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D3QN-PER.py
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# -*- coding: utf-8 -*-
"""
Created on Mon Aug 30 13:03:23 2021
@author: ammar@scch
"""
############################################################################################################
# IMPORTING LIBRARIES
# ##########################################################################################################
import itertools
import time
import pandas as pd
import numpy as np
import os
import matplotlib.pyplot as plt
import gym
import random
import sklearn.preprocessing
import sklearn.pipeline
import torch
import random
import warnings
import copy
import seaborn as sns
import tensorflow as tf
from tensorflow import keras
import math
from IPython.display import clear_output
from gym import spaces
from stable_baselines.common.vec_env import DummyVecEnv
from stable_baselines.deepq.policies import LnMlpPolicy, LnCnnPolicy
from stable_baselines import DQN
from stable_baselines.common.env_checker import check_env
from IPython.display import display
from sklearn.linear_model import LinearRegression, SGDRegressor
from sklearn.kernel_approximation import RBFSampler
from sklearn.decomposition import PCA
from lib import plotting
from collections import deque
from sklearn.preprocessing import StandardScaler, MinMaxScaler
warnings.filterwarnings("ignore", category=DeprecationWarning)
standard = StandardScaler()
minmax = MinMaxScaler()
dir_path = os.getcwd()
############################################################################################################
# **********************************************************************************************************
# CASE STUDIES
# **********************************************************************************************************
# ##########################################################################################################
############################################################################################################
# NASA-CMAPSS
# ##########################################################################################################
dataset = 'train_FD002.txt'
df_full = pd.read_csv(dir_path + r'/CMAPSSData/' + dataset, sep=" ", header=None, skipinitialspace=True).dropna(axis=1)
df_full = df_full.rename(columns={0: 'unit', 1: 'cycle', 2: 'W1', 3: 'W2', 4: 'W3'})
# df = df_full
# mapping
train_set = [*range(1, 23), *range(24, 32), *range(33, 39), 40, 44, 45, 46, 49, 51, 53,
*range(55, 61), 62, 63, 64, 66, 67, 69, 70, 71, 74, 78, 81, 88, 94, 97, 102, 103, 105,
106, 107, 108, 118, 120, 128, 133, 136, 137, 141, 165, 173, 176, 178]
test_set = [185, 188, 192, 194, 197, 208, 212, 214, 217, 219, 225, 231, 234, 238, 244, 252, 253, 256, 258, 260]
combined_set = train_set + test_set
df = pd.DataFrame()
for engines in combined_set:
df = pd.concat([df, df_full[df_full['unit'] == engines]], ignore_index=True)
zip_iterator = zip(combined_set, list(range(1, 101)))
mapping_dict = dict(zip_iterator)
df["unit"] = df["unit"].map(mapping_dict)
df_A = df[df.columns[[0, 1]]]
df_W = df[df.columns[[2, 3, 4]]]
df_S = df[df.columns[list(range(5, 26))]]
df_X = pd.concat([df_W, df_S], axis=1)
# RUL as sensor reading
# df_A['RUL'] = 0
# for i in range(1, 101):
# df_A['RUL'].loc[df_A['unit'] == i] = df_A[df_A['unit'] == i].cycle.max() - df_A[df_A['unit'] == i].cycle
# Standardization
df_X = standard.fit_transform(df_X)
# train_test split
engine_unit = 1
'''##
# %% ENGINE UNIT SPECIFIC DATA
engine_unit = 1
engine_df_A = df_A[df_A['unit'] == engine_unit]
engine_df_X = df_X.iloc[engine_df_A.index[0]:engine_df_A.index[-1] + 1]
engine_df_W = df_W.iloc[engine_df_A.index[0]:engine_df_A.index[-1] + 1]
##
# %% NORMALIZE DATA
X = scaler.fit_transform(engine_df_X)
# X = (((engine_df_X - engine_df_X.mean()) / engine_df_X.std()).fillna(0))
# X = ((engine_df_X - engine_df_X.min()) / (engine_df_X.max() - engine_df_X.min())).fillna(0)).values'''
'''
##
# %% READ RUL & APPEND
# df_RUL = pd.read_csv(dir_path + '/CMAPSSData/RUL_FD001.txt', sep=" ", header=None, skipinitialspace=True).dropna(axis=1)
# df_RUL.columns = ['RUL']
# df_z_scaled_RUL = df_z_scaled.join(df_RUL, 1)
##
# %% REGRESSION TO GET "RUL distribution"
# x = df_z_scaled_RUL.iloc[:,list(range(5, 26))]
# y = df_RUL
##
# %% DIMENSIONALITY REDUCTION TO GET "HEALTH INDICATOR"
sensor_data = df_z_scaled.iloc[:, list(range(5, 26))].dropna(axis=1)
pca = PCA(n_components=1)
principalComponents = (1 - pca.fit_transform(sensor_data))
pdf = pd.DataFrame(data=principalComponents, columns=['health indicator'])
pdf_normalized = (pdf - pdf.min()) / (pdf.max() - pdf.min()) * 100
df_scaled_principal = df_z_scaled.join(pdf_normalized, 1)
df_scaled_principal = df_scaled_principal.rename(columns={0: 'engine unit', 1: 'cycle'})
##
# %% VISUALIZATION
engine_unit = 76
engine_df = df_scaled_principal[df_scaled_principal['engine unit'] == engine_unit]
# engine_df.plot.line('cycle', 'health indicator')
# plt.show()
HI = np.array(engine_df['health indicator'])[0:191].astype(np.float32)
# plt.plot(HI)
# plt.show()
'''
############################################################################################################
# HYDRAULIC SYSTEM
# ##########################################################################################################
''''''
# PS1 = np.loadtxt(r'C:\Users\abbas\Desktop\case_studies\Datasets\HydraulicSystems\PS1.txt').mean(axis=1)
# PS2 = np.loadtxt(r'C:\Users\abbas\Desktop\case_studies\Datasets\HydraulicSystems\PS2.txt').mean(axis=1)
# PS3 = np.loadtxt(r'C:\Users\abbas\Desktop\case_studies\Datasets\HydraulicSystems\PS3.txt').mean(axis=1)
# PS4 = np.loadtxt(r'C:\Users\abbas\Desktop\case_studies\Datasets\HydraulicSystems\PS4.txt').mean(axis=1)
# PS5 = np.loadtxt(r'C:\Users\abbas\Desktop\case_studies\Datasets\HydraulicSystems\PS5.txt').mean(axis=1)
# PS6 = np.loadtxt(r'C:\Users\abbas\Desktop\case_studies\Datasets\HydraulicSystems\PS6.txt').mean(axis=1)
# EPS1 = np.loadtxt(r'C:\Users\abbas\Desktop\case_studies\Datasets\HydraulicSystems\EPS1.txt').mean(axis=1)
# FS1 = np.loadtxt(r'C:\Users\abbas\Desktop\case_studies\Datasets\HydraulicSystems\FS1.txt').mean(axis=1)
# FS2 = np.loadtxt(r'C:\Users\abbas\Desktop\case_studies\Datasets\HydraulicSystems\FS2.txt').mean(axis=1)
# TS1 = np.loadtxt(r'C:\Users\abbas\Desktop\case_studies\Datasets\HydraulicSystems\TS1.txt').mean(axis=1)
# TS2 = np.loadtxt(r'C:\Users\abbas\Desktop\case_studies\Datasets\HydraulicSystems\TS2.txt').mean(axis=1)
# TS3 = np.loadtxt(r'C:\Users\abbas\Desktop\case_studies\Datasets\HydraulicSystems\TS3.txt').mean(axis=1)
# TS4 = np.loadtxt(r'C:\Users\abbas\Desktop\case_studies\Datasets\HydraulicSystems\TS4.txt').mean(axis=1)
# VS1 = np.loadtxt(r'C:\Users\abbas\Desktop\case_studies\Datasets\HydraulicSystems\VS1.txt').mean(axis=1)
# CE = np.loadtxt(r'C:\Users\abbas\Desktop\case_studies\Datasets\HydraulicSystems\CE.txt').mean(axis=1)
# CP = np.loadtxt(r'C:\Users\abbas\Desktop\case_studies\Datasets\HydraulicSystems\CP.txt').mean(axis=1)
# SE = np.loadtxt(r'C:\Users\abbas\Desktop\case_studies\Datasets\HydraulicSystems\SE.txt').mean(axis=1)
#
# X = np.array([PS1, PS2, PS3, PS4, PS5, PS6, EPS1, FS1, FS2, TS1, TS2, TS3, TS4, VS1, CE, CP, SE]).T
# np.savetxt(r"C:\Users\abbas\Desktop\case_studies\Datasets\HydraulicSystems\sensors.csv", X, delimiter=" ")
# df_X = pd.read_csv(r"C:\Users\abbas\Desktop\case_studies\Datasets\HydraulicSystems\sensors.csv", sep=" ", header=None)
# df_X.columns = ['PS1', 'PS2', 'PS3', 'PS4', 'PS5', 'PS6', 'EPS1', 'FS1', 'FS2', 'TS1', 'TS2', 'TS3', 'TS4', 'VS1',
# 'CE', 'CP', 'SE']
#
# df_Y = pd.read_csv(r"C:\Users\abbas\Desktop\case_studies\Datasets\HydraulicSystems\profile.txt", sep="\t", header=None)
# df_Y.columns = ['Cooler_condition', 'Valve_condition', 'Internal_pump_leakage', 'Hydraulic_accumulator', 'stable_flag']
'''fig, ax = plt.subplots()
ax.plot(df_Y['Valve condition'], color='red', label='Valve condition')
ax.tick_params(axis='y', labelcolor='red')
ax.legend(loc="upper right")
ax2 = ax.twinx()
ax2.plot(df_Y['Cooler condition'], color='green', label='Cooler condition')
ax2.tick_params(axis='y', labelcolor='green')
ax2.legend(loc="upper left")
ax3 = ax.twinx()
ax3.plot(df_Y['Internal pump leakage'], color='green', label='Internal pump leakage')
ax3.tick_params(axis='y', labelcolor='green')
ax3.legend(loc="lower right")
ax4 = ax.twinx()
ax4.plot(df_Y['Hydraulic accumulator'], color='blue', label='Hydraulic accumulator')
ax4.tick_params(axis='y', labelcolor='blue')
ax4.legend(loc="lower left")
ax5 = ax.twinx()
ax5.plot(df_Y['stable flag'], color='orange', label='stable flag')
ax5.tick_params(axis='y', labelcolor='orange')
ax5.legend(loc="upper center")
plt.show()'''
############################################################################################################
# YOKOGAWA
# ##########################################################################################################
'''import datetime
df_yoko = pd.read_csv(r'C:/Users/abbas/Desktop/case_studies/Datasets/Yokogawa/CYG-2019-OCT-NOV edited.csv', sep=";")
df_yoko[['Date', 'Time']] = df_yoko['TimeStamp'].str.split(' ', 1, expand=True)
df_yoko['Date'] = pd.to_datetime(df_yoko['Date'], format='%d.%m.%Y')
df_yoko['Time_'] = pd.to_datetime(df_yoko['TimeStamp'])
df_yoko["Month"] = df_yoko["Date"].dt.month
df_yoko["Day"] = df_yoko["Date"].dt.day
df_yoko["Time"] = df_yoko["Time_"].dt.time
df_yoko["Hour"] = df_yoko["Time_"].dt.hour
df_yoko["Minute"] = df_yoko["Time_"].dt.minute
df_yoko["SeverityLevel"] = df_yoko["Severity"] * df_yoko["AlarmLevel"]
df_yoko['Cons'] = df_yoko['TagName'].shift(periods=1)
df_yoko['Cons2'] = df_yoko['TagName'].shift(periods=2)
df_yoko['Cons3'] = df_yoko['TagName'].shift(periods=3)
df_yoko = df_yoko.drop(columns=['SubConditionName', 'TimeStampNS', 'EngUnit', 'StationTimeMilli', 'ItemName', 'Source',
'ModeStatName'])
df_yoko_sub = df_yoko[df_yoko['TagName'] != '025TIC010']
df_yoko_sub = df_yoko_sub[['TimeStamp', 'TagName', 'StationName', 'ConditionName', 'Severity', 'AlarmLevel',
'SeverityLevel', 'AlarmOff', 'AlarmBlink', 'AckRequired', "Month", "Day", "Time",
"Hour", "Minute", 'Cons', 'Cons2', 'Cons3']]
count = df_yoko_sub['Severity'].value_counts()
sort = df_yoko_sub.groupby(["TagName", "Severity"]).size().reset_index(name="Frequency").sort_values(by='Frequency',
ascending=[False])
df_yoko_sub.groupby(["Month", "Day", "Hour"])['TagName'].nunique().reset_index(name="Frequency").sort_values(by='Month')
event = df_yoko_sub.loc[
(df_yoko_sub["Month"] == 11) & (df_yoko_sub["Day"] == 5) & (df_yoko_sub["Time"] == datetime.time(15, 16, 3))]
# Generate a mask for the upper triangle
mask = np.triu(np.ones_like(df_yoko_sub.corr(), dtype=bool))
sns.heatmap(df_yoko_sub.corr(), mask=mask)
'''
############################################################################################################
# **********************************************************************************************************
# HIDDEN MARKOV MODEL (LIBRARY)
# **********************************************************************************************************
# ##########################################################################################################
'''from hmmlearn import hmm
from random import randint
import pickle
# df_S = df[df.columns[[6, 8, 11, 12, 15, 16, 19]]]
# df_hmm = pd.concat([df_A['cycle'], df_S], axis=1)
df_hmm = minmax.fit_transform(df_S)
df_hmm = pd.DataFrame(df_hmm)
cols_to_drop = df_hmm.nunique()[df_hmm.nunique() == 1].index
df_hmm = df_hmm.drop(cols_to_drop, axis=1)
cols_to_drop = df_hmm.nunique()[df_hmm.nunique() == 2].index
df_hmm = df_hmm.drop(cols_to_drop, axis=1).to_numpy()
lengths = [df[df['unit'] == i].cycle.max() for i in range(1, df_A['unit'].max() + 1)]
# o = df_X[df_A[df_A['unit'] == 1].index[0]:df_A[df_A['unit'] == 1].index[-1] + 1]
num_states = 15
remodel = hmm.GaussianHMM(n_components=num_states,
n_iter=500,
verbose=True, )
# init_params="cm", params="cmt")
transmat = np.zeros((num_states, num_states))
# Left-to-right: each state is connected to itself and its
# direct successor.
for i in range(num_states):
if i == num_states - 1:
transmat[i, i] = 1.0
else:
transmat[i, i] = transmat[i, i + 1] = 0.5
# Always start in first state
# startprob = np.zeros(num_states)
# startprob[0] = 1.0
# remodel.startprob_ = startprob
# remodel.transmat_ = transmat
remodel.fit(df_hmm, lengths)
# with open("HMM_model.pkl", "wb") as file: pickle.dump(remodel, file)
# with open("filename.pkl", "rb") as file: pickle.load(file)
state_seq = remodel.predict(df_hmm, lengths)
pred = [state_seq[df[df['unit'] == i].index[0]:df[df['unit'] == i].index[-1] + 1] for i in
range(1, df_A['unit'].max() + 1)]
prob = remodel.predict_proba(df_hmm, lengths)
prob_next_step = remodel.transmat_[state_seq, :]
HMM_out = [prob[df[df['unit'] == i].index[0]:df[df['unit'] == i].index[-1] + 1]
for i in range(1, df_A['unit'].max() + 1)]
failure_states = [pred[i][-1] for i in range(df_A['unit'].max())]
# RUL Prediction - Monte Carlo Simulation
from sklearn.utils import check_random_state
transmat_cdf = np.cumsum(remodel.transmat_, axis=1)
random_state = check_random_state(remodel.random_state)
predRUL = []
for i in range(df_A[df_A['unit'] == 1]['cycle'].max()):
RUL = []
for j in range(100):
cycle = 0
pred_obs_seq = [df_hmm[i]]
pred_state_seq = remodel.predict(pred_obs_seq)
while pred_state_seq[-1] not in set(failure_states):
cycle += 1
prob_next_state = (transmat_cdf[pred_state_seq[-1]] > random_state.rand()).argmax()
prob_next_obs = remodel._generate_sample_from_state(prob_next_state, random_state)
pred_obs_seq = np.append(pred_obs_seq, [prob_next_obs], 0)
pred_state_seq = remodel.predict(pred_obs_seq)
RUL.append(cycle)
# noinspection PyTypeChecker
predRUL.append(round(np.mean(RUL)))
plt.plot(predRUL)
plt.plot(df_A[df_A['unit'] == 1].RUL)
plt.show()
plt.figure(0)
plt.plot(pred[0])
plt.plot(pred[1])
plt.plot(pred[2])
plt.xlabel('# Flights')
plt.ylabel('HMM states')
plt.show()
plt.figure(1)
E = [randint(1, df_A['unit'].max()) for p in range(0, 10)]
for e in E:
plt.plot(pred[e - 1])
plt.xlabel('# Flights')
plt.ylabel('HMM states')
plt.legend(E, title='engine unit')
plt.figure(2)
plt.scatter(list(range(1, len(failure_states) + 1)), failure_states)
plt.xlabel('Engine units')
plt.ylabel('HMM states')
plt.legend(title='failure states')
plt.figure(3)
pca = PCA(n_components=2).fit_transform(df_hmm)
for class_value in range(num_states):
# get row indexes for samples with this class
row_ix = np.where(state_seq == class_value)
plt.scatter(pca[row_ix, 0], pca[row_ix, 1])
plt.xlabel('PCA Feature 1')
plt.ylabel('PCA Feature 2')
plt.legend(list(range(0, num_states)), title='HMM states')
plt.show()
import seaborn as sns
sns.heatmap(df_hmm.corr())'''
'''# Generate samples
X, Y = remodel._generate_sample_from_state(np.array([df_X[0]]))
# Plot the sampled data
plt.plot(X[:, 0], X[:, 1], ".-", label="observations", ms=6,
mfc="orange", alpha=0.7)
plt.show()'''
'''
from scipy.stats import multivariate_normal
from sklearn.mixture import GaussianMixture
df_X = PCA(n_components=2).fit_transform(df_X)
gmm = GaussianMixture(n_components=2, n_init=10)
gmm.fit(df_X)
print("using sklearn")
print("best pi : ", gmm.weights_)
print("best mu :", gmm.means_)
# def plot_densities(data, mu, sigma, alpha = 0.5, colors='grey'):
# grid_x, grid_y = np.mgrid[X[:,0].min():X[:,0].max():200j,
# X[:,1].min():X[:,1].max():200j]
# grid = np.stack([grid_x, grid_y], axis=-1)
# for mu_c, sigma_c in zip(mu, sigma):
# plt.contour(grid_x, grid_y, multivariate_normal(mu_c, sigma_c).pdf(grid), colors=colors, alpha=alpha)
def plot_contours(data, means, covs):
"""visualize the gaussian components over the data"""
plt.figure()
plt.plot(data[:, 0], data[:, 1], 'ko')
delta = 0.025
k = means.shape[0]
x = np.arange(-2.5, 10.0, delta)
y = np.arange(-2.5, 10.0, delta)
x_grid, y_grid = np.meshgrid(x, y)
coordinates = np.array([x_grid.ravel(), y_grid.ravel()]).T
col = ['green', 'red', 'indigo', 'yellow', 'blue']
for i in range(k):
mean = means[i]
cov = covs[i]
z_grid = multivariate_normal(mean, cov).pdf(coordinates).reshape(x_grid.shape)
plt.contour(x_grid, y_grid, z_grid, colors=col[i])
plt.tight_layout()
print("check whether the best one converged: ", gmm.converged_)
print("how many steps to convergence: ", gmm.n_iter_)
plot_contours(df_X, gmm.means_, gmm.covariances_)
plt.xlabel("data[:, 0]", fontsize=12)
plt.ylabel("data[:, 1]", fontsize=12)
plt.show()
def E_step(data, pi, mu, sigma):
N = data.shape[0] # number of data-points
K = pi.shape[0] # number of clusters, following notation used before in description
d = mu.shape[1] # dimension of each data point, think of these as attributes
zeta = np.zeros((N, K)) # this is basically responsibility which should be equal to posterior.
for nk in range(K):
zeta[:, nk] = pi[nk] * multivariate_normal.pdf(data, mean=mu[nk], cov=sigma[nk])
# calculate responsibility for each cluster
zeta = zeta / np.sum(zeta, axis=1, keepdims=True)
# use the sum over all the clusters, thus axis=1. Denominator term.
# print ("zeta shape: ", zeta.shape)
return zeta
def M_step(data, zeta):
N, D = data.shape
K = zeta.shape[1] # use the posterior shape calculated in E-step to determine the no. of clusters
pi = np.zeros(K)
mu = np.zeros((K, D))
sigma = np.zeros((K, D, D))
for ik in range(K):
n_k = zeta[:, ik].sum() # we use the definition of N_k
pi[ik] = n_k / N # definition of the weights
elements = np.reshape(zeta[:, ik], (zeta.shape[0], 1))
# get each columns and reshape it (K, 1) form so that later broadcasting is possible.
mu[ik, :] = (np.multiply(elements, data)).sum(axis=0) / n_k
sigma_sum = 0.
for i in range(N):
var = data[i] - mu[ik]
sigma_sum = sigma_sum + zeta[i, ik] * np.outer(var, var) # outer product creates the covariance matrix
sigma[ik, :] = sigma_sum / n_k
return pi, mu, sigma
def elbo(data, zeta, pi, mu, sigma):
N = data.shape[0] # no. of data-points
K = zeta.shape[1] # no. of clusters
d = data.shape[1] # dim. of each object
l = 0.
for i in range(N):
x = data[i]
for k in range(K):
pos_dist = zeta[i, k] # p(z_i=k|x) = zeta_ik
log_lik = np.log(multivariate_normal.pdf(x, mean=mu[k, :], cov=sigma[k, :, :]) + 1e-20) # log p(x|z)
log_q = np.log(zeta[i, k] + 1e-20) # log q(z) = log p(z_i=k|x)
log_pz = np.log(pi[k] + 1e-20) # log p(z_k =1) =\pi _k
l = (l + np.multiply(pos_dist, log_pz) + np.multiply(pos_dist, log_lik) +
np.multiply(pos_dist, -log_q))
# print ("check loss: ", loss)
return l
def train_loop(data, K, tolerance=1e-3, max_iter=500, restart=50):
N, d = data.shape
elbo_best = -np.inf # loss set to the lowest value
pi_best = None
mu_best = None
sigma_best = None
zeta_f = None
for _ in range(restart):
pi = np.ones(K) / K # if 3 clusters then an array of [.33, .33, .33] # the sum of pi's should be one
# that's why normalized
mu = np.random.rand(K, d) # no condition on
sigma = np.tile(np.eye(d), (K, 1, 1)) # to initialize sigma we first start with ones only at the diagonals
# the sigmas are postive semi-definite and symmetric
last_iter_loss = None
all_losses = []
try:
for i in range(max_iter):
zeta = E_step(data, pi, mu, sigma)
pi, mu, sigma = M_step(data, zeta)
l = elbo(data, zeta, pi, mu, sigma)
if l > elbo_best:
elbo_best = l
pi_best = pi
mu_best = mu
sigma_best = sigma
zeta_f = zeta
if last_iter_loss and abs(
(l - last_iter_loss) / last_iter_loss) < tolerance: # insignificant improvement
break
last_iter_loss = l
all_losses.append(l)
except np.linalg.LinAlgError: # avoid the delta function situation
pass
return elbo_best, pi_best, mu_best, sigma_best, all_losses, zeta_f
best_loss, pi_best, mu_best, sigma_best, ls_lst, final_posterior = train_loop(df_X, 5)
'''
############################################################################################################
# **********************************************************************************************************
# HIDDEN MARKOV MODEL 1
# **********************************************************************************************************
# ##########################################################################################################
'''engine_df_A = df_A[df_A['unit'] == engine_unit]
X = df_X[engine_df_A.index[0]:engine_df_A.index[-1] + 1]
class ProbabilityVector:
def __init__(self, probabilities: dict):
states = probabilities.keys()
probs = probabilities.values()
assert len(states) == len(probs)
"The probabilities must match the states."
assert len(states) == len(set(states))
"The states must be unique."
assert abs(sum(probs) - 1.0) < 1e-12
"Probabilities must sum up to 1."
assert len(list(filter(lambda x: 0 <= x <= 1, probs))) == len(probs), \
"Probabilities must be numbers from [0, 1] interval."
self.states = sorted(probabilities)
self.values = np.array(list(map(lambda x:
probabilities[x], self.states))).reshape(1, -1)
@classmethod
def initialize(cls, states: list):
size = len(states)
rand = np.random.rand(size) / (size ** 2) + 1 / size
rand /= rand.sum(axis=0)
return cls(dict(zip(states, rand)))
@classmethod
def from_numpy(cls, array: np.ndarray, states: list):
return cls(dict(zip(states, list(array))))
@property
def dict(self):
return {k: v for k, v in zip(self.states, list(self.values.flatten()))}
@property
def df(self):
return pd.DataFrame(self.values, columns=self.states, index=['probability'])
def __repr__(self):
return "P({}) = {}.".format(self.states, self.values)
def __eq__(self, other):
if not isinstance(other, ProbabilityVector):
raise NotImplementedError
if (self.states == other.states) and (self.values == other.values).all():
return True
return False
def __getitem__(self, state: str) -> float:
if state not in self.states:
raise ValueError("Requesting unknown probability state from vector.")
index = self.states.index(state)
return float(self.values[0, index])
def __mul__(self, other) -> np.ndarray:
if isinstance(other, ProbabilityVector):
return self.values * other.values
elif isinstance(other, (int, float)):
return self.values * other
else:
NotImplementedError
def __rmul__(self, other) -> np.ndarray:
return self.__mul__(other)
def __matmul__(self, other) -> np.ndarray:
if isinstance(other, ProbabilityMatrix):
return self.values @ other.values
def __truediv__(self, number) -> np.ndarray:
if not isinstance(number, (int, float)):
raise NotImplementedError
x = self.values
return x / number if number != 0 else x / (number + 1e-12)
def argmax(self):
index = self.values.argmax()
return self.states[index]
class ProbabilityMatrix:
def __init__(self, prob_vec_dict: dict):
assert len(prob_vec_dict) > 1, \
"The numebr of input probability vector must be greater than one."
assert len(set([str(x.states) for x in prob_vec_dict.values()])) == 1, \
"All internal states of all the vectors must be indentical."
assert len(prob_vec_dict.keys()) == len(set(prob_vec_dict.keys())), \
"All observables must be unique."
self.states = sorted(prob_vec_dict)
self.observables = prob_vec_dict[self.states[0]].states
self.values = np.stack([prob_vec_dict[x].values \
for x in self.states]).squeeze()
@classmethod
def initialize(cls, states: list, observables: list):
size = len(states)
rand = np.random.rand(size, len(observables)) \
/ (size ** 2) + 1 / size
rand /= rand.sum(axis=1).reshape(-1, 1)
aggr = [dict(zip(observables, rand[i, :])) for i in range(len(states))]
pvec = [ProbabilityVector(x) for x in aggr]
return cls(dict(zip(states, pvec)))
@classmethod
def from_numpy(cls, array:
np.ndarray,
states: list,
observables: list):
p_vecs = [ProbabilityVector(dict(zip(observables, x)))
for x in array]
return cls(dict(zip(states, p_vecs)))
@property
def dict(self):
return self.df.to_dict()
@property
def df(self):
return pd.DataFrame(self.values,
columns=self.observables, index=self.states)
def __repr__(self):
return "PM {} states: {} -> obs: {}.".format(
self.values.shape, self.states, self.observables)
def __getitem__(self, observable: str) -> np.ndarray:
if observable not in self.observables:
raise ValueError("Requesting unknown probability observable from the matrix.")
index = self.observables.index(observable)
return self.values[:, index].reshape(-1, 1)
from itertools import product
from functools import reduce
class HiddenMarkovChain:
def __init__(self, T, E, pi):
self.T = T # transmission matrix A
self.E = E # emission matrix B
self.pi = pi
self.states = pi.states
self.observables = E.observables
def __repr__(self):
return "HML states: {} -> observables: {}.".format(
len(self.states), len(self.observables))
@classmethod
def initialize(cls, states: list, observables: list):
T = ProbabilityMatrix.initialize(states, states)
E = ProbabilityMatrix.initialize(states, observables)
pi = ProbabilityVector.initialize(states)
return cls(T, E, pi)
def _create_all_chains(self, chain_length):
return list(product(*(self.states,) * chain_length))
def score(self, observations: list) -> float:
def mul(x, y): return x * y
score = 0
all_chains = self._create_all_chains(len(observations))
for idx, chain in enumerate(all_chains):
expanded_chain = list(zip(chain, [self.T.states[0]] + list(chain)))
expanded_obser = list(zip(observations, chain))
p_observations = list(map(lambda x: self.E.df.loc[x[1], x[0]], expanded_obser))
p_hidden_state = list(map(lambda x: self.T.df.loc[x[1], x[0]], expanded_chain))
p_hidden_state[0] = self.pi[chain[0]]
score += reduce(mul, p_observations) * reduce(mul, p_hidden_state)
return score
class HiddenMarkovChain_FP(HiddenMarkovChain):
def _alphas(self, observations: list) -> np.ndarray:
alphas = np.zeros((len(observations), len(self.states)))
alphas[0, :] = self.pi.values * self.E[observations[0]].T
for t in range(1, len(observations)):
alphas[t, :] = (alphas[t - 1, :].reshape(1, -1)
@ self.T.values) * self.E[observations[t]].T
return alphas
def score(self, observations: list) -> float:
alphas = self._alphas(observations)
return float(alphas[-1].sum())
class HiddenMarkovChain_Simulation(HiddenMarkovChain):
def run(self, length: int) -> (list, list):
assert length >= 0, "The chain needs to be a non-negative number."
s_history = [0] * (length + 1)
o_history = [0] * (length + 1)
prb = self.pi.values
obs = prb @ self.E.values
s_history[0] = np.random.choice(self.states, p=prb.flatten())
o_history[0] = np.random.choice(self.observables, p=obs.flatten())
for t in range(1, length + 1):
prb = prb @ self.T.values
obs = prb @ self.E.values
s_history[t] = np.random.choice(self.states, p=prb.flatten())
o_history[t] = np.random.choice(self.observables, p=obs.flatten())
return o_history, s_history
class HiddenMarkovChain_Uncover(HiddenMarkovChain_Simulation):
def _alphas(self, observations: list) -> np.ndarray:
alphas = np.zeros((len(observations), len(self.states)))
alphas[0, :] = list(self.pi.values()) * self.E[observations[0]].T
for t in range(1, len(observations)):
alphas[t, :] = (alphas[t - 1, :].reshape(1, -1) @ self.T.values) \
* self.E[observations[t]].T
return alphas
def _betas(self, observations: list) -> np.ndarray:
betas = np.zeros((len(observations), len(self.states)))
betas[-1, :] = 1
for t in range(len(observations) - 2, -1, -1):
betas[t, :] = (self.T.values @ (self.E[observations[t + 1]] * betas[t + 1, :].reshape(-1, 1))).reshape(1,
-1)
return betas
def uncover(self, observations: list) -> list:
alphas = self._alphas(observations)
betas = self._betas(observations)
maxargs = (alphas * betas).argmax(axis=1)
return list(map(lambda x: self.states[x], maxargs))
class HiddenMarkovLayer(HiddenMarkovChain_Uncover):
def _digammas(self, observations: list) -> np.ndarray:
L, N = len(observations), len(self.states)
digammas = np.zeros((L - 1, N, N))
alphas = self._alphas(observations)
betas = self._betas(observations)
score = self.score(observations)
for t in range(L - 1):
P1 = (alphas[t, :].reshape(-1, 1) * self.T.values)
P2 = self.E[observations[t + 1]].T * betas[t + 1].reshape(1, -1)
digammas[t, :, :] = P1 * P2 / score
return digammas
class HiddenMarkovModel:
def __init__(self, hml: HiddenMarkovLayer):
self.layer = hml
self._score_init = 0
self.score_history = []
@classmethod
def initialize(cls, states: list, observables: list):
layer = HiddenMarkovLayer.initialize(states, observables)
return cls(layer)
def update(self, observations: list) -> float:
alpha = self.layer._alphas(observations)
beta = self.layer._betas(observations)
digamma = self.layer._digammas(observations)
score = alpha[-1].sum()
gamma = alpha * beta / score
L = len(alpha)
obs_idx = [self.layer.observables.index(x) \
for x in observations]
capture = np.zeros((L, len(self.layer.states), len(self.layer.observables)))
for t in range(L):
capture[t, :, obs_idx[t]] = 1.0
pi = gamma[0]
T = digamma.sum(axis=0) / gamma[:-1].sum(axis=0).reshape(-1, 1)
E = (capture * gamma[:, :, np.newaxis]).sum(axis=0) / gamma.sum(axis=0).reshape(-1, 1)
self.layer.pi = ProbabilityVector.from_numpy(pi, self.layer.states)
self.layer.T = ProbabilityMatrix.from_numpy(T, self.layer.states, self.layer.states)
self.layer.E = ProbabilityMatrix.from_numpy(E, self.layer.states, self.layer.observables)
return score
def train(self, observations: list, epochs: int, tol=None):
self._score_init = 0
self.score_history = (epochs + 1) * [0]
early_stopping = isinstance(tol, (int, float))
for epoch in range(1, epochs + 1):
score = self.update(observations)
print("Training... epoch = {} out of {}, score = {}.".format(epoch, epochs, score))
if early_stopping and abs(self._score_init - score) / score < tol:
print("Early stopping.")
break
self._score_init = score
self.score_history[epoch] = score
# HI = ["0.", "0.1", "0.2", "0.3", "0.4", "0.5", "0.6", "0.7", "0.8", "0.9", "1."]
HI = np.arange(0., 1.1, 0.1)
pi = {0.: 0, 0.1: 0, 0.2: 0, 0.3: 0, 0.4: 0, 0.5: 0, 0.6: 0, 0.7: 0, 0.8: 0, 0.9: 0, 1.: 1}
model = HiddenMarkovModel.initialize(HI, df_X[0:100, 0])
model.layer.pi = pi
model.train(df_X[0:100, 0], epochs=100)
fig, ax = plt.subplots(1, 1, figsize=(10, 5))
ax.semilogy(model.score_history)
ax.set_xlabel('Epoch')
ax.set_ylabel('Score')
ax.set_title('Training history')
plt.grid()
plt.show()'''
############################################################################################################
# **********************************************************************************************************
# HIDDEN MARKOV MODEL 2
# **********************************************************************************************************
# ##########################################################################################################
'''def forward(V, a, b, initial_distribution):
alpha = np.zeros((V.shape[0], a.shape[0]))
alpha[0, :] = initial_distribution * b[:, V[0]]
for t in range(1, V.shape[0]):
for j in range(a.shape[0]):
# Matrix Computation Steps
# ((1x2) . (1x2)) * (1)
# (1) * (1)
alpha[t, j] = alpha[t - 1].dot(a[:, j]) * b[j, V[t]]
return alpha
def backward(V, a, b):
beta = np.zeros((V.shape[0], a.shape[0]))
# setting beta(T) = 1
beta[V.shape[0] - 1] = np.ones((a.shape[0]))
# Loop in backward way from T-1 to
# Due to python indexing the actual loop will be T-2 to 0
for t in range(V.shape[0] - 2, -1, -1):
for j in range(a.shape[0]):
beta[t, j] = (beta[t + 1] * b[:, V[t + 1]]).dot(a[j, :])
return beta
def baum_welch(V, a, b, initial_distribution, n_iter=100):
M = a.shape[0]
T = len(V)
for n in range(n_iter):
alpha = forward(V, a, b, initial_distribution)
beta = backward(V, a, b)
xi = np.zeros((M, M, T - 1))
for t in range(T - 1):
denominator = np.dot(np.dot(alpha[t, :].T, a) * b[:, V[t + 1]].T, beta[t + 1, :])
for i in range(M):
numerator = alpha[t, i] * a[i, :] * b[:, V[t + 1]].T * beta[t + 1, :].T
xi[i, :, t] = numerator / denominator
gamma = np.sum(xi, axis=1)
a = np.sum(xi, 2) / np.sum(gamma, axis=1).reshape((-1, 1))
# Add additional T'th element in gamma
gamma = np.hstack((gamma, np.sum(xi[:, :, T - 2], axis=0).reshape((-1, 1))))
K = b.shape[1]
denominator = np.sum(gamma, axis=1)
for l in range(K):
b[:, l] = np.sum(gamma[:, V == l], axis=1)
b = np.divide(b, denominator.reshape((-1, 1)))
return (a, b)
def viterbi(V, a, b, initial_distribution):
T = V.shape[0]
M = a.shape[0]
omega = np.zeros((T, M))
omega[0, :] = np.log(initial_distribution * b[:, V[0]])
prev = np.zeros((T - 1, M))
for t in range(1, T):
for j in range(M):
# Same as Forward Probability
probability = omega[t - 1] + np.log(a[:, j]) + np.log(b[j, V[t]])
# This is our most probable state given previous state at time t (1)
prev[t - 1, j] = np.argmax(probability)
# This is the probability of the most probable state (2)
omega[t, j] = np.max(probability)
# Path Array
S = np.zeros(T)
# Find the most probable last hidden state
last_state = np.argmax(omega[T - 1, :])
S[0] = last_state
backtrack_index = 1
for i in range(T - 2, -1, -1):
S[backtrack_index] = prev[i, int(last_state)]
last_state = prev[i, int(last_state)]
backtrack_index += 1
# Flip the path array since we were backtracking
S = np.flip(S, axis=0)
# Convert numeric values to actual hidden states
result = []
for s in S:
if s == 0:
result.append("A")
else:
result.append("B")
return result
engine_df_A = df_A[df_A['unit'] == engine_unit]
V = df_X[engine_df_A.index[0]:engine_df_A.index[-1] + 1]
# Transition Probabilities
a = np.ones((30, 30))
a = a / np.sum(a, axis=1)
# Emission Probabilities
b = np.ones((V.shape[0], V.shape[1]))
b = b / np.sum(b, axis=1).reshape((-1, 1))
# Equal Probabilities for the initial distribution
initial_distribution = np.ones((V.shape[1], V.shape[0]))*0.5
a, b = baum_welch(V, a, b, initial_distribution, n_iter=1000)
predicted_observations = np.array((viterbi(V, a, b, initial_distribution)))
print(predicted_observations)'''
############################################################################################################
# **********************************************************************************************************
# INPUT OUTPUT HIDDEN MARKOV MODEL (LIBRARY)
# **********************************************************************************************************