def simulate(self, Tend, nIntervals, gridWidth):
problem = Implicit_Problem(self.rhs, self.y0, self.yd0)
problem.name = 'IDA'
# solver.rhs = self.right_hand_side
problem.handle_result = self.handle_result
problem.state_events = self.state_events
problem.handle_event = self.handle_event
problem.time_events = self.time_events
problem.finalize = self.finalize
# Create IDA object and set additional parameters
simulation = IDA(problem)
simulation.atol = self.atol
simulation.rtol = self.rtol
simulation.verbosity = self.verbosity
if hasattr(simulation, 'continuous_output'):
simulation.continuous_output = False # default 0, if one step approach should be used
elif hasattr(simulation, 'report_continuously'):
simulation.report_continuously = False # default 0, if one step approach should be used
simulation.tout1 = self.tout1
simulation.lsoff = self.lsoff
# Calculate nOutputIntervals:
if gridWidth <> None:
nOutputIntervals = int((Tend - self.t0) / gridWidth)
else:
nOutputIntervals = nIntervals
# Check for feasible input parameters
if nOutputIntervals == 0:
print 'Error: gridWidth too high or nIntervals set to 0! Continue with nIntervals=1'
nOutputIntervals = 1
# Perform simulation
simulation.simulate(Tend, nOutputIntervals) # to get the values: t_new, y_new, yd_new = simulation.simulate
def simulate(self, Tend, nIntervals, gridWidth):
problem = Implicit_Problem(self.rhs, self.y0, self.yd0)
problem.name = 'IDA'
# solver.rhs = self.right_hand_side
problem.handle_result = self.handle_result
problem.state_events = self.state_events
problem.handle_event = self.handle_event
problem.time_events = self.time_events
problem.finalize = self.finalize
# Create IDA object and set additional parameters
simulation = IDA(problem)
simulation.atol = self.atol
simulation.rtol = self.rtol
simulation.verbosity = self.verbosity
if hasattr(simulation, 'continuous_output'):
simulation.continuous_output = False # default 0, if one step approach should be used
elif hasattr(simulation, 'report_continuously'):
simulation.report_continuously = False # default 0, if one step approach should be used
simulation.tout1 = self.tout1
simulation.lsoff = self.lsoff
# Calculate nOutputIntervals:
if gridWidth <> None:
nOutputIntervals = int((Tend - self.t0) / gridWidth)
else:
nOutputIntervals = nIntervals
# Check for feasible input parameters
if nOutputIntervals == 0:
print 'Error: gridWidth too high or nIntervals set to 0! Continue with nIntervals=1'
nOutputIntervals = 1
# Perform simulation
simulation.simulate(Tend, nOutputIntervals) # to get the values: t_new, y_new, yd_new = simulation.simulate
def solve(self):
# Setup IDA
assert self._initial_time is not None
problem = Implicit_Problem(self._residual_vector_eval,
self.solution.vector(),
self.solution_dot.vector(),
self._initial_time)
problem.jac = self._jacobian_matrix_eval
problem.handle_result = self._monitor
# Define an Assimulo IDA solver
solver = IDA(problem)
# Setup options
assert self._time_step_size is not None
solver.inith = self._time_step_size
if self._absolute_tolerance is not None:
solver.atol = self._absolute_tolerance
if self._max_time_steps is not None:
solver.maxsteps = self._max_time_steps
if self._relative_tolerance is not None:
solver.rtol = self._relative_tolerance
if self._report:
solver.verbosity = 10
solver.display_progress = True
solver.report_continuously = True
else:
solver.display_progress = False
solver.verbosity = 50
# Assert consistency of final time and time step size
assert self._final_time is not None
final_time_consistency = (
self._final_time - self._initial_time) / self._time_step_size
assert isclose(
round(final_time_consistency), final_time_consistency
), ("Final time should be occuring after an integer number of time steps"
)
# Prepare monitor computation if not provided by parameters
if self._monitor_initial_time is None:
self._monitor_initial_time = self._initial_time
assert isclose(
round(self._monitor_initial_time / self._time_step_size),
self._monitor_initial_time / self._time_step_size
), ("Monitor initial time should be a multiple of the time step size"
)
if self._monitor_time_step_size is None:
self._monitor_time_step_size = self._time_step_size
assert isclose(
round(self._monitor_time_step_size / self._time_step_size),
self._monitor_time_step_size / self._time_step_size
), ("Monitor time step size should be a multiple of the time step size"
)
monitor_t = arange(
self._monitor_initial_time,
self._final_time + self._monitor_time_step_size / 2.,
self._monitor_time_step_size)
# Solve
solver.simulate(self._final_time, ncp_list=monitor_t)
def solve_squeezer(self):
model = Implicit_Problem(self.squeezer_func, self.y, self.yp, self.t)
sim = IDA(model)
tfinal = 10.0
ncp = 1000
sim.atol = 1.0e-6
sim.suppress_alg = True
for i in range(sim.algvar.size):
if i > 14:
sim.algvar[i] = 0
print(sim.algvar)
t, y, yd = sim.simulate(tfinal, ncp)
sim.plot()
def run_example(with_plots=True):
"""
The same as example :doc:`EXAMPLE_cvode_basic` but now integrated backwards in time.
on return:
- :dfn:`exp_mod` problem instance
- :dfn:`exp_sim` solver instance
"""
# Define the rhs
def f(t, y, yd):
res = yd[0] + y[0] * param
return N.array([res])
param = 2
# Define an Assimulo problem
imp_mod = Implicit_Problem(
f,
t0=5,
y0=0.02695,
yd0=-0.02695,
name='IDA Example: $\dot y + y = 0$ (reverse time)')
# Define an explicit solver
imp_sim = IDA(imp_mod) # Create a IDA solver
# Sets the parameters
imp_sim.atol = [1e-8] # Default 1e-6
imp_sim.rtol = 1e-8 # Default 1e-6
imp_sim.backward = True
# Simulate
t, y, yd = imp_sim.simulate(0) # Simulate 5 seconds (t0=5 -> tf=0)
# Basic test
#nose.tools.assert_almost_equal(float(y[-1]), 4.00000000, 3)
# Plot
if with_plots:
P.plot(t, y, color="b")
P.xlabel('Time')
P.ylabel('State')
P.title(imp_mod.name)
P.show()
return imp_mod, imp_sim
def initialize_ode_solver(self, y_0, yd_0, t_0):
model = Implicit_Problem(self.residual, y_0, yd_0, t_0)
model.handle_result = self.handle_result
solver = IDA(model)
solver.rtol = self.solver_rtol
solver.atol = self.solver_atol # * np.array([100, 10, 1e-4, 1e-4])
solver.inith = 0.1 # self.wind.R_g / const.C
solver.maxh = self.dt * self.wind.R_g / const.C
solver.report_continuously = True
solver.display_progress = False
solver.verbosity = 50 # 50 = quiet
solver.num_threads = 3
# solver.display_progress = True
return solver
def run_example(index="ind1", with_plots=True, with_test=False):
my_pend_sys = pendulum()
my_pend = my_pend_sys.generate_problem(index)
my_pend.name = 'Index = {}'.format(index)
dae_pend = IDA(my_pend) if index not in ('ovstab2',
'ovstab1') else ODASSL(my_pend)
dae_pend.atol = 1.e-6
dae_pend.rtol = 1.e-6
dae_pend.suppress_alg = True
t, y, yd = dae_pend.simulate(10., 100)
final_residual = my_pend.res(0., dae_pend.y, dae_pend.yd)
print(my_pend.name + " Residuals after the integration run\n")
print(final_residual, 'Norm: ', sl.norm(final_residual))
if with_test:
assert (sl.norm(final_residual) < 1.5e-1)
if with_plots:
dae_pend.plot(mask=[1, 1] + (len(my_pend.y0) - 2) * [0])
return my_pend, dae_pend
def buildsim(self, ):
"""
Setup the assimulo IDA simulator.
"""
# Create an Assimulo implicit solver (IDA)
imp_sim = IDA(self.imp_mod) # Create a IDA solver
# Sets the paramters
# 1e-4 #Default 1e-6
imp_sim.atol = self.p.RunInput['TIMESTEPPING']['SOLVER_TOL']
# 1e-4 #Default 1e-6
imp_sim.rtol = self.p.RunInput['TIMESTEPPING']['SOLVER_TOL']
# Suppres the algebraic variables on the error test
imp_sim.suppress_alg = True
imp_sim.display_progress = False
imp_sim.verbosity = 50
imp_sim.report_continuously = True
imp_sim.time_limit = 10.
self.imp_sim = imp_sim
def main():
y0 = [1.0, 0.0, 0.0, 0.0, 5]
yd0 = [0.0, 0.0, 0.0, -9.82, 0.0]
# tout = [1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 5.0]
tout = np.linspace(0.0, 10.0, 500)
implicit_model = Implicit_Problem(res, y0, yd0, name="Example problem")
# implicit_model.jac = jac
implicit_model.algvar = [1.0, 1.0, 1.0, 1.0, 0.0]
implicit_solver = IDA(implicit_model)
implicit_solver.atol = 1E-6
implicit_solver.rtol = 1E-6
implicit_solver.suppress_alg = True
implicit_solver.make_consistent("IDA_YA_YDP_INIT")
t, y, yd = implicit_solver.simulate(10.0, ncp=500)
plt.plot(t, y, linestyle="dashed", marker="o")
plt.xlabel("Time")
plt.ylabel("State")
plt.title(implicit_model.name)
plt.show()
# -*- coding: utf-8 -*-
from __future__ import division
from scipy import *
from matplotlib.pyplot import *
import numpy as np
from assimulo.problem import Implicit_Problem
from assimulo.solvers import IDA
import squeezer
y0,yp0=squeezer.init_squeezer() # Initial values
t0 = 0 # Initial time
squeezemodel = Implicit_Problem(squeezer.squeezer, y0, yp0, t0)
algvar = 7*[1.]+13*[0.]
sim = IDA(squeezemodel) # Create solver instance
sim.algvar = algvar
sim.suppress_alg=True
sim.atol = 1e-7
tf = .03 # End time for simulation
t, y, yd = sim.simulate(tf)
sim.plot(mask=7*[1]+13*[0])
grid(1)
axis([0, .03, -1.5, 1.5])
xlabel('Time, t [s]')
ylabel('Angle, [rad]')
def run_example(with_plots=True):
r"""
Example for demonstrating the use of a user supplied Jacobian
ODE:
.. math::
\dot y_1-y_3 &= 0 \\
\dot y_2-y_4 &= 0 \\
\dot y_3+y_5 y_1 &= 0 \\
\dot y_4+y_5 y_2+9.82&= 0 \\
y_3^2+y_4^2-y_5(y_1^2+y_2^2)-9.82 y_2&= 0
on return:
- :dfn:`imp_mod` problem instance
- :dfn:`imp_sim` solver instance
"""
#Defines the residual
def f(t, y, yd):
res_0 = yd[0] - y[2]
res_1 = yd[1] - y[3]
res_2 = yd[2] + y[4] * y[0]
res_3 = yd[3] + y[4] * y[1] + 9.82
res_4 = y[2]**2 + y[3]**2 - y[4] * (y[0]**2 + y[1]**2) - y[1] * 9.82
return N.array([res_0, res_1, res_2, res_3, res_4])
#Defines the Jacobian
def jac(c, t, y, yd):
jacobian = N.zeros([len(y), len(y)])
#Derivative
jacobian[0, 0] = 1 * c
jacobian[1, 1] = 1 * c
jacobian[2, 2] = 1 * c
jacobian[3, 3] = 1 * c
#Differentiated
jacobian[0, 2] = -1
jacobian[1, 3] = -1
jacobian[2, 0] = y[4]
jacobian[3, 1] = y[4]
jacobian[4, 0] = y[0] * 2 * y[4] * -1
jacobian[4, 1] = y[1] * 2 * y[4] * -1 - 9.82
jacobian[4, 2] = y[2] * 2
jacobian[4, 3] = y[3] * 2
#Algebraic
jacobian[2, 4] = y[0]
jacobian[3, 4] = y[1]
jacobian[4, 4] = -(y[0]**2 + y[1]**2)
return jacobian
#The initial conditons
y0 = [1.0, 0.0, 0.0, 0.0, 5] #Initial conditions
yd0 = [0.0, 0.0, 0.0, -9.82, 0.0] #Initial conditions
#Create an Assimulo implicit problem
imp_mod = Implicit_Problem(f,
y0,
yd0,
name='Example using an analytic Jacobian')
#Sets the options to the problem
imp_mod.jac = jac #Sets the jacobian
imp_mod.algvar = [1.0, 1.0, 1.0, 1.0, 0.0] #Set the algebraic components
#Create an Assimulo implicit solver (IDA)
imp_sim = IDA(imp_mod) #Create a IDA solver
#Sets the paramters
imp_sim.atol = 1e-6 #Default 1e-6
imp_sim.rtol = 1e-6 #Default 1e-6
imp_sim.suppress_alg = True #Suppres the algebraic variables on the error test
#Let Sundials find consistent initial conditions by use of 'IDA_YA_YDP_INIT'
imp_sim.make_consistent('IDA_YA_YDP_INIT')
#Simulate
t, y, yd = imp_sim.simulate(
5, 1000) #Simulate 5 seconds with 1000 communication points
#Basic tests
nose.tools.assert_almost_equal(y[-1][0], 0.9401995, places=4)
nose.tools.assert_almost_equal(y[-1][1], -0.34095124, places=4)
nose.tools.assert_almost_equal(yd[-1][0], -0.88198927, places=4)
nose.tools.assert_almost_equal(yd[-1][1], -2.43227069, places=4)
#Plot
if with_plots:
import pylab as P
P.plot(t, y, linestyle="dashed", marker="o") #Plot the solution
P.xlabel('Time')
P.ylabel('State')
P.title(imp_mod.name)
P.show()
return imp_mod, imp_sim
def run_example(with_plots=True):
r"""
This is the same example from the Sundials package (cvsRoberts_FSA_dns.c)
Its purpose is to demonstrate the use of parameters in the differential equation.
This simple example problem for IDA, due to Robertson
see http://www.dm.uniba.it/~testset/problems/rober.php,
is from chemical kinetics, and consists of the system:
.. math::
\dot y_1 -( -p_1 y_1 + p_2 y_2 y_3)&=0 \\
\dot y_2 -(p_1 y_1 - p_2 y_2 y_3 - p_3 y_2^2)&=0 \\
\dot y_3 -( p_3 y_ 2^2)&=0
on return:
- :dfn:`imp_mod` problem instance
- :dfn:`imp_sim` solver instance
"""
def f(t, y, yd, p):
res1 = -p[0] * y[0] + p[1] * y[1] * y[2] - yd[0]
res2 = p[0] * y[0] - p[1] * y[1] * y[2] - p[2] * y[1] ** 2 - yd[1]
res3 = y[0] + y[1] + y[2] - 1
return N.array([res1, res2, res3])
# The initial conditons
y0 = N.array([1.0, 0.0, 0.0]) # Initial conditions for y
yd0 = N.array([0.1, 0.0, 0.0]) # Initial conditions for dy/dt
p0 = [0.040, 1.0e4, 3.0e7] # Initial conditions for parameters
# Create an Assimulo implicit problem
imp_mod = Implicit_Problem(f, y0, yd0, p0=p0)
# Create an Assimulo implicit solver (IDA)
imp_sim = IDA(imp_mod) # Create a IDA solver
# Sets the paramters
imp_sim.atol = N.array([1.0e-8, 1.0e-14, 1.0e-6])
imp_sim.algvar = [1.0, 1.0, 0.0]
imp_sim.suppress_alg = False # Suppres the algebraic variables on the error test
imp_sim.report_continuously = True # Store data continuous during the simulation
imp_sim.pbar = p0
imp_sim.suppress_sens = False # Dont suppress the sensitivity variables in the error test.
# Let Sundials find consistent initial conditions by use of 'IDA_YA_YDP_INIT'
imp_sim.make_consistent('IDA_YA_YDP_INIT')
# Simulate
t, y, yd = imp_sim.simulate(4, 400) # Simulate 4 seconds with 400 communication points
print(imp_sim.p_sol[0][-1], imp_sim.p_sol[1][-1], imp_sim.p_sol[0][-1])
# Basic test
nose.tools.assert_almost_equal(y[-1][0], 9.05518032e-01, 4)
nose.tools.assert_almost_equal(y[-1][1], 2.24046805e-05, 4)
nose.tools.assert_almost_equal(y[-1][2], 9.44595637e-02, 4)
nose.tools.assert_almost_equal(imp_sim.p_sol[0][-1][0], -1.8761, 2) # Values taken from the example in Sundials
nose.tools.assert_almost_equal(imp_sim.p_sol[1][-1][0], 2.9614e-06, 8)
nose.tools.assert_almost_equal(imp_sim.p_sol[2][-1][0], -4.9334e-10, 12)
# Plot
if with_plots:
P.plot(t, y)
P.title(imp_mod.name)
P.xlabel('Time')
P.ylabel('State')
P.show()
return imp_mod, imp_sim
#ax[2].plot( imp_mod.x_m_a, z_out[imp_mod.N:imp_mod.N+imp_mod.Na,:-1] )
#ax[2].plot( imp_mod.x_m_c, z_out[-imp_mod.Nc:,:-1] )
#plt.show()
#print z_out
#Sets the options to the problem
#imp_mod.jac = jac #Sets the jacobian
imp_mod.algvar = [1.0 for i in range(N)] + [0.0 for i in range(N+Na+Nc)] #Set the algebraic components
#imp_mod.algvar = [1.0 for i in range(N)] + [0.0 for i in range(N)] #Set the algebraic components
#Create an Assimulo implicit solver (IDA)
imp_sim = IDA(imp_mod) #Create a IDA solver
#Sets the paramters
imp_sim.atol = 1e-5 #Default 1e-6
imp_sim.rtol = 1e-5 #Default 1e-6
imp_sim.suppress_alg = True #Suppres the algebraic variables on the error test
### Simulate
imp_mod.set_j_vec( I_app )
#res_test = imp_mod.res( 0.0, y0, yd0 )
#jac_test = imp_mod.jac( 2, 0.0, y0, yd0 )
#Let Sundials find consistent initial conditions by use of 'IDA_YA_YDP_INIT'
imp_sim.make_consistent('IDA_YA_YDP_INIT')
# Sim step 1
t1, y1, yd1 = imp_sim.simulate(100,100)
#t1, y1, yd1 = imp_sim.simulate(1000,1000)
def main():
import numpy as np
import time
from matplotlib import pyplot as plt
from li_ion_battery_p2d_functions import Extended_Problem
from assimulo.solvers import IDA
from li_ion_battery_p2d_inputs import Inputs as inp
from li_ion_battery_p2d_init import anode, cathode, separator, SV_0, algvar
from li_ion_battery_p2d_post_process import Label_Columns, tag_strings, plot_sims
# Close any open pyplot objects:
plt.close()
# Start a timer:
t_count = time.time()
# Calculate the time span, which should be enough to charge or discharge fully
# (i.e. 3600 seconds divided by the C-rate):
t_0 = 0
t_f = 3600 / inp.C_rate
# SV_0 = anode.SV_0
# SV_0 = np.concatenate((anode.SV_0, separator.SV_0, cathode.SV_0))
#SV_0 = np.concatenate((anode.SV_0, separator.SV_0))
SV_dot_0 = np.zeros_like(SV_0)
"""----------Equilibration----------"""
# Equilibrate by integrating at zero current:
print('\nEquilibrating...')
# Create problem instance
#Battery_equil = Extended_Problem(Battery_Func, SV_0, SV_dot_0, t_0)
anode.i_ext = 0
cathode.i_ext = 0
Battery_equil = Extended_Problem.Battery_Func(t_0, SV_0, SV_dot_0, True)
Battery_equil.external_event_detection = True
# algvar = anode.algvar
# algvar = np.concatenate((anode.algvar, separator.algvar, cathode.algvar))
#algvar = np.concatenate((anode.algvar, separator.algvar))
# Battery_equil.algvar = algvar
# Simulation parameters
equil_sim = IDA(Battery_equil) # Create simulation instance
equil_sim.atol = atol1 # Solver absolute tolerance
equil_sim.rtol = rtol1 # Solver relative tolerance
equil_sim.verbosity = 50
equil_sim.make_consistent('IDA_YA_YDP_INIT')
t_eq, SV_eq, SV_dot_eq = equil_sim.simulate(t_f)
# Put solution into pandas dataframe with labeled columns
SV_eq_df = Label_Columns(t_eq, SV_eq)
# Obtain tag strings for dataframe columns
tags = tag_strings(SV_eq_df)
print('Done equilibrating\n')
"""---------------------------------"""
"""------------Charging-------------"""
print('\nCharging...')
# New initial conditions are the final equilibrium conditions
t_0 = t_eq[-1]
t_f1 = t_0 + t_f
SV_0 = SV_eq[-1, :]
SV_dot_0 = SV_dot_eq[-1:]
# Charge the battery
anode.params['i_ext'] = anode.i_ext
cathode.params['i_ext'] = -cathode.i_ext
# Create problem instance
Battery_charge = Extended_Problem(Charge, SV_0, SV_dot_0, t_0)
Battery_charge.external_event_detection = True
Battery_charge.algvar = algvar
# Simulation parameters
charge_sim = IDA(Battery_charge)
charge_sim.atol = atol2
charge_sim.rtol = rtol2
charge_sim.verbosity = 50
charge_sim.make_consistent('IDA_YA_YDP_INIT')
# charge_sim.maxh = 0.5
t_charge, SV_charge, SV_dot_charge = charge_sim.simulate(t_f1)
t_flag1 = anode.t_flag
SV_charge_df = Label_Columns(t_charge, SV_charge)
print('Done charging\n')
"""---------------------------------"""
"""------------Re_equilibrating-------------"""
# New initial conditions are the final charge conditions
t_0 = t_charge[-1] #anode.t_flag
t_f2 = t_0 + t_f
SV_0 = SV_charge[-1, :]
SV_dot_0 = SV_dot_charge[-1, :]
# Equilibrate again. Note - this is a specific choice to reflect
# equilibration after the charging steps. We may want, at times, to
# simulate a situation where the battery is not equilibrated between
# charge and discharge, or is equilibrated for a shorter amount of time.
print('\nRe-equilibrating...')
Battery_re_equil = Extended_Problem(Re_equilibrate, SV_0, SV_dot_0, t_0)
Battery_re_equil.external_event_detection = True
Battery_re_equil.algvar = algvar
# Simulation parameters
re_equil_sim = IDA(Battery_re_equil)
re_equil_sim.atol = atol3
re_equil_sim.rtol = rtol3
re_equil_sim.verbosity = 50
re_equil_sim.make_consistent('IDA_YA_YDP_INIT')
t_req, SV_req, SV_dot_req = re_equil_sim.simulate(t_f2)
SV_req_df = Label_Columns(t_req, SV_req)
print('Done re-equilibrating\n')
"""---------------------------------"""
"""------------Discharging-------------"""
print('\nDischarging...')
t_0 = t_req[-1]
t_f3 = t_f2 + t_f
SV_0 = SV_req[-1, :]
SV_dot_0 = SV_dot_req[-1, :]
anode.params['i_ext'] = -anode.i_ext
cathode.params['i_ext'] = cathode.i_ext
Battery_discharge = Extended_Problem(Discharge, SV_0, SV_dot_0, t_0)
Battery_discharge.external_event_detection = True
Battery_discharge.algvar = algvar
# Simulation parameters
Battery_discharge = IDA(Battery_discharge)
Battery_discharge.atol = atol4
Battery_discharge.rtol = rtol4
Battery_discharge.verbosity = 50
Battery_discharge.make_consistent('IDA_YA_YDP_INIT')
t_discharge, SV_discharge, SV_dot_discharge = Battery_discharge.simulate(
t_f3)
t_flag2 = anode.t_flag
SV_discharge_df = Label_Columns(t_discharge, SV_discharge)
print('Done discharging\n')
"""---------------------------------"""
SV_dict = {}
SV_dict['SV_eq'] = SV_eq_df
SV_dict['SV_charge'] = SV_charge_df
SV_dict['SV_req'] = SV_req_df
SV_dict['SV_discharge'] = SV_discharge_df
# SV_charge_df = SV_charge_df.loc[SV_charge_df['Time'] <= t_flag1]
# SV_discharge_df = SV_discharge_df.loc[SV_discharge_df['Time'] <= t_flag2]
# dt_cap = t_flag1 - t_eq[-1]
# t_80 = 0.8*dt_cap + t_eq[-1]
# elyte80_charge = SV_charge_df.loc[SV_charge_df['Time'] <= t_80]
# elyte75_charge = SV_charge_df.loc[SV_charge_df['X_an15'] <= 0.20]
# el80 = elyte80_charge[X_elyte].iloc[0]
# el80 = list(el80)
# el80.append(inp.C_rate)
# import openpyxl
# book = openpyxl.load_workbook('Elyte_depth_profiles.xlsx')
# sheet = book.active
# sheet.append(el80)
# book.save('Elyte_depth_profiles.xlsx')
# print('Elyte Li+ at 80% SOC = ', elyte75_charge, '\n')
plot_sims(tags['V_an'], tags['X_an'], tags['X_el_an'], SV_dict, t_f1, t_f3,
t_flag1, t_flag2)
# plot_sims(tags['V_cat'], tags['X_cat'], tags['X_el_cat'], SV_dict, t_f1, t_f3, t_flag1, t_flag2)
# fig, axes = plt.subplots(sharey = "row", figsize = (18, 8), nrows=1, ncols=4)
# plt.subplots_adjust(wspace=0, hspace=0.5)
#
# V_cell_plot = V_cell_eq.plot(ax = axes[0])
# V_cell_plot.set_title('Equilibration')
# V_cell_plot.set_ylabel('Cell Voltage')
# V_cell_plot.legend().set_visible(False)
#
# V_cell_plot = V_cell_charge.plot(ax = axes[1])
# V_cell_plot.set_title('Charging')
# V_cell_plot.set_ylabel('Cell Voltage')
# V_cell_plot.legend().set_visible(False)
#
# V_cell_plot = V_cell_req.plot(ax = axes[2])
# V_cell_plot.set_title('Re-Equilibration')
# V_cell_plot.set_ylabel('Cell Voltage')
# V_cell_plot.legend().set_visible(False)
#
# V_cell_plot = V_cell_discharge.plot(ax = axes[3])
# V_cell_plot.set_title('Discharge')
# V_cell_plot.set_ylabel('Cell Voltage')
# V_cell_plot.legend().set_visible(False)
"""---------------------------------"""
# Post processing
V_charge = np.array(SV_charge_df['V_dl1'])
V_discharge = np.array(SV_discharge_df['V_dl1'])
t_charge = np.array(SV_charge_df['Time'])
t_discharge = np.array(SV_discharge_df['Time'])
dt_charge = t_charge - t_charge[0]
dt_discharge = t_discharge - t_discharge[0]
# Plot charge-discharge curve
Capacity_charge = -dt_charge * anode.i_ext / 3600 # A-h/m^2
Capacity_discharge = -dt_discharge * anode.i_ext / 3600 # A-h/m^2
fig1, ax1 = plt.subplots()
ax1.plot(Capacity_charge, V_charge)
ax1.plot(Capacity_discharge, V_discharge)
# ax1.set_ylim((0, 1.2))
# ax1.set_xlim((-0.1, 18.5))
ax1.set_xlabel("Capacity [Ah/m^2]")
ax1.set_ylabel("Voltage [V]")
ax1.legend(("Charge capacity", "Discharge capacity"))
# Calculate battery energy storage/recovery and calculate round-trip
# efficiency. Anode voltage is referenced to its initial equilibrium
# value (i.e. in the discharged state).
# NOTE: This is in W-h/m^2, per unit area of battery. For the specific
# capacity, you want W-h/g of anode material.
# E_stored = 0
# E_recovered = 0
# for k in np.arange(1, len(t_charge)):
# E_stored = (E_stored - (anode.V_cathode - 0.5*(V_charge[k] + V_charge[k-1]))
# *ep.i_ext*(dt_charge[k] - dt_charge[k-1]))
#
# for k in np.arange(1, len(t_discharge)):
# E_recovered = (E_recovered - (ep.V_cathode -
# 0.5*(V_discharge[k] + V_discharge[k-1]))
# *ep.i_ext*(dt_discharge[k] - dt_discharge[k-1]))
#
# Cap_recovered = Capacity_discharge[-1]
# Eta_RT = E_recovered/E_stored
# print('Cap_recovered = ', Cap_recovered, '\n')
# print(E_stored, '\n')
# print(E_recovered, '\n')
# print('Eta_RT = ', Eta_RT, '\n')
elapsed = time.time() - t_count
print('t_cpu=', elapsed, '\n')
plt.show()
return t_req, SV_req, SV_dot_req
def DAE_integration_assimulo(self, **kwargs):
"""
Perform time integration for DAEs with the assimulo package
"""
assert self.set_time_setting == 1, 'Time discretization must be specified first'
if self.tclose > 0:
close = True
else:
close = False
# Control vector
self.U = interpolate(self.boundary_cntrl_space, self.Vb).vector()[self.bndr_i_b]
if self.discontinous_boundary_values == 1:
self.U[self.Corner_indices] = self.U[self.Corner_indices]/2
# Definition of the sparse solver for the DAE res function to
# be defined next M should be invertible !!
my_solver = factorized(csc_matrix(self.M))
rhs = self.my_mult(self.J, self.my_mult(self.Q,self.A0)) + self.my_mult(self.Bext,self.U* self.boundary_cntrl_time(0.,self.tclose))
self.AD0 = my_solver(rhs)
# Definition of the rhs function required in assimulo
def res(t,y,yd):
"""
Definition of the residual function required in the DAE part of assimulo
"""
if close:
if t < self.tclose:
z = self.my_mult(self.M,yd) - self.my_mult(self.J, self.my_mult(self.Q,y)) - self.my_mult(self.Bext,self.U* self.boundary_cntrl_time(t,self.tclose))
else:
z = self.my_mult(self.M,yd) - self.my_mult((self.J - self.R), self.my_mult(self.Q,y))
else:
z = self.my_mult(self.M,yd) - self.my_mult(self.J, self.my_mult(self.Q,y)) - self.my_mult(self.Bext,self.U* self.boundary_cntrl_time(t,self.tclose))
return z
# Definition of the jacobian function required in assimulo
def jac(c,t,y,yd):
"""
Definition of the Jacobian matrix required in the DAE part of assimulo
"""
Matrix = csr_matrix(self.my_mult(self.J,self.Q))
if close and t > self.tclose:
Matrix = csr_matrix(self.my_mult(self.J - self.R, self.Q))
return c*csr_matrix(self.M) - Matrix
# Definition of the jacobian matrix vector function required in assimulo
def jacv(t,y,yd,res,v,c):
"""
Jacobian matrix-vector product required in the DAE part of assimulo
"""
w = self.my_mult(self.Q, v)
z = self.my_mult(self.J, w)
if close and t > self.tclose:
z -= self.my_mult(self.R, w)
return c*self.my_mult(self.M,v) - z
print('DAE Integration using assimulo built-in functions:')
model = Implicit_Problem(res,self.A0,self.AD0,self.tinit)
model.jacv = jacv
#sim = Radau5DAE(model,**kwargs)
#
# IDA method from Assimulo
#
sim = IDA(model,**kwargs)
sim.algvar = [1 for i in range(self.M.shape[0])]
sim.atol = 1.e-6
sim.rtol = 1.e-6
sim.report_continuously = True
ncp = self.Nt
sim.usejac = True
sim.suppress_alg = True
sim.inith = self.dt
sim.maxord = 5
#sim.linear_solver = 'SPGMR'
time_span, DAE_y, DAE_yd = sim.simulate(self.tfinal,ncp)
#print(sim.get_options())
print(sim.print_statistics())
A_dae = DAE_y.transpose()
# Hamiltonian
self.Nt = A_dae.shape[1]
self.tspan = np.array(time_span)
Ham_dae = np.zeros(self.Nt)
for k in range(self.Nt):
#Ham_dae[k] = 1/2 * A_dae[:,k] @ self.M @ self.Q @ A_dae[:,k]
Ham_dae[k] = 1/2 * self.my_mult(A_dae[:,k].T, \
self.my_mult(self.M, self.my_mult(self.Q, A_dae[:,k])))
# Get q variables
Aq_dae = A_dae[:self.Nq,:]
# Get p variables
Ap_dae = A_dae[self.Nq:,:]
# Get Deformation
Rho = np.zeros(self.Np)
for i in range(self.Np):
Rho[i] = self.rho(self.coord_p[i])
W_dae = np.zeros((self.Np,self.Nt))
theta = .5
for k in range(self.Nt-1):
W_dae[:,k+1] = W_dae[:,k] + self.dt * 1/Rho[:] * ( theta * Ap_dae[:,k+1] + (1-theta) * Ap_dae[:,k] )
self.Ham_dae = Ham_dae
return Aq_dae, Ap_dae, Ham_dae, W_dae, np.array(time_span)
def main():
res_class = eval(inputs.test_type)
# plt.close('all')
t_count = time.time()
SV_0 = sol_init.SV_0
SV_dot_0 = np.zeros_like(SV_0)
t_0 = 0.
t_f = 3600. / inputs.C_rate #63006.69900049 93633
algvar = sol_init.algvar
atol = np.ones_like(SV_0) * 1e-6
atol[cat.ptr_vec['eps_S8']] = 1e-15
atol[cat.ptr_vec['eps_Li2S']] = 1e-15
atol[cat.ptr_vec['rho_k_el']] = 1e-16 # 1e-16 for Bessler
rtol = 1e-6
sim_output = 50
rtol_ch = 1e-6
atol_ch = np.ones_like(SV_0) * 1e-6
atol_ch[cat.ptr_vec['eps_S8']] = 1e-15
atol_ch[cat.ptr_vec['eps_Li2S']] = 1e-15
atol_ch[cat.ptr_vec['rho_k_el']] = 1e-30
rate_tag = str(inputs.C_rate) + "C"
# if 'cascade' in inputs.ctifile:
# ncols = 2 + inputs.flag_req
# else:
ncols = 1 + inputs.flag_req
fig, axes = plt.subplots(sharey="row",
figsize=(9, 12),
nrows=3,
ncols=(ncols) * inputs.n_cycles,
num=1)
plt.subplots_adjust(wspace=0.15, hspace=0.4)
fig.text(0.35,
0.85,
rate_tag,
fontsize=20,
bbox=dict(facecolor='white', alpha=0.5))
# Set up user function to build figures based on inputs
"----------Equilibration----------"
print('\nEquilibrating...')
# Set external current to 0 for equilibration
cat.set_i_ext(0)
# cat.nucleation_flag = 1
# Create problem object
bat_eq = res_class(res_class.res_fun, SV_0, SV_dot_0, t_0)
bat_eq.external_event_detection = True
bat_eq.algvar = algvar
# Create simulation object
sim_eq = IDA(bat_eq)
sim_eq.atol = atol
sim_eq.rtol = rtol
sim_eq.verbosity = sim_output
sim_eq.make_consistent('IDA_YA_YDP_INIT')
t_eq, SV_eq, SV_dot_eq = sim_eq.simulate(t_f)
# Put solution into pandas dataframe with labeled columns
SV_eq_df = label_columns(t_eq, SV_eq, an.npoints, sep.npoints, cat.npoints)
# Obtain tag strings for dataframe columns
tags = tag_strings(SV_eq_df)
# plot_sim(tags, SV_eq_df, 'Equilibrating', 0, fig, axes)
t_equilibrate = time.time() - t_count
print("Equilibration time = ", t_equilibrate, '\n')
print('Done equilibrating\n')
for cycle_num in np.arange(0, inputs.n_cycles):
"------------Discharging-------------"
print('Discharging...')
# cat.np_L = inputs.np_Li2S_init
cat.nucleation_flag = np.zeros((inputs.npoints_cathode, 1))
# New initial conditions from previous simulation
if cycle_num == 0:
# SV_0 = SV_0
SV_0 = SV_eq[-1, :]
# SV_dot_0 = SV_dot_0
SV_dot_0 = SV_dot_eq[-1, :]
else:
SV_0 = SV_0_cycle
SV_dot_0 = SV_dot_0_cycle
# Set external current
cat.set_i_ext(cat.i_ext_amp)
# Update problem instance initial conditions
bat_dch = res_class(res_class.res_fun, SV_0, SV_dot_0, t_0)
bat_dch.external_event_detection = True
bat_dch.algvar = algvar
# Re-initialize simulation object
sim_dch = IDA(bat_dch)
sim_dch.atol = atol
sim_dch.rtol = rtol
# sim_dch.maxh = 57
sim_dch.verbosity = sim_output
sim_dch.make_consistent('IDA_YA_YDP_INIT')
t_dch, SV_dch, SV_dot_dch = sim_dch.simulate(131865.32)
SV_dch_df = label_columns(t_dch, SV_dch, an.npoints, sep.npoints,
cat.npoints)
# Obtain tag strings for dataframe columns
tags = tag_strings(SV_dch_df)
plot_sim(tags, SV_dch_df, 'Discharging', 0 + 2 * cycle_num, fig, axes)
# plot_meanPS(SV_dch_df, tags, 'Discharging')
print('Done Discharging\n')
"--------Re-equilibration---------"
if inputs.flag_req == 1:
print('Re-equilibrating...')
# New initial conditions from previous simulation
SV_0 = SV_dch[-1, :]
SV_dot_0 = SV_dot_dch[-1, :]
# Set external current
cat.set_i_ext(0)
# Update problem instance initial conditions
bat_req = res_class(res_class.res_fun, SV_0, SV_dot_0, t_0)
bat_req.external_event_detection = True
bat_req.algvar = algvar
# Re-initialize simulation object
sim_req = IDA(bat_req)
sim_req.atol = atol
sim_req.rtol = rtol
sim_req.verbosity = sim_output
sim_req.make_consistent('IDA_YA_YDP_INIT')
t_req, SV_req, SV_dot_req = sim_req.simulate(t_f)
SV_req_df = label_columns(t_req, SV_req, an.npoints, sep.npoints,
cat.npoints)
# plot_sim(tags, SV_req_df, 'Re-Equilibrating', 1, fig, axes)
print('Done re-equilibrating\n')
else:
SV_req = SV_dch
SV_dot_req = SV_dot_dch
"-----------Charging-----------"
if 'dog' in inputs.ctifile:
print('Charging...')
SV_0 = SV_req[-1, :]
SV_dot_0 = SV_dot_req[-1, :]
SV_0[cat.ptr_vec['eps_S8']] = cat.eps_cutoff
cat.set_i_ext(-cat.i_ext_amp)
# Update problem instance initial conditions
bat_ch = res_class(res_class.res_fun, SV_0, SV_dot_0, t_0)
bat_ch.external_event_detection = True
bat_ch.algvar = algvar
# Re-initialize simulation object
sim_ch = IDA(bat_ch)
sim_ch.atol = atol_ch
sim_ch.rtol = rtol_ch
if cycle_num > 0:
sim_ch.maxh = 0.1
sim_ch.verbosity = sim_output
sim_ch.make_consistent('IDA_YA_YDP_INIT')
t_ch, SV_ch, SV_dot_ch = sim_ch.simulate(t_f)
SV_ch_df = label_columns(t_ch, SV_ch, an.npoints, sep.npoints,
cat.npoints)
plot_sim(tags, SV_ch_df, 'Charging',
1 + inputs.flag_req + 2 * cycle_num, fig, axes)
plot_meanPS(SV_ch_df, tags, 'Charging')
SV_ch_df = 0
#
# print('Max S_8(e) concentration = ', max(SV_ch[:, 6]))
# SV_0_cycle = SV_ch[-1, :]
# SV_dot_0_cycle = SV_ch[-1, :]
print('Done Charging\n')
exp_data_01C = pd.read_csv(r'0.1C Data.csv', header=None)
exp_data_05C = pd.read_csv(r'0.5C Data.csv', header=None)
exp_data_1C = pd.read_csv(r'1C Data.csv', header=None)
Bessler = pd.read_csv(r'Bessler Dennis Data.csv', header=None)
SV_copy = SV_dch_df.copy()
SV_copy.loc[:, 'Time'] *= -cat.i_ext_amp * inputs.A_cat / 3600 / (
cat.m_S_tot_0)
"Set up your figure"
fig = plt.figure(3)
ax = fig.add_axes([0.2, 0.2, 0.6, 0.75])
fig.set_size_inches((10., 5.0))
# ax2 = ax.twinx()
"Formatting for the figure:"
fs = 20 #font size for plots
lw = 3.0 #line width for plots
# font = plt.matplotlib.font_manager.FontProperties(family='Times New Roman',size=fs-1)
for tick in ax.xaxis.get_major_ticks():
tick.label1.set_fontsize(fs)
tick.label1.set_fontname('Times New Roman')
for tick in ax.yaxis.get_major_ticks():
tick.label1.set_fontsize(fs)
tick.label1.set_fontname('Times New Roman')
color = matplotlib.cm.plasma(inputs.C_rate)
p1, = plt.plot(SV_copy.loc[:, 'Time'],
SV_copy.loc[:, 'Phi_ed1'],
'k-',
linewidth=lw)
# p2, = plt.plot(exp_data_01C.iloc[:,0], exp_data_01C.iloc[:,1], 'ro')
# p3, = plt.plot(exp_data_05C.iloc[:,0], exp_data_05C.iloc[:,1], 'co')
# p4, = plt.plot(exp_data_1C.iloc[:,0], exp_data_1C.iloc[:,1], 'ko')
p5, = plt.plot(Bessler.iloc[:, 0], Bessler.iloc[:, 1], 'mo', ms=4)
plt.xlim((0, 1700))
plt.xticks([0, 400, 800, 1200, 1600])
plt.ylim((1.8, 2.6))
plt.ylabel(r'Cell Voltage $[\mathrm{V}]$',
fontstyle='normal',
fontname='Times new Roman',
fontsize=fs + 2,
labelpad=5.0)
plt.xlabel(
r'Capacity $[\mathrm{Ah} \hspace{0.5} \mathrm{kg}^{-1}_{\mathrm{sulfur}}]$',
fontstyle='normal',
fontname='Times new Roman',
fontsize=fs + 2,
labelpad=5.0)
# plt.legend(["Discharge", "Charge"])
file_name_dch = 'dch' + str(inputs.C_rate) + "C_" + inputs.mech + '.csv'
SV_dch = SV_dch_df.copy()
SV_dch.loc[:,
'Time'] *= -cat.i_ext_amp * inputs.A_cat / 3600 / (cat.m_S_0 +
cat.m_S_el)
SV_dch.to_csv(file_name_dch, index=False, header=True)
t_elapsed = time.time() - t_count
print('t_cpu=', t_elapsed, '\n')
return SV_eq_df, SV_dch_df, SV_ch_df, tags
def run_example(with_plots=True):
r"""
An example for IDA with scaled preconditioned GMRES method
as a special linear solver.
Note, how the operation Jacobian times vector is provided.
ODE:
.. math::
\dot y_1 - y_2 &= 0\\
\dot y_2 -9.82 &= 0
on return:
- :dfn:`imp_mod` problem instance
- :dfn:`imp_sim` solver instance
"""
#Defines the residual
def res(t, y, yd):
res_0 = yd[0] - y[1]
res_1 = yd[1] + 9.82
return N.array([res_0, res_1])
#Defines the Jacobian*vector product
def jacv(t, y, yd, res, v, c):
jy = N.array([[0, -1.], [0, 0]])
jyd = N.array([[1, 0.], [0, 1]])
j = jy + c * jyd
return N.dot(j, v)
#Initial conditions
y0 = [1.0, 0.0]
yd0 = [0.0, -9.82]
#Defines an Assimulo implicit problem
imp_mod = Implicit_Problem(
res, y0, yd0, name='Example using the Jacobian Vector product')
imp_mod.jacv = jacv #Sets the jacobian
imp_sim = IDA(imp_mod) #Create an IDA solver instance
#Set the parameters
imp_sim.atol = 1e-5 #Default 1e-6
imp_sim.rtol = 1e-5 #Default 1e-6
imp_sim.linear_solver = 'SPGMR' #Change linear solver
#imp_sim.options["usejac"] = False
#Simulate
t, y, yd = imp_sim.simulate(
5, 1000) #Simulate 5 seconds with 1000 communication points
#Basic tests
nose.tools.assert_almost_equal(y[-1][0], -121.75000000, 4)
nose.tools.assert_almost_equal(y[-1][1], -49.100000000)
#Plot
if with_plots:
P.plot(t, y)
P.xlabel('Time')
P.ylabel('State')
P.title(imp_mod.name)
P.show()
return imp_mod, imp_sim
def dae_solver(residual,
y0,
yd0,
t0,
p0=None,
jac=None,
name='DAE',
solver='IDA',
algvar=None,
atol=1e-6,
backward=False,
display_progress=True,
pbar=None,
report_continuously=False,
rtol=1e-6,
sensmethod='STAGGERED',
suppress_alg=False,
suppress_sens=False,
usejac=False,
usesens=False,
verbosity=30,
tfinal=10.,
ncp=500):
'''
DAE solver.
Parameters
----------
residual: function
Implicit DAE model.
y0: List[float]
Initial model state.
yd0: List[float]
Initial model state derivatives.
t0: float
Initial simulation time.
p0: List[float]
Parameters for which sensitivites are to be calculated.
jac: function
Model jacobian.
name: string
Model name.
solver: string
DAE solver.
algvar: List[bool]
A list for defining which variables are differential and which are algebraic.
The value True(1.0) indicates a differential variable and the value False(0.0) indicates an algebraic variable.
atol: float
Absolute tolerance.
backward: bool
Specifies if the simulation is done in reverse time.
display_progress: bool
Actives output during the integration in terms of that the current integration is periodically printed to the stdout.
Report_continuously needs to be activated.
pbar: List[float]
An array of positive floats equal to the number of parameters. Default absolute values of the parameters.
Specifies the order of magnitude for the parameters. Useful if IDAS is to estimate tolerances for the sensitivity solution vectors.
report_continuously: bool
Specifies if the solver should report the solution continuously after steps.
rtol: float
Relative tolerance.
sensmethod: string
Specifies the sensitivity solution method.
Can be either ‘SIMULTANEOUS’ or ‘STAGGERED’. Default is 'STAGGERED'.
suppress_alg: bool
Indicates that the error-tests are suppressed on algebraic variables.
suppress_sens: bool
Indicates that the error-tests are suppressed on the sensitivity variables.
usejac: bool
Sets the option to use the user defined jacobian.
usesens: bool
Aactivates or deactivates the sensitivity calculations.
verbosity: int
Determines the level of the output.
QUIET = 50 WHISPER = 40 NORMAL = 30 LOUD = 20 SCREAM = 10
tfinal: float
Simulation final time.
ncp: int
Number of communication points (number of return points).
Returns
-------
sol: solution [time, model states], List[float]
'''
if usesens is True: # parameter sensitivity
model = Implicit_Problem(residual, y0, yd0, t0, p0=p0)
else:
model = Implicit_Problem(residual, y0, yd0, t0)
model.name = name
if usejac is True: # jacobian
model.jac = jac
if algvar is not None: # differential or algebraic variables
model.algvar = algvar
if solver == 'IDA': # solver
from assimulo.solvers import IDA
sim = IDA(model)
sim.atol = atol
sim.rtol = rtol
sim.backward = backward # backward in time
sim.report_continuously = report_continuously
sim.display_progress = display_progress
sim.suppress_alg = suppress_alg
sim.verbosity = verbosity
if usesens is True: # sensitivity
sim.sensmethod = sensmethod
sim.pbar = np.abs(p0)
sim.suppress_sens = suppress_sens
# Simulation
# t, y, yd = sim.simulate(tfinal, ncp=(ncp - 1))
ncp_list = np.linspace(t0, tfinal, num=ncp, endpoint=True)
t, y, yd = sim.simulate(tfinal, ncp=0, ncp_list=ncp_list)
# Plot
# sim.plot()
# plt.figure()
# plt.subplot(221)
# plt.plot(t, y[:, 0], 'b.-')
# plt.legend([r'$\lambda$'])
# plt.subplot(222)
# plt.plot(t, y[:, 1], 'r.-')
# plt.legend([r'$\dot{\lambda}$'])
# plt.subplot(223)
# plt.plot(t, y[:, 2], 'k.-')
# plt.legend([r'$\eta$'])
# plt.subplot(224)
# plt.plot(t, y[:, 3], 'm.-')
# plt.legend([r'$\dot{\eta}$'])
# plt.figure()
# plt.subplot(221)
# plt.plot(t, yd[:, 0], 'b.-')
# plt.legend([r'$\dot{\lambda}$'])
# plt.subplot(222)
# plt.plot(t, yd[:, 1], 'r.-')
# plt.legend([r'$\ddot{\lambda}$'])
# plt.subplot(223)
# plt.plot(t, yd[:, 2], 'k.-')
# plt.legend([r'$\dot{\eta}$'])
# plt.subplot(224)
# plt.plot(t, yd[:, 3], 'm.-')
# plt.legend([r'$\ddot{\eta}$'])
# plt.figure()
# plt.subplot(121)
# plt.plot(y[:, 0], y[:, 1])
# plt.xlabel(r'$\lambda$')
# plt.ylabel(r'$\dot{\lambda}$')
# plt.subplot(122)
# plt.plot(y[:, 2], y[:, 3])
# plt.xlabel(r'$\eta$')
# plt.ylabel(r'$\dot{\eta}$')
# plt.figure()
# plt.subplot(121)
# plt.plot(yd[:, 0], yd[:, 1])
# plt.xlabel(r'$\dot{\lambda}$')
# plt.ylabel(r'$\ddot{\lambda}$')
# plt.subplot(122)
# plt.plot(yd[:, 2], yd[:, 3])
# plt.xlabel(r'$\dot{\eta}$')
# plt.ylabel(r'$\ddot{\eta}$')
# plt.figure()
# plt.subplot(121)
# plt.plot(y[:, 0], y[:, 2])
# plt.xlabel(r'$\lambda$')
# plt.ylabel(r'$\eta$')
# plt.subplot(122)
# plt.plot(y[:, 1], y[:, 3])
# plt.xlabel(r'$\dot{\lambda}$')
# plt.ylabel(r'$\dot{\eta}$')
# plt.figure()
# plt.subplot(121)
# plt.plot(yd[:, 0], yd[:, 2])
# plt.xlabel(r'$\dot{\lambda}$')
# plt.ylabel(r'$\dot{\eta}$')
# plt.subplot(122)
# plt.plot(yd[:, 1], yd[:, 3])
# plt.xlabel(r'$\ddot{\lambda}$')
# plt.ylabel(r'$\ddot{\eta}$')
# plt.show()
sol = [t, y, yd]
return sol
from assimulo.solvers import IDA
import matplotlib.pyplot as P
import numpy as N
t0 = 0.0
tfinal = 2.0
y0, yd0, switches0 = init_woodpecker()
model = Implicit_Problem(res, y0, yd0, t0, sw0=switches0)
model.state_events = state_event
model.handle_event = handle_event
sim = IDA(model)
sim.algvar = [1, 1, 1, 0, 0, 0, 0, 0]
sim.suppress_alg = True
sim.atol = [1e-5, 1e-5, 1e-5, 1e15, 1e15, 1e15, 1e15, 1e15]
t, y, yd = sim.simulate(tfinal)
#sim.print_event_data()
"""
Plotting
y[:,0] - plots z (height)
y[:,1] - plots sleeve angle
y[:,2] - plots bird angle
"""
# Plot z (height)
P.plot(t, y[:, 0])
P.title('Woodpecker')
P.ylabel('Height z (m)')
from Project_2 import squeezer as sq
from Project_2 import squeezer2 as sq2
import matplotlib.pyplot as plt
t0 = 0
tfinal = 0.03
# Model 1, squeezer with index 3 constraints
y0_1,yp0_1 = sq.init_squeezer()
ncp_1 = 100
model_1 = Implicit_Problem(sq.squeezer, y0_1, yp0_1, t0)
model_1.name = 'Squeezer index 3 constraints'
sim_1 = IDA(model_1)
sim_1.suppress_alg = True
sim_1.algvar = array([1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0])
sim_1.atol = ones(20,)
for i in range(size(sim_1.atol)):
if 0 <= i <= 6:
sim_1.atol[i] = pow(10,-6)
else:
sim_1.atol[i] = pow(10,5)
t, y, yd = sim_1.simulate(tfinal, ncp_1)
plt.plot(t,y[:,14:shape(y)[1]]) # Plots the Lagrange multipliers
plt.show()
plt.plot(t,(y[:,0:7]+pi)%(2*pi)-pi) # Plots the position variables i.e beta,gamma etc, modulo 2pi.
plt.show()
# Model 2, squeezer with index 2 constraints
y0_2,yp0_2 = sq2.init_squeezer()
ncp_2 = 100
model_2 = Implicit_Problem(sq2.squeezer2, y0_2, yp0_2, t0)
def DAE_integration_assimulo_lagrangian(self, **kwargs):
"""
Perform time integration for DAEs with the assimulo package
Lagrangian variant
"""
assert self.set_time_setting == 1, 'Time discretization must be specified first'
if self.tclose > 0:
close = True
else:
close = False
# Control vector
self.U = interpolate(self.boundary_cntrl_space, self.Vl).vector()[self.bndr_i_l]
if self.discontinous_boundary_values == 1:
self.U[self.Corner_indices] = self.U[self.Corner_indices]/2
self.UU = np.zeros(self.Nb)
for i in range(self.Nb):
self.UU[i] = self.boundary_cntrl_space(self.coord_b[i])
# Definition of the sparse solver for the DAE res function to
# be defined next M should be invertible !!
#my_solver = factorized(csc_matrix(self.M))
#rhs = self.my_mult(self.J, self.my_mult(self.Q,self.A0)) + self.my_mult(self.Bext,self.U* self.boundary_cntrl_time(0.,self.tclose))
#self.AD0 = my_solver(rhs)
# Definition of the rhs function required in assimulo
def res(t,y,yd):
"""
Definition of the residual function required in the DAE part of assimulo
"""
z = np.zeros(self.Np+self.Nl)
z[0:self.Np] = self.my_mult(self.M_class, yd[0:self.Np]) + self.my_mult(self.D_class, y[0:self.Np]) - self.my_mult(self.C_class, y[self.Np:])
z[self.Np:self.Np+self.Nl] = self.my_mult(self.C_class.T, y[0:self.Np]) - self.L_class * self.boundary_cntrl_time(t,self.tclose)
return z
# Definition of the jacobian function required in assimulo
def jac(c,t,y,yd):
"""
Definition of the Jacobian matrix required in the DAE part of assimulo
"""
#Matrix = csr_matrix(self.my_mult(self.J,self.Q))
#if close and t > self.tclose:
# Matrix = csr_matrix(self.my_mult(self.J - self.R, self.Q))
#return c*csr_matrix(self.M) - Matrix
return None
# Definition of the jacobian matrix vector function required in assimulo
def jacv(t,y,yd,res,v,c):
"""
Jacobian matrix-vector product required in the DAE part of assimulo
"""
#w = self.my_mult(self.Q, v)
#z = self.my_mult(self.J, w)
#if close and t > self.tclose:
# z -= self.my_mult(self.R, w)
#return c*self.my_mult(self.M,v) - z
return None
print('DAE Integration using assimulo built-in functions:')
#def handle_result(solver, t ,y, yd):
# global order
# order.append(solver.get_last_order())
#
# solver.t_sol.extend([t])
# solver.y_sol.extend([y])
# solver.yd_sol.extend([yd])
# The initial conditons
y0 = np.concatenate(( self.Tp0, np.zeros(self.Nl) ))
yd0 = np.zeros(self.Np + self.Nl)
model = Implicit_Problem(res,y0,yd0,self.tinit)
#model.handle_result = handle_result
#model.jacv = jacv
#sim = Radau5DAE(model,**kwargs)
#
# IDA method from Assimulo
#
sim = IDA(model,**kwargs)
sim.algvar = list(np.concatenate((np.ones(self.Np), np.zeros(self.Nl) )) )
sim.atol = 1.e-6
sim.rtol = 1.e-6
sim.report_continuously = True
ncp = self.Nt
#sim.usejac = True
sim.suppress_alg = True
sim.inith = self.dt
sim.maxord = 5
#sim.linear_solver = 'SPGMR'
sim.make_consistent('IDA_YA_YDP_INIT')
#time_span, DAE_y, DAE_yd = sim.simulate(self.tfinal,ncp, self.tspan)
time_span, DAE_y, DAE_yd = sim.simulate(self.tfinal, 0, self.tspan)
#print(sim.get_options())
print(sim.print_statistics())
A_dae = DAE_y[:,0:self.Np].transpose()
# Hamiltonian
self.Nt = A_dae.shape[1]
self.tspan = np.array(time_span)
Ham_dae = np.zeros(self.Nt)
for k in range(self.Nt):
Ham_dae[k] = 1/2 * self.my_mult(A_dae[:,k].T, \
self.my_mult(self.Mp_rho_Cv, A_dae[:,k]))
self.Ham_dae = Ham_dae
return Ham_dae, np.array(time_span)
velocityIndex = list(range(7,14))
lambdaIndex = list(range(14,20))
algvar = numpy.ones(numpy.size(y0))
indexNumber = 1
#1 - expl runge - index1 solution
#2 - index2
#3 - index3
if indexNumber == 3:
problem = Implicit_Problem(squeezer3, y0, yd0, t0)
algvar[lambdaIndex] = 0
algvar[velocityIndex] = 0
sim = IDA(problem)
sim.atol = numpy.ones(numpy.size(y0))*1e-7
sim.atol[lambdaIndex] = 1e-1
sim.atol[velocityIndex] = 1e-5
elif indexNumber == 2:
problem = Implicit_Problem(squeezer2, y0, yd0, t0)
algvar[lambdaIndex] = 0
algvar[velocityIndex] = 1
sim = IDA(problem)
sim.atol = numpy.ones(numpy.size(y0))*1e-7
sim.atol[lambdaIndex] = 1e-5
sim.atol[velocityIndex] = 1e-5
elif indexNumber == 1:
problem = Explicit_Problem(squeezer1, y0[0:14], t0)
sim = RungeKutta34(problem)
sim.atol = numpy.ones(14)*1e-7
SEI_ctr = 0
phi_ctr += 1
# Volume fraction of SEI per cell
res[-1] = SV_dot[-1]
return res
"""------------------------------------------------------------------------"""
# Set up problem instance
SEI_1D = Implicit_Problem(residual, SV_0, SV_dot_0, t_0)
# Define simulation parameters
simulation = IDA(SEI_1D) # Create simulation instance
simulation.atol = 1e-6 # Solver absolute tolerance
simulation.rtol = 1e-6 # Solver relative tolerance
simulation.maxh = 0.1 # Solver max step size
# Set simulation end time, slope flag (for anode voltage cycle), and run simulation
t_f = ((phi_bounds[1] - phi_anode_0)/R)*5
#ncp_list = np.arange(0, t_f, 0.15)
#ncp = 10000
# Run simulation
t, SV, SV_dot = simulation.simulate(t_f)
# %% Organize data and plot
y20,yp20=squeezer_ind2.init_squeezer2() # Initial values
y30,yp30=squeezer_ind3.init_squeezer3() # Initial values
t0 = 0 # Initial time
squeezemodel2 = Implicit_Problem(squeezer_ind2.squeezer2, y20, yp20, t0)
squeezemodel3 = Implicit_Problem(squeezer_ind3.squeezer3, y30, yp30, t0)
algvar = 7*[1.]+13*[0.]
solver2 = IDA(squeezemodel2) # Create solver instance
solver3 = IDA(squeezemodel3) # Create solver instance
solver2.algvar = algvar
solver3.algvar = algvar
solver2.suppress_alg=True
solver3.suppress_alg=True
solver2.atol = 1e-7
solver3.atol = 1e-7
solver3.maxsteps = 322
print(solver3.maxsteps)
tf = .03 # End time for simulation
t2, y2, yd2 = solver2.simulate(tf)
t3, y3, yd3 = solver3.simulate(tf)
figure(1)
plot(t2,y2[:,14:16])
title('Index 2')
figure(2)
plot(t3,y3[:,14:16])
title('Index 3')
def main():
SV_0 = solver_inputs.SV_0
SV_dot_0 = np.zeros_like(SV_0)
algvar = solver_inputs.algvar
# Close any open pyplot objects:
plt.close('all')
atol = np.ones_like(SV_0)*1e-8
rtol = 1e-4
# Start a timer:
t_count = time.time()
# Calculate the time span, which should be enough to charge or discharge fully
# (i.e. 3600 seconds divided by the C-rate):
t_0 = 0
t_f = 3600/Inputs.C_rate
rate_tag = str(Inputs.C_rate)+"C"
"""----------Figures----------"""
if Inputs.plot_profiles_flag:
fig1, axes1, fig2, axes2, fig3, axes3 = setup_plots(plt, rate_tag)
for cycle in np.arange(0, Inputs.n_cycles):
"""----------Equilibration----------"""
# Equilibrate by integrating at zero current:
print('\nEquilibrating...')
# Create problem instance
current.set_i_ext(0)
battery_eq = li_ion(li_ion.res_fun, SV_0, SV_dot_0, t_0)
battery_eq.external_event_detection = True
battery_eq.algvar = algvar
# Simulation parameters
sim_eq = IDA(battery_eq) # Create simulation instance
sim_eq.atol = atol # Solver absolute tolerance
sim_eq.rtol = rtol # Solver relative tolerance
sim_eq.verbosity = 50
sim_eq.make_consistent('IDA_YA_YDP_INIT')
t_eq, SV_eq, SV_dot_eq = sim_eq.simulate(0.1*t_f)
# Put solution into pandas dataframe with labeled columns
SV_eq_df = Label_Columns(t_eq, SV_eq, an.npoints, sep.npoints,
cat.npoints)
# Obtain tag strings for dataframe columns
tags = tag_strings(SV_eq_df)
print('Done equilibrating\n')
"""------------Charging-------------"""
print('\nCharging...')
# New initial conditions are the final equilibrium conditions
t_0 = 0
SV_0 = SV_eq[-1, :]
SV_dot_0 = SV_dot_eq[-1 :]
# Charge the battery
current.set_i_ext(current.i_ext_set)
# Create problem instance
battery_ch = li_ion(li_ion.res_fun, SV_0, SV_dot_0, t_0)
battery_ch.external_event_detection = True
battery_ch.algvar = algvar
# Simulation parameters
sim_ch = IDA(battery_ch)
sim_ch.atol = atol
sim_ch.rtol = rtol
sim_ch.verbosity = 50
sim_ch.make_consistent('IDA_YA_YDP_INIT')
t_ch, SV_ch, SV_dot_ch = sim_ch.simulate(t_f)
SV_ch_df = Label_Columns(t_ch, SV_ch, an.npoints,
sep.npoints, cat.npoints)
if Inputs.plot_potential_profiles == 1:
plot_potential(tags['Phi_an'], tags['Phi_cat'], SV_ch_df,
'Charging', 0, fig1, axes1)
if Inputs.plot_electrode_profiles == 1:
plot_electrode(tags['X_an'], tags['X_cat'], SV_ch_df,
'Charging', 0, fig2, axes2)
if Inputs.plot_elyte_profiles == 1:
plot_elyte(tags['X_el_an'], tags['X_el_cat'], tags['X_el_sep'], SV_ch_df,
'Charging', 0, fig3, axes3)
print('Done charging\n')
"""------------Re_equilibrating-------------"""
if Inputs.flag_re_equil == 1:
# New initial conditions are the final charge conditions
SV_0 = SV_ch[-2, :]
SV_dot_0 = SV_dot_ch[-2, :]
# Equilibrate again. Note - this is a specific choice to reflect
# equilibration after the charging steps. We may want, at times, to
# simulate a situation where the battery is not equilibrated between
# charge and discharge, or is equilibrated for a shorter amount of time.
print('\nRe-equilibrating...')
current.set_i_ext(0)
battery_req = li_ion(li_ion.res_fun, SV_0, SV_dot_0, t_0)
battery_req.external_event_detection = True
battery_req.algvar = algvar
# Simulation parameters
sim_req = IDA(battery_req)
sim_req.atol = atol
sim_req.rtol = rtol
sim_req.verbosity = 50
sim_req.make_consistent('IDA_YA_YDP_INIT')
t_req, SV_req, SV_dot_req = sim_req.simulate(t_f)
SV_req_df = Label_Columns(t_req, SV_req, an.npoints, sep.npoints,
cat.npoints)
if Inputs.plot_potential_profiles*Inputs.phi_time == 1:
plot_potential(tags['Phi_an'], tags['Phi_cat'], SV_req_df,
'Re-equilibrating', 1, None, fig1, axes1)
if Inputs.plot_electrode_profiles == 1:
plot_electrode(tags['X_an'], tags['X_cat'], SV_req_df,
'Re-equilibrating', 1, fig2, axes2)
if Inputs.plot_elyte_profiles == 1:
plot_elyte(tags['X_el_an'], tags['X_el_cat'], tags['X_el_sep'], SV_req_df,
'Re-equilibrating', 1, fig3, axes3)
print('Done re-equilibrating\n')
else:
SV_req = SV_ch
SV_dot_req = SV_dot_ch
SV_req_df = SV_req
"""------------Discharging-------------"""
print('\nDischarging...')
SV_0 = SV_req[-1, :]
SV_dot_0 = SV_dot_req[-1, :]
current.set_i_ext(-current.i_ext_set)
battery_dch = li_ion(li_ion.res_fun, SV_0, SV_dot_0, t_0)
battery_dch.external_event_detection = True
battery_dch.algvar = algvar
# Simulation parameters
sim_dch = IDA(battery_dch)
sim_dch.atol = atol
sim_dch.rtol = rtol
sim_dch.verbosity = 50
sim_dch.make_consistent('IDA_YA_YDP_INIT')
t_dch, SV_dch, SV_dot_dch = sim_dch.simulate(t_f)
SV_dch_df = Label_Columns(t_dch, SV_dch, an.npoints, sep.npoints,
cat.npoints)
if Inputs.plot_potential_profiles == 1:
plot_potential(tags['Phi_an'], tags['Phi_cat'], SV_dch_df,
'Discharging', 1+(Inputs.flag_re_equil*Inputs.phi_time), fig1, axes1)
if Inputs.plot_electrode_profiles == 1:
plot_electrode(tags['X_an'], tags['X_cat'], SV_dch_df,
'Discharging', 1+Inputs.flag_re_equil, fig2, axes2)
if Inputs.plot_elyte_profiles == 1:
plot_elyte(tags['X_el_an'], tags['X_el_cat'], tags['X_el_sep'], SV_dch_df,
'Discharging', 1+Inputs.flag_re_equil, fig3, axes3)
print('Done discharging\n')
"""---------------------------------"""
SV_0 = SV_dch[-1, :]
SV_dot_0 = np.zeros_like(SV_0)
# %% Plot capacity if flagged
plt.show('all')
plot_cap(SV_ch_df, SV_dch_df, rate_tag, current.i_ext_set,
Inputs.plot_cap_flag, tags)
elapsed = time.time() - t_count
print('t_cpu=', elapsed, '\n')
plt.show()
return SV_eq_df, SV_ch_df, SV_req_df, SV_dch_df
def run_example(with_plots=True):
r"""
Example for demonstrating the use of a user supplied Jacobian
ODE:
.. math::
\dot y_1-y_3 &= 0 \\
\dot y_2-y_4 &= 0 \\
\dot y_3+y_5 y_1 &= 0 \\
\dot y_4+y_5 y_2+9.82&= 0 \\
y_3^2+y_4^2-y_5(y_1^2+y_2^2)-9.82 y_2&= 0
on return:
- :dfn:`imp_mod` problem instance
- :dfn:`imp_sim` solver instance
"""
global order
order = []
#Defines the residual
def f(t, y, yd):
res_0 = yd[0] - y[2]
res_1 = yd[1] - y[3]
res_2 = yd[2] + y[4] * y[0]
res_3 = yd[3] + y[4] * y[1] + 9.82
res_4 = y[2]**2 + y[3]**2 - y[4] * (y[0]**2 + y[1]**2) - y[1] * 9.82
return N.array([res_0, res_1, res_2, res_3, res_4])
def handle_result(solver, t, y, yd):
global order
order.append(solver.get_last_order())
solver.t_sol.extend([t])
solver.y_sol.extend([y])
solver.yd_sol.extend([yd])
#The initial conditons
y0 = [1.0, 0.0, 0.0, 0.0, 5] #Initial conditions
yd0 = [0.0, 0.0, 0.0, -9.82, 0.0] #Initial conditions
#Create an Assimulo implicit problem
imp_mod = Implicit_Problem(f,
y0,
yd0,
name='Example for plotting used order')
imp_mod.handle_result = handle_result
#Sets the options to the problem
imp_mod.algvar = [1.0, 1.0, 1.0, 1.0, 0.0] #Set the algebraic components
#Create an Assimulo implicit solver (IDA)
imp_sim = IDA(imp_mod) #Create a IDA solver
#Sets the paramters
imp_sim.atol = 1e-6 #Default 1e-6
imp_sim.rtol = 1e-6 #Default 1e-6
imp_sim.suppress_alg = True #Suppres the algebraic variables on the error test
imp_sim.report_continuously = True
#Let Sundials find consistent initial conditions by use of 'IDA_YA_YDP_INIT'
imp_sim.make_consistent('IDA_YA_YDP_INIT')
#Simulate
t, y, yd = imp_sim.simulate(5) #Simulate 5 seconds
#Basic tests
nose.tools.assert_almost_equal(y[-1][0], 0.9401995, places=4)
nose.tools.assert_almost_equal(y[-1][1], -0.34095124, places=4)
nose.tools.assert_almost_equal(yd[-1][0], -0.88198927, places=4)
nose.tools.assert_almost_equal(yd[-1][1], -2.43227069, places=4)
nose.tools.assert_almost_equal(order[-1], 5, places=4)
#Plot
if with_plots:
P.figure(1)
P.plot(t, y, linestyle="dashed", marker="o") #Plot the solution
P.xlabel('Time')
P.ylabel('State')
P.title(imp_mod.name)
P.figure(2)
P.plot([0] + N.add.accumulate(N.diff(t)).tolist(), order)
P.title("Used order during the integration")
P.xlabel("Time")
P.ylabel("Order")
P.show()
return imp_mod, imp_sim
def run_example():
def residual(t,y,yd):
return squeezer(t, y, yd)
def residual2(t,y,yd):
return squeezer2(t, y, yd)
#The initial conditons
t0 = 0
y0, yd0 = init_squeezer()
model = Implicit_Problem(residual, y0, yd0, t0) #Create an Assimulo problem
model2 = Implicit_Problem(residual2, y0, yd0, t0) #Create an Assimulo problem
sim = IDA(model) #Create the IDA solver
sim2 = IDA(model2) #Create the IDA solver
# index 3
sim.algvar = 7*[True] + 7*[False] + 6*[False]
sim.suppress_alg = True
sim.atol = 7*[1e-6] + 7*[1e5] + 6*[1e5]
# index 2
sim2.algvar = 7*[True] + 7*[True] + 6*[False]
sim2.suppress_alg = True
sim2.atol = 7*[1e-6] + 7*[1e-6] + 6*[1e5]
tfinal = 0.03 #Specify the final time
ncp = 500 #Number of communcation points (number of return points)
t,y,yd = sim.simulate(tfinal, ncp) #Use the .simulate method to simulate and provide the final time and ncp (optional)
t2,y2,yd2 = sim2.simulate(tfinal, ncp) #Use the .simulate method to simulate and provide the final time and ncp (optional)
print("500####################")
print("####################")
fig, ax = P.subplots()
P.title('IDA, difference between index 3 and index 2 formulation')
P.xlabel('Time')
P.ylabel('Angle')
#P.ylabel('Step size')
#P.axis([0, tfinal + 0.01, -0.7, 0.7])
#P.plot(t[1:], np.diff(t))
#P.plot(t, y[:, 0], label='beta')
#P.plot(t, y[:, 1], label='theta')
#P.plot(t, y[:, 2], label='gamma')
#P.plot(t, y[:, 3], label='phi')
#P.plot(t, y[:, 4], label='delta')
#P.plot(t, y[:, 5], label='omega')
#P.plot(t, y[:, 6], label='epsilon')
P.plot(t, y[:, 0] - y2[:, 0], label='beta')
P.plot(t, y[:, 1] - y2[:, 1], label='theta')
P.plot(t, y[:, 2] - y2[:, 2], label='gamma')
P.plot(t, y[:, 3] - y2[:, 3], label='phi')
P.plot(t, y[:, 4] - y2[:, 4], label='delta')
P.plot(t, y[:, 5] - y2[:, 5], label='omega')
#P.plot(t, y[:, 6], label='epsilon')
legend = ax.legend(shadow=True, loc = 'upper left')
'''
P.plot(t, y[:, 14])
P.plot(t, y[:, 15])
P.plot(t, y[:, 16])
P.plot(t, y[:, 17])
P.plot(t, y[:, 18])
P.plot(t, y[:, 19])
P.axis([0, tfinal, -100, 200])
'''
P.grid()
P.show()
def run_example(with_plots=True):
"""
This example show how to use Assimulo and IDA for simulating sensitivities
for initial conditions.::
0 = dy1/dt - -(k01+k21+k31)*y1 - k12*y2 - k13*y3 - b1
0 = dy2/dt - k21*y1 + (k02+k12)*y2
0 = dy3/dt - k31*y1 + k13*y3
y1(0) = p1, y2(0) = p2, y3(0) = p3
p1=p2=p3 = 0
See http://sundials.2283335.n4.nabble.com/Forward-sensitivities-for-initial-conditions-td3239724.html
on return:
- :dfn:`imp_mod` problem instance
- :dfn:`imp_sim` solver instance
"""
def f(t, y, yd, p):
y1, y2, y3 = y
yd1, yd2, yd3 = yd
k01 = 0.0211
k02 = 0.0162
k21 = 0.0111
k12 = 0.0124
k31 = 0.0039
k13 = 0.000035
b1 = 49.3
res_0 = -yd1 - (k01 + k21 + k31) * y1 + k12 * y2 + k13 * y3 + b1
res_1 = -yd2 + k21 * y1 - (k02 + k12) * y2
res_2 = -yd3 + k31 * y1 - k13 * y3
return N.array([res_0, res_1, res_2])
#The initial conditions
y0 = [0.0, 0.0, 0.0] #Initial conditions for y
yd0 = [49.3, 0., 0.]
p0 = [0.0, 0.0, 0.0] #Initial conditions for parameters
yS0 = N.array([[1, 0, 0], [0, 1, 0], [0, 0, 1.]])
#Create an Assimulo implicit problem
imp_mod = Implicit_Problem(f,
y0,
yd0,
p0=p0,
name='Example: Computing Sensitivities')
#Sets the options to the problem
imp_mod.yS0 = yS0
#Create an Assimulo explicit solver (IDA)
imp_sim = IDA(imp_mod)
#Sets the paramters
imp_sim.rtol = 1e-7
imp_sim.atol = 1e-6
imp_sim.pbar = [
1, 1, 1
] #pbar is used to estimate the tolerances for the parameters
imp_sim.report_continuously = True #Need to be able to store the result using the interpolate methods
imp_sim.sensmethod = 'SIMULTANEOUS' #Defines the sensitvity method used
imp_sim.suppress_sens = False #Dont suppress the sensitivity variables in the error test.
#Simulate
t, y, yd = imp_sim.simulate(400) #Simulate 400 seconds
#Basic test
nose.tools.assert_almost_equal(y[-1][0], 1577.6552477, 3)
nose.tools.assert_almost_equal(y[-1][1], 611.9574565, 3)
nose.tools.assert_almost_equal(y[-1][2], 2215.88563217, 3)
nose.tools.assert_almost_equal(imp_sim.p_sol[0][1][0], 1.0)
#Plot
if with_plots:
P.figure(1)
P.subplot(221)
P.plot(t,
N.array(imp_sim.p_sol[0])[:, 0], t,
N.array(imp_sim.p_sol[0])[:, 1], t,
N.array(imp_sim.p_sol[0])[:, 2])
P.title("Parameter p1")
P.legend(("p1/dy1", "p1/dy2", "p1/dy3"))
P.subplot(222)
P.plot(t,
N.array(imp_sim.p_sol[1])[:, 0], t,
N.array(imp_sim.p_sol[1])[:, 1], t,
N.array(imp_sim.p_sol[1])[:, 2])
P.title("Parameter p2")
P.legend(("p2/dy1", "p2/dy2", "p2/dy3"))
P.subplot(223)
P.plot(t,
N.array(imp_sim.p_sol[2])[:, 0], t,
N.array(imp_sim.p_sol[2])[:, 1], t,
N.array(imp_sim.p_sol[2])[:, 2])
P.title("Parameter p3")
P.legend(("p3/dy1", "p3/dy2", "p3/dy3"))
P.subplot(224)
P.title('ODE Solution')
P.plot(t, y)
P.suptitle(imp_mod.name)
P.show()
return imp_mod, imp_sim
def main():
res_class = eval(inputs.test_type)
# plt.close('all')
t_count = time.time()
SV_0 = sol_init.SV_0
SV_dot_0 = np.zeros_like(SV_0)
t_0 = 0.
t_f = 3600. / inputs.C_rate
algvar = sol_init.algvar
atol = np.ones_like(SV_0) * 1e-5
atol[cat.ptr_vec['eps_S8']] = 1e-25
atol[cat.ptr_vec['eps_Li2S']] = 1e-25
atol[cat.ptr_vec['rho_k_el']] = 1e-25
# atol = 1e-30;
rtol = 1e-4
sim_output = 50
rate_tag = str(inputs.C_rate) + "C"
fig, axes = plt.subplots(sharey="row", figsize=(9, 12), nrows=3, ncols=1)
plt.subplots_adjust(wspace=0.15, hspace=0.4)
fig.text(0.15,
0.8,
rate_tag,
fontsize=20,
bbox=dict(facecolor='white', alpha=0.5))
# Set up user function to build figures based on inputs
"----------Equilibration----------"
print('\nEquilibrating...')
# Set external current to 0 for equilibration
cat.set_i_ext(0)
# Create problem object
bat_eq = res_class(res_class.res_fun, SV_0, SV_dot_0, t_0)
bat_eq.external_event_detection = True
bat_eq.algvar = algvar
# Create simulation object
sim_eq = IDA(bat_eq)
sim_eq.atol = atol
sim_eq.rtol = rtol
sim_eq.verbosity = sim_output
sim_eq.make_consistent('IDA_YA_YDP_INIT')
t_eq, SV_eq, SV_dot_eq = sim_eq.simulate(t_f)
# Put solution into pandas dataframe with labeled columns
SV_eq_df = label_columns(t_eq, SV_eq, an.npoints, sep.npoints, cat.npoints)
# SV_eq_df = []
# Obtain tag strings for dataframe columns
tags = tag_strings(SV_eq_df)
# plot_sim(tags, SV_eq_df, 'Equilibrating', 0, fig, axes)
# print(SV_eq_df[tags['rho_el'][4:10]].iloc[-1])
print('Done equilibrating\n')
"------------Discharging-------------"
print('Discharging...')
# New initial conditions from previous simulation
SV_0 = SV_eq[-1, :]
SV_dot_0 = SV_dot_eq[-1, :]
# Set external current
cat.set_i_ext(cat.i_ext_amp)
# Update problem instance initial conditions
bat_dch = res_class(res_class.res_fun, SV_0, SV_dot_0, t_0)
bat_dch.external_event_detection = True
bat_dch.algvar = algvar
# Re-initialize simulation object
sim_dch = IDA(bat_dch)
sim_dch.atol = atol
sim_dch.rtol = rtol
sim_dch.maxh = 5
sim_dch.verbosity = sim_output
sim_dch.make_consistent('IDA_YA_YDP_INIT')
t_dch, SV_dch, SV_dot_dch = sim_dch.simulate(t_f)
# if hasattr(cathode, 'get_tflag'):
# t_flag_ch = cathode.get_tflag
SV_dch_df = label_columns(t_dch, SV_dch, an.npoints, sep.npoints,
cat.npoints)
# SV_dch_df = []
# Obtain tag strings for dataframe columns
# tags = tag_strings(SV_ch_df)
plot_sim(tags, SV_dch_df, 'Discharging', 1, fig, axes)
plot_meanPS(SV_dch_df, tags)
print('Done Discharging\n')
"--------Re-equilibration---------"
# if inputs.flag_req == 1:
#
# print('Re-equilibrating...')
#
# # New initial conditions from previous simulation
# SV_0 = SV_ch[-1, :]
# SV_dot_0 = SV_dot_ch[-1, :]
#
# # Set external current
# cat.set_i_ext(0)
#
# # Update problem instance initial conditions
# bat_req = res_class(res_class.res_fun, SV_0, SV_dot_0, t_0)
# bat_req.external_event_detection = True
# bat_req.algvar = algvar
#
# # Re-initialize simulation object
# sim_req = IDA(bat_req)
# sim_req.atol = atol
# sim_req.rtol = rtol
# sim_req.verbosity = sim_output
# sim_req.make_consistent('IDA_YA_YDP_INIT')
#
# t_req, SV_req, SV_dot_req = sim_req.simulate(t_f)
#
# SV_req_df = label_columns(t_req, SV_req, an.npoints, sep.npoints, cat.npoints)
#
## plot_sim(tags, SV_req_df, 'Re-Equilibrating', 2-1, fig, axes)
#
# print('Done re-equilibrating\n')
# else:
# SV_req = SV_ch
# SV_dot_req = SV_dot_ch
"-----------Charging-----------"
# print('Charging...')
#
# SV_0 = SV_req[-1, :]
# SV_dot_0 = SV_dot_req[-1, :]
#
# cat.set_i_ext(-cat.i_ext_amp)
#
# # Update problem instance initial conditions
# bat_dch = res_class(res_class.res_fun, SV_0, SV_dot_0, t_0)
# bat_dch.external_event_detection = True
# bat_dch.algvar = algvar
#
# # Re-initialize simulation object
# sim_dch = IDA(bat_dch)
# sim_dch.atol = atol
# sim_dch.rtol = rtol
# sim_dch.verbosity = sim_output
# sim_dch.make_consistent('IDA_YA_YDP_INIT')
#
# t_dch, SV_dch, SV_dot_dch = sim_dch.simulate(t_f)
#
## if hasattr(cathode, 'get_tflag'):
## t_flag_dch = cathode.get_tflag
#
# SV_dch_df = label_columns(t_dch, SV_dch, an.npoints, sep.npoints, cat.npoints)
#
# plot_sim(tags, SV_dch_df, 'Charging', 3, fig, axes)
#
# print('Done Charging\n')
t_elapsed = time.time() - t_count
print('t_cpu=', t_elapsed, '\n')
return SV_eq_df, SV_dch_df, tags #SV_eq_df, SV_req_df #, SV_dch_df
