How to extract optimal composite attributes from a variety of conventional seismic attributes to detect reservoir features is a reservoir predication key,which is usually solved by reducing dimensionality.Principle co...How to extract optimal composite attributes from a variety of conventional seismic attributes to detect reservoir features is a reservoir predication key,which is usually solved by reducing dimensionality.Principle component analysis（PCA） is the most widely-used linear dimensionality reduction method at present.However,the relationships between seismic attributes and reservoir features are non-linear,so seismic attribute dimensionality reduction based on linear transforms can＇t solve non-linear problems well,reducing reservoir prediction precision.As a new non-linear learning method,manifold learning supplies a new method for seismic attribute analysis.It can discover the intrinsic features and rules hidden in the data by computing low-dimensional,neighborhood-preserving embeddings of high-dimensional inputs.In this paper,we try to extract seismic attributes using locally linear embedding（LLE）,realizing inter-horizon attributes dimensionality reduction of 3D seismic data first and discuss the optimization of its key parameters.Combining model analysis and case studies,we compare the dimensionality reduction and clustering effects of LLE and PCA,both of which indicate that LLE can retain the intrinsic structure of the inputs.The composite attributes and clustering results based on LLE better characterize the distribution of sedimentary facies,reservoir,and even reservoir fluids.展开更多
Rendezvous in circular or near circular orbits has been investigated in great detail, while rendezvous in arbitrary eccentricity elliptical orbits is not sufficiently explored. Among the various optimization methods p...Rendezvous in circular or near circular orbits has been investigated in great detail, while rendezvous in arbitrary eccentricity elliptical orbits is not sufficiently explored. Among the various optimization methods proposed for fuel optimal orbital rendezvous, Lawden＇s primer vector theory is favored by many researchers with its clear physical concept and simplicity in solu- tion. Prussing has applied the primer vector optimization theory to minimum-fuel, multiple-impulse, time-fixed orbital ren- dezvous in a near circular orbit and achieved great success. Extending Prussing＇s work, this paper will employ the primer vec- tor theory to study trajectory optimization problems of arbitrary eccentricity elliptical orbit rendezvous. Based on linearized equations of relative motion on elliptical reference orbit （referred to as T-H equations）, the primer vector theory is used to deal with time-fixed multiple-impulse optimal rendezvous between two coplanar, coaxial elliptical orbits with arbitrary large ec- centricity. A parameter adjustment method is developed for the prime vector to satisfy the Lawden＇s necessary condition for the optimal solution. Finally, the optimal multiple-impulse rendezvous solution including the time, direction and magnitudes of the impulse is obtained by solving the two-point boundary value problem. The rendezvous error of the linearized equation is also analyzed. The simulation results confirmed the analyzed results that the rendezvous error is small for the small eccentric- ity case and is large for the higher eccentricity. For better rendezvous accuracy of high eccentricity orbits, a combined method of multiplier penalty function with the simplex search method is used for local optimization. The simplex search method is sensitive to the initial values of optimization variables, but the simulation results show that initial values with the primer vector theory, and the local optimization algorithm can improve the rendezvous accuracy effectively with fast convergence, because the optimal results obtained by the primer vector theory are already very close to the actual optimal solution.展开更多
The locally optimal block preconditioned 4-d conjugate gradient method(LOBP4dC G) for the linear response eigenvalue problem was proposed by Bai and Li(2013) and later was extended to the generalized linear response e...The locally optimal block preconditioned 4-d conjugate gradient method(LOBP4dC G) for the linear response eigenvalue problem was proposed by Bai and Li(2013) and later was extended to the generalized linear response eigenvalue problem by Bai and Li(2014). We put forward two improvements to the method: A shifting deflation technique and an idea of extending the search subspace. The deflation technique is able to deflate away converged eigenpairs from future computation, and the idea of extending the search subspace increases convergence rate per iterative step. The resulting algorithm is called the extended LOBP4 dC G(ELOBP4dC G).Numerical results of the ELOBP4 dC G strongly demonstrate the capability of deflation technique and effectiveness the search space extension for solving linear response eigenvalue problems arising from linear response analysis of two molecule systems.展开更多
基金National Key Science & Technology Special Projects(Grant No.2008ZX05000-004)CNPC Projects(Grant No.2008E-0610-10).
文摘How to extract optimal composite attributes from a variety of conventional seismic attributes to detect reservoir features is a reservoir predication key,which is usually solved by reducing dimensionality.Principle component analysis（PCA） is the most widely-used linear dimensionality reduction method at present.However,the relationships between seismic attributes and reservoir features are non-linear,so seismic attribute dimensionality reduction based on linear transforms can＇t solve non-linear problems well,reducing reservoir prediction precision.As a new non-linear learning method,manifold learning supplies a new method for seismic attribute analysis.It can discover the intrinsic features and rules hidden in the data by computing low-dimensional,neighborhood-preserving embeddings of high-dimensional inputs.In this paper,we try to extract seismic attributes using locally linear embedding（LLE）,realizing inter-horizon attributes dimensionality reduction of 3D seismic data first and discuss the optimization of its key parameters.Combining model analysis and case studies,we compare the dimensionality reduction and clustering effects of LLE and PCA,both of which indicate that LLE can retain the intrinsic structure of the inputs.The composite attributes and clustering results based on LLE better characterize the distribution of sedimentary facies,reservoir,and even reservoir fluids.
基金supported by the National Natural Science Foundation of China(Grant Nos. 10832004 and 11072122)
文摘Rendezvous in circular or near circular orbits has been investigated in great detail, while rendezvous in arbitrary eccentricity elliptical orbits is not sufficiently explored. Among the various optimization methods proposed for fuel optimal orbital rendezvous, Lawden＇s primer vector theory is favored by many researchers with its clear physical concept and simplicity in solu- tion. Prussing has applied the primer vector optimization theory to minimum-fuel, multiple-impulse, time-fixed orbital ren- dezvous in a near circular orbit and achieved great success. Extending Prussing＇s work, this paper will employ the primer vec- tor theory to study trajectory optimization problems of arbitrary eccentricity elliptical orbit rendezvous. Based on linearized equations of relative motion on elliptical reference orbit （referred to as T-H equations）, the primer vector theory is used to deal with time-fixed multiple-impulse optimal rendezvous between two coplanar, coaxial elliptical orbits with arbitrary large ec- centricity. A parameter adjustment method is developed for the prime vector to satisfy the Lawden＇s necessary condition for the optimal solution. Finally, the optimal multiple-impulse rendezvous solution including the time, direction and magnitudes of the impulse is obtained by solving the two-point boundary value problem. The rendezvous error of the linearized equation is also analyzed. The simulation results confirmed the analyzed results that the rendezvous error is small for the small eccentric- ity case and is large for the higher eccentricity. For better rendezvous accuracy of high eccentricity orbits, a combined method of multiplier penalty function with the simplex search method is used for local optimization. The simplex search method is sensitive to the initial values of optimization variables, but the simulation results show that initial values with the primer vector theory, and the local optimization algorithm can improve the rendezvous accuracy effectively with fast convergence, because the optimal results obtained by the primer vector theory are already very close to the actual optimal solution.
基金supported by National Science Foundation of USA(Grant Nos.DMS1522697,CCF-1527091,DMS-1317330 and CCF-1527091)National Natural Science Foundation of China(Grant No.11428104)
文摘The locally optimal block preconditioned 4-d conjugate gradient method(LOBP4dC G) for the linear response eigenvalue problem was proposed by Bai and Li(2013) and later was extended to the generalized linear response eigenvalue problem by Bai and Li(2014). We put forward two improvements to the method: A shifting deflation technique and an idea of extending the search subspace. The deflation technique is able to deflate away converged eigenpairs from future computation, and the idea of extending the search subspace increases convergence rate per iterative step. The resulting algorithm is called the extended LOBP4 dC G(ELOBP4dC G).Numerical results of the ELOBP4 dC G strongly demonstrate the capability of deflation technique and effectiveness the search space extension for solving linear response eigenvalue problems arising from linear response analysis of two molecule systems.
