Four-dimensional variational data assimilation （4DVar） is one of the most promising methods to provide optimal analysis for numerical weather prediction （NWP）. Five national NWP centers in the world have successfu...Four-dimensional variational data assimilation （4DVar） is one of the most promising methods to provide optimal analysis for numerical weather prediction （NWP）. Five national NWP centers in the world have successfully applied 4DVar methods in their global NWPs, thanks to the increment method and adjoint technique. However, the application of 4DVar is still limited by the computer resources available at many NWP centers and research institutes. It is essential, therefore, to further reduce the computational cost of 4DVar. Here, an economical approach to implement 4DVar is proposed, using the technique of dimension- reduced projection （DRP）, which is called ＂DRP-4DVar.＂ The proposed approach is based on dimension reduction using an ensemble of historical samples to define a subspace. It directly obtains an optimal solution in the reduced space by fitting observations with historical time series generated by the model to form consistent forecast states, and therefore does not require implementation of the adjoint of tangent linear approximation. To evaluate the performance of the DRP-4DVar on assimilating different types of mesoscale observations, some observing system simulation experiments are conducted using MM5 and a comparison is made between adjoint-based 4DVar and DRP-4DVar using a 6-hour assimilation window.展开更多
We provide an introduction to the use of the spectral-elementmethod (SEM)in seismology. Following a brief review of the basic equations that govern seismicwave propagation, we discuss in some detail how these equation...We provide an introduction to the use of the spectral-elementmethod (SEM)in seismology. Following a brief review of the basic equations that govern seismicwave propagation, we discuss in some detail how these equations may be solved numericallybased upon the SEM to address the forward problem in seismology. Examplesof synthetic seismograms calculated based upon the SEM are compared to datarecorded by the Global Seismographic Network. Finally, we discuss the challenge ofusing the remaining differences between the data and the synthetic seismograms toconstrain better Earth models and source descriptions. This leads naturally to adjointmethods, which provide a practical approach to this formidable computational challengeand enables seismologists to tackle the inverse problem.展开更多
In order to obtain an accurate tide description in the China Seas, the 2-dimensional nonlinear numerical Princeton Ocean Model （POM） is employed to incorporate in situ tidal measurements both from tide gauges and TO...In order to obtain an accurate tide description in the China Seas, the 2-dimensional nonlinear numerical Princeton Ocean Model （POM） is employed to incorporate in situ tidal measurements both from tide gauges and TOPEX/POSEIDON （T/P） derived datasets by means of the variational adjoint approach in such a way that unknown internal model parameters, bottom topography, friction coefficients and open boundary conditions, for example, are adjusted during the process. The numerical model is used as a forward model. After the along-track T/P data are processed, two classical methods, i.e. harmonic and response analysis, are implemented to estimate the tide from such datasets with a domain covering the model area extending from 0° to 41°N in latitude and from 99°E to 142°E in longitude. And the results of these two methods are compared and interpreted. The numerical simulation is performed for 16 major constituents. In the data assimilation experiments, three types of unknown parameters （water depth, bottom friction and tidal open boundary conditions in the model equations） are chosen as control variables. Among the various types of data assimilation experiments, the calibration of water depth brings the most promising results. By comparing the results with selected tide gauge data, the average absolute errors are decreased from 7.9 cm to 6.8 cm for amplitude and from 13.0° to 9.0° for phase with respect to the semidiurnal tide M2 constituent, which is the largest tidal constituent in the model area. After the data assimilation experiment is performed, the comparison between model results and tide gauge observation for water levels shows that the RMS errors decrease by 9 cm for a total of 14 stations, mostly selected along the coast of China's Mainland, when a one-month period is considered, and the correlation coefficients improve for most tidal stations among these stations.展开更多
A soliton hierarchy of multicomponent AKNS equations is generated from an arbitraryorder matrix spectral problem, along with its bi-Hamiltonian formulation. Adjoint symmetry constraints are presented to manipulate bi...A soliton hierarchy of multicomponent AKNS equations is generated from an arbitraryorder matrix spectral problem, along with its bi-Hamiltonian formulation. Adjoint symmetry constraints are presented to manipulate binary nonlinearization for the associated arbitrary order matrix spectral problem. The resulting spatial and temporal constrained flows are shown to provide integrable decompositions of the multicomponent AKNS equations.展开更多
Let Sn be the star with n vertices, and let G be any connected graph with p vertices. We denote by Eτp＋（r-1）^G（i） the graph obtained from Sr and rG by coinciding the i-th vertex of G with the vertex of degree r ...Let Sn be the star with n vertices, and let G be any connected graph with p vertices. We denote by Eτp＋（r-1）^G（i） the graph obtained from Sr and rG by coinciding the i-th vertex of G with the vertex of degree r - 1 of S,, while the i-th vertex of each component of （r - 1）G be adjacented to r - 1 vertices of degree 1 of St, respectively. By applying the properties of adjoint polynomials, We prove that factorization theorem of adjoint polynomials of kinds of graphs Eτp＋（r-1）^G（i）∪（r - 1）K1 （1 ≤i≤p）. Furthermore, we obtain structure characteristics of chromatically equivalent graphs of their complements.展开更多
This paper is devoted to studying the recollement of the categories of finitely generated modules over finite dimensional algebras. We prove that for algebras A, B and C, if A-mod admits a recollement relative to B-mo...This paper is devoted to studying the recollement of the categories of finitely generated modules over finite dimensional algebras. We prove that for algebras A, B and C, if A-mod admits a recollement relative to B-mod and C-mod, then A[R]-mod admits a recollement relative to B[S]-mod and C-mod, where A[R]and B[S]are the one-point extensions of A by R and of B by S.展开更多
A high-efficiency inverse design of"digital"subwavelength nanophotonic devices using the adjoint method is proposed.We design a single-mode 3dB power divider and a dual-mode demultiplexer to demonstrate the ...A high-efficiency inverse design of"digital"subwavelength nanophotonic devices using the adjoint method is proposed.We design a single-mode 3dB power divider and a dual-mode demultiplexer to demonstrate the efficiency of the proposed inverse design approach,called the digitized adjoint method,for single-and dual-object optimization,respectively.The optimization comprises three stages:1)continuous variation for an"analog"pattern;2)forced permittivity biasing for a"quasi-digital"pattern;and 3)a multilevel digital pattern.Compared with the conventional brute-force method,the proposed method can improve design efficiency by about five times,and the performance optimization can reach approximately the same level.The method takes advantages of adjoint sensitivity analysis and digital subwavelength structure and creates a new way for the efficient and high-performance design of compact digital subwavelength nanophotonic devices,which could overcome the efficiency bottleneck of the brute-force method,which is restricted by the number of pixels of a digital pattern,and improve the device performance by extending a conventional binary pattern to a multilevel one.展开更多
The paper is concerned with a stochastic optimal control problem where the controlled systems are driven by Teugel＇s martingales and an independent multi-dimensional Brownian motion, Necessary and sufficient conditio...The paper is concerned with a stochastic optimal control problem where the controlled systems are driven by Teugel＇s martingales and an independent multi-dimensional Brownian motion, Necessary and sufficient conditions for an optimal control of the control problem with the control domain being convex are proved by the classical method of convex variation, and the coefficients appearing in the systems are allowed to depend on the control variables, As an application, the linear quadratic stochastic optimal control problem is studied.展开更多
We discuss a transfer line consisting of a reliable machine, an unreliable machine and a storage buffer. This transfer line can be described by a group of partial differential equations with integral boundary conditio...We discuss a transfer line consisting of a reliable machine, an unreliable machine and a storage buffer. This transfer line can be described by a group of partial differential equations with integral boundary conditions. First we show that the operator corresponding to these equations generates a positive contraction C0-semigroup T(t), and prove that T(t) is a quasi-compact operator. Next we verify that 0 is an eigenvalue of this operator and its adjoint operator with geometric multiplicity one. Last, by using the above results we obtain that the time-dependent solution of these equations converges strongly to their steady-state solution.展开更多
Designing a controller for the docking maneuver in Probe-Drogue Refueling(PDR) is an important but challenging task, due to the complex system model and the high precision requirement.In order to overcome the disadvan...Designing a controller for the docking maneuver in Probe-Drogue Refueling(PDR) is an important but challenging task, due to the complex system model and the high precision requirement.In order to overcome the disadvantage of only feedback control, a feedforward control scheme known as Iterative Learning Control(ILC) is adopted in this paper.First, Additive State Decomposition(ASD) is used to address the tight coupling of input saturation, nonlinearity and the property of Non Minimum Phase(NMP) by separating these features into two subsystems(a primary system and a secondary system).After system decomposition, an adjoint-type ILC is applied to the Linear Time-Invariant(LTI) primary system with NMP to achieve entire output trajectory tracking, whereas state feedback is used to stabilize the secondary system with input saturation.The two controllers designed for the two subsystems can be combined to achieve the original control goal of the PDR system.Furthermore, to compensate for the receiverindependent uncertainties, a correction action is proposed by using the terminal docking error,which can lead to a smaller docking error at the docking moment.Simulation tests have been carried out to demonstrate the performance of the proposed control method, which has some advantages over the traditional derivative-type ILC and adjoint-type ILC in the docking control of PDR.展开更多
Whether the initial conditions contain pronounced mesoscale signals is important to the simulation of the southwest vortex. An eastward-moving southwest vortex is simulated using the PSU/NCAR MM5. A modest degree of s...Whether the initial conditions contain pronounced mesoscale signals is important to the simulation of the southwest vortex. An eastward-moving southwest vortex is simulated using the PSU/NCAR MM5. A modest degree of success is achieved, but the most serious failure is that the formation and displacement of the simulated vortex in its early phase are about fourteen hours later than the observed vortex. Considering the relatively sparse data on the mesoscale vortex and in an attempt to understand the cause of the forecast failure, an adjoint model is used to examine the sensitivity of the southwest vortex to perturbations of initial conditions. The adjoint sensitivity indicates how small perturbations of model variables at the initial time in the model domain can influence the vortex. A large sensitivity for zonal wind is located under 400 hPa, a large sensitivity for meridional wind is located under 500 hPa, a large sensitivity for temperature is located between 500 and 900 hPa, and almost all of the large sensitivity areas are located in the southwestern area. Based on the adjoint sensitivity results, perturbations are added to initial conditions to improve the simulation of the southwest vortex. The results show that the initial conditions with perturbations can successfully simulate the formation and displacement of the vortex; the wind perturbations added to the initial conditions appear to be a cyclone circulation under the middle level of the atmosphere in the southwestern area with an anticyclone circulation to its southwest; a water vapor perturbation added to initial conditions can strengthen the vortex and the speed of its displacement.展开更多
The basic sets of solutions in classH(orH *) for the characteristic equation and its adjoint equation with Hilbert kernel are given respectively. Thus the expressions of solutions and its solvable conditions are simpl...The basic sets of solutions in classH(orH *) for the characteristic equation and its adjoint equation with Hilbert kernel are given respectively. Thus the expressions of solutions and its solvable conditions are simplified. On this basis the solutions and the solvable conditions in classH 1 * as well as the generalized Noether theorem for the complete equation are obtained. Key words Hilbert kernel - solution with singularity of order one - basic set of solutions - Noether theorem - characteristic equation and its adjoint equation CLC number O 175.5 Foundation item: Supported by the National Natural Science Foundation of China (19971064) and Ziqiang Invention Foundation of Wuhan University (201990336)Biography: Zhong Shou-guo(1941-), male, Professor, research direction: singular integral equations and their applications.展开更多
A variant constrained genetic algorithm （VCGA） for effective tracking of conditional nonlinear optimal perturbations （CNOPs） is presented. Compared with traditional constraint handling methods, the treatment of th...A variant constrained genetic algorithm （VCGA） for effective tracking of conditional nonlinear optimal perturbations （CNOPs） is presented. Compared with traditional constraint handling methods, the treatment of the constraint condition in VCGA is relatively easy to implement. Moreover, it does not require adjustments to indefinite pararneters. Using a hybrid crossover operator and the newly developed multi-ply mutation operator, VCGA improves the performance of GAs. To demonstrate the capability of VCGA to catch CNOPS in non-smooth cases, a partial differential equation, which has ＂on off＂ switches in its forcing term, is employed as the nonlinear model. To search global CNOPs of the nonlinear model, numerical experiments using VCGA, the traditional gradient descent algorithm based on the adjoint method （ADJ）, and a GA using tournament selection operation and the niching technique （GA-DEB） were performed. The results with various initial reference states showed that, in smooth cases, all three optimization methods are able to catch global CNOPs. Nevertheless, in non-smooth situations, a large proportion of CNOPs captured by the ADJ are local. Compared with ADJ, the performance of GA-DEB shows considerable improvement, but it is far below VCGA. Further, the impacts of population sizes on both VCGA and GA-DEB were investigated. The results were used to estimate the computation time of ~CGA and GA-DEB in obtaining CNOPs. The computational costs for VCGA, GA-DEB and ADJ to catch CNOPs of the nonlinear model are also compared.展开更多
By using a general scheme for decomposing a zero-curvature equation into two commut- ing x-and t_n-finite-dimensional integrable Hamiltonian systems (FDIHS),a systematic deduction of the Lax representation for all con...By using a general scheme for decomposing a zero-curvature equation into two commut- ing x-and t_n-finite-dimensional integrable Hamiltonian systems (FDIHS),a systematic deduction of the Lax representation for all constrained flows of the AKNS hierarchy from the adjoint repre- sentation of the two auxiliary linear problems is presented.The Darboux transformation for these FDIHSs is derived.展开更多
Abstract A first study on the continuous adjoint formulation for aerodynamic optimization design of high pressure turbines based on S2 surface governed by the Euler equations with source terms is presented. The object...Abstract A first study on the continuous adjoint formulation for aerodynamic optimization design of high pressure turbines based on S2 surface governed by the Euler equations with source terms is presented. The objective function is defined as an integral function along the boundaries, and the adjoint equations and the boundary conditions are derived by introducing the adjoint variable vec- tors. The gradient expression of the objective function then includes only the terms related to phys- ical shape variations. The numerical solution of the adjoint equation is conducted by a finite- difference method with the Jameson spatial scheme employing the first and the third order dissipa- tive fluxes. A gradient-based aerodynamic optimization system is established by integrating the blade stagger angles, the stacking lines and the passage perturbation parameterization with the quasi-Newton method of Broyden Fletcher Goldfarb-Shanno （BFGS）. The application of the continuous adjoint method is validated through a single stage high pressure turbine optimization case. The adiabatic efficiency increases from 0.8875 to 0.8931, whilst the mass flow rate and the pressure ratio remain almost unchanged. The optimization design is shown to reduce the passage vortex loss as well as the mixing loss due to the cooling air injection.展开更多
Manufactured blades are inevitably different from their design intent,which leads to a deviation of the performance from the intended value.To quantify the associated performance uncertainty,many approaches have been ...Manufactured blades are inevitably different from their design intent,which leads to a deviation of the performance from the intended value.To quantify the associated performance uncertainty,many approaches have been developed.The traditional Monte Carlo method based on a Computational Fluid Dynamics solver(MC-CFD)for a three-dimensional compressor is prohibitively expensive.Existing alternatives to the MC-CFD,such as surrogate models and secondorder derivatives based on the adjoint method,can greatly reduce the computational cost.Nevertheless,they will encounter’the curse of dimensionality’except for the linear model based on the adjoint gradient(called MC-adj-linear).However,the MC-adj-linear model neglects the nonlinearity of the performance function.In this work,an improved method is proposed to circumvent the lowaccuracy problem of the MC-adj-linear without incurring the high cost of other alternative models.The method is applied to the study of the aerodynamic performance of an annular transonic compressor cascade,subject to prescribed geometric variability with industrial relevance.It is found that the proposed method achieves a significant accuracy improvement over the MC-adj-linear with low computational cost,showing the great potential for fast uncertainty quantification.展开更多
This paper presents the fundamentals of a continuous adjoint method and the applications of this method to the aerodynamic design optimization of both external and internal flows.General formulation of the continuous ...This paper presents the fundamentals of a continuous adjoint method and the applications of this method to the aerodynamic design optimization of both external and internal flows.General formulation of the continuous adjoint equations and the corresponding boundary conditions are derived.With the adjoint method,the complete gradient information needed in the design optimization can be obtained by solving the governing flow equations and the corresponding adjoint equations only once for each cost function,regardless of the number of design parameters.An inverse design of airfoil is firstly performed to study the accuracy of the adjoint gradient and the effectiveness of the adjoint method as an inverse design method.Then the method is used to perform a series of single and multiple point design optimization problems involving the drag reduction of airfoil,wing,and wing-body configuration,and the aerodynamic performance improvement of turbine and compressor blade rows.The results demonstrate that the continuous adjoint method can efficiently and significantly improve the aerodynamic performance of the design in a shape optimization problem.展开更多
A least-squares reverse-time migration scheme is presented for reflectivity imaging. Based on an accurate reflection modeling formula, this scheme produces amplitude-preserved stacked reflectivity images with zero pha...A least-squares reverse-time migration scheme is presented for reflectivity imaging. Based on an accurate reflection modeling formula, this scheme produces amplitude-preserved stacked reflectivity images with zero phase. Spatial preconditioning, weighting and the Barzilai-Borwein method are applied to speed up the convergence of the least-squares inversion. In addition, this scheme compensates the effect of ghost waves to broaden the bandwidth of the reflectivity images. Furthermore, roughness penalty constraint is used to regularize the inversion, which in turn stabilizes inversion and removes high-wavenumber artifacts and mitigates spatial aliasing. The examples of synthetic and field datasets demonstrate the scheme can generate zerophase reflectivity images with broader bandwidth, higher resolution, fewer artifacts and more reliable amplitudes than conventional reverse-time migration.展开更多
基金the Ministry of Science and Technology of China for funding the 973 project (Grant No. 2004CB418304) the Ministry of Finance of China and the China Meteorological Administration for the Special Project of Meteorological Sector [Grant No. GYHY(QX)2007-6-15]
文摘Four-dimensional variational data assimilation （4DVar） is one of the most promising methods to provide optimal analysis for numerical weather prediction （NWP）. Five national NWP centers in the world have successfully applied 4DVar methods in their global NWPs, thanks to the increment method and adjoint technique. However, the application of 4DVar is still limited by the computer resources available at many NWP centers and research institutes. It is essential, therefore, to further reduce the computational cost of 4DVar. Here, an economical approach to implement 4DVar is proposed, using the technique of dimension- reduced projection （DRP）, which is called ＂DRP-4DVar.＂ The proposed approach is based on dimension reduction using an ensemble of historical samples to define a subspace. It directly obtains an optimal solution in the reduced space by fitting observations with historical time series generated by the model to form consistent forecast states, and therefore does not require implementation of the adjoint of tangent linear approximation. To evaluate the performance of the DRP-4DVar on assimilating different types of mesoscale observations, some observing system simulation experiments are conducted using MM5 and a comparison is made between adjoint-based 4DVar and DRP-4DVar using a 6-hour assimilation window.
基金Broadband data were obtained from the IRIS Data Management Center.
文摘We provide an introduction to the use of the spectral-elementmethod (SEM)in seismology. Following a brief review of the basic equations that govern seismicwave propagation, we discuss in some detail how these equations may be solved numericallybased upon the SEM to address the forward problem in seismology. Examplesof synthetic seismograms calculated based upon the SEM are compared to datarecorded by the Global Seismographic Network. Finally, we discuss the challenge ofusing the remaining differences between the data and the synthetic seismograms toconstrain better Earth models and source descriptions. This leads naturally to adjointmethods, which provide a practical approach to this formidable computational challengeand enables seismologists to tackle the inverse problem.
文摘In order to obtain an accurate tide description in the China Seas, the 2-dimensional nonlinear numerical Princeton Ocean Model （POM） is employed to incorporate in situ tidal measurements both from tide gauges and TOPEX/POSEIDON （T/P） derived datasets by means of the variational adjoint approach in such a way that unknown internal model parameters, bottom topography, friction coefficients and open boundary conditions, for example, are adjusted during the process. The numerical model is used as a forward model. After the along-track T/P data are processed, two classical methods, i.e. harmonic and response analysis, are implemented to estimate the tide from such datasets with a domain covering the model area extending from 0° to 41°N in latitude and from 99°E to 142°E in longitude. And the results of these two methods are compared and interpreted. The numerical simulation is performed for 16 major constituents. In the data assimilation experiments, three types of unknown parameters （water depth, bottom friction and tidal open boundary conditions in the model equations） are chosen as control variables. Among the various types of data assimilation experiments, the calibration of water depth brings the most promising results. By comparing the results with selected tide gauge data, the average absolute errors are decreased from 7.9 cm to 6.8 cm for amplitude and from 13.0° to 9.0° for phase with respect to the semidiurnal tide M2 constituent, which is the largest tidal constituent in the model area. After the data assimilation experiment is performed, the comparison between model results and tide gauge observation for water levels shows that the RMS errors decrease by 9 cm for a total of 14 stations, mostly selected along the coast of China's Mainland, when a one-month period is considered, and the correlation coefficients improve for most tidal stations among these stations.
基金Research Grants Council of Hong Kong(CERG 9040466)City University of Hong Kong(SRGs 7001041,7001178)+2 种基金National Science Foundation of China(No.19801031)Special Grant of Excellent PhD Thesis(No.200013)Special Funds for Major State Basjc Reaca
文摘A soliton hierarchy of multicomponent AKNS equations is generated from an arbitraryorder matrix spectral problem, along with its bi-Hamiltonian formulation. Adjoint symmetry constraints are presented to manipulate binary nonlinearization for the associated arbitrary order matrix spectral problem. The resulting spatial and temporal constrained flows are shown to provide integrable decompositions of the multicomponent AKNS equations.
文摘Let Sn be the star with n vertices, and let G be any connected graph with p vertices. We denote by Eτp＋（r-1）^G（i） the graph obtained from Sr and rG by coinciding the i-th vertex of G with the vertex of degree r - 1 of S,, while the i-th vertex of each component of （r - 1）G be adjacented to r - 1 vertices of degree 1 of St, respectively. By applying the properties of adjoint polynomials, We prove that factorization theorem of adjoint polynomials of kinds of graphs Eτp＋（r-1）^G（i）∪（r - 1）K1 （1 ≤i≤p）. Furthermore, we obtain structure characteristics of chromatically equivalent graphs of their complements.
基金the National Natural Science Foundation of China (Grant No. 10671161)
文摘This paper is devoted to studying the recollement of the categories of finitely generated modules over finite dimensional algebras. We prove that for algebras A, B and C, if A-mod admits a recollement relative to B-mod and C-mod, then A[R]-mod admits a recollement relative to B[S]-mod and C-mod, where A[R]and B[S]are the one-point extensions of A by R and of B by S.
基金National Natural Science Foundation of China(61635004,61775069)Technology Innovation Program of Hubei Province of China(2018AAA037)。
文摘A high-efficiency inverse design of"digital"subwavelength nanophotonic devices using the adjoint method is proposed.We design a single-mode 3dB power divider and a dual-mode demultiplexer to demonstrate the efficiency of the proposed inverse design approach,called the digitized adjoint method,for single-and dual-object optimization,respectively.The optimization comprises three stages:1)continuous variation for an"analog"pattern;2)forced permittivity biasing for a"quasi-digital"pattern;and 3)a multilevel digital pattern.Compared with the conventional brute-force method,the proposed method can improve design efficiency by about five times,and the performance optimization can reach approximately the same level.The method takes advantages of adjoint sensitivity analysis and digital subwavelength structure and creates a new way for the efficient and high-performance design of compact digital subwavelength nanophotonic devices,which could overcome the efficiency bottleneck of the brute-force method,which is restricted by the number of pixels of a digital pattern,and improve the device performance by extending a conventional binary pattern to a multilevel one.
基金Supported by the National Natural Science Foundation of China (Grant No. 10325101)the National Basic Research Program of China (GrantNo. 2007CB814904)the Natural Science Foundation of Zhejiang Province (Grant Nos. Y605478, Y606667)
文摘The paper is concerned with a stochastic optimal control problem where the controlled systems are driven by Teugel＇s martingales and an independent multi-dimensional Brownian motion, Necessary and sufficient conditions for an optimal control of the control problem with the control domain being convex are proved by the classical method of convex variation, and the coefficients appearing in the systems are allowed to depend on the control variables, As an application, the linear quadratic stochastic optimal control problem is studied.
基金This research is supported by Excellent Youth Reward Foundation of the Higher Education Institution of Xinjiang (No: XJEDU2004E05) the Major Project of the Ministry of Education of China(No. 205180).
文摘We discuss a transfer line consisting of a reliable machine, an unreliable machine and a storage buffer. This transfer line can be described by a group of partial differential equations with integral boundary conditions. First we show that the operator corresponding to these equations generates a positive contraction C0-semigroup T(t), and prove that T(t) is a quasi-compact operator. Next we verify that 0 is an eigenvalue of this operator and its adjoint operator with geometric multiplicity one. Last, by using the above results we obtain that the time-dependent solution of these equations converges strongly to their steady-state solution.
基金supported by the National Natural Science Foundation of China(No.61473012)。
文摘Designing a controller for the docking maneuver in Probe-Drogue Refueling(PDR) is an important but challenging task, due to the complex system model and the high precision requirement.In order to overcome the disadvantage of only feedback control, a feedforward control scheme known as Iterative Learning Control(ILC) is adopted in this paper.First, Additive State Decomposition(ASD) is used to address the tight coupling of input saturation, nonlinearity and the property of Non Minimum Phase(NMP) by separating these features into two subsystems(a primary system and a secondary system).After system decomposition, an adjoint-type ILC is applied to the Linear Time-Invariant(LTI) primary system with NMP to achieve entire output trajectory tracking, whereas state feedback is used to stabilize the secondary system with input saturation.The two controllers designed for the two subsystems can be combined to achieve the original control goal of the PDR system.Furthermore, to compensate for the receiverindependent uncertainties, a correction action is proposed by using the terminal docking error,which can lead to a smaller docking error at the docking moment.Simulation tests have been carried out to demonstrate the performance of the proposed control method, which has some advantages over the traditional derivative-type ILC and adjoint-type ILC in the docking control of PDR.
文摘Whether the initial conditions contain pronounced mesoscale signals is important to the simulation of the southwest vortex. An eastward-moving southwest vortex is simulated using the PSU/NCAR MM5. A modest degree of success is achieved, but the most serious failure is that the formation and displacement of the simulated vortex in its early phase are about fourteen hours later than the observed vortex. Considering the relatively sparse data on the mesoscale vortex and in an attempt to understand the cause of the forecast failure, an adjoint model is used to examine the sensitivity of the southwest vortex to perturbations of initial conditions. The adjoint sensitivity indicates how small perturbations of model variables at the initial time in the model domain can influence the vortex. A large sensitivity for zonal wind is located under 400 hPa, a large sensitivity for meridional wind is located under 500 hPa, a large sensitivity for temperature is located between 500 and 900 hPa, and almost all of the large sensitivity areas are located in the southwestern area. Based on the adjoint sensitivity results, perturbations are added to initial conditions to improve the simulation of the southwest vortex. The results show that the initial conditions with perturbations can successfully simulate the formation and displacement of the vortex; the wind perturbations added to the initial conditions appear to be a cyclone circulation under the middle level of the atmosphere in the southwestern area with an anticyclone circulation to its southwest; a water vapor perturbation added to initial conditions can strengthen the vortex and the speed of its displacement.
文摘The basic sets of solutions in classH(orH *) for the characteristic equation and its adjoint equation with Hilbert kernel are given respectively. Thus the expressions of solutions and its solvable conditions are simplified. On this basis the solutions and the solvable conditions in classH 1 * as well as the generalized Noether theorem for the complete equation are obtained. Key words Hilbert kernel - solution with singularity of order one - basic set of solutions - Noether theorem - characteristic equation and its adjoint equation CLC number O 175.5 Foundation item: Supported by the National Natural Science Foundation of China (19971064) and Ziqiang Invention Foundation of Wuhan University (201990336)Biography: Zhong Shou-guo(1941-), male, Professor, research direction: singular integral equations and their applications.
基金supported by the National Natural Science Foundation of China(Grant No.40975063)the National Natural Science Foundation of China(Grant No.41331174)
文摘A variant constrained genetic algorithm （VCGA） for effective tracking of conditional nonlinear optimal perturbations （CNOPs） is presented. Compared with traditional constraint handling methods, the treatment of the constraint condition in VCGA is relatively easy to implement. Moreover, it does not require adjustments to indefinite pararneters. Using a hybrid crossover operator and the newly developed multi-ply mutation operator, VCGA improves the performance of GAs. To demonstrate the capability of VCGA to catch CNOPS in non-smooth cases, a partial differential equation, which has ＂on off＂ switches in its forcing term, is employed as the nonlinear model. To search global CNOPs of the nonlinear model, numerical experiments using VCGA, the traditional gradient descent algorithm based on the adjoint method （ADJ）, and a GA using tournament selection operation and the niching technique （GA-DEB） were performed. The results with various initial reference states showed that, in smooth cases, all three optimization methods are able to catch global CNOPs. Nevertheless, in non-smooth situations, a large proportion of CNOPs captured by the ADJ are local. Compared with ADJ, the performance of GA-DEB shows considerable improvement, but it is far below VCGA. Further, the impacts of population sizes on both VCGA and GA-DEB were investigated. The results were used to estimate the computation time of ~CGA and GA-DEB in obtaining CNOPs. The computational costs for VCGA, GA-DEB and ADJ to catch CNOPs of the nonlinear model are also compared.
基金Supported by the Chinese National Basic Research Project"Nonlinear Science"
文摘By using a general scheme for decomposing a zero-curvature equation into two commut- ing x-and t_n-finite-dimensional integrable Hamiltonian systems (FDIHS),a systematic deduction of the Lax representation for all constrained flows of the AKNS hierarchy from the adjoint repre- sentation of the two auxiliary linear problems is presented.The Darboux transformation for these FDIHSs is derived.
基金funded by the Aeronautical Science Foundation of China–China(No.2010ZB51023)
文摘Abstract A first study on the continuous adjoint formulation for aerodynamic optimization design of high pressure turbines based on S2 surface governed by the Euler equations with source terms is presented. The objective function is defined as an integral function along the boundaries, and the adjoint equations and the boundary conditions are derived by introducing the adjoint variable vec- tors. The gradient expression of the objective function then includes only the terms related to phys- ical shape variations. The numerical solution of the adjoint equation is conducted by a finite- difference method with the Jameson spatial scheme employing the first and the third order dissipa- tive fluxes. A gradient-based aerodynamic optimization system is established by integrating the blade stagger angles, the stacking lines and the passage perturbation parameterization with the quasi-Newton method of Broyden Fletcher Goldfarb-Shanno （BFGS）. The application of the continuous adjoint method is validated through a single stage high pressure turbine optimization case. The adiabatic efficiency increases from 0.8875 to 0.8931, whilst the mass flow rate and the pressure ratio remain almost unchanged. The optimization design is shown to reduce the passage vortex loss as well as the mixing loss due to the cooling air injection.
基金funded by the National Natural Science Foundation of China(No.52006177)National Science and Technology Major Project,China(No.2017-II-0009-0023)。
文摘Manufactured blades are inevitably different from their design intent,which leads to a deviation of the performance from the intended value.To quantify the associated performance uncertainty,many approaches have been developed.The traditional Monte Carlo method based on a Computational Fluid Dynamics solver(MC-CFD)for a three-dimensional compressor is prohibitively expensive.Existing alternatives to the MC-CFD,such as surrogate models and secondorder derivatives based on the adjoint method,can greatly reduce the computational cost.Nevertheless,they will encounter’the curse of dimensionality’except for the linear model based on the adjoint gradient(called MC-adj-linear).However,the MC-adj-linear model neglects the nonlinearity of the performance function.In this work,an improved method is proposed to circumvent the lowaccuracy problem of the MC-adj-linear without incurring the high cost of other alternative models.The method is applied to the study of the aerodynamic performance of an annular transonic compressor cascade,subject to prescribed geometric variability with industrial relevance.It is found that the proposed method achieves a significant accuracy improvement over the MC-adj-linear with low computational cost,showing the great potential for fast uncertainty quantification.
基金supported by the National Natural Science Foundation of China(Grant Nos.51206003 and 51376009)the National Science Foundation for Post-doctoral Scientists of China(Grant Nos.2012M510267 and 2013T60035)
文摘This paper presents the fundamentals of a continuous adjoint method and the applications of this method to the aerodynamic design optimization of both external and internal flows.General formulation of the continuous adjoint equations and the corresponding boundary conditions are derived.With the adjoint method,the complete gradient information needed in the design optimization can be obtained by solving the governing flow equations and the corresponding adjoint equations only once for each cost function,regardless of the number of design parameters.An inverse design of airfoil is firstly performed to study the accuracy of the adjoint gradient and the effectiveness of the adjoint method as an inverse design method.Then the method is used to perform a series of single and multiple point design optimization problems involving the drag reduction of airfoil,wing,and wing-body configuration,and the aerodynamic performance improvement of turbine and compressor blade rows.The results demonstrate that the continuous adjoint method can efficiently and significantly improve the aerodynamic performance of the design in a shape optimization problem.
基金partly supported by the National Naural Science Foundation of China(Grant No.41272099)the Science Foundation of China University of Petroleum,Beijing(Grant No.2462015YJRC012)
文摘A least-squares reverse-time migration scheme is presented for reflectivity imaging. Based on an accurate reflection modeling formula, this scheme produces amplitude-preserved stacked reflectivity images with zero phase. Spatial preconditioning, weighting and the Barzilai-Borwein method are applied to speed up the convergence of the least-squares inversion. In addition, this scheme compensates the effect of ghost waves to broaden the bandwidth of the reflectivity images. Furthermore, roughness penalty constraint is used to regularize the inversion, which in turn stabilizes inversion and removes high-wavenumber artifacts and mitigates spatial aliasing. The examples of synthetic and field datasets demonstrate the scheme can generate zerophase reflectivity images with broader bandwidth, higher resolution, fewer artifacts and more reliable amplitudes than conventional reverse-time migration.
