The Experts below are selected from a list of 12198 Experts worldwide ranked by ideXlab platform
Junsheng Cheng - One of the best experts on this subject based on the ideXlab platform.
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An early fault diagnosis method of gear based on improved Symplectic Geometry mode decomposition
Measurement, 2020Co-Authors: Jian Cheng, Yu Yang, Haiyang Pan, Junsheng ChengAbstract:Abstract Symplectic Geometry mode decomposition (SGMD) is an effective signal processing method, and it has been applied in compound fault diagnosis successfully. However, for early gear fault vibration signals, SGMD has two shortcomings. On the one hand, SGMD directly reconstructs the trajectory matrix through the original time series, which may cause the weak fault features submerged in global time series. Therefore, add a slip window to preprocess the original time series. On the other hand, the Symplectic Geometry components (SGCs) with low energy and fault feature information are eliminated for denoise. Therefore, variable entropy (VE) weighting is proposed to obtain the weighted Symplectic Geometry components (WSGCs) containing the vast majority of fault feature information. In conclusion, an improved Symplectic Geometry mode decomposition (ISGMD) is proposed to overcome the above two shortcomings. Simulated and experimental results indicate that ISGMD is effective for raw vibration signals.
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Symplectic Geometry mode decomposition and its application to rotating machinery compound fault diagnosis
Mechanical Systems and Signal Processing, 2019Co-Authors: Haiyang Pan, Yu Yang, Jinde Zheng, Junsheng ChengAbstract:Abstract Various existed time-series decomposition methods, including wavelet transform, ensemble empirical mode decomposition (EEMD), local characteristic-scale decomposition (LCD), singular spectrum analysis (SSA), etc., have some defects for nonlinear system signal analysis. When the signal is more complex, especially noisy signal, the component signal is forced to decompose into several incomplete components by LCD and SSA. In addition, the wavelet transform and EEMD need user-defined parameters, and they are very sensitive to the parameters. Therefore, a new signal decomposition algorithm, Symplectic Geometry mode decomposition (SGMD), is proposed in this paper to decompose a time series into a set of independent mode components. SGMD uses the Symplectic Geometry similarity transformation to solve the eigenvalues of the Hamiltonian matrix and reconstruct the single component signals with its corresponding eigenvectors. Meanwhile, SGMD can efficiently reconstruct the existed modes and remove the noise without any user-defined parameters. The essence of this method is that signal decomposition is converted into Symplectic Geometry transformation problem, and the signal is decomposed into a set of Symplectic Geometry components (SGCs). The analysis results of simulation signals and experimental signals indicate that the proposed time-series decomposition approach can decompose the analyzed signals accurately and effectively.
Zhong Yang - One of the best experts on this subject based on the ideXlab platform.
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Theoretical solution for rectangular thick plate with arbitrary boundary conditions by Symplectic Geometry method
Journal of Dalian University of Technology, 2005Co-Authors: Zhong YangAbstract:The theoretical solution for rectangular thick plate with arbitrary boundary conditions is derived by Symplectic Geometry method.Firstly,the basic equations for elastic thick plate are transferred into Hamilton canonical equations.Then the Symplectic Geometry method is used to separate the whole variables and the eigenvalues are obtained.Finally,according to the method of eigen function expansion,the explicit solution for rectangular thick plate with arbitrary boundary conditions is presented.Due to the fact that the basic elasticity equations of thick plate is only used and there is no need to select the deformation function arbitrary,the solution achieved is reasonable.A numerical example testifies the correctness of formulations.
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Solute elastic rectangular thin plate by Symplectic Geometry method
Journal of Guangzhou University, 2003Co-Authors: Zhong YangAbstract:In this paper, the analytical solution to elastic rectangular thin plate is derived by Symplectic Geometry method. Therefore, the theory foundation for solving this kind of problem with general supporting conditions is set up. Finally, the numerical examples are presented for comparing and proving the correction of formulations.
Socrates Dokos - One of the best experts on this subject based on the ideXlab platform.
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Symplectic Geometry spectrum regression for prediction of noisy time series.
Physical review. E, 2016Co-Authors: Hong-bo Xie, Socrates Dokos, Bellie Sivakumar, Kerrie MengersenAbstract:We present the Symplectic Geometry spectrum regression (SGSR) technique as well as a regularized method based on SGSR for prediction of nonlinear time series. The main tool of analysis is the Symplectic Geometry spectrum analysis, which decomposes a time series into the sum of a small number of independent and interpretable components. The key to successful regularization is to damp higher order Symplectic Geometry spectrum components. The effectiveness of SGSR and its superiority over local approximation using ordinary least squares are demonstrated through prediction of two noisy synthetic chaotic time series (Lorenz and R\"ossler series), and then tested for prediction of three real-world data sets (Mississippi River flow data and electromyographic and mechanomyographic signal recorded from human body).
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A Symplectic Geometry-based method for nonlinear time series decomposition and prediction
Applied Physics Letters, 2013Co-Authors: Hong-bo Xie, Socrates DokosAbstract:We present a technique to decompose a time series into the sum of a small number of independent and interpretable components based on Symplectic Geometry theory. The proposed Symplectic Geometry spectrum analysis technique consists of embedding, Symplectic QR decomposition of the matrix into an orthogonal matrix and a triangular matrix, grouping, and diagonal averaging steps. As an example application, the noisy Lorenz series demonstrate the effectiveness of this technique in nonlinear prediction.
Hong-bo Xie - One of the best experts on this subject based on the ideXlab platform.
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Symplectic Geometry spectrum regression for prediction of noisy time series.
Physical review. E, 2016Co-Authors: Hong-bo Xie, Socrates Dokos, Bellie Sivakumar, Kerrie MengersenAbstract:We present the Symplectic Geometry spectrum regression (SGSR) technique as well as a regularized method based on SGSR for prediction of nonlinear time series. The main tool of analysis is the Symplectic Geometry spectrum analysis, which decomposes a time series into the sum of a small number of independent and interpretable components. The key to successful regularization is to damp higher order Symplectic Geometry spectrum components. The effectiveness of SGSR and its superiority over local approximation using ordinary least squares are demonstrated through prediction of two noisy synthetic chaotic time series (Lorenz and R\"ossler series), and then tested for prediction of three real-world data sets (Mississippi River flow data and electromyographic and mechanomyographic signal recorded from human body).
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A Symplectic Geometry-based method for nonlinear time series decomposition and prediction
Applied Physics Letters, 2013Co-Authors: Hong-bo Xie, Socrates DokosAbstract:We present a technique to decompose a time series into the sum of a small number of independent and interpretable components based on Symplectic Geometry theory. The proposed Symplectic Geometry spectrum analysis technique consists of embedding, Symplectic QR decomposition of the matrix into an orthogonal matrix and a triangular matrix, grouping, and diagonal averaging steps. As an example application, the noisy Lorenz series demonstrate the effectiveness of this technique in nonlinear prediction.
Christopher L. Rogers - One of the best experts on this subject based on the ideXlab platform.
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Higher Symplectic Geometry
arXiv: Mathematical Physics, 2011Co-Authors: Christopher L. RogersAbstract:Author(s): Rogers, Christopher Lee | Advisor(s): Baez, John C | Abstract: In higher Symplectic Geometry, we consider generalizations of Symplectic manifolds called n-plectic manifolds. We say a manifold is n-plectic if it is equipped with a closed, non-degenerate form of degree (n+1). We show that certain higher algebraic and geometric structures naturally arise on these manifolds. These structures can be understood as the categorified or homotopy analogues of important structures studied in Symplectic Geometry and geometric quantization. Our results imply that higher Symplectic Geometry is closely related to several areas of current interest including string theory, loop groups, and generalized Geometry.We begin by showing that, just as a Symplectic manifold gives a Poisson algebra of functions, any n-plectic manifold gives a Lie n-algebra containing certain differential forms which we call Hamiltonian. Lie n-algebras are examples of strongly homotopy Lie algebras. They consist of an n-term chain complex equipped with a collection of skew-symmetric multi-brackets that satisfy a generalized Jacobi identity.We then develop the machinery necessary to geometrically quantize n-plectic manifolds. In particular, just as a prequantized Symplectic manifold is equipped with a principal U(1)-bundle with connection, we show that a prequantized 2-plectic manifold is equipped with a U(1)-gerbe with 2-connection. A gerbe is a categorified sheaf, or stack, which generalizes the notion of a principal bundle. Furthermore, over any 2-plectic manifold there is a vector bundle equipped with extra structure called a Courant algebroid. This bundle is the 2-plectic analogue of the Atiyah algebroid over a prequantized Symplectic manifold. Its space of global sections also forms a Lie 2-algebra. We use this Lie 2-algebra to prequantize the Lie 2-algebra of Hamiltonian forms.Finally, we introduce the 2-plectic analogue of the Bohr-Sommerfeld variety associated to a real polarization, and use this to geometrically quantize 2-plectic manifolds. For Symplectic manifolds, the output from quantization is a Hilbert space of quantum states. Similarly, quantizing a 2-plectic manifold gives a category of quantum states. We consider a particular example in which the objects of this category can be identified with representations of the Lie group SU(2).
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Categorified Symplectic Geometry and the string Lie 2-algebra
Homology Homotopy and Applications, 2010Co-Authors: John C. Baez, Christopher L. RogersAbstract:MultiSymplectic Geometry is a generalization of Symplectic Geometry suitable for n-dimensional field theories, in which the nondegenerate 2-form of Symplectic Geometry is replaced by a nondegenerate (n + 1)-form. The case n = 2 is relevant to string theory: we call this '2-plectic Geometry.' Just as the Poisson bracket makes the smooth functions on a Symplectic manifold into a Lie algebra, the observables associated to a 2-plectic manifold form a 'Lie 2-algebra,' which is a categorified version of a Lie algebra. Any compact simple Lie group G has a canonical 2-plectic structure, so it is natural to wonder what Lie 2-algebra this example yields. This Lie 2-algebra is infinite-dimensional, but we show here that the sub-Lie-2-algebra of left-invariant observables is finite-dimensional, and isomorphic to the already known 'string Lie 2-algebra' associated to G. So, categorified Symplectic Geometry gives a geometric construction of the string Lie 2-algebra. © 2010, John C. Baez and Christopher L. Rogers.
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Categorified Symplectic Geometry and the String Lie 2-Algebra
arXiv: Mathematical Physics, 2009Co-Authors: John C. Baez, Christopher L. RogersAbstract:MultiSymplectic Geometry is a generalization of Symplectic Geometry suitable for n-dimensional field theories, in which the nondegenerate 2-form of Symplectic Geometry is replaced by a nondegenerate (n+1)-form. The case n = 2 is relevant to string theory: we call this 2-plectic Geometry. Just as the Poisson bracket makes the smooth functions on a Symplectic manifold into a Lie algebra, the observables associated to a 2-plectic manifold form a "Lie 2-algebra", which is a categorified version of a Lie algebra. Any compact simple Lie group G has a canonical 2-plectic structure, so it is natural to wonder what Lie 2-algebra this example yields. This Lie 2-algebra is infinite-dimensional, but we show here that the sub-Lie-2-algebra of left-invariant observables is finite-dimensional, and isomorphic to the already known "string Lie 2-algebra" associated to G. So, categorified Symplectic Geometry gives a geometric construction of the string Lie 2-algebra.
