The main purpose of this paper is to provide a systematic geometric frame for generalized controlled Hamiltonian systems. The pseudo-Poisson manifold and the ω-manifold are proposed as the statespace of the generaliz...The main purpose of this paper is to provide a systematic geometric frame for generalized controlled Hamiltonian systems. The pseudo-Poisson manifold and the ω-manifold are proposed as the statespace of the generalized controlled Hamiltonian systems. A Lie group, calledN-group, and its Lie algebra, calledN-algebra, are introduced for the structure analysis of the systems. Some properties, including spectrum, structure-preservation, etc. are investigated. As an example the theoretical results are applied to power systems. The stabilization of excitation systems is investigated.展开更多
Incomplete fault signal characteristics and ease of noise contamination are issues with the current rolling bearing early fault diagnostic methods,making it challenging to ensure the fault diagnosis accuracy and relia...Incomplete fault signal characteristics and ease of noise contamination are issues with the current rolling bearing early fault diagnostic methods,making it challenging to ensure the fault diagnosis accuracy and reliability.A novel approach integrating enhanced Symplectic geometry mode decomposition with cosine difference limitation and calculus operator(ESGMD-CC)and artificial fish swarm algorithm(AFSA)optimized extreme learning machine(ELM)is proposed in this paper to enhance the extraction capability of fault features and thus improve the accuracy of fault diagnosis.Firstly,SGMD decomposes the raw vibration signal into multiple Symplectic geometry components(SGCs).Secondly,the iterations are reset by the cosine difference limitation to effectively separate the redundant components from the representative components.Additionally,the calculus operator is performed to strengthen weak fault features and make them easier to extract,and the singular value decomposition(SVD)weighted by power spectrum entropy(PSE)can be utilized as the sample feature representation.Finally,AFSA iteratively optimized ELM is adopted as the optimized classifier for fault identification.The superior performance of the proposed method has been validated by various experiments.展开更多
Based on the Hellinger_Reissner variatonal principle for Reissner plate bending and introducing dual variables,Hamiltonian dual equations for Reissner plate bending were presented.Therefore Hamiltonian solution system...Based on the Hellinger_Reissner variatonal principle for Reissner plate bending and introducing dual variables,Hamiltonian dual equations for Reissner plate bending were presented.Therefore Hamiltonian solution system can also be applied to Reissner plate bending problem,and the transformation from Euclidian space to symplectic space and from Lagrangian system to Hamiltonian system was realized.So in the symplectic space which consists of the original variables and their dual variables,the problem can be solved via effective mathematical physics methods such as the method of separation of variables and eigenfunction_vector expansion.All the eigensolutions and Jordan canonical form eigensolutions for zero eigenvalue of the Hamiltonian operator matrix are solved in detail,and their physical meanings are showed clearly.The adjoint symplectic orthonormal relation of the eigenfunction vectors for zero eigenvalue are formed.It is showed that the all eigensolutions for zero eigenvalue are basic solutions of the Saint_Venant problem and they form a perfect symplectic subspace for zero eigenvalue.And the eigensolutions for nonzero eigenvalue are covered by the Saint_Venant theorem.The symplectic solution method is not the same as the classical semi_inverse method and breaks through the limit of the traditional semi_inverse solution.The symplectic solution method will have vast application.展开更多
A new state vector is presented for symplectic solution to three dimensional couple stress problem. Without relying on the analogy relationship, the dual PDEs of couple stress problem are derived by a new state vector...A new state vector is presented for symplectic solution to three dimensional couple stress problem. Without relying on the analogy relationship, the dual PDEs of couple stress problem are derived by a new state vector. The duality solution methodology in a new form is thus extended to three dimensional couple stress. A new symplectic orthonormality relationship is proved. The symplectic solution to couple stress theory based a new state vector is more accordant with the custom of classical elasticity and is more convenient to process boundary conditions. A Hamilton mixed energy variational principle is derived by the integral method.展开更多
文摘The main purpose of this paper is to provide a systematic geometric frame for generalized controlled Hamiltonian systems. The pseudo-Poisson manifold and the ω-manifold are proposed as the statespace of the generalized controlled Hamiltonian systems. A Lie group, calledN-group, and its Lie algebra, calledN-algebra, are introduced for the structure analysis of the systems. Some properties, including spectrum, structure-preservation, etc. are investigated. As an example the theoretical results are applied to power systems. The stabilization of excitation systems is investigated.
基金supported by National Key Research and Development Project (2020YFE0204900)National Natural Science Foundation of China (Grant Numbers 62073193,61873333)Key Research and Development Plan of Shandong Province (Grant Numbers 2019TSLH0301,2021CXGC010204).
文摘Incomplete fault signal characteristics and ease of noise contamination are issues with the current rolling bearing early fault diagnostic methods,making it challenging to ensure the fault diagnosis accuracy and reliability.A novel approach integrating enhanced Symplectic geometry mode decomposition with cosine difference limitation and calculus operator(ESGMD-CC)and artificial fish swarm algorithm(AFSA)optimized extreme learning machine(ELM)is proposed in this paper to enhance the extraction capability of fault features and thus improve the accuracy of fault diagnosis.Firstly,SGMD decomposes the raw vibration signal into multiple Symplectic geometry components(SGCs).Secondly,the iterations are reset by the cosine difference limitation to effectively separate the redundant components from the representative components.Additionally,the calculus operator is performed to strengthen weak fault features and make them easier to extract,and the singular value decomposition(SVD)weighted by power spectrum entropy(PSE)can be utilized as the sample feature representation.Finally,AFSA iteratively optimized ELM is adopted as the optimized classifier for fault identification.The superior performance of the proposed method has been validated by various experiments.
文摘In this paper, two new constructions of Cartesian authentication codes from symplectic geometry are presented and their size parameters are computed.
文摘Based on the Hellinger_Reissner variatonal principle for Reissner plate bending and introducing dual variables,Hamiltonian dual equations for Reissner plate bending were presented.Therefore Hamiltonian solution system can also be applied to Reissner plate bending problem,and the transformation from Euclidian space to symplectic space and from Lagrangian system to Hamiltonian system was realized.So in the symplectic space which consists of the original variables and their dual variables,the problem can be solved via effective mathematical physics methods such as the method of separation of variables and eigenfunction_vector expansion.All the eigensolutions and Jordan canonical form eigensolutions for zero eigenvalue of the Hamiltonian operator matrix are solved in detail,and their physical meanings are showed clearly.The adjoint symplectic orthonormal relation of the eigenfunction vectors for zero eigenvalue are formed.It is showed that the all eigensolutions for zero eigenvalue are basic solutions of the Saint_Venant problem and they form a perfect symplectic subspace for zero eigenvalue.And the eigensolutions for nonzero eigenvalue are covered by the Saint_Venant theorem.The symplectic solution method is not the same as the classical semi_inverse method and breaks through the limit of the traditional semi_inverse solution.The symplectic solution method will have vast application.
文摘A new state vector is presented for symplectic solution to three dimensional couple stress problem. Without relying on the analogy relationship, the dual PDEs of couple stress problem are derived by a new state vector. The duality solution methodology in a new form is thus extended to three dimensional couple stress. A new symplectic orthonormality relationship is proved. The symplectic solution to couple stress theory based a new state vector is more accordant with the custom of classical elasticity and is more convenient to process boundary conditions. A Hamilton mixed energy variational principle is derived by the integral method.
