modifications

kalman/aorta.yaml

@@ -6,14 +6,14 @@ fluid:
     dynamic_viscosity: 0.035
 
 io:
-    write_path: 'results/aorta/'
+    write_path: 'results/aorta'
     restart:
         path: ''  # './projects/nse_coa3d/results/test_restart2/' 
         time: 0
     write_xdmf: True
     write_checkpoints: True
     write_hdf5_timeseries: False
-    write_velocity: 'update'     # tentative
+    write_velocity: 'update'     # update or tentative
 
 boundary_conditions:
     - 
@@ -25,29 +25,29 @@ boundary_conditions:
         type: 'dirichlet'
         value: ['0','0','-U*sin(DOLFIN_PI*t/Th)*(t<=Th) + (Th<t)*(-3.67949466208*U*sin(9*DOLFIN_PI*t/Th)*exp(-t*10))']
         parameters:
-            U: 30
+            U: 60
             Th: 0.35
             t: 0   
     - 
         id: 3
         type: 'windkessel'
-        value: [10,0.01,1000]
+        value: [20,0,0]
-        p0: [47,1333.223874]
+        p0: [0,1333.223874]
     - 
         id: 4
         type: 'windkessel'
-        value: [250,0.0001,8000]
+        value: [500,0,0]
-        p0: [47,1333.223874]
+        p0: [0,1333.223874]
     - 
         id: 5
         type: 'windkessel'
-        value: [250,0.0001,8000]
+        value: [500,0,0]
-        p0: [47,1333.223874]
+        p0: [0,1333.223874]
     - 
         id: 6
         type: 'windkessel'
-        value: [250,0.0001,8000]
+        value: [500,0,0]
-        p0: [47,1333.223874]
+        p0: [0,1333.223874]
 
 timemarching:
     velocity_pressure_coupling: 'fractionalstep'    # monolithic, fractionalstep
@@ -111,12 +111,30 @@ linear_solver:
 
 estimation:
     boundary_conditions:
+        - 
+            id: 3
+            type: 'windkessel'
+            initial_stddev: 1
         - 
             id: 4
             type: 'windkessel'
+            initial_stddev: 1
+        - 
+            id: 5
+            type: 'windkessel'
+            initial_stddev: 1
+        - 
+            id: 6
+            type: 'windkessel'
+            initial_stddev: 1
+        - 
+            id: 2
+            type: 'dirichlet'
             parameters: 'U'
             initial_stddev: 1
 
+
+
     measurements:
         -
             mesh: './meshes/coaortaH1.h5'
@@ -125,7 +143,7 @@ estimation:
             file_root: 'results/aorta/measurements/u{i}.h5'
             indices: 0 # indices of checkpoints to be processed. 0 == all
             velocity_direction: ~
-            noise_stddev: 1.5     # standard deviation of Gaussian noise
+            noise_stddev: 25     # standard deviation of Gaussian noise
     
     roukf:
         particles: 'simplex' # unique or simplex

kalman/aorta_C.yaml

@@ -0,0 +1,133 @@
+
+mesh: './meshes/coaortaH1.h5'
+# Physical parameters of the fluid
+fluid:
+    density: 1.2
+    dynamic_viscosity: 0.035
+
+io:
+    write_path: 'results/aorta/'
+    restart:
+        path: ''  # './projects/nse_coa3d/results/test_restart2/' 
+        time: 0
+    write_xdmf: True
+    write_checkpoints: True
+    write_hdf5_timeseries: False
+    write_velocity: 'update'     # tentative
+
+boundary_conditions:
+    - 
+        id: 1
+        type: 'dirichlet'
+        value: ['0','0','0']
+    - 
+        id: 2
+        type: 'dirichlet'
+        value: ['0','0','-U*sin(DOLFIN_PI*t/Th)*(t<=Th) + (Th<t)*(-3.67949466208*U*sin(9*DOLFIN_PI*t/Th)*exp(-t*10))']
+        parameters:
+            U: 30
+            Th: 0.35
+            t: 0   
+    - 
+        id: 3
+        type: 'windkessel'
+        value: [10,1000,0.01]
+        p0: [47,1333.223874]
+    - 
+        id: 4
+        type: 'windkessel'
+        value: [250,8000,0.0001]
+        p0: [47,1333.223874]
+    - 
+        id: 5
+        type: 'windkessel'
+        value: [250,8000,0.0001]
+        p0: [47,1333.223874]
+    - 
+        id: 6
+        type: 'windkessel'
+        value: [250,8000,0.0001]
+        p0: [47,1333.223874]
+
+timemarching:
+    velocity_pressure_coupling: 'fractionalstep'    # monolithic, fractionalstep
+
+    monolithic:
+        timescheme: 'gmp'   # generalized midpoint, steady FIXME TODO
+        theta: 1            # 1: Euler, 0.5: implicit midpoint rule (one-legged)
+        nonlinear:
+            method: 'constant_extrapolation'   # constant_extrapolation, linear_extrapolation, newton, picard, snes
+            maxit: 20
+            init_steps: 30
+            use_aitken: 1   #  0: False, 1: Picard only, 2: all
+            report: 1       # 0: None, 1: residuals, 2: residuals and energy (inflow/driving/forcing via ESSENTIAL Dbcs!)
+            atol: 1.e-6    # note: dot required!!
+            rtol: 1.e-16
+            stol: 0.0
+
+    fractionalstep:
+        scheme: 'CT'      # CT, IPCS
+        coupled_velocity: False     # False faster, True needed if robin_bc implicit
+        robin_bc_velocity_scheme: 'implicit' # explicit, semi-implicit, implicit
+        transpiration_bc_projection: 'robin'      # robin, dirichlet
+        flux_report_normalize_boundary: 1
+
+    T: 0.8       # end time
+    dt: 0.01
+    write_dt: 0.04
+    checkpoint_dt:  0.04 # <= 0: only last; else value + last
+    report: 1   # 0: print nothing, 1: print time step and writeout, 2: 1 + flux
+
+# solver setup
+fem:
+    velocity_space: p1  # p1 p1b/p1+ p2
+    pressure_space: p1  # p1 p0/dg0 dg1
+
+    strain_symmetric: False
+    convection_skew_symmetric: True    # aka Temam term
+    stabilization:
+        forced_normal:
+            enabled: True
+            boundaries: [6]
+            gamma: 10
+        backflow_boundaries: [3,4,5,6]
+        streamline_diffusion:
+            enabled: False
+            parameter: 'standard'   # standard, shakib, codina, klr
+            length_scale: 'metric' # average, max, metric
+            parameter_element_constant: True
+            Cinv: ~
+        monolithic:
+            infsup: 'pspg'    # pspg, pressure-stabilization
+            graddiv: False
+            consistent: False
+            pressure_stab_constant: 1.
+
+    fix_pressure: False
+    fix_pressure_point: [0., 0. , 0.]
+
+linear_solver:
+    method: 'lu'
+
+estimation:
+    boundary_conditions:
+        - 
+            id: 2
+            type: 'dirichlet'
+            parameters: 'U'
+            initial_stddev: 1
+
+    measurements:
+        -
+            mesh: './meshes/coaortaH1.h5'
+            fe_degree: 1
+            xdmf_file: 'results/aorta/measurements/u_all.xdmf'
+            file_root: 'results/aorta/measurements/u{i}.h5'
+            indices: 0 # indices of checkpoints to be processed. 0 == all
+            velocity_direction: ~
+            noise_stddev: 12.5     # standard deviation of Gaussian noise
+    
+    roukf:
+        particles: 'simplex' # unique or simplex
+        observation_operator: 'postprocessing'         #state or postprocessing
+        reparameterize: True

kalman/channel3d.yaml

@@ -5,12 +5,12 @@ fluid:
     dynamic_viscosity: 0.035
 
 io:
-    write_path: 'results/channel3d/'
+    write_path: 'results/channel3d/60/'
     restart:
         path: ''  # './projects/nse_coa3d/results/test_restart2/' 
         time: 0
     write_xdmf: True
-    write_checkpoints: True
+    write_checkpoints: False
     write_hdf5_timeseries: False
     write_velocity: 'update'     # update or tentative
 
@@ -26,7 +26,7 @@ boundary_conditions:
         type: 'dirichlet'
         value: ['0','0','U*(1-x[0]*x[0] - x[1]*x[1])*sin(DOLFIN_PI*t/T)']
         parameters:
-            U: 30
+            U: 60
             T: 0.9
             t: 0
     -    
@@ -111,7 +111,7 @@ estimation:
             file_root: 'results/channel3d/measurements/u{i}.h5'
             indices: 0 # indices of checkpoints to be processed. 0 == all
             velocity_direction: ~
-            noise_stddev: 1.0     # standard deviation of Gaussian noise
+            noise_stddev: 10.0     # standard deviation of Gaussian noise
     
     roukf:
         particles: 'simplex' # unique or simplex

kalman/graphics/figure1.py

@@ -0,0 +1,112 @@
+import matplotlib.pyplot as plt
+import numpy as np
+from itertools import cycle
+import argparse
+import pickle
+
+
+def is_ipython():
+    ''' Check if script is run in IPython.
+
+    Returns:
+        bool: True if IPython, else False '''
+    try:
+        get_ipython()
+        ipy = True
+    except NameError:
+        ipy = False
+
+    return ipy
+
+
+def load_data(file):
+    ''' Load numpy data from file.
+
+    Returns
+        dict: data dictionary
+    '''
+    dat = np.load(file)
+
+    return dat
+
+
+def plot_parameters(dat):
+    ''' Plot the parameters in separate subplots with uncertainties.
+
+    Args:
+        dat (dict):  data dictionary
+        deparameterize (bool):  flag indicating if parameters should be
+          deparameterized via 2**theta
+        ref:    reference value to be plotted with parameters
+    '''
+    if is_ipython():
+        plt.ion()
+
+
+    fig1, axes = plt.subplots(1, 1,figsize=(8,6))
+    axes.set_ylabel(r'$\theta$',fontsize=18)
+
+    col = cycle(['C0', 'C1', 'C2', 'C3'])
+    
+
+    for k in dat.keys():
+        
+        t = dat[k]['times']
+        theta = dat[k]['theta']
+        P = dat[k]['P_theta']
+
+                
+        theta = theta.reshape((-1, 1))
+        P = P.reshape((-1, 1, 1))
+        
+        #theta = 2**theta*float(k)
+        
+        sP = np.sqrt(P[:,0,0])
+        sP_up = 2**sP
+        sP_down = 2**(-sP)
+
+        col_ = next(col)
+        
+        axes.plot(t, theta[:, 0], '-', c=col_)
+        #axes.fill_between(t, theta[:, 0]*sP_down[:], theta[:, 0]*sP_up[:], alpha=0.3,color=col_)
+        axes.fill_between(t, theta[:, 0]  - np.sqrt(P[:, 0, 0]),theta[:, 0]  + np.sqrt(P[:, 0, 0]), alpha=0.3,color=col_)
+        axes.set_xlabel(r'time',fontsize=18)
+        axes.plot(t, t*0 + np.log(30/float(k))/np.log(2), '-', c='black',ls='--')
+
+        
+    axes.set_xlim([-0.01,0.2])
+    
+
+    if not is_ipython():
+        plt.show()
+
+
+def get_parser():
+    parser = argparse.ArgumentParser(
+        description='''
+Plot the time evolution of the ROUKF estimated parameters.
+
+To execute in IPython::
+
+    %run plot_roukf_parameters.py [-d] [-r N [N \
+...]] file
+''',
+        formatter_class=argparse.RawDescriptionHelpFormatter)
+    parser.add_argument('file', type=str, help='path to ROUKF stats file')
+    parser.add_argument('-d', '--deparameterize', action='store_true',
+                        help='deparameterize the parameters by 2**theta')
+    parser.add_argument('-r', '--ref', metavar='N', nargs='+', default=None,
+                        type=float, help='Reference values for parameters')
+    return parser
+
+
+if __name__ == '__main__':
+    args = get_parser().parse_args()
+    files = ['10','30','60']
+    dat_array = {}
+
+    for ff in files:
+        path = args.file + ff + '/theta_stats.npz'
+        dat_array[ff] = load_data(path)
+
+    plot_parameters(dat_array)

kalman/graphics/figure2.py

@@ -0,0 +1,135 @@
+import matplotlib.pyplot as plt
+import numpy as np
+from itertools import cycle
+import argparse
+import pickle
+import yaml
+
+def is_ipython():
+    ''' Check if script is run in IPython.
+
+    Returns:
+        bool: True if IPython, else False '''
+    try:
+        get_ipython()
+        ipy = True
+    except NameError:
+        ipy = False
+
+    return ipy
+
+
+def load_data(file):
+    ''' Load numpy data from file.
+
+    Returns
+        dict: data dictionary
+    '''
+    dat = np.load(file)
+
+    return dat
+
+
+def plot_parameters(dat, deparameterize=False, ref=None):
+    ''' Plot the parameters in separate subplots with uncertainties.
+
+    Args:
+        dat (dict):  data dictionary
+        deparameterize (bool):  flag indicating if parameters should be
+          deparameterized via 2**theta
+        ref:    reference value to be plotted with parameters
+    '''
+    if is_ipython():
+        plt.ion()
+
+
+    inputfile_path = 'results/aorta/input.yaml'
+    with open(inputfile_path) as file:
+        inputfile = yaml.full_load(file)
+
+    true_val = [10,250,250,250,30]
+    current_val = []
+    current_val.append(inputfile['boundary_conditions'][2]['value'][0])
+    current_val.append(inputfile['boundary_conditions'][3]['value'][0])
+    current_val.append(inputfile['boundary_conditions'][4]['value'][0])
+    current_val.append(inputfile['boundary_conditions'][5]['value'][0])
+    current_val.append(inputfile['boundary_conditions'][1]['parameters']['U'])
+    
+
+    dim = dat['theta'].shape[-1]
+    fig1, axes = plt.subplots(1,1,figsize=(8,6))
+
+
+
+    axes.set_ylabel(r'$\theta$',fontsize=18)
+
+    t = dat['times']
+    theta = dat['theta']
+    P = dat['P_theta']
+
+    col = cycle(['C0', 'C1', 'C2', 'C3','C4'])
+    ls = cycle(['-', '-', '--', '--', ':', ':', '-.', '-.'])
+    legends = cycle(['$R_3$','$R_4$','$R_5$','$R_6$','$U$'])
+
+    col_ = next(col)
+    ls_ = next(ls)
+    legends_=next(legends)
+
+    if dim == 1:
+        theta = theta.reshape((-1, 1))
+        P = P.reshape((-1, 1, 1))
+
+
+    for i in range(dim):
+        axes.plot(t, theta[:, i] + 1.5*i, '-', color=col_,label=legends_)
+        axes.fill_between(t, theta[:, i] + 1.5*i - np.sqrt(P[:, i, i]),
+                        theta[:, i] + 1.5*i + np.sqrt(P[:, i, i]), alpha=0.3,
+                        color=col_)
+        
+
+        true_level =  np.log(true_val[i]/current_val[i])/np.log(2)
+        axes.plot(t,1.5*i + t*0 + true_level , color=col_,ls='--')
+        col_ = next(col)
+        legends_=next(legends)
+
+    axes.legend(fontsize=14,loc='lower right')
+    axes.set_xlim([-0.01,0.81])
+    axes.set_xlabel(r'time (s)',fontsize=18)
+    # print('theta_peak: \t {}'.format(theta[round(len(theta)/2), :]))
+    print('Final value theta: \t {}'.format(theta[-1, :]))
+    print('Deparameterized: 2^theta_end: \t {}'.format(2**theta[-1, :]))
+    print('Real values: \t {}'.format(np.round(2**theta[-1, :]*current_val,2)))
+
+
+
+    plt.savefig('windk_res')
+    if not is_ipython():
+        plt.show()
+
+
+def get_parser():
+    parser = argparse.ArgumentParser(
+        description='''
+Plot the time evolution of the ROUKF estimated parameters.
+
+To execute in IPython::
+
+    %run plot_roukf_parameters.py [-d] [-r N [N \
+...]] file
+''',
+        formatter_class=argparse.RawDescriptionHelpFormatter)
+    parser.add_argument('file', type=str, help='path to ROUKF stats file')
+    parser.add_argument('-d', '--deparameterize', action='store_true',
+                        help='deparameterize the parameters by 2**theta')
+    parser.add_argument('-r', '--ref', metavar='N', nargs='+', default=None,
+                        type=float, help='Reference values for parameters')
+
+    return parser
+
+
+if __name__ == '__main__':
+    args = get_parser().parse_args()
+
+    dat = load_data(args.file)
+
+    plot_parameters(dat, deparameterize=args.deparameterize, ref=args.ref)