Vyhodnocení tlakové zkoušky na betonových krychlích¶

In [1]:

import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
from scipy import stats

In [2]:

%matplotlib inline

Načtení dat¶

Načtení předem připravených dat¶

In [3]:

# pandas
df = pd.read_csv('tlakova_zkouska-data.txt', 
                 sep=';', header=None)
f_cube = df.values.flatten()

# numpy
f_cube = np.loadtxt('tlakova_zkouska-data.txt', delimiter=';')
f_cube

Out[3]:

array([31.1, 26.1, 33.5, 30.9, 29.7, 31.3, 22.1, 34. , 34.8, 41.6, 30.4,
       31. , 31.9, 39.5, 32.8, 28.1, 32.5, 33.6, 30.7, 35.6, 30.4, 36.5,
       32.6, 33.9, 25.2, 37.1, 25.6, 34.1, 34.6, 29.7, 29.3, 31.7, 34. ,
       29.5, 29.5, 32.4, 32. , 24.5, 24.2, 29.6, 34.4, 32. , 31.1, 33.7,
       35. , 35.5, 33.2, 30.9, 35.8, 38.1, 30.5, 30.8, 36.4, 27.8, 30.1,
       27.4, 34.1, 26.7, 24.1, 34.6, 33.7, 32.6, 31.8, 25.8, 35.1, 30. ,
       33.6, 36.4, 34.3, 32.1, 32.3, 26.9, 24.9, 28.1, 33.8, 30.8, 35.3,
       29.7, 32.7, 31.2, 30.1, 32.6, 36.4, 31.4, 33.8, 37. , 38.9, 29.6,
       30.1, 29.7, 28.6, 38.5, 28.7, 25.6, 31.8, 26.7, 29.2, 36.6, 37. ,
       27.3])

Stanovení charakteristik souboru naměřených hodnot¶

In [4]:

width = 8
print('{:>{width}} = {: d}'.format('n', f_cube.shape[0], width=width))
print('{:>{width}} = {: .1f}'.format('min', f_cube.min(), width=width))
print('{:>{width}} = {: .1f}'.format('max', f_cube.max(), width=width))
print('{:>{width}} = {: .3f}'.format('mu', f_cube.mean(), width=width))
print('{:>{width}} = {: .3f}'.format('std', f_cube.std(ddof=1), width=width))
print('{:>{width}} = {: .6f}'.format('skew', stats.skew(f_cube, bias=False), width=width))
print('{:>{width}} = {: .6f}'.format('kurtosis', stats.kurtosis(f_cube), width=width))
print('{:>{width}} = {: .2f} %'.format('CoV', f_cube.std() / f_cube.mean() * 100, width=width))

       n =  100
     min =  22.1
     max =  41.6
      mu =  31.705
     std =  3.770
    skew = -0.094538
kurtosis = -0.140057
     CoV =  11.83 %

Aproximace pomocí známých hustot pravděpodobnosti¶

In [5]:

params = stats.norm.fit(f_cube)
rv_norm = stats.norm(*params)
print('params =', params)
print('mu, std =', rv_norm.mean(), rv_norm.std())

params = (31.705, 3.7511698175369244)
mu, std = 31.705 3.7511698175369244

In [6]:

params = stats.lognorm.fit(f_cube, floc=0)
rv_lognorm = stats.lognorm(*params)
print('params =', params)
print('mu, std =', rv_lognorm.mean(), rv_lognorm.std())

params = (0.12102468381267445, 0.0, 31.47761020411158)
mu, std = 31.708982265721623 3.851664722157557

In [7]:

params = stats.weibull_min.fit(f_cube, floc=0)
rv_weib = stats.weibull_min(*params)
print('params =', params)
print('mu, std =', rv_weib.mean(), rv_weib.std())

params = (9.229216368943419, 0, 33.36086954302854)
mu, std = 31.627341745240383 4.1039050900775

Grafické zobrazení hustot¶

In [8]:

fig, ax = plt.subplots(figsize=(6,3), tight_layout=True)
ax.hist(f_cube, bins='sqrt', ec='k', density=True, label='data', alpha=.5)

x = np.linspace(20, 45, 100)
ax.plot(x, rv_norm.pdf(x), label='norm')

ax.plot(x, rv_lognorm.pdf(x), label='lognorm')

ax.plot(x, rv_weib.pdf(x), label='weibull')

ax.legend();

No description has been provided for this image

Grafické zobrazení distribučních funkcí¶

In [9]:

fig, ax = plt.subplots(figsize=(6,3), tight_layout=True)
ax.hist(f_cube, bins='sqrt', ec='k', density=True, label='data', 
        alpha=.5, cumulative=True)

x = np.linspace(20, 45, 100)
ax.plot(x, rv_norm.cdf(x), label='norm')

ax.plot(x, rv_lognorm.cdf(x), label='lognorm')

ax.plot(x, rv_weib.cdf(x), label='weibull')

ax.legend();

Výpočet kvantilů¶

In [11]:

def print_quantils(rv, name):
    print(name)
    print('\tf_0.05  =', rv.ppf(0.05))
    print('\tf_0.95  =', rv.ppf(0.95))
    print('\tf_0.001 =', rv.ppf(0.001))
print_quantils(rv_norm, 'rv_norm')
print_quantils(rv_lognorm, 'rv_lognorm')
print_quantils(rv_weib, 'rv_weib')

rv_norm
	f_0.05  = 25.534874720313493
	f_0.95  = 37.8751252796865
	f_0.001 = 20.113013843925774
rv_lognorm
	f_0.05  = 25.795720751131043
	f_0.95  = 38.41101994091577
	f_0.001 = 21.655990598220484
rv_weib
	f_0.05  = 24.180786003431493
	f_0.95  = 37.572250185559724
	f_0.001 = 15.78360548445582