Using the projective Riccati equation expansion （PREE） method, new families of variable separation solutions （including solitary wave solutions, periodic wave solutions and rational function solutions） with arbitr...Using the projective Riccati equation expansion （PREE） method, new families of variable separation solutions （including solitary wave solutions, periodic wave solutions and rational function solutions） with arbitrary functions for two nonlinear physical models are obtained. Based on one of the variable separation solutions and by choosing appropriate functions, new types of interactions between the multi-valued and single-valued solitons, such as a peakon-like semi-foldon and a peakon, a compacton-like semi-foldon and a compacton, are investigated.展开更多
Separable nonlinear models are widely used in various fields such as time series analysis, system modeling, and machine learning, due to their flexible structures and ability to capture nonlinear behavior of data. How...Separable nonlinear models are widely used in various fields such as time series analysis, system modeling, and machine learning, due to their flexible structures and ability to capture nonlinear behavior of data. However, identifying the parameters of these models is challenging, especially when sparse models with better interpretability are desired by practitioners. Previous theoretical and practical studies have shown that variable projection (VP) is an efficient method for identifying separable nonlinear models, but these are based on \(L_2\) penalty of model parameters, which cannot be directly extended to deal with sparse constraint. Based on the exploration of the structural characteristics of separable models, this paper proposes gradient-based and trust-region-based variable projection algorithms, which mainly solve two key problems: how to eliminate linear parameters under sparse constraint;and how to deal with the coupling relationship between linear and nonlinear parameters in the model. Finally, numerical experiments on synthetic data and real time series data are conducted to verify the effectiveness of the proposed algorithms.展开更多
Baosteel＇s 60000 m……3/h air separation unit （ASU）, the first domestically-integrated unit of its class, is a milestone in the Chinese air separation industry. In this paper,the process characteristics of the unit...Baosteel＇s 60000 m……3/h air separation unit （ASU）, the first domestically-integrated unit of its class, is a milestone in the Chinese air separation industry. In this paper,the process characteristics of the unit and the application of the original techniques are expatiated. Some difficulties in the process design, the risk control, the quality control, the control system integration and the system commissioning are analyzed and appraised. The mode of the project integration and innovation, the cooperation among industries and the user-orientated project management mode are introduced. Finally,the successful experiences in innovation are summarized with the focus on the integration of the project.展开更多
基金Project supported by the National Natural Science Foundation of China （Grant No 10272071）, the Natural Science Foundation of Zhejiang Province, China （Grant No Y606049） and the Key Academic Discipline of Zhejiang Province, China （Grant No 200412）. Acknowledgments The authors are indebted to Professors Zhang J F, Zheng C L and Drs Zhu J M, Huang W H for their helpful suggestions and fruitful discussions.
文摘Using the projective Riccati equation expansion （PREE） method, new families of variable separation solutions （including solitary wave solutions, periodic wave solutions and rational function solutions） with arbitrary functions for two nonlinear physical models are obtained. Based on one of the variable separation solutions and by choosing appropriate functions, new types of interactions between the multi-valued and single-valued solitons, such as a peakon-like semi-foldon and a peakon, a compacton-like semi-foldon and a compacton, are investigated.
基金supported in part by the National Nature Science Foundation of China(Nos.62173091,62073082)in part by the Natural Science Foundation of Fujian Province(No.2023J01268)in part by the Taishan Scholar Program of Shandong Province.
文摘Separable nonlinear models are widely used in various fields such as time series analysis, system modeling, and machine learning, due to their flexible structures and ability to capture nonlinear behavior of data. However, identifying the parameters of these models is challenging, especially when sparse models with better interpretability are desired by practitioners. Previous theoretical and practical studies have shown that variable projection (VP) is an efficient method for identifying separable nonlinear models, but these are based on \(L_2\) penalty of model parameters, which cannot be directly extended to deal with sparse constraint. Based on the exploration of the structural characteristics of separable models, this paper proposes gradient-based and trust-region-based variable projection algorithms, which mainly solve two key problems: how to eliminate linear parameters under sparse constraint;and how to deal with the coupling relationship between linear and nonlinear parameters in the model. Finally, numerical experiments on synthetic data and real time series data are conducted to verify the effectiveness of the proposed algorithms.
文摘Baosteel＇s 60000 m……3/h air separation unit （ASU）, the first domestically-integrated unit of its class, is a milestone in the Chinese air separation industry. In this paper,the process characteristics of the unit and the application of the original techniques are expatiated. Some difficulties in the process design, the risk control, the quality control, the control system integration and the system commissioning are analyzed and appraised. The mode of the project integration and innovation, the cooperation among industries and the user-orientated project management mode are introduced. Finally,the successful experiences in innovation are summarized with the focus on the integration of the project.
