Grey Bernoulli model based on Conformable fractional order derivatives

doi:10.3785/j.issn.1008-9497.2024.02.008

Journal of Zhejiang University (Science Edition)

2024, Vol. 51

Issue (2): 196-204 DOI: 10.3785/j.issn.1008-9497.2024.02.008

Mathematics and Computer Science

Grey Bernoulli model based on Conformable fractional order derivatives

Shiguang LUO¹(

),Liang ZENG²(

)

^1.School of Financial Mathematics and Statistics，Guangdong University of Fiance，Guangzhou 510521，China
^2.Department of Basic Courses，Guangdong Technology College，Zhaoqing 526100，Guangdong Province，China

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Abstract

To enhance the adaptability of the grey Bernoulli model to various real data series, a grey Bernoulli model based on Conformable fractional order derivatives is proposed by taking advantage of the fractional order calculus in describing complex systems. It is found that the proposed model can be converted to some classical grey prediction models by replacing its structural parameters, which reflects its uniformity. Moreover, the particle swarm optimization algorithm is used to solve the planning model to obtain the optimal hyperparameters of the proposed model. The experimental results show that the two evaluation indicators of the proposed model are superior to the five competing algorithms, which confirms the validity and feasibility of the new model.

Key words： grey system Conformable fractional derivative grey Bernoulli model particle swarm optimization algorithm

Received: 10 August 2022 Published: 08 March 2024

CLC:

N 941.5

Corresponding Authors: Liang ZENG E-mail: sgluomaths@gduf.edu.cn;zengliang19820809@126.com

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Cite this article:

Shiguang LUO,Liang ZENG. Grey Bernoulli model based on Conformable fractional order derivatives. Journal of Zhejiang University (Science Edition), 2024, 51(2): 196-204.

URL:

https://www.zjujournals.com/sci/EN/Y2024/V51/I2/196

基于Conformable分数阶导数的灰色Bernoulli模型

为增强灰色Bernoulli模型对各种实际数据序列的适应性，借助分数阶微积分在描述复杂系统中的优势，提出了一种基于Conformable分数阶导数的灰色Bernoulli模型。研究发现，可通过改变结构参数将模型转换为不同的经典灰色预测模型，体现了其统一性。此外，采用粒子群优化算法求解规划模型，获取了模型的最优超参数。最后，用所提模型和5个竞争模型对3个真实案例进行了预测建模，结果表明，所提模型的2项评估指标均优于5个竞争模型，验证了所提模型的有效性和可行性。

关键词： 灰色系统, Conformable分数阶导数, 灰色Bernoulli模型, 粒子群优化算法

Fig.1 Curve of restored value under different parameter values

Table 1 Prediction results of six prediction models for foundation settlement in a certain engineering construction project

Table 2 Predictions results of six prediction models for China's total health expenditure data

Table 3 The predictions results of six prediction models for the case of per capita natural gas consumption in China

Fig.2 MAPE and RMSE of each model in three cases


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