杂乱的曲线拟合给出了错误的答案

2024-03-29 01:47:59 发布

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我有一个振荡数据如下图所示,并希望拟合一个正弦曲线。然而,我的结果是不正确的。在

我想要拟合到这条曲线的函数是:

def radius (z,phi, a0, k0,):

    Z = z.reshape(z.shape[0],1)

    k = np.array([k0,])
    a = np.array([a0,])
    r0 = 110
    rs  = r0 + np.sum(a*np.sin(k*Z +phi), axis=1)
    return rs

正确的解决方案如下:

^{pr2}$

enter image description here

但是,拟合曲线的结果如下:

^{3}$

enter image description here

我的数据如下:

r = np.array([100.09061214, 100.17932773, 100.45526772, 102.27891728,
       113.12440802, 119.30644014, 119.86570527, 119.75184665,
       117.12160143, 101.55081608, 100.07280857, 100.12880236,
       100.39251753, 103.05404178, 117.15257288, 119.74048706,
       119.86955437, 119.37452005, 112.83384329, 101.0507198 ,
       100.05521567])

z = np.array([-407.90074345, -360.38004677, -312.99221012, -266.36934609,
       -224.36240585, -188.55933945, -155.21242348, -122.02778866,
        -87.84335638,  -47.0274899 ,    0.        ,   47.54559191,
         94.97469981,  141.33801462,  181.59490575,  215.77219256,
        248.95956379,  282.28027286,  318.16440024,  360.7246922 ,
        407.940799  ])

因为我的函数只是表示一个傅立叶级数,所以我也尝试了scipy.fftpack.fft(r) 但是我无法重现一个接近我计算过的fft信号。在


Tags: 数据函数fftdefnpa0array曲线
2条回答

这是一个正弦函数,它是一个拟合函数scipy.optimize公司微分进化遗传算法模块,用于确定曲线拟合非线性求解器的初始参数估计。scipy模块使用拉丁超立方体算法来确保对需要搜索范围的参数空间进行彻底搜索。在本例中,这些界限取自数据的最大值和最小值。在

plot3

import numpy, scipy, matplotlib
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
from scipy.optimize import differential_evolution
import warnings

r = numpy.array([100.09061214, 100.17932773, 100.45526772, 102.27891728,
       113.12440802, 119.30644014, 119.86570527, 119.75184665,
       117.12160143, 101.55081608, 100.07280857, 100.12880236,
       100.39251753, 103.05404178, 117.15257288, 119.74048706,
       119.86955437, 119.37452005, 112.83384329, 101.0507198 ,
       100.05521567])

z = numpy.array([-407.90074345, -360.38004677, -312.99221012, -266.36934609,
       -224.36240585, -188.55933945, -155.21242348, -122.02778866,
        -87.84335638,  -47.0274899 ,    0.        ,   47.54559191,
         94.97469981,  141.33801462,  181.59490575,  215.77219256,
        248.95956379,  282.28027286,  318.16440024,  360.7246922 ,
        407.940799  ])

 # rename data to match previous example code
xData = z
yData = r


def func (x, amplitude, center, width, offset): # equation sine[radians] + offset from zunzun.com
 return amplitude * numpy.sin(numpy.pi * (x - center) / width) + offset


# function for genetic algorithm to minimize (sum of squared error)
def sumOfSquaredError(parameterTuple):
    warnings.filterwarnings("ignore") # do not print warnings by genetic algorithm
    val = func(xData, *parameterTuple)
    return numpy.sum((yData - val) ** 2.0)


def generate_Initial_Parameters():
    # min and max used for bounds
    maxX = max(xData)
    minX = min(xData)
    maxY = max(yData)
    minY = min(yData)

    diffY = maxY - minY
    diffX = maxX - minX

    parameterBounds = []
    parameterBounds.append([0.0, diffY]) # search bounds for amplitude
    parameterBounds.append([minX, maxX]) # search bounds for center
    parameterBounds.append([0.0, diffX]) # search bounds for width
    parameterBounds.append([minY, maxY]) # search bounds for offset

    # "seed" the numpy random number generator for repeatable results
    result = differential_evolution(sumOfSquaredError, parameterBounds, seed=3)
    return result.x

# by default, differential_evolution completes by calling curve_fit() using parameter bounds
geneticParameters = generate_Initial_Parameters()

# now call curve_fit without passing bounds from the genetic algorithm,
# just in case the best fit parameters are aoutside those bounds
fittedParameters, pcov = curve_fit(func, xData, yData, geneticParameters)
print('Fitted parameters:', fittedParameters)
print()

modelPredictions = func(xData, *fittedParameters) 

absError = modelPredictions - yData

SE = numpy.square(absError) # squared errors
MSE = numpy.mean(SE) # mean squared errors
RMSE = numpy.sqrt(MSE) # Root Mean Squared Error, RMSE
Rsquared = 1.0 - (numpy.var(absError) / numpy.var(yData))

print()
print('RMSE:', RMSE)
print('R-squared:', Rsquared)

print()


##########################################################
# graphics output section
def ModelAndScatterPlot(graphWidth, graphHeight):
    f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
    axes = f.add_subplot(111)

    # first the raw data as a scatter plot
    axes.plot(xData, yData,  'D')

    # create data for the fitted equation plot
    xModel = numpy.linspace(min(xData), max(xData))
    yModel = func(xModel, *fittedParameters)

    # now the model as a line plot
    axes.plot(xModel, yModel)

    axes.set_xlabel('X Data') # X axis data label
    axes.set_ylabel('Y Data') # Y axis data label

    plt.show()
    plt.close('all') # clean up after using pyplot

graphWidth = 800
graphHeight = 600
ModelAndScatterPlot(graphWidth, graphHeight)

问题是,如果不提供初始猜测,解决方案就无法收敛。尝试添加一个合理的初始猜测:

p0 = [np.pi/.8, 10, 0.017]
popt, pcov = curve_fit(radius, xdata=z, ydata=r, p0=p0)

请注意,如果您要使用其他方法之一,例如trf或{},那么如果没有最初的猜测,那么由于参数无法收敛,这将更有可能返回运行时错误。在

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