The amount of oxygen blown into the converter is one of the key parameters for the control of the converter blowing process,which directly affects the tap-to-tap time of converter. In this study, a hybrid model based ...The amount of oxygen blown into the converter is one of the key parameters for the control of the converter blowing process,which directly affects the tap-to-tap time of converter. In this study, a hybrid model based on oxygen balance mechanism (OBM) and deep neural network (DNN) was established for predicting oxygen blowing time in converter. A three-step method was utilized in the hybrid model. First, the oxygen consumption volume was predicted by the OBM model and DNN model, respectively. Second, a more accurate oxygen consumption volume was obtained by integrating the OBM model and DNN model. Finally, the converter oxygen blowing time was calculated according to the oxygen consumption volume and the oxygen supply intensity of each heat. The proposed hybrid model was verified using the actual data collected from an integrated steel plant in China, and compared with multiple linear regression model, OBM model, and neural network model including extreme learning machine, back propagation neural network, and DNN. The test results indicate that the hybrid model with a network structure of 3 hidden layer layers, 32-16-8 neurons per hidden layer, and 0.1 learning rate has the best prediction accuracy and stronger generalization ability compared with other models. The predicted hit ratio of oxygen consumption volume within the error±300 m^(3)is 96.67%;determination coefficient (R^(2)) and root mean square error (RMSE) are0.6984 and 150.03 m^(3), respectively. The oxygen blow time prediction hit ratio within the error±0.6 min is 89.50%;R2and RMSE are0.9486 and 0.3592 min, respectively. As a result, the proposed model can effectively predict the oxygen consumption volume and oxygen blowing time in the converter.展开更多
This paper deals with the blow up properties of the positive solutions to the nonlocal degenerate semilinear parabolic equation u t-(x αu x) x=∫ a 0f(u) d x in (0,a)×(0,T) under homogeneous Dirichl...This paper deals with the blow up properties of the positive solutions to the nonlocal degenerate semilinear parabolic equation u t-(x αu x) x=∫ a 0f(u) d x in (0,a)×(0,T) under homogeneous Dirichlet conditions. The local existence and uniqueness of classical solution are established. Under appropriate hypotheses, the global existence and blow up in finite time of positive solutions are obtained. It is also proved that the blow up set is almost the whole domain. This differs from the local case. Furthermore, the blow up rate is precisely determined for the special case: f(u)=u p,p>1.展开更多
Finite time blow up of the solutions to Boussinesq equation with linear restoring force and combined power nonlinearities is studied. Sufficient conditions on the initial data for nonexistence of global solutions are ...Finite time blow up of the solutions to Boussinesq equation with linear restoring force and combined power nonlinearities is studied. Sufficient conditions on the initial data for nonexistence of global solutions are derived. The results are valid for initial data with arbitrary high positive energy. The proofs are based on the concave method and new sign preserving functionals.展开更多
The high efficient blowing technique includes increasing oxygen supply intensity and optimizing slag forming. The oxygen supply intensity on 300 t converters of No. 1 steelmaking shop at Baosteel reaches 3.83 m^3/(t ...The high efficient blowing technique includes increasing oxygen supply intensity and optimizing slag forming. The oxygen supply intensity on 300 t converters of No. 1 steelmaking shop at Baosteel reaches 3.83 m^3/(t · min), and at Taiyuan Steel, Lianyuan Steel, Pingxiang Steel and other steel plants, the oxygen supply intensity on medium converters is in the range of 4.0--4.4m^3/(t · min). The productivity of converter can be increased by 8% -- 15% with adopting this technique. The whole technique, including design and manufacture of lance nozzle with reasonable pacnolontenue of outlets, technique of oxygen supply and slag forming, has been developed by CISRI to meet the need of technique transfer.展开更多
In this paper,a class of slow reaction-diffusion equations with nonlocal source and inner absorption terms are studied.By using the technique of improved differential inequality,the lower bounds of blow up time for th...In this paper,a class of slow reaction-diffusion equations with nonlocal source and inner absorption terms are studied.By using the technique of improved differential inequality,the lower bounds of blow up time for the system under either homogeneous Dirichlet or nonhomogeneous Neumann boundary conditions are obtained.展开更多
In the paper,the asymptotic behavior of the solution for the parabolic equation system of porous media coupled by three variables and with weighted nonlocal boundaries and nonlinear internal sources is studied.by cons...In the paper,the asymptotic behavior of the solution for the parabolic equation system of porous media coupled by three variables and with weighted nonlocal boundaries and nonlinear internal sources is studied.by constructing the upper and lower solutions with the ordinary differential equation as well as introducing the comparison theorem,the global existence and finite time blow-up of the solution of parabolic equations of porous media coupled by the power function and the logarithm function are obtained.The differential inequality technique is used to obtain the lower bounds on the blow up time of the above equations under Dirichlet and Neumann boundaryconditions.展开更多
In this paper,we establish the lower bounds estimate of the blow up time for solutions to the nonlocal cross-coupled porous medium equations with nonlocal source terms under Dirichlet and Neumann boundary conditions.T...In this paper,we establish the lower bounds estimate of the blow up time for solutions to the nonlocal cross-coupled porous medium equations with nonlocal source terms under Dirichlet and Neumann boundary conditions.The results are obtained by using some differential inequality technique.展开更多
基金financially supported by the National Natural Science Foundation of China (Nos.51974023 and52374321)the funding of State Key Laboratory of Advanced Metallurgy,University of Science and Technology Beijing,China (No.41620007)。
文摘The amount of oxygen blown into the converter is one of the key parameters for the control of the converter blowing process,which directly affects the tap-to-tap time of converter. In this study, a hybrid model based on oxygen balance mechanism (OBM) and deep neural network (DNN) was established for predicting oxygen blowing time in converter. A three-step method was utilized in the hybrid model. First, the oxygen consumption volume was predicted by the OBM model and DNN model, respectively. Second, a more accurate oxygen consumption volume was obtained by integrating the OBM model and DNN model. Finally, the converter oxygen blowing time was calculated according to the oxygen consumption volume and the oxygen supply intensity of each heat. The proposed hybrid model was verified using the actual data collected from an integrated steel plant in China, and compared with multiple linear regression model, OBM model, and neural network model including extreme learning machine, back propagation neural network, and DNN. The test results indicate that the hybrid model with a network structure of 3 hidden layer layers, 32-16-8 neurons per hidden layer, and 0.1 learning rate has the best prediction accuracy and stronger generalization ability compared with other models. The predicted hit ratio of oxygen consumption volume within the error±300 m^(3)is 96.67%;determination coefficient (R^(2)) and root mean square error (RMSE) are0.6984 and 150.03 m^(3), respectively. The oxygen blow time prediction hit ratio within the error±0.6 min is 89.50%;R2and RMSE are0.9486 and 0.3592 min, respectively. As a result, the proposed model can effectively predict the oxygen consumption volume and oxygen blowing time in the converter.
文摘This paper deals with the blow up properties of the positive solutions to the nonlocal degenerate semilinear parabolic equation u t-(x αu x) x=∫ a 0f(u) d x in (0,a)×(0,T) under homogeneous Dirichlet conditions. The local existence and uniqueness of classical solution are established. Under appropriate hypotheses, the global existence and blow up in finite time of positive solutions are obtained. It is also proved that the blow up set is almost the whole domain. This differs from the local case. Furthermore, the blow up rate is precisely determined for the special case: f(u)=u p,p>1.
基金partially supported by Grant No.DFNI I-02/9 of the Bulgarian Science Fund
文摘Finite time blow up of the solutions to Boussinesq equation with linear restoring force and combined power nonlinearities is studied. Sufficient conditions on the initial data for nonexistence of global solutions are derived. The results are valid for initial data with arbitrary high positive energy. The proofs are based on the concave method and new sign preserving functionals.
文摘The high efficient blowing technique includes increasing oxygen supply intensity and optimizing slag forming. The oxygen supply intensity on 300 t converters of No. 1 steelmaking shop at Baosteel reaches 3.83 m^3/(t · min), and at Taiyuan Steel, Lianyuan Steel, Pingxiang Steel and other steel plants, the oxygen supply intensity on medium converters is in the range of 4.0--4.4m^3/(t · min). The productivity of converter can be increased by 8% -- 15% with adopting this technique. The whole technique, including design and manufacture of lance nozzle with reasonable pacnolontenue of outlets, technique of oxygen supply and slag forming, has been developed by CISRI to meet the need of technique transfer.
基金Supported by the Natural Science Foundation of Shaanxi Province(2019JM-534)the Youth Innovation Team of Shaanxi Universities+7 种基金the 14th Five Year Plan for Educational Science in Shaanxi Province(SGH21Y0308)Key Topic of China Higher Education Association(21DFD04)Higher Education Teaching Reform Project of Xi’an International University(2023B03)2022 Annual Planning Project of China Association of Private Education(School Development)(CANFZG22222)Project of Department of Education of Shaanxi Provincethe 2022 Annual Topic of the"14th Five-Year Plan"of Shaanxi Provincial Educational Science(SGH22Y1885)Project of Qi Fang Education Research Institute of Xi’an International University(23mjy10)Special Project of the Shaanxi Provincial Social Science Found in 2023(2023SJ12,2023LS04)。
文摘In this paper,a class of slow reaction-diffusion equations with nonlocal source and inner absorption terms are studied.By using the technique of improved differential inequality,the lower bounds of blow up time for the system under either homogeneous Dirichlet or nonhomogeneous Neumann boundary conditions are obtained.
基金supported by Natural Science Basic Research Project of Shaanxi Province(2019JM-534)Soft Science Project of Shaanxi Province(2019KRM169)+3 种基金Project of Qi Fang Education Research Institute of Xian International University(21mjy07)Special project support of the 14th five year plan of the China Association of Higher Education(Topic name:Research on the adaptability of specialty structure and industrial structure of Local Universities-a case study of Shaanxi Province,No:21DFD04)2021 youth innovation team construction scientific research plan project of Shaanxi Provincial Department of Education(21JP105)The Youth Innovation Team of Shaanxi Universities,Shaanxi educational science"14th five year plan"project(SGH21Y0308).
文摘In the paper,the asymptotic behavior of the solution for the parabolic equation system of porous media coupled by three variables and with weighted nonlocal boundaries and nonlinear internal sources is studied.by constructing the upper and lower solutions with the ordinary differential equation as well as introducing the comparison theorem,the global existence and finite time blow-up of the solution of parabolic equations of porous media coupled by the power function and the logarithm function are obtained.The differential inequality technique is used to obtain the lower bounds on the blow up time of the above equations under Dirichlet and Neumann boundaryconditions.
基金supported by Natural Science Basic Research Project of Shaanxi Province(2019JM-534)Soft Science Project of Shaanxi Province(2019KRM169)+2 种基金Planned Projects of the 13th Five-year Plan for Education Science of Shaanxi Province(SGH18H544)Project on Higher Education Teaching Reform of Xi'an International University(2019B36)the Youth Innovation Team of Shaanxi Universities.
文摘In this paper,we establish the lower bounds estimate of the blow up time for solutions to the nonlocal cross-coupled porous medium equations with nonlocal source terms under Dirichlet and Neumann boundary conditions.The results are obtained by using some differential inequality technique.