A novel gappy technology, gappy autoencoder with proper orthogonal decomposition(Gappy POD-AE), is proposed for reconstructing physical fields from sparse data. High-dimensional data are reduced via proper orthogonal ...A novel gappy technology, gappy autoencoder with proper orthogonal decomposition(Gappy POD-AE), is proposed for reconstructing physical fields from sparse data. High-dimensional data are reduced via proper orthogonal decomposition(POD),and low-dimensional data are used to train an autoencoder(AE). By integrating the POD operator with the decoder, a nonlinear solution form is established and incorporated into a new maximum-a-posteriori(MAP)-based objective for online reconstruction.The numerical results on the two-dimensional(2D) Bhatnagar-Gross-Krook-Boltzmann(BGK-Boltzmann) equation, wave equation, shallow-water equation, and satellite data show that Gappy POD-AE achieves higher accuracy than gappy proper orthogonal decomposition(Gappy POD), especially for the data with slowly decaying singular values,and is more efficient in training than gappy autoencoder(Gappy AE). The MAP-based formulation and new gappy procedure further enhance the reconstruction accuracy.展开更多
Proper Orthogonal Decomposition （POD） provides a powerful modal transformation tool for stochastic dynamics. In this paper, coherency matrix-based proper orthogonal decomposition （CPOD） is presented as an innovati...Proper Orthogonal Decomposition （POD） provides a powerful modal transformation tool for stochastic dynamics. In this paper, coherency matrix-based proper orthogonal decomposition （CPOD） is presented as an innovative form of the POD based on cross power spectral density matrices. By introducing a discretizing scheme, the CPOD-based spectral representation method is obtained for use in stochastic simulation. Moreover, some criteria are proposed that allow the truncation order of CPOD to be conveniently determined. A numerical example to illustrate the application of the proposed method for the simulation of a wind velocity field is provided.展开更多
Time-resolved particle image velocimetry（TRPIV） experiments are performed to investigate the coherent structure＇s performance of riblets in a turbulent boundary layer（TBL） at a friction Reynolds number of 185. To...Time-resolved particle image velocimetry（TRPIV） experiments are performed to investigate the coherent structure＇s performance of riblets in a turbulent boundary layer（TBL） at a friction Reynolds number of 185. To visualize the energetic large-scale coherent structures（CSs） over a smooth surface and riblets, the proper orthogonal decomposition（POD） and finite-time Lyapunov exponent（FTLE） are used to identify the CSs in the TBL. Spatial-temporal correlation is implemented to obtain the characters and transport properties of typical CSs in the FTLE fields. The results demonstrate that the generic flow structures, such as hairpin-like vortices, are also observed in the boundary layer flow over the riblets, consistent with its smooth counterpart. Low-order POD modes are more sensitive to the riblets in comparison with the high-order ones,and the wall-normal movement of the most energy-containing structures are suppressed over riblets. The spatial correlation analysis of the FTLE fields indicates that the evolution process of the hairpin vortex over riblets are inhibited. An apparent decrease of the convection velocity over riblets is noted, which is believed to reduce the ejection/sweep motions associated with high shear stress from the viscous sublayer. These reductions exhibit inhibition of momentum transfer among the structures near the wall in the TBL flows.展开更多
Since the empirical mode decomposition （EMD） lacks strict orthogonality, the method of orthogonal empirical mode decomposition （OEMD） is innovationally proposed. The primary thought of this method is to obtain the...Since the empirical mode decomposition （EMD） lacks strict orthogonality, the method of orthogonal empirical mode decomposition （OEMD） is innovationally proposed. The primary thought of this method is to obtain the intrinsic mode function （IMF） and the residual function by auto-adaptive band-pass filtering. OEMD is proved to preserve strict orthogonality and completeness theoretically, and the orthogonal basis function of OEMD is generated, then an algorithm to implement OEMD fast, IMF binary searching algorithm is built based on the point that the analytical band-pass filtering preserves perfect band-pass feature in the frequency domain. The application into harmonic detection shows that OEMD successfully conquers mode aliasing, avoids the occurrence of false mode, and is featured by fast computing speed. Furthermore, it can achieve harmonic detection accurately combined with the least square method.展开更多
The proper orthogonal decomposition (POD) method for the instationary Navier-Stokes equations is considered. Several numerical approaches to evaluating the POD eigenfunctions are presented. The POD eigenfunctions are ...The proper orthogonal decomposition (POD) method for the instationary Navier-Stokes equations is considered. Several numerical approaches to evaluating the POD eigenfunctions are presented. The POD eigenfunctions are applied as a basis for a Galerkin projection of the instationary Navier-Stokes equations. And a low-dimensional ordinary differential models for fluid flows governed by the instationary Navier-Stokes equations are constructed. The numerical examples show that the method is feasible and efficient for optimal control of fluids.展开更多
The reduced-order model （ROM） for the two-dimensional supersonic cavity flow based on proper orthogonal decomposition （POD） and Galerkin projection is investigated. Presently, popular ROMs in cavity flows are base...The reduced-order model （ROM） for the two-dimensional supersonic cavity flow based on proper orthogonal decomposition （POD） and Galerkin projection is investigated. Presently, popular ROMs in cavity flows are based on an isentropic assumption, valid only for flows at low or moderate Mach numbers. A new ROM is constructed involving primitive variables of the fully compressible Navier-Stokes （N-S） equations, which is suitable for flows at high Mach numbers. Compared with the direct numerical simulation （DNS） results, the proposed model predicts flow dynamics （e.g., dominant frequency and amplitude） accurately for supersonic cavity flows, and is robust. The comparison between the present transient flow fields and those of the DNS shows that the proposed ROM can capture self-sustained oscillations of a shear layer. In addition, the present model reduction method can be easily extended to other supersonic flows.展开更多
A high robust approach for the additive spread spectrum audio watermarking scheme based on orthogonal decomposition of the host signal has been proposed.By analyzing traditional spread spectrum（SS）,the section of th...A high robust approach for the additive spread spectrum audio watermarking scheme based on orthogonal decomposition of the host signal has been proposed.By analyzing traditional spread spectrum（SS）,the section of the audio signal which is parallel to the direction of watermark signal acts as an interference source in decoder.The watermark is only embedded in the section which is perpendicular to watermark signal in the proposed scheme.In this way,the interference of host signal can be removed completely in decoder.Whether the watermarks have been embedded in the audio or not is researched and an optimal threshold in detector is given to achieve the minimum false alarm probability.The simulation results show that the proposed method can achieve high robustness against various attacks.展开更多
A three-dimensional incompressible annular jet is simulated by the large eddy simulation(LES)method at a Reynolds number Re=8500.The time-averaged velocity field shows an asymmetric wake behind the central bluff-body ...A three-dimensional incompressible annular jet is simulated by the large eddy simulation(LES)method at a Reynolds number Re=8500.The time-averaged velocity field shows an asymmetric wake behind the central bluff-body although the flow geometry is symmetric.The proper orthogonal decomposition(POD)analysis of the velocity fluctuation vectors is conducted to study the flow dynamics of the wake flow.The distribution of turbulent kinetic energy across the three-dimensional POD modes shows that the first four eigenmodes each capture more than 1%of the turbulent kinetic energy,and hence their impact on the wake dynamics is studied.The results demonstrate that the asymmetric mean flow in the near-field of the annular jet is related to the first two POD modes which correspond to a radial shift of the stagnation point.The modes 3 and 4 involve the stretching or squeezing effects of the recirculation region in the radial direction.In addition,the spatial structure of these four POD eigenmodes also shows the counter-rotating vortices in the streamwise direction downstream of the flow reversal region.展开更多
Based on mathematical orthogonality and mechanical equilibrium,a deformation energy decomposition method for classical isotropic square and cube elements is proposed by considering the physical parameters of materials...Based on mathematical orthogonality and mechanical equilibrium,a deformation energy decomposition method for classical isotropic square and cube elements is proposed by considering the physical parameters of materials.By aid of this method,the comprehensive deformation energy of planar discrete elastomers can be decomposed into five basic deformation energies,and the comprehensive deformation energy of spatial discrete elastomers can be decomposed into eighteen basic deformation energies.The quantification and visualization of structural deformation performance can be realized.According to the magnitude of different deformation energy in the same element,the decomposition diagram is drawn,which can visually display the area dominated by each basic deformation energy.The cloud diagram is drawn based on the distribution of specific deformation energy in different elements,which can be used to analyze the gradient change of deformation energy in the structure.Finally,the deformation properties of cantilever beam and four-sided consolidation plate are analyzed by deformation energy decomposition method.The correctness and superiority of this method are verified by comparing with the results of strain energy decomposition.展开更多
Proper orthogonal decomposition （POD） is an effective statistical technique for data reduction and feature extraction of the random field including the wind field. This paper introduces the theory of the POD and ill...Proper orthogonal decomposition （POD） is an effective statistical technique for data reduction and feature extraction of the random field including the wind field. This paper introduces the theory of the POD and illustrates engineering of structures. Using the POD technique, it is shown that wind pressure data can be accurately reconstructed with a limited number of modes using the wind pressure data from wind tunnel test. Comparing the reconstructed values by POD with the original measured values from the wind tunnel test both in the time and frequency domains, it is concluded that the proper orthogonal decomposition（POD） is an efficient and practical technique for deriving the random wind pressure field from limited known data as shown in the pitched roof example in this paper.展开更多
Let f ： Ω→Gr（n,H） be a holomorphic curve, where Ω is a bounded open simple connected domain on the complex plane C and Gr（n,H） the Grassmannian manifold. Denote by Ef the ＂pull back＂ bundle induced by f. We ...Let f ： Ω→Gr（n,H） be a holomorphic curve, where Ω is a bounded open simple connected domain on the complex plane C and Gr（n,H） the Grassmannian manifold. Denote by Ef the ＂pull back＂ bundle induced by f. We show the uniqueness of the orthogonal decomposition for those complex bundles. As a direct application, we give a complete description of the HIR decomposition of a Cowen- Douglas operator T ∈ Bn（Ω）. Moreover, we compute the maximal self-adjoint subalgebra of A＇（Ef） and A＇（T） respectively. Finally, we fix the masa of A＇（Ef） and .A＇ （T） which depends on the HIR decomposition of Ef or T respectively.展开更多
For square contingency tables with ordered categories, this article proposes new models, which are the extension of Tomizawa’s [1] diagonal exponent symmetry model. Also it gives the decomposition of proposed model, ...For square contingency tables with ordered categories, this article proposes new models, which are the extension of Tomizawa’s [1] diagonal exponent symmetry model. Also it gives the decomposition of proposed model, and shows the orthogonality of the test statistics for decomposed models. Examples are given and the simulation studies based on the bivariate normal distribution are also given.展开更多
The large storage requirement is a critical issue in cross-correlation imaging-condition based reverse time migration(RTM),because it requires the operation of the source and receiver wavefields at the same time.The b...The large storage requirement is a critical issue in cross-correlation imaging-condition based reverse time migration(RTM),because it requires the operation of the source and receiver wavefields at the same time.The boundary value method(BVM),based on the finite difference method(FDM),can be used to reconstruct the source wavefield in the reverse time propagation in the same way as the receiver wavefield,which can reduce the storage burden of the RTM data.Considering that the FDM cannot well handle models with discontinuous material properties and rough interfaces,we develop a source wavefield reconstruction strategy based on the finite element method(FEM),using proper orthogonal decomposition(POD)to enhance computational efficiency.In this method,we divide the whole time period into several segments,and construct the POD basis functions to get a reduced order model(ROM)for the source wavefield reconstruction in each segment.We show the corresponding quantitative analysis of the storage requirement of the POD-FEM.Numerical tests on the homogeneous model show the effectiveness of the proposed method,while the layered model and part of the Marmousi model tests indicate that the POD-FEM can keep an excellent balance between computational efficiency and memory usage compared with the full-stored method(FSM)and the BVM,and can be effectively applied in imaging.展开更多
Application of micro-resonator is limited by different types of surface inhomogeneity. The 1-th derivative of inhomogeneity (i.e. Δrˊ(φ)) affects the wave transport as well as the height of inhomogeneity (i.e. Δr...Application of micro-resonator is limited by different types of surface inhomogeneity. The 1-th derivative of inhomogeneity (i.e. Δrˊ(φ)) affects the wave transport as well as the height of inhomogeneity (i.e. Δrˊ(φ)). A method based on orthogonal decomposition is proposed to analysis both scattering mechanism respectively. Then surface roughness effect on Q-factor of micro-disk waveguide gallery mode (WGM) resonator is investigated with our method and the analysis fits well with FDTD simulation results.展开更多
The purpose of this study is to describe an economical approach to an existing adaptive localization technique and its implementation in the proper orthogonal decomposition-based ensemble four-dimensional variational ...The purpose of this study is to describe an economical approach to an existing adaptive localization technique and its implementation in the proper orthogonal decomposition-based ensemble four-dimensional variational assimilation method(PODEn4DVar). Owing to the applications of the sparse processing and EOF decomposition techniques, the computational costs of this proposed sparse flow-adaptive moderation(SFAM) localization scheme are significantly reduced. The effectiveness of PODEn4 DVar with SFAM localization is demonstrated by using the Lorenz-96 model in comparison with the Smoothed ENsemble Correlations Raised to a Power(SENCORP) and static localization schemes, separately. The performance of PODEn4 DVar with SFAM localization shows a moderate improvement over the schemes with SENCORP and static localization, with low computational costs under the imperfect model.展开更多
Over the recent years there has been an increased trend in the use of Reduced Order Models （ROM） for modeling the coupled aeroelastic system. Of all the ROM models, the Proper Orthogonal Decomposition Method （POD）...Over the recent years there has been an increased trend in the use of Reduced Order Models （ROM） for modeling the coupled aeroelastic system. Of all the ROM models, the Proper Orthogonal Decomposition Method （POD） has been the most widely used, reason being the relative simplicity of implementation and the physical insight that it offers towards the physical problem. In this paper we begin by briefly recalling the recent work using POD for the computational aeroelasticity followed by the mathematical formulation. Mathematical formulation is important as it provides understanding of how POD method works. Implementation issues related to the POD method are presented next. Since POD is an empirical technique therefore, it is marred by the robustness issues as is the case with all the ROMs. In the end the variations of POD method, developed over the years are presented along with the most recent trend of using hybrid ROM.展开更多
This paper demonstrates that the spatial distribution of the ionospheric TEC over the Indian region can be reconstructed with appreciable accuracy using minimal numbers of empirical orthogonal functions as a basis.The...This paper demonstrates that the spatial distribution of the ionospheric TEC over the Indian region can be reconstructed with appreciable accuracy using minimal numbers of empirical orthogonal functions as a basis.These basis functions were derived using the Singular Value Decomposition of a matrix composed of pragmatic vertical Total Electron Content(VTEC)values collected across varied ionospheric conditions and measured over the region of interest.The reconstruction was achieved by linearly combining the appropriately chosen significant bases with corresponding weight factors.The reconstruction accuracy of the algorithm was found to be better than 4 TECU(TECU=1016electrons/m2)for more than 99.9%of the time when tested over the complete year of 2016 with only eight basis vectors.The containment factor,defined here,indicates the goodness of the chosen bases in representing the arbitrary VTEC distributions and is found to remain typically high,aiding in improved algorithm performance.The performance,however,was found to be sensitive to the seasons and geomagnetic conditions.Deteriorated performance was observed when tested for the St.Patrick's Day storm data.The deterioration was attributed to the structural alteration of the ionospheric plasma density and the presence of atypical modes during the storm.The results ascertain the prospect of a faithful representation of the spatial distribution of the ionospheric VTEC using limited parametric variables,which may find utility in navigation,radar,and various other applications.展开更多
A direct linear discriminant analysis algorithm based on economic singular value decomposition （DLDA/ESVD） is proposed to address the computationally complex problem of the conventional DLDA algorithm, which directl...A direct linear discriminant analysis algorithm based on economic singular value decomposition （DLDA/ESVD） is proposed to address the computationally complex problem of the conventional DLDA algorithm, which directly uses ESVD to reduce dimension and extract eigenvectors corresponding to nonzero eigenvalues. Then a DLDA algorithm based on column pivoting orthogonal triangular （QR） decomposition and ESVD （DLDA/QR-ESVD） is proposed to improve the performance of the DLDA/ESVD algorithm by processing a high-dimensional low rank matrix, which uses column pivoting QR decomposition to reduce dimension and ESVD to extract eigenvectors corresponding to nonzero eigenvalues. The experimental results on ORL, FERET and YALE face databases show that the proposed two algorithms can achieve almost the same performance and outperform the conventional DLDA algorithm in terms of computational complexity and training time. In addition, the experimental results on random data matrices show that the DLDA/QR-ESVD algorithm achieves better performance than the DLDA/ESVD algorithm by processing high-dimensional low rank matrices.展开更多
The invertibility of combinations of two orthogonal projectors aP ＋ bQ - cPQ - dQP is researched by using the CSdecomposition of matrices and properties of orthogonal projectors. The Moore-enrose inverse of the combi...The invertibility of combinations of two orthogonal projectors aP ＋ bQ - cPQ - dQP is researched by using the CSdecomposition of matrices and properties of orthogonal projectors. The Moore-enrose inverse of the combinations is presented under some special conditions.展开更多
Based on feature compression with orthogonal locality preserving projection(OLPP),a novel fault diagnosis model is proposed in this paper to achieve automation and high-precision of fault diagnosis of rotating machine...Based on feature compression with orthogonal locality preserving projection(OLPP),a novel fault diagnosis model is proposed in this paper to achieve automation and high-precision of fault diagnosis of rotating machinery.With this model,the original vibration signals of training and test samples are first decomposed through the empirical mode decomposition(EMD),and Shannon entropy is constructed to achieve high-dimensional eigenvectors.In order to replace the traditional feature extraction way which does the selection manually,OLPP is introduced to automatically compress the high-dimensional eigenvectors of training and test samples into the low-dimensional eigenvectors which have better discrimination.After that,the low-dimensional eigenvectors of training samples are input into Morlet wavelet support vector machine(MWSVM)and a trained MWSVM is obtained.Finally,the low-dimensional eigenvectors of test samples are input into the trained MWSVM to carry out fault diagnosis.To evaluate our proposed model,the experiment of fault diagnosis of deep groove ball bearings is made,and the experiment results indicate that the recognition accuracy rate of the proposed diagnosis model for outer race crack、inner race crack and ball crack is more than 90%.Compared to the existing approaches,the proposed diagnosis model combines the strengths of EMD in fault feature extraction,OLPP in feature compression and MWSVM in pattern recognition,and realizes the automation and high-precision of fault diagnosis.展开更多
基金supported by the National Natural Science Foundation of China(No.12472197)。
文摘A novel gappy technology, gappy autoencoder with proper orthogonal decomposition(Gappy POD-AE), is proposed for reconstructing physical fields from sparse data. High-dimensional data are reduced via proper orthogonal decomposition(POD),and low-dimensional data are used to train an autoencoder(AE). By integrating the POD operator with the decoder, a nonlinear solution form is established and incorporated into a new maximum-a-posteriori(MAP)-based objective for online reconstruction.The numerical results on the two-dimensional(2D) Bhatnagar-Gross-Krook-Boltzmann(BGK-Boltzmann) equation, wave equation, shallow-water equation, and satellite data show that Gappy POD-AE achieves higher accuracy than gappy proper orthogonal decomposition(Gappy POD), especially for the data with slowly decaying singular values,and is more efficient in training than gappy autoencoder(Gappy AE). The MAP-based formulation and new gappy procedure further enhance the reconstruction accuracy.
基金Research Fund for Communications in Western China Under Grant No. 200431800028
文摘Proper Orthogonal Decomposition （POD） provides a powerful modal transformation tool for stochastic dynamics. In this paper, coherency matrix-based proper orthogonal decomposition （CPOD） is presented as an innovative form of the POD based on cross power spectral density matrices. By introducing a discretizing scheme, the CPOD-based spectral representation method is obtained for use in stochastic simulation. Moreover, some criteria are proposed that allow the truncation order of CPOD to be conveniently determined. A numerical example to illustrate the application of the proposed method for the simulation of a wind velocity field is provided.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11332006,11732010,11572221,and 11502066)the Natural Science Foundation of Tianjin City(Grant No.18JCQNJC5100)
文摘Time-resolved particle image velocimetry（TRPIV） experiments are performed to investigate the coherent structure＇s performance of riblets in a turbulent boundary layer（TBL） at a friction Reynolds number of 185. To visualize the energetic large-scale coherent structures（CSs） over a smooth surface and riblets, the proper orthogonal decomposition（POD） and finite-time Lyapunov exponent（FTLE） are used to identify the CSs in the TBL. Spatial-temporal correlation is implemented to obtain the characters and transport properties of typical CSs in the FTLE fields. The results demonstrate that the generic flow structures, such as hairpin-like vortices, are also observed in the boundary layer flow over the riblets, consistent with its smooth counterpart. Low-order POD modes are more sensitive to the riblets in comparison with the high-order ones,and the wall-normal movement of the most energy-containing structures are suppressed over riblets. The spatial correlation analysis of the FTLE fields indicates that the evolution process of the hairpin vortex over riblets are inhibited. An apparent decrease of the convection velocity over riblets is noted, which is believed to reduce the ejection/sweep motions associated with high shear stress from the viscous sublayer. These reductions exhibit inhibition of momentum transfer among the structures near the wall in the TBL flows.
基金National Natural Science Foundation of China(No.50575233)
文摘Since the empirical mode decomposition （EMD） lacks strict orthogonality, the method of orthogonal empirical mode decomposition （OEMD） is innovationally proposed. The primary thought of this method is to obtain the intrinsic mode function （IMF） and the residual function by auto-adaptive band-pass filtering. OEMD is proved to preserve strict orthogonality and completeness theoretically, and the orthogonal basis function of OEMD is generated, then an algorithm to implement OEMD fast, IMF binary searching algorithm is built based on the point that the analytical band-pass filtering preserves perfect band-pass feature in the frequency domain. The application into harmonic detection shows that OEMD successfully conquers mode aliasing, avoids the occurrence of false mode, and is featured by fast computing speed. Furthermore, it can achieve harmonic detection accurately combined with the least square method.
基金National Natural Science Foundation of China (No.10671153)
文摘The proper orthogonal decomposition (POD) method for the instationary Navier-Stokes equations is considered. Several numerical approaches to evaluating the POD eigenfunctions are presented. The POD eigenfunctions are applied as a basis for a Galerkin projection of the instationary Navier-Stokes equations. And a low-dimensional ordinary differential models for fluid flows governed by the instationary Navier-Stokes equations are constructed. The numerical examples show that the method is feasible and efficient for optimal control of fluids.
基金Project supported by the National Natural Science Foundation of China(Nos.11232011,11402262,11572314,and 11621202)
文摘The reduced-order model （ROM） for the two-dimensional supersonic cavity flow based on proper orthogonal decomposition （POD） and Galerkin projection is investigated. Presently, popular ROMs in cavity flows are based on an isentropic assumption, valid only for flows at low or moderate Mach numbers. A new ROM is constructed involving primitive variables of the fully compressible Navier-Stokes （N-S） equations, which is suitable for flows at high Mach numbers. Compared with the direct numerical simulation （DNS） results, the proposed model predicts flow dynamics （e.g., dominant frequency and amplitude） accurately for supersonic cavity flows, and is robust. The comparison between the present transient flow fields and those of the DNS shows that the proposed ROM can capture self-sustained oscillations of a shear layer. In addition, the present model reduction method can be easily extended to other supersonic flows.
基金Supported by the National Natural Science Foundation of China(61471271)
文摘A high robust approach for the additive spread spectrum audio watermarking scheme based on orthogonal decomposition of the host signal has been proposed.By analyzing traditional spread spectrum（SS）,the section of the audio signal which is parallel to the direction of watermark signal acts as an interference source in decoder.The watermark is only embedded in the section which is perpendicular to watermark signal in the proposed scheme.In this way,the interference of host signal can be removed completely in decoder.Whether the watermarks have been embedded in the audio or not is researched and an optimal threshold in detector is given to achieve the minimum false alarm probability.The simulation results show that the proposed method can achieve high robustness against various attacks.
文摘A three-dimensional incompressible annular jet is simulated by the large eddy simulation(LES)method at a Reynolds number Re=8500.The time-averaged velocity field shows an asymmetric wake behind the central bluff-body although the flow geometry is symmetric.The proper orthogonal decomposition(POD)analysis of the velocity fluctuation vectors is conducted to study the flow dynamics of the wake flow.The distribution of turbulent kinetic energy across the three-dimensional POD modes shows that the first four eigenmodes each capture more than 1%of the turbulent kinetic energy,and hence their impact on the wake dynamics is studied.The results demonstrate that the asymmetric mean flow in the near-field of the annular jet is related to the first two POD modes which correspond to a radial shift of the stagnation point.The modes 3 and 4 involve the stretching or squeezing effects of the recirculation region in the radial direction.In addition,the spatial structure of these four POD eigenmodes also shows the counter-rotating vortices in the streamwise direction downstream of the flow reversal region.
基金supported by the National Natural Science Foundation of China(Grant Nos.52208322 and 51878621)the Postdoctoral Science Foundation of China(Grant No.2022M712905)the Key Research Projects of Henan Higher Education Institutions(Grant No.22A560005).
文摘Based on mathematical orthogonality and mechanical equilibrium,a deformation energy decomposition method for classical isotropic square and cube elements is proposed by considering the physical parameters of materials.By aid of this method,the comprehensive deformation energy of planar discrete elastomers can be decomposed into five basic deformation energies,and the comprehensive deformation energy of spatial discrete elastomers can be decomposed into eighteen basic deformation energies.The quantification and visualization of structural deformation performance can be realized.According to the magnitude of different deformation energy in the same element,the decomposition diagram is drawn,which can visually display the area dominated by each basic deformation energy.The cloud diagram is drawn based on the distribution of specific deformation energy in different elements,which can be used to analyze the gradient change of deformation energy in the structure.Finally,the deformation properties of cantilever beam and four-sided consolidation plate are analyzed by deformation energy decomposition method.The correctness and superiority of this method are verified by comparing with the results of strain energy decomposition.
基金Acknowledgements The authors are grateful for the support of this research by the Committee of National Science Foundation of China （50908077） and Foundation of Heilongjiang Province Educational Committee （11551368）.
文摘Proper orthogonal decomposition （POD） is an effective statistical technique for data reduction and feature extraction of the random field including the wind field. This paper introduces the theory of the POD and illustrates engineering of structures. Using the POD technique, it is shown that wind pressure data can be accurately reconstructed with a limited number of modes using the wind pressure data from wind tunnel test. Comparing the reconstructed values by POD with the original measured values from the wind tunnel test both in the time and frequency domains, it is concluded that the proper orthogonal decomposition（POD） is an efficient and practical technique for deriving the random wind pressure field from limited known data as shown in the pitched roof example in this paper.
文摘Let f ： Ω→Gr（n,H） be a holomorphic curve, where Ω is a bounded open simple connected domain on the complex plane C and Gr（n,H） the Grassmannian manifold. Denote by Ef the ＂pull back＂ bundle induced by f. We show the uniqueness of the orthogonal decomposition for those complex bundles. As a direct application, we give a complete description of the HIR decomposition of a Cowen- Douglas operator T ∈ Bn（Ω）. Moreover, we compute the maximal self-adjoint subalgebra of A＇（Ef） and A＇（T） respectively. Finally, we fix the masa of A＇（Ef） and .A＇ （T） which depends on the HIR decomposition of Ef or T respectively.
文摘For square contingency tables with ordered categories, this article proposes new models, which are the extension of Tomizawa’s [1] diagonal exponent symmetry model. Also it gives the decomposition of proposed model, and shows the orthogonality of the test statistics for decomposed models. Examples are given and the simulation studies based on the bivariate normal distribution are also given.
基金This work was supported by Natural Science Basic Research Program of Shaanxi(Program No.2023-JC-YB-269)the National Natural Science Foundation of China(Grant No.41974122).
文摘The large storage requirement is a critical issue in cross-correlation imaging-condition based reverse time migration(RTM),because it requires the operation of the source and receiver wavefields at the same time.The boundary value method(BVM),based on the finite difference method(FDM),can be used to reconstruct the source wavefield in the reverse time propagation in the same way as the receiver wavefield,which can reduce the storage burden of the RTM data.Considering that the FDM cannot well handle models with discontinuous material properties and rough interfaces,we develop a source wavefield reconstruction strategy based on the finite element method(FEM),using proper orthogonal decomposition(POD)to enhance computational efficiency.In this method,we divide the whole time period into several segments,and construct the POD basis functions to get a reduced order model(ROM)for the source wavefield reconstruction in each segment.We show the corresponding quantitative analysis of the storage requirement of the POD-FEM.Numerical tests on the homogeneous model show the effectiveness of the proposed method,while the layered model and part of the Marmousi model tests indicate that the POD-FEM can keep an excellent balance between computational efficiency and memory usage compared with the full-stored method(FSM)and the BVM,and can be effectively applied in imaging.
文摘Application of micro-resonator is limited by different types of surface inhomogeneity. The 1-th derivative of inhomogeneity (i.e. Δrˊ(φ)) affects the wave transport as well as the height of inhomogeneity (i.e. Δrˊ(φ)). A method based on orthogonal decomposition is proposed to analysis both scattering mechanism respectively. Then surface roughness effect on Q-factor of micro-disk waveguide gallery mode (WGM) resonator is investigated with our method and the analysis fits well with FDTD simulation results.
基金partially supported by the National High Technology Research and Development Program of China (Grant No. 2013AA122002)the Knowledge Innovation Program of the Chinese Academy of Sciences (Grant No. KZCX2EW-QN207)the Special Fund for Meteorological Scientific Research in the Public Interest (Grant No. GYHY201306045)
文摘The purpose of this study is to describe an economical approach to an existing adaptive localization technique and its implementation in the proper orthogonal decomposition-based ensemble four-dimensional variational assimilation method(PODEn4DVar). Owing to the applications of the sparse processing and EOF decomposition techniques, the computational costs of this proposed sparse flow-adaptive moderation(SFAM) localization scheme are significantly reduced. The effectiveness of PODEn4 DVar with SFAM localization is demonstrated by using the Lorenz-96 model in comparison with the Smoothed ENsemble Correlations Raised to a Power(SENCORP) and static localization schemes, separately. The performance of PODEn4 DVar with SFAM localization shows a moderate improvement over the schemes with SENCORP and static localization, with low computational costs under the imperfect model.
文摘Over the recent years there has been an increased trend in the use of Reduced Order Models （ROM） for modeling the coupled aeroelastic system. Of all the ROM models, the Proper Orthogonal Decomposition Method （POD） has been the most widely used, reason being the relative simplicity of implementation and the physical insight that it offers towards the physical problem. In this paper we begin by briefly recalling the recent work using POD for the computational aeroelasticity followed by the mathematical formulation. Mathematical formulation is important as it provides understanding of how POD method works. Implementation issues related to the POD method are presented next. Since POD is an empirical technique therefore, it is marred by the robustness issues as is the case with all the ROMs. In the end the variations of POD method, developed over the years are presented along with the most recent trend of using hybrid ROM.
文摘This paper demonstrates that the spatial distribution of the ionospheric TEC over the Indian region can be reconstructed with appreciable accuracy using minimal numbers of empirical orthogonal functions as a basis.These basis functions were derived using the Singular Value Decomposition of a matrix composed of pragmatic vertical Total Electron Content(VTEC)values collected across varied ionospheric conditions and measured over the region of interest.The reconstruction was achieved by linearly combining the appropriately chosen significant bases with corresponding weight factors.The reconstruction accuracy of the algorithm was found to be better than 4 TECU(TECU=1016electrons/m2)for more than 99.9%of the time when tested over the complete year of 2016 with only eight basis vectors.The containment factor,defined here,indicates the goodness of the chosen bases in representing the arbitrary VTEC distributions and is found to remain typically high,aiding in improved algorithm performance.The performance,however,was found to be sensitive to the seasons and geomagnetic conditions.Deteriorated performance was observed when tested for the St.Patrick's Day storm data.The deterioration was attributed to the structural alteration of the ionospheric plasma density and the presence of atypical modes during the storm.The results ascertain the prospect of a faithful representation of the spatial distribution of the ionospheric VTEC using limited parametric variables,which may find utility in navigation,radar,and various other applications.
基金The National Natural Science Foundation of China (No.61374194)
文摘A direct linear discriminant analysis algorithm based on economic singular value decomposition （DLDA/ESVD） is proposed to address the computationally complex problem of the conventional DLDA algorithm, which directly uses ESVD to reduce dimension and extract eigenvectors corresponding to nonzero eigenvalues. Then a DLDA algorithm based on column pivoting orthogonal triangular （QR） decomposition and ESVD （DLDA/QR-ESVD） is proposed to improve the performance of the DLDA/ESVD algorithm by processing a high-dimensional low rank matrix, which uses column pivoting QR decomposition to reduce dimension and ESVD to extract eigenvectors corresponding to nonzero eigenvalues. The experimental results on ORL, FERET and YALE face databases show that the proposed two algorithms can achieve almost the same performance and outperform the conventional DLDA algorithm in terms of computational complexity and training time. In addition, the experimental results on random data matrices show that the DLDA/QR-ESVD algorithm achieves better performance than the DLDA/ESVD algorithm by processing high-dimensional low rank matrices.
基金Supported by the Hubei Normal University Research Grant (2008D54)
文摘The invertibility of combinations of two orthogonal projectors aP ＋ bQ - cPQ - dQP is researched by using the CSdecomposition of matrices and properties of orthogonal projectors. The Moore-enrose inverse of the combinations is presented under some special conditions.
基金supported by Fundamental Research Funds for the Central Universities of China(Grant No.CDJZR10118801)
文摘Based on feature compression with orthogonal locality preserving projection(OLPP),a novel fault diagnosis model is proposed in this paper to achieve automation and high-precision of fault diagnosis of rotating machinery.With this model,the original vibration signals of training and test samples are first decomposed through the empirical mode decomposition(EMD),and Shannon entropy is constructed to achieve high-dimensional eigenvectors.In order to replace the traditional feature extraction way which does the selection manually,OLPP is introduced to automatically compress the high-dimensional eigenvectors of training and test samples into the low-dimensional eigenvectors which have better discrimination.After that,the low-dimensional eigenvectors of training samples are input into Morlet wavelet support vector machine(MWSVM)and a trained MWSVM is obtained.Finally,the low-dimensional eigenvectors of test samples are input into the trained MWSVM to carry out fault diagnosis.To evaluate our proposed model,the experiment of fault diagnosis of deep groove ball bearings is made,and the experiment results indicate that the recognition accuracy rate of the proposed diagnosis model for outer race crack、inner race crack and ball crack is more than 90%.Compared to the existing approaches,the proposed diagnosis model combines the strengths of EMD in fault feature extraction,OLPP in feature compression and MWSVM in pattern recognition,and realizes the automation and high-precision of fault diagnosis.
