This article discusses the dynamic state analysis of underwater towed-cable when tow-ship changes its speed in a direction making parabolic profile path. A three-dimensional model of underwater towed system is studied...This article discusses the dynamic state analysis of underwater towed-cable when tow-ship changes its speed in a direction making parabolic profile path. A three-dimensional model of underwater towed system is studied. The established governing equations for the system have been solved using the central implicit finite-difference method. The obtained difference non-linear coupled equations are solved by Newton＇s method and satisfactory results were achieved. The solution of this problem has practical importance in the estimation of dynamic loading and motion, and hence it is directly applicable to the enhancement of safety and the effectiveness of the offshore activities.展开更多
A motion parameter optimization method based on the objective of minimizing the total energy consumption in segment positioning was proposed for segment erector of shield tunneling machine. The segment positioning pro...A motion parameter optimization method based on the objective of minimizing the total energy consumption in segment positioning was proposed for segment erector of shield tunneling machine. The segment positioning process was decomposed into rotation, lifting and sliding actions in deriving the energy calculation model of segment erection. The work of gravity was taken into account in the mathematical modeling of energy consumed by each actuator. In order to investigate the relationship between the work done by the actuator and the path moved along by the segment, the upward and downward directions as well as the operating quadrant of the segment erector were defined. Piecewise nonlinear function of energy was presented, of which the result is determined by closely coupled components as working parameters and some intermediate variables. Finally, the effectiveness of the optimization method was proved by conducting a case study with a segment erector for the tunnel with a diameter of 3 m and drawing comparisons between different assembling paths. The results show that the energy required by assembling a ring of segments along the optimized moving path can be reduced up to 5%. The method proposed in this work definitely provides an effective energy saving solution for shield tunneling machine.展开更多
In this letter, using a Baecklund transformation and the new variableseparation approach, we find a new general solution of the (N+1)-dimensional Burgers system. Theform of the universal formula obtained from many (2+...In this letter, using a Baecklund transformation and the new variableseparation approach, we find a new general solution of the (N+1)-dimensional Burgers system. Theform of the universal formula obtained from many (2+1)-dimensional system is extended.展开更多
This paper considers dealing with path constraints in the framework of the improved control vector iteration （CVI） approach. Two available ways for enforcing equality path constraints are presented, which can be dir...This paper considers dealing with path constraints in the framework of the improved control vector iteration （CVI） approach. Two available ways for enforcing equality path constraints are presented, which can be directly incorporated into the improved CVI approach. Inequality path constraints are much more difficult to deal with, even for small scale problems, because the time intervals where the inequality path constraints are active are unknown in advance. To overcome the challenge, the ll penalty function and a novel smoothing technique are in-troduced, leading to a new effective approach. Moreover, on the basis of the relevant theorems, a numerical algo-rithm is proposed for nonlinear dynamic optimization problems with inequality path constraints. Results obtained from the classic batch reaCtor operation problem are in agreement with the literature reoorts, and the comoutational efficiency is also high.展开更多
This study proposes an efficient indirect approach for general nonlinear dynamic optimization problems without path constraints. The approach incorporates the virtues both from indirect and direct methods: it solves t...This study proposes an efficient indirect approach for general nonlinear dynamic optimization problems without path constraints. The approach incorporates the virtues both from indirect and direct methods: it solves the optimality conditions like the traditional indirect methods do, but uses a discretization technique inspired from direct methods. Compared with other indirect approaches, the proposed approach has two main advantages: (1) the discretized optimization problem only employs unconstrained nonlinear programming (NLP) algorithms such as BFGS (Broyden-Fletcher-Goldfarb-Shanno), rather than constrained NLP algorithms, therefore the computational efficiency is increased; (2) the relationship between the number of the discretized time intervals and the integration error of the four-step Adams predictor-corrector algorithm is established, thus the minimal number of time intervals that under desired integration tolerance can be estimated. The classic batch reactor problem is tested and compared in detail with literature reports, and the results reveal the effectiveness of the proposed approach. Dealing with path constraints requires extra techniques, and will be studied in the second paper.展开更多
Based on a barotropic inflow-outflow model,we examine the formation of the Kuroshio large meander(LM) using conditional nonlinear optimal perturbation(CNOP) method.Both linear and nonlinear evolutions of such perturba...Based on a barotropic inflow-outflow model,we examine the formation of the Kuroshio large meander(LM) using conditional nonlinear optimal perturbation(CNOP) method.Both linear and nonlinear evolutions of such perturbations obtained by this method are investigated.The results show that the nonlinear evolution can result in the Kuroshio transition from a straight to LM path,whereas the linear evolution cannot.This implies that nonlinearity plays an important role in the formation of the Kuroshio LM path.The nonlinearity exists as advection in the evolution equations of the perturbation derived from the barotropic inflow-outflow model,namely the nonlinear advection of the perturbation by the perturbation(NAPP).By examining the role of this nonlinearity,we find that the NAPP tends to move the cyclonic eddy induced by the CNOP-type perturbation westward.Together with the beta effect,this offsets part of the eastward advection caused by the interaction between the perturbation and the background flow.Hence,the eastward movement of the cyclonic eddy is significantly weakened,effectively causing the eddy to develop.The sufficient evolution of this cyclonic eddy leads to the formation of the Kuroshio LM.展开更多
The multi-linear variable separation approach method is very useful to solve (2+1)-dimensional integrable systems. In this letter, we extend this method to solve (1+1)-dimensional Boiti system, (2+1)-dimensional Burge...The multi-linear variable separation approach method is very useful to solve (2+1)-dimensional integrable systems. In this letter, we extend this method to solve (1+1)-dimensional Boiti system, (2+1)-dimensional Burgers system, (2+1)-dimensional breaking soliton system, and (2+1)-dimensional Maccari system. Some new exact solutions are obtained and the universal formula obtained from many (2+1)-dimensional systems is extended or modified.展开更多
We introduce a new type of path-dependent quasi-linear parabolic PDEs in which the continuous paths on an interval [0, t] become the basic variables in the place of classical variables （t, x） ∈[0, T]× R^d. Thi...We introduce a new type of path-dependent quasi-linear parabolic PDEs in which the continuous paths on an interval [0, t] become the basic variables in the place of classical variables （t, x） ∈[0, T]× R^d. This new type of PDEs are formulated through a classical BSDE in which the terminal values and the generators are allowed to be general function of Brownian motion paths. In this way, we establish the nonlinear Feynman- Kac formula for a general non-Markoviau BSDE. Some main properties of solutions of this new PDEs are also obtained.展开更多
文摘This article discusses the dynamic state analysis of underwater towed-cable when tow-ship changes its speed in a direction making parabolic profile path. A three-dimensional model of underwater towed system is studied. The established governing equations for the system have been solved using the central implicit finite-difference method. The obtained difference non-linear coupled equations are solved by Newton＇s method and satisfactory results were achieved. The solution of this problem has practical importance in the estimation of dynamic loading and motion, and hence it is directly applicable to the enhancement of safety and the effectiveness of the offshore activities.
基金Project(51305328)supported by the National Natural Science Foundation of ChinaProject(2012AA041803)supported by the NationalHigh Technology R&D Program of China+1 种基金Project(GZKF-201210)supported by the Open Fund of State Key Laboratory of Fluid Power Transmission and Control of Zhejiang University,ChinaProject(2013M532031)supported by the China Postdoctoral Science Foundation
文摘A motion parameter optimization method based on the objective of minimizing the total energy consumption in segment positioning was proposed for segment erector of shield tunneling machine. The segment positioning process was decomposed into rotation, lifting and sliding actions in deriving the energy calculation model of segment erection. The work of gravity was taken into account in the mathematical modeling of energy consumed by each actuator. In order to investigate the relationship between the work done by the actuator and the path moved along by the segment, the upward and downward directions as well as the operating quadrant of the segment erector were defined. Piecewise nonlinear function of energy was presented, of which the result is determined by closely coupled components as working parameters and some intermediate variables. Finally, the effectiveness of the optimization method was proved by conducting a case study with a segment erector for the tunnel with a diameter of 3 m and drawing comparisons between different assembling paths. The results show that the energy required by assembling a ring of segments along the optimized moving path can be reduced up to 5%. The method proposed in this work definitely provides an effective energy saving solution for shield tunneling machine.
文摘In this letter, using a Baecklund transformation and the new variableseparation approach, we find a new general solution of the (N+1)-dimensional Burgers system. Theform of the universal formula obtained from many (2+1)-dimensional system is extended.
基金Supported by the National Natural Science Foundation of China(U1162130)the National High Technology Research and Development Program of China(2006AA05Z226)Outstanding Youth Science Foundation of Zhejiang Province(R4100133)
文摘This paper considers dealing with path constraints in the framework of the improved control vector iteration （CVI） approach. Two available ways for enforcing equality path constraints are presented, which can be directly incorporated into the improved CVI approach. Inequality path constraints are much more difficult to deal with, even for small scale problems, because the time intervals where the inequality path constraints are active are unknown in advance. To overcome the challenge, the ll penalty function and a novel smoothing technique are in-troduced, leading to a new effective approach. Moreover, on the basis of the relevant theorems, a numerical algo-rithm is proposed for nonlinear dynamic optimization problems with inequality path constraints. Results obtained from the classic batch reaCtor operation problem are in agreement with the literature reoorts, and the comoutational efficiency is also high.
基金Supported by the National Natural Science Foundation of China (U1162130)the National High Technology Research and Development Program of China (2006AA05Z226)the Outstanding Youth Science Foundation,Zhejiang Province (R4100133)
文摘This study proposes an efficient indirect approach for general nonlinear dynamic optimization problems without path constraints. The approach incorporates the virtues both from indirect and direct methods: it solves the optimality conditions like the traditional indirect methods do, but uses a discretization technique inspired from direct methods. Compared with other indirect approaches, the proposed approach has two main advantages: (1) the discretized optimization problem only employs unconstrained nonlinear programming (NLP) algorithms such as BFGS (Broyden-Fletcher-Goldfarb-Shanno), rather than constrained NLP algorithms, therefore the computational efficiency is increased; (2) the relationship between the number of the discretized time intervals and the integration error of the four-step Adams predictor-corrector algorithm is established, thus the minimal number of time intervals that under desired integration tolerance can be estimated. The classic batch reactor problem is tested and compared in detail with literature reports, and the results reveal the effectiveness of the proposed approach. Dealing with path constraints requires extra techniques, and will be studied in the second paper.
基金Supported by the National Natural Science Foundation of China(Nos.41230420,41306023)the Basic Research Program of Science and Technology Projects of Qingdao(No.11-1-4-95-jch)the Open Fund of LASG,Institute of Atmospheric Physics,Chinese Academy of Sciences
文摘Based on a barotropic inflow-outflow model,we examine the formation of the Kuroshio large meander(LM) using conditional nonlinear optimal perturbation(CNOP) method.Both linear and nonlinear evolutions of such perturbations obtained by this method are investigated.The results show that the nonlinear evolution can result in the Kuroshio transition from a straight to LM path,whereas the linear evolution cannot.This implies that nonlinearity plays an important role in the formation of the Kuroshio LM path.The nonlinearity exists as advection in the evolution equations of the perturbation derived from the barotropic inflow-outflow model,namely the nonlinear advection of the perturbation by the perturbation(NAPP).By examining the role of this nonlinearity,we find that the NAPP tends to move the cyclonic eddy induced by the CNOP-type perturbation westward.Together with the beta effect,this offsets part of the eastward advection caused by the interaction between the perturbation and the background flow.Hence,the eastward movement of the cyclonic eddy is significantly weakened,effectively causing the eddy to develop.The sufficient evolution of this cyclonic eddy leads to the formation of the Kuroshio LM.
文摘The multi-linear variable separation approach method is very useful to solve (2+1)-dimensional integrable systems. In this letter, we extend this method to solve (1+1)-dimensional Boiti system, (2+1)-dimensional Burgers system, (2+1)-dimensional breaking soliton system, and (2+1)-dimensional Maccari system. Some new exact solutions are obtained and the universal formula obtained from many (2+1)-dimensional systems is extended or modified.
基金supported by National Natural Science Foundation of China(Grant No.10921101)the Programme of Introducing Talents of Discipline to Universities of China(Grant No.B12023)the Fundamental Research Funds of Shandong University
文摘We introduce a new type of path-dependent quasi-linear parabolic PDEs in which the continuous paths on an interval [0, t] become the basic variables in the place of classical variables （t, x） ∈[0, T]× R^d. This new type of PDEs are formulated through a classical BSDE in which the terminal values and the generators are allowed to be general function of Brownian motion paths. In this way, we establish the nonlinear Feynman- Kac formula for a general non-Markoviau BSDE. Some main properties of solutions of this new PDEs are also obtained.
