The problem of linear time-varying（LTV） system modal analysis is considered based on time-dependent state space representations, as classical modal analysis of linear time-invariant systems and current LTV system mo...The problem of linear time-varying（LTV） system modal analysis is considered based on time-dependent state space representations, as classical modal analysis of linear time-invariant systems and current LTV system modal analysis under the ＂frozen-time＂ assumption are not able to determine the dynamic stability of LTV systems. Time-dependent state space representations of LTV systems are first introduced, and the corresponding modal analysis theories are subsequently presented via a stabilitypreserving state transformation. The time-varying modes of LTV systems are extended in terms of uniqueness, and are further interpreted to determine the system＇s stability. An extended modal identification is proposed to estimate the time-varying modes, consisting of the estimation of the state transition matrix via a subspace-based method and the extraction of the time-varying modes by the QR decomposition. The proposed approach is numerically validated by three numerical cases, and is experimentally validated by a coupled moving-mass simply supported beam exper- imental case. The proposed approach is capable of accurately estimating the time-varying modes, and provides anew way to determine the dynamic stability of LTV systems by using the estimated time-varying modes.展开更多
Many complex systems are frequently subject to the influence of uncertain disturbances,which can exert a profound effect on the critical transitions(CTs),potentially resulting in catastrophic consequences.Consequently...Many complex systems are frequently subject to the influence of uncertain disturbances,which can exert a profound effect on the critical transitions(CTs),potentially resulting in catastrophic consequences.Consequently,it is of uttermost importance to provide warnings for noise-induced CTs in various applications.Although capturing certain generic symptoms of transition behaviors from observational and simulated data poses a challenging problem,this work attempts to extract information regarding CTs from simulated data of a Gaussian white noise-induced tri-stable system.Using the extended dynamic mode decomposition(EDMD)algorithm,we initially obtain finite-dimensional approximations of both the stochastic Koopman operator and the generator.Subsequently,the drift parameters and the noise intensity within the system are identified from the simulated data.Utilizing the identified system,the parameter-dependent basin of the unsafe regime(PDBUR)is quantified,enabling data-driven early warning of Gaussian white noise-induced CTs.Finally,an error analysis is carried out to verify the effectiveness of the data-driven results.Our findings may serve as a paradigm for understanding and predicting noise-induced CTs in complex systems based on data.展开更多
Nonlinear dynamic inversion(NDI)has been applied to the control law design of quad-rotors mainly thanks to its good robustness and simplicity of parameter tuning.However,the weakness of relying on accurate model great...Nonlinear dynamic inversion(NDI)has been applied to the control law design of quad-rotors mainly thanks to its good robustness and simplicity of parameter tuning.However,the weakness of relying on accurate model greatly restrains its application on quad-rotors,especially nano quad-rotors(NQRs).NQRs are easy to be influenced by uncertainties such as model uncertainties(mainly from complicated aerodynamic interferences,strong coupling in roll-pitch-yaw channels and inaccurate aerodynamic prediction of rotors)and external uncertainties(mainly from winds or gusts),particularly persistent ones.Therefore,developing accurate model for altitude and attitude control of NQRs is difficult.To solve this problem,in this paper,an improved nonlinear dynamic inversion(INDI)method is developed,which can reject the above-mentioned uncertainties by estimating them and then counteracting in real time using linear extended state observer(LESO).Comparison with the traditional NDI(TNDI)method was carried out numerically,and the results show that,in coping with persistent uncertainties,the INDI-based method presents significant superiority.展开更多
Global bifurcations and multi-pulse chaotic dynamics for a simply supported rectangular thin plate are studied by the extended Melnikov method. The rectangular thin plate is subject to transversal and in-plane excitat...Global bifurcations and multi-pulse chaotic dynamics for a simply supported rectangular thin plate are studied by the extended Melnikov method. The rectangular thin plate is subject to transversal and in-plane excitation. A two-degree-of-freedom nonlinear nonautonomous system governing equations of motion for the rectangular thin plate is derived by the von Karman type equation and the Galerkin approach. A one-to- one internal resonance is considered. An averaged equation is obtained with a multi-scale method. After transforming the averaged equation into a standard form, the extended Melnikov method is used to show the existence of multi-pulse chaotic dynamics, which can be used to explain the mechanism of modal interactions of thin plates. A method for calculating the Melnikov function is given without an explicit analytical expression of homoclinic orbits. Furthermore, restrictions on the damping, excitation, and detuning parameters are obtained, under which the multi-pulse chaotic dynamics is expected. The results of numerical simulations are also given to indicate the existence of small amplitude multi-pulse chaotic responses for the rectangular thin plate.展开更多
The approach to the synthesis of autopilot with aerody- namic uncertainty is investigated in order to achieve large maneu- verability of agile missiles. The dynamics of the agile missile with reaction-jet control syst...The approach to the synthesis of autopilot with aerody- namic uncertainty is investigated in order to achieve large maneu- verability of agile missiles. The dynamics of the agile missile with reaction-jet control system （RCS） are presented. Subsequently, the cascade control scheme based on the bank-to-turn （B-I-T） steering technique is described. To address the aerodynamic un- certainties encountered by the control system, the active distur- bance rejection control （ADRC） method is introduced in the autopi- lot design. Furthermore, a compound controller, using extended state observer （ESO） to online estimate system uncertainties and calculate derivative of command signals, is designed based on dynamic surface control （DSC）. Nonlinear simulation results show the feasibility of the proposed approach and validate the robust- ness of the controller with severe unmodeled dynamics.展开更多
A high-speed dynamic-range-extended white light interferometry(HS-DRE-WLI) system is developed for fast,high-resolution 3D surface profiling across varying reflectance levels. The system combines high-speed fiber-stre...A high-speed dynamic-range-extended white light interferometry(HS-DRE-WLI) system is developed for fast,high-resolution 3D surface profiling across varying reflectance levels. The system combines high-speed fiber-stretcher-based optical path difference modulation with an asymmetric line-illumination technique to enhance imaging speed and dynamic range. Chromatic and polarization-induced distortions are minimized through dispersion compensation using optimized fiber lengths and a Faraday rotator, achieving 14.2-μm axial resolution. Validated on diverse samples, the system captures fine and large-scale features with high fidelity,demonstrating strong potential for industrial and biomedical applications requiring accurate, robust surface measurements.展开更多
Variables fields such as enstrophy, meridional-wind and zonal-wind variables are derived from monthly 500 hPa geopotential height anomalous fields. In this work, we select original predictors from monthly 500-hPa geop...Variables fields such as enstrophy, meridional-wind and zonal-wind variables are derived from monthly 500 hPa geopotential height anomalous fields. In this work, we select original predictors from monthly 500-hPa geopotential height anomalous fields and their variables in June of 1958 - 2001, and determine comprehensive predictors by conducting empirical orthogonal function (EOF) respectively with the original predictors. A downscaling forecast model based on the back propagation (BP) neural network is built by use of the comprehensive predictors to predict the monthly precipitation in June over Guangxi with the monthly dynamic extended range forecast products. For comparison, we also build another BP neural network model with the same predictands by using the former comprehensive predictors selected from 500-hPa geopotential height anomalous fields in May to December of 1957 - 2000 and January to April of 1958 - 2001. The two models are tested and results show that the precision of superposition of the downscaling model is better than that of the one based on former comprehensive predictors, but the prediction accuracy of the downscaling model depends on the output of monthly dynamic extended range forecast.展开更多
Identification of the splice sites is a critical and tough issue in eukaryotic genome annotation. Here, a statistical study is introduced for detecting the splicing signals in the human hemoglobin （Hb） pre-mRNAs by ...Identification of the splice sites is a critical and tough issue in eukaryotic genome annotation. Here, a statistical study is introduced for detecting the splicing signals in the human hemoglobin （Hb） pre-mRNAs by using the approaches of regional pairwise alignment, splicing weight matrix scoring, and dynamic extended folding. First, the regional pairwise alignment results show that the coding regions of the human Hb genes are at a high level for both conservation and fluctuation. Second, the weighted matrix scoring results indicate that, although the authentic splicing motifs are always scored the highest in a sequence, the sequence motif alone is inadequate to precisely define the splice sites. Finally, we deduce the RNA frame structures by applying an extended folding approach to analyze the stable folding elements. We find out that the splice sequences tend to take stretching and partially paired conformations, which benefit recognition and competitive binding of the splicing factors. These results indicate that precise splicing is an integrated effect of multiple mechanisms of signal recognition at the level of sequence and structure.展开更多
This study presents a conceptual design for a cost-effective submersible gravity-type fish cage with a single-point mooring design.The performance of the new design in reducing environmental loads under extreme sea co...This study presents a conceptual design for a cost-effective submersible gravity-type fish cage with a single-point mooring design.The performance of the new design in reducing environmental loads under extreme sea con-ditions is demonstrated using an in-house numerical code package.The effectiveness of the submerging and surfacing operations of the fish cages is validated through numerical simulations.In the present code package,irregular wave modelling is employed to generate the wave elevations,velocities and accelerations,and the hydrodynamic forces acting on the fish cages and mooring system are calculated using the Morison model.A submersible model for the floating collar is developed to simulate the submerging and surfacing operations of the fish cages.The deformations of the fish cage system are calculated using a modified extended position based dynamics(XPBD)method combined with a mode superposition method.Results show that tension in the mooring system is significantly reduced when fish cages are submerged in the water layer with lower current speeds,and extending the buoy line to lower the conjunction point helps maintain fish cages in the desired water layer under extreme sea conditions.Flooding the outer tubes of the floating collar allows the fish cages to smoothly submerge to the desired water depth.The surfacing designs based on the compressed air and the lifting operation of the bottom sinker can enable the cages to ascend to the water surface.The submerging and surface operations are proved to be completed within six minutes.The new design based on the lifting operation of the bottom sinker,is safer and more cost-effective than the design based on compressed air for the surfacing operation.The design of the submersible single-point mooring gravity-type fish cage is thereby validated through the present numerical methods,offering valuable insights for future aquaculture design and implementation.展开更多
Systematic errors have recently been founded to be distinct in the zonal mean component forecasts, which account for a large portion of the total monthly-mean forecast errors. To overcome the difficulty of numerical m...Systematic errors have recently been founded to be distinct in the zonal mean component forecasts, which account for a large portion of the total monthly-mean forecast errors. To overcome the difficulty of numerical model, the monthly pentad-mean nonlinear dynamic regional prediction models of the zonal mean geopotential height at 200, 300, 500, and 700 hPa based on a large number of historical data （NCEP/NCAR reanalysis data） were constituted by employing the local approximation of the phase space reconstruction theory and nonlinear spatio-temporal series prediction method. The 12-month forecast experiments of 1996 indicated that the results of the nonlinear model are better than those of the persistent, climatic prediction, and T42L9 model either over the high- and mid-latitude areas of the Northern and Southern Hemispheres or the tropical area. The root-mean-square of the monthly-mean height of T42L9 model was considerably decreased with a change of 30.4%, 26.6%, 82.6%, and 39.4%, respectively, over the high- and mid-latitudes of the Northern Hemisphere, over the high- and mid-latitudes of the Southern Hemisphere, over the tropics and over the globe, and also the corresponding anomaly correlation coefficients over the four areas were respectively increased by 0.306-0.312, 0.304-0.429, 0.739-0.746, and 0.360-0.400 （averagely a relative change of 11.0% over the globe） by nonlinear correction after integration, implying that the forecasts given by nonlinear model include more useful information than those of T42L9 model.展开更多
Based on Chen et al. （2006）, the scheme of the combination of the pentad-mean zonal height departure nonlinear prediction with the T42L9 model prediction was designed, in which the pentad zonal heights at all the 12...Based on Chen et al. （2006）, the scheme of the combination of the pentad-mean zonal height departure nonlinear prediction with the T42L9 model prediction was designed, in which the pentad zonal heights at all the 12-initial-value-input isobar levels from 50 hPa to 1000 hPa except 200, 300, 500, and 700 hPa were derived from nonlinear forecasts of the four levels by means of a good correlation between neighboring levels. Then the above pentad zonal heights at 12 isobar-levels were transformed to the spectrum coefficients of the temperature at each integration step of T42L9 model. At last, the nudging was made. On account of a variety of error accumulation, the pentad zonal components of the monthly height at isobar levels output by T42L9 model were replaced by the corresponding nonlinear results once more when integration was over. Multiple case experiments showed that such combination of two kinds of prediction made an improvement in the wave component as a result of wave-flow nonlinear interaction while reducing the systematical forecast errors. Namely the monthly-mean height anomaly correlation coefficients over the high- and mid-latitudes of the Northern Hemisphere, over the Southern Hemisphere and over the globe increased respectively from 0.249 to 0.347, from 0.286 to 0.387, and from 0.343 to 0.414 （relative changes of 31.5%, 41.0%, and 18.3%）. The monthly-mean root-mean-square error （RMSE） of T42L9 model over the three areas was considerably decreased, the relative change over the globe reached 44.2%. The monthly-mean anomaly correlation coeffi- cients of wave 4-9 over the areas were up to 0.392, 0.200, and 0.295, with the relative change of 53.8%, 94.1%, and 61.2%, and correspondingly their RMSEs were decreased respectively with the rate of 8.5%, 6.3%, and 8.1%. At the same time the monthly-mean pattern of parts of cases were presented better.展开更多
基金Supported by the China Scholarship Council,National Natural Science Foundation of China(Grant No.11402022)the Interuniversity Attraction Poles Programme of the Belgian Science Policy Office(DYSCO)+1 种基金the Fund for Scientific Research–Flanders(FWO)the Research Fund KU Leuven
文摘The problem of linear time-varying（LTV） system modal analysis is considered based on time-dependent state space representations, as classical modal analysis of linear time-invariant systems and current LTV system modal analysis under the ＂frozen-time＂ assumption are not able to determine the dynamic stability of LTV systems. Time-dependent state space representations of LTV systems are first introduced, and the corresponding modal analysis theories are subsequently presented via a stabilitypreserving state transformation. The time-varying modes of LTV systems are extended in terms of uniqueness, and are further interpreted to determine the system＇s stability. An extended modal identification is proposed to estimate the time-varying modes, consisting of the estimation of the state transition matrix via a subspace-based method and the extraction of the time-varying modes by the QR decomposition. The proposed approach is numerically validated by three numerical cases, and is experimentally validated by a coupled moving-mass simply supported beam exper- imental case. The proposed approach is capable of accurately estimating the time-varying modes, and provides anew way to determine the dynamic stability of LTV systems by using the estimated time-varying modes.
基金Project supported by the National Natural Science Foundation of China(No.12402033)the National Natural Science Foundation for Distinguished Young Scholars of China(No.52225211)。
文摘Many complex systems are frequently subject to the influence of uncertain disturbances,which can exert a profound effect on the critical transitions(CTs),potentially resulting in catastrophic consequences.Consequently,it is of uttermost importance to provide warnings for noise-induced CTs in various applications.Although capturing certain generic symptoms of transition behaviors from observational and simulated data poses a challenging problem,this work attempts to extract information regarding CTs from simulated data of a Gaussian white noise-induced tri-stable system.Using the extended dynamic mode decomposition(EDMD)algorithm,we initially obtain finite-dimensional approximations of both the stochastic Koopman operator and the generator.Subsequently,the drift parameters and the noise intensity within the system are identified from the simulated data.Utilizing the identified system,the parameter-dependent basin of the unsafe regime(PDBUR)is quantified,enabling data-driven early warning of Gaussian white noise-induced CTs.Finally,an error analysis is carried out to verify the effectiveness of the data-driven results.Our findings may serve as a paradigm for understanding and predicting noise-induced CTs in complex systems based on data.
基金supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD)the Advanced Research Project of Army Equipment Development(No.301020803)
文摘Nonlinear dynamic inversion(NDI)has been applied to the control law design of quad-rotors mainly thanks to its good robustness and simplicity of parameter tuning.However,the weakness of relying on accurate model greatly restrains its application on quad-rotors,especially nano quad-rotors(NQRs).NQRs are easy to be influenced by uncertainties such as model uncertainties(mainly from complicated aerodynamic interferences,strong coupling in roll-pitch-yaw channels and inaccurate aerodynamic prediction of rotors)and external uncertainties(mainly from winds or gusts),particularly persistent ones.Therefore,developing accurate model for altitude and attitude control of NQRs is difficult.To solve this problem,in this paper,an improved nonlinear dynamic inversion(INDI)method is developed,which can reject the above-mentioned uncertainties by estimating them and then counteracting in real time using linear extended state observer(LESO).Comparison with the traditional NDI(TNDI)method was carried out numerically,and the results show that,in coping with persistent uncertainties,the INDI-based method presents significant superiority.
基金Project supported the National Natural Science Foundation of China (Nos. 10732020,11072008,and 11102226)the Scientific Research Foundation of Civil Aviation University of China (No. 2010QD04X)the Fundamental Research Funds for the Central Universities of China (Nos. ZXH2011D006 and ZXH2012K004)
文摘Global bifurcations and multi-pulse chaotic dynamics for a simply supported rectangular thin plate are studied by the extended Melnikov method. The rectangular thin plate is subject to transversal and in-plane excitation. A two-degree-of-freedom nonlinear nonautonomous system governing equations of motion for the rectangular thin plate is derived by the von Karman type equation and the Galerkin approach. A one-to- one internal resonance is considered. An averaged equation is obtained with a multi-scale method. After transforming the averaged equation into a standard form, the extended Melnikov method is used to show the existence of multi-pulse chaotic dynamics, which can be used to explain the mechanism of modal interactions of thin plates. A method for calculating the Melnikov function is given without an explicit analytical expression of homoclinic orbits. Furthermore, restrictions on the damping, excitation, and detuning parameters are obtained, under which the multi-pulse chaotic dynamics is expected. The results of numerical simulations are also given to indicate the existence of small amplitude multi-pulse chaotic responses for the rectangular thin plate.
基金supported by the National Natural Science Foundation of China(11202024)
文摘The approach to the synthesis of autopilot with aerody- namic uncertainty is investigated in order to achieve large maneu- verability of agile missiles. The dynamics of the agile missile with reaction-jet control system （RCS） are presented. Subsequently, the cascade control scheme based on the bank-to-turn （B-I-T） steering technique is described. To address the aerodynamic un- certainties encountered by the control system, the active distur- bance rejection control （ADRC） method is introduced in the autopi- lot design. Furthermore, a compound controller, using extended state observer （ESO） to online estimate system uncertainties and calculate derivative of command signals, is designed based on dynamic surface control （DSC）. Nonlinear simulation results show the feasibility of the proposed approach and validate the robust- ness of the controller with severe unmodeled dynamics.
基金National Research Foundation of Korea(NRFRS-2021-NR060086)Korea Evaluation Institute of Industrial Technology(1415181752)Institute of Civil-Military Technology Cooperation(23-SF-EL-09).
文摘A high-speed dynamic-range-extended white light interferometry(HS-DRE-WLI) system is developed for fast,high-resolution 3D surface profiling across varying reflectance levels. The system combines high-speed fiber-stretcher-based optical path difference modulation with an asymmetric line-illumination technique to enhance imaging speed and dynamic range. Chromatic and polarization-induced distortions are minimized through dispersion compensation using optimized fiber lengths and a Faraday rotator, achieving 14.2-μm axial resolution. Validated on diverse samples, the system captures fine and large-scale features with high fidelity,demonstrating strong potential for industrial and biomedical applications requiring accurate, robust surface measurements.
基金Publicity of New Techniques of China Meteorological Administration (CMATG2005M38)
文摘Variables fields such as enstrophy, meridional-wind and zonal-wind variables are derived from monthly 500 hPa geopotential height anomalous fields. In this work, we select original predictors from monthly 500-hPa geopotential height anomalous fields and their variables in June of 1958 - 2001, and determine comprehensive predictors by conducting empirical orthogonal function (EOF) respectively with the original predictors. A downscaling forecast model based on the back propagation (BP) neural network is built by use of the comprehensive predictors to predict the monthly precipitation in June over Guangxi with the monthly dynamic extended range forecast products. For comparison, we also build another BP neural network model with the same predictands by using the former comprehensive predictors selected from 500-hPa geopotential height anomalous fields in May to December of 1957 - 2000 and January to April of 1958 - 2001. The two models are tested and results show that the precision of superposition of the downscaling model is better than that of the one based on former comprehensive predictors, but the prediction accuracy of the downscaling model depends on the output of monthly dynamic extended range forecast.
基金Supported by the National Natural Science Foundation of China (30971454, 9030318, and 90208018)
文摘Identification of the splice sites is a critical and tough issue in eukaryotic genome annotation. Here, a statistical study is introduced for detecting the splicing signals in the human hemoglobin （Hb） pre-mRNAs by using the approaches of regional pairwise alignment, splicing weight matrix scoring, and dynamic extended folding. First, the regional pairwise alignment results show that the coding regions of the human Hb genes are at a high level for both conservation and fluctuation. Second, the weighted matrix scoring results indicate that, although the authentic splicing motifs are always scored the highest in a sequence, the sequence motif alone is inadequate to precisely define the splice sites. Finally, we deduce the RNA frame structures by applying an extended folding approach to analyze the stable folding elements. We find out that the splice sequences tend to take stretching and partially paired conformations, which benefit recognition and competitive binding of the splicing factors. These results indicate that precise splicing is an integrated effect of multiple mechanisms of signal recognition at the level of sequence and structure.
基金supported by the Research Council of Norway through the project“Unleashing the sustainable value creation potential of offshore ocean aquaculture”(Project number:328724).
文摘This study presents a conceptual design for a cost-effective submersible gravity-type fish cage with a single-point mooring design.The performance of the new design in reducing environmental loads under extreme sea con-ditions is demonstrated using an in-house numerical code package.The effectiveness of the submerging and surfacing operations of the fish cages is validated through numerical simulations.In the present code package,irregular wave modelling is employed to generate the wave elevations,velocities and accelerations,and the hydrodynamic forces acting on the fish cages and mooring system are calculated using the Morison model.A submersible model for the floating collar is developed to simulate the submerging and surfacing operations of the fish cages.The deformations of the fish cage system are calculated using a modified extended position based dynamics(XPBD)method combined with a mode superposition method.Results show that tension in the mooring system is significantly reduced when fish cages are submerged in the water layer with lower current speeds,and extending the buoy line to lower the conjunction point helps maintain fish cages in the desired water layer under extreme sea conditions.Flooding the outer tubes of the floating collar allows the fish cages to smoothly submerge to the desired water depth.The surfacing designs based on the compressed air and the lifting operation of the bottom sinker can enable the cages to ascend to the water surface.The submerging and surface operations are proved to be completed within six minutes.The new design based on the lifting operation of the bottom sinker,is safer and more cost-effective than the design based on compressed air for the surfacing operation.The design of the submersible single-point mooring gravity-type fish cage is thereby validated through the present numerical methods,offering valuable insights for future aquaculture design and implementation.
基金Supported by the National Natural Science Foundation of China under Grant No. 40175013the National Key Project for Development of Science and Technology (96-908-02-01)the Project of Chinese Academy of Sciences (ZKCX2-SW-210).
文摘Systematic errors have recently been founded to be distinct in the zonal mean component forecasts, which account for a large portion of the total monthly-mean forecast errors. To overcome the difficulty of numerical model, the monthly pentad-mean nonlinear dynamic regional prediction models of the zonal mean geopotential height at 200, 300, 500, and 700 hPa based on a large number of historical data （NCEP/NCAR reanalysis data） were constituted by employing the local approximation of the phase space reconstruction theory and nonlinear spatio-temporal series prediction method. The 12-month forecast experiments of 1996 indicated that the results of the nonlinear model are better than those of the persistent, climatic prediction, and T42L9 model either over the high- and mid-latitude areas of the Northern and Southern Hemispheres or the tropical area. The root-mean-square of the monthly-mean height of T42L9 model was considerably decreased with a change of 30.4%, 26.6%, 82.6%, and 39.4%, respectively, over the high- and mid-latitudes of the Northern Hemisphere, over the high- and mid-latitudes of the Southern Hemisphere, over the tropics and over the globe, and also the corresponding anomaly correlation coefficients over the four areas were respectively increased by 0.306-0.312, 0.304-0.429, 0.739-0.746, and 0.360-0.400 （averagely a relative change of 11.0% over the globe） by nonlinear correction after integration, implying that the forecasts given by nonlinear model include more useful information than those of T42L9 model.
基金Supported by the National Natural Science Foundation of China under Grant No. 40175013the National Key Project for Development of Science and Technology (96-908-02-01)the Project of Chinese Academy of Sciences (ZKCX2-SW-210).
文摘Based on Chen et al. （2006）, the scheme of the combination of the pentad-mean zonal height departure nonlinear prediction with the T42L9 model prediction was designed, in which the pentad zonal heights at all the 12-initial-value-input isobar levels from 50 hPa to 1000 hPa except 200, 300, 500, and 700 hPa were derived from nonlinear forecasts of the four levels by means of a good correlation between neighboring levels. Then the above pentad zonal heights at 12 isobar-levels were transformed to the spectrum coefficients of the temperature at each integration step of T42L9 model. At last, the nudging was made. On account of a variety of error accumulation, the pentad zonal components of the monthly height at isobar levels output by T42L9 model were replaced by the corresponding nonlinear results once more when integration was over. Multiple case experiments showed that such combination of two kinds of prediction made an improvement in the wave component as a result of wave-flow nonlinear interaction while reducing the systematical forecast errors. Namely the monthly-mean height anomaly correlation coefficients over the high- and mid-latitudes of the Northern Hemisphere, over the Southern Hemisphere and over the globe increased respectively from 0.249 to 0.347, from 0.286 to 0.387, and from 0.343 to 0.414 （relative changes of 31.5%, 41.0%, and 18.3%）. The monthly-mean root-mean-square error （RMSE） of T42L9 model over the three areas was considerably decreased, the relative change over the globe reached 44.2%. The monthly-mean anomaly correlation coeffi- cients of wave 4-9 over the areas were up to 0.392, 0.200, and 0.295, with the relative change of 53.8%, 94.1%, and 61.2%, and correspondingly their RMSEs were decreased respectively with the rate of 8.5%, 6.3%, and 8.1%. At the same time the monthly-mean pattern of parts of cases were presented better.
