问题
I have a dataset consisting of a certain temperature profile and I wanna fit or map the measurement points on temperature profile which is following:
Dwell-time: 30 mins
Ramp-time: 1 min
Number of periods: 1000 cycles
Measure points period: 16 mins
Measure points can be happened in either in high regim +150 or low regim -40
Note: The T0 (initial time) is not clear so time reference is not clear eg. T0=0 .
I already fetched the data in Pandas DataFrame:
import numpy as np
import pandas as pd
from scipy.optimize import curve_fit
df = pd.read_csv('D:\SOF.csv', header=None)
data = {'A': A[:,0], 'B': B[:,0], 'Temperature': Temperature[:,0],
'S':S, 'C':C , 'Measurement_Points':MP}
dff = pd.DataFrame(data, columns=['A','B','Temperature','S','C','MP'], index = id_set[:,0])
# Temperature's range is [-40,+150]
# MP's range is [0-3000] from 1st MP till last one
MP = int(len(dff)/480) # calculate number of measurement points
print(MP)
for cycle in range(MP):
j = cycle * 480
#use mean or average of each 480 values from temperature column of DataFrame to pass for fit on Thermal profile
Mean_temp = np.mean(df['Temperature'].iloc[j:j+480]) # by using Mean from numpy
#Mean_temp = df.groupby('Temperature').mean() #by using groupby
So far I just find curve_fit from scipy.optimize based on this answer and this post
but I am wondering how the fitting process could work right here in the other hand I would like Temperature values round only to the nearest either -40 or +150 .
I would be nice if someone can help me!
Update: Standard periodic Thermal profile pic is following:
expected result:
updated Data sample: data
回答1:
If you are only interested in the two temperature levels, this might be useful:
import matplotlib.pyplot as plt
import numpy as np
from scipy.optimize import curve_fit
inData = np.loadtxt('SOF.csv', skiprows=1, delimiter=',' )
def gauss( x, s ):
return 1. / np.sqrt( 2. * np.pi * s**2 ) * np.exp( -x**2 / ( 2. * s**2 ) )
def two_peak( x , a1, mu1, s1, a2, mu2, s2 ):
return a1 * gauss( x - mu1, s1 ) + a2 * gauss( x - mu2, s2 )
fList = inData[ :, 2 ]
nBins = 2 * int( max( fList ) - min( fList ) )
fig = plt.figure()
ax = fig.add_subplot( 2, 1 , 1 )
ax.plot( fList , marker='x' )
bx = fig.add_subplot( 2, 1 , 2 )
histogram, binEdges, _ = bx.hist( fList, bins=nBins )
binCentre = np.fromiter( ( ( a + b ) / 2. for a,b in zip( binEdges[ 1: ], binEdges[ :-1 ] ) ) , np.float )
sol, err = curve_fit( two_peak, binCentre, histogram, [ 120, min( fList ), 1 ] + [ 500, max( fList ), 1 ] )
print sol[1], sol[4]
print sol[2], sol[5]
bx.plot( binCentre, two_peak( binCentre, *sol ) )
bx.set_yscale( 'log' )
bx.set_ylim( [ 1e-0, 5e3] )
plt.show()
providing:
>> -46.01513424923528 150.06381412858244
>> 1.8737971845243133 0.6964990809008554
and
Interestingly your non-plateau data is all around zero, so that's probably not due to the ramp, but a different effect.
回答2:
This would be my starting point:
import matplotlib.pyplot as plt
import numpy as np
from scipy.optimize import curve_fit
### to generate test data
def temp( t , low, high, period, ramp ):
tRed = t % period
dwell = period / 2. - ramp
if tRed < dwell:
out = high
elif tRed < dwell + ramp:
out = high - ( tRed - dwell ) / ramp * ( high - low )
elif tRed < 2 * dwell + ramp:
out = low
elif tRed <= period:
out = low + ( tRed - 2 * dwell - ramp)/ramp * ( high -low )
else:
assert 0
return out + np.random.normal()
### A continuous function that somewhat fits the data
### but definitively gets the period and levels.
### The ramp is less well defined
def fit_func( t, low, high, period, s, delta):
return ( high + low ) / 2. + ( high - low )/2. * np.tanh( s * np.sin( 2 * np.pi * ( t - delta ) / period ) )
time1List = np.arange( 300 ) * 16
time2List = np.linspace( 0, 300 * 16, 7213 )
tempList = np.fromiter( ( temp(t - 6.3 , 41, 155, 63.3, 2.05 ) for t in time1List ), np.float )
funcList = np.fromiter( ( fit_func(t , 41, 155, 63.3, 10., 0 ) for t in time2List ), np.float )
sol, err = curve_fit( fit_func, time1List, tempList, [ 40, 150, 63, 10, 0 ] )
print sol
fittedLow, fittedHigh, fittedPeriod, fittedS, fittedOff = sol
realHigh = fit_func( fittedPeriod / 4., *sol)
realLow = fit_func( 3 / 4. * fittedPeriod, *sol)
print "high, low : ", [ realHigh, realLow ]
print "apprx ramp: ", fittedPeriod/( 2 * np.pi * fittedS ) * 2
realAmp = realHigh - realLow
rampX, rampY = zip( *[ [ t, d ] for t, d in zip( time1List, tempList ) if ( ( d < realHigh - 0.05 * realAmp ) and ( d > realLow + 0.05 * realAmp ) ) ] )
topX, topY = zip( *[ [ t, d ] for t, d in zip( time1List, tempList ) if ( ( d > realHigh - 0.05 * realAmp ) ) ] )
botX, botY = zip( *[ [ t, d ] for t, d in zip( time1List, tempList ) if ( ( d < realLow + 0.05 * realAmp ) ) ] )
fig = plt.figure()
ax = fig.add_subplot( 2, 1, 1 )
bx = fig.add_subplot( 2, 1, 2 )
ax.plot( time1List, tempList, marker='x', linestyle='', zorder=100 )
ax.plot( time2List, fit_func( time2List, *sol ), zorder=0 )
bx.plot( time1List, tempList, marker='x', linestyle='' )
bx.plot( time2List, fit_func( time2List, *sol ) )
bx.plot( rampX, rampY, linestyle='', marker='o', markersize=10, fillstyle='none', color='r')
bx.plot( topX, topY, linestyle='', marker='o', markersize=10, fillstyle='none', color='#00FFAA')
bx.plot( botX, botY, linestyle='', marker='o', markersize=10, fillstyle='none', color='#80DD00')
bx.set_xlim( [ 0, 800 ] )
plt.show()
providing:
>> [155.0445024 40.7417905 63.29983807 13.07677546 -26.36945489]
>> high, low : [155.04450237880076, 40.741790521444436]
>> apprx ramp: 1.540820542195840
There is a few things to note. My fit function works better if the ramp is small compared to the dwell time. Moreover, one will find several posts here where the fitting of step functions is discussed. In general, as fitting requires a meaningful derivative, discrete functions are a problem. There are at least two solutions. a) make a continuous version, fit, and make the result discrete to your liking or b) provide a discrete function and a manual continuous derivative.
EDIT
So here is what I get working with your newly posted data set:
import matplotlib.pyplot as plt
import numpy as np
from scipy.optimize import curve_fit, minimize
def partition( inList, n ):
return zip( *[ iter( inList ) ] * n )
def temp( t, low, high, period, ramp, off ):
tRed = (t - off ) % period
dwell = period / 2. - ramp
if tRed < dwell:
out = high
elif tRed < dwell + ramp:
out = high - ( tRed - dwell ) / ramp * ( high - low )
elif tRed < 2 * dwell + ramp:
out = low
elif tRed <= period:
out = low + ( tRed - 2 * dwell - ramp)/ramp * ( high -low )
else:
assert 0
return out
def chi2( params, xData=None, yData=None, verbose=False ):
low, high, period, ramp, off = params
th = np.fromiter( ( temp( t, low, high, period, ramp, off ) for t in xData ), np.float )
diff = ( th - yData )
diff2 = diff**2
out = np.sum( diff2 )
if verbose:
print '-----------'
print th
print diff
print diff2
print '-----------'
return out
# ~ return th
def fit_func( t, low, high, period, s, delta):
return ( high + low ) / 2. + ( high - low )/2. * np.tanh( s * np.sin( 2 * np.pi * ( t - delta ) / period ) )
inData = np.loadtxt('SOF2.csv', skiprows=1, delimiter=',' )
inData2 = inData[ :, 2 ]
xList = np.arange( len(inData2) )
inData480 = partition( inData2, 480 )
xList480 = partition( xList, 480 )
inDataMean = np.fromiter( (np.mean( x ) for x in inData480 ), np.float )
xMean = np.arange( len( inDataMean) ) * 16
time1List = np.linspace( 0, 16 * len(inDataMean), 500 )
sol, err = curve_fit( fit_func, xMean, inDataMean, [ -40, 150, 60, 10, 10 ] )
print sol
# ~ print chi2([-49,155,62.5,1 , 8.6], xMean, inDataMean )
res = minimize( chi2, [-44.12, 150.0, 62.0, 8.015, 12.3 ], args=( xMean, inDataMean ), method='nelder-mead' )
# ~ print res
print res.x
# ~ print chi2( res.x, xMean, inDataMean, verbose=True )
# ~ print chi2( [-44.12, 150.0, 62.0, 8.015, 6.3], xMean, inDataMean, verbose=True )
fig = plt.figure()
ax = fig.add_subplot( 2, 1, 1 )
bx = fig.add_subplot( 2, 1, 2 )
for x,y in zip( xList480, inData480):
ax.plot( x, y, marker='x', linestyle='', zorder=100 )
bx.plot( xMean, inDataMean , marker='x', linestyle='' )
bx.plot( time1List, fit_func( time1List, *sol ) )
bx.plot( time1List, np.fromiter( ( temp( t , *res.x ) for t in time1List ), np.float) )
bx.plot( time1List, np.fromiter( ( temp( t , -44.12, 150.0, 62.0, 8.015, 12.3 ) for t in time1List ), np.float) )
plt.show()
>> [-49.53569904 166.92138068 62.56131027 1.8547409 8.75673747]
>> [-34.12188737 150.02194584 63.81464913 8.26491754 13.88344623]
As you can see, the data point on the ramp does not fit in. So, it might be that the 16 min time is not that constant? That would be a problem as this is not a local x-error but an accumulating effect.
来源：https://stackoverflow.com/questions/55270346/how-can-fit-the-data-on-temperature-thermal-profile