A Novel Adaptive Intelligent Ensemble Model for Forecasting Primary Energy Demand
Abstract
:1. Introduction
- (1)
- The APSO algorithm based on adaptive inertia weight is proposed. The inertial weight of PSO is an important factor affecting global search ability. In this paper, an adaptive adjustment method of inertia weight was used to improve the PSO algorithm. A “momentum” factor was added to PSO to adjust the adaptive inertia weight of the particles so as to improve the global search ability of PSO.
- (2)
- An adaptive variable weight ensemble forecasting model (APSO-RGM-SVR) is proposed to predict primary energy demand and energy structure. This paper combines the GM (1,1), RGM, and ARIMA in time-series model with SVR in machine learning method, and constructs GM (1,1) -SVR, RGM-SVR, and ARIMA-SVR ensemble models based on the standard deviation weight method. Through comparative experiments, we found RGM-SVR had higher precision. Then, the RGM-SVR model with higher accuracy was optimized by the APSO algorithm, and the APSO-RGM-SVR model was obtained. The new method proposed in this paper was used to forecast China’s primary energy demand and structure. The empirical results showed that the new method had higher accuracy and better generalization.
2. Literature Review
2.1. Time-Series Forecasting Model
2.2. Soft-Computing Technology
2.3. Optimization Algorithm
2.4. Ensemble-Based Methods
3. Methodology
3.1. GM (1,1)
3.2. RGM
- Step 1.
- Construct GM (1, 1) by using the original sequence .
- Step 2.
- Forecast a new datum as , add it to the original data , and remove the oldest original datum to keep the original data dimension unchanged, the new sequence is recorded as .
- Step 3.
- Establish GM (1,1) with .
- Step 4.
- Forecast the next value, denoted as . Add it to the original datum and remove one of the oldest raw datum to form a new sequence: .
3.3. ARIMA
3.4. SVR
3.5. Model Evaluation Criteria
4. Construction of Ensemble Forecasting Model
4.1. Construction of the Ensemble Model Based on the Standard Deviation Weight Method
4.1.1. Standard Deviation Method
4.1.2. GM (1,1)-SVR
- Step 1.
- GM (1,1) and SVR are constructed, respectively. According to Step 4 of Section 3.1., the parameters a and u of GM (1,1) are calculated as shown in Table 2. The Lagrangian multiplier method is used to transform SVR into a “dual problem”, and then the parameters are solved using sequential minimal optimization (SMO). The parameters of SVR have been tested repeatedly. It is shown that the fitting result is optimal when C = 10000 and = 0.01. The parameters and b of the SVR are estimated, as shown in Table 3.
- Step 2.
- The results of GM (1,1) and SVR are assigned weights according to the standard deviation method, and the weight distribution is as shown in Table 4.
- Step 3.
- The accuracy of the GM (1,1)-SVR is evaluated by MAE, MAPE, and MSPE.
4.1.3. RGM-SVR
- Step 1.
- RGM and SVR are constructed, respectively. Take China’s primary energy consumption from 2005 to 2012 as a training set, which is brought into the model for parameter estimation. The training samples are unchanged, therefore, the estimated parameters of the SVR model are unchanged. The parameter estimation results of the RGM model are shown in Table 5. The parameters of SVR have been tested repeatedly. C = 10000, = 0.01. The parameters and b of the SVR are estimated as shown in Table 3.
- Step 2.
- The prediction results of RGM and SVR are assigned weights according to the standard deviation method. The weight distribution is shown in Table 6.
- Step 3.
- The accuracy of RGM-SVR is evaluated by MAE, MAPE, and MSPE.
4.1.4. ARIMA-SVR
- Step 1.
- Establish an ARIMA (p, d, q) model for China’s primary energy demand forecast and examine whether the input samples are stationary time-series.
- Step 2.
- Perform a time-series difference d on the sample. Begin with the first-order difference and observe the sequence. After the d-order difference, the sequence tends to be stationary, and the difference order is the parameter d of ARIMA.
- Step 3.
- Estimate the parameters p and q. Check and observe the autocorrelation and partial correlation graphs of the stationary time series to obtain q and p, and so that the parameters of ARIMA are determined which are shown in Table 7.
- Step 4.
- Assign weights to ARIMA and SVR by the standard deviation method, and the weight distribution is as shown in Table 8.
- Step 5.
- The accuracy of ARIMA-SVR is evaluated by MAE, MAPE, and MSPE.
4.2. Construction of the Adaptive Weight Ensemble Forecasting Model
4.2.1. PSO
4.2.2. APSO
4.2.3. Contrast Test of Optimization Algorithms
4.2.4. Construction of APSO-RGM-SVR Based on Adaptive Inertia Weight
- Step 1.
- Step 2.
- The sum of the absolute values of the prediction errors is used as the cost function of the adaptive weight. The expression is
- Step 3.
- The optimal weighted model is obtained by the APSO based on the adaptive inertia weight, and thus, an optimal ensemble forecasting model is constructed. The optimal weight is shown in Table 11:
- Step 4.
- The prediction accuracy of the APSO-RGM-SVR prediction model is evaluated by MAE, MAPE, and MSPE.
5. Results
5.1. Data
5.2. Model Adaptability
5.3. Prediction Results
6. Conclusions
- (1)
- The improved PSO algorithm with the “momentum” factor added had better global search capabilities.
- (2)
- By comparing a variety of single-prediction models and fixed-weight ensemble models, the prediction results of the APSO-RGM-SVR model proposed in this study showed the smallest error, and the prediction accuracy of energy demand was significantly improved. The ensemble model (APSO-RGM-SVR), which was optimized by the APSO algorithm, effectively combined the characteristics of a time-series model and artificial intelligence, and could adjust the optimal weight at any time with the change of samples. The new method proposed in this paper is a prediction method with higher accuracy and better generalization.
- (3)
- The APSO-RGM-SVR method was used to forecast China’s primary energy consumption from 2017 to 2025. Prediction results indicate that China’s energy demand will continue to rise. By 2020, China’s primary energy demand was predicted to reach about 4656.41 mtce, and the proportions of coal, oil, natural gas, and hydropower and nuclear power were predicted to be 56.6%, 19.8%, 8.8%, and 14.8%, respectively. By 2025, China’s primary energy demand was predicted to reach about 4656.41 mtce, and the proportion of coal, oil, natural gas, and hydro, nuclear, and wind power were predicted to be 45.7%, 20.5%, 11.2%, and 22.6%, respectively.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Models | Feature | Advantages | Disadvantages | Applied to |
---|---|---|---|---|
Regression analysis | Establishing the regression equation through the correlation between variables. | The correlation degree between the factors can be analyzed. | Poor generalization and low accuracy. | Finding the relationship between energy consumption and economic growth [4]; forecasting long-term electricity consumption [20]. |
ARIMA | Treating the data sequence formed by the prediction object over time as a random sequence, and then establishing a model to express the sequence. | The model is simple and only requires endogenous variables. | Requirements are stable time-series data or are stable after differentiation; essentially only captures linear relationships, not non-linear relationships. | Forecasting the next-day electricity price in the Spanish mainland [21]; forecasting monthly electricity consumption in Eastern Saudi Arabia [22]. |
Grey | Using small sample data to establish a grey differential equation and describing the development trend of things over a long time. | Less sample size required; short-term prediction accuracy is higher; less model parameters. | Cannot consider the relationship between factors; medium- and long-term prediction error is relatively large. | Forecasting annual power load in Shanghai, China [24]; forecasting growth trends in renewable energy [25]. |
ANN | A highly complex non-linear dynamic learning system; suitable for handling inaccurate and fuzzy information processing problems under various factors and conditions. | Can fully approximate complex non-linear relationships; parallel distributed processing; highly robust and fault tolerant. | More model parameters; learning time is too long; large sample size required for model training. | Forecasting long-term energy demand in Greece [29]; forecasting Iran’s future monthly energy consumption [30]. |
LSTM | Long-term save input; identifying useful information. | Suitable for dealing with problems highly related to time-series; solves long sequence dependency problems. | The training time of the model is a little long. | Forecasting photovoltaic power generation [33,35]. |
SVR | Application of Support Vector in Regression Function; maps data to a high-dimensional feature space through a non-linear mapping and performs regression in this space. | Small samples; simplifies regression problems; high flexibility. | With the increase of sample size, the time complexity of model training will increase. | Forecasting buildings’ energy consumption in New York [44]; forecasting the electrical load of four typical office buildings [45]. |
Parameter | The Total Energy Consumption | Coal | Oil | Natural Gas | Water, Wind, and Nuclear Power |
---|---|---|---|---|---|
a | −0.056 | −0.047 | −0.055 | −0.153 | −0.096 |
u | 2.656 | 1.966 | 4.528 | 6.285 | 1.875 |
Parameter | The Total Energy Consumption | Coal | Oil | Natural Gas | Water, Wind, and Nuclear Power |
---|---|---|---|---|---|
0.9999 | 0.9999 | 0.9999 | 0.9999 | 0.9999 | |
0.9999 | 0.9999 | 0.9999 | 0.9999 | 0.9999 | |
−2.1974 | 0.9999 | −1.9356 | −8.1981 | −2.4216 | |
0.9999 | 0.9999 | 0.9999 | 0.9999 | 0.9999 | |
0.9999 | 0.9999 | 0.9999 | 0.9999 | 0.9999 | |
−6.8117 | −8.0748 | 0.9999 | 0.9999 | 0.9999 | |
0.9999 | 0.9999 | −4.5862 | 0.9999 | −7.3687 | |
0.9999 | 0.9999 | 0.9999 | −1.4721 | 0.9999 | |
b | 0.5148 | 0.4971 | 0.5021 | 0.5119 | 0.4878 |
Weight | The Total Energy Consumption | Coal | Oil | Natural Gas | Water, Wind, and Nuclear Power |
---|---|---|---|---|---|
0.1201 | 0.2437 | 0.1871 | 0.1606 | 0.5512 | |
0.8799 | 0.7563 | 0.8129 | 0.8394 | 0.4488 |
Parameter | The Total Energy Consumption | Coal | Oil | Natural Gas | Water, Wind, and Nuclear Power |
---|---|---|---|---|---|
−0.056 | −0.047 | −0.055 | −0.153 | −0.096 | |
0.055 | −0.045 | −0.057 | −0.152 | −0.094 | |
0.058 | −0.047 | −0.060 | −0.152 | −0.092 | |
0.057 | −0.047 | −0.059 | −0.153 | −0.093 | |
2.656 | 1.966 | 4.528 | 6.285 | 1.876 | |
2.816 | 2.073 | 4.719 | 7.327 | 2.087 | |
2.940 | 2.139 | 4.906 | 8.456 | 2.325 | |
3.121 | 2.250 | 5.239 | 9.807 | 2.522 |
Weight | The Total Energy Consumption | Coal | Oil | Natural Gas | Water, Wind, and Nuclear Power |
---|---|---|---|---|---|
0.2201 | 0.2407 | 0.1809 | 0.2501 | 0.4748 | |
0.7799 | 0.7593 | 0.8191 | 0.7599 | 0.5254 |
Parameter | The Total Energy Consumption | Coal | Oil | Natural Gas | Water, Wind, and Nuclear Power |
---|---|---|---|---|---|
p | 2 | 2 | 1 | 5 | 1 |
d | 1 | 1 | 2 | 1 | 2 |
q | 2 | 2 | 2 | 2 | 1 |
Weight | The Total Energy Consumption | Coal | Oil | Natural Gas | Water, Wind, Nuclear Power |
---|---|---|---|---|---|
0.2928 | 0.3252 | 0.1281 | 0.5436 | 0.0981 | |
0.7072 | 0.6748 | 0.8719 | 0.4564 | 0.9019 |
Function | GWO | MFO | WOA | POS | APSO | |
---|---|---|---|---|---|---|
F1 | Std. Dev | 8.24E − 007 | 3.34E + 001 | 1.07E − 006 | 2.32E + 001 | 1.00E − 010 |
F2 | Std. Dev | 8.47E − 001 | 4.22E − 001 | 1.26E − 001 | 1.95E + 005 | 2.63E − 001 |
F3 | Std. Dev | 7.67E − 004 | 2.80E − 003 | 3.85E − 004 | 7.97E − 002 | 5.27E − 005 |
F4 | Std. Dev | 1.03E + 003 | 6.45E + 002 | 2.75E + 002 | 3.94E + 002 | 2.39E + 001 |
F5 | Std. Dev | 5.69E + 000 | 0.79E + 000 | 0.12E + 000 | 2.98E + 001 | 0.04E + 000 |
F6 | Std. Dev | 6.45E − 003 | 6.50E − 002 | 3.78E − 003 | 3.98E − 001 | 8.25E − 009 |
Function | Formula | Dimension | Range | Theoretical Optimum |
---|---|---|---|---|
Schwefel 2.21 | 30 | [−100, 100) | 0 | |
Rosenbrock | 30 | [−30, 30] | 0 | |
Quartic | 30 | [−1.28, 1.28] | 0 | |
Schwefel 2.26 | 30 | [−500, 500] | 0 | |
Rastrigin | 30 | 0 | ||
Griewank | 30 | [−600, 600] | 0 |
Weight | The Total Energy Consumption | Coal | Oil | Natural Gas | Water, Wind, Nuclear Power |
---|---|---|---|---|---|
0.2928 | 0.3252 | 0.1281 | 0.5436 | 0.0981 | |
0.7072 | 0.6748 | 0.8719 | 0.4564 | 0.9019 |
Year | The Total Energy Consumption | Coal | Oil | Natural Gas | Water, Wind, and Nuclear Power |
---|---|---|---|---|---|
2005 | 2613.69 | 1892.31 | 465.24 | 62.73 | 193.41 |
2006 | 2864.67 | 2074.02 | 501.32 | 77.35 | 211.99 |
2007 | 3114.42 | 2257.95 | 529.45 | 93.43 | 233.58 |
2008 | 3206.11 | 2292.37 | 535.42 | 109.01 | 269.31 |
2009 | 3361.26 | 2406.66 | 551.25 | 117.64 | 285.71 |
2010 | 3606.48 | 2495.68 | 627.53 | 144.26 | 339.01 |
2011 | 3870.43 | 2717.04 | 650.23 | 178.04 | 325.12 |
2012 | 4021.38 | 2754.65 | 683.63 | 193.03 | 390.07 |
2013 | 4169.13 | 2809.99 | 712.92 | 220.96 | 425.25 |
2014 | 4258.06 | 2793.29 | 740.90 | 242.71 | 481.16 |
2015 | 4299.05 | 2738.49 | 786.73 | 253.64 | 520.19 |
2016 | 4360.00 | 2703.20 | 797.88 | 279.04 | 579.88 |
Method | Total Energy Consumption | |||||
Training | Testing | |||||
MAE | MAPE | MSPE | MAE | MAPE | MSPE | |
PSO-RGM (1,1)-SVR | 38.765 | 0.01174 | 0.00510 | 26.252 | 0.00616 | 0.00352 |
RGM (1,1)-SVR | 41.123 | 0.01263 | 0.00548 | 28.092 | 0.00655 | 0.00378 |
GM (1,1)-SVR | 42.503 | 0.01306 | 0.00570 | 35.005 | 0.00817 | 0.00457 |
ARIMA-SVR | 54.939 | 0.01716 | 0.00767 | 56.142 | 0.01319 | 0.00680 |
SVR | 52.555 | 0.01617 | 0.00747 | 99.841 | 0.02336 | 0.02741 |
RGM (1,1) | 28.310 | 0.00840 | 0.00384 | 149.875 | 0.03483 | 0.02055 |
GM (1,1) | 28.310 | 0.00840 | 0.00384 | 184.505 | 0.04282 | 0.02595 |
ARIMA | 89.969 | 0.02818 | 0.01148 | 187.109 | 0.04332 | 0.02741 |
Method | Coal | |||||
Training | Testing | |||||
MAE | MAPE | MSPE | MAE | MAPE | MSPE | |
PSO-RGM (1,1)-SVR | 32.901 | 0.01439 | 0.00691 | 14.066 | 0.00505 | 0.00320 |
RGM (1,1)-SVR | 33.417 | 0.01460 | 0.00693 | 14.693 | 0.00528 | 0.00324 |
GM (1,1)-SVR | 34.124 | 0.01493 | 0.00715 | 19.086 | 0.00689 | 0.00424 |
ARIMA-SVR | 48.061 | 0.02143 | 0.00899 | 27.532 | 0.00997 | 0.00516 |
SVR | 38.434 | 0.01694 | 0.00862 | 124.293 | 0.04520 | 0.02343 |
RGM (1,1) | 29.404 | 0.01207 | 0.00516 | 254.165 | 0.09259 | 0.04987 |
GM (1,1) | 29.399 | 0.01207 | 0.00516 | 315.762 | 0.11520 | 0.06403 |
ARIMA | 113.113 | 0.04979 | 0.02029 | 327.478 | 0.11966 | 0.06900 |
Oil | ||||||
Method | Training | Testing | ||||
MAE | MAPE | MSPE | MAE | MAPE | MSPE | |
PSO-RGM (1,1)-SVR | 4.936 | 0.00814 | 0.00625 | 5.956 | 0.00785 | 0.00448 |
RGM (1,1)-SVR | 5.430 | 0.00908 | 0.00611 | 6.397 | 0.00842 | 0.00464 |
GM (1,1)-SVR | 5.924 | 0.01008 | 0.00623 | 7.128 | 0.00936 | 0.00499 |
ARIMA-SVR | 6.827 | 0.01176 | 0.00615 | 21.482 | 0.02735 | 0.01732 |
SVR | 4.345 | 0.00700 | 0.00651 | 14.118 | 0.02039 | 0.01386 |
RGM (1,1) | 10.349 | 0.01851 | 0.00846 | 23.671 | 0.03050 | 0.01822 |
GM (1,1) | 10.351 | 0.01852 | 0.00846 | 31.507 | 0.04047 | 0.02415 |
ARIMA | 8.302 | 0.01471 | 0.00683 | 37.090 | 0.04777 | 0.02666 |
Natural gas | ||||||
Method | Training | Testing | ||||
MAE | MAPE | MSPE | MAE | MAPE | MSPE | |
PSO-RGM (1,1)-SVR | 1.034 | 0.00837 | 0.00512 | 2.092 | 0.01259 | 0.00895 |
RGM (1,1)-SVR | 1.034 | 0.00837 | 0.00512 | 4.497 | 0.01896 | 0.01153 |
GM (1,1)-SVR | 1.042 | 0.00830 | 0.00528 | 4.626 | 0.01897 | 0.00977 |
ARIMA-SVR | 12.977 | 0.01023 | 0.00539 | 7.751 | 0.03031 | 0.01659 |
SVR | 0.622 | 0.00549 | 0.00514 | 7.864 | 0.03196 | 0.01727 |
RGM (1,1) | 3.190 | 0.02351 | 0.01073 | 22.625 | 0.08952 | 0.04906 |
GM (1,1) | 3.188 | 0.02348 | 0.01073 | 43.689 | 0.16699 | 0.09828 |
ARIMA | 2.283 | 0.01663 | 0.00795 | 24.671 | 0.09433 | 0.05736 |
Hydro, Nuclear and Wind Power | ||||||
Method | Training | Testing | ||||
MAE | MAPE | MSPE | MAE | MAPE | MSPE | |
PSO-RGM (1,1)-SVR | 8.092 | 0.02608 | 0.01435 | 10.947 | 0.02024 | 0.01232 |
RGM (1,1)-SVR | 8.337 | 0.02694 | 0.01369 | 12.021 | 0.02237 | 0.01328 |
GM (1,1)-SVR | 8.404 | 0.02718 | 0.01356 | 14.419 | 0.02679 | 0.01599 |
ARIMA-SVR | 8.342 | 0.02698 | 0.01514 | 23.598 | 0.04405 | 0.02589 |
SVR | 7.912 | 0.02546 | 0.01501 | 14.594 | 0.02707 | 0.01703 |
RGM (1,1) | 8.808 | 0.02859 | 0.01333 | 15.707 | 0.02997 | 0.01660 |
GM (1,1) | 8.805 | 0.02858 | 0.01333 | 17.408 | 0.03322 | 0.01840 |
ARIMA | 13.768 | 0.04618 | 0.02123 | 127.062 | 0.24883 | 0.12645 |
Year | The Total Energy Consumption | Coal | Oil | Natural Gas | Hydro, Nuclear, and Wind Power |
---|---|---|---|---|---|
2020 | 4656.41 | 2637.23 | 922.15 | 409.53 | 687.50 |
2025 | 4825.43 | 2203.86 | 989.19 | 540.64 | 1091.74 |
Energy | Total Energy Consumption | Coal | Oil | Natural Gas | Hydro, Nuclear, and Wind Power |
---|---|---|---|---|---|
Average annual growth rate | 1.14 | −2.2 | 2.42 | 7.43 | 7.70 |
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Share and Cite
Zhao, W.; Zhao, J.; Yao, X.; Jin, Z.; Wang, P. A Novel Adaptive Intelligent Ensemble Model for Forecasting Primary Energy Demand. Energies 2019, 12, 1347. https://doi.org/10.3390/en12071347
Zhao W, Zhao J, Yao X, Jin Z, Wang P. A Novel Adaptive Intelligent Ensemble Model for Forecasting Primary Energy Demand. Energies. 2019; 12(7):1347. https://doi.org/10.3390/en12071347
Chicago/Turabian StyleZhao, Wenting, Juanjuan Zhao, Xilong Yao, Zhixin Jin, and Pan Wang. 2019. "A Novel Adaptive Intelligent Ensemble Model for Forecasting Primary Energy Demand" Energies 12, no. 7: 1347. https://doi.org/10.3390/en12071347