基于概率累加的离散GM(1,1)模型及其在海洋天然气产量预测中的应用  

A discrete GM(1,1)model based on probabilistic accumulation and its application to offshore gas production forecasting

作　　者：殷克东 张凯 杨文栋[1,2] YIN Kedong;ZHANG Kai;YANG Wendong(School of Management Science and Engineering,Shandong University of Finance and Economics,Jinan 250014,China;Institute of Marine Economics and Management,Shandong University of Finance and Economics,Jinan 250014,China)

机构地区：[1]山东财经大学管理科学与工程学院,济南250014 [2]山东财经大学海洋经济与管理研究院,济南250014

出　　处：《系统工程理论与实践》2024年第8期2733-2746,共14页Systems Engineering-Theory & Practice

基　　金：国家社会科学基金重大项目(22&ZD126);国家自然科学基金(72301157,72101138);教育部人文社会科学基金(21YJCZH198)。

摘　　要：准确预测海洋天然气产量对于带动海洋装备制造业发展,重塑国内能源供应体系结构,推动引领性科技攻关具有重要的现实意义.针对灰色信息叠加建模方法在表征系统运行特性时的不足,本文提出了基于概率累加的离散GM(1,1)模型(PDGM(1,1)).首先,提出模型依托概率累加算子甄别提取灰色有效信息,深度挖掘灰色系统运行的行为规律;其次,使用矩阵扰动理论证明了提出模型对于小样本数据集的适用性,保证了对小样本数据的预测优势;再次,对于提出模型中复杂信息参数的求解问题,提出了基于启发式算法的模型求解框架;然后,设计数值仿真实验模拟非线性数据环境,检验了PDGM(1,1)模型的建模能力和预测能力.同时,引入实际案例验证了PDGM(1,1)模型的鲁棒性和普适性;最后,应用PDGM(1,1)模型预测海洋天然气产量.本研究成果一是精细化了灰色预测模型建模的信息基础,提出了一种新的预测建模方法,对于丰富和完善预测模型方法体系具有积极意义;二是海洋天然气产量预测结果将为新发展格局下拓展我国海洋经济发展空间的路径实施提供参考依据.Accurate prediction of marine natural gas production is of great practical significance for driving the development of marine equipment manufacturing industry,reshaping the structure of domestic energy supply system and promoting leading scientific and technological research.Aiming at the shortcomings of the grey information superposition modeling approach in characterizing the operational properties of the system,this paper proposes a discrete GM(1,1)model based on probabilistic accumulation(PDGM(1,1)).First,the proposed model relies on the probabilistic accumulation operator to screen and extract the grey effective information,and deeply excavate the behavioral laws of the grey system operation;Second,the applicability of the proposed model to small sample data sets is demonstrated using matrix perturbation theory,which ensures the predictive advantage for small sample data;Third,for the problem of solving complex information parameters in the proposed model,a model solving framework based on heuristic algorithms is proposed;Then,numerical simulation experiments were designed to simulate the nonlinear data environment to test the modeling and prediction capabilities of the PDGM(1,1)model.Meanwhile,real cases are introduced to verify the robustness and generalizability of the PDGM(1,1)model;Finally,the PDGM(1,1)model is applied to predict the offshore gas production.The results of this research,firstly,refined the information base of the grey prediction model modeling and proposed a new prediction modeling method,which is of positive significance for enriching and improving the system of prediction modeling methods;Secondly,the results of the offshore gas production forecast will provide a reference basis for the implementation of the path to expand China’s marine economic development space under the new development pattern.

关 键 词：灰色预测模型 概率累加算子 区间灰数 灰色有效信息 海洋天然气预测 

分 类 号：N941.5[自然科学总论—系统科学]