSwind, RNAload
) #Gravity is already accounted for by Frame3DD for concentrated masses: Jacket.Twr.RNAmass*aux['g_z'],np.zeros(3))) self.RNA_F.reshape([2,3]).T
if not (TwrRigidTop):
twr_ndsfrc[-1, 1:] += RNAload.T.flatten()
else:
twr_ndsfrc = np.vstack(
(twr_ndsfrc, np.hstack((twrndIDs[-1], RNAload.T.flatten()))))
# If we apply this load at tower-top and not tower-top+CMzoff we need to account for different DeltaZ
## if not(TwrRigidTop):
## RNAload[0,1] -= RNAload[1,0]*ThOffset_z #*CMzoff #Mxx
## RNAload[1,1] += RNAload[0,0]*CMzoff #Myy
## twr_ndsfrc[-1,1:] += RNAload.T.flatten()
## else: #Put forces at the RNA.CM location
## RNAload[0,1] -= RNAload[1,0]*ThOffset_z #*CMzoff #Mxx
## RNAload[1,1] += RNAload[0,0]*CMzoff #Myy
##
## twr_ndsfrc[-1,:] += np.hstack((twrndIDs[-1],RNAload.T.flatten()))
#STACK ALLOF THEM TOGETHER
self.Loadouts.nds_frc = np.vstack(
(pilleg_ndsfrc, twr_ndsfrc)) #Concentrated loads
def linearize(self, params, unknowns, resids):
#wlevel = params['wlevel']
#if wlevel > 0.0: wlevel *= -1.0
rho = params['rho']
U = params['U']
#U0 = params['U0']
d = params['d']
#zrel= params['z']-wlevel
mu = params['mu']
beta = params['beta']
#beta0 = params['beta0']
# dynamic pressure
q = 0.5*rho*U**2
#q0= 0.5*rho*U0**2
# Reynolds number and drag
if params['cd_usr'] in [np.inf, -np.inf, None, np.nan]:
cd = params['cd_usr']*np.ones_like(d)
Re = 1.0
dcd_dRe = 0.0
else:
Re = rho*U*d/mu
cd, dcd_dRe = cylinderDrag(Re)
# derivatives
dq_dU = rho*U
const = (dq_dU*cd + q*dcd_dRe*rho*d/mu)*d
dPx_dU = const*cosd(beta)
dPy_dU = const*sind(beta)
const = (cd + dcd_dRe*Re)*q + rho*params['cm']*math.pi/4.0*2*d*params['A']
dPx_dd = const*cosd(beta)
dPy_dd = const*sind(beta)
const = rho*params['cm']*math.pi/4.0*d**2
dPx_dA = const*cosd(beta)
dPy_dA = const*sind(beta)
n = len(params['z'])
zeron = np.zeros((n, n))
J = {}
J['waveLoads.Px', 'U'] = np.diag(dPx_dU)
J['waveLoads.Px', 'A'] = np.diag(dPx_dA)
J['waveLoads.Px', 'z'] = zeron
J['waveLoads.Px', 'd'] = np.diag(dPx_dd)
J['waveLoads.Px', 'p'] = zeron
J['waveLoads.Py', 'U'] = np.diag(dPy_dU)
J['waveLoads.Py', 'A'] = np.diag(dPy_dA)
J['waveLoads.Py', 'z'] = zeron
J['waveLoads.Py', 'd'] = np.diag(dPy_dd)
J['waveLoads.Py', 'p'] = zeron
J['waveLoads.Pz', 'U'] = zeron
J['waveLoads.Pz', 'A'] = zeron
J['waveLoads.Pz', 'z'] = zeron
J['waveLoads.Pz', 'd'] = zeron
J['waveLoads.Pz', 'p'] = zeron
J['waveLoads.qdyn', 'U'] = np.diag(dq_dU)
J['waveLoads.qdyn', 'A'] = zeron
J['waveLoads.qdyn', 'z'] = zeron
J['waveLoads.qdyn', 'd'] = zeron
J['waveLoads.qdyn', 'p'] = zeron
J['waveLoads.pt', 'U'] = np.diag(dq_dU)
J['waveLoads.pt', 'A'] = zeron
J['waveLoads.pt', 'z'] = zeron
J['waveLoads.pt', 'd'] = zeron
J['waveLoads.pt', 'p'] = 1.0
J['waveLoads.z', 'U'] = zeron
J['waveLoads.z', 'A'] = zeron
J['waveLoads.z', 'z'] = np.eye(n)
J['waveLoads.z', 'd'] = zeron
J['waveLoads.z', 'p'] = zeron
return J
def solve_nonlinear(self, params, unknowns, resids):
#wlevel = params['wlevel']
#if wlevel > 0.0: wlevel *= -1.0
rho = params['rho']
U = params['U']
#U0 = params['U0']
d = params['d']
#zrel= params['z']-wlevel
mu = params['mu']
beta = params['beta']
#beta0 = params['beta0']
if not (params['rho'] == 0. or all(params['U'] == 0.) or params['mu'] == 0.):
# dynamic pressure
q = 0.5*rho*U**2
#q0= 0.5*rho*U0**2
# Reynolds number and drag
if params['cd_usr'] in [np.inf, -np.inf, None, np.nan]:
Re = rho*U*d/mu
cd, dcd_dRe = cylinderDrag(Re)
else:
cd = params['cd_usr']*np.ones_like(d)
Re = 1.0
dcd_dRe = 0.0
# inertial and drag forces
Fi = rho*params['cm']*math.pi/4.0*d**2*params['A'] # Morrison's equation
Fd = q*cd*d
Fp = Fi + Fd
# components of distributed loads
Px = Fp*cosd(beta)
Py = Fp*sind(beta)
Pz = 0.*Fp
#FORCES [N/m] AT z=0 m
#idx0 = np.abs(zrel).argmin() # closest index to z=0, used to find d at z=0
#d0 = d[idx0] # initialize
#cd0 = cd[idx0] # initialize
#if (zrel[idx0]<0.) and (idx0< (zrel.size-1)): # point below water
# d0 = np.mean(d[idx0:idx0+2])
# cd0 = np.mean(cd[idx0:idx0+2])
#elif (zrel[idx0]>0.) and (idx0>0): # point above water
# d0 = np.mean(d[idx0-1:idx0+1])
# cd0 = np.mean(cd[idx0-1:idx0+1])
#Fi0 = rho*params['cm']*math.pi/4.0*d0**2*params['A0'] # Morrison's equation
#Fd0 = q0*cd0*d0
#Fp0 = Fi0 + Fd0
#Px0 = Fp0*cosd(beta0)
#Py0 = Fp0*sind(beta0)
#Pz0 = 0.*Fp0
#Store qties at z=0 MSL
#unknowns['waveLoads_Px0'] = Px0
#unknowns['waveLoads_Py0'] = Py0
#unknowns['waveLoads_Pz0'] = Pz0
#unknowns['waveLoads_qdyn0'] = q0
#unknowns['waveLoads_beta0'] = beta0
# pack data
unknowns['waveLoads_Px'] = Px
unknowns['waveLoads_Py'] = Py
unknowns['waveLoads_Pz'] = Pz
unknowns['waveLoads_qdyn'] = q
unknowns['waveLoads_pt'] = q + params['p']
unknowns['waveLoads_beta'] = beta
unknowns['waveLoads_d'] = d
unknowns['waveLoads_z'] = params['z']