1.3 參考文獻

2. 代碼實現(xiàn)

2.1 數(shù)據(jù)解讀

import pandas as pd

df = pd.read_excel('數(shù)據(jù).xlsx',index_col=0, parse_dates=['數(shù)據(jù)時間'])

import matplotlib.pyplot as plt

plt.rcParams['font.sans-serif'] = 'SimHei' # 設置中文顯示

plt.rcParams['axes.unicode_minus'] = False

plt.figure(figsize=(15, 5))

plt.plot(df['總有功功率（kw）'], label='原始數(shù)據(jù)', color='r',  alpha=0.3)

plt.title('時序圖')

plt.grid(True)

plt.legend()

plt.show()

在電力行業(yè)，對每日功率波動進行準確預測對于電網(wǎng)調(diào)度和能源規(guī)劃至關重要。通過深度學習模型，可以更好地理解數(shù)據(jù)的復雜關系，從而提高預測的準確性，首先，加載數(shù)據(jù)（此數(shù)據(jù)已經(jīng)過一定的異常值、缺失值處理）該數(shù)據(jù)為每日平均總有功功率（kw）。

2.2 LSTM模型建立

# 0-1標準化

arr_max = np.max(np.array(df))

arr_min = np.min(np.array(df))

data_bz = (np.array(df)-arr_min)/(arr_max-arr_min)

data_bz = data_bz.ravel() # 轉(zhuǎn)換為一維數(shù)組

def dataset(data, win_size=12):



    X = []  # 用于存儲輸入特征的列表

    Y = []  # 用于存儲目標值的列表



    # 遍歷數(shù)據(jù)，形成樣本窗口

    for i in range(len(data) - win_size):

        temp_x = data[i:i + win_size]  # 提取窗口大小范圍內(nèi)的輸入特征

        temp_y = data[i + win_size]    # 提取對應的目標值

        X.append(temp_x)

        Y.append(temp_y)



    # 轉(zhuǎn)換列表為 NumPy 數(shù)組

    X = np.asarray(X)

    Y = np.asarray(Y)



    return X, Y



data_x, data_y = dataset(data_bz, 12)



data_x = np.expand_dims(data_x, axis=1)

from sklearn.model_selection import train_test_split

from keras.layers import LSTM, Dense

from keras.models import Sequential



train_x, test_x, train_y, test_y = train_test_split(data_x, data_y, test_size = 0.2, shuffle = False)



# 使用 Sequential API 構(gòu)建模型

model =Sequential()



#  LSTM 層中有 256 個隱藏單元 input_shape參數(shù)指定輸入數(shù)據(jù)的形狀，這里為(1, 時間步數(shù))

model.add(LSTM(256, input_shape=(train_x.shape[1], train_x.shape[2])))



# 這里定義激活函數(shù)為sigmoid（請文對輸出數(shù)據(jù)進行歸一化處理）

model.add(Dense(1, activation='sigmoid'))

# 編譯模型

# 損失函數(shù)（loss）為均方誤差（Mean Squared Error），適用于回歸問題

# 優(yōu)化器（optimizer）為 Adam，是一種常用的優(yōu)化算法

model.compile(loss='mse', optimizer='adam')



# 訓練模型

# epochs：訓練的輪數(shù)，即遍歷整個訓練數(shù)據(jù)的次數(shù)

# batch_size：每批次訓練的樣本數(shù)

# validation_split：用于在訓練過程中劃分一部分數(shù)據(jù)作為驗證集，這里是取訓練數(shù)據(jù)的20%作為驗證集

# shuffle：是否在每個 epoch 之前隨機打亂訓練數(shù)據(jù)

history = model.fit(train_x, train_y, epochs=18, batch_size=64, validation_split=0.2, shuffle=False)
plt.plot(history.history['loss'])

plt.plot(history.history['val_loss'], c='r')

plt.legend(['loss', 'val_loss'])

plt.show()
from sklearn import metrics

# 計算均方誤差（MSE）

mse = metrics.mean_squared_error(test_y, np.array([i for arr in y_pred for i in arr]))

# 計算均方根誤差（RMSE）

rmse = np.sqrt(mse)

# 計算平均絕對誤差（MAE）

mae = metrics.mean_absolute_error(test_y, np.array([i for arr in y_pred for i in arr]))

from sklearn.metrics import r2_score # 擬合優(yōu)度

r2 = r2_score(test_y, np.array([i for arr in y_pred for i in arr]))

print("均方誤差 (MSE):", mse)

print("均方根誤差 (RMSE):", rmse)

print("平均絕對誤差 (MAE):", mae)

print("擬合優(yōu)度:", r2)
def predict_all(model, last_x, num=24):

    pred_y=[]

    for i in range(num):

        temp_y = model.predict(last_x)

        pred_y.append(temp_y[0,0])

        temp_y = np.expand_dims(temp_y, 0)

        last_x = np.concatenate([last_x[:,:,1:], temp_y], axis = 2)

    return np.asarray(pred_y)



last_x = test_x[-1]

last_x = np.expand_dims(last_x, 0)



series_pre = predict_all(model, last_x, num=30)

series = series_pre*(arr_max-arr_min)+arr_min # 未來30天波動預測值歸一化數(shù)據(jù)還原



plt.figure(figsize=(15,4), dpi =300)

plt.plot(test_y*(arr_max-arr_min)+arr_min, color = 'c', label = '每日實際功率波動曲線')

plt.plot(y_pred*(arr_max-arr_min)+arr_min, color = 'r', label = '預測每日功率波動曲線')

plt.plot(range(len(y_pred), len(y_pred)+len(series)), series, color = 'b', label = '向后預測30天')

plt.title('每日實際功率波動與預測每日功率波動比對圖')

plt.grid(True)

plt.xlabel('時間')

plt.ylabel('總有功功率（kw）')

plt.legend()

plt.show()

這里將不進行代碼解讀，代碼解讀請參考往期文章末尾也將給出往期文章鏈接，通過建立LSTM模型可以發(fā)現(xiàn)普通的LSTM模型對于預測任務的表現(xiàn)不夠理想，預測結(jié)果與實際結(jié)果之間存在較大的誤差，擬合優(yōu)度也不高，說明模型并未很好地擬合數(shù)據(jù)的變異性?？赡苄枰M一步優(yōu)化模型結(jié)構(gòu)、調(diào)整超參數(shù)或者嘗試其他模型來提高預測精度，為了提高模型精確度接下來將引入模型VMD-LSTM進行模型建立。

2.3 VMD分解時間序列

from vmdpy import VMD 

# VMD 的一些參數(shù)

alpha = 1300        # 適度的頻帶寬度約束

tau = 0.            # 容忍噪聲（沒有嚴格的保真度要求）

K = 5               # 3個模態(tài)

DC = 0              # 不強制直流分量

init = 1            # 均勻初始化角頻率

tol = 1e-7



# 運行 VMD

u, u_hat, omega = VMD(df['總有功功率（kw）'], alpha, tau, K, DC, init, tol)

# 可視化分解后的 5 個 IMF

plt.figure(figsize=(15, 8))



for i in range(K):

    plt.subplot(K, 1, i+1)

    plt.plot(u[i, :])

    plt.title(f'IMF {i+1}')

    plt.xlabel('時間')

    plt.ylabel('幅度')



plt.tight_layout()

plt.show()



# 保存每個 IMF 到不同的 DataFrame

imf_dataframes = {}

for i in range(len(u)):

    imf_name = 'imf_{}'.format(i+1)

    imf_dataframes[imf_name] = pd.DataFrame({'Value': u[i]})

通過代碼，可以清晰地展示VMD分解后得到的每個本征模態(tài)函數(shù)，以及得到分解后的數(shù)據(jù)，接下來將對每一個分解數(shù)據(jù)進行LSTM模型建立。

2.3.1 IMF1—LSTM

arr_max_1 = np.max(np.array(imf_dataframes['imf_1']))

arr_min_1 = np.min(np.array(imf_dataframes['imf_1']))

data_bz_1 = (np.array(imf_dataframes['imf_1'])-arr_min_1)/(arr_max_1-arr_min_1)

data_bz_1 = data_bz_1.ravel() # 轉(zhuǎn)換為一維數(shù)組

data_x_1, data_y_1 = dataset(data_bz_1, 12)

data_x_1 = np.expand_dims(data_x_1, axis=1)

train_x_1, test_x_1, train_y_1, test_y_1 = train_test_split(data_x_1, data_y_1, test_size = 0.2, shuffle = False)

model_1 =Sequential()

model_1.add(LSTM(256, input_shape=(train_x_1.shape[1], train_x_1.shape[2])))

model_1.add(Dense(1, activation='sigmoid'))

model_1.compile(loss='mse', optimizer='adam')

history_1 = model_1.fit(train_x_1, train_y_1, epochs=18, batch_size=64, validation_split=0.2, shuffle=False)
plt.plot(history_1.history['loss'])

plt.plot(history_1.history['val_loss'], c='r')

plt.legend(['loss', 'val_loss'])

plt.show()
y_pred_1 = model_1.predict(test_x_1)

# 計算均方誤差（MSE）

mse = metrics.mean_squared_error(test_y_1, np.array([i for arr in y_pred_1 for i in arr]))

# 計算均方根誤差（RMSE）

rmse = np.sqrt(mse)

# 計算平均絕對誤差（MAE）

mae = metrics.mean_absolute_error(test_y_1, np.array([i for arr in y_pred_1 for i in arr]))

from sklearn.metrics import r2_score # 擬合優(yōu)度

r2 = r2_score(test_y_1, np.array([i for arr in y_pred_1 for i in arr]))

print("均方誤差 (MSE):", mse)

print("均方根誤差 (RMSE):", rmse)

print("平均絕對誤差 (MAE):", mae)

print("擬合優(yōu)度:", r2)
last_x_1 = test_x_1[-1]

last_x_1 = np.expand_dims(last_x_1, 0)



series_pre_1 = predict_all(model_1, last_x_1, num=30)

series_1 = series_pre_1*(arr_max_1-arr_min_1)+arr_min_1 # 未來10天波動預測值歸一化數(shù)據(jù)還原



plt.figure(figsize=(15,4), dpi =300)

plt.plot(test_y_1*(arr_max_1-arr_min_1)+arr_min_1, color = 'c', label = 'imf_1測試集實際功率波動曲線')

plt.plot(y_pred_1*(arr_max_1-arr_min_1)+arr_min_1, color = 'r', label = 'imf_1測試集預測功率波動曲線')

plt.plot(range(len(y_pred_1), len(y_pred_1)+len(series_1)), series, color = 'b', label = 'imf_1向后預測30天功率波動曲線')

plt.title('imf_1')

plt.grid(True)

plt.xlabel('時間')

plt.ylabel('總有功功率（kw）')

plt.legend()

plt.show()

2.3.2?IMF2—LSTM

arr_max_2 = np.max(np.array(imf_dataframes['imf_2']))

arr_min_2 = np.min(np.array(imf_dataframes['imf_2']))

data_bz_2 = (np.array(imf_dataframes['imf_2'])-arr_min_2)/(arr_max_2-arr_min_2)

data_bz_2 = data_bz_2.ravel() # 轉(zhuǎn)換為一維數(shù)組

data_x_2, data_y_2 = dataset(data_bz_2, 12)

data_x_2 = np.expand_dims(data_x_2, axis=1)

train_x_2, test_x_2, train_y_2, test_y_2 = train_test_split(data_x_2, data_y_2, test_size = 0.2, shuffle = False)

model_2 =Sequential()

model_2.add(LSTM(256, input_shape=(train_x_2.shape[1], train_x_2.shape[2])))

model_2.add(Dense(1, activation='sigmoid'))

model_2.compile(loss='mse', optimizer='adam')

history_2 = model_2.fit(train_x_2, train_y_2, epochs=18, batch_size=64, validation_split=0.2, shuffle=False)



plt.plot(history_2.history['loss'])

plt.plot(history_2.history['val_loss'], c='r')

plt.legend(['loss', 'val_loss'])

plt.show()



y_pred_2 = model_2.predict(test_x_2)

# 計算均方誤差（MSE）

mse = metrics.mean_squared_error(test_y_2, np.array([i for arr in y_pred_2 for i in arr]))

# 計算均方根誤差（RMSE）

rmse = np.sqrt(mse)

# 計算平均絕對誤差（MAE）

mae = metrics.mean_absolute_error(test_y_2, np.array([i for arr in y_pred_2 for i in arr]))

from sklearn.metrics import r2_score # 擬合優(yōu)度

r2 = r2_score(test_y_2, np.array([i for arr in y_pred_2 for i in arr]))

print("均方誤差 (MSE):", mse)

print("均方根誤差 (RMSE):", rmse)

print("平均絕對誤差 (MAE):", mae)

print("擬合優(yōu)度:", r2)



last_x_2 = test_x_2[-1]

last_x_2 = np.expand_dims(last_x_2, 0)



series_pre_2 = predict_all(model_2, last_x_2, num=30)

series_2 = series_pre_2*(arr_max_2-arr_min_2)+arr_min_2 # 未來10天波動預測值歸一化數(shù)據(jù)還原



plt.figure(figsize=(15,4), dpi =300)

plt.plot(test_y_2*(arr_max_2-arr_min_2)+arr_min_2, color = 'c', label = 'imf_2測試集實際功率波動曲線')

plt.plot(y_pred_2*(arr_max_2-arr_min_2)+arr_min_2, color = 'r', label = 'imf_2測試集預測功率波動曲線')

plt.plot(range(len(y_pred_2), len(y_pred_2)+len(series_2)), series_2, color = 'b', label = 'imf_2向后預測30天功率波動曲線')

plt.title('imf_2')

plt.grid(True)

plt.xlabel('時間')

plt.ylabel('總有功功率（kw）')

plt.legend()

plt.show()

2.3.3 IMF3—LSTM

arr_max_3 = np.max(np.array(imf_dataframes['imf_3']))

arr_min_3 = np.min(np.array(imf_dataframes['imf_3']))

data_bz_3 = (np.array(imf_dataframes['imf_3'])-arr_min_3)/(arr_max_3-arr_min_3)

data_bz_3 = data_bz_3.ravel() # 轉(zhuǎn)換為一維數(shù)組

data_x_3, data_y_3 = dataset(data_bz_3, 12)

data_x_3 = np.expand_dims(data_x_3, axis=1)

train_x_3, test_x_3, train_y_3, test_y_3 = train_test_split(data_x_3, data_y_3, test_size = 0.2, shuffle = False)

model_3 =Sequential()

model_3.add(LSTM(256, input_shape=(train_x_3.shape[1], train_x_3.shape[2])))

model_3.add(Dense(1, activation='sigmoid'))

model_3.compile(loss='mse', optimizer='adam')

history_3 = model_3.fit(train_x_3, train_y_3, epochs=18, batch_size=64, validation_split=0.2, shuffle=False)



plt.plot(history_3.history['loss'])

plt.plot(history_3.history['val_loss'], c='r')

plt.legend(['loss', 'val_loss'])

plt.show()



y_pred_3 = model_3.predict(test_x_3)

# 計算均方誤差（MSE）

mse = metrics.mean_squared_error(test_y_3, np.array([i for arr in y_pred_3 for i in arr]))

# 計算均方根誤差（RMSE）

rmse = np.sqrt(mse)

# 計算平均絕對誤差（MAE）

mae = metrics.mean_absolute_error(test_y_3, np.array([i for arr in y_pred_3 for i in arr]))

from sklearn.metrics import r2_score # 擬合優(yōu)度

r2 = r2_score(test_y_3, np.array([i for arr in y_pred_3 for i in arr]))

print("均方誤差 (MSE):", mse)

print("均方根誤差 (RMSE):", rmse)

print("平均絕對誤差 (MAE):", mae)

print("擬合優(yōu)度:", r2)



last_x_3 = test_x_3[-1]

last_x_3 = np.expand_dims(last_x_3, 0)



series_pre_3 = predict_all(model_3, last_x_3, num=30)

series_3 = series_pre_3*(arr_max_3-arr_min_3)+arr_min_3 # 未來10天波動預測值歸一化數(shù)據(jù)還原



plt.figure(figsize=(15,4), dpi =300)

plt.plot(test_y_3*(arr_max_3-arr_min_3)+arr_min_3, color = 'c', label = 'imf_3測試集實際功率波動曲線')

plt.plot(y_pred_3*(arr_max_3-arr_min_3)+arr_min_3, color = 'r', label = 'imf_3測試集預測功率波動曲線')

plt.plot(range(len(y_pred_3), len(y_pred_3)+len(series_3)), series_3, color = 'b', label = 'imf_3向后預測30天功率波動曲線')

plt.title('imf_3')

plt.grid(True)

plt.xlabel('時間')

plt.ylabel('總有功功率（kw）')

plt.legend()

plt.show()

2.3.4 IMF4—LSTM

arr_max_4 = np.max(np.array(imf_dataframes['imf_4']))

arr_min_4 = np.min(np.array(imf_dataframes['imf_4']))

data_bz_4 = (np.array(imf_dataframes['imf_4'])-arr_min_4)/(arr_max_4-arr_min_4)

data_bz_4 = data_bz_4.ravel() # 轉(zhuǎn)換為一維數(shù)組

data_x_4, data_y_4 = dataset(data_bz_4, 12)

data_x_4 = np.expand_dims(data_x_4, axis=1)

train_x_4, test_x_4, train_y_4, test_y_4 = train_test_split(data_x_4, data_y_4, test_size = 0.2, shuffle = False)

model_4 =Sequential()

model_4.add(LSTM(256, input_shape=(train_x_4.shape[1], train_x_4.shape[2])))

model_4.add(Dense(1, activation='sigmoid'))

model_4.compile(loss='mse', optimizer='adam')

history_4 = model_4.fit(train_x_4, train_y_4, epochs=18, batch_size=64, validation_split=0.2, shuffle=False)



plt.plot(history_4.history['loss'])

plt.plot(history_4.history['val_loss'], c='r')

plt.legend(['loss', 'val_loss'])

plt.show()



y_pred_4 = model_4.predict(test_x_4)

# 計算均方誤差（MSE）

mse = metrics.mean_squared_error(test_y_4, np.array([i for arr in y_pred_4 for i in arr]))

# 計算均方根誤差（RMSE）

rmse = np.sqrt(mse)

# 計算平均絕對誤差（MAE）

mae = metrics.mean_absolute_error(test_y_4, np.array([i for arr in y_pred_4 for i in arr]))

from sklearn.metrics import r2_score # 擬合優(yōu)度

r2 = r2_score(test_y_4, np.array([i for arr in y_pred_4 for i in arr]))

print("均方誤差 (MSE):", mse)

print("均方根誤差 (RMSE):", rmse)

print("平均絕對誤差 (MAE):", mae)

print("擬合優(yōu)度:", r2)



last_x_4 = test_x_4[-1]

last_x_4 = np.expand_dims(last_x_4, 0)



series_pre_4 = predict_all(model_4, last_x_4, num=30)

series_4 = series_pre_4*(arr_max_4-arr_min_4)+arr_min_4 # 未來10天波動預測值歸一化數(shù)據(jù)還原



plt.figure(figsize=(15,4), dpi =300)

plt.plot(test_y_4*(arr_max_4-arr_min_4)+arr_min_4, color = 'c', label = 'imf_4測試集實際功率波動曲線')

plt.plot(y_pred_4*(arr_max_4-arr_min_4)+arr_min_4, color = 'r', label = 'imf_4測試集預測功率波動曲線')

plt.plot(range(len(y_pred_4), len(y_pred_4)+len(series_4)), series_4, color = 'b', label = 'imf_4向后預測30天功率波動曲線')

plt.title('imf_4')

plt.grid(True)

plt.xlabel('時間')

plt.ylabel('總有功功率（kw）')

plt.legend()

plt.show()

2.3.5?IMF5—LSTM

arr_max_5 = np.max(np.array(imf_dataframes['imf_5']))

arr_min_5 = np.min(np.array(imf_dataframes['imf_5']))

data_bz_5 = (np.array(imf_dataframes['imf_5'])-arr_min_5)/(arr_max_5-arr_min_5)

data_bz_5 = data_bz_5.ravel() # 轉(zhuǎn)換為一維數(shù)組

data_x_5, data_y_5 = dataset(data_bz_5, 12)

data_x_5 = np.expand_dims(data_x_5, axis=1)

train_x_5, test_x_5, train_y_5, test_y_5 = train_test_split(data_x_5, data_y_5, test_size = 0.2, shuffle = False)

model_5 =Sequential()

model_5.add(LSTM(256, input_shape=(train_x_5.shape[1], train_x_5.shape[2])))

model_5.add(Dense(1, activation='sigmoid'))

model_5.compile(loss='mse', optimizer='adam')

history_5 = model_5.fit(train_x_5, train_y_5, epochs=18, batch_size=64, validation_split=0.2, shuffle=False)



plt.plot(history_5.history['loss'])

plt.plot(history_5.history['val_loss'], c='r')

plt.legend(['loss', 'val_loss'])

plt.show()



y_pred_5 = model_5.predict(test_x_5)

# 計算均方誤差（MSE）

mse = metrics.mean_squared_error(test_y_5, np.array([i for arr in y_pred_5 for i in arr]))

# 計算均方根誤差（RMSE）

rmse = np.sqrt(mse)

# 計算平均絕對誤差（MAE）

mae = metrics.mean_absolute_error(test_y_5, np.array([i for arr in y_pred_5 for i in arr]))

from sklearn.metrics import r2_score # 擬合優(yōu)度

r2 = r2_score(test_y_5, np.array([i for arr in y_pred_5 for i in arr]))

print("均方誤差 (MSE):", mse)

print("均方根誤差 (RMSE):", rmse)

print("平均絕對誤差 (MAE):", mae)

print("擬合優(yōu)度:", r2)



last_x_5 = test_x_5[-1]

last_x_5 = np.expand_dims(last_x_5, 0)



series_pre_5 = predict_all(model_5, last_x_5, num=30)

series_5 = series_pre_5*(arr_max_5-arr_min_5)+arr_min_5 # 未來10天波動預測值歸一化數(shù)據(jù)還原



plt.figure(figsize=(15,4), dpi =300)

plt.plot(test_y_5*(arr_max_5-arr_min_5)+arr_min_5, color = 'c', label = 'imf_5測試集實際功率波動曲線')

plt.plot(y_pred_5*(arr_max_5-arr_min_5)+arr_min_5, color = 'r', label = 'imf_5測試集預測功率波動曲線')

plt.plot(range(len(y_pred_5), len(y_pred_5)+len(series_5)), series_5, color = 'b', label = 'imf_5向后預測30天功率波動曲線')

plt.title('imf_5')

plt.grid(True)

plt.xlabel('時間')

plt.ylabel('總有功功率（kw）')

plt.legend()

plt.show()

這里的模型雖然是一模一樣的只是更改了數(shù)據(jù)集沒有利用循環(huán)來進行建立模型是為了去強調(diào)每次建立的LSTM模型可以修改相關參數(shù)進行模型優(yōu)化，并不影響VMD-LSTM最后的構(gòu)建。

如果不需要參數(shù)修改，直接進行for循環(huán)構(gòu)建模型省略代碼復雜度請參考以下代碼。

from vmdpy import VMD 

import matplotlib.pyplot as plt

import pandas as pd

import numpy as np

from sklearn.model_selection import train_test_split

from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score

from tensorflow.keras.models import Sequential

from tensorflow.keras.layers import LSTM, Dense

from tensorflow.keras import metrics



plt.rcParams['font.sans-serif'] = 'SimHei'  # 設置中文顯示

plt.rcParams['axes.unicode_minus'] = False



# VMD 的一些參數(shù)

alpha = 1300        # 適度的頻帶寬度約束

tau = 0.            # 容忍噪聲（沒有嚴格的保真度要求）

K = 5               # 5個模態(tài)

DC = 0              # 不強制直流分量

init = 1            # 均勻初始化角頻率

tol = 1e-7



# 運行 VMD

u, _, _ = VMD(df['總有功功率（kw）'], alpha, tau, K, DC, init, tol)



# 創(chuàng)建 LSTM 模型

def create_lstm_model(input_shape):

    model = Sequential()

    model.add(LSTM(256, input_shape=input_shape))

    model.add(Dense(1, activation='sigmoid'))

    model.compile(loss='mse', optimizer='adam')

    return model



# 準備訓練數(shù)據(jù)

def prepare_data(imf_data):

    arr_max = np.max(np.array(imf_data))

    arr_min = np.min(np.array(imf_data))

    data_bz = (np.array(imf_data) - arr_min) / (arr_max - arr_min)

    data_bz = data_bz.ravel()  # 轉(zhuǎn)換為一維數(shù)組

    data_x, data_y = dataset(data_bz, 12)

    data_x = np.expand_dims(data_x, axis=1)

    train_x, test_x, train_y, test_y = train_test_split(data_x, data_y, test_size=0.2, shuffle=False)

    return train_x, test_x, train_y, test_y, arr_max, arr_min



# 訓練模型并進行預測

def train_and_predict(model, train_x, train_y, test_x, test_y, arr_max, arr_min):

    history = model.fit(train_x, train_y, epochs=18, batch_size=64, validation_split=0.2, shuffle=False)

    y_pred = model.predict(test_x)

    mse = mean_squared_error(test_y, y_pred)

    rmse = np.sqrt(mse)

    mae = mean_absolute_error(test_y, y_pred)

    r2 = r2_score(test_y, y_pred)

    print("均方誤差 (MSE):", mse)

    print("均方根誤差 (RMSE):", rmse)

    print("平均絕對誤差 (MAE):", mae)

    print("擬合優(yōu)度:", r2)



    last_x = test_x[-1]

    last_x = np.expand_dims(last_x, 0)



    series_pre = predict_all(model, last_x, num=30)

    series = series_pre * (arr_max - arr_min) + arr_min



    plt.figure(figsize=(15, 4), dpi=300)

    plt.plot(test_y * (arr_max - arr_min) + arr_min, color='c', label='測試集實際功率波動曲線')

    plt.plot(y_pred * (arr_max - arr_min) + arr_min, color='r', label='測試集預測功率波動曲線')

    plt.plot(range(len(y_pred), len(y_pred) + len(series)), series, color='b', label='向后預測30天功率波動曲線')

    plt.title('IMF')

    plt.grid(True)

    plt.xlabel('時間')

    plt.ylabel('總有功功率（kw）')

    plt.legend()

    plt.show()



# 循環(huán)處理每個 IMFs

for i, imf in enumerate(u):

    imf_name = f'imf_{i+1}'

    train_x, test_x, train_y, test_y, arr_max, arr_min = prepare_data(imf)

    model = create_lstm_model((train_x.shape[1], train_x.shape[2]))

    train_and_predict(model, train_x, train_y, test_x, test_y, arr_max, arr_min)

2.4?VMD—LSTM

pred = y_pred_1*(arr_max_1-arr_min_1)+arr_min_1+y_pred_2*(arr_max_2-arr_min_2)+arr_min_2+y_pred_3*(arr_max_3-arr_min_3)+arr_min_3+y_pred_4*(arr_max_4-arr_min_4)+arr_min_4+y_pred_5*(arr_max_5-arr_min_5)+arr_min_5

prophet = series_1+series_2+series_3+series_4+series_5

test = test_y*(arr_max-arr_min)+arr_min



plt.figure(figsize=(15,4), dpi =300)

plt.plot(test, color = 'c', label = '測試集實際功率波動曲線')

plt.plot(pred, color = 'r', label = 'vmd_lstm測試集預測功率波動曲線')

plt.plot(range(len(pred), len(pred)+len(prophet)), prophet, color = 'b', label = 'vmd_lstm向后預測30天功率波動曲線')

plt.title('vmd_lstm')

plt.grid(True)

plt.xlabel('時間')

plt.ylabel('總有功功率（kw）')

plt.legend()

plt.show()

2.5 VMD—LSTM與LSTM模型評價指標比較

# 計算均方誤差（MSE）

mse = metrics.mean_squared_error(test, np.array([i for arr in pred for i in arr]))

# 計算均方根誤差（RMSE）

rmse = np.sqrt(mse)

# 計算平均絕對誤差（MAE）

mae = metrics.mean_absolute_error(test, np.array([i for arr in pred for i in arr]))

from sklearn.metrics import r2_score # 擬合優(yōu)度

r2 = r2_score(test, np.array([i for arr in pred for i in arr]))

print("均方誤差 (MSE):", mse)

print("均方根誤差 (RMSE):", rmse)

print("平均絕對誤差 (MAE):", mae)

print("擬合優(yōu)度:", r2)

這里的均方誤差、均方根誤差、平均絕對誤差都是對歸一化還原數(shù)據(jù)進行計算得到，前文的LSTM模型評價指標是對歸一化的數(shù)據(jù)計算得到，為了比較兩個模型的差異對前文LSTM模型也進行還原數(shù)據(jù)計算評價指標。

# 更好對比對lstm數(shù)據(jù)進行歸一化還原輸出評價指標

# 計算均方誤差（MSE）

test = test_y*(arr_max-arr_min)+arr_min

pred_1 = y_pred*(arr_max-arr_min)+arr_min

mse = metrics.mean_squared_error(test, np.array([i for arr in pred_1 for i in arr]))

# 計算均方根誤差（RMSE）

rmse = np.sqrt(mse)

# 計算平均絕對誤差（MAE）

mae = metrics.mean_absolute_error(test, np.array([i for arr in pred_1 for i in arr]))

from sklearn.metrics import r2_score # 擬合優(yōu)度

r2 = r2_score(test, np.array([i for arr in pred_1 for i in arr]))

print("均方誤差 (MSE):", mse)

print("均方根誤差 (RMSE):", rmse)

print("平均絕對誤差 (MAE):", mae)

print("擬合優(yōu)度:", r2)
# 定義模型和評價指標

models = ['LSTM', 'VMD-LSTM']

metrics = ['MSE', 'RMSE', 'MAE', 'R2']

values = {

    'LSTM': [433308080.1553673, 20816.053424109174, 14396.407640033123, 0.490216331578196],

    'VMD-LSTM': [169117880.61997274, 13004.53307966006, 9261.236531374, 0.801034096693379]

}



# 繪制柱狀圖

fig, axs = plt.subplots(2, 2, figsize=(12, 10))



for i, metric in enumerate(metrics):

    ax = axs[i//2, i%2]

    ax.bar(models, [values[model][i] for model in models], color=['skyblue', 'lightgreen'])

    ax.set_title(metric)

    ax.set_xlabel('Model')

    ax.set_ylabel(metric)



plt.tight_layout()

plt.show()

綜合來看，VMD-LSTM模型相對于普通的LSTM模型在各個評價指標上表現(xiàn)更好，具有更低的預測誤差、更高的預測精度和更好的數(shù)據(jù)擬合效果。

文章轉(zhuǎn)自微信公眾號@Python機器學習AI

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