import pandas as pd  
 import numpy as np  
 from datetime import datetime  
 import matplotlib.pyplot as plt  
   
 # 生成模擬能源生產(chǎn)數(shù)據(jù)  
 start_date = datetime(2023, 1, 1)  
 end_date = datetime(2023, 3, 1)  
 datetime_index = pd.date_range(start=start_date, end=end_date, freq='10T')  
   
 # 創(chuàng)建具有晝夜周期的能源生產(chǎn)值  
 np.random.seed(42)  # 設(shè)置隨機(jī)種子以確?？芍貜?fù)性
 base_energy = []  
 for dt in datetime_index:  
     hour = dt.hour  
     if 6 <= hour <= 18:  # 白天時(shí)段：較高的能源生產(chǎn)
         energy = np.random.normal(loc=300, scale=30)  
     else:  # 夜間時(shí)段：較低的能源生產(chǎn)
         energy = np.random.normal(loc=50, scale=15)  
     base_energy.append(energy)  
   
 energy_production = pd.Series(base_energy)  
   
 # 隨機(jī)引入缺失值  
 num_missing = int(0.1 * len(energy_production))  
 missing_indices = np.random.choice(len(energy_production), num_missing, replace=False)  
 energy_production.iloc[missing_indices] = np.nan  
   
 # 創(chuàng)建數(shù)據(jù)框架
 mock_energy_data_with_missing = pd.DataFrame({  
     'Datetime': datetime_index,  
     'Energy_Production': energy_production  
 })  
   
 # 添加時(shí)間索引便于后續(xù)分析
 data_with_index = mock_energy_data_with_missing.reset_index()  
 data_with_index['Time_Index'] = np.arange(len(data_with_index))  
   
 # 數(shù)據(jù)可視化
 plt.figure(figsize=(14, 7))  
 plt.plot(mock_energy_data_with_missing['Datetime'],
          mock_energy_data_with_missing['Energy_Production'],  
          label='Energy Production (With Missing)', color='blue', alpha=0.7)  
 plt.scatter(mock_energy_data_with_missing['Datetime'],
             mock_energy_data_with_missing['Energy_Production'],  
             c=mock_energy_data_with_missing['Energy_Production'].isna(),
             cmap='coolwarm',  
             label='Missing Values', s=10)  
 plt.title('模擬能源生產(chǎn)數(shù)據(jù)集（10分鐘間隔采樣）')  
 plt.xlabel('時(shí)間')  
 plt.ylabel('能源生產(chǎn)量')  
 plt.legend(['能源生產(chǎn)（含缺失值）', '缺失值'])  
 plt.grid(True)  
 plt.show()

import pandas as pd  
 import numpy as np  
 from datetime import datetime  
 import matplotlib.pyplot as plt  
 from sklearn.linear_model import LinearRegression  
   
 # 第一步：數(shù)據(jù)預(yù)處理
 # 將時(shí)間索引作為特征，能源生產(chǎn)量作為目標(biāo)變量
 features = data_with_index[['Time_Index']]  
 target = data_with_index['Energy_Production']  
   
 # 第二步：分離完整數(shù)據(jù)和缺失數(shù)據(jù)
 non_missing_data = data_with_index.dropna(subset=['Energy_Production'])  
 missing_data = data_with_index[data_with_index['Energy_Production'].isna()]  
   
 # 第三步：模型訓(xùn)練
 # 使用完整數(shù)據(jù)訓(xùn)練線性回歸模型
 regressor = LinearRegression()  
 regressor.fit(non_missing_data[['Time_Index']], non_missing_data['Energy_Production'])  
   
 # 第四步：缺失值預(yù)測(cè)
 predicted_values = regressor.predict(missing_data[['Time_Index']])  
   
 # 第五步：將預(yù)測(cè)值填充到原始數(shù)據(jù)集
 filled_data = data_with_index.copy()  
 filled_data.loc[filled_data['Energy_Production'].isna(), 'Energy_Production'] = predicted_values  
 filled_data = filled_data[['Datetime', 'Energy_Production']]  
   
 # 第六步：結(jié)果可視化（展示2023年1月數(shù)據(jù)）
 start_month = datetime(2023, 1, 1)  
 end_month = datetime(2023, 1, 31)  
 original_month_data = mock_energy_data_with_missing[  
    (mock_energy_data_with_missing['Datetime'] >= start_month) &  
    (mock_energy_data_with_missing['Datetime'] <= end_month)  
 ]  
 imputed_month_data = filled_data[  
    (filled_data['Datetime'] >= start_month) &  
    (filled_data['Datetime'] <= end_month)  
 ]  
   
 plt.figure(figsize=(14, 7))  
 plt.plot(imputed_month_data['Datetime'], imputed_month_data['Energy_Production'],  
          label='補(bǔ)充后數(shù)據(jù)', color='green', alpha=0.8)  
 plt.plot(original_month_data['Datetime'], original_month_data['Energy_Production'],  
          label='原始數(shù)據(jù)（含缺失）', color='red', alpha=0.9)  
 plt.title('原始數(shù)據(jù)與線性回歸補(bǔ)充數(shù)據(jù)對(duì)比（2023年1月）')  
 plt.xlabel('時(shí)間')  
 plt.ylabel('能源生產(chǎn)量')  
 plt.legend()  
 plt.grid(True)  
 plt.show()

from statsmodels.tsa.seasonal import seasonal_decompose  
   
 # 統(tǒng)計(jì)特征分析
 original_stats = mock_energy_data_with_missing['Energy_Production'].describe()  
 imputed_stats = filled_data['Energy_Production'].describe()  
   
 # 創(chuàng)建比較表
 stats_comparison = pd.DataFrame({  
     'Metric': original_stats.index,  
     'Original Data': original_stats.values,  
     'Imputed Data (Linear Regression)': imputed_stats.values  
 })  
 
 # 輸出統(tǒng)計(jì)比較結(jié)果
 print("數(shù)據(jù)統(tǒng)計(jì)特征對(duì)比：")
 print(stats_comparison)

import statsmodels.api as sm  
   
 def plot_acf_comparison(original_series, imputed_series, lags=50):  
     """
    繪制并比較原始數(shù)據(jù)和補(bǔ)充數(shù)據(jù)的自相關(guān)函數(shù)
    參數(shù)：
        original_series: 原始時(shí)間序列
        imputed_series: 補(bǔ)充后的時(shí)間序列
        lags: 滯后階數(shù)
    """
     plt.figure(figsize=(14, 5))  
       
     # 分析原始數(shù)據(jù)的自相關(guān)性
     plt.subplot(1, 2, 1)  
     sm.graphics.tsa.plot_acf(original_series.dropna(), lags=lags,
                             ax=plt.gca(), title="原始數(shù)據(jù)的自相關(guān)函數(shù)")  
     plt.grid(True)  
       
     # 分析補(bǔ)充數(shù)據(jù)的自相關(guān)性
     plt.subplot(1, 2, 2)  
     sm.graphics.tsa.plot_acf(imputed_series, lags=lags,
                             ax=plt.gca(), title="補(bǔ)充數(shù)據(jù)的自相關(guān)函數(shù)")  
     plt.grid(True)  
       
     plt.tight_layout()  
     plt.show()  
   
 # 執(zhí)行自相關(guān)分析
 plot_acf_comparison(mock_energy_data_with_missing['Energy_Production'],
                    filled_data['Energy_Production'])

# 執(zhí)行STL分解
 original_series = mock_energy_data_with_missing['Energy_Production']  
 imputed_series = filled_data['Energy_Production']  
   
 # 考慮每日144個(gè)觀測(cè)值的周期（10分鐘采樣間隔）
 original_decompose = seasonal_decompose(original_series.interpolate(),
                                      model='additive', period=144)  
 imputed_decompose = seasonal_decompose(imputed_series.interpolate(),
                                      model='additive', period=144)  
   
 # 繪制趨勢(shì)比較
 plt.figure(figsize=(14, 5))  
 plt.plot(original_decompose.trend, label='原始趨勢(shì)', color='blue')  
 plt.plot(imputed_decompose.trend, label='補(bǔ)充數(shù)據(jù)趨勢(shì)',
          color='green', linestyle='--')  
 plt.title('趨勢(shì)組件比較：原始數(shù)據(jù) vs 線性回歸補(bǔ)充')  
 plt.legend()  
 plt.grid(True)  
 plt.show()  
   
 # 繪制季節(jié)性比較
 plt.figure(figsize=(14, 5))  
 plt.plot(original_decompose.seasonal, label='原始季節(jié)性', color='blue')  
 plt.plot(imputed_decompose.seasonal, label='補(bǔ)充數(shù)據(jù)季節(jié)性',
          color='green', linestyle='--')  
 plt.xlim(0, 4000)  
 plt.title('季節(jié)性組件比較：原始數(shù)據(jù) vs 線性回歸補(bǔ)充')  
 plt.legend()  
 plt.grid(True)  
 plt.show()

from sklearn.tree import DecisionTreeRegressor  
   
 # 配置并訓(xùn)練決策樹模型
 # max_depth=5用于防止過擬合，同時(shí)保持足夠的模型復(fù)雜度
 tree_regressor = DecisionTreeRegressor(max_depth=5, random_state=42)  
 tree_regressor.fit(non_missing_data[['Time_Index']],
                   non_missing_data['Energy_Production'])  
   
 # 使用訓(xùn)練好的模型預(yù)測(cè)缺失值
 tree_predicted_values = tree_regressor.predict(missing_data[['Time_Index']])  
   
 # 將預(yù)測(cè)值填充到原始數(shù)據(jù)集
 tree_filled_data = data_with_index.copy()  
 tree_filled_data.loc[tree_filled_data['Energy_Production'].isna(),
                     'Energy_Production'] = tree_predicted_values  
 tree_filled_data = tree_filled_data[['Datetime', 'Energy_Production']]  
 
 # 可視化決策樹補(bǔ)充結(jié)果
 plt.figure(figsize=(14, 7))  
 plt.plot(tree_imputed_month_data['Datetime'],
          tree_imputed_month_data['Energy_Production'],  
          label='決策樹補(bǔ)充數(shù)據(jù)', color='orange', alpha=0.8)  
 plt.plot(original_month_data['Datetime'],
          original_month_data['Energy_Production'],  
          label='原始數(shù)據(jù)（含缺失）', color='red', alpha=0.9)  
 plt.title('原始數(shù)據(jù)與決策樹補(bǔ)充數(shù)據(jù)對(duì)比（2023年1月）')  
 plt.xlabel('時(shí)間')  
 plt.ylabel('能源生產(chǎn)量')  
 plt.legend()  
 plt.grid(True)  
 plt.show()

# 統(tǒng)計(jì)指標(biāo)比較
 stats_comparison['決策樹補(bǔ)充數(shù)據(jù)'] = tree_filled_data['Energy_Production'].describe()

Metric         Original Data   Linear Regression   Decision Tree
 count           7648.000000     8497.000000         8497.000000
 mean           185.073509     185.073842         184.979184
 std             126.816229     120.313162         120.633636
 min             -7.549833       -7.549833           -7.549833
 25%             51.793304       54.186258           53.797479
 50%             256.996772     185.197681         185.545605
 75%             302.217789     298.324435         298.531049
 max             415.581945     415.581945         415.581945