python - 运行时警告 : invalid value encountered in power in scipy. 优化

Question

使用 scipy.optimize 时收到以下警告:RuntimeWarning:电源中遇到无效值据我了解，这来自 numpy 的 exp 函数，但我不知道如何解决我的问题

我查找了已提出的多种解决方案，但似乎没有一个能够解决我的问题，或者我根本不够熟练，无法将它们应用于我的特定问题

我正在尝试将以下数据拟合到修改后的 3 参数 Weibull 函数

模块:

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

我的数据如下:

k = np.array([0.19624784, 0.24164188, 0.25641914, 0.30762518, 0.35346055,
       0.38394795, 0.43306334, 0.45042259, 0.48428853, 0.50895787,
       0.54263082, 0.5795924 , 0.588977  , 0.59078306, 0.61547335,
       0.66019107, 0.68048225, 0.67923856, 0.68521766, 0.72072055,
       0.75214316, 0.74576285, 0.7398933 , 0.73672459, 0.76617277,
       0.79304079, 0.79531024, 0.78652484, 0.81252188, 0.82150161,
       0.83746662, 0.86754186, 0.85742784, 0.88497858, 0.88234556,
       0.90162162, 0.93864255, 0.92455724, 0.92188063, 0.899652  ,
       0.94256297, 0.97279928, 0.95750676, 0.9395713 , 0.94953204,
       1.        , 0.99591568, 0.97808785, 0.96963366, 0.97140757,
       0.97813063, 0.95783083, 0.94360437, 0.91859959, 0.91154328,
       0.90502759, 0.86196873, 0.85309616, 0.85776327, 0.85093222,
       0.80796675, 0.79844975, 0.79033716, 0.78440427, 0.74708102,
       0.72567559, 0.72527317, 0.71904074, 0.68425383, 0.65547696,
       0.64717119, 0.63439336, 0.6291027 , 0.59739265, 0.58711217,
       0.58749354, 0.56884387, 0.56339959, 0.54077923, 0.54585967,
       0.54278178, 0.51729934, 0.51325348, 0.50718134, 0.51529603,
       0.49221335, 0.4770514 , 0.47483486, 0.47918123, 0.46902945,
       0.45048035, 0.44986787, 0.44836071, 0.44506315, 0.42633282,
       0.41056783, 0.40685124, 0.40554987, 0.39086833, 0.37326042])

t = np.array([0.30110593, 0.30342784, 0.30574744, 0.30806935, 0.31039127,
       0.31271318, 0.3150351 , 0.31735701, 0.31967893, 0.32200084,
       0.32432276, 0.32664467, 0.32896659, 0.33129082, 0.33361274,
       0.33593465, 0.33825657, 0.34057848, 0.3429004 , 0.34522231,
       0.34754423, 0.34986382, 0.35218573, 0.35450765, 0.35682956,
       0.35915148, 0.36147339, 0.36379531, 0.36611722, 0.36843914,
       0.37076338, 0.37308529, 0.37540721, 0.37772912, 0.38005104,
       0.38237295, 0.38469487, 0.38701446, 0.3893387 , 0.39165829,
       0.3939802 , 0.39630212, 0.39862403, 0.40094595, 0.40326786,
       0.40558978, 0.40791169, 0.41023361, 0.41255784, 0.41487976,
       0.41720167, 0.41952359, 0.4218455 , 0.42416742, 0.42648933,
       0.42881125, 0.43113084, 0.43345276, 0.43577467, 0.43809659,
       0.4404185 , 0.44274042, 0.44506233, 0.44738425, 0.44970616,
       0.45202808, 0.45435231, 0.45667423, 0.45899614, 0.46131806,
       0.46363997, 0.46596189, 0.4682838 , 0.47060572, 0.47292531,
       0.47524723, 0.47756914, 0.47989106, 0.48221297, 0.48453489,
       0.4868568 , 0.48917872, 0.49150063, 0.49382487, 0.49614678,
       0.4984687 , 0.50079061, 0.50311253, 0.50543444, 0.50775636,
       0.51007595, 0.51239786, 0.51471978, 0.51704169, 0.51936361,
       0.52168552, 0.52400744, 0.52632935, 0.52865127, 0.53097318])

要拟合的函数:

def weib_4_p(t,a,b,c,d):
    return d*(a/b)*((t-c)/b)**(a-1)*np.exp(-((t-c)/b)**a)

拟合和可视化:

popt, pcov = curve_fit(weib_4_p, t, k, p0 = [1.2, 0.1, 0.3, 10], bounds=((1.1,0,0.1,0),(100,1,100, 1000)))

plt.plot(t, k, 'bo')
plt.plot(t, weib_4_p(t, *popt), 'r-')
plt.show()

有人可以帮我消除这个错误吗？

Answer 1

这并不完全是一个错误，而主要是一个警告。 当您尝试将负数求分数幂时，会弹出此窗口。

例如试试这个:1.055 * (np.array([-2.0]) ** (1.0/2.4)) - 0.055

在您的代码中，由于边界的原因，会发生这种情况，但没有问题并且优化完成。

popt, pcov = curve_fit(weib_4_p, t, k, p0 = [1.2, 0.1, 0.3, 10], bounds=((1.1,0,0.1,0),(100,1,100, 1000)))

print(popt)
# [1.94400274 0.15991757 0.28674807 0.17655357]
print(pcov)
# [[ 2.16729151e-03  7.53415378e-05 -1.21896311e-04 -2.82748341e-05]
#  [ 7.53415378e-05  4.76623815e-06 -5.38376253e-06  4.01774320e-07]
#  [-1.21896311e-04 -5.38376253e-06  7.76347347e-06  8.65238209e-07]
#  [-2.82748341e-05  4.01774320e-07  8.65238209e-07  2.07468076e-06]]