Prediction of servo industry development in China by an optimized reverse Hausdorff fractional discrete grey power model

In order to accurately predict the development of the servo industry in China, this study proposes a Hausdorff fractional reverse accumulated grey power model. Accumulation operation and differential equation modeling are the essential modeling steps of grey models different from other algorithms. Given the importance of information prioritization and the nonlinear characteristics in the data, the proposed model introduces enhancements from two key aspects: data feature extraction and structural representation. Firstly, an improved reverse accumulation operation is introduced into Hausdorff fractional accumulation, which can avoid the defect that Hausdorff fractional accumulation does not have the priority of new information. Secondly, an improved structure-adaptative discrete grey power model is proposed to simulate the nonlinear relationship between temporal factors and system states. Unlike traditional grey power models that only consider nonlinear relationships between historical values or temporal factors, the proposed improved grey model can comprehensively consider the complex characteristics of uncertain systems, providing valuable insights for the further expansion of nonlinear grey models. Furthermore, a cost function is established to adaptively adjust the model's information prioritization and nonlinear features. And the whale optimization algorithm is used to optimize the two hyperparameters of the proposed model. Finally, numerical examples are provided to validate the suitability of the proposed model, which predicts the trajectory of the servo industry and its downstream sectors in China. The forecasting results indicate that by 2025, the market size of China's servo industry is expected to reach 61 billion yuan. The production of computer numerical control cutting machine tools in China is projected to reach 880,000 sets by 2025. Additionally, the production of industrial robots in China is anticipated to reach 557,004 units, with an average annual growth rate of approximately 26%, meeting the government's development target of 20%. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.