Deep Hybrid Model Based on EMD with Classification by Frequency Characteristics for Long-Term Air Quality Prediction
<p>Correspondence of each intrinsic mode function (IMF) between time domain and frequency domain after decomposition. Left to right: IMFs in the (<b>a</b>) time domain, (<b>b</b>) frequency domain by the fast Fourier transform (FFT).</p> "> Figure 2
<p>Convolution results for each IMF in the frequency domain.</p> "> Figure 3
<p>The number of IMFs within different time intervals of PM2.5.</p> "> Figure 4
<p>Schematic of one-dimensional convolutional neural network (CNN).</p> "> Figure 5
<p>The network structure of gated recurrent unit (GRU).</p> "> Figure 6
<p>Flowchart of a PM2.5 hybrid predictor for an air quality monitoring system.</p> "> Figure 7
<p>The predictions of hourly PM2.5 in Beijing from 1 to 20 December, 2017 by RNN [<a href="#B31-mathematics-08-00214" class="html-bibr">31</a>], LSTM [<a href="#B32-mathematics-08-00214" class="html-bibr">32</a>], GRU [<a href="#B34-mathematics-08-00214" class="html-bibr">34</a>].</p> "> Figure 8
<p>The predictions of hourly PM2.5 in Beijing from 1 to 20 December, 2017 by EMDCNN_RNN, EMDCNN_LSTM, and the proposed method.</p> ">
Abstract
:1. Introduction
2. Related Works
- (1)
- After EMD, the obtained IMF components are further analyzed for their frequency characteristics, and all the components are divided into a fixed number of groups by convolutional neural network (CNN) networks. Different from [44,45,46], the fixed number can effectively solve the problem that a variable number of IMF components will be obtained when predicting different time intervals.
- (2)
- We present a general framework that predicts the PM2.5 data from air quality monitoring systems and obtains accurate long-term predictions that can meet the needs of precision in air quality warning.
3. Hybrid Deep Predictor
3.1. Decomposition and Analysis of PM2.5 Time Series
- (1)
- Identify the local maximum point of the given time series data and fit the maximum point with a cubic spline interpolation function to form an upper envelope of the original data.
- (2)
- Similarly, find the local minimum point of and fit all the minimum points through the cubic spline interpolation function to form the lower envelope of the original data.
- (3)
- Calculate the mean of the upper envelope and the lower envelope, denoted as .
- (4)
- Subtract the average of the envelope from the original data sequence to obtain a new data sequence : .
- (5)
- Repeat steps 1-4 with until one of the following stop criteria is met: ①, the preset maximum number of iterations is reached; ②, the last IMF separated is small; ③, the maximum or minimum value of the signal is less than 2; ④, is monotonic curve.
- (6)
- Treat as an IMF, and calculate the remainder .
- (7)
- Use as the new , and repeat steps (1)–(6) until all IMFs are obtained.
3.2. Classification and Combination for IMFs
3.3. Deep Prediction Network for Combined IMFs
3.4. Hybrid Model Framework
- (1)
- Decompose the data into IMFs by EMD and label each IMF into three groups based on its frequency characteristics as Group1–3.
- (2)
- Train the CNN by IMFs and labels, and add the sequences to each group.
- (3)
- Train GRU models for each group to get three GRU sub-predictors.
- (1)
- Decompose the input data into IMFs by EMD.
- (2)
- Use CNN to classify IMFs into three groups, and add the sequences of the same group together.
- (3)
- Use GRU models to obtain the predictions of all the groups.
- (4)
- Fuse all the predictions to obtain the integrated output of the original time series.
4. Experiment Results and Discussion
4.1. Dataset and Experimental Setup
4.2. Case 1: Prediction Performance Analysis of Different Predictor
4.3. Case 2: Prediction Performance Analysis of Different Combinations for IMFs
- (1)
- Mode No. 1: IMFs is divided into a group, i.e., {IMF 1–10}. Removing noise term, IMF0, others use one GRU to predict;
- (2)
- Mode No. 2: do not decompose the PM2.5 data, using one GRU for prediction;
- (3)
- Mode No. 3: IMFs is divided into two groups, i.e., {IMF 0}, {IMF 1–10}. Using two GRUs for two sub-sequences prediction separately;
- (4)
- Mode No. 4: IMFs is divided into two groups, i.e., {IMF 0–2}, {IMF 3–10}. Using two GRUs for two sub-sequences prediction separately;
- (5)
- Mode No. 5: IMFs is divided into three groups, i.e., {IMF 0–2}, {IMF 3–4}, {IMF 5–10}. Using three GRUs for three sub-sequences prediction separately;
- (6)
- Mode No. 6: IMFs is divided into four groups, i.e., {IMF 0–2}, {IMF 3–4}, {IMF 5–6}, {IMF 7–10}. Using four GRUs for four sub-sequences prediction separately;
- (7)
- Mode No. 7: IMFs is divided into five groups, i.e., {IMF 0}, {IMF 1–2} {IMF 3–4}, {IMF 5–6}, {IMF 7–10}. Using five GRUs for five sub-sequences prediction separately;
- (8)
- Mode No. 8: IMFs is divided into six groups, i.e., {IMF 0}, {IMF 1–2}, {IMF 3–4}, {IMF 5–6}, {IMF 7–8}, {IMF 9–10}. Using six GRUs for six sub-sequences prediction separately;
- (9)
- Mode No. 9: IMFs is divided into seven groups, i.e., {IMF 0}, {IMF 1–2}, {IMF 3}, {IMF 4}, {IMF 5–6}, {IMF 7–8}, {IMF 9–10}. Using seven GRUs for seven sub-sequences prediction separately.
- (10)
- Mode No. 10: IMFs is divided into eight groups, i.e., {IMF 0}, {IMF 1–2}, {IMF 3}, {IMF 4}, {IMF 5}, {IMF 6}, {IMF 7–8}, {IMF 9–10}. Using eight GRUs for eight sub-sequences prediction separately;
- (11)
- Mode No. 11: IMFs is divided into nine groups, i.e., {IMF 0}, {IMF 1–2}, {IMF 3}, {IMF 4}, {IMF 5}, {IMF 6}, {IMF 7}, {IMF 8}, {IMF 9–10}. Using nine GRUs for nine sub-sequences prediction separately;
- (12)
- Mode No. 12: IMFs is divided into ten groups, i.e., {IMF 0}, {IMF 1–2}, {IMF 3}, {IMF 4}, {IMF 5}, {IMF 6}, {IMF 7}, {IMF 8}, {IMF 9}, {IMF 10}. Using ten GRUs for ten sub-sequences prediction separately.
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Model | RMSE | NRMSE | MAE | SMAPE | R |
---|---|---|---|---|---|
RNN [31] | 64.0560 | 0.1817 | 48.7331 | 0.6256 | 0.6604 |
LSTM [32] | 65.4283 | 0.2275 | 49.7205 | 0.5667 | 0.6426 |
GRU [34] | 63.1271 | 0.2064 | 47.4970 | 0.5251 | 0.6523 |
Decomposition-ARIMA -GRU-GRU [35] | 61.2917 | 0.1933 | 46.9718 | 0.5233 | 0.6508 |
EMDCNN_RNN [31] | 54.5575 | 0.1632 | 41.8000 | 0.4918 | 0.7423 |
EMDCNN_LSTM [32] | 51.1781 | 0.1394 | 40.9414 | 0.5100 | 0.7749 |
The proposed method | 46.2619 | 0.1223 | 34.9598 | 0.4848 | 0.8185 |
Combination Mode | Number of Groups | RMSE | NRMSE | MAE | SMAPE | R |
---|---|---|---|---|---|---|
Mode No. 1 | 1 group | 58.7715 | 0.1835 | 43.8560 | 0.4976 | 0.6792 |
Mode No. 2 | 1 group | 63.1271 | 0.2064 | 47.4970 | 0.5251 | 0.6523 |
Mode No. 3 | 2 groups | 59.6399 | 0.1823 | 44.0517 | 0.4942 | 0.6801 |
Mode No. 4 | 2 groups | 87.2678 | 0.1415 | 54.2545 | 0.5964 | 0.5098 |
Mode No. 5 | 3 groups | 46.2619 | 0.1223 | 34.9598 | 0.4848 | 0.8185 |
Mode No. 6 | 4 groups | 46.0065 | 0.1109 | 34.7076 | 0.4432 | 0.8192 |
Mode No. 7 | 5 groups | 45.0356 | 0.1001 | 33.6287 | 0.4318 | 0.8207 |
Mode No. 8 | 6 groups | 48.3503 | 0.1333 | 37.0070 | 0.5336 | 0.8172 |
Mode No. 9 | 7 groups | 48.0602 | 0.1281 | 35.8617 | 0.4978 | 0.8096 |
Mode No. 10 | 8 groups | 51.8219 | 0.1155 | 38.0779 | 0.5009 | 0.7756 |
Mode No.11 | 9 groups | 72.8165 | 0.1500 | 55.9136 | 0.8114 | 0.6812 |
Mode No.12 | 10 groups | 52.2820 | 0.1298 | 39.2668 | 0.4800 | 0.7860 |
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Jin, X.-B.; Yang, N.-X.; Wang, X.-Y.; Bai, Y.-T.; Su, T.-L.; Kong, J.-L. Deep Hybrid Model Based on EMD with Classification by Frequency Characteristics for Long-Term Air Quality Prediction. Mathematics 2020, 8, 214. https://doi.org/10.3390/math8020214
Jin X-B, Yang N-X, Wang X-Y, Bai Y-T, Su T-L, Kong J-L. Deep Hybrid Model Based on EMD with Classification by Frequency Characteristics for Long-Term Air Quality Prediction. Mathematics. 2020; 8(2):214. https://doi.org/10.3390/math8020214
Chicago/Turabian StyleJin, Xue-Bo, Nian-Xiang Yang, Xiao-Yi Wang, Yu-Ting Bai, Ting-Li Su, and Jian-Lei Kong. 2020. "Deep Hybrid Model Based on EMD with Classification by Frequency Characteristics for Long-Term Air Quality Prediction" Mathematics 8, no. 2: 214. https://doi.org/10.3390/math8020214
APA StyleJin, X. -B., Yang, N. -X., Wang, X. -Y., Bai, Y. -T., Su, T. -L., & Kong, J. -L. (2020). Deep Hybrid Model Based on EMD with Classification by Frequency Characteristics for Long-Term Air Quality Prediction. Mathematics, 8(2), 214. https://doi.org/10.3390/math8020214