how to get reproducible result in Tensorflow - random

I built 5-layer neural network by using tensorflow.
I have a problem to get reproducible results (or stable results).
I found similar questions regarding reproducibility of tensorflow and the corresponding answers, such as How to get stable results with TensorFlow, setting random seed
But the problem is not solved yet.
I also set random seed like the following
tf.set_random_seed(1)
Furthermore, I added seed options to every random function such as
b1 = tf.Variable(tf.random_normal([nHidden1], seed=1234))
I confirmed that the first epoch shows the identical results, but not identical from the second epoch little by little.
How can I get the reproducible results?
Am I missing something?
Here is a code block I use.
def xavier_init(n_inputs, n_outputs, uniform=True):
if uniform:
init_range = tf.sqrt(6.0 / (n_inputs + n_outputs))
return tf.random_uniform_initializer(-init_range, init_range, seed=1234)
else:
stddev = tf.sqrt(3.0 / (n_inputs + n_outputs))
return tf.truncated_normal_initializer(stddev=stddev, seed=1234)
import numpy as np
import tensorflow as tf
import dataSetup
from scipy.stats.stats import pearsonr
tf.set_random_seed(1)
x_train, y_train, x_test, y_test = dataSetup.input_data()
# Parameters
learningRate = 0.01
trainingEpochs = 1000000
batchSize = 64
displayStep = 100
thresholdReduce = 1e-6
thresholdNow = 0.6
#dropoutRate = tf.constant(0.7)
# Network Parameter
nHidden1 = 128 # number of 1st layer nodes
nHidden2 = 64 # number of 2nd layer nodes
nInput = 24 #
nOutput = 1 # Predicted score: 1 output for regression
# save parameter
modelPath = 'model/model_layer5_%d_%d_mini%d_lr%.3f_noDrop_rollBack.ckpt' %(nHidden1, nHidden2, batchSize, learningRate)
# tf Graph input
X = tf.placeholder("float", [None, nInput])
Y = tf.placeholder("float", [None, nOutput])
# Weight
W1 = tf.get_variable("W1", shape=[nInput, nHidden1], initializer=xavier_init(nInput, nHidden1))
W2 = tf.get_variable("W2", shape=[nHidden1, nHidden2], initializer=xavier_init(nHidden1, nHidden2))
W3 = tf.get_variable("W3", shape=[nHidden2, nHidden2], initializer=xavier_init(nHidden2, nHidden2))
W4 = tf.get_variable("W4", shape=[nHidden2, nHidden2], initializer=xavier_init(nHidden2, nHidden2))
WFinal = tf.get_variable("WFinal", shape=[nHidden2, nOutput], initializer=xavier_init(nHidden2, nOutput))
# biases
b1 = tf.Variable(tf.random_normal([nHidden1], seed=1234))
b2 = tf.Variable(tf.random_normal([nHidden2], seed=1234))
b3 = tf.Variable(tf.random_normal([nHidden2], seed=1234))
b4 = tf.Variable(tf.random_normal([nHidden2], seed=1234))
bFinal = tf.Variable(tf.random_normal([nOutput], seed=1234))
# Layers for dropout
L1 = tf.nn.relu(tf.add(tf.matmul(X, W1), b1))
L2 = tf.nn.relu(tf.add(tf.matmul(L1, W2), b2))
L3 = tf.nn.relu(tf.add(tf.matmul(L2, W3), b3))
L4 = tf.nn.relu(tf.add(tf.matmul(L3, W4), b4))
hypothesis = tf.add(tf.matmul(L4, WFinal), bFinal)
print "Layer setting DONE..."
# define loss and optimizer
cost = tf.reduce_mean(tf.square(hypothesis - Y))
optimizer = tf.train.AdamOptimizer(learning_rate=learningRate).minimize(cost)
# Initialize the variable
init = tf.initialize_all_variables()
# save op to save and restore all the variables
saver = tf.train.Saver()
with tf.Session() as sess:
# initialize
sess.run(init)
print "Initialize DONE..."
# Training
costPrevious = 100000000000000.0
best = float("INF")
totalBatch = int(len(x_train)/batchSize)
print "Total Batch: %d" %totalBatch
for epoch in range(trainingEpochs):
#print "EPOCH: %04d" %epoch
avgCost = 0.
for i in range(totalBatch):
np.random.seed(i+epoch)
randidx = np.random.randint(len(x_train), size=batchSize)
batch_xs = x_train[randidx,:]
batch_ys = y_train[randidx,:]
# Fit traiing using batch data
sess.run(optimizer, feed_dict={X:batch_xs, Y:batch_ys})
# compute average loss
avgCost += sess.run(cost, feed_dict={X:batch_xs, Y:batch_ys})/totalBatch
# compare the current cost and the previous
# if current cost > the previous
# just continue and make the learning rate half
#print "Cost: %1.8f --> %1.8f at epoch %05d" %(costPrevious, avgCost, epoch+1)
if avgCost > costPrevious + .5:
#sess.run(init)
load_path = saver.restore(sess, modelPath)
print "Cost increases at the epoch %05d" %(epoch+1)
print "Cost: %1.8f --> %1.8f" %(costPrevious, avgCost)
continue
costNow = avgCost
reduceCost = abs(costPrevious - costNow)
costPrevious = costNow
#Display logs per epoch step
if costNow < best:
best = costNow
bestMatch = sess.run(hypothesis, feed_dict={X:x_test})
# model save
save_path = saver.save(sess, modelPath)
if epoch % displayStep == 0:
print "step {}".format(epoch)
pearson = np.corrcoef(bestMatch.flatten(), y_test.flatten())
print 'train loss = {}, current loss = {}, test corrcoef={}'.format(best, costNow, pearson[0][1])
if reduceCost < thresholdReduce or costNow < thresholdNow:
print "Epoch: %04d, Cost: %.9f, Prev: %.9f, Reduce: %.9f" %(epoch+1, costNow, costPrevious, reduceCost)
break
print "Optimization Finished"

It seems that your results are perhaps not reproducible because you are using Saver to write/restore from checkpoint each time? (i.e. the second time that you run the code, the variable values aren't initialized using your random seed -- they are restored from your previous checkpoint)
Please trim down your code example to just the code necessary to reproduce irreproducibility.

Related

Comparing Biweekly HFMD Cases with and without using the Squared Error Objective & L1-Norm Objective

I wish to model the biweekly HFMD cases in Malaysia.
Then, I want to show that the model using the Squared Error Objective and L1-Norm Objective can better model the biweekly HFMD cases than the model without objectives.
My question is, is it possible to model the biweekly HFMD cases without using the Squared Error Objective and L1-Norm Objective?
With this, I have attached the coding below:
from gekko import GEKKO
import numpy as np
import matplotlib.pyplot as plt
m1 = GEKKO(remote=False)
m2 = GEKKO(remote=False)
m = m1
# Known parameters
nb = 26 # Number of biweeks in a year
ny = 3 # Number of years
biweeks = np.zeros((nb,ny*nb+1))
biweeks[0][0] = 1
for i in range(nb):
for j in range(ny):
biweeks[i][j*nb+i+1] = 1
# Write csv data file
tm = np.linspace(0,78,79)
# case data
# Malaysia weekly HFMD data from the year 2013 - 2015
cases = np.array([506,506,700,890,1158,1605,1694,1311,1490,1310,1368,\
1009,1097,934,866,670,408,481,637,749,700,648,710,\
740,627,507,516,548,636,750,1066,1339,1565,\
1464,1575,1759,1631,1601,1227,794,774,623,411,\
750,1017,976,1258,1290,1546,1662,1720,1553,1787,1291,1712,2227,2132,\
2550,2140,1645,1743,1296,1153,871,621,570,388,\
347,391,446,442,390,399,421,398,452,470,437,411])
data = np.vstack((tm,cases))
data = data.T
# np.savetxt('measles_biweek_2.csv',data,delimiter=',',header='time,cases')
np.savetxt('hfmd_biweek_2.csv',data,delimiter=',',header='time,cases')
# Load data from csv
# m.time, cases_meas = np.loadtxt('measles_biweek_2.csv', \
m.time, cases_hfmd = np.loadtxt('hfmd_biweek_2.csv', \
delimiter=',',skiprows=1,unpack=True)
# m.Vr = m.Param(value = 0)
# Variables
# m.N = m.FV(value = 3.2e6)
# m.mu = m.FV(value = 7.8e-4)
# m.N = m.FV(value = 3.11861e7)
# m.mu = m.FV(value = 6.42712e-4)
m.N = m.FV(value = 3.16141e7) # Malaysia average total population (2015 - 2017)
m.mu = m.FV(value = 6.237171519e-4) # Malaysia scaled birth rate (births/biweek/total population)
m.rep_frac = m.FV(value = 0.45) # Percentage of underreporting
# Beta values (unknown parameters in the model)
m.beta = [m.FV(value=1, lb=0.1, ub=5) for i in range(nb)]
# Predicted values
m.S = m.SV(value = 0.162492875*m.N.value, lb=0,ub=m.N) # Susceptibles (Kids from 0 - 9 YO: 5137066 people) - Average of 94.88% from total reported cases
m.I = m.SV(value = 7.907863896e-5*m.N.value, lb=0,ub=m.N) #
# m.V = m.Var(value = 2e5)
# measured values
m.cases = m.CV(value = cases_hfmd, lb=0)
# turn on feedback status for CASES
m.cases.FSTATUS = 1
# weight on prior model predictions
m.cases.WMODEL = 0
# meas_gap = deadband that represents level of
# accuracy / measurement noise
db = 100
m.cases.MEAS_GAP = db
for i in range(nb):
m.beta[i].STATUS=1
#m.gamma = m.FV(value=0.07)
m.gamma = m.FV(value=0.07)
m.gamma.STATUS = 1
m.gamma.LOWER = 0.05
m.gamma.UPPER = 0.5
m.biweek=[None]*nb
for i in range(nb):
m.biweek[i] = m.Param(value=biweeks[i])
# Intermediate
m.Rs = m.Intermediate(m.S*m.I/m.N)
# Equations
sum_biweek = sum([m.biweek[i]*m.beta[i]*m.Rs for i in range(nb)])
# m.Equation(m.S.dt()== -sum_biweek + m.mu*m.N - m.Vr)
m.Equation(m.S.dt()== -sum_biweek + m.mu*m.N)
m.Equation(m.I.dt()== sum_biweek - m.gamma*m.I)
m.Equation(m.cases == m.rep_frac*sum_biweek)
# m.Equation(m.V.dt()==-m.Vr)
# options
m.options.SOLVER = 1
m.options.NODES=3
# imode = 5, dynamic estimation
m.options.IMODE = 5
# ev_type = 1 (L1-norm) or 2 (squared error)
m.options.EV_TYPE = 2
# solve model and print solver output
m.solve()
[print('beta['+str(i+1)+'] = '+str(m.beta[i][0])) \
for i in range(nb)]
print('gamma = '+str(m.gamma.value[0]))
# export data
# stack time and avg as column vectors
my_data = np.vstack((m.time,np.asarray(m.beta),m.gamma))
# transpose data
my_data = my_data.T
# save text file with comma delimiter
beta_str = ''
for i in range(nb):
beta_str = beta_str + ',beta[' + str(i+1) + ']'
header_name = 'time,gamma' + beta_str
##np.savetxt('solution_data.csv',my_data,delimiter=',',\
## header = header_name, comments='')
np.savetxt('solution_data_EVTYPE_'+str(m.options.EV_TYPE)+\
'_gamma'+str(m.gamma.STATUS)+'.csv',\
my_data,delimiter=',',header = header_name)
plt.figure(num=1, figsize=(16,8))
plt.suptitle('Estimation')
plt.subplot(2,2,1)
plt.plot(m.time,m.cases, label='Cases (model)')
plt.plot(m.time,cases_hfmd, label='Cases (measured)')
if m.options.EV_TYPE==2:
plt.plot(m.time,cases_hfmd+db/2, 'k-.',\
lw=0.5, label=r'$Cases_{db-hi}$')
plt.plot(m.time,cases_hfmd-db/2, 'k-.',\
lw=0.5, label=r'$Cases_{db-lo}$')
plt.fill_between(m.time,cases_hfmd-db/2,\
cases_hfmd+db/2,color='gold',alpha=.5)
plt.legend(loc='best')
plt.ylabel('Cases')
plt.subplot(2,2,2)
plt.plot(m.time,m.S,'r--')
plt.ylabel('S')
plt.subplot(2,2,3)
[plt.plot(m.time,m.beta[i], label='_nolegend_')\
for i in range(nb)]
plt.plot(m.time,m.gamma,'c--', label=r'$\gamma$')
plt.legend(loc='best')
plt.ylabel(r'$\beta, \gamma$')
plt.xlabel('Time')
plt.subplot(2,2,4)
plt.plot(m.time,m.I,'g--')
plt.xlabel('Time')
plt.ylabel('I')
plt.subplots_adjust(hspace=0.2,wspace=0.4)
name = 'cases_EVTYPE_'+ str(m.options.EV_TYPE) +\
'_gamma' + str(m.gamma.STATUS) + '.png'
plt.savefig(name)
plt.show()
To define a custom objective, use the m.Minimize() or m.Maximize() functions instead of the squared error or l1-norm objectives that are built into the m.CV() objects. To create a custom objective, use m.Var() instead of m.CV() such as:
from gekko import GEKKO
import numpy as np
m = GEKKO()
x = m.Array(m.Var,4,value=1,lb=1,ub=5)
x1,x2,x3,x4 = x
# change initial values
x2.value = 5; x3.value = 5
m.Equation(x1*x2*x3*x4>=25)
m.Equation(x1**2+x2**2+x3**2+x4**2==40)
m.Minimize(x1*x4*(x1+x2+x3)+x3)
m.solve()
print('x: ', x)
print('Objective: ',m.options.OBJFCNVAL)
Here is a similar problem with disease prediction (Measles) that uses m.CV().
import numpy as np
from gekko import GEKKO
import matplotlib.pyplot as plt
# Import Data
# write csv data file
t_s = np.linspace(0,78,79)
# case data
cases_s = np.array([180,180,271,423,465,523,649,624,556,420,\
423,488,441,268,260,163,83,60,41,48,65,82,\
145,122,194,237,318,450,671,1387,1617,2058,\
3099,3340,2965,1873,1641,1122,884,591,427,282,\
174,127,84,97,68,88,79,58,85,75,121,174,209,458,\
742,929,1027,1411,1885,2110,1764,2001,2154,1843,\
1427,970,726,416,218,160,160,188,224,298,436,482,468])
# Initialize gekko model
m = GEKKO()
# Number of collocation nodes
nodes = 4
# Number of phases (years in this case)
n = 3
#Biweek periods per year
bi = 26
# Time horizon (for all 3 phases)
m.time = np.linspace(0,1,bi+1)
# Parameters that will repeat each year
N = m.Param(3.2e6)
mu = m.Param(7.8e-4)
rep_frac = m.Param(0.45)
Vr = m.Param(0)
beta = m.MV(2,lb = 0.1)
beta.STATUS = 1
gamma = m.FV(value=0.07)
gamma.STATUS = 1
gamma.LOWER = 0.05
gamma.UPPER = 0.5
# Data used to control objective function
casesobj1 = m.Param(cases_s[0:(bi+1)])
casesobj2 = m.Param(cases_s[bi:(2*bi+1)])
casesobj3 = m.Param(cases_s[2*bi:(3*bi+1)])
# Variables that vary between years, one version for each year
cases = [m.CV(value = cases_s[(i*bi):(i+1)*(bi+1)-i],lb=0) for i in range(n)]
for i in cases:
i.FSTATUS = 1
i.WMODEL = 0
i.MEAS_GAP = 100
S = [m.Var(0.06*N,lb = 0,ub = N) for i in range(n)]
I = [m.Var(0.001*N, lb = 0,ub = N) for i in range(n)]
V = [m.Var(2e5) for i in range(n)]
# Equations (created for each year)
for i in range(n):
R = m.Intermediate(beta*S[i]*I[i]/N)
m.Equation(S[i].dt() == -R + mu*N - Vr)
m.Equation(I[i].dt() == R - gamma*I[i])
m.Equation(cases[i] == rep_frac*R)
m.Equation(V[i].dt() == -Vr)
# Connect years together at endpoints
for i in range(n-1):
m.Connection(cases[i+1],cases[i],1,bi,1,nodes)#,1,nodes)
m.Connection(cases[i+1],'CALCULATED',pos1=1,node1=1)
m.Connection(S[i+1],S[i],1,bi,1,nodes)
m.Connection(S[i+1],'CALCULATED',pos1=1,node1=1)
m.Connection(I[i+1],I[i],1,bi,1,nodes)
m.Connection(I[i+1],'CALCULATED',pos1=1, node1=1)
# Solver options
m.options.IMODE = 5
m.options.NODES = nodes
m.EV_TYPE = 1
m.options.SOLVER = 1
# Solve
m.Obj(2*(casesobj1-cases[0])**2+(casesobj3-cases[2])**2)
m.solve()
# Calculate the start time of each phase
ts = np.linspace(1,n,n)
# Plot
plt.figure()
plt.subplot(4,1,1)
tm = np.empty(len(m.time))
for i in range(n):
tm = m.time + ts[i]
plt.plot(tm,cases[i].value,label='Cases Year %s'%(i+1))
plt.plot(tm,cases_s[(i*bi):(i+1)*(bi+1)-i],'.')
plt.legend()
plt.ylabel('Cases')
plt.subplot(4,1,2)
for i in range(n):
tm = m.time + ts[i]
plt.plot(tm,beta.value,label='Beta Year %s'%(i+1))
plt.legend()
plt.ylabel('Contact Rate')
plt.subplot(4,1,3)
for i in range(n):
tm = m.time + ts[i]
plt.plot(tm,I[i].value,label='I Year %s'%(i+1))
plt.legend()
plt.ylabel('Infectives')
plt.subplot(4,1,4)
for i in range(n):
tm = m.time + ts[i]
plt.plot(tm,S[i].value,label='S Year %s'%(i+1))
plt.legend()
plt.ylabel('Susceptibles')
plt.xlabel('Time (yr)')
plt.show()

Using GEKKO for Moving Horizon Estimation online 2

This is the following question after appyling comments from: Using GEKKO for Moving Horizon Estimation online
I have studied example from estimation iterative example on the Dynamic Optimization course website and revised my code as follows:
from gekko import GEKKO
import numpy as np
import matplotlib.pyplot as plt
import matplotlib; matplotlib.use('TkAgg')
class Observer():
def __init__(self, window_size, r_init, alpha_init):
self.m = GEKKO(remote=False)
self.dt = 0.05
self.m.time = [i*self.dt for i in range(window_size)]
#Parameters
self.m.u = self.m.MV()
#Variables
self.m.r = self.m.CV(lb=0) # value=r_init) #ub=20 can be over 20
self.m.alpha = self.m.CV() # value=alpha_init) #ub lb for angle?
#Equations
self.m.Equation(self.m.r.dt()== -self.m.cos(self.m.alpha))
self.m.Equation(self.m.alpha.dt()== self.m.sin(self.m.alpha)/self.m.r - self.m.u) # differential equation
#Options
self.m.options.MV_STEP_HOR = 2
self.m.options.IMODE = 5 # dynamic estimation
self.m.options.EV_TYPE = 2 #Default 1: absolute error form 2: squared error form
self.m.options.DIAGLEVEL = 0 #diagnostic level
self.m.options.NODES = 5 #nodes # collocation nodes default:2
self.m.options.SOLVER = 3 #solver_num
# STATUS = 0, optimizer doesn't adjust value
# STATUS = 1, optimizer can adjust
self.m.u.STATUS = 0
self.m.r.STATUS = 1
self.m.alpha.STATUS = 1
# FSTATUS = 0, no measurement
# FSTATUS = 1, measurement used to update model
self.m.u.FSTATUS = 1 #default
self.m.r.FSTATUS = 1
self.m.alpha.FSTATUS = 1
self.m.r.TR_INIT = 0
self.m.alpha.TR_INIT = 0
self.count = 0
def MHE(self, observed_state, u_data):
self.count =+ 1
self.m.u.MEAS = u_data
self.m.r.MEAS = observed_state[0]
self.m.alpha.MEAS = observed_state[1]
self.m.solve(disp=False)
return self.m.r.MODEL, self.m.alpha.MODEL
if __name__=="__main__":
FILE_PATH00 = '/home/shane16/Project/model_guard/uav_paper/adversarial/SA_PPO/src/DATA/4end_estimation_results_r.csv'
FILE_PATH01 = '/home/shane16/Project/model_guard/uav_paper/adversarial/SA_PPO/src/DATA/4end_estimation_results_alpha.csv'
FILE_PATH02 = '/home/shane16/Project/model_guard/uav_paper/adversarial/SA_PPO/src/DATA/4end_action_buffer_eps0.0_sig0.0.csv'
cycles = 55
x = np.arange(cycles) # 1...300
matrix00 = np.loadtxt(FILE_PATH00, delimiter=',')
matrix01 = np.loadtxt(FILE_PATH01, delimiter=',')
matrix02 = np.loadtxt(FILE_PATH02, delimiter=',')
vanilla_action_sigma_0 = matrix02
vanilla_estimation_matrix_r = np.zeros(cycles)
vanilla_estimation_matrix_alpha = np.zeros(cycles)
# sigma = 0.0
# vanilla model true/observed states
r_vanilla_sigma_0_true = matrix00[0, 3:] # from step 1
r_vanilla_sigma_0_observed = matrix00[1, 3:] # from step1
alpha_vanilla_sigma_0_true = matrix01[0, 3:]
alpha_vanilla_sigma_0_observed = matrix01[1, 3:]
# initialize estimator
sigma = 0.0 #1.0
solver_num = 3
nodes = 5
# for window_size in [5, 10, 20, 30, 40, 50]:
window_size = 5
observer = Observer(window_size, r_vanilla_sigma_0_observed[0], alpha_vanilla_sigma_0_observed[0])
for i in range(cycles):
if i % 100 == 0:
print('cylcle: {}'.format(i))
vanilla_observed_states = np.hstack((r_vanilla_sigma_0_observed[i], alpha_vanilla_sigma_0_observed[i])) # from current observed state
r_hat, alpha_hat = observer.MHE(vanilla_observed_states, vanilla_action_sigma_0[i]) # and current action -> estimate current state
vanilla_estimation_matrix_r[i] = r_hat
vanilla_estimation_matrix_alpha[i] = alpha_hat
#plot vanilla
plt.figure()
plt.subplot(3,1,1)
plt.title('Vanilla model_sig{}'.format(sigma))
plt.plot(x, vanilla_action_sigma_0[:cycles],'b:',label='action (w)')
plt.legend()
plt.subplot(3,1,2)
plt.ylabel('r')
plt.plot(x, r_vanilla_sigma_0_true[:cycles], 'k-', label='true_r')
plt.plot(x, r_vanilla_sigma_0_observed[:cycles], 'gx', label='observed_r')
plt.plot(x, vanilla_estimation_matrix_r, 'r--', label='time window: 10')
# plt.legend()
plt.subplot(3,1,3)
plt.xlabel('time steps')
plt.ylabel('alpha')
plt.plot(x, alpha_vanilla_sigma_0_true[:cycles], 'k-', label='true_alpha')
plt.plot(x, alpha_vanilla_sigma_0_observed[:cycles], 'gx', label='observed_alpha')
plt.plot(x, vanilla_estimation_matrix_alpha, 'r--', label='time window: {}'.format(window_size))
plt.legend()
plt.savefig('plot/revision/4estimated_STATES_vanilla_sig{}_window{}_cycles{}_solver{}_nodes{}.png'.format(sigma, window_size,cycles, solver_num, nodes))
plt.show()
csv files: https://drive.google.com/drive/folders/1jW_6zBCdbJHB7yU3HmCIhamEyOT1LJqD?usp=sharing
The code works when initialized with values specified at line 15,16 (m.r, m.alpha).
However, if I try with no initial value,(as same condition in example), solution is not found.
terminal output:
cylcle: 0 Traceback (most recent call last): File
"4observer_mhe.py", line 86, in
r_hat, alpha_hat = observer.MHE(vanilla_observed_states, vanilla_action_sigma_0[i]) # and current action -> estimate current
state File "4observer_mhe.py", line 49, in MHE
self.m.solve(disp=False) File "/home/shane16/Project/model_guard/LipSDP/lipenv/lib/python3.7/site-packages/gekko/gekko.py",
line 2140, in solve
raise Exception(apm_error) Exception: #error: Solution Not Found
What could be the solution to this problem?
I have tried below strategies, but couldn't find the solution.
Reduce the number of decision variables by using m.FV() or m.MV() with m.options.MV_STEP_HOR=2+ to reduce the degrees of freedom for the solver for the unknown parameters.
Try other solvers with m.options.SOLVER=1 or m.options.SOLVER=2.
I expect to see estimation results that follow the true state well.
But I guess I'm doing something wrong.
Could anyone help me please?
Thank you.
Solvers sometimes need good initial guess values or constraints (lower and upper bounds) on the degrees of freedom (MV or FV) to find the optimal solution.
One of the equations may be the source of the problem:
self.m.alpha.dt() == self.m.sin(self.m.alpha)/self.m.r - self.m.u
The initial value of r is zero (default) because no initial value is provided when it is declared as self.m.r = self.m.CV(lb=0). A comment suggests that it was formerly initialized with value r_init. The zero value creates a divide-by-zero for that equation. Try rearranging the equation into an equivalent form that avoids the potential for divide-by-zero either with the initial guess or when the solver is iterating.
self.m.r*self.m.alpha.dt() == self.m.sin(self.m.alpha) - self.m.r*self.m.u
There may be other things that are also causing the model to not converge. When the solution does not converge then the infeasibilities.txt file can be a source to troubleshoot the specific equations that are having trouble. Here are instructions to retrieve the infeasibilities.txt file: How to retrieve the 'infeasibilities.txt' from the gekko

How to add MV overshoot as a constraint in optimal PID parameters estimation problem?

This question is related to this my previous question how to formulate the problem of finding the optimal PID paramters in gekko?
I have successfully estimated the optimal PID parameters by minimizing the IAE based on the answer to the above question. However, I would like to add a constraint of MV overshoot in the objective function. Below is the pseudo code to add the constraint that the MV overshoot should be less than 10 % .
MV_Overshoot= Max_MV - SteadyState_MV
MV_Overshoot < 0.1*Steady_State MV # constraint
However, I am stuck with the 2 questions below
How to find the steady state_MV ?
How to find the maximum MV from MV array ?
or is there any better way to calculate the MV overshoot ?
Solve a first step with a steady state calculation to determine the OP (MV) and PV values.
from gekko import GEKKO
import numpy as np
import matplotlib.pyplot as plt
# Process model
Kp = 0.5 # process gain
tauP = 10.0 # process time constant
# pre-solve for steady state values
m = GEKKO()
OP = m.Var(value=0.0) # controller output (MV)
PV = m.Var(value=0.0) # process variable
SP = m.Param(value=5.0) # final set point
m.Equation(SP==PV) # assume PV reaches set point
m.Equation(tauP*PV.dt() + PV == Kp*OP)
m.options.IMODE = 1
m.solve(disp=False)
print('Steady state target values')
print('OP: ' + str(OP.value[0]))
print('PV: ' + str(PV.value[0]))
print('SP: ' + str(SP.value[0]))
PV_ss = PV.value[0]
OP_ss = OP.value[0]
Solve a second step to optimize the tuning parameters to stay under the requested overshoot targets. Overshoot is typically defined in terms of the distance above the setpoint, not the amount over the MV target. Both are included in the example.
# dynamic optimization of controller tuning
m = GEKKO()
tf = 40
m.time = np.linspace(0,tf,2*tf+1)
step = np.zeros(2*tf+1)
step[3:40] = 0.0
step[40:] = 5.0
# Controller model
Kc = m.FV(15.0,lb=0,ub=100) # controller gain
tauI = m.FV(100.0,lb=0.01,ub=100) # controller reset time
tauD = m.FV(0.0,lb=0,ub=100) # derivative constant
Kc.STATUS = 1; tauI.STATUS = 1; tauD.STATUS = 1
OP_0 = m.Const(value=0.0) # OP bias
OP = m.Var(value=0.0,ub=OP_ss*1.1) # controller output
# with overshoot bound on OP (MV)
PV = m.Var(value=0.0,ub=PV_ss*1.1) # process variable
# with overshoot bound on PV
SP = m.Param(value=step) # set point
Intgl = m.Var(value=0.0) # integral of the error
err = m.Intermediate(SP-PV) # set point error
m.Equation(Intgl.dt()==err) # integral of the error
m.Equation(OP == OP_0 + Kc*err + (Kc/tauI)*Intgl - PV.dt())
m.Equation(tauP*PV.dt() + PV == Kp*OP)
m.Minimize((SP-PV)**2)
m.options.IMODE=6
m.solve(disp=False)
print('Tuning values')
print('Kc: ' + str(Kc.value[0]))
print('tauI: ' + str(tauI.value[0]))
print('tauD: ' + str(tauD.value[0]))
plt.figure()
plt.subplot(2,1,1)
plt.plot([0,max(m.time)],[1.1*OP_ss,1.1*OP_ss],\
'b-',label='Upper bound')
plt.plot(m.time,OP.value,'b:',label='OP')
plt.ylabel('Output')
plt.legend()
plt.subplot(2,1,2)
plt.plot(m.time,SP.value,'k-',label='SP')
plt.plot(m.time,PV.value,'r--',label='PV')
plt.plot([0,max(m.time)],[1.1*PV_ss,1.1*PV_ss],\
'b-',label='Upper bound')
plt.xlabel('Time (sec)')
plt.ylabel('Process')
plt.legend()
plt.show()

Fit Amplitude (Frequency response) of a capacitor with lmfit

I am trying to fit measured data with lmfit.
My goal is to get the parameters of the capacitor with an equivalent circuit diagram.
So, I want to create a model with parameters (C, R1, L1,...) and fit it to the measured data.
I know that the resonance frequency is at the global minimum and there must also be R1. Also known is C.
So I could fix the parameter C and R1. With the resonance frequency I could calculate L1 too.
I created the model, but the fit doesn't work right.
Maybe someone could help me with this.
Thanks in advance.
from lmfit import minimize, Parameters
from lmfit import report_fit
params = Parameters()
params.add('C', value = 220e-9, vary = False)
params.add('L1', value = 0.00001, min = 0, max = 0.1)
params.add('R1', value = globalmin, vary = False)
params.add('Rp', value = 10000, min = 0, max = 10e20)
params.add('Cp', value = 0.1, min = 0, max = 0.1)
def get_elements(params, freq, data):
C = params['C'].value
L1 = params['L1'].value
R1 = params['R1'].value
Rp = params['Rp'].value
Cp = params['Cp'].value
XC = 1/(1j*2*np.pi*freq*C)
XL = 1j*2*np.pi*freq*L1
XP = 1/(1j*2*np.pi*freq*Cp)
Z1 = R1 + XC*Rp/(XC+Rp) + XL
real = np.real(Z1*XP/(Z1+XP))
imag = np.imag(Z1*XP/(Z1+XP))
model = np.sqrt(real**2 + imag**2)
#model = np.sqrt(R1**2 + ((2*np.pi*freq*L1 - 1/(2*np.pi*freq*C))**2))
#model = (np.arctan((2*np.pi*freq*L1 - 1/(2*np.pi*freq*C))/R1)) * 360/((2*np.pi))
return data - model
out = minimize(get_elements, params , args=(freq, data))
report_fit(out)
#make reconstruction for plotting
C = out.params['C'].value
L1 = out.params['L1'].value
R1 = out.params['R1'].value
Rp = out.params['Rp'].value
Cp = out.params['Cp'].value
XC = 1/(1j*2*np.pi*freq*C)
XL = 1j*2*np.pi*freq*L1
XP = 1/(1j*2*np.pi*freq*Cp)
Z1 = R1 + XC*Rp/(XC+Rp) + XL
real = np.real(Z1*XP/(Z1+XP))
imag = np.imag(Z1*XP/(Z1+XP))
reconst = np.sqrt(real**2 + imag**2)
reconst_phase = np.arctan(imag/real)* 360/(2*np.pi)
'''
PLOTTING
'''
#plot of filtred signal vs measered data (AMPLITUDE)
fig = plt.figure(figsize=(40,15))
file_title = 'Measured Data'
plt.subplot(311)
plt.xscale('log')
plt.yscale('log')
plt.xlim([min(freq), max(freq)])
plt.ylabel('Amplitude')
plt.xlabel('Frequency in Hz')
plt.grid(True, which="both")
plt.plot(freq, z12_fac, 'g', alpha = 0.7, label = 'data')
#Plot Impedance of model in magenta
plt.plot(freq, reconst, 'm', label='Reconstruction (Model)')
plt.legend()
#(PHASE)
plt.subplot(312)
plt.xscale('log')
plt.xlim([min(freq), max(freq)])
plt.ylabel('Phase in °')
plt.xlabel('Frequency in Hz')
plt.grid(True, which="both")
plt.plot(freq, z12_deg, 'g', alpha = 0.7, label = 'data')
#Plot Phase of model in magenta
plt.plot(freq, reconst_phase, 'm', label='Reconstruction (Model)')
plt.legend()
plt.savefig(file_title)
plt.close(fig)
measured data
equivalent circuit diagram (model)
Edit 1:
Fit-Report:
[[Fit Statistics]]
# fitting method = leastsq
# function evals = 28
# data points = 4001
# variables = 3
chi-square = 1197180.70
reduced chi-square = 299.444897
Akaike info crit = 22816.4225
Bayesian info crit = 22835.3054
## Warning: uncertainties could not be estimated:
L1: at initial value
Rp: at boundary
Cp: at initial value
Cp: at boundary
[[Variables]]
C: 2.2e-07 (fixed)
L1: 1.0000e-05 (init = 1e-05)
R1: 0.06375191 (fixed)
Rp: 0.00000000 (init = 10000)
Cp: 0.10000000 (init = 0.1)
Edit 2:
Data can be found here:
https://1drv.ms/u/s!AsLKp-1R8HlZhcdlJER5T7qjmvfmnw?e=r8G2nN
Edit 3:
I now have simplified my model to a simple RLC-series. With a another set of data this works pretty good. see here the plot with another set of data
def get_elements(params, freq, data):
C = params['C'].value
L1 = params['L1'].value
R1 = params['R1'].value
#Rp = params['Rp'].value
#Cp = params['Cp'].value
#k = params['k'].value
#freq = np.log10(freq)
XC = 1/(1j*2*np.pi*freq*C)
XL = 1j*2*np.pi*freq*L1
# XP = 1/(1j*2*np.pi*freq*Cp)
# Z1 = R1*k + XC*Rp/(XC+Rp) + XL
# real = np.real(Z1*XP/(Z1+XP))
# imag = np.imag(Z1*XP/(Z1+XP))
Z1 = R1 + XC + XL
real = np.real(Z1)
imag= np.imag(Z1)
model = np.sqrt(real**2 + imag**2)
return np.sqrt(np.real(data)**2+np.imag(data)**2) - model
out = minimize(get_elements, params , args=(freq, data))
Report:
Chi-Square is really high...
[[Fit Statistics]]
# fitting method = leastsq
# function evals = 25
# data points = 4001
# variables = 2
chi-square = 5.0375e+08
reduced chi-square = 125968.118
Akaike info crit = 46988.8798
Bayesian info crit = 47001.4684
[[Variables]]
C: 3.3e-09 (fixed)
L1: 5.2066e-09 +/- 1.3906e-08 (267.09%) (init = 1e-05)
R1: 0.40753691 +/- 24.5685882 (6028.56%) (init = 0.05)
[[Correlations]] (unreported correlations are < 0.100)
C(L1, R1) = -0.174
With my originally set of data I get this:
plot original data (complex)
Which is not bad, but also not good. That's why I want to make my model more detailed, so I can fit also in higher frequency regions...
Report of this one:
[[Fit Statistics]]
# fitting method = leastsq
# function evals = 25
# data points = 4001
# variables = 2
chi-square = 109156.170
reduced chi-square = 27.2958664
Akaike info crit = 13232.2473
Bayesian info crit = 13244.8359
[[Variables]]
C: 2.2e-07 (fixed)
L1: 2.3344e-08 +/- 1.9987e-10 (0.86%) (init = 1e-05)
R1: 0.17444702 +/- 0.29660571 (170.03%) (init = 0.05)
Please note: I also have changed the input data of the model. Now I give the model complex values and then I calculate the Amplitude. Find this also here: https://1drv.ms/u/s!AsLKp-1R8HlZhcdlJER5T7qjmvfmnw?e=qnrZk1

How to set up GEKKO for parameter estimation from multiple independent sets of data?

I am learning how to use GEKKO for kinetic parameter estimation based on laboratory batch reactor data, which essentially consists of the concentration profiles of three species A, C, and P. For the purposes of my question, I am using a model that I previously featured in a question related to parameter estimation from a single data set.
My ultimate goal is to be able to use multiple experimental runs for parameter estimation, leveraging data that may be collected at different temperatures, species concentrations, etc. Due to the independent nature of individual batch reactor experiments, each data set features samples collected at different time points. These different time points (and in the future, different temperatures for instance) are difficult for me to implement into a GEKKO model, as I previosly used the experimental data collection time points as the m.time parameter for the GEKKO model. (See end of post for code) I have solved problems like this in the past with gPROMS and Athena Visual Studio.
To illustrate my problem, I generated an artificial data set of 'experimental' data from my original model by introducing noise to the species concentration profiles, and shifting the experimental time points slightly. I then combined all data sets of the same experimental species into new arrays featuring multiple columns. My thought process here was that GEKKO would carry out the parameter estimation by using the experimental data of each corresponding column of the arrays, so that times_comb[:,0] would be related to A_comb[:,0] while times_comb[:,1] would be related to A_comb[:,1].
When I attempt to run the GEKKO model, the system does obtain a solution for the parameter estimation, but it is unclear to me if the problem solution is reasonable, as I notice that the GEKKO Variables A, B, C, and P are 34 element vectors, which is double the elements in each of the experimental data sets. I presume GEKKO is somehow combining both columns of the time and Parameter vectors during model setup that leads to those 34 element variables? I am also concerned that during this combination of the columns of each input parameter, that the relationship between a certain time point and the collected species information is lost.
How could I improve the use of multiple data sets that GEKKO can simultaneously use for parameter estimation, with the consideration that the time points of each data set may be different? I looked on the GEKKO documentation examples as well as the APMonitor website, but I could not find examples featuring multiple data sets that I could use for guidance, as I am fairly new to the GEKKO package.
Thank you for your time reading my question and for any help/ideas you may have.
Code below:
import numpy as np
import matplotlib.pyplot as plt
from gekko import GEKKO
#Experimental data
times = np.array([0.0, 0.071875, 0.143750, 0.215625, 0.287500, 0.359375, 0.431250,
0.503125, 0.575000, 0.646875, 0.718750, 0.790625, 0.862500,
0.934375, 1.006250, 1.078125, 1.150000])
A_obs = np.array([1.0, 0.552208, 0.300598, 0.196879, 0.101175, 0.065684, 0.045096,
0.028880, 0.018433, 0.011509, 0.006215, 0.004278, 0.002698,
0.001944, 0.001116, 0.000732, 0.000426])
C_obs = np.array([0.0, 0.187768, 0.262406, 0.350412, 0.325110, 0.367181, 0.348264,
0.325085, 0.355673, 0.361805, 0.363117, 0.327266, 0.330211,
0.385798, 0.358132, 0.380497, 0.383051])
P_obs = np.array([0.0, 0.117684, 0.175074, 0.236679, 0.234442, 0.270303, 0.272637,
0.274075, 0.278981, 0.297151, 0.297797, 0.298722, 0.326645,
0.303198, 0.277822, 0.284194, 0.301471])
#Generate second set of 'experimental data'
times_new = times + np.random.uniform(0.0,0.01)
P_obs_noisy = P_obs+np.random.normal(0,0.05,P_obs.shape)
A_obs_noisy = A_obs+np.random.normal(0,0.05,A_obs.shape)
C_obs_noisy = A_obs+np.random.normal(0,0.05,C_obs.shape)
#Combine two data sets into multi-column arrays
times_comb = np.array([times, times_new]).T
P_comb = np.array([P_obs, P_obs_noisy]).T
A_comb = np.array([A_obs, A_obs_noisy]).T
C_comb = np.array([C_obs, C_obs_noisy]).T
m = GEKKO(remote=False)
t = m.time = times_comb #using two column time array
Am = m.Param(value=A_comb) #Using the two column data as observed parameter
Cm = m.Param(value=C_comb)
Pm = m.Param(value=P_comb)
A = m.Var(1, lb = 0)
B = m.Var(0, lb = 0)
C = m.Var(0, lb = 0)
P = m.Var(0, lb = 0)
k = m.Array(m.FV,6,value=1,lb=0)
for ki in k:
ki.STATUS = 1
k1,k2,k3,k4,k5,k6 = k
r1 = m.Var(0, lb = 0)
r2 = m.Var(0, lb = 0)
r3 = m.Var(0, lb = 0)
r4 = m.Var(0, lb = 0)
r5 = m.Var(0, lb = 0)
r6 = m.Var(0, lb = 0)
m.Equation(r1 == k1 * A)
m.Equation(r2 == k2 * A * B)
m.Equation(r3 == k3 * C * B)
m.Equation(r4 == k4 * A)
m.Equation(r5 == k5 * A)
m.Equation(r6 == k6 * A * B)
#mass balance diff eqs, function calls rxn function
m.Equation(A.dt() == - r1 - r2 - r4 - r5 - r6)
m.Equation(B.dt() == r1 - r2 - r3 - r6)
m.Equation(C.dt() == r2 - r3 + r4)
m.Equation(P.dt() == r3 + r5 + r6)
m.Minimize((A-Am)**2)
m.Minimize((P-Pm)**2)
m.Minimize((C-Cm)**2)
m.options.IMODE = 5
m.options.SOLVER = 3 #IPOPT optimizer
m.options.NODES = 6
m.solve()
k_opt = []
for ki in k:
k_opt.append(ki.value[0])
print(k_opt)
plt.plot(t,A)
plt.plot(t,C)
plt.plot(t,P)
plt.plot(t,B)
plt.plot(times,A_obs,'bo')
plt.plot(times,C_obs,'gx')
plt.plot(times,P_obs,'rs')
plt.plot(times_new, A_obs_noisy,'b*')
plt.plot(times_new, C_obs_noisy,'g*')
plt.plot(times_new, P_obs_noisy,'r*')
plt.show()
To have multiple data sets with different times and data points, you can join the data sets as a pandas dataframe. Here is a simple example:
# data set 1
t_data1 = [0.0, 0.1, 0.2, 0.4, 0.8, 1.00]
x_data1 = [2.0, 1.6, 1.2, 0.7, 0.3, 0.15]
# data set 2
t_data2 = [0.0, 0.15, 0.25, 0.45, 0.85, 0.95]
x_data2 = [3.6, 2.25, 1.75, 1.00, 0.35, 0.20]
The merged data has NaN where the data is missing:
x1 x2
Time
0.00 2.0 3.60
0.10 1.6 NaN
0.15 NaN 2.25
0.20 1.2 NaN
0.25 NaN 1.75
Take note of where the data is missing with a 1=measured and 0=not measured.
# indicate which points are measured
z1 = (data['x1']==data['x1']).astype(int) # 0 if NaN
z2 = (data['x2']==data['x2']).astype(int) # 1 if number
The final step is to set up Gekko variables, equations, and objective to accommodate the data sets.
xm = m.Array(m.Param,2)
zm = m.Array(m.Param,2)
for i in range(2):
m.Equation(x[i].dt()== -k * x[i]) # differential equations
m.Minimize(zm[i]*(x[i]-xm[i])**2) # objectives
You can also calculate the initial condition with m.free_initial(x[i]). This gives an optimal solution for one parameter value (k) over the 2 data sets. This approach can be expanded to multiple variables or multiple data sets with different times.
from gekko import GEKKO
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
# data set 1
t_data1 = [0.0, 0.1, 0.2, 0.4, 0.8, 1.00]
x_data1 = [2.0, 1.6, 1.2, 0.7, 0.3, 0.15]
# data set 2
t_data2 = [0.0, 0.15, 0.25, 0.45, 0.85, 0.95]
x_data2 = [3.6, 2.25, 1.75, 1.00, 0.35, 0.20]
# combine with dataframe join
data1 = pd.DataFrame({'Time':t_data1,'x1':x_data1})
data2 = pd.DataFrame({'Time':t_data2,'x2':x_data2})
data1.set_index('Time', inplace=True)
data2.set_index('Time', inplace=True)
data = data1.join(data2,how='outer')
print(data.head())
# indicate which points are measured
z1 = (data['x1']==data['x1']).astype(int) # 0 if NaN
z2 = (data['x2']==data['x2']).astype(int) # 1 if number
# replace NaN with any number (0)
data.fillna(0,inplace=True)
m = GEKKO(remote=False)
# measurements
xm = m.Array(m.Param,2)
xm[0].value = data['x1'].values
xm[1].value = data['x2'].values
# index for objective (0=not measured, 1=measured)
zm = m.Array(m.Param,2)
zm[0].value=z1
zm[1].value=z2
m.time = data.index
x = m.Array(m.Var,2) # fit to measurement
x[0].value=x_data1[0]; x[1].value=x_data2[0]
k = m.FV(); k.STATUS = 1 # adjustable parameter
for i in range(2):
m.free_initial(x[i]) # calculate initial condition
m.Equation(x[i].dt()== -k * x[i]) # differential equations
m.Minimize(zm[i]*(x[i]-xm[i])**2) # objectives
m.options.IMODE = 5 # dynamic estimation
m.options.NODES = 2 # collocation nodes
m.solve(disp=True) # solve
k = k.value[0]
print('k = '+str(k))
# plot solution
plt.plot(m.time,x[0].value,'b.--',label='Predicted 1')
plt.plot(m.time,x[1].value,'r.--',label='Predicted 2')
plt.plot(t_data1,x_data1,'bx',label='Measured 1')
plt.plot(t_data2,x_data2,'rx',label='Measured 2')
plt.legend(); plt.xlabel('Time'); plt.ylabel('Value')
plt.xlabel('Time');
plt.show()
Including my updated code (not fully cleaned up to minimize number of variables) incorporating the selected answer to my question for reference. The model does a regression of 3 measured species in two separate 'datasets.'
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
from gekko import GEKKO
#Experimental data
times = np.array([0.0, 0.071875, 0.143750, 0.215625, 0.287500, 0.359375, 0.431250,
0.503125, 0.575000, 0.646875, 0.718750, 0.790625, 0.862500,
0.934375, 1.006250, 1.078125, 1.150000])
A_obs = np.array([1.0, 0.552208, 0.300598, 0.196879, 0.101175, 0.065684, 0.045096,
0.028880, 0.018433, 0.011509, 0.006215, 0.004278, 0.002698,
0.001944, 0.001116, 0.000732, 0.000426])
C_obs = np.array([0.0, 0.187768, 0.262406, 0.350412, 0.325110, 0.367181, 0.348264,
0.325085, 0.355673, 0.361805, 0.363117, 0.327266, 0.330211,
0.385798, 0.358132, 0.380497, 0.383051])
P_obs = np.array([0.0, 0.117684, 0.175074, 0.236679, 0.234442, 0.270303, 0.272637,
0.274075, 0.278981, 0.297151, 0.297797, 0.298722, 0.326645,
0.303198, 0.277822, 0.284194, 0.301471])
#Generate second set of 'experimental data'
times_new = times + np.random.uniform(0.0,0.01)
P_obs_noisy = (P_obs+ np.random.normal(0,0.05,P_obs.shape))
A_obs_noisy = (A_obs+np.random.normal(0,0.05,A_obs.shape))
C_obs_noisy = (C_obs+np.random.normal(0,0.05,C_obs.shape))
#Combine two data sets into multi-column arrays using pandas DataFrames
#Set dataframe index to be combined time discretization of both data sets
exp1 = pd.DataFrame({'Time':times,'A':A_obs,'C':C_obs,'P':P_obs})
exp2 = pd.DataFrame({'Time':times_new,'A':A_obs_noisy,'C':C_obs_noisy,'P':P_obs_noisy})
exp1.set_index('Time',inplace=True)
exp2.set_index('Time',inplace=True)
exps = exp1.join(exp2, how ='outer',lsuffix = '_1',rsuffix = '_2')
#print(exps.head())
#Combine both data sets into a single data frame
meas_data = pd.DataFrame().reindex_like(exps)
#define measurement locations for each data set, with NaN written for time points
#not common in both data sets
for cols in exps:
meas_data[cols] = (exps[cols]==exps[cols]).astype(int)
exps.fillna(0,inplace = True) #replace NaN with 0
m = GEKKO(remote=False)
t = m.time = exps.index #set GEKKO time domain to use experimental time points
#Generate two-column GEKKO arrays to store observed values of each species, A, C and P
Am = m.Array(m.Param,2)
Cm = m.Array(m.Param,2)
Pm = m.Array(m.Param,2)
Am[0].value = exps['A_1'].values
Am[1].value = exps['A_2'].values
Cm[0].value = exps['C_1'].values
Cm[1].value = exps['C_2'].values
Pm[0].value = exps['P_1'].values
Pm[1].value = exps['P_2'].values
#Define GEKKO variables that determine if time point contatins data to be used in regression
#If time point contains species data, meas_ variable = 1, else = 0
meas_A = m.Array(m.Param,2)
meas_C = m.Array(m.Param,2)
meas_P = m.Array(m.Param,2)
meas_A[0].value = meas_data['A_1'].values
meas_A[1].value = meas_data['A_2'].values
meas_C[0].value = meas_data['C_1'].values
meas_C[1].value = meas_data['C_2'].values
meas_P[0].value = meas_data['P_1'].values
meas_P[1].value = meas_data['P_2'].values
#Define Variables for differential equations A, B, C, P, with initial conditions set by experimental observation at first time point
A = m.Array(m.Var,2, lb = 0)
B = m.Array(m.Var,2, lb = 0)
C = m.Array(m.Var,2, lb = 0)
P = m.Array(m.Var,2, lb = 0)
A[0].value = exps['A_1'][0] ; A[1].value = exps['A_2'][0]
B[0].value = 0 ; B[1].value = 0
C[0].value = exps['C_1'][0] ; C[1].value = exps['C_2'][0]
P[0].value = exps['P_1'][0] ; P[1].value = exps['P_2'][0]
#Define kinetic coefficients, k1-k6 as regression FV's
k = m.Array(m.FV,6,value=1,lb=0,ub = 20)
for ki in k:
ki.STATUS = 1
k1,k2,k3,k4,k5,k6 = k
#If doing paramrter estimation, enable free_initial condition, else not include them in model to reduce DOFs (for simulation, for example)
if k1.STATUS == 1:
for i in range(2):
m.free_initial(A[i])
m.free_initial(B[i])
m.free_initial(C[i])
m.free_initial(P[i])
#Define reaction rate variables
r1 = m.Array(m.Var,2, value = 1, lb = 0)
r2 = m.Array(m.Var,2, value = 1, lb = 0)
r3 = m.Array(m.Var,2, value = 1, lb = 0)
r4 = m.Array(m.Var,2, value = 1, lb = 0)
r5 = m.Array(m.Var,2, value = 1, lb = 0)
r6 = m.Array(m.Var,2, value = 1, lb = 0)
#Model Equations
for i in range(2):
#Rate equations
m.Equation(r1[i] == k1 * A[i])
m.Equation(r2[i] == k2 * A[i] * B[i])
m.Equation(r3[i] == k3 * C[i] * B[i])
m.Equation(r4[i] == k4 * A[i])
m.Equation(r5[i] == k5 * A[i])
m.Equation(r6[i] == k6 * A[i] * B[i])
#Differential species balances
m.Equation(A[i].dt() == - r1[i] - r2[i] - r4[i] - r5[i] - r6[i])
m.Equation(B[i].dt() == r1[i] - r2[i] - r3[i] - r6[i])
m.Equation(C[i].dt() == r2[i] - r3[i] + r4[i])
m.Equation(P[i].dt() == r3[i] + r5[i] + r6[i])
#Minimization objective functions
m.Obj(meas_A[i]*(A[i]-Am[i])**2)
m.Obj(meas_P[i]*(P[i]-Pm[i])**2)
m.Obj(meas_C[i]*(C[i]-Cm[i])**2)
#Solver options
m.options.IMODE = 5
m.options.SOLVER = 3 #APOPT optimizer
m.options.NODES = 6
m.solve()
k_opt = []
for ki in k:
k_opt.append(ki.value[0])
print(k_opt)
plt.plot(t,A[0],'b-')
plt.plot(t,A[1],'b--')
plt.plot(t,C[0],'g-')
plt.plot(t,C[1],'g--')
plt.plot(t,P[0],'r-')
plt.plot(t,P[1],'r--')
plt.plot(times,A_obs,'bo')
plt.plot(times,C_obs,'gx')
plt.plot(times,P_obs,'rs')
plt.plot(times_new, A_obs_noisy,'b*')
plt.plot(times_new, C_obs_noisy,'g*')
plt.plot(times_new, P_obs_noisy,'r*')
plt.show()

Resources