目录

• 相关链接
• 完整代码下载链接
• 1 读取数据预处理的文件
• 2 查看时序
• 3 异常值缺失值
• • 3.1 HeatMap颜色
  • 3.2 缺失值处理（多种填充方式）
• 4 数据平滑与采样
• 5 平稳性检验
• 6 数据转换
• 7 特征工程
• • 7.1 时序提取
  • 7.2 编码循环特征
  • 7.3 时间序列分解
  • 7.4 滞后特征
  • 7.6 探索性数据分析
  • 7.7 相关性分析
  • 7.8 自相关分析
• 8 建模
• • 8.1 时序中交叉验证
  • 8.2 单变量时间序列模型
  • • 8.2.1 ARIMA
    • 8.2.2 LSTM
    • 8.2.3 AutoARIMA
  • 8.3 多元时序预测
  • • 8.3.1 多元Propher

相关链接 （1）【第十届“泰迪杯”数据挖掘挑战赛】B题：电力系统负荷预测分析 问题一Baseline方案
（2）【第十届“泰迪杯”数据挖掘挑战赛】B题：电力系统负荷预测分析 问题一ARIMA、AutoARIMA、LSTM、Prophet 多方案实现
（3）【第十届“泰迪杯”数据挖掘挑战赛】B题：电力系统负荷预测分析 问题二 时间突变分析 Python实现
完整代码下载链接 https://mianbaoduo.com/o/bread/YpiZmp9v
1 读取数据预处理的文件

import numpy as np import pandas as pdimport seaborn as sns import matplotlib.pyplot as plt from colorama import Forefrom sklearn.metrics import mean_absolute_error, mean_squared_error import mathimport warnings # Supress warnings warnings.filterwarnings('ignore') plt.rcParams['font.sans-serif'] = ['SimHei']# 用来正常显示中文标签 plt.rcParams['axes.unicode_minus'] = False# 用来正常显示负号 np.random.seed(7)df = pd.read_csv(r"./data/泰迪杯数据2.csv") df.head()

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df= df.rename(columns={'日期1':'date'}) df

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2 查看时序

from datetime import datetime, date df['date'] = pd.to_datetime(df['date']) df.head().style.set_properties(subset=['date'], **{'background-color': 'dodgerblue'})

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# To compelte the data, as naive method, we will use ffill f, ax = plt.subplots(nrows=7, ncols=1, figsize=(15, 25))for i, column in enumerate(df.drop('date', axis=1).columns): 。。。略

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df = df.sort_values(by='date')# Check time intervals df['delta'] = df['date'] - df['date'].shift(1)df[['date', 'delta']].head()

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df['delta'].sum(), df['delta'].count()

(Timedelta(‘13 days 23:45:00’), 1439)

df = df.drop('delta', axis=1) df.isna().sum()

date 0
总有功功率（kw） 51
最高温度 6
最低温度 0
白天风力风向 0
夜晚风力风向 0
天气1 0
天气2 0
dtype: int64

3 异常值缺失值

f, ax = plt.subplots(nrows=2, ncols=1, figsize=(15, 15))。。。略ax[1].set_xlim([date(2018, 1, 1), date(2018, 1, 15)])

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3.1 HeatMap颜色

Accent, Accent_r, Blues, Blues_r, BrBG, BrBG_r, BuGn, BuGn_r,
BuPu, BuPu_r, CMRmap, CMRmap_r, Dark2, Dark2_r, GnBu, GnBu_r,
Greens, Greens_r, Greys, Greys_r, OrRd, OrRd_r,
Oranges, Oranges_r, PRGn, PRGn_r, Paired, Paired_r, Pastel1, Pastel1_r, Pastel2, Pastel2_r,
PiYG, PiYG_r, PuBu, PuBuGn, PuBuGn_r, PuBu_r, PuOr, PuOr_r, PuRd, PuRd_r, Purples, Purples_r,
RdBu, RdBu_r, RdGy, RdGy_r, RdPu, RdPu_r, RdYlBu, RdYlBu_r, RdYlGn, RdYlGn_r, Reds, Reds_r,
Set1, Set1_r, Set2, Set2_r, Set3, Set3_r, Spectral, Spectral_r, Wistia, Wistia_r, YlGn, YlGnBu,
YlGnBu_r, YlGn_r, YlOrBr, YlOrBr_r, YlOrRd, YlOrRd_r, afmhot, afmhot_r, autumn, autumn_r, binary,
binary_r, bone, bone_r, brg, brg_r, bwr, bwr_r, cividis, cividis_r, cool, cool_r, coolwarm,
coolwarm_r, copper, copper_r, cubehelix, cubehelix_r, flag, flag_r, gist_earth, gist_earth_r,
gist_gray, gist_gray_r, gist_heat, gist_heat_r, gist_ncar, gist_ncar_r, gist_rainbow,
gist_rainbow_r, gist_stern, gist_stern_r, gist_yarg, gist_yarg_r, gnuplot, gnuplot2,
gnuplot2_r, gnuplot_r, gray, gray_r, hot, hot_r, hsv, hsv_r, icefire, icefire_r, inferno,
inferno_r, jet, jet_r, magma, magma_r, mako, mako_r, nipy_spectral, nipy_spectral_r,
ocean, ocean_r, pink, pink_r, plasma, plasma_r, prism, prism_r, rainbow, rainbow_r,
rocket, rocket_r, seismic, seismic_r, spring, spring_r, summer, summer_r, tab10, tab10_r,
tab20, tab20_r, tab20b, tab20b_r, tab20c, tab20c_r, terrain, terrain_r, twilight, twilight_r,
twilight_shifted, twilight_shifted_r, viridis, viridis_r, vlag, vlag_r, winter, winter_r

f, ax = plt.subplots(nrows=1, ncols=1, figsize=(16,5))sns.heatmap(df.T.isna(), cmap='Reds_r') ax.set_title('Missing Values', fontsize=16)for tick in ax.yaxis.get_major_ticks(): tick.label.set_fontsize(14) plt.show()

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3.2 缺失值处理（多种填充方式）

f, ax = plt.subplots(nrows=4, ncols=1, figsize=(15, 12))sns.lineplot(x=df['date'], y=df['总有功功率（kw）'].fillna(0), ax=ax[0], color='darkorange', label = 'modified') sns.lineplot(x=df['date'], y=df['总有功功率（kw）'].fillna(np.inf), ax=ax[0], color='dodgerblue', label = 'original') ax[0].set_title('Fill NaN with 0', fontsize=14) ax[0].set_ylabel(ylabel='Volume', fontsize=14)。。。略for i in range(4): ax[i].set_xlim([date(2018, 1, 1), date(2018, 1, 15)])plt.tight_layout() plt.show()

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df['总有功功率（kw）'] = df['总有功功率（kw）'].interpolate()

4 数据平滑与采样

重采样可以提供数据的附加信息。有两种类型的重采样:
上采样是指增加采样频率(例如从几天到几小时)
下采样是指降低采样频率(例如，从几天到几周)
在这个例子中，我们将使用。resample()函数

fig, ax = plt.subplots(ncols=1, nrows=3, sharex=True, figsize=(16,12))sns.lineplot(df['date'], df['总有功功率（kw）'], color='dodgerblue', ax=ax[0]) ax[0].set_title('总有功功率（kw） Volume', fontsize=14)。。。略 for i in range(3): ax[i].set_xlim([date(2018, 1, 1), date(2018, 1, 14)])

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# As we can see, downsample to weekly could smooth the data and hgelp with analysis downsample = df[['date', '总有功功率（kw）', ]].resample('7D', on='date').mean().reset_index(drop=False)# df = downsample.copy() downsample

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5 平稳性检验

目测:绘制时间序列并检查趋势或季节性
基本统计:分割时间序列并比较每个分区的平均值和方差
统计检验:增强的迪基富勒检验

# A year has 52 weeks (52 weeks * 7 days per week) aporx. rolling_window = 52 f, ax = plt.subplots(nrows=1, ncols=1, figsize=(15, 6))。。。略 plt.show()

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现在，我们将检查每个变量: p值小于0.05 检查ADF统计值与critical_values的比较范围

from statsmodels.tsa.stattools import adfullerresult = adfuller(df['总有功功率（kw）'].values) result

(-5.279986646245767, 6.0232754503160645e-06, 24, 1415,
{‘1%’: -3.434979825137732, ‘5%’: -2.8635847436211317, ‘10%’: -2.5678586114197954}, 29608.16365155926)

# Thanks to https://www.kaggle.com/iamleonie for this function! f, ax = plt.subplots(nrows=1, ncols=1, figsize=(12, 6))def visualize_adfuller_results(series, title, ax): 。。。略visualize_adfuller_results(df['总有功功率（kw）'].values, '总有功功率（kw）',ax=ax) # visualize_adfuller_results(df['temperature'].values, 'Temperature', ax[1, 0]) # visualize_adfuller_results(df['river_hydrometry'].values, 'River_Hydrometry', ax[0, 1]) # visualize_adfuller_results(df['drainage_volume'].values, 'Drainage_Volume', ax[1, 1]) # visualize_adfuller_results(df['depth_to_groundwater'].values, 'Depth_to_Groundwater', ax[2, 0])# f.delaxes(ax[2, 1]) plt.tight_layout() plt.show()

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如果数据不是静态的，但我们想使用一个模型，如ARIMA(需要这个特征)，数据必须转换。
将序列转换为平稳序列的两种最常见的方法是:
? 变换:例如对数或平方根，以稳定非恒定方差
? 差分:从以前的值中减去当前值

6 数据转换 （1）对数

df['总有功功率（kw）_log'] = np.log(abs(df['总有功功率（kw）']))。。。略 sns.distplot(df['总有功功率（kw）_log'], ax=ax[1])

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（2）一阶差分

# First Order Differencing ts_diff = np.diff(df['总有功功率（kw）']) df['总有功功率（kw）_diff_1'] = np.append([0], ts_diff)f, ax = plt.subplots(nrows=1, ncols=1, figsize=(15, 6)) visualize_adfuller_results(df['总有功功率（kw）_diff_1'], 'Differenced (1. Order) \n Depth to Groundwater', ax)

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7 特征工程 7.1 时序提取

df['year'] = pd.DatetimeIndex(df['date']).year df['month'] = pd.DatetimeIndex(df['date']).month df['day'] = pd.DatetimeIndex(df['date']).day 。。。略df[['date', 'year', 'month', 'day', 'day_of_year', 'week_of_year', 'quarter', 'season']].head()

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7.2 编码循环特征

f, ax = plt.subplots(nrows=1, ncols=1, figsize=(20, 3))sns.lineplot(x=df['date'], y=df['month'], color='dodgerblue') ax.set_xlim([date(2018, 1, 1), date(2018, 1, 14)]) plt.show()

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month_in_year = 12 df['month_sin'] = np.sin(2*np.pi*df['month']/month_in_year) df['month_cos'] = np.cos(2*np.pi*df['month']/month_in_year)f, ax = plt.subplots(nrows=1, ncols=1, figsize=(6, 6))sns.scatterplot(x=df.month_sin, y=df.month_cos, color='dodgerblue') plt.show()

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7.3 时间序列分解

from statsmodels.tsa.seasonal import seasonal_decomposecore_columns =[ '总有功功率（kw）'] 。。。略

fig, ax = plt.subplots(ncols=2, nrows=4, sharex=True, figsize=(16,8))for i, column in enumerate(['总有功功率（kw）', '最低温度']):res = seasonal_decompose(df[column], freq=52, model='additive', extrapolate_trend='freq')ax[0,i].set_title('Decomposition of {}'.format(column), fontsize=16) res.observed.plot(ax=ax[0,i], legend=False, color='dodgerblue') ax[0,i].set_ylabel('Observed', fontsize=14) 。。。略plt.show()

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7.4 滞后特征

weeks_in_month = 4for column in core_columns: df[f'{column}_seasonal_shift_b_2m'] = df[f'{column}_seasonal'].shift(-2 * weeks_in_month) df[f'{column}_seasonal_shift_b_1m'] = df[f'{column}_seasonal'].shift(-1 * weeks_in_month) df[f'{column}_seasonal_shift_1m'] = df[f'{column}_seasonal'].shift(1 * weeks_in_month) df[f'{column}_seasonal_shift_2m'] = df[f'{column}_seasonal'].shift(2 * weeks_in_month) df[f'{column}_seasonal_shift_3m'] = df[f'{column}_seasonal'].shift(3 * weeks_in_month)

7.6 探索性数据分析

f, ax = plt.subplots(nrows=1, ncols=1, figsize=(15, 6)) f.suptitle('Seasonal Components of Features', fontsize=16)for i, column in enumerate(core_columns): 。。。略plt.tight_layout() plt.show()

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7.7 相关性分析

f, ax = plt.subplots(nrows=1, ncols=1, figsize=(8, 8))。。。略plt.tight_layout() plt.show()

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7.8 自相关分析

from pandas.plotting import autocorrelation_plotautocorrelation_plot(df['总有功功率（kw）_diff_1']) plt.show()

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from statsmodels.graphics.tsaplots import plot_acf from statsmodels.graphics.tsaplots import plot_pacff, ax = plt.subplots(nrows=2, ncols=1, figsize=(16, 8)) 。。。略plt.show()

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8 建模 8.1 时序中交叉验证

from sklearn.model_selection import TimeSeriesSplitN_SPLITS = 3X = df['date'] y = df['总有功功率（kw）']folds = TimeSeriesSplit(n_splits=N_SPLITS)

f, ax = plt.subplots(nrows=N_SPLITS, ncols=2, figsize=(16, 9))for i, (train_index, valid_index) in enumerate(folds.split(X)): 。。。略 for i in range(N_SPLITS): ax[i, 0].set_xlim([date(2018, 1, 1), date(2018, 1, 14)]) ax[i, 1].set_xlim([date(2018, 1, 1), date(2018, 6, 30)])plt.tight_layout() plt.show()

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8.2 单变量时间序列模型

train_size = int(0.85 * len(df)) test_size = len(df) - train_size df = df.fillna(0) univariate_df = df[['date', '总有功功率（kw）']].copy() univariate_df.columns = ['ds', 'y']train = univariate_df.iloc[:train_size, :]x_train, y_train = pd.DataFrame(univariate_df.iloc[:train_size, 0]), pd.DataFrame(univariate_df.iloc[:train_size, 1]) x_valid, y_valid = pd.DataFrame(univariate_df.iloc[train_size:, 0]), pd.DataFrame(univariate_df.iloc[train_size:, 1])print(len(train), len(x_valid))

8.2.1 ARIMA

from statsmodels.tsa.arima_model import ARIMA import warnings warnings.ignore=True。。。略# Prediction with ARIMA # y_pred, se, conf = model_fit.forecast(202) y_pred, se, conf = model_fit.forecast(216)# Calcuate metrics score_mae = mean_absolute_error(y_valid, y_pred) score_rmse = math.sqrt(mean_squared_error(y_valid, y_pred))print(Fore.GREEN + 'RMSE: {}'.format(score_rmse))

RMSE: 30973.353510293528

f, ax = plt.subplots(1) f.set_figheight(6) f.set_figwidth(15)model_fit.plot_predict(1, 1300, ax=ax) sns.lineplot(x=x_valid.index, y=y_valid['y'], ax=ax, color='orange', label='Ground truth') #navajowhiteax.set_title(f'Prediction \n MAE: {score_mae:.2f}, RMSE: {score_rmse:.2f}', fontsize=14) ax.set_xlabel(xlabel='Date', fontsize=14) ax.set_ylabel(ylabel='总有功功率（kw）', fontsize=14)ax.set_ylim(100000, 350392) plt.show()

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f, ax = plt.subplots(1) f.set_figheight(4) f.set_figwidth(15)sns.lineplot(x=x_valid.index, y=y_pred, ax=ax, color='blue', label='predicted') #navajowhite sns.lineplot(x=x_valid.index, y=y_valid['y'], ax=ax, color='orange', label='Ground truth') #navajowhiteax.set_xlabel(xlabel='Date', fontsize=14) ax.set_ylabel(ylabel='总有功功率（kw）', fontsize=14)plt.show()

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8.2.2 LSTM

from sklearn.preprocessing import MinMaxScalerdata = https://www.it610.com/article/univariate_df.filter(['y']) #Convert the dataframe to a numpy array dataset = data.valuesscaler = MinMaxScaler(feature_range=(-1, 0)) scaled_data = https://www.it610.com/article/scaler.fit_transform(dataset)scaled_data[:10]

array([[-0.50891613], [-0.50891613], [-0.59567808], [-0.59567808], [-0.60361527], [-1. ], [-0.63509216], [-0.63509216], [-0.58983584], [-0.58983584]])

# Defines the rolling window look_back = 52 # Split into train and test sets train, test = scaled_data[:train_size-look_back,:], scaled_data[train_size-look_back:,:]d。。。略 x_train, y_train = create_dataset(train, look_back) x_test, y_test = create_dataset(test, look_back)# reshape input to be [samples, time steps, features] x_train = np.reshape(x_train, (x_train.shape[0], 1, x_train.shape[1])) x_test = np.reshape(x_test, (x_test.shape[0], 1, x_test.shape[1]))print(len(x_train), len(x_test))

from keras.models import Sequential from keras.layers import Dense, LSTM#Build the LSTM model model = Sequential() model.add(LSTM(128, return_sequences=True, input_shape=(x_train.shape[1], x_train.shape[2]))) model.add(LSTM(64, return_sequences=False)) model.add(Dense(25)) model.add(Dense(1))# Compile the model model.compile(optimizer='adam', loss='mean_squared_error')#Train the model model.fit(x_train, y_train, batch_size=16, epochs=10, validation_data=https://www.it610.com/article/(x_test, y_test))model.summary()

Epoch 1/10 70/70 [] - 15s 10ms/step - loss: 0.0417 - val_loss: 0.0071 Epoch 2/10 70/70 [] - 0s 3ms/step - loss: 0.0104 - val_loss: 0.0036 Epoch 3/10 70/70 [] - 0s 6ms/step - loss: 0.0081 - val_loss: 0.0023 Epoch 4/10 70/70 [] - 0s 4ms/step - loss: 0.0064 - val_loss: 0.0017 Epoch 5/10 70/70 [] - 0s 4ms/step - loss: 0.0059 - val_loss: 0.0017 Epoch 6/10 70/70 [] - 0s 3ms/step - loss: 0.0053 - val_loss: 0.0019 Epoch 7/10 70/70 [] - 0s 3ms/step - loss: 0.0065 - val_loss: 0.0019 Epoch 8/10 70/70 [] - 0s 3ms/step - loss: 0.0051 - val_loss: 0.0013 Epoch 9/10 70/70 [] - 0s 3ms/step - loss: 0.0048 - val_loss: 0.0023 Epoch 10/10 70/70 [] - 0s 4ms/step - loss: 0.0052 - val_loss: 0.0012 Model: “sequential” _________________________________________________________________
Layer (type) Output Shape Param # =================================================================
lstm (LSTM) (None, 1, 128) 92672
stm_1 (LSTM) (None, 64) 49408
dense (Dense) (None, 25) 1625
dense_1 (Dense) (None, 1) 26 =================================================================
Total params: 143,731 Trainable params: 143,731 Non-trainable params: 0

# Lets predict with the model train_predict = model.predict(x_train) test_predict = model.predict(x_test)# invert predictions train_predict = scaler.inverse_transform(train_predict) y_train = scaler.inverse_transform([y_train])test_predict = scaler.inverse_transform(test_predict) y_test = scaler.inverse_transform([y_test])# Get the root mean squared error (RMSE) and MAE score_rmse = np.sqrt(mean_squared_error(y_test[0], test_predict[:,0])) score_mae = mean_absolute_error(y_test[0], test_predict[:,0]) print(Fore.GREEN + 'RMSE: {}'.format(score_rmse)) from sklearn.metrics import r2_score print('R2-score:',r2_score(y_test[0], test_predict[:,0]))

RMSE: 4502.091881948914
R2-score: 0.9519027039841994

x_train_ticks = univariate_df.head(train_size)['ds'] y_train = univariate_df.head(train_size)['y'] x_test_ticks = univariate_df.tail(test_size)['ds']# Plot the forecast f, ax = plt.subplots(1) f.set_figheight(6) f.set_figwidth(15)sns.lineplot(x=x_train_ticks, y=y_train, ax=ax, label='Train Set') #navajowhite sns.lineplot(x=x_test_ticks, y=test_predict[:,0], ax=ax, color='green', label='Prediction') #navajowhite sns.lineplot(x=x_test_ticks, y=y_test[0], ax=ax, color='orange', label='Ground truth') #navajowhiteax.set_title(f'Prediction \n MAE: {score_mae:.2f}, RMSE: {score_rmse:.2f}', fontsize=14) ax.set_xlabel(xlabel='Date', fontsize=14) ax.set_ylabel(ylabel='总有功功率（kw）', fontsize=14)plt.show()

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8.2.3 AutoARIMA

from statsmodels.tsa.arima_model import ARIMA import pmdarima as pm 。。。略 print(model.summary())

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y_pred = model.predict(216) from sklearn.metrics import r2_score print('R2-score:',r2_score(y_valid, y_pred))

R2-score: -0.08425358340633804

model.plot_diagnostics(figsize=(16,8)) plt.show()

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8.3 多元时序预测

df.columns

【数学建模|【第十届“泰迪杯”数据挖掘挑战赛】B题（电力系统负荷预测分析 ARIMA、AutoARIMA、LSTM、Prophet、多元Prophet 实现）】Index([‘date’, ‘总有功功率（kw）’, ‘最高温度’, ‘最低温度’, ‘白天风力风向’, ‘夜晚风力风向’, ‘天气1’, ‘天气2’], dtype=‘object’)

feature_columns = [ '最高温度', '最低温度', '白天风力风向', '夜晚风力风向', '天气1', '天气2' ] target_column = ['总有功功率（kw）']train_size = int(0.85 * len(df))multivariate_df = df[['date'] + target_column + feature_columns].copy() multivariate_df.columns = ['ds', 'y'] + feature_columnstrain = multivariate_df.iloc[:train_size, :] x_train, y_train = pd.DataFrame(multivariate_df.iloc[:train_size, [0,2,3,4,5,6,7]]), pd.DataFrame(multivariate_df.iloc[:train_size, 1]) x_valid, y_valid = pd.DataFrame(multivariate_df.iloc[train_size:, [0,2,3,4,5,6,7]]), pd.DataFrame(multivariate_df.iloc[train_size:, 1])train.head()

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train=multivariate_df.iloc[:train_size, :] train

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8.3.1 多元Propher

from fbprophet import Prophet# Train the model model = Prophet() # model.add_regressor('最高温度') # model.add_regressor('最低温度') # model.add_regressor('白天风力风向') # model.add_regressor('夜晚风力风向') # model.add_regressor('天气1') # model.add_regressor('天气2') # Fit the model with train set model.fit(train)# Predict on valid set y_pred = model.predict(x_valid)# Calcuate metrics score_mae = mean_absolute_error(y_valid, y_pred['yhat']) score_rmse = math.sqrt(mean_squared_error(y_valid, y_pred['yhat']))print(Fore.GREEN + 'RMSE: {}'.format(score_rmse))

from sklearn.metrics import r2_score print('R2-score:',r2_score(y_valid, y_pred['yhat']))

# Plot the forecast f, ax = plt.subplots(1) f.set_figheight(6) f.set_figwidth(15)model.plot(y_pred, ax=ax) sns.lineplot(x=x_valid['ds'], y=y_valid['y'], ax=ax, color='orange', label='Ground truth') #navajowhiteax.set_title(f'Prediction \n MAE: {score_mae:.2f}, RMSE: {score_rmse:.2f}', fontsize=14) ax.set_xlabel(xlabel='Date', fontsize=14) ax.set_ylabel(ylabel='总有功功率（kw）', fontsize=14)plt.show()

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