Orthogonal conditional nonlinear optimal perturbations(O-CNOPs)have been used to generate ensemble forecasting members for achieving high forecasting skill of high-impact weather and climate events.However,highly effi...Orthogonal conditional nonlinear optimal perturbations(O-CNOPs)have been used to generate ensemble forecasting members for achieving high forecasting skill of high-impact weather and climate events.However,highly efficient calculations for O-CNOPs are still challenging in the field of ensemble forecasting.In this study,we combine a gradient-based iterative idea with the Gram‒Schmidt orthogonalization,and propose an iterative optimization method to compute O-CNOPs.This method is different from the original sequential optimization method,and allows parallel computations of O-CNOPs,thus saving a large amount of computational time.We evaluate this method by using the Lorenz-96 model on the basis of the ensemble forecasting ability achieved and on the time consumed for computing O-CNOPs.The results demonstrate that the parallel iterative method causes O-CNOPs to yield reliable ensemble members and to achieve ensemble forecasting skills similar to or even slightly higher than those produced by the sequential method.Moreover,the parallel method significantly reduces the computational time for O-CNOPs.Therefore,the parallel iterative method provides a highly effective and efficient approach for calculating O-CNOPs for ensemble forecasts.Expectedly,it can play an important role in the application of the O-CNOPs to realistic ensemble forecasts for high-impact weather and climate events.展开更多
The Conditional Nonlinear Optimal Perturbation(CNOP)method works essentially for conventional numerical models;however,it is not fully applicable to the commonly used deep-learning forecasting models(DLMs),which typic...The Conditional Nonlinear Optimal Perturbation(CNOP)method works essentially for conventional numerical models;however,it is not fully applicable to the commonly used deep-learning forecasting models(DLMs),which typically input multiple time slices without deterministic dependencies.In this study,the CNOP for DLMs(CNOP-DL)is proposed as an extension of the CNOP in the time dimension.This method is useful for targeted observations as it indicates not only where but also when to deploy additional observations.The CNOP-DL is calculated for a forecast case of sea surface temperature in the South China Sea with a DLM.The CNOP-DL identifies a sensitive area northwest of Palawan Island at the last input time.Sensitivity experiments demonstrate that the sensitive area identified by the CNOP-DL is effective not only for the CNOP-DL itself,but also for random perturbations.Therefore,this approach holds potential for guiding practical field campaigns.Notably,forecast errors are more sensitive to time than to location in the sensitive area.It highlights the crucial role of identifying the time of the sensitive area in targeted observations,corroborating the usefulness of extending the CNOP in the time dimension.展开更多
A reduced-gravity barotropic shallow-water model was used to simulate the Kuroshio path variations. The results show that the model was able to capture the essential features of these path variations. We used one simu...A reduced-gravity barotropic shallow-water model was used to simulate the Kuroshio path variations. The results show that the model was able to capture the essential features of these path variations. We used one simulation of the model as the reference state and investigated the effects of errors in model parameters on the prediction of the transition to the Kuroshio large meander （KLM） state using the conditional nonlinear optimal parameter perturbation （CNOP-P） method. Because of their relatively large uncertainties, three model parameters were considered： the interracial friction coefficient, the wind-stress amplitude, and the lateral friction coefficient. We determined the CNOP-Ps optimized for each of these three parameters independently, and we optimized all three parameters simultaneously using the Spectral Projected Gradient 2 （SPG2） algorithm. Similarly, the impacts caused by errors in initial conditions were examined using the conditional nonlinear optimal initial perturbation （CNOP-I） method. Both the CNOP-I and CNOP-Ps can result in significant prediction errors of the KLM over a lead time of 240 days. But the prediction error caused by CNOP-I is greater than that caused by CNOP-P. The results of this study indicate not only that initial condition errors have greater effects on the prediction of the KLM than errors in model parameters but also that the latter cannot be ignored. Hence, to enhance the forecast skill of the KLM in this model, the initial conditions should first be improved, the model parameters should use the best possible estimates.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
Due to uncertainties in initial conditions and parameters, the stability and uncertainty of grassland ecosystem simulations using ecosystem models are issues of concern. Our objective is to determine the types and pat...Due to uncertainties in initial conditions and parameters, the stability and uncertainty of grassland ecosystem simulations using ecosystem models are issues of concern. Our objective is to determine the types and patterns of initial and parameter perturbations that yield the greatest instability and uncertainty in simulated grassland ecosystems using theoretical models. We used a nonlinear optimization approach, i.e., a conditional nonlinear optimal perturbation related to initial and parameter perturbations （CNOP） approach, in our work. Numerical results indicated that the CNOP showed a special and nonlinear optimal pattern when the initial state variables and multiple parameters were considered simultaneously. A visibly different complex optimal pattern characterizing the CNOPs was obtained by choosing different combinations of initial state variables and multiple parameters in different physical processes. We propose that the grassland modeled ecosystem caused by the CNOP-type perturbation is unstable and exhibits two aspects： abrupt change and the time needed for the abrupt change from a grassland equilibrium state to a desert equilibrium state when the initial state variables and multiple parameters are considered simultaneously. We compared these findings with results affected by the CNOPs obtained by considering only uncertainties in initial state variables and in a single parameter. The numerical results imply that the nonlinear optimal pattern of initial perturbations and parameter perturbations, especially for more parameters or when special parameters are involved, plays a key role in determining stabilities and uncertainties associated with a simulated or predicted grassland ecosystem.展开更多
Platform planning is one of the important problems in the command and control(C2) field. Hereto, we analyze the platform planning problem and present nonlinear optimal model aiming at maximizing the task completion qu...Platform planning is one of the important problems in the command and control(C2) field. Hereto, we analyze the platform planning problem and present nonlinear optimal model aiming at maximizing the task completion qualities. Firstly, we take into account the relation among tasks and build the single task nonlinear optimal model with a set of platform constraints. The Lagrange relaxation method and the pruning strategy are used to solve the model. Secondly, this paper presents optimization-based planning algorithms for efficiently allocating platforms to multiple tasks. To achieve the balance of the resource assignments among tasks, the m-best assignment algorithm and the pair-wise exchange(PWE)method are used to maximize multiple tasks completion qualities.Finally, a series of experiments are designed to verify the superiority and effectiveness of the proposed model and algorithms.展开更多
The conditional nonlinear optimal perturbation （CNOP）, which is a nonlinear generalization of the linear singular vector （LSV）, is applied in important problems of atmospheric and oceanic sciences, including ENSO ...The conditional nonlinear optimal perturbation （CNOP）, which is a nonlinear generalization of the linear singular vector （LSV）, is applied in important problems of atmospheric and oceanic sciences, including ENSO predictability, targeted observations, and ensemble forecast. In this study, we investigate the computational cost of obtaining the CNOP by several methods. Differences and similarities, in terms of the computational error and cost in obtaining the CNOP, are compared among the sequential quadratic programming （SQP） algorithm, the limited memory Broyden-Fletcher-Goldfarb-Shanno （L-BFGS） algorithm, and the spectral projected gradients （SPG2） algorithm. A theoretical grassland ecosystem model and the classical Lorenz model are used as examples. Numerical results demonstrate that the computational error is acceptable with all three algorithms. The computational cost to obtain the CNOP is reduced by using the SQP algorithm. The experimental results also reveal that the L-BFGS algorithm is the most effective algorithm among the three optimization algorithms for obtaining the CNOP. The numerical results suggest a new approach and algorithm for obtaining the CNOP for a large-scale optimization problem.展开更多
Using a simplified nonlinearly theoretical grassland ecosystem proposed by Zeng et al.,we study the sensitivity and nonlinear instability of the grassland ecosystem to finiteamplitude initial perturbations with the ap...Using a simplified nonlinearly theoretical grassland ecosystem proposed by Zeng et al.,we study the sensitivity and nonlinear instability of the grassland ecosystem to finiteamplitude initial perturbations with the approach of conditional nonlinear optimal perturbation （CNOP）.The results show that the linearly stable grassland （desert or latent desert） states can turn to be nonlinearly unstable with finite amplitude initial perturbations.When the precipitation is between the two bifurcation points,a large enough finite amplitude initial perturbation can induce a transition between the grassland statethe desert state or the latent desert.展开更多
A two-layer quasi-geostrophic model is used to study the stability and sensitivity of motions on smallscale vortices in Jupiter＇s atmosphere. Conditional nonlinear optimal perturbations （CNOPs） and linear singular ...A two-layer quasi-geostrophic model is used to study the stability and sensitivity of motions on smallscale vortices in Jupiter＇s atmosphere. Conditional nonlinear optimal perturbations （CNOPs） and linear singular vectors （LSVs） are both obtained numerically and compared in this paper. The results show that CNOPs can capture the nonlinear characteristics of motions in small-scale vortices in Jupiter＇s atmosphere and show great difference from LSVs under the condition that the initial constraint condition is large or the optimization time is not very short or both. Besides, in some basic states, local CNOPs are found. The pattern of LSV is more similar to local CNOP than global CNOP in some cases. The elementary application of the method of CNOP to the Jovian atmosphere helps us to explore the stability of variousscale motions of Jupiter＇s atmosphere and to compare the stability of motions in Jupiter＇s atmosphere and Earth＇s atmosphere further.展开更多
In the typhoon adaptive observation based on conditional nonlinear optimal perturbation (CNOP), the ‘on-off’ switch caused by moist physical parameterization in prediction models prevents the conventional adjoint me...In the typhoon adaptive observation based on conditional nonlinear optimal perturbation (CNOP), the ‘on-off’ switch caused by moist physical parameterization in prediction models prevents the conventional adjoint method from providing correct gradient during the optimization process. To address this problem, the capture of CNOP, when the "on-off" switches are included in models, is treated as non-smooth optimization in this study, and the genetic algorithm (GA) is introduced. After detailed algorithm procedures are formulated using an idealized model with parameterization "on-off" switches in the forcing term, the impacts of "on-off" switches on the capture of CNOP are analyzed, and three numerical experiments are conducted to check the effectiveness of GA in capturing CNOP and to analyze the impacts of different initial populations on the optimization result. The result shows that GA is competent for the capture of CNOP in the context of the idealized model with parameterization ‘on-off’ switches in this study. Finally, the advantages and disadvantages of GA in capturing CNOP are analyzed in detail.展开更多
By converting an optimal control problem for nonlinear systems to a Hamiltonian system,a symplecitc-preserving method is proposed.The state and costate variables are approximated by the Lagrange polynomial.The state v...By converting an optimal control problem for nonlinear systems to a Hamiltonian system,a symplecitc-preserving method is proposed.The state and costate variables are approximated by the Lagrange polynomial.The state variables at two ends of the time interval are taken as independent variables.Based on the dual variable principle,nonlinear optimal control problems are replaced with nonlinear equations.Furthermore,in the implementation of the symplectic algorithm,based on the 2N algorithm,a multilevel method is proposed.When the time grid is refined from low level to high level,the initial state and costate variables of the nonlinear equations can be obtained from the Lagrange interpolation at the low level grid to improve efficiency.Numerical simulations show the precision and the efficiency of the proposed algorithm in this paper.展开更多
The interaction between the typhoons Fengshen and Fung-wong over the Western Pacific in 2002 is studied with the Conditional Nonlinear Optimal Perturbation(CNOP) method.The study discovered that the CNOP method reveal...The interaction between the typhoons Fengshen and Fung-wong over the Western Pacific in 2002 is studied with the Conditional Nonlinear Optimal Perturbation(CNOP) method.The study discovered that the CNOP method reveals the process of one-way interaction between Fengshen and Fung-wong.Moreover,if the region of Fung-wong was selected for verification,the sensitivity area was mainly located in the region of Fengshen and presented a half-ring structure;if the region of Fengshen was selected for verification,most of the sensitivity areas were located in the region between the Fengshen and the subtropical high,far away from Fung-wong.This indicated that Fung-wong is mainly steered by Fengshen,but Fengshen is mainly affected by the subtropical high.The sensitivity experiment showed that the initial errors in the CNOP-identified sensitive areas have larger impacts on the verification-area prediction than those near the typhoon center and their developments take a large proportion in the whole domain.This suggests that the CNOP-identified sensitive areas do have large influence on the verification-area prediction.展开更多
Motion cueing algorithms(MCA)are often applied in the motion simulators.In this paper,a nonlinear optimal MCA,taking into account translational and rotational motions of a simulator within its physical limitation,is d...Motion cueing algorithms(MCA)are often applied in the motion simulators.In this paper,a nonlinear optimal MCA,taking into account translational and rotational motions of a simulator within its physical limitation,is designed for the motion platform aiming to minimize human’s perception error in order to provide a high degree of fidelity.Indeed,the movement sensation center of most MCA is placed at the center of the upper platform,which may cause a certain error.Pilot’s station should be paid full attention to in the MCA.Apart from this,the scaling and limiting module plays an important role in optimizing the motion platform workspace and reducing false cues during motion reproduction.It should be used along within the washout filter to decrease the amplitude of the translational and rotational motion signals uniformly across all frequencies through the MCA.A nonlinear scaling method is designed to accurately duplicate motions with high realistic behavior and use the platform more efficiently without violating its physical limitations.The simulation experiment is verified in the longitudinal/pitch direction for motion simulator.The result implies that the proposed method can not only overcome the problem of the workspace limitations in the simulator motion reproduction and improve the realism of movement sensation,but also reduce the false cues to improve dynamic fidelity during the motion simulation process.展开更多
Simulations and predictions using numerical models show considerable uncertainties,and parameter uncertainty is one of the most important sources.It is impractical to improve the simulation and prediction abilities by...Simulations and predictions using numerical models show considerable uncertainties,and parameter uncertainty is one of the most important sources.It is impractical to improve the simulation and prediction abilities by reducing the uncertainties of all parameters.Therefore,identifying the sensitive parameters or parameter combinations is crucial.This study proposes a novel approach:conditional nonlinear optimal perturbations sensitivity analysis(CNOPSA)method.The CNOPSA method fully considers the nonlinear synergistic effects of parameters in the whole parameter space and quantitatively estimates the maximum effects of parameter uncertainties,prone to extreme events.Results of the analytical g-function test indicate that the CNOPSA method can effectively identify the sensitivity of variables.Numerical results of the theoretical five-variable grassland ecosystem model show that the maximum influence of the simulated wilted biomass caused by parameter uncertainty can be estimated and computed by employing the CNOPSA method.The identified sensitive parameters can easily change the simulation or prediction of the wilted biomass,which affects the transformation of the grassland state in the grassland ecosystem.The variance-based approach may underestimate the parameter sensitivity because it only considers the influence of limited parameter samples from a statistical view.This study verifies that the CNOPSA method is effective and feasible for exploring the important and sensitive physical parameters or parameter combinations in numerical models.展开更多
Safety-critical control enables intelligent robots to have better secure operation and resistance to adverse environments, hence greatly enhancing their interaction and adaptability to the environment. In this paper, ...Safety-critical control enables intelligent robots to have better secure operation and resistance to adverse environments, hence greatly enhancing their interaction and adaptability to the environment. In this paper, we propose a safety-critical control scheme for robotic systems using an adaptive error elimination algorithm and optimization-based nonlinear optimal predictive control(NOPC) framework. The novelty of the proposed work lies in that an adaptive error elimination controller is designed to deal with the problem of stabilization of walking gait, which ensures that robot joint trajectory can compensate for the limitation of the template model. In order to be independent of system parameters and disturbances, a sliding mode controller is further designed under an uncertain environment. This approach takes into account simultaneously with foot position and orientation based on NOPC optimization. It tracks the modified trajectories constrained with the centroidal momentum dynamics. Finally, simulations is utilized to verify the efectiveness of the mentioned methods. The results indicate that the tracking efect of joint trajectory is better safety-critical nonlinear optimal predictive control with adaptive error elimination algorithm.展开更多
Intercepting high-maneuverability hypersonic targets in near-space environments poses significant challenges due to their extreme speeds and evasive capabilities.To address these challenges,this study presents an inte...Intercepting high-maneuverability hypersonic targets in near-space environments poses significant challenges due to their extreme speeds and evasive capabilities.To address these challenges,this study presents an integrated approach that combines a Three-Dimensional Finite-Time Optimal Cooperative Guidance Law(FTOC)with an Information Fusion Anti-saturation Predefined-time Observer(IFAPO).The proposed FTOC guidance law employs a nonlinear,non-quadratic finite-time optimal control strategy designed for rapid convergence within the limited timeframes of near-space interceptions,avoiding the need for remaining flight time estimation or linear decoupling inherent in traditional methods.To complement the guidance strategy,the IFAPO leverages multi-source information fusion theory and incorporates anti-saturation mechanisms to enhance target maneuver estimation.This method ensures accurate and real-time prediction of target acceleration while maintaining predefined convergence performance,even under complex interception conditions.By integrating the FTOC guidance law and IFAPO,the approach optimizes cooperative missile positioning,improves interception success rates,and minimizes fuel consumption,addressing practical constraints in military applications.Simulation results and comparative analyses confirm the effectiveness of the integrated approach,demonstrating its capability to achieve cooperative interception of highly maneuvering targets with enhanced efficiency and reduced economic costs,aligning with realistic combat scenarios.展开更多
The optimal control of nonlinear systems has been studied for years by many researchers. However, the application of optimal control problem to nonlinear non-affine systems needs more attention. In this paper we propo...The optimal control of nonlinear systems has been studied for years by many researchers. However, the application of optimal control problem to nonlinear non-affine systems needs more attention. In this paper we propose an optimal control design technique for a class of nonlinear and control non-affine equations. The dynamic equations of a flexible shaft supported by a pair of active magnetic bearings (AMBs) are used as the nonlinear control non-affine equations. Mathematical model for the flexible beam is chosen to be the well known Timoshenko beam model, which takes rotary inertia and shear deformations into account, and it is assumed that the shaft is supported by two frictionless bearings at the ends. The effective control of such systems is extremely important for very high angular velocity shafts which are a feature of many modern machines. The control must be able to cope with unbalanced masses and hence be very robust. We shall approach the problem by discretising the Timoshenko beam model and using standard difference formulae to develop a finite-dimensional model of the system. Then we use a recently developed technique for controlling nonlinear systems by reducing the problem to a sequence of linear time-varying (LTV) systems. An optimal control designed for each approximating linear, time-varying system and recent results show that this method will converge uniformly on compact time intervals to the optimal solution.展开更多
Conditional nonlinear optimal perturbation(CNOP) is an extension of the linear singular vector technique in the nonlinear regime.It represents the initial perturbation that is subjected to a given physical constraint,...Conditional nonlinear optimal perturbation(CNOP) is an extension of the linear singular vector technique in the nonlinear regime.It represents the initial perturbation that is subjected to a given physical constraint,and results in the largest nonlinear evolution at the prediction time.CNOP-type errors play an important role in the predictability of weather and climate.Generally,when calculating CNOP in a complicated numerical model,we need the gradient of the objective function with respect to the initial perturbations to provide the descent direction for searching the phase space.The adjoint technique is widely used to calculate the gradient of the objective function.However,it is difficult and cumbersome to construct the adjoint model of a complicated numerical model,which imposes a limitation on the application of CNOP.Based on previous research,this study proposes a new ensemble projection algorithm based on singular vector decomposition(SVD).The new algorithm avoids the localization procedure of previous ensemble projection algorithms,and overcomes the uncertainty caused by choosing the localization radius empirically.The new algorithm is applied to calculate the CNOP in an intermediate forecasting model.The results show that the CNOP obtained by the new ensemble-based algorithm can effectively approximate that calculated by the adjoint algorithm,and retains the general spatial characteristics of the latter.Hence,the new SVD-based ensemble projection algorithm proposed in this study is an effective method of approximating the CNOP.展开更多
This paper reviews progress in the application of conditional nonlinear optimal perturbation to targeted observation studies of the atmosphere and ocean in recent years, with a focus on the E1 Nifio-Southern Oscillati...This paper reviews progress in the application of conditional nonlinear optimal perturbation to targeted observation studies of the atmosphere and ocean in recent years, with a focus on the E1 Nifio-Southern Oscillation （ENSO）, Kuroshio path variations, and blocking events. Through studying the optimal precursor （OPR） and optimally growing initial error （OGE） of the occurrence of the above events, the similarity and localization features of OPR and OGE spatial structures have been found for each event. Ideal hindcasting experiments have shown that, if initial errors are reduced in the areas with the largest amplitude for the OPR and OGE for ENSO and Kuroshio path variations, the forecast skill of the model for these events is significantly improved. Due to the similarity between patterns of the OPR and OGE, additional observations implemented in the same sensitive region would help to not only capture the precursors, but also reduce the initial errors in the predictions, greatly increasing the forecast abilities. The similarity and localization of the spatial structures of the OPR and OGE during the onset of blocking events have also been investigated, but their application to targeted observation requires further study.展开更多
基金sponsored by the National Natural Science Foundation of China(Grant Nos.41930971,42330111,and 42405061)the National Key Scientific and Technological Infrastructure project“Earth System Numerical Simulation Facility”(Earth Lab).
文摘Orthogonal conditional nonlinear optimal perturbations(O-CNOPs)have been used to generate ensemble forecasting members for achieving high forecasting skill of high-impact weather and climate events.However,highly efficient calculations for O-CNOPs are still challenging in the field of ensemble forecasting.In this study,we combine a gradient-based iterative idea with the Gram‒Schmidt orthogonalization,and propose an iterative optimization method to compute O-CNOPs.This method is different from the original sequential optimization method,and allows parallel computations of O-CNOPs,thus saving a large amount of computational time.We evaluate this method by using the Lorenz-96 model on the basis of the ensemble forecasting ability achieved and on the time consumed for computing O-CNOPs.The results demonstrate that the parallel iterative method causes O-CNOPs to yield reliable ensemble members and to achieve ensemble forecasting skills similar to or even slightly higher than those produced by the sequential method.Moreover,the parallel method significantly reduces the computational time for O-CNOPs.Therefore,the parallel iterative method provides a highly effective and efficient approach for calculating O-CNOPs for ensemble forecasts.Expectedly,it can play an important role in the application of the O-CNOPs to realistic ensemble forecasts for high-impact weather and climate events.
基金supported by the National Natural Science Foundation of China (Grant No. 42288101, 42375062, 42476192, 42275158)the National Key Scientific and Technological Infrastructure project “Earth System Science Numerical Simulator Facility” (Earth Lab)the GHfund C (202407036001)
文摘The Conditional Nonlinear Optimal Perturbation(CNOP)method works essentially for conventional numerical models;however,it is not fully applicable to the commonly used deep-learning forecasting models(DLMs),which typically input multiple time slices without deterministic dependencies.In this study,the CNOP for DLMs(CNOP-DL)is proposed as an extension of the CNOP in the time dimension.This method is useful for targeted observations as it indicates not only where but also when to deploy additional observations.The CNOP-DL is calculated for a forecast case of sea surface temperature in the South China Sea with a DLM.The CNOP-DL identifies a sensitive area northwest of Palawan Island at the last input time.Sensitivity experiments demonstrate that the sensitive area identified by the CNOP-DL is effective not only for the CNOP-DL itself,but also for random perturbations.Therefore,this approach holds potential for guiding practical field campaigns.Notably,forecast errors are more sensitive to time than to location in the sensitive area.It highlights the crucial role of identifying the time of the sensitive area in targeted observations,corroborating the usefulness of extending the CNOP in the time dimension.
基金provided by the Knowledge Innovation Program of the Chinese Academy of Sciences(Grant No. KZCX2-EW-201)the Basic Research Program of Science and Technology Projects of Qingdao (Grant No.11-1-4-95-jch)the National Natural Science Foundation of China (Grant No. 40821092)
文摘A reduced-gravity barotropic shallow-water model was used to simulate the Kuroshio path variations. The results show that the model was able to capture the essential features of these path variations. We used one simulation of the model as the reference state and investigated the effects of errors in model parameters on the prediction of the transition to the Kuroshio large meander （KLM） state using the conditional nonlinear optimal parameter perturbation （CNOP-P） method. Because of their relatively large uncertainties, three model parameters were considered： the interracial friction coefficient, the wind-stress amplitude, and the lateral friction coefficient. We determined the CNOP-Ps optimized for each of these three parameters independently, and we optimized all three parameters simultaneously using the Spectral Projected Gradient 2 （SPG2） algorithm. Similarly, the impacts caused by errors in initial conditions were examined using the conditional nonlinear optimal initial perturbation （CNOP-I） method. Both the CNOP-I and CNOP-Ps can result in significant prediction errors of the KLM over a lead time of 240 days. But the prediction error caused by CNOP-I is greater than that caused by CNOP-P. The results of this study indicate not only that initial condition errors have greater effects on the prediction of the KLM than errors in model parameters but also that the latter cannot be ignored. Hence, to enhance the forecast skill of the KLM in this model, the initial conditions should first be improved, the model parameters should use the best possible estimates.
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provided by grants from National Natural Science Foundation of China (Grant Nos. 40905050and 40830955)the Chinese Academy of Sciences (CASGrant No. KZCX3-SW-230)
文摘Due to uncertainties in initial conditions and parameters, the stability and uncertainty of grassland ecosystem simulations using ecosystem models are issues of concern. Our objective is to determine the types and patterns of initial and parameter perturbations that yield the greatest instability and uncertainty in simulated grassland ecosystems using theoretical models. We used a nonlinear optimization approach, i.e., a conditional nonlinear optimal perturbation related to initial and parameter perturbations （CNOP） approach, in our work. Numerical results indicated that the CNOP showed a special and nonlinear optimal pattern when the initial state variables and multiple parameters were considered simultaneously. A visibly different complex optimal pattern characterizing the CNOPs was obtained by choosing different combinations of initial state variables and multiple parameters in different physical processes. We propose that the grassland modeled ecosystem caused by the CNOP-type perturbation is unstable and exhibits two aspects： abrupt change and the time needed for the abrupt change from a grassland equilibrium state to a desert equilibrium state when the initial state variables and multiple parameters are considered simultaneously. We compared these findings with results affected by the CNOPs obtained by considering only uncertainties in initial state variables and in a single parameter. The numerical results imply that the nonlinear optimal pattern of initial perturbations and parameter perturbations, especially for more parameters or when special parameters are involved, plays a key role in determining stabilities and uncertainties associated with a simulated or predicted grassland ecosystem.
基金supported by the National Natural Science Foundation of China(61573017 61703425)+2 种基金the Aeronautical Science Fund(20175796014)the Shaanxi Province Natural Science Foundation Research Project(2016JQ6062 2017JM6062)
文摘Platform planning is one of the important problems in the command and control(C2) field. Hereto, we analyze the platform planning problem and present nonlinear optimal model aiming at maximizing the task completion qualities. Firstly, we take into account the relation among tasks and build the single task nonlinear optimal model with a set of platform constraints. The Lagrange relaxation method and the pruning strategy are used to solve the model. Secondly, this paper presents optimization-based planning algorithms for efficiently allocating platforms to multiple tasks. To achieve the balance of the resource assignments among tasks, the m-best assignment algorithm and the pair-wise exchange(PWE)method are used to maximize multiple tasks completion qualities.Finally, a series of experiments are designed to verify the superiority and effectiveness of the proposed model and algorithms.
基金provided by grants from National Natural Science Foundation of China (Nos.40905050,40805020,40830955)the state Key Development Program for Basic Research (Grant No.2006CB400503)the KZCX3-SW-230 of the Chinese Academy of Sciences (CAS),LASG Free Exploration Fund,and LASG State Key Laboratory Special Fund
文摘The conditional nonlinear optimal perturbation （CNOP）, which is a nonlinear generalization of the linear singular vector （LSV）, is applied in important problems of atmospheric and oceanic sciences, including ENSO predictability, targeted observations, and ensemble forecast. In this study, we investigate the computational cost of obtaining the CNOP by several methods. Differences and similarities, in terms of the computational error and cost in obtaining the CNOP, are compared among the sequential quadratic programming （SQP） algorithm, the limited memory Broyden-Fletcher-Goldfarb-Shanno （L-BFGS） algorithm, and the spectral projected gradients （SPG2） algorithm. A theoretical grassland ecosystem model and the classical Lorenz model are used as examples. Numerical results demonstrate that the computational error is acceptable with all three algorithms. The computational cost to obtain the CNOP is reduced by using the SQP algorithm. The experimental results also reveal that the L-BFGS algorithm is the most effective algorithm among the three optimization algorithms for obtaining the CNOP. The numerical results suggest a new approach and algorithm for obtaining the CNOP for a large-scale optimization problem.
基金Supported by the NSF of Chian（4080502010702050+1 种基金60704015） Supported by the Natural Science Foundation of Henan Education Department（2010A100003）
文摘Using a simplified nonlinearly theoretical grassland ecosystem proposed by Zeng et al.,we study the sensitivity and nonlinear instability of the grassland ecosystem to finiteamplitude initial perturbations with the approach of conditional nonlinear optimal perturbation （CNOP）.The results show that the linearly stable grassland （desert or latent desert） states can turn to be nonlinearly unstable with finite amplitude initial perturbations.When the precipitation is between the two bifurcation points,a large enough finite amplitude initial perturbation can induce a transition between the grassland statethe desert state or the latent desert.
基金The work was jointly supported by the Chinese Academy of Sciences （Grant No. KZCX3-SW-230） the National Natural Science Foundation of China （Grant Nos. 40233029 and 40221503）
文摘A two-layer quasi-geostrophic model is used to study the stability and sensitivity of motions on smallscale vortices in Jupiter＇s atmosphere. Conditional nonlinear optimal perturbations （CNOPs） and linear singular vectors （LSVs） are both obtained numerically and compared in this paper. The results show that CNOPs can capture the nonlinear characteristics of motions in small-scale vortices in Jupiter＇s atmosphere and show great difference from LSVs under the condition that the initial constraint condition is large or the optimization time is not very short or both. Besides, in some basic states, local CNOPs are found. The pattern of LSV is more similar to local CNOP than global CNOP in some cases. The elementary application of the method of CNOP to the Jovian atmosphere helps us to explore the stability of variousscale motions of Jupiter＇s atmosphere and to compare the stability of motions in Jupiter＇s atmosphere and Earth＇s atmosphere further.
基金Application investigation of conditional nonlinear optimal perturbation in typhoon adaptive observation (40830955)
文摘In the typhoon adaptive observation based on conditional nonlinear optimal perturbation (CNOP), the ‘on-off’ switch caused by moist physical parameterization in prediction models prevents the conventional adjoint method from providing correct gradient during the optimization process. To address this problem, the capture of CNOP, when the "on-off" switches are included in models, is treated as non-smooth optimization in this study, and the genetic algorithm (GA) is introduced. After detailed algorithm procedures are formulated using an idealized model with parameterization "on-off" switches in the forcing term, the impacts of "on-off" switches on the capture of CNOP are analyzed, and three numerical experiments are conducted to check the effectiveness of GA in capturing CNOP and to analyze the impacts of different initial populations on the optimization result. The result shows that GA is competent for the capture of CNOP in the context of the idealized model with parameterization ‘on-off’ switches in this study. Finally, the advantages and disadvantages of GA in capturing CNOP are analyzed in detail.
基金supported by the National Natural Science Foundation of China(Nos.10632030,10902020,and 10721062)the Research Fund for the Doctoral Program of Higher Education of China(No.20070141067)+2 种基金the Doctoral Fund of Liaoning Province(No.20081091)the Key Laboratory Fund of Liaoning Province of China(No.2009S018)the Young Researcher Funds of Dalian University of Technology(No.SFDUT07002)
文摘By converting an optimal control problem for nonlinear systems to a Hamiltonian system,a symplecitc-preserving method is proposed.The state and costate variables are approximated by the Lagrange polynomial.The state variables at two ends of the time interval are taken as independent variables.Based on the dual variable principle,nonlinear optimal control problems are replaced with nonlinear equations.Furthermore,in the implementation of the symplectic algorithm,based on the 2N algorithm,a multilevel method is proposed.When the time grid is refined from low level to high level,the initial state and costate variables of the nonlinear equations can be obtained from the Lagrange interpolation at the low level grid to improve efficiency.Numerical simulations show the precision and the efficiency of the proposed algorithm in this paper.
基金National Natural Science Foundation of China(41105038)National Science and Technology Support Program(2012BAC22B03)
文摘The interaction between the typhoons Fengshen and Fung-wong over the Western Pacific in 2002 is studied with the Conditional Nonlinear Optimal Perturbation(CNOP) method.The study discovered that the CNOP method reveals the process of one-way interaction between Fengshen and Fung-wong.Moreover,if the region of Fung-wong was selected for verification,the sensitivity area was mainly located in the region of Fengshen and presented a half-ring structure;if the region of Fengshen was selected for verification,most of the sensitivity areas were located in the region between the Fengshen and the subtropical high,far away from Fung-wong.This indicated that Fung-wong is mainly steered by Fengshen,but Fengshen is mainly affected by the subtropical high.The sensitivity experiment showed that the initial errors in the CNOP-identified sensitive areas have larger impacts on the verification-area prediction than those near the typhoon center and their developments take a large proportion in the whole domain.This suggests that the CNOP-identified sensitive areas do have large influence on the verification-area prediction.
基金Supported by Natural Science Foundation of Hubei Province(2019CFB693)Scientific Research Guiding Project of Education Department of Hubei Province(B2020418)。
文摘Motion cueing algorithms(MCA)are often applied in the motion simulators.In this paper,a nonlinear optimal MCA,taking into account translational and rotational motions of a simulator within its physical limitation,is designed for the motion platform aiming to minimize human’s perception error in order to provide a high degree of fidelity.Indeed,the movement sensation center of most MCA is placed at the center of the upper platform,which may cause a certain error.Pilot’s station should be paid full attention to in the MCA.Apart from this,the scaling and limiting module plays an important role in optimizing the motion platform workspace and reducing false cues during motion reproduction.It should be used along within the washout filter to decrease the amplitude of the translational and rotational motion signals uniformly across all frequencies through the MCA.A nonlinear scaling method is designed to accurately duplicate motions with high realistic behavior and use the platform more efficiently without violating its physical limitations.The simulation experiment is verified in the longitudinal/pitch direction for motion simulator.The result implies that the proposed method can not only overcome the problem of the workspace limitations in the simulator motion reproduction and improve the realism of movement sensation,but also reduce the false cues to improve dynamic fidelity during the motion simulation process.
基金supported by the National Nature Science Foundation of China(41975132)the Guangdong Major Project of Basic and Applied Basic Research(Grant No.2020B0301030004).
文摘Simulations and predictions using numerical models show considerable uncertainties,and parameter uncertainty is one of the most important sources.It is impractical to improve the simulation and prediction abilities by reducing the uncertainties of all parameters.Therefore,identifying the sensitive parameters or parameter combinations is crucial.This study proposes a novel approach:conditional nonlinear optimal perturbations sensitivity analysis(CNOPSA)method.The CNOPSA method fully considers the nonlinear synergistic effects of parameters in the whole parameter space and quantitatively estimates the maximum effects of parameter uncertainties,prone to extreme events.Results of the analytical g-function test indicate that the CNOPSA method can effectively identify the sensitivity of variables.Numerical results of the theoretical five-variable grassland ecosystem model show that the maximum influence of the simulated wilted biomass caused by parameter uncertainty can be estimated and computed by employing the CNOPSA method.The identified sensitive parameters can easily change the simulation or prediction of the wilted biomass,which affects the transformation of the grassland state in the grassland ecosystem.The variance-based approach may underestimate the parameter sensitivity because it only considers the influence of limited parameter samples from a statistical view.This study verifies that the CNOPSA method is effective and feasible for exploring the important and sensitive physical parameters or parameter combinations in numerical models.
基金supported by the National Natural Science Foundation of China (No. 61573260,No. 62073245,No. U1713211)
文摘Safety-critical control enables intelligent robots to have better secure operation and resistance to adverse environments, hence greatly enhancing their interaction and adaptability to the environment. In this paper, we propose a safety-critical control scheme for robotic systems using an adaptive error elimination algorithm and optimization-based nonlinear optimal predictive control(NOPC) framework. The novelty of the proposed work lies in that an adaptive error elimination controller is designed to deal with the problem of stabilization of walking gait, which ensures that robot joint trajectory can compensate for the limitation of the template model. In order to be independent of system parameters and disturbances, a sliding mode controller is further designed under an uncertain environment. This approach takes into account simultaneously with foot position and orientation based on NOPC optimization. It tracks the modified trajectories constrained with the centroidal momentum dynamics. Finally, simulations is utilized to verify the efectiveness of the mentioned methods. The results indicate that the tracking efect of joint trajectory is better safety-critical nonlinear optimal predictive control with adaptive error elimination algorithm.
基金supported by the National Natural Science Foundation of China(Grant No.61773142).
文摘Intercepting high-maneuverability hypersonic targets in near-space environments poses significant challenges due to their extreme speeds and evasive capabilities.To address these challenges,this study presents an integrated approach that combines a Three-Dimensional Finite-Time Optimal Cooperative Guidance Law(FTOC)with an Information Fusion Anti-saturation Predefined-time Observer(IFAPO).The proposed FTOC guidance law employs a nonlinear,non-quadratic finite-time optimal control strategy designed for rapid convergence within the limited timeframes of near-space interceptions,avoiding the need for remaining flight time estimation or linear decoupling inherent in traditional methods.To complement the guidance strategy,the IFAPO leverages multi-source information fusion theory and incorporates anti-saturation mechanisms to enhance target maneuver estimation.This method ensures accurate and real-time prediction of target acceleration while maintaining predefined convergence performance,even under complex interception conditions.By integrating the FTOC guidance law and IFAPO,the approach optimizes cooperative missile positioning,improves interception success rates,and minimizes fuel consumption,addressing practical constraints in military applications.Simulation results and comparative analyses confirm the effectiveness of the integrated approach,demonstrating its capability to achieve cooperative interception of highly maneuvering targets with enhanced efficiency and reduced economic costs,aligning with realistic combat scenarios.
文摘The optimal control of nonlinear systems has been studied for years by many researchers. However, the application of optimal control problem to nonlinear non-affine systems needs more attention. In this paper we propose an optimal control design technique for a class of nonlinear and control non-affine equations. The dynamic equations of a flexible shaft supported by a pair of active magnetic bearings (AMBs) are used as the nonlinear control non-affine equations. Mathematical model for the flexible beam is chosen to be the well known Timoshenko beam model, which takes rotary inertia and shear deformations into account, and it is assumed that the shaft is supported by two frictionless bearings at the ends. The effective control of such systems is extremely important for very high angular velocity shafts which are a feature of many modern machines. The control must be able to cope with unbalanced masses and hence be very robust. We shall approach the problem by discretising the Timoshenko beam model and using standard difference formulae to develop a finite-dimensional model of the system. Then we use a recently developed technique for controlling nonlinear systems by reducing the problem to a sequence of linear time-varying (LTV) systems. An optimal control designed for each approximating linear, time-varying system and recent results show that this method will converge uniformly on compact time intervals to the optimal solution.
基金jointly sponsored by the National Natural Science Foundation of China(Grant Nos.41176013,41230420 and 41006007)
文摘Conditional nonlinear optimal perturbation(CNOP) is an extension of the linear singular vector technique in the nonlinear regime.It represents the initial perturbation that is subjected to a given physical constraint,and results in the largest nonlinear evolution at the prediction time.CNOP-type errors play an important role in the predictability of weather and climate.Generally,when calculating CNOP in a complicated numerical model,we need the gradient of the objective function with respect to the initial perturbations to provide the descent direction for searching the phase space.The adjoint technique is widely used to calculate the gradient of the objective function.However,it is difficult and cumbersome to construct the adjoint model of a complicated numerical model,which imposes a limitation on the application of CNOP.Based on previous research,this study proposes a new ensemble projection algorithm based on singular vector decomposition(SVD).The new algorithm avoids the localization procedure of previous ensemble projection algorithms,and overcomes the uncertainty caused by choosing the localization radius empirically.The new algorithm is applied to calculate the CNOP in an intermediate forecasting model.The results show that the CNOP obtained by the new ensemble-based algorithm can effectively approximate that calculated by the adjoint algorithm,and retains the general spatial characteristics of the latter.Hence,the new SVD-based ensemble projection algorithm proposed in this study is an effective method of approximating the CNOP.
基金Supported by the National Natural Science Foundation of China(41230420 and 41306023)China Meteorological Administration Special Public Welfare Research Fund(GYHY201306018)
文摘This paper reviews progress in the application of conditional nonlinear optimal perturbation to targeted observation studies of the atmosphere and ocean in recent years, with a focus on the E1 Nifio-Southern Oscillation （ENSO）, Kuroshio path variations, and blocking events. Through studying the optimal precursor （OPR） and optimally growing initial error （OGE） of the occurrence of the above events, the similarity and localization features of OPR and OGE spatial structures have been found for each event. Ideal hindcasting experiments have shown that, if initial errors are reduced in the areas with the largest amplitude for the OPR and OGE for ENSO and Kuroshio path variations, the forecast skill of the model for these events is significantly improved. Due to the similarity between patterns of the OPR and OGE, additional observations implemented in the same sensitive region would help to not only capture the precursors, but also reduce the initial errors in the predictions, greatly increasing the forecast abilities. The similarity and localization of the spatial structures of the OPR and OGE during the onset of blocking events have also been investigated, but their application to targeted observation requires further study.
