You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
342 lines
11 KiB
342 lines
11 KiB
2 months ago
|
# -*- coding: utf-8 -*-
|
||
|
|
"""
|
||
|
|
@Time : 2020/6/14 16:42
|
||
|
|
@Author : 杰森·家乐森
|
||
|
|
@File : sae_diagnosis.py
|
||
|
|
@Software: PyCharm
|
||
|
|
"""
|
||
|
|
import json
|
||
|
|
import time
|
||
|
|
import torch
|
||
|
|
import itertools
|
||
|
|
import numpy as np
|
||
|
|
import pandas as pd
|
||
|
|
import torch.nn as nn
|
||
|
|
import torch.utils.data as Data
|
||
|
|
from torch.autograd import Variable
|
||
|
|
from sklearn.metrics import r2_score, mean_squared_error
|
||
|
|
from sklearn.preprocessing import MinMaxScaler
|
||
|
|
from matplotlib import pyplot as plt
|
||
|
|
from warnings import warn
|
||
|
|
from scipy.stats import f
|
||
|
|
|
||
|
|
|
||
|
|
class Diagnosis(nn.Module):
|
||
|
|
def __init__(self, model, dir):
|
||
|
|
super(Diagnosis, self).__init__()
|
||
|
|
self.model = model
|
||
|
|
self.dir = torch.from_numpy(dir).float()
|
||
|
|
self.tile = nn.Parameter(torch.ones(dir.shape[0], 1))
|
||
|
|
for p in self.parameters():
|
||
|
|
p.requires_grad = False
|
||
|
|
self.amp = nn.Parameter(torch.zeros(*dir.shape))
|
||
|
|
|
||
|
|
def forward(self, x):
|
||
|
|
input = self.tile.mm(x) + self.dir * self.amp
|
||
|
|
output = predict(input, self.model)
|
||
|
|
return input, output
|
||
|
|
|
||
|
|
|
||
|
|
class RMSELoss(nn.Module):
|
||
|
|
def __init__(self):
|
||
|
|
super().__init__()
|
||
|
|
self.mse = nn.MSELoss(reduce=False, size_average=False)
|
||
|
|
|
||
|
|
def forward(self, y_true, y_pred):
|
||
|
|
mse_loss = self.mse(y_true, y_pred)
|
||
|
|
return torch.sqrt(mse_loss).data.numpy()[0][0]
|
||
|
|
|
||
|
|
|
||
|
|
def mse_list(y_true, y_pre):
|
||
|
|
return torch.sqrt(torch.mean(torch.pow(y_true - y_pre, 2), dim=1))
|
||
|
|
|
||
|
|
|
||
|
|
def predict(data, model):
|
||
|
|
k = (len(model['weights']) // 2) - 1
|
||
|
|
output = [data]
|
||
|
|
for i in range(len(model['weights'])):
|
||
|
|
# if i == k:
|
||
|
|
# output.append(output[i].mm(model['weights'][i]) + model["bias"][i])
|
||
|
|
# else:
|
||
|
|
output.append(torch.sigmoid(output[i].mm(model['weights'][i]) + model["bias"][i]))
|
||
|
|
return output[-1]
|
||
|
|
|
||
|
|
|
||
|
|
def get_dir_array(data_dim, fault_num):
|
||
|
|
"""
|
||
|
|
获取方向矩阵
|
||
|
|
:param data_dim: 样本维度
|
||
|
|
:param fault_num: 故障个数
|
||
|
|
:return: 方向矩阵
|
||
|
|
"""
|
||
|
|
cols = np.array(list(itertools.combinations(range(data_dim), fault_num)))
|
||
|
|
rows = np.array([[i] * fault_num for i in range(cols.shape[0])])
|
||
|
|
array = np.zeros([cols.shape[0], data_dim])
|
||
|
|
array[rows, cols] = 1
|
||
|
|
return array
|
||
|
|
|
||
|
|
|
||
|
|
def bessel_correction(x, y):
|
||
|
|
n1 = x.shape[0] - 1
|
||
|
|
if y is None:
|
||
|
|
n2 = 0
|
||
|
|
else:
|
||
|
|
n2 = y.shape[0] - 1
|
||
|
|
return n1, n2
|
||
|
|
|
||
|
|
|
||
|
|
def pooled_covariance_matrix(x, y, bessel=True):
|
||
|
|
""" pooled covariance
|
||
|
|
Compute the pooled covariance matrix
|
||
|
|
Equation:
|
||
|
|
The pooled covariance matrix is defined as:
|
||
|
|
.. math::
|
||
|
|
S = \\frac{n_xS_x + n_yS_y}{n_x+n_y}
|
||
|
|
And with bessel correction as:
|
||
|
|
.. math::
|
||
|
|
S = \\frac{(n_x-1)S_x + (n_y-1)S_y}{n_x+n_y-2}
|
||
|
|
Reference
|
||
|
|
---------
|
||
|
|
see: https://en.wikipedia.org/wiki/Hotelling%27s_T-squared_distribution#Pooled_covariance_matrix
|
||
|
|
:param x: array-like, samples of observations
|
||
|
|
:param y: array-like, samples of observations
|
||
|
|
:param bessel: bool, apply bessel correction (default)
|
||
|
|
:return: float, the pooled variance
|
||
|
|
"""
|
||
|
|
_, *p = x.shape
|
||
|
|
p = p[0] if p else 1
|
||
|
|
|
||
|
|
if bessel:
|
||
|
|
n1, n2 = bessel_correction(x, y)
|
||
|
|
else:
|
||
|
|
n1 = x.shape[0]
|
||
|
|
n2 = y.shape[0]
|
||
|
|
try:
|
||
|
|
s1 = n1 * x.cov()
|
||
|
|
except AttributeError:
|
||
|
|
s1 = n1 * np.cov(x, rowvar=False)
|
||
|
|
try:
|
||
|
|
s2 = n2 * y.cov()
|
||
|
|
except AttributeError:
|
||
|
|
s2 = n2 * np.cov(y, rowvar=False)
|
||
|
|
s = (s1 + s2) / (n1 + n2)
|
||
|
|
|
||
|
|
return s
|
||
|
|
|
||
|
|
|
||
|
|
def inverse_covariance_matrix(x, y, bessel=True):
|
||
|
|
"""
|
||
|
|
:param x: array-like, samples of observations
|
||
|
|
:param y: array-like, samples of observations
|
||
|
|
:param bessel: bool, apply bessel correction (default)
|
||
|
|
:return: float, the pooled variance inverse, the pooled variance
|
||
|
|
"""
|
||
|
|
_, *p = x.shape
|
||
|
|
p = p[0] if p else 1
|
||
|
|
s = pooled_covariance_matrix(x, y, bessel)
|
||
|
|
inv = np.linalg.solve(s, np.identity(p))
|
||
|
|
return inv, s
|
||
|
|
|
||
|
|
|
||
|
|
def hotelling_t2(x, y=None, bessel=True, S=None):
|
||
|
|
"""
|
||
|
|
Compute the Hotelling (T2) test statistic.
|
||
|
|
It is the multivariate extension of the Student's t-test.
|
||
|
|
Test the null hypothesis that two multivariate samples have the same underlying
|
||
|
|
probability distribution, when specifying samples for x and y. The number of samples do not have
|
||
|
|
to be the same, but the number of features does have to be equal.
|
||
|
|
Equation:
|
||
|
|
Hotelling's t-squared statistic is defined as:
|
||
|
|
.. math::
|
||
|
|
T^2 = n (\\bar{x} - {\mu})^{T} S^{-1} (\\bar{x} - {\mu})
|
||
|
|
Where S is the pooled covariance matrix and ᵀ represents the transpose.
|
||
|
|
The two sample t-squared statistic is defined as:
|
||
|
|
.. math::
|
||
|
|
T^2 = (\\bar{x} - \\bar{y})^{T} [S(\\frac1 n_x +\\frac 1 n_y)]^{-1} (\\bar{x}̄ - \\bar{y})
|
||
|
|
References:
|
||
|
|
- Hotelling, Harold. (1931). The Generalization of Student's Ratio. Ann. Math. Statist. 2, no. 3, 360--378.
|
||
|
|
doi:10.1214/aoms/1177732979. https://projecteuclid.org/euclid.aoms/1177732979
|
||
|
|
- Hotelling, Harold. (1955) Les Rapports entre les Methodes Statistiques recentes portant sur des Variables Multiples
|
||
|
|
et l'Analyse Factorielle. 107-119.
|
||
|
|
In: L'Analyse Factorielle et ses Applications. Centre National de la Recherche Scientifique, Paris.
|
||
|
|
- Anderson T.W. (1992) Introduction to Hotelling (1931) The Generalization of Student’s Ratio.
|
||
|
|
In: Kotz S., Johnson N.L. (eds) Breakthroughs in Statistics.
|
||
|
|
Springer Series in Statistics (Perspectives in Statistics). Springer, New York, NY
|
||
|
|
:param x: array-like, samples of observations for one or two sample test (required)
|
||
|
|
:param y: for two sample test, array-like, samples of observations (optional), for one sample, list of means to test
|
||
|
|
:param bessel: bool, apply bessel correction (default)
|
||
|
|
:return:
|
||
|
|
statistic: float,
|
||
|
|
the t2 statistic
|
||
|
|
f_value: float,
|
||
|
|
the f value
|
||
|
|
p_value: float,
|
||
|
|
the p value
|
||
|
|
s: 2d array,
|
||
|
|
the pooled variance
|
||
|
|
"""
|
||
|
|
|
||
|
|
try:
|
||
|
|
nx, p = x.shape
|
||
|
|
except AttributeError as ex:
|
||
|
|
if "list" in str(ex):
|
||
|
|
x = np.asarray(x)
|
||
|
|
nx, *p = x.shape
|
||
|
|
p = p[0] if p else 1
|
||
|
|
y = np.asarray(y)
|
||
|
|
else:
|
||
|
|
warn(f"Error: The two samples must be in arrays or dataframes format.")
|
||
|
|
raise ValueError
|
||
|
|
|
||
|
|
# samples observed means
|
||
|
|
x_bar = x.mean(0)
|
||
|
|
|
||
|
|
one_sample = False
|
||
|
|
if y is None:
|
||
|
|
# One sample T-squared
|
||
|
|
one_sample = True
|
||
|
|
y = np.zeros(p)
|
||
|
|
ny = None
|
||
|
|
py = p
|
||
|
|
diff_bar = x_bar - y
|
||
|
|
|
||
|
|
else:
|
||
|
|
ny, *py = y.shape
|
||
|
|
if len(py) == 0:
|
||
|
|
one_sample = True
|
||
|
|
py = p
|
||
|
|
diff_bar = x_bar - y
|
||
|
|
else:
|
||
|
|
# Two sample T-squared
|
||
|
|
py = py[0] if py else 1
|
||
|
|
y_bar = y.mean(0)
|
||
|
|
# difference of means
|
||
|
|
diff_bar = x_bar - y_bar
|
||
|
|
if p != py:
|
||
|
|
warn(
|
||
|
|
f"Error: the two samples must have the same number of features ({p} != {py})."
|
||
|
|
)
|
||
|
|
raise ValueError
|
||
|
|
|
||
|
|
# bessel correction ( -1 )
|
||
|
|
if bessel:
|
||
|
|
n1, n2 = bessel_correction(x, y)
|
||
|
|
else:
|
||
|
|
n1 = nx
|
||
|
|
n2 = ny
|
||
|
|
if one_sample:
|
||
|
|
n = nx
|
||
|
|
else:
|
||
|
|
n = n1 + n2
|
||
|
|
|
||
|
|
# calculate the T2 statistics
|
||
|
|
# Technically, we use diff_bar.T for the transpose, but with Pandas, a 1 dimensional dataframe
|
||
|
|
# is automatically aligned for @ and is not required
|
||
|
|
if one_sample:
|
||
|
|
if S is not None:
|
||
|
|
cov = S
|
||
|
|
else:
|
||
|
|
try:
|
||
|
|
cov = x.cov()
|
||
|
|
except AttributeError:
|
||
|
|
cov = np.cov(x, rowvar=False)
|
||
|
|
inv_cov = np.linalg.pinv(cov)
|
||
|
|
t2_stat = n * (diff_bar.T @ inv_cov @ diff_bar)
|
||
|
|
if S is not None:
|
||
|
|
return t2_stat
|
||
|
|
# f statistic
|
||
|
|
# TODO: use chi square instead of f statistic for large sample
|
||
|
|
f_value = (n - p) * t2_stat / ((n - 1) * p)
|
||
|
|
else:
|
||
|
|
# pooled covariance
|
||
|
|
inv_s, s = inverse_covariance_matrix(x, y, bessel)
|
||
|
|
t2_stat = nx * ny / (nx + ny) * (diff_bar.T @ inv_s @ diff_bar)
|
||
|
|
# f statistic
|
||
|
|
# TODO: use chi square instead of f statistic for large sample
|
||
|
|
f_value = (nx + ny - p - 1) * t2_stat / (n * p)
|
||
|
|
|
||
|
|
# p-value
|
||
|
|
p_value = f.sf(f_value, p, n - p) # survival function, 1 - cdf
|
||
|
|
|
||
|
|
# return the list of results
|
||
|
|
return t2_stat, f_value, p_value, cov if one_sample else s
|
||
|
|
|
||
|
|
|
||
|
|
def rb_diagnosis(model, data, spe, dir_array, epochs=8000):
|
||
|
|
"""
|
||
|
|
重构诊断
|
||
|
|
:param model: 建模模型
|
||
|
|
:param data: 故障数据
|
||
|
|
:param spe: spe限值
|
||
|
|
:param dir_array: 方向矩阵
|
||
|
|
:param epochs: 迭代次数
|
||
|
|
:return: 故障矩阵
|
||
|
|
"""
|
||
|
|
data = np.atleast_2d(data)
|
||
|
|
diagnosis = Diagnosis(model, dir_array)
|
||
|
|
optimizer = torch.optim.SGD(filter(lambda p: p.requires_grad, diagnosis.parameters()), lr=0.4)
|
||
|
|
loss_func = nn.MSELoss()
|
||
|
|
data = torch.from_numpy(data).float()
|
||
|
|
dataset = Data.TensorDataset(data, data)
|
||
|
|
train_set = Data.DataLoader(dataset=dataset)
|
||
|
|
# 训练模型
|
||
|
|
for epoch in range(epochs):
|
||
|
|
for step, (x, y) in enumerate(train_set):
|
||
|
|
b_x = Variable(x).float()
|
||
|
|
b_y = Variable(x).float()
|
||
|
|
b_label = Variable(y)
|
||
|
|
|
||
|
|
compensate, decoded = diagnosis(b_x)
|
||
|
|
if step == 0 and epoch % 100 == 0 and (mse_list(decoded, compensate) < spe).nonzero().shape[0] > 0:
|
||
|
|
break
|
||
|
|
loss = loss_func(decoded, compensate)
|
||
|
|
|
||
|
|
optimizer.zero_grad()
|
||
|
|
loss.backward()
|
||
|
|
optimizer.step()
|
||
|
|
|
||
|
|
else:
|
||
|
|
continue
|
||
|
|
break
|
||
|
|
diagnosis.eval()
|
||
|
|
com, pre = diagnosis(data)
|
||
|
|
|
||
|
|
return dir_array[mse_list(com, pre) < spe], (com - data).data.numpy()[mse_list(com, pre) < spe]
|
||
|
|
|
||
|
|
|
||
|
|
def diagnosis(model, data, spe):
|
||
|
|
"""
|
||
|
|
诊断函数
|
||
|
|
:param model: 建模模型
|
||
|
|
:param data: 诊断数据
|
||
|
|
:param spe: spe限值
|
||
|
|
:return: 故障矩阵
|
||
|
|
"""
|
||
|
|
for i in range(len(model['weights'])):
|
||
|
|
model['weights'][i] = torch.tensor(model['weights'][i])
|
||
|
|
model['bias'][i] = torch.tensor(model['bias'][i])
|
||
|
|
test_data = torch.from_numpy(data).float()
|
||
|
|
predict_data = predict(test_data, model)
|
||
|
|
mse = mse_list(predict_data, test_data).data.numpy()
|
||
|
|
dection_array = np.zeros(data.shape)
|
||
|
|
amp_array = np.zeros(data.shape)
|
||
|
|
# plt.hlines(spe, 0, 1000)
|
||
|
|
# plt.plot(mse)
|
||
|
|
# plt.show()
|
||
|
|
it = iter(np.where(mse > spe)[0])
|
||
|
|
for i in it:
|
||
|
|
time1 = time.time()
|
||
|
|
for j in range(data.shape[1] - 1):
|
||
|
|
dir = get_dir_array(data.shape[1], j + 1)
|
||
|
|
fault_dir, com_amp = rb_diagnosis(model, data[i, :], spe, dir)
|
||
|
|
if fault_dir.shape[0] > 0:
|
||
|
|
dection_array[i, :] = fault_dir[0, :]
|
||
|
|
amp_array[i, :] = com_amp[0, :]
|
||
|
|
time2 = time.time()
|
||
|
|
print("第%d轮诊断完成" % i)
|
||
|
|
print("耗时%f" % (time2 - time1))
|
||
|
|
print(fault_dir[0, :])
|
||
|
|
print(com_amp[0, :])
|
||
|
|
break
|
||
|
|
return dection_array, amp_array
|