A support vector machine with guadratic polynomial kernel function based nonlinear model multi-step-ahead optimizing predictive controller was presented. A support vector machine based predictive model was established...A support vector machine with guadratic polynomial kernel function based nonlinear model multi-step-ahead optimizing predictive controller was presented. A support vector machine based predictive model was established by black-box identification. And a quadratic objective function with receding horizon was selected to obtain the controller output. By solving a nonlinear optimization problem with equality constraint of model output and boundary constraint of controller output using Nelder-Mead simplex direct search method, a sub-optimal control law was achieved in feature space. The effect of the controller was demonstrated on a recognized benchmark problem and a continuous-stirred tank reactor. The simulation results show that the multi-step-ahead predictive controller can be well applied to nonlinear system, with better performance in following reference trajectory and disturbance-rejection.展开更多
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
In recent years,numerous recurrent neural network(RNN)models have been reported for solving time-dependent nonlinear optimization problems.However,few existing RNN models simultaneously involve nonlinear equality cons...In recent years,numerous recurrent neural network(RNN)models have been reported for solving time-dependent nonlinear optimization problems.However,few existing RNN models simultaneously involve nonlinear equality constraints,direct discretization,and noise suppression.This limitation presents challenges when existing models are applied to practical engineering problems.Additionally,most current discrete-time RNN models are derived from continuous-time models,which may not perform well for solving essentially discrete problems.To handle these issues,a robust direct-discretized RNN(RDD-RNN)model is proposed to efficiently realize time-dependent optimization constrained by nonlinear equalities(TDOCNE)in the presence of various time-dependent noises.Theoretical analyses are provided to reveal that the proposed RDD-RNN model possesses excellent convergence and noise-suppressing capability.Furthermore,numerical experiments and manipulator control instances are conducted and analyzed to validate the superior robustness of the proposed RDD-RNN model under various time-dependent noises,particularly quadratic polynomial noise.Eventually,small target detection experiments further demonstrate the practicality of the RDD-RNN model in image processing applications.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
There are three common types of predictability problems in weather and climate, which each involve different constrained nonlinear optimization problems： the lower bound of maximum predictable time, the upper bound o...There are three common types of predictability problems in weather and climate, which each involve different constrained nonlinear optimization problems： the lower bound of maximum predictable time, the upper bound of maximum prediction error, and the lower bound of maximum allowable initial error and parameter error. Highly effcient algorithms have been developed to solve the second optimization problem. And this optimization problem can be used in realistic models for weather and climate to study the upper bound of the maximum prediction error. Although a filtering strategy has been adopted to solve the other two problems, direct solutions are very time-consuming even for a very simple model, which therefore limits the applicability of these two predictability problems in realistic models. In this paper, a new strategy is designed to solve these problems, involving the use of the existing highly effcient algorithms for the second predictability problem in particular. Furthermore, a series of comparisons between the older filtering strategy and the new method are performed. It is demonstrated that the new strategy not only outputs the same results as the old one, but is also more computationally effcient. This would suggest that it is possible to study the predictability problems associated with these two nonlinear optimization problems in realistic forecast models of weather or climate.展开更多
A control algorithm for improving vehicle handling was proposed by applying right angle to the steering wheel,based on the nonlinear adaptive optimal control(NAOC).A nonlinear 4-DOF model was initially developed,then ...A control algorithm for improving vehicle handling was proposed by applying right angle to the steering wheel,based on the nonlinear adaptive optimal control(NAOC).A nonlinear 4-DOF model was initially developed,then it was simplified to a 2-DOF model with reasonable assumptions to design observer and optimal controllers.Then a simplified model was developed for steering system.The numerical simulations were carried out using vehicle parameters for standard maneuvers in dry and wet road conditions.Moreover,the hardware in the loop method was implemented to prove the controller ability in realistic conditions.Simulation results obviously show the effectiveness of NAOC on vehicle handling and reveal that the proposed controller can significantly improve vehicle handling during severe maneuvers.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
Ship floating condition in regular waves is calculated. New equations controlling any ship＇s floating condition are proposed by use of the vector operation. This form is a nonlinear optimization problem which can be ...Ship floating condition in regular waves is calculated. New equations controlling any ship＇s floating condition are proposed by use of the vector operation. This form is a nonlinear optimization problem which can be solved using the penalty function method with constant coefficients. And the solving process is accelerated by dichotomy. During the solving process, the ship＇s displacement and buoyant centre have been calculated by the integration of the ship surface according to the waterline. The ship surface is described using an accumulative chord length theory in order to determine the displacement, the buoyancy center and the waterline. The draught forming the waterline at each station can be found out by calculating the intersection of the ship surface and the wave surface. The results of an example indicate that this method is exact and efficient. It can calculate the ship floating condition in regular waves as well as simplify the calculation and improve the computational efficiency and the precision of results.展开更多
Huge calculation burden and difficulty in convergence are the two central conundrums of nonlinear topology optimization(NTO).To this end,a multi-resolution nonlinear topology optimization(MR-NTO)method is proposed bas...Huge calculation burden and difficulty in convergence are the two central conundrums of nonlinear topology optimization(NTO).To this end,a multi-resolution nonlinear topology optimization(MR-NTO)method is proposed based on the multiresolution design strategy(MRDS)and the additive hyperelasticity technique(AHT),taking into account the geometric nonlinearity and material nonlinearity.The MR-NTO strategy is established in the framework of the solid isotropic material with penalization(SIMP)method,while the Neo-Hookean hyperelastic material model characterizes the material nonlinearity.The coarse analysis grid is employed for finite element(FE)calculation,and the fine material grid is applied to describe the material configuration.To alleviate the convergence problem and reduce sensitivity calculation complexity,the software ANSYS coupled with AHT is utilized to perform the nonlinear FE calculation.A strategy for redistributing strain energy is proposed during the sensitivity analysis,i.e.,transforming the strain energy of the analysis element into that of the material element,including Neo-Hooken and second-order Yeoh material.Numerical examples highlight three distinct advantages of the proposed method,i.e.,it can(1)significantly improve the computational efficiency,(2)make up for the shortcoming that NTO based on AHT may have difficulty in convergence when solving the NTO problem,especially for 3D problems,(3)successfully cope with high-resolution 3D complex NTO problems on a personal computer.展开更多
Nonlinear development of salinity perturbations in the Atlantic thermohaline circulation(THC) is investigated with a three-dimensional ocean circulation model,using the conditional nonlinear optimal perturbation metho...Nonlinear development of salinity perturbations in the Atlantic thermohaline circulation(THC) is investigated with a three-dimensional ocean circulation model,using the conditional nonlinear optimal perturbation method.The results show two types of optimal initial perturbations of sea surface salinity,one associated with freshwater and the other with salinity.Both types of perturbations excite decadal variability of the THC.Under the same amplitude of initial perturbation,the decadal variation induced by the freshwater perturbation is much stronger than that by the salinity perturbation,suggesting that the THC is more sensitive to freshwater than salinity perturbation.As the amplitude of initial perturbation increases,the decadal variations become stronger for both perturbations.For salinity perturbations,recovery time of the THC to return to steady state gradually saturates with increasing amplitude,whereas this recovery time increases remarkably for freshwater perturbations.A nonlinear(advective) feedback between density and velocity anomalies is proposed to explain these characteristics of decadal variability excitation.The results are consistent with previous ones from simple box models,and highlight the importance of nonlinear feedback in decadal THC variability.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 decadal variability of the North Atlantic thermohaline circulation(THC) is investigated within a three-dimensional ocean circulation model using the conditional nonlinear optimal perturbation method. The results s...The decadal variability of the North Atlantic thermohaline circulation(THC) is investigated within a three-dimensional ocean circulation model using the conditional nonlinear optimal perturbation method. The results show that the optimal initial perturbations of temperature and salinity exciting the strongest decadal THC variations have similar structures: the perturbations are mainly in the northwestern basin at a depth ranging from 1500 to 3000 m. These temperature and salinity perturbations act as the optimal precursors for future modifications of the THC, highlighting the importance of observations in the northwestern basin to monitor the variations of temperature and salinity at depth. The decadal THC variation in the nonlinear model initialized by the optimal salinity perturbations is much stronger than that caused by the optimal temperature perturbations, indicating that salinity variations might play a relatively important role in exciting the decadal THC variability. Moreover, the decadal THC variations in the tangent linear and nonlinear models show remarkably different characteristics, suggesting the importance of nonlinear processes in the decadal variability of the THC.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 new method to solve dynamic nonlinear constrained optimization problems （DNCOP） is proposed. First, the time （environment） variable period of DNCOP is divided into several equal subperiods. In each subperiod, th...A new method to solve dynamic nonlinear constrained optimization problems （DNCOP） is proposed. First, the time （environment） variable period of DNCOP is divided into several equal subperiods. In each subperiod, the DNCOP is approximated by a static nonlinear constrained optimization problem （SNCOP）. Second, for each SNCOP, inspired by the idea of multiobjective optimization, it is transformed into a static bi-objective optimization problem. As a result, the original DNCOP is approximately transformed into several static bi-objective optimization problems. Third, a new multiobjective evolutionary algorithm is proposed based on a new selection operator and an improved nonuniformity mutation operator. The simulation results indicate that the proposed algorithm is effective for DNCOP.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
This paper proposes a discrete-time robust control technique for an uncertain nonlinear system. The uncertainty mainly affects the system dynamics due to mismatched parameter variation which is bounded by a predefined...This paper proposes a discrete-time robust control technique for an uncertain nonlinear system. The uncertainty mainly affects the system dynamics due to mismatched parameter variation which is bounded by a predefined known function. In order to compensate the effect of uncertainty, a robust control input is derived by formulating an equivalent optimal control problem for a virtual nominal system with a modified costfunctional. To derive the stabilizing control law for a mismatched system, this paper introduces another control input named as virtual input. This virtual input is not applied directly to stabilize the uncertain system, rather it is used to define a sufficient condition. To solve the nonlinear optimal control problem, a discretetime general Hamilton-Jacobi-Bellman(DT-GHJB) equation is considered and it is approximated numerically through a neural network(NN) implementation. The approximated solution of DTGHJB is used to compute the suboptimal control input for the virtual system. The suboptimal inputs for the virtual system ensure the asymptotic stability of the closed-loop uncertain system. A numerical example is illustrated with simulation results to prove the efficacy of the proposed control algorithm.展开更多
文摘A support vector machine with guadratic polynomial kernel function based nonlinear model multi-step-ahead optimizing predictive controller was presented. A support vector machine based predictive model was established by black-box identification. And a quadratic objective function with receding horizon was selected to obtain the controller output. By solving a nonlinear optimization problem with equality constraint of model output and boundary constraint of controller output using Nelder-Mead simplex direct search method, a sub-optimal control law was achieved in feature space. The effect of the controller was demonstrated on a recognized benchmark problem and a continuous-stirred tank reactor. The simulation results show that the multi-step-ahead predictive controller can be well applied to nonlinear system, with better performance in following reference trajectory and disturbance-rejection.
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supported in part by the National Key Research and Development Program of China(2023YFC3011100)the National Natural Science Foundation of China(62476294)+1 种基金the Science and Technology Planning Project of Guangdong Province,China(2021B1212040017)the Guangdong Basic and Applied Basic Research Foundation(2025A1515010377,2023A1515110697).
文摘In recent years,numerous recurrent neural network(RNN)models have been reported for solving time-dependent nonlinear optimization problems.However,few existing RNN models simultaneously involve nonlinear equality constraints,direct discretization,and noise suppression.This limitation presents challenges when existing models are applied to practical engineering problems.Additionally,most current discrete-time RNN models are derived from continuous-time models,which may not perform well for solving essentially discrete problems.To handle these issues,a robust direct-discretized RNN(RDD-RNN)model is proposed to efficiently realize time-dependent optimization constrained by nonlinear equalities(TDOCNE)in the presence of various time-dependent noises.Theoretical analyses are provided to reveal that the proposed RDD-RNN model possesses excellent convergence and noise-suppressing capability.Furthermore,numerical experiments and manipulator control instances are conducted and analyzed to validate the superior robustness of the proposed RDD-RNN model under various time-dependent noises,particularly quadratic polynomial noise.Eventually,small target detection experiments further demonstrate the practicality of the RDD-RNN model in image processing applications.
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sponsored by the Key Knowledge Innovation Program of the Chinese Academy of Sciences (Grant. No. KZCX2-YW-QN203)the National Basic Research Program of China(2007CB411800),the GYHY200906009 of China Meteorological Administration
文摘There are three common types of predictability problems in weather and climate, which each involve different constrained nonlinear optimization problems： the lower bound of maximum predictable time, the upper bound of maximum prediction error, and the lower bound of maximum allowable initial error and parameter error. Highly effcient algorithms have been developed to solve the second optimization problem. And this optimization problem can be used in realistic models for weather and climate to study the upper bound of the maximum prediction error. Although a filtering strategy has been adopted to solve the other two problems, direct solutions are very time-consuming even for a very simple model, which therefore limits the applicability of these two predictability problems in realistic models. In this paper, a new strategy is designed to solve these problems, involving the use of the existing highly effcient algorithms for the second predictability problem in particular. Furthermore, a series of comparisons between the older filtering strategy and the new method are performed. It is demonstrated that the new strategy not only outputs the same results as the old one, but is also more computationally effcient. This would suggest that it is possible to study the predictability problems associated with these two nonlinear optimization problems in realistic forecast models of weather or climate.
文摘A control algorithm for improving vehicle handling was proposed by applying right angle to the steering wheel,based on the nonlinear adaptive optimal control(NAOC).A nonlinear 4-DOF model was initially developed,then it was simplified to a 2-DOF model with reasonable assumptions to design observer and optimal controllers.Then a simplified model was developed for steering system.The numerical simulations were carried out using vehicle parameters for standard maneuvers in dry and wet road conditions.Moreover,the hardware in the loop method was implemented to prove the controller ability in realistic conditions.Simulation results obviously show the effectiveness of NAOC on vehicle handling and reveal that the proposed controller can significantly improve vehicle handling during severe maneuvers.
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financially supported by the Science Fund for Creative Research Groups of the National Natural Science Foundation of China(Grant No.51321065)the Research Fund of State Key Laboratory of Ocean Engineering of Shanghai Jiao Tong University(Grant No.1104)
文摘Ship floating condition in regular waves is calculated. New equations controlling any ship＇s floating condition are proposed by use of the vector operation. This form is a nonlinear optimization problem which can be solved using the penalty function method with constant coefficients. And the solving process is accelerated by dichotomy. During the solving process, the ship＇s displacement and buoyant centre have been calculated by the integration of the ship surface according to the waterline. The ship surface is described using an accumulative chord length theory in order to determine the displacement, the buoyancy center and the waterline. The draught forming the waterline at each station can be found out by calculating the intersection of the ship surface and the wave surface. The results of an example indicate that this method is exact and efficient. It can calculate the ship floating condition in regular waves as well as simplify the calculation and improve the computational efficiency and the precision of results.
基金supported by the National Natural Science Foundation of China(Grant Nos.11902085 and 11832009)the Science and Technology Association Young Scientific and Technological Talents Support Project of Guangzhou City(Grant No.SKX20210304)the Natural Science Foundation of Guangdong Province(Grant No.2021Al515010320).
文摘Huge calculation burden and difficulty in convergence are the two central conundrums of nonlinear topology optimization(NTO).To this end,a multi-resolution nonlinear topology optimization(MR-NTO)method is proposed based on the multiresolution design strategy(MRDS)and the additive hyperelasticity technique(AHT),taking into account the geometric nonlinearity and material nonlinearity.The MR-NTO strategy is established in the framework of the solid isotropic material with penalization(SIMP)method,while the Neo-Hookean hyperelastic material model characterizes the material nonlinearity.The coarse analysis grid is employed for finite element(FE)calculation,and the fine material grid is applied to describe the material configuration.To alleviate the convergence problem and reduce sensitivity calculation complexity,the software ANSYS coupled with AHT is utilized to perform the nonlinear FE calculation.A strategy for redistributing strain energy is proposed during the sensitivity analysis,i.e.,transforming the strain energy of the analysis element into that of the material element,including Neo-Hooken and second-order Yeoh material.Numerical examples highlight three distinct advantages of the proposed method,i.e.,it can(1)significantly improve the computational efficiency,(2)make up for the shortcoming that NTO based on AHT may have difficulty in convergence when solving the NTO problem,especially for 3D problems,(3)successfully cope with high-resolution 3D complex NTO problems on a personal computer.
基金Supported by the National Basic Research Program of China(973 Program)(No.2012CB417404)
文摘Nonlinear development of salinity perturbations in the Atlantic thermohaline circulation(THC) is investigated with a three-dimensional ocean circulation model,using the conditional nonlinear optimal perturbation method.The results show two types of optimal initial perturbations of sea surface salinity,one associated with freshwater and the other with salinity.Both types of perturbations excite decadal variability of the THC.Under the same amplitude of initial perturbation,the decadal variation induced by the freshwater perturbation is much stronger than that by the salinity perturbation,suggesting that the THC is more sensitive to freshwater than salinity perturbation.As the amplitude of initial perturbation increases,the decadal variations become stronger for both perturbations.For salinity perturbations,recovery time of the THC to return to steady state gradually saturates with increasing amplitude,whereas this recovery time increases remarkably for freshwater perturbations.A nonlinear(advective) feedback between density and velocity anomalies is proposed to explain these characteristics of decadal variability excitation.The results are consistent with previous ones from simple box models,and highlight the importance of nonlinear feedback in decadal THC variability.
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supported by the National Basic Research Program of China(973 Program,Grant No.2012CB417404)
文摘The decadal variability of the North Atlantic thermohaline circulation(THC) is investigated within a three-dimensional ocean circulation model using the conditional nonlinear optimal perturbation method. The results show that the optimal initial perturbations of temperature and salinity exciting the strongest decadal THC variations have similar structures: the perturbations are mainly in the northwestern basin at a depth ranging from 1500 to 3000 m. These temperature and salinity perturbations act as the optimal precursors for future modifications of the THC, highlighting the importance of observations in the northwestern basin to monitor the variations of temperature and salinity at depth. The decadal THC variation in the nonlinear model initialized by the optimal salinity perturbations is much stronger than that caused by the optimal temperature perturbations, indicating that salinity variations might play a relatively important role in exciting the decadal THC variability. Moreover, the decadal THC variations in the tangent linear and nonlinear models show remarkably different characteristics, suggesting the importance of nonlinear processes in the decadal variability of the THC.
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supported by the National Natural Science Foundation of China (60374063)the Natural Science Basic Research Plan Project in Shaanxi Province (2006A12)+1 种基金the Science and Technology Research Project of the Educational Department in Shaanxi Province (07JK180)the Emphasis Research Plan Project of Baoji University of Arts and Science (ZK0840)
文摘A new method to solve dynamic nonlinear constrained optimization problems （DNCOP） is proposed. First, the time （environment） variable period of DNCOP is divided into several equal subperiods. In each subperiod, the DNCOP is approximated by a static nonlinear constrained optimization problem （SNCOP）. Second, for each SNCOP, inspired by the idea of multiobjective optimization, it is transformed into a static bi-objective optimization problem. As a result, the original DNCOP is approximately transformed into several static bi-objective optimization problems. Third, a new multiobjective evolutionary algorithm is proposed based on a new selection operator and an improved nonuniformity mutation operator. The simulation results indicate that the proposed algorithm is effective for DNCOP.
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.
文摘This paper proposes a discrete-time robust control technique for an uncertain nonlinear system. The uncertainty mainly affects the system dynamics due to mismatched parameter variation which is bounded by a predefined known function. In order to compensate the effect of uncertainty, a robust control input is derived by formulating an equivalent optimal control problem for a virtual nominal system with a modified costfunctional. To derive the stabilizing control law for a mismatched system, this paper introduces another control input named as virtual input. This virtual input is not applied directly to stabilize the uncertain system, rather it is used to define a sufficient condition. To solve the nonlinear optimal control problem, a discretetime general Hamilton-Jacobi-Bellman(DT-GHJB) equation is considered and it is approximated numerically through a neural network(NN) implementation. The approximated solution of DTGHJB is used to compute the suboptimal control input for the virtual system. The suboptimal inputs for the virtual system ensure the asymptotic stability of the closed-loop uncertain system. A numerical example is illustrated with simulation results to prove the efficacy of the proposed control algorithm.
