关键词: GM(1,N)模型, 病态性, 粒子群算法, 生态创新

Abstract: The rapid economic growth model has led to the excessive consumption of resources, and a series of ecological problems are increasingly prominent. Ecological innovation not only solves the pressure caused by the bottleneck of resources and environment, but also promotes the sustainable development of national economy. However, the amount of data related to eco-innovation indicators that can be collected is limited. The structure of the corporate eco-innovation system is complex, with certain grey characteristics such as uncertainty and small samples. Therefore, this paper takes Chinese industrial enterprises as the research object, and explores the grey model forecasting technology applicable to the characteristics of ecological innovation-related indicators with multiple variables and few data. The possible pathology of traditional grey prediction in parameter estimation is studied.
In the actual data, there may be more influencing factor sequences than the number of samples, or there may be a strong grey correlation between influencing factors. When using the ordinary least squares method, pathological features may occur when the covariance matrix is close to singular. Therefore, the model parameters are estimated based on L₂ regular terms, and the relative optimal value of the regular term coefficients is found by combining with particle swarm arithmetic, so as to solve the morbidity problem and improve the prediction accuracy of the grey model. In addition, one of the reasons for the poor prediction effect of the traditional GM(1,N) model is the non-homology of parameter application, so this paper directly obtains the time response and parameter estimation from the difference equation to solve the non-homology problem.
The GM(1,N) model of the optimization algorithm is applied to the prediction of the number of patents of industrial enterprises in Jiangsu province and the north of China, and the results show that the number of patents of industrial enterprises in Jiangsu province and the north of China shows an increasing trend every year, and the total daily treatment capacity of urban sewage in Jiangsu province and the total current assets of industrial enterprises above designated size have a greater impact on the number of patents, and the number of units of industrial enterprises above designated size and the daily treatment capacity of urban sewage in the north of China are the main influence sequences.

Key words: the GM(1,N) model, illness conditioned, particle swarm optimization algorithm, ecological innovation