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Developing a hybrid probabilistic model for short-term wind speed forecasting

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Abstract

Probabilistic forecasting can provide quantitative and comprehensive information about future wind speed uncertainty, which exhibits increasing importance for the vital integration of wind power into power systems. However, many conventional forecasting models cannot better handle the uncertainty generated by the intermittent and stochastic nature of wind patterns. This paper develops a hybrid versatile forecasting framework that presents point estimation and different forms of probabilistic wind speed forecasting, such as interval prediction and probability density prediction. In this proposed model, the hybrid of empirical wavelet transform and neural network-based quantile regression is proposed to improve the generalization and robustness of probabilistic forecasts and to capture the probabilistic meaning output of wind speed forecasts. To further emphasize the importance of probabilistic forecasting, an adaptive density estimation method based on the Gaussian kernel function as determined by the firefly algorithm is developed to generate more predictive probability information. Wind datasets from three sites in Penglai, China, are used to validate the proposed approach. The experimental results demonstrate that the developed probabilistic wind speed forecasting model can provide value and comprehensive information about future wind speed and is a promising tool for the decision-making process in wind power operation and management.

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Abbreviations

ARMA:

Autoregressive moving average

ARIMA:

Autoregressive integrated moving average

ANN:

Artificial neural network

SVM:

Support vector machine

LSSVM:

Least square support vector machine)

BPNN:

Back propagation neural network

GRNN:

General regression neural network

WNN:

Wavelet neural network

ELM:

Extreme learning machine

GA-BPNN:

Genetic algorithm-BPNN

DBN:

Deep belief network

QR:

Quantile regression

QRNN:

Quantile regression neural network

EWTQR:

Improved QRNN by EWT

NWP:

Numerical weather predictions

SDEs:

Stochastic differential equations

BMA:

Bayesian model averaging

GPR:

Gaussian process regression

WT:

Wavelet transform

EWT:

Empirical wavelet transform

AM-FM:

Amplitude modulated-frequency modulated

EMD:

Empirical mode decomposition

SVR:

Support vector regression

IMF:

Intrinsic mode function

KDE:

Kernel density estimation

ANFIS:

Adaptive network-based fuzzy inference system

CS:

Cuckoo search

FA:

Firefly algorithm

GA:

Genetic algorithm

PACF:

Partial autocorrelation function

AIC:

Akaike information criterion

HPP:

Highest probability point

ICP:

Interval coverage probability

IAW:

Interval average width

DIAW:

Deviation of average width

CWC:

Coverage width-based criterion

MAE:

Mean absolute error

RMSE:

Root mean square error

MAPE:

Mean absolute percent error

DM:

Diebold-mariano

\( {\hat{\varPhi}}_n \) :

Empirical scaling function of EWT

\( {\hat{\varPsi}}_n \) :

Empirical wavelets function

Λ n :

Fourier spectrum support

ω n :

Segment Boundary of Fourier spectrum support

\( {W}_f^{\varepsilon}\left(n,t\right) \) :

Detail coefficients of EWT

\( {W}_f^{\varepsilon}\left(0,t\right) \) :

Approximation coefficients of EWT

τ :

Quantile

g 1(·):

Activation function of hidden nodes in QRNN

g 2(·):

Activation function of output node in QRNN

λ 1,λ 2 :

Regularization parameters of QRNN

W(τ), β(τ):

Connection weights of QRNN

\( {\hat{f}}_h \) :

Kernel density estimation

K(·):

Kernel function

h :

Bandwidth

β(r):

Attractiveness of the firefly

β 0 :

Attractiveness at r = 0

r ij :

Distance between any two fireflies

Ut :

Upper bound of forecast interval

L t :

Lower bound of forecast interval

\( {f}_t^{\boldsymbol{actual}} \) :

Observed value at time t

\( {f}_t^{\boldsymbol{predicted}} \) :

Estimated value at time t

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Acknowledgments

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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Authors and Affiliations

  1. Business School, Zhengzhou University, Zhengzhou, 450001, China

    Xiaobo Zhang

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  1. Xiaobo Zhang
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Correspondence to Xiaobo Zhang.

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We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work. This manuscript is our own work and the content of this paper has not been copied from elsewhere. This manuscript has not been published before nor submitted to another journal for the consideration of publication and all data measurements are genuine results and have not been manipulated. In addition, none of the authors have any financial or scientific conflicts of interest with regard to the research described in this manuscript.

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Zhang, X. Developing a hybrid probabilistic model for short-term wind speed forecasting. Appl Intell 53, 728–745 (2023). https://doi.org/10.1007/s10489-022-03644-8

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