Short-Term Load Forecasting for Residential Buildings Based on Multivariate Variational Mode Decomposition and Temporal Fusion Transformer
<p>Search for the optimal decomposition level and the corresponding penalty factor.</p> "> Figure 2
<p>Architecture of the TFT.</p> "> Figure 3
<p>Architecture of MVMD-TFT.</p> "> Figure 4
<p>The procedure for MVMD-TFT optimization through the WOA.</p> "> Figure 5
<p>Maximum residual entropy in different decomposition levels.</p> "> Figure 6
<p>Relationship between the penalty factor and sample entropy of the residual.</p> "> Figure 7
<p>WOA optimization for the MVMD-TFT.</p> "> Figure 8
<p>Variable importance of past inputs.</p> "> Figure 9
<p>Variable importance of future variables.</p> "> Figure 10
<p>Variable importance of static variables.</p> "> Figure 11
<p>Forecasting results for Case A (22 January 2018 00:00:00 to 29 January 2018 23:00:00).</p> "> Figure 12
<p>Forecasting results for Case B (14 September 2017 00:00:00 to 31 October 2017 23:00:00).</p> "> Figure 13
<p>Nemenyi post-hoc test (<span class="html-italic">p</span>-value (calculated by Friedman test) = 5.3 × 10<sup>−19</sup>).</p> "> Figure 14
<p>Quantile prediction results of the MVMD-TFT and TFT. Case A (R25) (22 January 2018 00:00:00 to 29 January 2018 23:00:00). Case B (R22) (24 October 2017 00:00:00 to 31 October 2017 23:00:00).</p> ">
Abstract
:1. Introduction
- (1)
- We proposea hybrid MVMD-WOA-TFT model, which can forecast load for multiple houses accurately. MVMD is employed to decompose multi-load data into multiple IMFs, extracting the common features shared among different load sequences. The WOA is utilized to optimize the hyperparameter of the MVMD-TFT, enhancing its overall performance.
- (2)
- We select an appropriate decomposition level and penalty factor for MVMD from an entropy-based perspective.
- (3)
- We validate the performance of the proposed model by comparing it to the original TFT and multiple separate training models.
2. Methodology
2.1. Multivariate Variational Mode Decomposition
2.2. Parameter Setting for MVMD Based on Sample Entropy
2.3. Combination of MVMD and TFT
- (1)
- Gated residual network: The GRN is designed to control the flexibility of nonlinear mapping in the model.
- (2)
- Variable selection network: The VSN is designed to provide instance-wise variable selection. It can learn the most salient input variable, which contributes to the prediction problem. It provides access to static information that enhances the weight-generation process.
- (3)
- Attention mechanism: The TFT applies an average attention mechanism that prevents the model from attending to different input features at different times and facilitates the evaluation of the importance of instance-wise attention weights.
- (4)
- Quantile loss: The TFT provides a distribution of possible future outcomes along with point estimates through quantile output, and it is trained using quantile loss. In our research, the quantile is set to {0.1, 0.5, 0.9}.
2.4. The Process of Optimizing MVMD-TFT Using WOA
3. Results and Discussion
3.1. Experimental Setup
3.2. Data Preprocessing
- (1)
- In order to minimize the missing values within the selected time range, we have stipulated that the proportion of missing values for all variables employed in model training within the specified time range be less than 0.5%. Variables exceeding this missing value threshold were excluded from consideration. In order to facilitate a comparison between LSTM and CNN-LSTM, we opted for two non-overlapping time ranges. One time range spans approximately 3 months (1 November 2017 to 29 January 2018) (Case A), similar to [7], while the second time range encompasses roughly 16 months (26 June 2016 to 30 October 2017) (Case B).
- (2)
- The meteorological data for the selected buildings all originate from the same weather station. Additionally, each building is accompanied by its corresponding descriptive information. Buildings that have incomplete descriptions are excluded from the analysis. Following the aforementioned criteria, Case A comprises 14 buildings, while Case B includes 10 buildings.
3.3. Entropy Computation Results of MVMD
3.4. Optimization Results Using WOA
3.5. Interpretability of MVMD-TFT
3.6. Model Evaluation
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
AdaBoost | Adaptive boosting |
ADMM | Alternating direction method of multipliers |
ARIMA | Autoregressive integrated moving average |
BiGRU | Bidirectional Gated recurrent unit network |
BiLSTM | Bidirectional long short-term memory network |
CD | Critical Difference |
CNN | Convolutional neural network |
DBSCAN | Density-based spatial clustering of applications with noise |
EEMD | Ensemble empirical mode decomposition |
ELM | Extreme learning machine |
EMD | Empirical mode decomposition |
EWT | Empirical wavelet transform |
GRU | Gated recurrent unit network |
IMF | Intrinsic mode function |
LSSVM | Least squared support vector machine |
LSTM | Long short-term memory network |
MAE | Mean absolute error |
MAPE | Mean absolute percentage error |
MedAE | Median absolute error |
MLR | Multiple linear regression |
MSE | Mean squared error |
MVMD | Multivariate variational mode decomposition |
RNN | Recurrent neural network |
SVR | Support vector regression |
TFT | Temporal fusion transformer |
VMD | Variational mode decomposition |
VSN | Variable selection network |
WAPE | Weighted average percentage error |
XGBoost | Extreme gradient boosting |
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Variable | Datatype | Description |
---|---|---|
building_id | Category | Identification of buildings |
RUs | Category | The number of rental suites in the house |
facing | Category | What direction the house is facing |
housetype | Category | House types |
weather | Category | A textual description of the type of weather |
day | Category | Day of the week |
weekend | Category | Boolean value to indicate weekend |
hour | Category | Hour of the recording, from 1 to 24 |
temperature | Continuous | Outside ambient temperature in degrees Celsius (°C) |
humidity | Continuous | Outside humidity in percentage (%) |
pressure | Continuous | Atmospheric pressure in kilopascals (kPa) |
energy_Kwh | Continuous | Hourly consumption (kWh) |
Hyperparameter | Case A | Case B | Search Range |
---|---|---|---|
batch size | 108 | 16 | [4, 128] |
hidden layer size | 27 | 19 | [5, 100] |
number of heads | 1 | 1 | [1, 4] |
learning rate | 0.002 | 0.001 | [0.0001, 0.01] |
dropout rate | 0.209 | 0.134 | [0.1, 0.9] |
max gradient norm | 0.093 | 0.883 | [0.1, 1] |
Model | Description |
---|---|
MVMD-TFT | (epochs = 50, patience = 5, loss = ‘quantile’) |
TFT | (epochs = 50, patience = 5, loss = ‘quantile’, unit = 20, batch size = 54, number of heads = 4) |
LSTM | same as [6] (epochs = 300, patience = 30, loss = ‘MAE’) |
CNN-LSTM | same as [7] (epochs = 300, patience = 30, loss = ‘MAE’) |
BiGRU-CNN | same as [28] (epochs = 300, patience = 30, loss = ‘MAE’, units = 20, filter = 20) |
MVMD-LSTM | same as [6] (epochs = 300, patience = 30, loss = ‘MAE’) |
MVMD-CNN-LSTM | same as [7] (epochs = 300, patience = 30, loss = ‘MAE’) |
Building Name | Metric | MVMD-TFT | TFT | LSTM | CNN-LSTM | MVMD-LSTM | MVMD-CNN-LSTM | BiGRU-CNN |
---|---|---|---|---|---|---|---|---|
R3 | MAE (kWh) | 0.095 | 0.294 | 0.245 | 0.268 | 0.109 | 0.128 | 0.319 |
MSE (kWh)2 | 0.016 | 0.272 | 0.211 | 0.243 | 0.023 | 0.034 | 0.372 | |
WAPE | 10.2 | 31.5 | 26.3 | 28.8 | 11.7 | 13.7 | 34.2 | |
MedAE (kWh) | 0.073 | 0.138 | 0.111 | 0.116 | 0.101 | 0.085 | 0.115 | |
R4 | MAE (kWh) | 0.128 | 0.370 | 0.358 | 0.389 | 0.137 | 0.157 | 0.365 |
MSE (kWh)2 | 0.030 | 0.303 | 0.294 | 0.312 | 0.037 | 0.047 | 0.295 | |
WAPE | 7.5 | 21.9 | 21.2 | 23.0 | 8.2 | 9.3 | 21.7 | |
MedAE (kWh) | 0.108 | 0.246 | 0.228 | 0.280 | 0.101 | 0.112 | 0.236 | |
R5 | MAE (kWh) | 0.127 | 0.376 | 0.395 | 0.417 | 0.140 | 0.178 | 0.399 |
MSE (kWh)2 | 0.031 | 0.433 | 0.469 | 0.544 | 0.045 | 0.070 | 0.532 | |
WAPE | 13.3 | 39.2 | 41.3 | 43.5 | 14.6 | 18.6 | 41.7 | |
MedAE (kWh) | 0.090 | 0.166 | 0.174 | 0.196 | 0.101 | 0.115 | 0.177 | |
R6 | MAE (kWh) | 0.044 | 0.131 | 0.129 | 0.139 | 0.049 | 0.083 | 0.131 |
MSE (kWh)2 | 0.003 | 0.042 | 0.043 | 0.046 | 0.004 | 0.012 | 0.046 | |
WAPE | 9.1 | 26.9 | 26.5 | 28.7 | 10.1 | 17.2 | 26.9 | |
MedAE (kWh) | 0.036 | 0.081 | 0.072 | 0.086 | 0.038 | 0.065 | 0.073 | |
R9 | MAE (kWh) | 0.089 | 0.182 | 0.159 | 0.187 | 0.109 | 0.122 | 0.176 |
MSE (kWh)2 | 0.015 | 0.088 | 0.080 | 0.109 | 0.023 | 0.023 | 0.090 | |
WAPE | 13.2 | 27.0 | 23.5 | 27.7 | 16.1 | 18.1 | 26.0 | |
MedAE (kWh) | 0.065 | 0.093 | 0.072 | 0.091 | 0.080 | 0.115 | 0.083 | |
R10 | MAE (kWh) | 0.111 | 0.273 | 0.293 | 0.315 | 0.133 | 0.147 | 0.384 |
MSE (kWh)2 | 0.033 | 0.308 | 0.331 | 0.337 | 0.043 | 0.056 | 0.486 | |
WAPE | 16.7 | 41.1 | 44.0 | 47.3 | 20.0 | 22.0 | 57.7 | |
MedAE (kWh) | 0.075 | 0.115 | 0.110 | 0.139 | 0.092 | 0.089 | 0.184 | |
R11 | MAE (kWh) | 0.077 | 0.209 | 0.195 | 0.217 | 0.081 | 0.091 | 0.218 |
MSE (kWh)2 | 0.011 | 0.111 | 0.112 | 0.126 | 0.012 | 0.015 | 0.134 | |
WAPE | 13.7 | 36.9 | 34.5 | 38.3 | 14.4 | 16.2 | 38.5 | |
MedAE (kWh) | 0.056 | 0.123 | 0.102 | 0.087 | 0.069 | 0.073 | 0.097 | |
R13 | MAE (kWh) | 0.121 | 0.363 | 0.325 | 0.332 | 0.113 | 0.152 | 0.383 |
MSE (kWh)2 | 0.027 | 0.371 | 0.330 | 0.360 | 0.025 | 0.043 | 0.409 | |
WAPE | 10.1 | 30.3 | 27.1 | 27.8 | 9.4 | 12.7 | 32.0 | |
MedAE (kWh) | 0.101 | 0.182 | 0.159 | 0.104 | 0.093 | 0.130 | 0.170 | |
R14 | MAE (kWh) | 0.107 | 0.374 | 0.395 | 0.446 | 0.136 | 0.159 | 0.402 |
MSE (kWh)2 | 0.020 | 0.322 | 0.337 | 0.382 | 0.035 | 0.041 | 0.360 | |
WAPE | 6.7 | 23.6 | 24.8 | 28.1 | 8.6 | 10.0 | 25.3 | |
MedAE (kWh) | 0.085 | 0.232 | 0.264 | 0.316 | 0.096 | 0.122 | 0.250 | |
R19 | MAE (kWh) | 0.123 | 0.386 | 0.346 | 0.342 | 0.120 | 0.139 | 0.367 |
MSE (kWh)2 | 0.025 | 0.264 | 0.252 | 0.241 | 0.025 | 0.033 | 0.272 | |
WAPE | 6.1 | 18.9 | 17.0 | 16.8 | 5.9 | 6.8 | 18.0 | |
MedAE (kWh) | 0.095 | 0.299 | 0.250 | 0.231 | 0.103 | 0.106 | 0.258 | |
R20 | MAE (kWh) | 0.115 | 0.333 | 0.322 | 0.294 | 0.119 | 0.135 | 0.343 |
MSE (kWh)2 | 0.021 | 0.273 | 0.247 | 0.191 | 0.028 | 0.036 | 0.283 | |
WAPE | 9.1 | 26.2 | 24.7 | 23.1 | 9.3 | 10.6 | 27.0 | |
MedAE (kWh) | 0.100 | 0.181 | 0.185 | 0.179 | 0.077 | 0.099 | 0.205 | |
R21 | MAE (kWh) | 0.049 | 0.124 | 0.127 | 0.139 | 0.053 | 0.078 | 0.124 |
MSE (kWh)2 | 0.005 | 0.070 | 0.074 | 0.079 | 0.008 | 0.015 | 0.074 | |
WAPE | 16.9 | 42.8 | 44.6 | 48.2 | 18.5 | 26.9 | 42.9 | |
MedAE (kWh) | 0.033 | 0.059 | 0.067 | 0.053 | 0.034 | 0.054 | 0.056 | |
R24 | MAE (kWh) | 0.060 | 0.185 | 0.174 | 0.196 | 0.094 | 0.116 | 0.187 |
MSE (kWh)2 | 0.009 | 0.115 | 0.116 | 0.126 | 0.026 | 0.033 | 0.118 | |
WAPE | 11.6 | 35.7 | 33.6 | 37.7 | 18.2 | 22.3 | 36.1 | |
MedAE (kWh) | 0.037 | 0.094 | 0.079 | 0.102 | 0.062 | 0.080 | 0.108 | |
R25 | MAE (kWh) | 0.089 | 0.246 | 0.252 | 0.303 | 0.119 | 0.155 | 0.236 |
MSE (kWh)2 | 0.014 | 0.231 | 0.253 | 0.271 | 0.031 | 0.052 | 0.240 | |
WAPE | 14.2 | 39.5 | 40.4 | 48.5 | 19.1 | 24.8 | 37.9 | |
MedAE (kWh) | 0.071 | 0.118 | 0.122 | 0.161 | 0.083 | 0.103 | 0.093 |
Building Name | Metric | MVMD-TFT | TFT | LSTM | CNN-LSTM | MVMD-LSTM | MVMD-CNN-LSTM | BiGRU-CNN |
---|---|---|---|---|---|---|---|---|
R4 | MAE (kWh) | 0.070 | 0.304 | 0.314 | 0.329 | 0.079 | 0.150 | 0.323 |
MSE (kWh)2 | 0.008 | 0.206 | 0.212 | 0.229 | 0.010 | 0.038 | 0.227 | |
WAPE | 5.6 | 24.4 | 25.1 | 26.4 | 6.3 | 12.0 | 25.9 | |
MedAE (kWh) | 0.058 | 0.199 | 0.196 | 0.214 | 0.066 | 0.114 | 0.197 | |
R5 | MAE(kWh) | 0.084 | 0.335 | 0.365 | 0.385 | 0.098 | 0.168 | 0.377 |
MSE (kWh)2 | 0.012 | 0.403 | 0.457 | 0.518 | 0.018 | 0.058 | 0.482 | |
WAPE | 10.6 | 42.2 | 46.0 | 48.5 | 12.3 | 21.1 | 47.6 | |
MedAE (kWh) | 0.062 | 0.127 | 0.135 | 0.127 | 0.075 | 0.120 | 0.137 | |
R6 | MAE (kWh) | 0.028 | 0.115 | 0.103 | 0.103 | 0.028 | 0.048 | 0.112 |
MSE (kWh)2 | 0.002 | 0.041 | 0.040 | 0.038 | 0.001 | 0.005 | 0.047 | |
WAPE | 8.6 | 34.9 | 31.4 | 31.9 | 8.4 | 14.6 | 34.0 | |
MedAE (kWh) | 0.022 | 0.062 | 0.039 | 0.043 | 0.021 | 0.035 | 0.041 | |
R9 | MAE (kWh) | 0.048 | 0.186 | 0.186 | 0.187 | 0.060 | 0.100 | 0.193 |
MSE (kWh)2 | 0.004 | 0.119 | 0.121 | 0.133 | 0.007 | 0.024 | 0.136 | |
WAPE | 7.9 | 30.5 | 30.5 | 30.7 | 9.8 | 16.5 | 31.7 | |
MedAE (kWh) | 0.036 | 0.078 | 0.075 | 0.069 | 0.045 | 0.066 | 0.078 | |
R10 | MAE (kWh) | 0.062 | 0.228 | 0.228 | 0.243 | 0.066 | 0.106 | 0.237 |
MSE (kWh)2 | 0.007 | 0.207 | 0.210 | 0.251 | 0.008 | 0.028 | 0.233 | |
WAPE | 10.4 | 38.5 | 38.6 | 41.0 | 11.1 | 17.9 | 40.0 | |
MedAE (kWh) | 0.043 | 0.098 | 0.097 | 0.084 | 0.051 | 0.068 | 0.085 | |
R13 | MAE (kWh) | 0.083 | 0.295 | 0.333 | 0.364 | 0.098 | 0.160 | 0.337 |
MSE (kWh)2 | 0.011 | 0.315 | 0.358 | 0.431 | 0.017 | 0.045 | 0.403 | |
WAPE | 8.3 | 29.3 | 33.3 | 36.2 | 9.7 | 16.0 | 33.5 | |
MedAE (kWh) | 0.069 | 0.109 | 0.145 | 0.147 | 0.076 | 0.131 | 0.128 | |
R14 | MAE (kWh) | 0.084 | 0.372 | 0.371 | 0.385 | 0.085 | 0.162 | 0.382 |
MSE (kWh)2 | 0.014 | 0.390 | 0.387 | 0.417 | 0.016 | 0.058 | 0.412 | |
WAPE | 5.2 | 23.1 | 23.0 | 23.9 | 5.3 | 10.1 | 23.7 | |
MedAE (kWh) | 0.065 | 0.194 | 0.186 | 0.209 | 0.062 | 0.130 | 0.191 | |
R15 | MAE (kWh) | 0.161 | 0.643 | 0.512 | 0.552 | 0.332 | 0.321 | 0.611 |
MSE (kWh)2 | 0.056 | 1.700 | 1.418 | 1.428 | 0.230 | 0.231 | 1.723 | |
WAPE | 13.6 | 54.4 | 44.3 | 46.7 | 28.1 | 27.2 | 51.7 | |
MedAE (kWh) | 0.094 | 0.216 | 0.166 | 0.196 | 0.200 | 0.204 | 0.219 | |
R20 | MAE (kWh) | 0.055 | 0.258 | 0.257 | 0.272 | 0.062 | 0.101 | 0.268 |
MSE (kWh)2 | 0.005 | 0.181 | 0.178 | 0.205 | 0.007 | 0.022 | 0.200 | |
WAPE | 6.2 | 29.1 | 29.0 | 30.7 | 7.0 | 11.4 | 30.2 | |
MedAE (kWh) | 0.044 | 0.148 | 0.146 | 0.148 | 0.046 | 0.073 | 0.140 | |
R22 | MAE (kWh) | 0.060 | 0.245 | 0.210 | 0.205 | 0.084 | 0.105 | 0.213 |
MSE (kWh)2 | 0.008 | 0.210 | 0.235 | 0.235 | 0.015 | 0.024 | 0.245 | |
WAPE | 17.2 | 69.9 | 59.9 | 58.5 | 24.2 | 30.1 | 60.7 | |
MedAE (kWh) | 0.041 | 0.135 | 0.066 | 0.059 | 0.062 | 0.079 | 0.062 |
Metric | Case A | Case B | ||
---|---|---|---|---|
MVMD-TFT | TFT | MVMD-TFT | TFT | |
P50 loss | 0.104 | 0.271 | 0.094 | 0.315 |
P90 loss | 0.048 | 0.172 | 0.043 | 0.213 |
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Share and Cite
Ye, H.; Zhu, Q.; Zhang, X. Short-Term Load Forecasting for Residential Buildings Based on Multivariate Variational Mode Decomposition and Temporal Fusion Transformer. Energies 2024, 17, 3061. https://doi.org/10.3390/en17133061
Ye H, Zhu Q, Zhang X. Short-Term Load Forecasting for Residential Buildings Based on Multivariate Variational Mode Decomposition and Temporal Fusion Transformer. Energies. 2024; 17(13):3061. https://doi.org/10.3390/en17133061
Chicago/Turabian StyleYe, Haoda, Qiuyu Zhu, and Xuefan Zhang. 2024. "Short-Term Load Forecasting for Residential Buildings Based on Multivariate Variational Mode Decomposition and Temporal Fusion Transformer" Energies 17, no. 13: 3061. https://doi.org/10.3390/en17133061
APA StyleYe, H., Zhu, Q., & Zhang, X. (2024). Short-Term Load Forecasting for Residential Buildings Based on Multivariate Variational Mode Decomposition and Temporal Fusion Transformer. Energies, 17(13), 3061. https://doi.org/10.3390/en17133061