In this paper the large deflection dynamic problems of Euler beams are investigated. The vibration control equations are derived based on the multibody system method. A numerical procedure for solving the resulting di...In this paper the large deflection dynamic problems of Euler beams are investigated. The vibration control equations are derived based on the multibody system method. A numerical procedure for solving the resulting differential algebraic equations is presented on the basis of the Newmark direct integration method combined with the Newton-Raphson iterative method. The sub beams are treated as small deformation in the convected coordinate systems, which can greatly simplify the deformation description. The rigid motions of the sub beams are taken into account through the motions of the convected coordinate systems. Numerical ex- amples are carried out, where results show the effectiveness of the proposed method.展开更多
Two dynamical system methods are studied for solving linear ill-posed problems with both operator and right-hand nonexact. The methods solve a Cauchy problem for a linear operator equation which possesses a global sol...Two dynamical system methods are studied for solving linear ill-posed problems with both operator and right-hand nonexact. The methods solve a Cauchy problem for a linear operator equation which possesses a global solution. The limit of the global solution at infinity solves the original linear equation. Moreover, we also present a convergent iterative process for solving the Cauchy problem.展开更多
The invertible of the Large Air Dense Medium Fluidized Bed (ADMFB) were studied by introducing the concept of the inverse system theory of nonlinear systems. Then the ADMFB, which was a multivariable, nonlinear and co...The invertible of the Large Air Dense Medium Fluidized Bed (ADMFB) were studied by introducing the concept of the inverse system theory of nonlinear systems. Then the ADMFB, which was a multivariable, nonlinear and coupled strongly system, was decoupled into independent SISO pseudo-linear subsystems. Linear controllers were designed for each of subsystems based on linear systems theory. The practice output proves that this method improves the stability of the ADMFB obviously.展开更多
In this paper a new simplified method of stability study of dynamical nonlinear systems is proposed as an alternative to using Lyapunov’s method. Like the Lyapunov theorem, the new concept describes a sufficient cond...In this paper a new simplified method of stability study of dynamical nonlinear systems is proposed as an alternative to using Lyapunov’s method. Like the Lyapunov theorem, the new concept describes a sufficient condition for the systems to be globally stable. The proposed method is based on the assumption that, not only the state matrix contains information on the stability of the systems, but also the eigenvectors. So, first we will write the model of nonlinear systems in the state-space representation, then we use the eigenvectors of the state matrix as system stability indicators.展开更多
This research extensively evaluates three leading mathematical software packages: Python, MATLAB, and Scilab, in the context of solving nonlinear systems of equations with five unknown variables. The study’s core obj...This research extensively evaluates three leading mathematical software packages: Python, MATLAB, and Scilab, in the context of solving nonlinear systems of equations with five unknown variables. The study’s core objectives include comparing software performance using standardized benchmarks, employing key performance metrics for quantitative assessment, and examining the influence of varying hardware specifications on software efficiency across HP ProBook, HP EliteBook, Dell Inspiron, and Dell Latitude laptops. Results from this investigation reveal insights into the capabilities of these software tools in diverse computing environments. On the HP ProBook, Python consistently outperforms MATLAB in terms of computational time. Python also exhibits a lower robustness index for problems 3 and 5 but matches or surpasses MATLAB for problem 1, for some initial guess values. In contrast, on the HP EliteBook, MATLAB consistently exhibits shorter computational times than Python across all benchmark problems. However, Python maintains a lower robustness index for most problems, except for problem 3, where MATLAB performs better. A notable challenge is Python’s failure to converge for problem 4 with certain initial guess values, while MATLAB succeeds in producing results. Analysis on the Dell Inspiron reveals a split in strengths. Python demonstrates superior computational efficiency for some problems, while MATLAB excels in handling others. This pattern extends to the robustness index, with Python showing lower values for some problems, and MATLAB achieving the lowest indices for other problems. In conclusion, this research offers valuable insights into the comparative performance of Python, MATLAB, and Scilab in solving nonlinear systems of equations. It underscores the importance of considering both software and hardware specifications in real-world applications. The choice between Python and MATLAB can yield distinct advantages depending on the specific problem and computational environment, providing guidance for researchers and practitioners in selecting tools for their unique challenges.展开更多
A new staggered isolated system developed from the mid-story isolated system is the new staggered story isolated system. There are not many studies on this structure currently. In this study, an 18-story new staggered...A new staggered isolated system developed from the mid-story isolated system is the new staggered story isolated system. There are not many studies on this structure currently. In this study, an 18-story new staggered story isolated system model is established using SAP2000. The dynamic nonlinear dynamic alternate method is used to analyze the structure against progressive collapse. Results show that the structure has good resistance to progressive collapse, and there is no progressive collapse under each working condition. The progressive collapse does not occur for the case of removing only one vertical structural member of the new staggered of isolated system. The side column has big influence on this isolated structures’ progressive collapse;the removal of vertical structural member of the isolation layer has less impact on the structure than the removal of the bottom vertical structural member. After the removing of the member, the internal force of the structure will be redistributed, and the axial force of the adjacent columns will change obviously, showing a trend of “near large and far small”.展开更多
Autonomous underwater gliders are highly effcient,buoyancy-driven,winged autonomous underwater vehicles. Their dynamics are multivariable nonlinear systems. In addition,the gliders are underactuated and diffcult to ma...Autonomous underwater gliders are highly effcient,buoyancy-driven,winged autonomous underwater vehicles. Their dynamics are multivariable nonlinear systems. In addition,the gliders are underactuated and diffcult to maneuver,and also dependent on their operational environment. To confront these problems and to design an effective controller,the inverse system method was used to decouple the original system into two independent single variable linear subsystems. The stability of the zero dynamics was analyzed,and an additional closed-loop controller for each linear subsystem was designed by sliding mode control method to form a type of composite controller. Simulation results demonstrate that the derived nonlinear controller is able to cope with the aforementioned problems simultaneously and satisfactorily.展开更多
The integration of set-valued ordered rough set models and incremental learning signify a progressive advancement of conventional rough set theory, with the objective of tackling the heterogeneity and ongoing transfor...The integration of set-valued ordered rough set models and incremental learning signify a progressive advancement of conventional rough set theory, with the objective of tackling the heterogeneity and ongoing transformations in information systems. In set-valued ordered decision systems, when changes occur in the attribute value domain, such as adding conditional values, it may result in changes in the preference relation between objects, indirectly leading to changes in approximations. In this paper, we effectively addressed the issue of updating approximations that arose from adding conditional values in set-valued ordered decision systems. Firstly, we classified the research objects into two categories: objects with changes in conditional values and objects without changes, and then conducted theoretical studies on updating approximations for these two categories, presenting approximation update theories for adding conditional values. Subsequently, we presented incremental algorithms corresponding to approximation update theories. We demonstrated the feasibility of the proposed incremental update method with numerical examples and showed that our incremental algorithm outperformed the static algorithm. Ultimately, by comparing experimental results on different datasets, it is evident that the incremental algorithm efficiently reduced processing time. In conclusion, this study offered a promising strategy to address the challenges of set-valued ordered decision systems in dynamic environments.展开更多
By the method of dynamical system, we construct the exact travelling wave solu- tions of a new Hamiltonian amplitude equation and the Ostrovsky equation. Based on this method, the new exact travelling wave solutions o...By the method of dynamical system, we construct the exact travelling wave solu- tions of a new Hamiltonian amplitude equation and the Ostrovsky equation. Based on this method, the new exact travelling wave solutions of the new Hamiltonian am- plitude equation and the Ostrovsky equation, such as solitary wave solutions, kink and anti-kink wave solutions and periodic travelling wave solutions, are obtained, respectively.展开更多
In this paper,the field method for solving the equations of motion of holonomic nonconservative systems is extended to nonholonomic systems with constant mass and with variable mass.Two examples are given to illustrat...In this paper,the field method for solving the equations of motion of holonomic nonconservative systems is extended to nonholonomic systems with constant mass and with variable mass.Two examples are given to illustrate its application.展开更多
This paper focuses on studying the integration method of a generalized Birkhoffian system.The method of variation on parameters for the dynamical equations of a generalized Birkhoffian system is presented.The procedur...This paper focuses on studying the integration method of a generalized Birkhoffian system.The method of variation on parameters for the dynamical equations of a generalized Birkhoffian system is presented.The procedure for solving the problem can be divided into two steps:the first step,a system of auxiliary equations is constructed and its general solution is given;the second step,the parameters are varied,and the solution of the problem is obtained by using the properties of generalized canonical transformation.The method of variation on parameters for the generalized Birkhoffian system is of universal significance,and we take a nonholonomic system and a nonconservative system as examples to illustrate the application of the results of this paper.展开更多
Complex slopes are characterized by large numbers of failure modes,cut sets or link sets,or by statistical dependence between the failure modes.For such slopes,a systematic quantitative method,or matrix-based system r...Complex slopes are characterized by large numbers of failure modes,cut sets or link sets,or by statistical dependence between the failure modes.For such slopes,a systematic quantitative method,or matrix-based system reliability method,was described and improved for their reliability analysis.A construction formula of event vector c E was suggested to solve the difficulty of identifying any component E in sample space,and event vector c of system events can be calculated based on it,then the bounds of system failure probability can be obtained with the given probability information.The improved method was illustrated for four copper mine slopes with multiple failure modes,and the bounds of system failure probabilities were calculated by self-compiling program on the platform of the software MATLAB.Comparison in results from matrix-based system reliability method and two generic system methods suggests that identical accuracy could be obtained by all methods if there are only a few failure modes in slope system.Otherwise,the bounds by the Ditlevsen method or Cornell method are expanded obviously with the increase of failure modes and their precision can hardly satisfy the requirement of practical engineering while the results from the proposed method are still accurate enough.展开更多
CNC machining systems are inevitably confronted with frequent changes in energy behaviors because they are widely used to perform various machining tasks. It is a challenge to understand and analyze the flexible energ...CNC machining systems are inevitably confronted with frequent changes in energy behaviors because they are widely used to perform various machining tasks. It is a challenge to understand and analyze the flexible energy behaviors in CNC machining systems. A method to model flexible energy behaviors in CNC machining systems based on hierarchical objected-oriented Petri net(HOONet) is proposed. The structure of the HOONet is constructed of a high-level model and detail models. The former is used to model operational states for CNC machining systems, and the latter is used to analyze the component models for operational states. The machining parameters having great impacts on energy behaviors in CNC machining systems are declared with the data dictionary in HOONet models. A case study based on a CNC lathe is presented to demonstrate the proposed modeling method. The results show that it is effective for modeling flexible energy behaviors and providing a fine-grained description to quantitatively analyze the energy consumption of CNC machining systems.展开更多
Hydro-sodalites are zeolitic materials with a wide variety of applications.Fly ash is an abundant industrial solid waste,rich in silicon and aluminum,from which hydro-sodalite can be synthesized.However,traditional hy...Hydro-sodalites are zeolitic materials with a wide variety of applications.Fly ash is an abundant industrial solid waste,rich in silicon and aluminum,from which hydro-sodalite can be synthesized.However,traditional hydrothermal synthesis methods are complex and cannot produce high-purity products.Therefore,there is a demand for processing routes to obtain high-purity hydro-sodalites.In the present study,high-purity hydro-sodalite(90.2 wt%)was prepared from fly ash by applying a hydrothermal method to a submolten salt system.Samples were characterized by powder X-ray diffraction(XRD),scanning electron microscopy(SEM),thermogravimetry and differential thermal analysis(TG–DTA),and Fourier transform infrared spectroscopy(FTIR)to confirm and quantify conversion of the raw material into the product phase.Purity of the samples prepared with an H2O/Na OH mass ratio of 1.5 and an H2O/fly ash mass ratio of 10 was calculated and the conversion process of the product phase was studied.Crystallinity of the product was influenced more by the Na OH concentration,less by the H2O/fly ash mass ratio.The main reaction process of the system is that the Si O ions produced by dissolution of the vitreous body in the fly ash and Na+ions in the solution reacted on the destroyed mullite skeleton to produce hydro-sodalite.This processing route could help mitigate processing difficulties,while producing high-purity hydro-sodalite from fly ash.展开更多
This paper focuses on studying the Poisson theory and the integration method of a Birkhoffian system in the event space. The Birkhoff's equations in the event space are given. The Poisson theory of the Birkhoffian sy...This paper focuses on studying the Poisson theory and the integration method of a Birkhoffian system in the event space. The Birkhoff's equations in the event space are given. The Poisson theory of the Birkhoffian system in the event space is established. The definition of the Jacobi last multiplier of the system is given, and the relation between the Jacobi last multiplier and the first integrals of the system is discussed. The researches show that for a Birkhoffian system in the event space, whose configuration is determined by (2n + 1) Birkhoff's variables, the solution of the system can be found by the Jacobi last multiplier if 2n first integrals are known. An example is given to illustrate the application of the results.展开更多
A new method for analyzing high-speed circuit systems is presented. The method adds transmission line end currents to the circuit variables of the classical modified nodal approach. Then the matrix equation describing...A new method for analyzing high-speed circuit systems is presented. The method adds transmission line end currents to the circuit variables of the classical modified nodal approach. Then the matrix equation describing high-speed circuit system can be formulated directly and analyzed conveniently for its normative form. A time-domain analysis method for transmission lines is also introduced. The two methods are combined together to efficiently analyze high-speed circuit systems having general transmission lines. Numerical experiment is presented and the results are compared with that calculated by Hspice.展开更多
The generalized variational data assimilation for non-differential dynamical systems is studied.There is no tangent linear model for non-differential systems and thus the general adjoint model can not be derived in th...The generalized variational data assimilation for non-differential dynamical systems is studied.There is no tangent linear model for non-differential systems and thus the general adjoint model can not be derived in the traditional way.The weak form of the original system was introduced, and then the generalized adjoint model was derived. The generalized variational data assimilation methods were developed for non-differential low dimensional system and non-differential high dimensional system with global and local observations. Furthermore, ideas in inverse problems are introduced to 4DVAR (Four-dimensional variational) of non-differential partial differential system with local observations.展开更多
Methods based on numerical optimization are useful and effective in the design of control systems. This paper describes the design of retarded fractional delay differential systems (RFDDSs) by the method of inequali...Methods based on numerical optimization are useful and effective in the design of control systems. This paper describes the design of retarded fractional delay differential systems (RFDDSs) by the method of inequalities, in which the design problem is formulated so that it is suitable for solution by numerical methods. Zakian's original formulation, which was first proposed in connection with rational systems, is extended to the case of RFDDSs. In making the use of this formulation possible for RFDDSs, the associated stability problems are resolved by using the stability test and the numerical algorithm for computing the abscissa of stability recently developed by the authors. During the design process, the time responses are obtained by a known method for the numerical inversion of Laplace transforms. Two numerical examples are given, where fractional controllers are designed for a time-delay and a heat-conduction plants.展开更多
A discrete event system is a dynamical system whose state evolves in time by the occurrence of events at possibly irregular time intervals. Timed Petri nets are a graphical and mathematical modeling tool applicable to...A discrete event system is a dynamical system whose state evolves in time by the occurrence of events at possibly irregular time intervals. Timed Petri nets are a graphical and mathematical modeling tool applicable to discrete event systems in order to represent its states evolution where the timing at which the state changes is taken into consideration. One of the most important performance issues to be considered in a discrete event system is its stability. Lyapunov theory provides the required tools needed to aboard the stability and stabilization problems for discrete event systems modeled with timed Petri nets whose mathematical model is given in terms of difference equations. By proving stability one guarantees a bound on the discrete event systems state dynamics. When the system is unstable, a sufficient condition to stabilize the system is given. It is shown that it is possible to restrict the discrete event systems state space in such a way that boundedness is achieved. However, the restriction is not numerically precisely known. This inconvenience is overcome by considering a specific recurrence equation, in the max-plus algebra, which is assigned to the timed Petri net graphical model.展开更多
文摘In this paper the large deflection dynamic problems of Euler beams are investigated. The vibration control equations are derived based on the multibody system method. A numerical procedure for solving the resulting differential algebraic equations is presented on the basis of the Newmark direct integration method combined with the Newton-Raphson iterative method. The sub beams are treated as small deformation in the convected coordinate systems, which can greatly simplify the deformation description. The rigid motions of the sub beams are taken into account through the motions of the convected coordinate systems. Numerical ex- amples are carried out, where results show the effectiveness of the proposed method.
基金Research was supported by the Jiang Xi Provincial Natural Science Foundation of China under Grant 0611005.
文摘Two dynamical system methods are studied for solving linear ill-posed problems with both operator and right-hand nonexact. The methods solve a Cauchy problem for a linear operator equation which possesses a global solution. The limit of the global solution at infinity solves the original linear equation. Moreover, we also present a convergent iterative process for solving the Cauchy problem.
文摘The invertible of the Large Air Dense Medium Fluidized Bed (ADMFB) were studied by introducing the concept of the inverse system theory of nonlinear systems. Then the ADMFB, which was a multivariable, nonlinear and coupled strongly system, was decoupled into independent SISO pseudo-linear subsystems. Linear controllers were designed for each of subsystems based on linear systems theory. The practice output proves that this method improves the stability of the ADMFB obviously.
文摘In this paper a new simplified method of stability study of dynamical nonlinear systems is proposed as an alternative to using Lyapunov’s method. Like the Lyapunov theorem, the new concept describes a sufficient condition for the systems to be globally stable. The proposed method is based on the assumption that, not only the state matrix contains information on the stability of the systems, but also the eigenvectors. So, first we will write the model of nonlinear systems in the state-space representation, then we use the eigenvectors of the state matrix as system stability indicators.
文摘This research extensively evaluates three leading mathematical software packages: Python, MATLAB, and Scilab, in the context of solving nonlinear systems of equations with five unknown variables. The study’s core objectives include comparing software performance using standardized benchmarks, employing key performance metrics for quantitative assessment, and examining the influence of varying hardware specifications on software efficiency across HP ProBook, HP EliteBook, Dell Inspiron, and Dell Latitude laptops. Results from this investigation reveal insights into the capabilities of these software tools in diverse computing environments. On the HP ProBook, Python consistently outperforms MATLAB in terms of computational time. Python also exhibits a lower robustness index for problems 3 and 5 but matches or surpasses MATLAB for problem 1, for some initial guess values. In contrast, on the HP EliteBook, MATLAB consistently exhibits shorter computational times than Python across all benchmark problems. However, Python maintains a lower robustness index for most problems, except for problem 3, where MATLAB performs better. A notable challenge is Python’s failure to converge for problem 4 with certain initial guess values, while MATLAB succeeds in producing results. Analysis on the Dell Inspiron reveals a split in strengths. Python demonstrates superior computational efficiency for some problems, while MATLAB excels in handling others. This pattern extends to the robustness index, with Python showing lower values for some problems, and MATLAB achieving the lowest indices for other problems. In conclusion, this research offers valuable insights into the comparative performance of Python, MATLAB, and Scilab in solving nonlinear systems of equations. It underscores the importance of considering both software and hardware specifications in real-world applications. The choice between Python and MATLAB can yield distinct advantages depending on the specific problem and computational environment, providing guidance for researchers and practitioners in selecting tools for their unique challenges.
文摘A new staggered isolated system developed from the mid-story isolated system is the new staggered story isolated system. There are not many studies on this structure currently. In this study, an 18-story new staggered story isolated system model is established using SAP2000. The dynamic nonlinear dynamic alternate method is used to analyze the structure against progressive collapse. Results show that the structure has good resistance to progressive collapse, and there is no progressive collapse under each working condition. The progressive collapse does not occur for the case of removing only one vertical structural member of the new staggered of isolated system. The side column has big influence on this isolated structures’ progressive collapse;the removal of vertical structural member of the isolation layer has less impact on the structure than the removal of the bottom vertical structural member. After the removing of the member, the internal force of the structure will be redistributed, and the axial force of the adjacent columns will change obviously, showing a trend of “near large and far small”.
基金the National Natural Science Foundation of China (No. 50979058)the Special Research Fund for the Doctoral Program of Higher Education (No. 20090073110012)
文摘Autonomous underwater gliders are highly effcient,buoyancy-driven,winged autonomous underwater vehicles. Their dynamics are multivariable nonlinear systems. In addition,the gliders are underactuated and diffcult to maneuver,and also dependent on their operational environment. To confront these problems and to design an effective controller,the inverse system method was used to decouple the original system into two independent single variable linear subsystems. The stability of the zero dynamics was analyzed,and an additional closed-loop controller for each linear subsystem was designed by sliding mode control method to form a type of composite controller. Simulation results demonstrate that the derived nonlinear controller is able to cope with the aforementioned problems simultaneously and satisfactorily.
文摘The integration of set-valued ordered rough set models and incremental learning signify a progressive advancement of conventional rough set theory, with the objective of tackling the heterogeneity and ongoing transformations in information systems. In set-valued ordered decision systems, when changes occur in the attribute value domain, such as adding conditional values, it may result in changes in the preference relation between objects, indirectly leading to changes in approximations. In this paper, we effectively addressed the issue of updating approximations that arose from adding conditional values in set-valued ordered decision systems. Firstly, we classified the research objects into two categories: objects with changes in conditional values and objects without changes, and then conducted theoretical studies on updating approximations for these two categories, presenting approximation update theories for adding conditional values. Subsequently, we presented incremental algorithms corresponding to approximation update theories. We demonstrated the feasibility of the proposed incremental update method with numerical examples and showed that our incremental algorithm outperformed the static algorithm. Ultimately, by comparing experimental results on different datasets, it is evident that the incremental algorithm efficiently reduced processing time. In conclusion, this study offered a promising strategy to address the challenges of set-valued ordered decision systems in dynamic environments.
文摘By the method of dynamical system, we construct the exact travelling wave solu- tions of a new Hamiltonian amplitude equation and the Ostrovsky equation. Based on this method, the new exact travelling wave solutions of the new Hamiltonian am- plitude equation and the Ostrovsky equation, such as solitary wave solutions, kink and anti-kink wave solutions and periodic travelling wave solutions, are obtained, respectively.
基金The project supported by the National Natural Science Foundation of China
文摘In this paper,the field method for solving the equations of motion of holonomic nonconservative systems is extended to nonholonomic systems with constant mass and with variable mass.Two examples are given to illustrate its application.
基金supported by the National Natural Science Foundation of China (10972151)
文摘This paper focuses on studying the integration method of a generalized Birkhoffian system.The method of variation on parameters for the dynamical equations of a generalized Birkhoffian system is presented.The procedure for solving the problem can be divided into two steps:the first step,a system of auxiliary equations is constructed and its general solution is given;the second step,the parameters are varied,and the solution of the problem is obtained by using the properties of generalized canonical transformation.The method of variation on parameters for the generalized Birkhoffian system is of universal significance,and we take a nonholonomic system and a nonconservative system as examples to illustrate the application of the results of this paper.
基金Project(51078170) supported by the National Natural Science Foundation of ChinaProject(10JDG097) supported by Jiangsu University Talents Funds,China
文摘Complex slopes are characterized by large numbers of failure modes,cut sets or link sets,or by statistical dependence between the failure modes.For such slopes,a systematic quantitative method,or matrix-based system reliability method,was described and improved for their reliability analysis.A construction formula of event vector c E was suggested to solve the difficulty of identifying any component E in sample space,and event vector c of system events can be calculated based on it,then the bounds of system failure probability can be obtained with the given probability information.The improved method was illustrated for four copper mine slopes with multiple failure modes,and the bounds of system failure probabilities were calculated by self-compiling program on the platform of the software MATLAB.Comparison in results from matrix-based system reliability method and two generic system methods suggests that identical accuracy could be obtained by all methods if there are only a few failure modes in slope system.Otherwise,the bounds by the Ditlevsen method or Cornell method are expanded obviously with the increase of failure modes and their precision can hardly satisfy the requirement of practical engineering while the results from the proposed method are still accurate enough.
基金Supported by National Natural Science Foundation of China(Grant No.51605058)Chongqing Research Program of Basic Research and Frontier Technology of China(Grant No.cstc2015jcyjBX0088)+2 种基金Fundamental Research Funds for the Central Universities of China(Grant No.106112016CDJCR021226)Six Talent Peaks Project in Jiangsu Province of China(Grant No.2014-ZBZZ-006)"Excellence Plans-Zijin Star" Foundation of Nanjing University of Science and Technology,China(Grant No.2015-zijin-07)
文摘CNC machining systems are inevitably confronted with frequent changes in energy behaviors because they are widely used to perform various machining tasks. It is a challenge to understand and analyze the flexible energy behaviors in CNC machining systems. A method to model flexible energy behaviors in CNC machining systems based on hierarchical objected-oriented Petri net(HOONet) is proposed. The structure of the HOONet is constructed of a high-level model and detail models. The former is used to model operational states for CNC machining systems, and the latter is used to analyze the component models for operational states. The machining parameters having great impacts on energy behaviors in CNC machining systems are declared with the data dictionary in HOONet models. A case study based on a CNC lathe is presented to demonstrate the proposed modeling method. The results show that it is effective for modeling flexible energy behaviors and providing a fine-grained description to quantitatively analyze the energy consumption of CNC machining systems.
基金financially supported by the National Natural Science Foundation of China (No. 51474028)the National Key Research and Development Program of China (No. 2017YFC0210301)+1 种基金China Postdoctoral Science Foundation (No. 2017M621034)the Science and Technology Benefiting Citizens Program of Ningbo, China (No. 2015C50058)
文摘Hydro-sodalites are zeolitic materials with a wide variety of applications.Fly ash is an abundant industrial solid waste,rich in silicon and aluminum,from which hydro-sodalite can be synthesized.However,traditional hydrothermal synthesis methods are complex and cannot produce high-purity products.Therefore,there is a demand for processing routes to obtain high-purity hydro-sodalites.In the present study,high-purity hydro-sodalite(90.2 wt%)was prepared from fly ash by applying a hydrothermal method to a submolten salt system.Samples were characterized by powder X-ray diffraction(XRD),scanning electron microscopy(SEM),thermogravimetry and differential thermal analysis(TG–DTA),and Fourier transform infrared spectroscopy(FTIR)to confirm and quantify conversion of the raw material into the product phase.Purity of the samples prepared with an H2O/Na OH mass ratio of 1.5 and an H2O/fly ash mass ratio of 10 was calculated and the conversion process of the product phase was studied.Crystallinity of the product was influenced more by the Na OH concentration,less by the H2O/fly ash mass ratio.The main reaction process of the system is that the Si O ions produced by dissolution of the vitreous body in the fly ash and Na+ions in the solution reacted on the destroyed mullite skeleton to produce hydro-sodalite.This processing route could help mitigate processing difficulties,while producing high-purity hydro-sodalite from fly ash.
基金Project supported by the National Natural Science Foundation of China(Grant No.10972151)
文摘This paper focuses on studying the Poisson theory and the integration method of a Birkhoffian system in the event space. The Birkhoff's equations in the event space are given. The Poisson theory of the Birkhoffian system in the event space is established. The definition of the Jacobi last multiplier of the system is given, and the relation between the Jacobi last multiplier and the first integrals of the system is discussed. The researches show that for a Birkhoffian system in the event space, whose configuration is determined by (2n + 1) Birkhoff's variables, the solution of the system can be found by the Jacobi last multiplier if 2n first integrals are known. An example is given to illustrate the application of the results.
文摘A new method for analyzing high-speed circuit systems is presented. The method adds transmission line end currents to the circuit variables of the classical modified nodal approach. Then the matrix equation describing high-speed circuit system can be formulated directly and analyzed conveniently for its normative form. A time-domain analysis method for transmission lines is also introduced. The two methods are combined together to efficiently analyze high-speed circuit systems having general transmission lines. Numerical experiment is presented and the results are compared with that calculated by Hspice.
文摘The generalized variational data assimilation for non-differential dynamical systems is studied.There is no tangent linear model for non-differential systems and thus the general adjoint model can not be derived in the traditional way.The weak form of the original system was introduced, and then the generalized adjoint model was derived. The generalized variational data assimilation methods were developed for non-differential low dimensional system and non-differential high dimensional system with global and local observations. Furthermore, ideas in inverse problems are introduced to 4DVAR (Four-dimensional variational) of non-differential partial differential system with local observations.
基金supported by the AUN/SEED-Net collaborative research program.
文摘Methods based on numerical optimization are useful and effective in the design of control systems. This paper describes the design of retarded fractional delay differential systems (RFDDSs) by the method of inequalities, in which the design problem is formulated so that it is suitable for solution by numerical methods. Zakian's original formulation, which was first proposed in connection with rational systems, is extended to the case of RFDDSs. In making the use of this formulation possible for RFDDSs, the associated stability problems are resolved by using the stability test and the numerical algorithm for computing the abscissa of stability recently developed by the authors. During the design process, the time responses are obtained by a known method for the numerical inversion of Laplace transforms. Two numerical examples are given, where fractional controllers are designed for a time-delay and a heat-conduction plants.
文摘A discrete event system is a dynamical system whose state evolves in time by the occurrence of events at possibly irregular time intervals. Timed Petri nets are a graphical and mathematical modeling tool applicable to discrete event systems in order to represent its states evolution where the timing at which the state changes is taken into consideration. One of the most important performance issues to be considered in a discrete event system is its stability. Lyapunov theory provides the required tools needed to aboard the stability and stabilization problems for discrete event systems modeled with timed Petri nets whose mathematical model is given in terms of difference equations. By proving stability one guarantees a bound on the discrete event systems state dynamics. When the system is unstable, a sufficient condition to stabilize the system is given. It is shown that it is possible to restrict the discrete event systems state space in such a way that boundedness is achieved. However, the restriction is not numerically precisely known. This inconvenience is overcome by considering a specific recurrence equation, in the max-plus algebra, which is assigned to the timed Petri net graphical model.