Grey Bernoulli model based on Conformable fractional order derivatives(基于Conformable分数阶导数的灰色Bernoulli模型)

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.(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。)

Keywords

• grey system(灰色系统)
• conformable fractional derivative(conformable分数阶导数)
• grey bernoulli model(灰色bernoulli模型)
• particle swarm optimization algorithm(粒子群优化算法)