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diff --git a/Butcher_tableau/Butcher_IRK5.txt b/Butcher_tableau/Butcher_IRK5.txt
new file mode 100644
index 0000000..defe051
--- /dev/null
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diff --git a/Butcher_tableau/Butcher_IRK50.txt b/Butcher_tableau/Butcher_IRK50.txt
new file mode 100644
index 0000000..7d95979
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\ No newline at end of file
diff --git a/Butcher_tableau/Butcher_IRK6.txt b/Butcher_tableau/Butcher_IRK6.txt
new file mode 100644
index 0000000..9da4267
--- /dev/null
+++ b/Butcher_tableau/Butcher_IRK6.txt
@@ -0,0 +1,48 @@
+0.04283112309479258626
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\ No newline at end of file
diff --git a/PIML_Converter.py b/PIML_Converter.py
new file mode 100644
index 0000000..b3bb4e7
--- /dev/null
+++ b/PIML_Converter.py
@@ -0,0 +1,363 @@
+"""
+==================================================================================================
+Author: Shuai Zhao @ Aalborg University, szh@energy.aau.dk
+Note:
+ * The code and data accompany the paper:
+ S. Zhao, Y. Peng, Y. Zhang, and H. Wang, "Parameter Estimation of Power Electronic
+ Converters with Physics-informed Machine Learning", IEEE Trans. Power Electronics, 2022
+
+ * The Tensorflow verion is 1.15.0. The code is developed based on the github repository
+ https://github.com/maziarraissi/PINNs, where more useful information can be found therein.
+==================================================================================================
+"""
+
+import sys
+import tensorflow as tf
+import numpy as np
+import time
+import scipy.io
+
+np.random.seed(1234)
+tf.set_random_seed(1234)
+
+
+class PhysicsInformedNN:
+ # Initialize the class
+ def __init__(self, x0, u0, x1, u1, layers, dt, lb, ub, q, splitIdx1, splitIdx2, splitIdx3, otherParams):
+
+ self.lb = lb
+ self.ub = ub
+
+ self.x0 = x0
+ self.x1 = x1
+
+ self.u0 = u0
+ self.u1 = u1
+
+ self.layers = layers
+ self.dt = dt
+ self.q = max(q, 1)
+
+ self.splitIdx1 = splitIdx1
+ self.splitIdx2 = splitIdx2
+ self.splitIdx3 = splitIdx3
+
+ # Initialize NN
+ self.weights, self.biases = self.initialize_NN(layers)
+ self.otherParams = otherParams
+
+ self.L = tf.Variable([2], dtype=tf.float32)
+ self.RL = tf.Variable([0.039], dtype=tf.float32)
+ self.C = tf.Variable([0.412], dtype=tf.float32)
+ self.RC = tf.Variable([1.59], dtype=tf.float32)
+ self.Rdson = tf.Variable([1.22], dtype=tf.float32)
+ self.Rload1 = tf.Variable([1.22], dtype=tf.float32)
+ self.Rload2 = tf.Variable([1.22], dtype=tf.float32)
+ self.Rload3 = tf.Variable([1.22], dtype=tf.float32)
+ self.vIn = tf.Variable([0.87], dtype=tf.float32)
+ self.vF = tf.Variable([0.1], dtype=tf.float32)
+
+ tmp = np.float32(np.loadtxt(
+ 'Butcher_tableau/Butcher_IRK%d.txt' % (q),
+ ndmin=2))
+ weights = np.reshape(tmp[0:q ** 2 + q], (q + 1, q))
+ self.IRK_alpha = weights[0:-1, :]
+ self.IRK_beta = weights[-1:, :]
+ self.IRK_times = tmp[q ** 2 + q:]
+
+ # tf placeholders and graph
+ self.sess = tf.Session(config=tf.ConfigProto(allow_soft_placement=True,
+ log_device_placement=True))
+
+ self.x0_tf = tf.placeholder(tf.float32, shape=(None, self.x0.shape[1]))
+ self.x1_tf = tf.placeholder(tf.float32, shape=(None, self.x1.shape[1]))
+ self.u0_tf = tf.placeholder(tf.float32, shape=(None, self.u0.shape[1]))
+ self.u1_tf = tf.placeholder(tf.float32, shape=(None, self.u1.shape[1]))
+
+ self.U0_pred, self.V0_pred = self.net_U0(self.x0_tf) # 2*N0 x q
+ self.U1_pred, self.V1_pred = self.net_U1(self.x1_tf) # 2*N1 x q
+
+ self.loss = tf.reduce_sum(tf.square(self.u0_tf[:, 1:2] - self.V0_pred)) + \
+ tf.reduce_sum(tf.square(self.u1_tf[:, 1:2] - self.V1_pred)) + \
+ tf.reduce_sum(tf.square(self.u0_tf[:, 0:1] - self.U0_pred)) + \
+ tf.reduce_sum(tf.square(self.u1_tf[:, 0:1] - self.U1_pred)) # + \
+
+ self.optimizer = tf.contrib.opt.ScipyOptimizerInterface(self.loss,
+ method='L-BFGS-B',
+ options={'iprint': 0,
+ 'maxiter': otherParams.LBFGSEpoch,
+ 'maxfun': otherParams.LBFGSEpoch,
+ 'maxcor': 50,
+ 'maxls': 100,
+ 'ftol': 1.0 * np.finfo(float).eps})
+
+ self.optimizer_Adam = tf.train.AdamOptimizer()
+ self.train_op_Adam = self.optimizer_Adam.minimize(self.loss)
+
+ init = tf.global_variables_initializer()
+ self.sess.run(init)
+
+ def initialize_NN(self, layers): # initialize a fully-connected neural network
+ weights = []
+ biases = []
+ num_layers = len(layers)
+ for l in range(0, num_layers - 1):
+ W = self.xavier_init(size=[layers[l], layers[l + 1]])
+ b = tf.Variable(tf.zeros([1, layers[l + 1]], dtype=tf.float32), dtype=tf.float32)
+ weights.append(W)
+ biases.append(b)
+ return weights, biases
+
+ def xavier_init(self, size):
+ in_dim = size[0]
+ out_dim = size[1]
+ xavier_stddev = np.sqrt(2 / (in_dim + out_dim))
+ return tf.Variable(tf.truncated_normal([in_dim, out_dim], stddev=xavier_stddev), dtype=tf.float32)
+
+ def neural_net(self, X, weights, biases):
+ num_layers = len(weights) + 1
+
+ H = 2.0 * (X - self.lb) / (self.ub - self.lb) - 1.0
+ for l in range(0, num_layers - 2):
+ W = weights[l]
+ b = biases[l]
+ H = tf.tanh(tf.add(tf.matmul(H, W), b))
+ W = weights[-1]
+ b = biases[-1]
+ Y = tf.add(tf.matmul(H, W), b)
+ return Y
+
+ def net_U0(self, x): # establish the backward relationship eq. (4)
+
+ L = tf.exp(self.L) * 1e-4
+ RL = tf.exp(self.RL) * 1e-1
+ C = tf.exp(self.C) * 1e-4
+ RC = tf.exp(self.RC) * 1e-1
+ Rdson = tf.exp(self.Rdson) * 1e-1
+ Rload1 = tf.exp(self.Rload1)
+ Rload2 = tf.exp(self.Rload2)
+ Rload3 = tf.exp(self.Rload3)
+ vIn = tf.exp(self.vIn) * 1e1
+ vF = tf.exp(self.vF)
+
+ y = x[:, 2:3]
+ yOff = x[:, 3:4]
+ dt = x[:, 4:5]
+
+ Rload = tf.concat((tf.ones((self.splitIdx1 * 2, 1)) * Rload1, tf.ones((self.splitIdx2 * 2, 1)) * Rload2,
+ tf.ones((self.splitIdx3 * 2, 1)) * Rload3), 0)
+
+ current_and_voltage = self.neural_net(x, self.weights, self.biases)
+ u = current_and_voltage[:, 0:self.q]
+ v = current_and_voltage[:, self.q:self.q * 2]
+
+ F_u = -((y * (RL + Rdson)) * u + (yOff * (RL)) * u + v - y * vIn + yOff * vF) / L # inductor current model
+ U0 = u - dt * tf.matmul(F_u, self.IRK_alpha.T)
+ F_v = (C * RC * Rload * (F_u) + Rload * u - v) / (C * (RC + Rload)) # output voltage model
+ V0 = v - dt * tf.matmul(F_v, self.IRK_alpha.T)
+
+ return U0, V0
+
+ def net_U1(self, x): # establish the forward relationship eq. (7)
+
+ L = tf.exp(self.L) * 1e-4
+ RL = tf.exp(self.RL) * 1e-1
+ C = tf.exp(self.C) * 1e-4
+ RC = tf.exp(self.RC) * 1e-1
+ Rdson = tf.exp(self.Rdson) * 1e-1
+ Rload1 = tf.exp(self.Rload1)
+ Rload2 = tf.exp(self.Rload2)
+ Rload3 = tf.exp(self.Rload3)
+ vIn = tf.exp(self.vIn) * 1e1
+ vF = tf.exp(self.vF)
+
+ y = x[:, 2:3]
+ yOff = x[:, 3:4]
+ dt = x[:, 4:5]
+
+ Rload = tf.concat((tf.ones((self.splitIdx1 * 2, 1)) * Rload1, tf.ones((self.splitIdx2 * 2, 1)) * Rload2,
+ tf.ones((self.splitIdx3 * 2, 1)) * Rload3), 0)
+
+ current_and_voltage = self.neural_net(x, self.weights, self.biases)
+ u = current_and_voltage[:, 0:self.q]
+ v = current_and_voltage[:, self.q:self.q * 2]
+
+ F_u = -((y * (RL + Rdson)) * u + (yOff * (RL)) * u + v - y * vIn + yOff * vF) / L # inductor current model
+ U1 = u + dt * tf.matmul(F_u, (self.IRK_beta - self.IRK_alpha).T)
+ F_v = (C * RC * Rload * (F_u) + Rload * u - v) / (C * (RC + Rload)) # output voltage model
+ V1 = v + dt * tf.matmul(F_v, (self.IRK_beta - self.IRK_alpha).T)
+
+ return U1, V1
+
+ def callback(self, loss, L, RL, C, RC, Rdson, Rload1, Rload2, Rload3, vIn, vF):
+ L_value = np.abs(np.exp(L) / self.otherParams.nL * 100 - 100)
+ RL_value = np.abs(np.exp(RL) / self.otherParams.nRL * 100 - 100)
+ C_value = np.abs(np.exp(C) / self.otherParams.nC * 100 - 100)
+ RC_value = np.abs(np.exp(RC) / self.otherParams.nRC * 100 - 100)
+ Rdson_value = np.abs(np.exp(Rdson) / self.otherParams.nRdson * 100 - 100)
+ Rload1_value = np.abs(np.exp(Rload1) / self.otherParams.nRload1 * 100 - 100)
+ Rload2_value = np.abs(np.exp(Rload2) / self.otherParams.nRload2 * 100 - 100)
+ Rload3_value = np.abs(np.exp(Rload3) / self.otherParams.nRload3 * 100 - 100)
+ vIn_value = np.abs(np.exp(vIn) / self.otherParams.nVin * 100 - 100)
+ vF_value = np.abs(np.exp(vF) / self.otherParams.nVF * 100 - 100)
+ meanError = np.mean([L_value, RL_value, C_value,
+ RC_value, Rdson_value, Rload1_value,
+ Rload2_value, Rload3_value,
+ vIn_value, vF_value])
+
+ print(
+ 'Loss: %.3e, mean: %.1f, L: %.1f, RL: %.1f, C: %.1f, RC: %.1f, Rdson: %.1f, Rload1: %.1f, Rload2: %.1f, Rload3: %.1f, vIn: %.1f, vF: %.1f' % (
+ loss, meanError, L_value, RL_value,
+ C_value, RC_value,
+ Rdson_value,
+ Rload1_value, Rload2_value,
+ Rload3_value,
+ vIn_value, vF_value))
+
+ def train(self, nIter):
+ tf_dict = {self.x0_tf: self.x0, self.u0_tf: self.u0,
+ self.x1_tf: self.x1, self.u1_tf: self.u1}
+
+ start_time = time.time()
+ for it in range(nIter):
+ self.sess.run(self.train_op_Adam, tf_dict)
+ # Print training info
+ if it % 10000 == 0:
+ elapsed = time.time() - start_time
+ loss_value = self.sess.run(self.loss, tf_dict)
+ L = np.abs(np.exp(self.sess.run(self.L)) / self.otherParams.nL * 100 - 100)
+ RL = np.abs(np.exp(self.sess.run(self.RL)) / self.otherParams.nRL * 100 - 100)
+ C = np.abs(np.exp(self.sess.run(self.C)) / self.otherParams.nC * 100 - 100)
+ RC = np.abs(np.exp(self.sess.run(self.RC)) / self.otherParams.nRC * 100 - 100)
+ Rdson = np.abs(np.exp(self.sess.run(self.Rdson)) / self.otherParams.nRdson * 100 - 100)
+ Rload1 = np.abs(np.exp(self.sess.run(self.Rload1)) / self.otherParams.nRload1 * 100 - 100)
+ Rload2 = np.abs(np.exp(self.sess.run(self.Rload2)) / self.otherParams.nRload2 * 100 - 100)
+ Rload3 = np.abs(np.exp(self.sess.run(self.Rload3)) / self.otherParams.nRload3 * 100 - 100)
+ vIn = np.abs(np.exp(self.sess.run(self.vIn)) / self.otherParams.nVin * 100 - 100)
+ vF = np.abs(np.exp(self.sess.run(self.vF)) / self.otherParams.nVF * 100 - 100)
+ meanError = np.mean([L, RL, C, RC, Rdson, Rload1, Rload2, Rload3, vIn, vF])
+
+ print(
+ 'Iterations: %d, Loss: %.3e, mean: %.1e, L: %.1f, RL: %.1f, C: %.1f, RC: %.1f, Rdson: %.1f, Rload1: %.1f, Rload2: %.1f, Rload3: %.1f, vIn: %.1f, vF: %.1f, Time: %.2f' %
+ (it, loss_value, meanError, L, RL, C, RC, Rdson, Rload1, Rload2, Rload3, vIn, vF, elapsed))
+ start_time = time.time()
+
+ self.optimizer.minimize(self.sess,
+ feed_dict=tf_dict,
+ fetches=[self.loss, self.L, self.RL, self.C, self.RC, self.Rdson, self.Rload1,
+ self.Rload2, self.Rload3, self.vIn, self.vF],
+ loss_callback=self.callback)
+
+ def predict(self, x_star_Backward, x_star_Forward, dt):
+
+ U0_star = self.sess.run(self.U0_pred,
+ {self.x0_tf: x_star_Backward})
+ V0_star = self.sess.run(self.V0_pred,
+ {self.x0_tf: x_star_Backward})
+ U1_star = self.sess.run(self.U1_pred,
+ {self.x1_tf: x_star_Forward})
+ V1_star = self.sess.run(self.V1_pred,
+ {self.x1_tf: x_star_Forward})
+
+ return U0_star, V0_star, U1_star, V1_star
+
+
+class otherParams: # simulation settings
+ def __init__(self):
+ self.AdamEpoch = 200000
+ self.AdamLearningRate = 1e-3
+ self.LBFGSEpoch = 50000
+ self.nL = 7.25
+ self.nRL = 3.14
+ self.nC = 1.645
+ self.nRC = 2.01
+ self.nRdson = 2.21
+ self.nRload1 = 3.1
+ self.nRload2 = 10.2
+ self.nRload3 = 6.1
+ self.nVin = 4.8
+ self.nVF = 1
+
+
+if __name__ == "__main__":
+
+ for testIdx in range(0, 7, 1): # loop to test all 7 cases automatically
+ fileNameAutoGen = 'Simulation_data/buckSimulation_%s.mat' % testIdx
+ data = scipy.io.loadmat(fileNameAutoGen)
+ xCurrent = data['CurrentInput']
+ xVoltage = data['VoltageInput']
+ xSwitch = data['Dswitch']
+ yCurrent = data['Current']
+ yVoltage = data['Voltage']
+ Indicator = data['forwaredBackwaredIndicator']
+ dt = data['dt']
+
+ idx_forward = np.transpose(np.nonzero(Indicator[:, 0:1] == -2))
+ idx_forward = idx_forward[:, 0:1]
+ idx_backward = np.transpose(np.nonzero(Indicator[:, 0:1] == 2))
+ idx_backward = idx_backward[:, 0:1]
+
+ q = 20
+ layers = [5, 50, 50, 50, 50, 50, q * 2] # architecture of the neural network
+ X = np.concatenate([xCurrent, xVoltage, xSwitch, 1 - xSwitch, dt], 1)
+ lb = X.min(0)
+ ub = X.max(0)
+
+ x0 = np.concatenate(
+ [xCurrent[idx_forward], xVoltage[idx_forward], xSwitch[idx_forward], 1 - xSwitch[idx_forward],
+ dt[idx_forward]], 1)
+ x0 = np.reshape(x0, (-1, 5))
+ u0 = np.concatenate([yCurrent[idx_forward], yVoltage[idx_forward]], 1)
+ u0 = np.reshape(u0, (-1, 2))
+
+ x1 = np.concatenate(
+ [xCurrent[idx_backward], xVoltage[idx_backward], xSwitch[idx_backward], 1 - xSwitch[idx_backward],
+ dt[idx_backward]], 1)
+ x1 = np.reshape(x1, (-1, 5))
+ u1 = np.concatenate([yCurrent[idx_backward], yVoltage[idx_backward]], 1)
+ u1 = np.reshape(u1, (-1, 2))
+
+ # the information of number of data points in each trasient regimes.
+ splitIdx1 = 120 # otherwise it will be 1 for no data case of the signal transient
+ splitIdx2 = 120
+ splitIdx3 = 120
+ Params = otherParams()
+
+ model = PhysicsInformedNN(x0, u0, x1, u1, layers, dt, lb, ub, q, splitIdx1, splitIdx2, splitIdx3, Params)
+ model.train(Params.AdamEpoch)
+
+ L = np.exp(model.sess.run(model.L))
+ RL = np.exp(model.sess.run(model.RL))
+ C = np.exp(model.sess.run(model.C))
+ RC = np.exp(model.sess.run(model.RC))
+ Rdson = np.exp(model.sess.run(model.Rdson))
+ Rload1 = np.exp(model.sess.run(model.Rload1))
+ Rload2 = np.exp(model.sess.run(model.Rload2))
+ Rload3 = np.exp(model.sess.run(model.Rload3))
+ vIn = np.exp(model.sess.run(model.vIn))
+ vF = np.exp(model.sess.run(model.vF))
+ RLRdson = RL + Rdson
+
+ # Norminal values of the simulation setting, please refer to Table I in the paper.
+ L_value = np.abs(np.mean(L) / Params.nL * 100 - 100)
+ RL_value = np.abs(np.mean(RL) / Params.nRL * 100 - 100)
+ C_value = np.abs(np.mean(C) / Params.nC * 100 - 100)
+ RC_value = np.abs(np.mean(RC) / Params.nRC * 100 - 100)
+ Rdson_value = np.abs(np.mean(Rdson) / Params.nRdson * 100 - 100)
+ Rload1_value = np.abs(np.mean(Rload1) / Params.nRload1 * 100 - 100)
+ Rload2_value = np.abs(np.mean(Rload2) / Params.nRload2 * 100 - 100)
+ Rload3_value = np.abs(np.mean(Rload3) / Params.nRload3 * 100 - 100)
+ vIn_value = np.abs(np.mean(vIn) / Params.nVin * 100 - 100)
+ vF_value = np.abs(np.mean(vF) / Params.nVF * 100 - 100)
+
+ meanError = np.mean([L_value, RL_value, C_value,
+ RC_value, Rdson_value, Rload1_value,
+ Rload2_value, Rload3_value, vIn_value, vF_value])
+
+ text_file = open("Result.txt", "a+")
+ text_file.write(
+ "buckSimulation_%s: mean:%.2f, L: %.2f, RL: %.2f, C: %.2f, RC: %.2f, Rdson: %.2f, Rload1: %.2f, Rload2: %.2f, Rload3: %.2f, vIn: %.2f, vF: %.2f\n" % (
+ testIdx, meanError, L_value, RL_value, C_value, RC_value, Rdson_value, Rload1_value,
+ Rload2_value,
+ Rload3_value, vIn_value, vF_value))
+ text_file.close()
diff --git a/Result.txt b/Result.txt
new file mode 100644
index 0000000..2455ea3
--- /dev/null
+++ b/Result.txt
@@ -0,0 +1,7 @@
+buckSimulation_0: mean:0.03, L: 0.01, RL: 0.02, C: 0.03, RC: 0.03, Rdson: 0.09, Rload1: 0.00, Rload2: 0.00, Rload3: 0.00, vIn: 0.00, vF: 0.09
+buckSimulation_1: mean:0.13, L: 0.00, RL: 0.23, C: 0.07, RC: 0.12, Rdson: 0.52, Rload1: 0.00, Rload2: 0.04, Rload3: 0.02, vIn: 0.01, vF: 0.25
+buckSimulation_2: mean:1.53, L: 0.35, RL: 0.54, C: 0.03, RC: 5.70, Rdson: 0.13, Rload1: 0.01, Rload2: 0.02, Rload3: 0.01, vIn: 0.17, vF: 8.37
+buckSimulation_3: mean:0.49, L: 0.13, RL: 0.30, C: 0.05, RC: 2.76, Rdson: 0.66, Rload1: 0.02, Rload2: 0.15, Rload3: 0.07, vIn: 0.01, vF: 0.79
+buckSimulation_4: mean:1.93, L: 0.21, RL: 1.16, C: 0.65, RC: 5.57, Rdson: 1.05, Rload1: 0.00, Rload2: 0.27, Rload3: 0.19, vIn: 0.22, vF: 9.93
+buckSimulation_5: mean:3.71, L: 0.84, RL: 6.42, C: 0.95, RC: 5.22, Rdson: 12.22, Rload1: 0.04, Rload2: 0.04, Rload3: 0.06, vIn: 0.26, vF: 11.01
+buckSimulation_6: mean:5.11, L: 1.03, RL: 13.22, C: 1.04, RC: 4.38, Rdson: 27.59, Rload1: 0.10, Rload2: 0.13, Rload3: 0.12, vIn: 0.16, vF: 3.30
diff --git a/Simulation_data/Dataset details.md b/Simulation_data/Dataset details.md
new file mode 100644
index 0000000..e790590
--- /dev/null
+++ b/Simulation_data/Dataset details.md
@@ -0,0 +1,5 @@
+# Dataset details
+
+The dataset includes six .mat files, from **buckSimulation_0** to **buckSimulation_6**. They correspond to the testing cases in the Table II in the paper, i.e., clean data, ADC error, Sync error, 5 noise, 10 noise, ADC-Sync-5noise, ADC-Sync-10noise.
+
+The datasets are generated by using the Buck converter model implemented in Matlab. The Matlab script is available upon request to szh@energy.aau.dk.
\ No newline at end of file
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