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A novel decomposition-based ensemble model for short-term load forecasting using hybrid artificial neural networks

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Abstract

Highly accurate short-term load forecasting (STLF) is essential in the operation of power systems. However, the existing predictive methods cannot achieve an effective balance between prediction accuracy and computational cost. Furthermore, the prediction residual is rarely used to improve the predictive accuracy in STLF. This paper proposes a novel decomposition-based ensemble model for the STLF task. First, an optimized empirical wavelet transform (OEWT) is developed to rationally decompose the STLF load by combining the approximate entropy method with the empirical wavelet transform. Particularly, OEWT improves both prediction accuracy and computational cost in STLF. Second, a new hybrid machine learning method (named master learner) is proposed by rationally combining long short-term memory networks (LSTMs) with broad learning system (BLS) in STLF, effectively strengthening the predictive accuracy without significantly increasing the computational cost. Third, a residual learning model (named residual learner) is developed in the master learner to extract the effective predictive information from residual results, further improving the prediction accuracy in STLF. Fourth, an auxiliary learner is proposed by introducing another BLS to connect the input and output of the proposed model, enhancing the predictive robustness. The proposed decomposition-based ensemble model is compared with state-of-the-art and traditional models in STLF. Experimental results show that the model not only has high predictive accuracy and robustness but also low computational cost.

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Abbreviations

AL:

Auxiliary learner

ANN:

Artificial neural network

APEN:

Approximate entropy

BLS:

Broad learning system

BLSTM:

Hybrid model composed of BLS and LSTM

CD:

Critical distance of the Nemenyi test

DBN:

Deep neural network

DNN:

Deep neural network

DWT:

Discrete wavelet transform

EMD:

Empirical mode decomposition

EWT:

Empirical wavelet transform

FT:

Fourier transform

LSTM:

Long short-term memory

MAE:

Means absolute error

ML:

Master learner

NSW:

New South Wales, Australia

OEWT:

Optimized empirical wavelet transform

RL:

Residual learner

RMSE:

Root means square error

SLTF:

Short-term load prediction

SVR:

Support vector regression

SSA:

Singular spectrum analysis

VMD:

Variational mode decomposition

WT:

Wavelet transforms

a f :

The activation function

B + :

The pseudo-inverse of B

DL :

Whether to have the direct link between the input layer and output layer

d :

The distance between two reconstructed m dimensional vectors En

E k :

The enhancement nodes of BLS

E n :

The reconstructed m-dimensional vector by APEN

eta :

The learning rate

e n :

The components decomposed by EWT

f RBF :

The radial basis functions

f t :

The forget gate of LSTM

g t :

The input node of LSTM

h t :

The intermediate output of LSTM

I :

The identity matrix

i t :

The input gate of LSTM

J i :

The feature nodes of BLS

M :

The maximum value of the Fourier spectrum

m :

The length of the comparison vector in APEN

m i :

The maximum number of iterations

N :

The number of components of EWT

n :

The total number of test samples

n ds :

The number of data sets in Nemenyi test

n e :

The number of enhancement nodes

layer and output layer

n f :

The number of feature nodes

n h :

The number of hidden nodes

n l :

The number of learning algorithms in Nemenyi test

o t :

The output gate of LSTM

q α :

The critical value based on the Studentized Range statistic

r :

The similarity in APEN

r b :

The random batch size of each time

r m :

The randomization methods

std :

The standard deviation of the time series

s t :

The memory cell state of LSTM

s RBF :

The spread of radial basis functions

v m :

The momentum

W :

The weight matrix between the feature nodes, enhancement nodes, and output of BLS

X :

The input data of BLS

\(\hat{Y}\) :

The final prediction value of BLS

Y :

The actual value

y i :

The load data at a certain moment

y max :

The maximum value in the load data

y min :

The minimum value in the load data

\(\tilde{y}_{i}\) :

The normalized result of yi

\({\hat{y}}_i\) :

The predicted data of yi

κ :

The relative amplitude ratio of EWT

ω n :

The midpoint of the corresponding frequencies of the two adjacent maximum values above the threshold

τ n :

The transition phase of EWT

ρ :

The interval for reorganizing the components en(t)

λ:

The regularization parameter of BLS

F −1(∙):

The inverse Fourier transform

η(∙):

The linear transformation

ξ(∙):

The nonlinear activation function

σ(∙):

The sigmoid activation function

φ(∙):

The tanh function.

g(t):

The signal to be decomposed

\({\hat{T}}_n\left(\omega \right)\) :

The scaling function

\({\hat{P}}_n\left(\omega \right)\) :

The wavelet function

β(x):

An arbitrary function that satisfiesCk([0, 1])

\({K}_g^{\varepsilon}\left(n,t\right)\) :

The detail coefficient

\({K}_g^{\varepsilon}\left(0,t\right)\) :

The approximate coefficient

\({\bar{P}}_n\) :

The complex conjugate of Pn

\({\bar{T}}_1\) :

The complex conjugate of T1

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grants 61863028, 81660299, and 61503177, and in part by the Science and Technology Department of Jiangxi Province of China under Grants 20161ACB21007, 20171BBE50071, and 20171BAB202033.

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Author notes

  1. Zhiyuan Liao, Jiehui Huang and Yuxin Cheng contributed to the work equally and should be regarded as co-first authors.

Authors and Affiliations

  1. The School of Information Engineering, Nanchang University, Nanchang, 330031, China

    Zhiyuan Liao, Jiehui Huang, Yuxin Cheng & Chunquan Li

  2. The Department of Systems and Computer Engineering, Carleton University, Ottawa, ON, Canada

    Peter X. Liu

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  1. Zhiyuan Liao
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  2. Jiehui Huang
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Correspondence to Chunquan Li.

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Liao, Z., Huang, J., Cheng, Y. et al. A novel decomposition-based ensemble model for short-term load forecasting using hybrid artificial neural networks. Appl Intell 52, 11043–11057 (2022). https://doi.org/10.1007/s10489-021-02864-8

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