Source-linked AI summary
Random vector functional link neural network based ensemble deep learning for short-term load forecasting
Ruobin Gao, Liang Du, P. N. Suganthan, Qin Zhou, Kum Fai Yuen
TL;DR
Electricity-load forecasting is important but difficult because reliable future-demand prediction remains challenging for power-system planning. The paper combines walk-forward EWT with an ensemble deep RVFL network and reports superior performance over eleven forecasting methods across twenty load series, while noting an open choice about discarding the highest frequency.
Problem
Accurate electricity-load forecasting matters for power-system planning and maintenance, but forecasting load is challenging.
Method
The paper combines walk-forward EWT feature decomposition with an ensemble deep RVFL whose randomly initialized enhancement-layer weights remain fixed while layer outputs are ensembled.
Results
The proposed models are superior in Nemenyi tests across three error metrics and outperform eleven benchmark methods evaluated on twenty electricity-load series.
Takeaways & Limitations
The approach provides an efficient electricity-load forecasting model that combines ensemble learning, deep representation, and leakage-aware EWT feature engineering.
Takeaways & Limitations
Whether to discard the highest-frequency component during walk-forward EWT remains an open problem.
Abstract
from arXiv · showhide
Electricity load forecasting is crucial for the power systems' planning and maintenance. However, its un-stationary and non-linear characteristics impose significant difficulties in anticipating future demand. This paper proposes a novel ensemble deep Random Vector Functional Link (edRVFL) network for electricity load forecasting. The weights of hidden layers are randomly initialized and kept fixed during the training process. The hidden layers are stacked to enforce deep representation learning. Then, the model generates the forecasts by ensembling the outputs of each layer. Moreover, we also propose to augment the random enhancement features by empirical wavelet transformation (EWT). The raw load data is decomposed by EWT in a walk-forward fashion, not introducing future data leakage problems in the decomposition process. Finally, all the sub-series generated by the EWT, including raw data, are fed into the edRVFL for forecasting purposes. The proposed model is evaluated on twenty publicly available time series from the Australian Energy Market Operator of the year 2020. The simulation results demonstrate the proposed model's superior performance over eleven forecasting methods in three error metrics and statistical tests on electricity load forecasting tasks.
I. INTRODUCTION
Short-term electricity-load forecasting supports power-system planning and timely operational decisions, but accurate prediction remains challenging because load is nonlinear and nonstationary. The paper proposes a fast ensemble deep-learning approach that combines edRVFL, walk-forward EWT, and broad benchmark evaluation.
- Accurate load forecasts support maintenance, construction, resource planning, and timely data-driven decisions.
- Electricity-load forecasting remains challenging despite extensive statistical, computational-intelligence, hybrid, ensemble, and deep-learning approaches.
- The proposed fast ensemble deep-learning algorithm combines deep RVFL with ensemble learning to reduce single-model uncertainty without imposing much computational burden.
- Walk-forward EWT augments edRVFL random features while avoiding future-data leakage during decomposition.
- The study evaluates the proposed models against diverse benchmarks on twenty load time series using three error metrics and two statistical tests.
II. METHODOLOGY
The methodology section introduces the paper’s two main methodological components: EWT with walk-forward decomposition, followed by ensemble deep RVFL modeling.
- The methodology first introduces empirical wavelet transformation.
- It then explains the walk-forward decomposition procedure.
- Finally, it describes the ensemble deep RVFL network and proposed model.
A. Empirical wavelet transformation
EWT automatically decomposes nonstationary time series by analyzing their Fourier-domain spectra and separating frequency bands with data-driven band-pass filters.
- EWT is an automatic signal-decomposition algorithm designed for nonstationary time series.
- Unlike DWT and EMD, EWT investigates the time series in the Fourier domain after fast Fourier transform.
- EWT separates the spectrum using data-driven band-pass filters.
- The procedure uses Littlewood-Paley and Meyer wavelets because their Fourier-domain formulations are analytically accessible.
- The resulting empirical scaling and wavelet functions form band-pass filters centered at different frequencies.
B. Walk-forward decomposition
Whole-series decomposition can leak future information into forecasting models, so the paper uses walk-forward EWT to decompose only historical observations before predicting the next load value.
- Applying signal decomposition to the whole time series causes forecasting data leakage through convolution operations involving future data.
- Proposed leakage-avoidance strategies include data-driven padding, moving windows, and walk-forward decomposition.
- Walk-forward EWT decomposes a rolling window of historical observations into k scales to predict x(t).
- Only the last order data points from the decomposition are supplied to the forecasting model, keeping decomposition and training historical-only.
C. Ensemble deep RVFL
The edRVFL stacks random enhancement layers for deep representation learning while training separate output weights at each layer. It ensembles the resulting forecasts to retain intermediate information and reduce single-model uncertainty.
- Architecture: The deep RVFL stacks enhancement layers whose features use clean inputs and preceding-layer features to create hierarchical representations.The architecture generates a diverse set of random features across layers.
- Architecture: Random enhancement weights are initialized randomly and remain fixed during training.
- Ensemble output: The edRVFL trains separate output weights for each layer instead of relying only on the final layer or concatenating all layer features.This preserves intermediate information while avoiding a very high-dimensional feature matrix.
- Ensemble output: Each layer minimizes a regularized loss whose solution is obtained through closed-form ridge regression.The output vector and regularization parameter are defined for each enhancement layer.
- Ensemble output: After producing L layer forecasts, the model combines them using the mean or median to form the final forecast.These operators define the Mea-edRVFL and Med-edRVFL variants.
D. EWT-edRVFL
EWT-edRVFL combines causal walk-forward EWT decomposition with the edRVFL network. Its layer-wise tuning accounts for dependencies between higher and lower enhancement layers.
- Model construction: The model first applies walk-forward EWT to load data, then feeds the raw series and extracted sub-series into the edRVFL.The layer outputs are combined by mean or median after their output weights are computed.
- Model construction: The walk-forward decomposition extracts features causally before forecasting, while the edRVFL learns from the resulting feature set.
- Hyper-parameter tuning: Hyper-parameters are tuned layer by layer because the performance of higher enhancement layers depends on lower ones.Once a shallow layer is selected, its hyper-parameters are fixed before tuning the next layer.
- Hyper-parameter tuning: Each enhancement layer receives its own regularization parameter, encouraging diverse output layers.
III. EMPIRICAL STUDY
The empirical study evaluates the forecasting methods on twenty load time series collected from the Australian Energy Market Operator. It covers data characteristics, preprocessing, benchmark models, hyper-parameter optimization, simulations, and discussion.
- Study design: The study uses twenty load time series from the Australian Energy Market Operator.The empirical section also describes preprocessing, benchmarks, hyper-parameter optimization, and simulation results.
A. Data and its nature
The dataset comprises 2020 half-hourly load series from five Australian states, with four selected months representing seasonal conditions. The data are normalized and split into training, validation, and test sets.
- Data characteristics: The twenty series come from South Australia, Queensland, New South Wales, Victoria, and Tasmania during 2020.January, April, July, and October are selected to represent four seasons; measurements occur every half hour.
- Data characteristics: Each day contains 48 recorded load points because the data are sampled every half hour.
- Preprocessing: Raw load data are preprocessed with max-min normalization using the training set's maximum and minimum.The transformation maps the data into the range [0,1].
- Data splitting: The datasets are divided into training, validation, and test sets, with validation and test portions of 10% and 20%, respectively.The remaining data form the training set.
B. Results and discussion
The evaluation uses three error metrics to compare the proposed model with classical and state-of-the-art forecasters across electricity-load datasets. Statistical tests place the proposed models among the strongest performers, while EWT increases computational time because decomposition occurs at each forecasting step.
- Evaluation metrics: Three forecasting error metrics—RMSE, MASE, and MAPE—are used to appraise model accuracy.RMSE is introduced first, followed by MASE and MAPE.
- Benchmark comparisons: The proposed model is compared with Persistence, ARIMA, SVR, MLP, LSTM, TCN, hybrid EWT models, LapESN, EWTRVFL, and RVFL.All models use the previous day’s 48 data points as input, with hyperparameters optimized by cross-validation.
- Statistical comparison: Nemenyi tests place the proposed models at the top across the three error metrics, while the Persistence method ranks last and ARIMA near the bottom.The same results report that LSTM outperforms many benchmarks except EWTRVFL and the proposed model.
- Statistical comparison: The mean ensemble operator performs better than the median operator in the edRVFL comparisons.This finding is reported from the Nemenyi test results.
- Forecast visualization: Figures 3–5 compare raw data with forecasts for the SA, QLD, and NSW datasets.The captions identify the datasets shown in the three forecast-comparison figures.
- Computational cost: EWT-based RVFL models are more time-consuming than their corresponding RVFL models because walk-forward EWT decomposition occurs at every forecasting step.The simulation-time analysis identifies the walk-forward EWT block as the main computational component.
IV. CONCLUSION
The paper concludes that combining ensemble deep RVFL forecasting with walk-forward EWT provides an effective and computationally efficient approach for short-term electricity-load forecasting. Its main unresolved issue is selecting whether to discard the highest-frequency EWT component.
- The edRVFL computes only output weights in closed form while retaining randomly initialized enhancement-layer weights, reducing training demands.
- Walk-forward EWT augments random features without introducing future-data leakage during decomposition.
- The proposed model demonstrates superiority and efficiency on twenty electricity-load datasets without the colossal computation burden of fully trained deep-learning models.
- The authors attribute performance gains to ensembling layer forecasts, combining direct-link linear patterns with nonlinear enhancement features, and EWT-based feature engineering.
- Whether the highest-frequency EWT component should be discarded remains an open problem, and incremental or semi-supervised learning are suggested for future improvement.