Short-Term Electricity Load Forecasting Based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise and Improved Sparrow Search Algorithm–Convolutional Neural Network–Bidirectional Long Short-Term Memory Model
Abstract
:1. Introduction
- Adoption of the good point set to initialize the population;
- Use of the golden sine strategy to update the discoverer position in the SSA;
- Introduction of the Lévy flight strategy into the population stochastic wandering in the SSA.
2. Methodology
2.1. Decomposition and Reconstruction
2.1.1. CEEMDAN
2.1.2. Sample Entropy
2.2. SSA and Its Improvement
2.2.1. SSA
- Division of Roles: Sparrows are categorized into producers (explorers with high fitness) and scroungers (followers) to balance exploration and exploitation.
- Competition Mechanism: Scroungers compete with producers for food resources. If a scrounger fails, it relocates to avoid stagnation.
- Anti-Predation Behavior: Sparrows at the population’s edge move toward safer areas when threatened, while those in the center adjust positions randomly to maintain diversity.
- Adaptive Search: Producers perform broad exploration, while scroungers refine solutions locally, ensuring dynamic adaptation to the search space.
2.2.2. ISSA
- (1)
- Implementation of a good point set for population initialization: Leveraging low-discrepancy sequence generation from good point set theory enhances initial population distribution in high-dimensional spaces. This geometrically driven initialization ensures spatial uniformity and diversity preservation, critically accelerating convergence kinetics while preventing premature solution stagnation.
- (2)
- Revision of discoverer dynamics via golden sine optimization: The golden sine (Gold-SA) mechanism is integrated into discoverer positional updating to maintain solution space dimensionality throughout iterations, effectively mitigating the local optima entrapment common in the conventional SSA.
- (3)
- Incorporation of Lévy flight for adaptive step size regulation: Lévy flight is used to improve the step size to increase the diversity of the population. The heavy-tailed distribution facilitates global optimum discovery through sporadic long-range jumps while maintaining intensive local search.
Algorithm 1: ISSA |
2.3. CNN-BiLSTM
2.3.1. CNN
2.3.2. BiLSTM
2.3.3. CNN-BiLSTM
2.4. Improved Hybrid Models for STLF
2.4.1. ISSA-CNN-BiLSTM for STLF
2.4.2. CEEMDAN-ISSA-CNN-BiLSTM for STLF
- Use CEEMDAN to decompose data into IMFs and a residual component.
- Calculate the sample entropy of each IMF and reorganize the K IMFs into four terms: high frequency, medium frequency, low frequency, and residual component.
- Set the sliding window and step size, construct the input matrix, and normalize it.
- Use the ISSA in Section 2.2.2 to optimize the hyperparameters in the K sub-models.
- Import the input matrix into the network and obtain the best parameters.
3. Case Study and Analysis
3.1. Data Sources and Processing
3.1.1. Data Partitioning
3.1.2. Data Normalization
3.1.3. Data Decomposition and Reconstruction
3.2. Performance Criteria
3.3. Data Sources and Processing
3.4. Error Analysis
- Dynamic Hyperparameter Tuning: Integration of real-time optimization where the ISSA adjusts model parameters hourly based on incoming data streams.
- Exogenous Variable Integration: Incorporation of weather forecasts, holiday calendars, and economic indicators to contextualize abrupt load changes.
- Hybrid Attention Mechanisms: Use of temporal attention layers in BiLSTM to prioritize recent peak-hour trends during decoding.
4. Discussion
5. Conclusions
- Good point set initialization, which ensures balanced population distribution.
- The golden sine strategy, which updates discoverer positions for faster convergence.
- Lévy flight, which enhances global search during population movement.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Model | Advantage | Disadvantage | Scenarios |
---|---|---|---|
CEEMDAN-ISSA-CNN-BiLSTM | Combining CEEMDAN to reduce data non-stationarity and improve prediction accuracy | High computational complexity | High precision requirements and complex temporal fluctuation scenarios |
ISSA optimization enhances the efficiency of hyperparameter search | Long training time and relies on a large number of data | ||
CNN extracts spatial features, BiLSTM captures bidirectional temporal dependencies | |||
CEEMDAN-IWOA-LSTM [77] | CEEMDAN optimizes input features to reduce noise interference | Using only unidirectional LSTM has limited temporal modeling capabilities | Medium complexity, univariate time series prediction |
The IWOA algorithm efficiently optimizes LSTM parameters with small errors | Unfused spatial feature extraction module | ||
CEEMDAN-TCN-LSTM [78] | TCN has strong parallel computing capability and fast training speed | TCN is sensitive to local features and may ignore global patterns | Large-scale data and high real-time requirements for scenarios |
LSTM supplements long-term dependency modeling | Unintegrated signal decomposition method | ||
Transformer-Based [79] | Self-attention mechanism captures long-range dependencies | Extremely high demand for computing resources | Ultra-long-sequence, multivariate correlation scenario |
No need for manual feature engineering | Strict requirements for data volume, poor performance in small sample sizes | ||
PSO-A2C-Lnet [80] | PSO hyperparameters to avoid overfitting | The model structure is complex and the deployment difficulty is high | Multi-source heterogeneous data and strong spatiotemporal correlation |
Multi-head attention enhances feature importance learning | Multi-stage training is required and time consuming |
Algorithm | Parameter | Settings |
---|---|---|
Population size | 10 | |
The number of iterations | 10 | |
SSA | Proportion of finders | 0.2 |
Warning value | 0.8 | |
lb | ||
ub | ||
Population size | 10 | |
The number of iterations | 10 | |
ISSA | Proportion of finders | 0.2 |
Warning value | 0.8 | |
lb | ||
ub |
Hyperparameter | Options | Optimization | Justification |
---|---|---|---|
Learning Rate | [0.0001, 0.01] | ISSA selects the optimum within bounds while balancing convergence speed and stability. | |
CNN Layers | Layers | 2 (Fixed) | Predefined to balance feature extraction and computational efficiency. |
CNN Filters | Layer 1: [10, 100] Layer 2: [10, 100] | Layer 1: 32 Layer 2: 64 | Optimized by ISSA to capture spatial patterns; higher filters in deeper layers enhance feature abstraction. |
BiLSTM Units | [10, 100] | 30 units | ISSA optimized to balance temporal modeling capacity and overfitting risks. |
Activation Functions | CNN: ReLU BiLSTM: Sigmoid | Fixed | ReLU avoids vanishing gradients in CNN; sigmoid in BiLSTM gates regulates information flow. |
Method | MAE | RMSE | MAPE/% |
---|---|---|---|
LSTM | 136.2837 | 172.9691 | 1.7710 |
BiLSTM | 131.6981 | 166.7711 | 1.6982 |
CNN-LSTM | 122.6703 | 163.6129 | 1.6022 |
CNN-BiLSTM | 123.4603 | 165.9294 | 1.5567 |
EMD-CNN-BiLSTM | 115.6594 | 145.3522 | 1.4440 |
CEEMDAN-CNN-LSTM | 101.0761 | 131.7941 | 1.3079 |
CEEMDAN-CNN-BiLSTM | 95.6848 | 127.2255 | 1.2567 |
CEEMDAN-SSA-CNN-BiLSTM | 88.0911 | 115.1259 | 1.1441 |
CEEMDAN-ISSA-CNN-BiLSTM | 76.3607 | 97.4285 | 0.9916 |
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Qiu, H.; Hu, R.; Chen, J.; Yuan, Z. Short-Term Electricity Load Forecasting Based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise and Improved Sparrow Search Algorithm–Convolutional Neural Network–Bidirectional Long Short-Term Memory Model. Mathematics 2025, 13, 813. https://doi.org/10.3390/math13050813
Qiu H, Hu R, Chen J, Yuan Z. Short-Term Electricity Load Forecasting Based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise and Improved Sparrow Search Algorithm–Convolutional Neural Network–Bidirectional Long Short-Term Memory Model. Mathematics. 2025; 13(5):813. https://doi.org/10.3390/math13050813
Chicago/Turabian StyleQiu, Han, Rong Hu, Jiaqing Chen, and Zihao Yuan. 2025. "Short-Term Electricity Load Forecasting Based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise and Improved Sparrow Search Algorithm–Convolutional Neural Network–Bidirectional Long Short-Term Memory Model" Mathematics 13, no. 5: 813. https://doi.org/10.3390/math13050813
APA StyleQiu, H., Hu, R., Chen, J., & Yuan, Z. (2025). Short-Term Electricity Load Forecasting Based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise and Improved Sparrow Search Algorithm–Convolutional Neural Network–Bidirectional Long Short-Term Memory Model. Mathematics, 13(5), 813. https://doi.org/10.3390/math13050813