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In [201]:

    
import matplotlib.pyplot as plt
from sklearn.pipeline import Pipeline
from sklearn import datasets, linear_model
from sklearn import cross_validation
import numpy as np
import pandas as pd
from sklearn import preprocessing



In [202]:

    
df = pd.read_excel("data0505.xlsx",header=0)
# clean up data
df = df.dropna(how = 'all')
df = df.fillna(0)
df = df.round(4)
df=df[df['Power']>=0]
df.head()



In [203]:

    
# min_max_scaler = preprocessing.MinMaxScaler()
# np_scaled = min_max_scaler.fit_transform(df)
# df_normalized = pd.DataFrame(np_scaled)
# df_normalized.head()



In [204]:

    
x = np.array(df.iloc[:,0:3])#first three column are SoC, SoH, power
y = np.array(df.iloc[:,5])#delta SEI
X_train, X_test, Y_train, Y_test = cross_validation.train_test_split(
x, y, test_size=0.2, random_state=42)
total_len = X_train.shape[0]
total_len









    Out[204]:





4880



In [205]:

    
y









    Out[205]:





array([ 44.8776,  46.1896,  47.5605, ...,  52.5202,  53.8887,  55.2809])



In [206]:

    
# Create linear regression object
regr = linear_model.LinearRegression()

# Train the model using the training sets
regr.fit(X_train, Y_train)









    Out[206]:





LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)



In [207]:

    
# The coefficients
print('Coefficients: \n', regr.coef_)
# The mean squared error
print("Mean squared error: %.4f"
      % np.mean((regr.predict(X_test) - Y_test) ** 2))
# Explained variance score: 1 is perfect prediction
print('Variance score: %.2f' % regr.score(X_test, Y_test))









    



Coefficients: 
 [  3.33356517e-03  -9.79759843e-01   1.09445592e+01]
Mean squared error: 5.7812
Variance score: 0.67



In [208]:

    
# Plot outputs
plt.scatter(regr.predict(X_test), Y_test, color='blue',
         linewidth=3)
plt.ylim([40,60])
plt.xlim([40,60])
plt.show()



In [209]:

    
E = 1; # battery energy
P = 1; # battery power
T = 900; # 1 hour, resolution 4 seconds
ts = 4/3600;



In [210]:

    
## Constant instruction signal
soc_arr = [0.2]; #initial SoC 0.2
soh_arr = [10**(-8)]; #initial SoH 1e-8
power_arr = [0.6]; #constant power instruction 0.6
for i in range(T):
    state = [soc_arr[i],soh_arr[i],power_arr[i]]
    state = np.array(state);
    delta_soh = regr.predict(state.reshape(1, -1))*10**(-16) #calculate the thickness change
    soh_new = soh_arr[-1]+delta_soh; # new SoH = previous SoH + thickness change
    soh_arr.append(soh_new)
    soc_new = soc_arr[-1]+(power_arr[-1]*ts)/E #new SoC = previous SoC + energy charged
    soc_arr.append(soc_new)
    power_new = 0.6
    power_arr.append(power_new)



In [211]:

    
f, axarr = plt.subplots(2, 2)
axarr[0, 0].plot(range(T), power_arr[0:T])
axarr[0, 0].set_title('Instruction signal')
axarr[0, 1].scatter(range(T), soc_arr[0:T])
axarr[0, 1].set_title('SoC')
axarr[1, 0].plot(range(T), soh_arr[0:T])
axarr[1, 0].set_title('SoH')
plt.subplots_adjust(left= 0.125, right = 0.9, bottom = 0.1, top = 0.9 , wspace = 0.2, hspace = 0.2 )
plt.tight_layout()
plt.show()



In [225]:

    
## Sine wave instruction signal
soc_arr = [0.6];
soh_arr = [10**(-8)];
power_arr = [0];
for i in range(T):
    if(power_arr[i]>=0):
        state = [soc_arr[i],soh_arr[i],power_arr[i]]
        state = np.array(state);
        delta_soh = regr.predict(state.reshape(1, -1))*10**(-16)
    else:
        delta_soh = 0
    soh_new = soh_arr[-1]+delta_soh;
    soh_arr.append(soh_new)
    soc_new = soc_arr[-1]+(power_arr[-1]*ts)/E
    soc_arr.append(soc_new)
    power_new = 3*np.sin(2*np.pi*(i+1)*4/600)
    power_arr.append(power_new)



In [226]:

    
f, axarr = plt.subplots(2, 2)
axarr[0, 0].plot(range(T), power_arr[0:T])
axarr[0, 0].set_title('Instruction signal')
axarr[0, 1].scatter(range(T), soc_arr[0:T])
axarr[0, 1].set_title('SoC')
axarr[1, 0].plot(range(T), soh_arr[0:T])
axarr[1, 0].set_title('SoH')
plt.subplots_adjust(left= 0.125, right = 0.9, bottom = 0.1, top = 0.9 , wspace = 0.2, hspace = 0.2 )
plt.tight_layout()
plt.show()
# Fine-tune figure; hide x ticks for top plots and y ticks for right plots



In [ ]:

	SOC	SOH	Power	T	SEI_delta
10	80	1.0	0.0526	23	44.8776
11	80	1.0	0.1579	23	46.1896
12	80	1.0	0.2632	23	47.5605
13	80	1.0	0.3684	23	48.9998
14	80	1.0	0.4737	23	50.4819