温度传感器曲线拟合的线性组合

Question

我正在尝试对不同的温度传感器进行线性组合，并使用应变传感器对其进行曲线化。

我所做的是我可以将一个温度传感器与一个应变传感器配合使用。

但我不知道如何在一个应变传感器上进行不同温度传感器的线性组合。

这是我的尝试：

def process_data_curve_fitting(temperature, strain):

   #mean_T = (temperature[[i for i in temperature.columns.tolist() if str(i)[:2] == 'TW']].mean(axis=1))
   print("process data")

   T1 = temperature['T1'].tolist()
   T2 = temperature['T2'].tolist()
   T3 = temperature['T3'].tolist()
   T4 = temperature['T4'].tolist()
   T5 = temperature['T5'].tolist()
   T6 = temperature['T6'].tolist()
   T7 = temperature['T7'].tolist()
   T8 = temperature['T8'].tolist()
   T9 = temperature['T9'].tolist()
   T10 = temperature['T10'].tolist()

   df = pd.DataFrame(list(zip(T1, T2, T3, T4, T5, T6, T7, T8, T9, T10)))
   mean_T = df.mean(axis = 1)

   print(mean_T)
   Sensor_Names = [ 'W_A1', 'W_A2', 'W_F1', 'W_F2', 'W_F4', 'W_S1', 'W_S2', 'W_S3', 'W_S4', 'W_KF1', 'W_KF2', 'W_KF3', 'W_KF4', 'W_DB1', 'W_DB2']
   ys = []
   for i in range(len(strain)):
       cof = np.polyfit(mean_T, strain[i], 2)
       poly = np.polyval(cof, mean_T)
       ys.append(poly)
       print (cof)
       print (poly)

   for i in range(len(strain)):
       fig = plt.figure()
       plt.scatter(mean_T, strain[i],s=0.1)
      # fig.savefig(r'c:\\ahmed\\'+Sensor_Names[i]+'.png')
       plt.plot(mean_T, ys[i], color='r')
       fig.savefig(r'c:\\ahmed\\'+"Curve_fitting__" + Sensor_Names[i]+'.png',dpi=300)

       plt.ylabel('strain' + Sensor_Names[i])
       plt.xlabel('temperature')

请看方程

Answer 1

作为两个温度传感器的“概念验证” （这里既不放噪音也不考虑实际参数）：

import matplotlib.pyplot as plt
import numpy as np
from scipy.optimize import leastsq

def strain( t, a, b, c, d ):
    return a * t**3 + b * t**2 + c * t + d

def residuals( params, x1Data, x2Data, yData ):
    s1, s2, a, b, c, d = params
    cxData = [ (s1**2 * x1 + s2**2 * x2) /( s1**2 + s2**2 ) for x1, x2 in zip( x1Data, x2Data) ]
    diff = [ strain( x, a, b, c, d ) -y for x, y in zip( cxData, yData ) ]
    return diff

timeList = np.linspace( 0, 25, 55 )
t1List = np.fromiter( (  5 + 25. * (1 - np.exp( -t / 9. ) )for t in timeList ), np.float )
t2List = np.fromiter( (30. * (1 - np.exp( -t / 7. ) ) * ( 1 - np.exp( -t / 3. ) ) for t in timeList ), np.float )

combinedList = np.fromiter( ( (.7 * a + .2 * b)/.9 for a, b in zip( t1List, t2List ) ), np.float )
strainList = np.fromiter( ( strain( t, .01, -.1, .88, .2 ) for t in combinedList  ), np.float )

fit, ier = leastsq( residuals, [.71,.22, 0,0, .1, .1 ], args=( t1List, t2List, strainList ), maxfev=5000 )
print fit 
fittedT = [ (fit[0]**2 * x1 + fit[1]**2 *x2 ) /( fit[0]**2 + fit[1]**2 ) for x1, x2 in zip( t1List, t2List) ]
fittedS = [ strain( t, *(fit[2:]) ) for t in fittedT ]

fig = plt.figure()
ax = fig.add_subplot( 3, 1, 1 )
bx = fig.add_subplot( 3, 1, 2 )
cx = fig.add_subplot( 3, 1, 3 )
ax.plot( timeList, t1List )
ax.plot( timeList, t2List )
ax.plot( timeList, combinedList )
bx.plot( combinedList, strainList, linestyle='', marker='x' )
bx.plot( fittedT, fittedS )
cx.plot( timeList, fittedT ,'--')
cx.plot( timeList, combinedList,':' )
plt.show()

给予

[ 4.21350842e+03  2.25221499e+03  1.00000000e-02 -1.00000000e-01 8.80000000e-01  2.00000000e-01]

并显示：

顶部：温度 1（蓝色）和 2（橙色）以及线性组合（绿色） 中心：“模拟数据”（蓝色）和拟合（橙色） 底部：拟合温度（蓝色），真实温度（橙色）

根据实际数据，可能需要进行一些调整。