Conditional nonlinear optimal perturbation and its applications to the studies of weather and climate predictability

Conditional nonlinear optimal perturbation （CNOP） is the initial perturbation that has the largest nonlinear evolution at prediction time for initial perturbations satisfying certain physical constraint condition. It does not only represent the optimal precursor of certain weather or climate event, but also stand for the initial error which has largest effect on the prediction uncertainties at the prediction time. In sensitivity and stability analyses of fluid motion, CNOP also describes the most unstable （or most sensitive） mode. CNOP has been used to estimate the upper bound of the prediction error. These physical characteristics of CNOP are examined by applying respectively them to ENSO predictability studies and ocean＇s thermohaline circulation （THC） sensitivity analysis. In ENSO predictability studies, CNOP, rather than linear singular vector （LSV）, represents the initial patterns that evolve into ENSO events most potentially, i.e. the optimal precursors for ENSO events. When initial perturbation is considered to be the initial error of ENSO, CNOP plays the role of the initial error that has largest effect on the prediction of ENSO. CNOP also derives the upper bound of prediction error of ENSO events. In the THC sensitivity and stability studies, by calculating the CNOP （most unstable perturbation） of THC, it is found that there is an asymmetric nonlinear response of ocean＇s THC to the finite amplitude perturbations. Finally, attention is paid to the feasibility of CNOP in more complicated model. It is shown that in a model with higher dimensions, CNOP can be computed successfully. The corresponding optimization algorithm is also shown to be efficient.     

Applications of nonlinear optimization methods to quantifying the predictability of a numerical model for El Nino-Southern Oscillation

The nonlinear optimization methods are applied to quantify the predictability of a numerical model for El Nino-Southern Oscillation (ENSO). We establish a lower bound of maximum predictability time for the model ENSO events (i.e. ENSO events in the numerical model), an upper bound of maximum prediction error, and a lower bound of maximum allowable initial error, all of which potentially quantify the predictability of model ENSO. Numerical results reveal the phenomenon of “spring predictability barrier” (SPB) for ENSO event and support the previous views on SPB. Additionally, we also explore the differences between the linear evolution of prediction error and its nonlinear counterpart. The results demonstrate the limitation of linear estimation of prediction error. All these above results suggest that the nonlinear optimization method is one of the useful tools of quantifying the predictability of the numerical model for ENSO.     

A new approach to the generation of initial perturbations for ensemble prediction: Conditional nonlinear optimal perturbation

Conditional nonlinear optimal perturbation （CNOP）, which is a natural extension of singular vector （SV） into the nonlinear regime, is applied to ensemble prediction study by using a quasi-geostrophic model under the perfect model assumption. SVs and CNOPs have been utilized to generate the initial perturbations for ensemble prediction experiments. The results are compared for forecast lengths of up to 14 d. It is found that the forecast skill of samples, in which the first SV is replaced by CNOP, is comparatively higher than that of samples composed of only SVs in the medium range （day 6-day 14）. This conclusion is valid under the condition that analysis error is a kind of fast-growing ones regardless of its magnitude, whose nonlinear growth is faster than that of SV in the later part of the forecast. Furthermore, similarity Index and empirical orthogonal function （EOF） analysis are performed to explain the above numerical results.     

Model Construct Based Enterprise Model Architecture and Its Modeling Approach

In order to support enterprise integration,a kind of model construct based enterprise model architecture and its modeling approach are studied in this paper.First,the structural makeup and internal relationships of enterprise model erchitecutre are discussed.Then,the concept of reusable model construct(MC) which belongs to the control view and can help to derive other views is propsed.The modeling approach based on model construct consists of three steps,reference model architecture synthesis,enterprise model customization,system design and implementation.According to MC based modeling approach a case study with the background of one-kind-productmachinery nanufactureing enterprises is illustrated.It is shown that proposal model construct based enterprise model architecture and modeling approach are practical and efficient.     

An integrated scheme of neural network and optimal predictive control

An approach of adaptive predictive control with a new structure and a fast algorithm of neural network (NN) is proposed. NN modeling and optimal predictive control are combined to achieve both accuracy and good control performance. The output of nonlinear network model is adopted as a measured disturbance that is therefore weakened in predictive feed-forward control. Simulation and practical application show the effectiveness of control by the proposed approach.     

An approach to improving the dynamical extended—range（monthly） prediction

Focusing on common and significant forecast errors-the zonal mean errors in the numerical prediction model,this report proposes an approach to improving the dynamical extended-range(monthly) prediction.Firstly,the monthly pentad-mean nonlinear dynamical regional predic-tion model of the zonal-mean haight based on a large number of historical data is constituted by employing the reconstruc-tion phase space theory and the spatio-temporal series pre-dictive method.The zonal height thus produced is trans-formed to its counterpart in the numerical model and fur-ther used to revise the numerical model prediction during the integration process.In this way,the two different kinds of prediction are combined.The forecasting experimenal results show that the above hybrid approach not only re-duces the systematical reeor of the numerical model,but also improves the forecast of the non-axisymmetric components due to the wave-flow interaction.     

Principal Resonance of Parametrically Excited Moving Viscoelastic Belts with Geometrical Nonlinearity

Nonlinear dynamic analysis is performed on moving belts subjected to geometric nonlinearity and initial tension fluctuation. To incorporate more accurately the damping mechanism of belt material,linear viscoelastic models are adopted in a unified form of differential operators. To circumvent high-order differential vibration equation of time-varying coefficients and with gyroscopic and nonlinear terms, where analytical solution is almost impossible, a systematic approach is presented by reforming the motion equation and directly using the method of multiple scales. To exemplify the procedure, the solutions at principal resonance are obtained and their stability conditions are derived for employing a Kelvin-Voigt model to reflect the property of the belt material. The solutions and stability conditions successfully reduce to those for using Kelvin model and elastic model, which validate the present approaches. Numerical simulations highlight the effects of tension fluctuations and translating speeds on the stability of the belt vibration.     

Neural network approach for modification and fitting of digitized data in reverse engineering

Reverse engineering in the manufacturing field is a process in which the digitized data are obtained from an existing object model or a part of it, and then the CAD model is reconstructed. This paper presents an RBF neural network approach to modify and fit the digitized data. The centers for the RBF are selected by using the orthogonal least squares learning algorithm. A mathematically known surface is used for generating a number of samples for training the networks. The trained networks then generated a number of new points which were compared with the calculating points from the equations. Moreover, a series of practice digitizing curves are used to test the approach. The results showed that this approach is effective in modifying and fitting digitized data and generating data points to reconstruct the surface model.     

Nonlinear Spline Kernel-based Partial Least Squares Regression Method and Its Application

Inspired by the traditional Wold＇s nonlinear PLS algorithm comprises of NIPALS approach and a spline inner function model, a novel nonlinear partial least squares algorithm based on spline kernel （named SK-PLS ） is proposed for nonlinear modeling in the presence of multicollinearity. Based on the inner-product kernel spanned by the spline basis functions with infinite number of nodes, this method firstly maps the input data into a highdimensional feature space, and then calculates a linear PLS model with reformed NIPALS procedure in the feature space and gives a unified framework of traditional PLS ＂kernel＂ algorithms in consequence. The linear PLS in the feature Space corresponds to a nonlinear PLS in the original input （primal） space. The good approximating property of spline kernel function enhances the generalization ability of the novel model, and two numerical experiments are given to illustrate the feasibility of the proposed method.     

Nonlinearity degree of short-term heart rate variability signal

A nonlinear autoregressive (NAR) model is built to model the heartbeat interval time series and the optimum model degree is proposed to be taken to evaluate the nonlinearity degree of heart rate variability (HRV). A group of healthy persons are studied and the results indicate that this method can effectively get nonlinear information from short (6—7 min) heartbeat series and consequently reflect the degree of heart rate variability, which supplies convenience in clinical application. Finally, a comparison with the traditional time domain method shows that the NAR model method can reflect the complexity of the whole signal and lessen the influence of noise and instability, in the signal.     

粒子群优化算法在可预报性问题中的应用

为了评价在强非线性影响下粒子群优化(PSO)算法解决可预报性问题的性能,借助二维Ikeda模式,基于传统伴随(ADJ)方法和PSO求取的条件非线性最优扰动(CNOP)方法,即ADJ-CNOP和PSOCNOP方法,研究了最大预报误差的上界和最大允许初始误差的下界的精度问题。数值试验的统计分析结果显示:不论在初始误差较大还是预报时间较长的情况下,PSO-CNOP方法都能有效捕捉全局CNOP,给出最大预报误差的上界和最大允许初始误差的下界的精确估计;由于强非线性的影响,ADJ-CNOP方法会以较大概率获得局部CNOP,从而影响可预报性问题研究中相关估计的精度。实验结果表明,PSO算法具有优良的性能,能有效克服动力模式的强非线性特征带来的影响,值得在可预报性问题中进一步研究和应用。     

改进的粒子群算法在求解条件非线性最优扰动的应用

通过对影响粒子群算法性能的两个关键因素进行改进,将一种改进的粒子群算法应用于条件非线性最优扰动(CNOP)的求解中,并与传统的基于梯度下降算法进行比较。比较数值结果显示,在非光滑情形下,传统的基于伴随模式提供梯度信息的SPG2求解出的CNOP绝大部分是局部的,只有少数是全局的。而改进的粒子群算法则在200次数值实验中均能够较好地求解出全局CNOP。     

Variational iteration solving method of a sea-air oscillator model for the ENSO

A time delay equation for sea-air oscillator model is studied. The aim is to create an asymtotic solving method of nonlinear equation for the ENSO model. And based on a class of oscillators of ENSO model, employing the variational iteration method, the approximate solution of corresponding problem is obtained. It is proven from the results that the method of variational iteration method can be used for analyzing the sea surface temperature anomaly in the equatorial eastern Pacific of the atmosphere-ocean oscillation for ENSO model.     

Variational iteration solving method of a sea-air oscillator model for the ENSO

A time delay equation for sea-air oscillator model is studied. The aim is to create an asymtotic solving method of nonlinear equation for the ENSO model. And based on a class of oscillators of ENSO model, employing the variational iteration method, the approximate solution of corresponding problem is obtained. It is proven from the results that the method of variational iteration method can be used for analyzing the sea surface temperature anomaly in the equatorial eastern Pacific of the atmosphere-ocean oscillation for ENSO model.     

基于相空间重构预测方法预测能力的评估

为了客观地评估基于相空间重构预测方法的预测能力,使用非线性局部Lyapunov指数来替代均方根误差。根据误差平均相对增长的饱和性质,可以确定预测方法的最大预测期限。通过计算得到重构Lorenz相空间和原始Lorenz相空间的最大预测期限分别是12,13s,k-近邻方法(k=1,2,3,4,5)的最大预测期限分别是12.0,9.8,9.7,9.2,8.8s,多变量预测方法的最大预测期限是12.8s,单变量预测方法的最大预测期限是12.0s。研究表明,重构的Lorenz系统的相空间可预报性与原始Lorenz相空间相当。此外,对于重构的Lorenz相空间,由于k-近邻方法集合了预测能力参差不齐的成员,导致其预测能力逊色于零级近似预测,多变量预测方法的预测能力与单变量预测方法几乎相当。     

ENSO非线性预报

运用非线性时间序列分析方法,结合全局函数拟合和lyapunov指数分析对厄尔尼诺．南方涛动（ENSO）的时间演变进行研究。方法包括：相空间重构,lyapunov指数分析,全局函数拟合,主分量分析,最小二乘拟合。资料为C,Z（Cane ＆ Zebiak）模式产生的月平均海表温度异常（SSTA）场。采用非线性混沌时间序列预报,不同于传统的时间序列分析方法。相比其他模式,它能用较少的资料得到较好的预报结果,为今后的ENSO预报提供了一个可供参考的方法。     

海-气振子ENSO模型的Sinc-Galerkin解法

研究一类厄尔尼诺-南方海涛(ENSO)的耦合系统振子的模型.利用Sinc-Galerkin方法,把求解非线性微分耦合系统问题转化为解非线性代数系统,并由Newton法得到其近似解.