An Improved Nonlinear Grey Bernoulli Model Based on the Whale Optimization Algorithm and Its Application

Jianming Jiang,Ting Feng,Caixia Liu,Leonid Shaikhet

doi:10.1155/2021/6691724

Abstract

In order to improve the prediction performance of the existing nonlinear grey Bernoulli model and extend its applicable range, an improved nonlinear grey Bernoulli model is presented by using a grey modeling technique and optimization methods. First, the traditional whitening equation of nonlinear grey Bernoulli model is transformed into its linear formulae. Second, improved structural parameters of the model are proposed to eliminate the inherent error caused by the leap jumping from the differential equation to the difference one. As a result, an improved nonlinear grey Bernoulli model is obtained. Finally, the structural parameters of the model are calculated by the whale optimization algorithm. The numerical results of several examples show that the presented model’s prediction accuracy is higher than that of the existing models, and the proposed model is more suitable for these practical cases.

Highlights

Professor Deng [1] originally proposed the grey system theory to solve the uncertain system with partially known and partially unknown information
In the past three decades, various grey models have been emerged rapidly according to practical applications
Wang et al [17] presented a data-grouping approach-based grey modeling method to predict quarterly hydropower production in China. They proposed a seasonal grey model based on the accumulation operators for forecasting the seasonal electricity consumption of China [18]

Summary

Introduction

Professor Deng [1] originally proposed the grey system theory to solve the uncertain system with partially known and partially unknown information. E main contributions of this paper are drawn as follows: (1) the grey differential equation is transformed into linear form rather than sharing the same form to the traditional NGBM (1, 1) model; (2) the optimized parameters are constructed and the whale optimization algorithm (WOA) is used to search for the optimal power index; (3) three cases are employed to verify the effectiveness of INGBM (1, 1). E solution of the NGBM (1, 1) model, either in linearization or in nonlinearization, is essentially approximate because the conversion of equations (11) and (12) is based on two-point trapezoidal formula regarded as an approximate method It implies that the “misplaced replacement” of the model parameters will cause the following: (i) the difference grey equation does not match with the differential grey equation because model parameters have different meanings in these equations; (ii) the prediction model is not satisfied in most situations. To evaluate the prediction accuracy of these grey models, the mean absolute percentage error (MAPE) and root mean square error (RMSE) are applied to measure the level of prediction performance, which are defined as 1 n 􏼌􏼌􏼌􏼌􏼌x􏽢(0)(k) − x(0)(k)􏼌􏼌􏼌􏼌􏼌

RMSE n

Actual data

Simulation Prediction

Findings

Best fitness