The general approach for solving the nonlinear equations is linearizing the equations and forming various iterative procedures, then executing the numerical simulation. For the strongly nonlinear problems, the solutio...The general approach for solving the nonlinear equations is linearizing the equations and forming various iterative procedures, then executing the numerical simulation. For the strongly nonlinear problems, the solution obtained in the iterative process is always difficult, even divergent due to the numerical instability. It can not fulfill the engineering requirements. Newton's method and its variants can not settle this problem. As a result, the application of numerical simulation for the strongly nonlinear problems is limited. An auto-adjustable damping method has been presented in this paper. This is a further improvement of Newton's method with damping factor. A set of vector of damping factor is introduced. This set of vector can be adjusted continuously during the iterative process in accordance with the judgement and adjustment. An effective convergence coefficient and quichening coefficient are employed to relax the restricted requirements for the initial values and to shorten the iterative process. Then, the numerical stability will be ensured for the solution of complicated strongly nonlinear equations. Using this method, some complicated strongly nonlinear heat transfer problems in airplanes and aeroengines have been numerically simulated successfully. It can be used for the numerical simulation of strongly nonlinear problems in engineering such as nonlinear hydrodynamics and aerodynamics, heat transfer and structural dynamic response etc.展开更多
The prediction of solitary wave run-up has important practical significance in coastal and ocean engineering, but the calculation precision is limited in the existing models. For improving the calculation precision, a...The prediction of solitary wave run-up has important practical significance in coastal and ocean engineering, but the calculation precision is limited in the existing models. For improving the calculation precision, a solitary wave run-up calculation model was established based on artificial neural networks in this study. A back-propagation （BP） network with one hidden layer was adopted and modified with the additional momentum method and the auto-adjusting learning factor. The model was applied to calculation of solitary wave run-up. The correlation coefficients between the neural network model results and the experimental values was 0.996 5. By comparison with the correlation coefficient of 0.963 5, between the Synolakis formula calculation results and the experimental values, it is concluded that the neural network model is an effective method for calculation and analysis of solitary wave ran-up.展开更多
文摘The general approach for solving the nonlinear equations is linearizing the equations and forming various iterative procedures, then executing the numerical simulation. For the strongly nonlinear problems, the solution obtained in the iterative process is always difficult, even divergent due to the numerical instability. It can not fulfill the engineering requirements. Newton's method and its variants can not settle this problem. As a result, the application of numerical simulation for the strongly nonlinear problems is limited. An auto-adjustable damping method has been presented in this paper. This is a further improvement of Newton's method with damping factor. A set of vector of damping factor is introduced. This set of vector can be adjusted continuously during the iterative process in accordance with the judgement and adjustment. An effective convergence coefficient and quichening coefficient are employed to relax the restricted requirements for the initial values and to shorten the iterative process. Then, the numerical stability will be ensured for the solution of complicated strongly nonlinear equations. Using this method, some complicated strongly nonlinear heat transfer problems in airplanes and aeroengines have been numerically simulated successfully. It can be used for the numerical simulation of strongly nonlinear problems in engineering such as nonlinear hydrodynamics and aerodynamics, heat transfer and structural dynamic response etc.
基金supported by State Key Development Program of Basic Research of China (Grant No.2010CB429001)
文摘The prediction of solitary wave run-up has important practical significance in coastal and ocean engineering, but the calculation precision is limited in the existing models. For improving the calculation precision, a solitary wave run-up calculation model was established based on artificial neural networks in this study. A back-propagation （BP） network with one hidden layer was adopted and modified with the additional momentum method and the auto-adjusting learning factor. The model was applied to calculation of solitary wave run-up. The correlation coefficients between the neural network model results and the experimental values was 0.996 5. By comparison with the correlation coefficient of 0.963 5, between the Synolakis formula calculation results and the experimental values, it is concluded that the neural network model is an effective method for calculation and analysis of solitary wave ran-up.
