Relationships between the Limit of Predictability and Initial Error in the Uncoupled and Coupled Lorenz Models

In this study, the relationship between the limit of predictability and initial error was investigated using two simple chaotic systems： the Lorenz model, which possesses a single characteristic time scale, and the coupled Lorenz model, which possesses two different characteristic time scales. The limit of predictability is defined here as the time at which the error reaches 95% of its saturation level; nonlinear behaviors of the error growth are therefore involved in the definition of the limit of predictability. Our results show that the logarithmic function performs well in describing the relationship between the limit of predictability and initial error in both models, although the coefficients in the logarithmic function were not constant across the examined range of initial errors. Compared with the Lorenz model, in the coupled Lorenz model in which the slow dynamics and the fast dynamics interact with each other--there is a more complex relationship between the limit of predictability and initial error. The limit of predictability of the Lorenz model is unbounded as the initial error becomes infinitesimally small; therefore, the limit of predictability of the Lorenz model may be extended by reducing the amplitude of the initial error. In contrast, if there exists a fixed initial error in the fast dynamics of the coupled Lorenz model, the slow dynamics has an intrinsic finite limit of predictability that cannot be extended by reducing the amplitude of the initial error in the slow dynamics, and vice versa. The findings reported here reveal the possible existence of an intrinsic finite limit of predictability in a coupled system that possesses many scales of time or motion.

An Online Model Correction Method Based on an Inverse Problem:Part I—Model Error Estimation by Iteration

Errors inevitably exist in numerical weather prediction （NWP） due to imperfect numeric and physical parameterizations. To eliminate these errors, by considering NWP as an inverse problem, an unknown term in the prediction equations can be estimated inversely by using the past data, which are presumed to represent the imperfection of the NWP model （model error, denoted as ME）. In this first paper of a two-part series, an iteration method for obtaining the MEs in past intervals is presented, and the results from testing its convergence in idealized experiments are reported. Moreover, two batches of iteration tests were applied in the global forecast system of the Global and Regional Assimilation and Prediction System （GRAPES-GFS） for July-August 2009 and January-February 2010. The datasets associated with the initial conditions and sea surface temperature （SST） were both based on NCEP （National Centers for Environmental Prediction） FNL （final） data. The results showed that 6th h forecast errors were reduced to 10% of their original value after a 20-step iteration. Then, off-line forecast error corrections were estimated linearly based on the 2-month mean MEs and compared with forecast errors. The estimated error corrections agreed well with the forecast errors, but the linear growth rate of the estimation was steeper than the forecast error. The advantage of this iteration method is that the MEs can provide the foundation for online correction. A larger proportion of the forecast errors can be expected to be canceled out by properly introducing the model error correction into GRAPES-GFS.

Auxiliary error and probability density function based neuro-fuzzy model and its application in batch processes

This paper focuses on resolving the identification problem of a neuro-fuzzy model(NFM) applied in batch processes. A hybrid learning algorithm is introduced to identify the proposed NFM with the idea of auxiliary error model and the identification principle based on the probability density function(PDF). The main contribution is that the NFM parameter updating approach is transformed into the shape control for the PDF of modeling error. More specifically, a virtual adaptive control system is constructed with the aid of the auxiliary error model and then the PDF shape control idea is used to tune NFM parameters so that the PDF of modeling error is controlled to follow a targeted PDF, which is in Gaussian or uniform distribution. Examples are used to validate the applicability of the proposed method and comparisons are made with the minimum mean square error based approaches.

Error model identification of inertial navigation platform based on errors-in-variables model

Because the real input acceleration cannot be obtained during the error model identification of inertial navigation platform, both the input and output data contain noises. In this case, the conventional regression model and the least squares （LS） method will result in bias. Based on the models of inertial navigation platform error and observation error, the errors-in-variables （EV） model and the total least squares （TLS） method axe proposed to identify the error model of the inertial navigation platform. The estimation precision is improved and the result is better than the conventional regression model based LS method. The simulation results illustrate the effectiveness of the proposed method.

An Online Model Correction Method Based on an Inverse Problem:PartⅡ——Systematic Model Error Correction

An online systematic error correction is presented and examined as a technique to improve the accuracy of real-time numerical weather prediction, based on the dataset of model errors （MEs） in past intervals. Given the analyses, the ME in each interval （6 h） between two analyses can be iteratively obtained by introducing an unknown tendency term into the prediction equation, shown in Part I of this two-paper series. In this part, after analyzing the 5-year （2001-2005） GRAPES- GFS （Global Forecast System of the Global and Regional Assimilation and Prediction System） error patterns and evolution, a systematic model error correction is given based on the least-squares approach by firstly using the past MEs. To test the correction, we applied the approach in GRAPES-GFS for July 2009 and January 2010. The datasets associated with the initial condition and SST used in this study were based on NCEP （National Centers for Environmental Prediction） FNL （final） data. The results indicated that the Northern Hemispheric systematically underestimated equator-to-pole geopotential gradient and westerly wind of GRAPES-GFS were largely enhanced, and the biases of temperature and wind in the tropics were strongly reduced. Therefore, the correction results in a more skillful forecast with lower mean bias and root-mean-square error and higher anomaly correlation coefficient.

Theoretical Basis and Application of an Analogue-Dynamical Model in the Lorenz System

The theoretical basis and application of an analogue-dynamical model （ADM） in the Lorenz system is studied. The ADM can effectively combine statistical and dynamical methods in which the small disturbance of the current initial value superimposed on the historical analogue reference state can be regarded as a prediction objective. Primary analyses show that under the condition of appending disturbances in model parameters, the model errors of ADM are much smaller than those of the pure dynamical model （PDM）. The characteristics of predictability on the ADM in the Lorenz system are analyzed in phase space by conducting case studies and global experiments. The results show that the ADM can quite effectively reduce prediction errors and prolong the valid time of the prediction in most situations in contrast to the PDM, but when model errors are considerably small, the latter will be superior to the former. To overcome such a problem, the multi-reference-state updating can be applied to introduce the information of multi-analogue and update analogue and can exhibit exciting performance in the ADM.

Modeling Boundary and Edge Effect of Chloride Diffusion for Durability Design of Concrete Structures Exposed in Marine Environment

According to the Fick＇s second law of diffusion, six analytical solutions of chloride profile in concrete were studied and discussed with regard to different boundary and initial conditions. In those analytical solutions, the most prevailing error-function solution which is based on semi-infinite assumption is the simple one, but may under-estimate the chloride content in concrete and over-rate the life time prediction of concrete structures. The experimental results show that compared with other solutions, the chloride content in concrete predicted by error-function model is the minimum, and the calculation difference produced by different analytical models should not be ignored. The influence of models on chloride content prediction is more than other environment and material coefficients in some time. In order to get a more realistic prediction model, modification to error-function model is suggested based on analysis and calculation examples concerning the boundary and edge effect.

Water level updating model for flow calculation of river networks

Complex water movement and insufficient observation stations are the unfavorable factors in improving the accuracy of flow calculation of river networks. A water level updating model for river networks was set up based on a three-step method at key nodes, and model correction values were collected from gauge stations. To improve the accuracy of water level and discharge forecasts for the entire network, the discrete coefficients of the Saint-Venant equations for river sections were regarded as the media carrying the correction values from observation locations to other cross-sections of the river network system. To examine the applicability, the updating model was applied to flow calculation of an ideal river network and the Chengtong section of the Yangtze River. Comparison of the forecast results with the observed data demonstrates that this updating model can improve the forecast accuracy in both ideal and real river networks.

A Comprehensive Study of Solar Energy Components by Using Various Models on Horizontal and Inclined Surfaces for Different Climate Zones

The main objective of this research is to analyze the monthly average daily of global (H), beams (B) and diffuses (D) solar irradiance on a horizontal surface at four selected sites (El-Kharga, Hurghada in Egypt and Dammam, Hail in Saudi Arabia) during the period time from 1980 to 2020. The empirical models between (H/Ho) and meteorological parameters along with the values of (MBE), (RMSE), MPE, R2 and the t-Test statics are discussed. The results in this study indicate good agreement between observed and calculated values of total solar energy and diffuse solar fraction. The results for south facing surfaces of the (RMSE) for different slope at different models in the present research are discussions. Nine different models between isotropic and anisotropic used to estimate the diffuse solar radiation on a tilted surface at selected sites in this study. The absolute relative values of RMSE for the south-facing surface ranges from 7 to 41.3 at El-Kharga and Hurghada sites, Egypt in the present study for Koronakis and Stevenand Unsworth (SU) models respectively. The values of (RMSE), for the south-facing surface ranges from 9.3 to 39.7 at Dammam and Hail sites, Saudi Arabia in the present research for Koronakis and Klucher models respectively. For west-facing surface the values of RMSE range from 11.2 to 47.3 for Badescu and Koronakis models at El-Kharga and Hurghada sites, Egypt respectively, while values of RMSE range from 6.5 to 38.5 for Klucher and Reindl et al. models at Dammam and Hail sites, Saudi Arabia. The models Koronakis, Klucher and Stevenand Unsworth (SU) models are given the most accurate estimate for the south-facing surface, and Badescu, Koronakis, Klucher and Reindl et al. models are good performs better estimated for the west-facing surface.

Model-Based Adaptive Predictive Control with Visual Servo of a Rotary Crane System

This paper investigated the implementation of an adaptive predictive controller using nonlinear dynamic echo state neural （ESN） model for a rotary crane system by the visual servo method. The control sequences within the control horizon were described using cubic spline interpolation to enlarge the predictive horizon. Verification of the proposed scheme in the face of exogenous disturbances and modeling error with inaccurate string length was demonstrated by both simulations and experiments.

基于HCPN的复杂BPMN协作模型数据流建模与验证

为了保证复杂BPMN协作模型的正确性,不仅要涵盖多实例和子进程等复杂元素,还要在检测控制流错误的同时检测数据流错误。但业务流程建模标注(BPMN 2.0)缺乏形式化语义的描述,这对模型正确性的验证造成了阻碍。因此,给出了一种具有弧权重的层次化着色Petri网(HCPN)的定义,它既可以对数据流进行形式化表示,又可以对多实例和子进程结构进行建模。进一步提出了从BPMN协作模型到HCPN模型的形式化映射方法。然后基于HCPN模型的弧权重给出了缺失、丢失和冗余3种数据流错误的定义,并提出了对应的检测算法。最后,设计了一个自动化建模与验证的框架,通过一个案例研究说明了该方法的有效性。

Near-Lossless Compression Based on a Full Range Gaussian Markov Random Field Model for 2D Monochrome Images

This paper proposes a Full Range Gaussian Markov Random Field (FRGMRF) model for monochrome image compression, where images are assumed to be Gaussian Markov Random Field. The parameters of the model are estimated based on Bayesian approach. The advantage of the proposed model is that it adapts itself according to the nature of the data (image) because it has infinite structure with a finite number of parameters, and so completely avoids the problem of order determination. The proposed model is fitted to reconstruct the image with the use of estimated parameters and seed values. The residual image is computed from the original and the reconstructed images. The proposed FRGMRF model is redefined as an error model to compress the residual image to obtain better quality of the reconstructed image. The parameters of the error model are estimated by employing the Metropolis-Hastings (M-H) algorithm. Then, the error model is fitted to reconstruct the compressed residual image. The Arithmetic coding is employed on seed values, average of the residuals and the model coefficients of both the input and residual images to achieve higher compression ratio. Different types of textured and structured images are considered for experiment to illustrate the efficiency of the proposed model. The results obtained by the FRGMRF model are compared to the JPEG2000. The proposed approach yields higher compression ratio than the JPEG whereas it produces Peak Signal to Noise Ratio (PSNR) with little higher than the JPEG, which is negligible.

Influence of Sino-US Agricultural Trade on China’s Total Agricultural Output Value Based on Cointegration Model

According to the data of the total trade of agricultural products between China and the United States from 2009 to 2018 and the general description of agriculture in China,this paper adopts the method of econometric model to make a detailed analysis of the agricultural trade between China and the United States by using cointegration analysis,Granger causality test and error correction model in order to explore the impact of agricultural trade between China and the United States on China’s agricultural development. The results of empirical analysis show that there is a balanced relationship between the trade of agricultural products between China and the United States and the development of agriculture in China. The total trade of agricultural products between China and the United States affects the development of China’s agriculture.In addition,in the short term,if the short-term fluctuation deviates from the long-term equilibrium,then the error correction term will reverse it with strength of 0. 378,so that the non-equilibrium state will gradually return to the equilibrium state.

Application of Polynomial Mathematical Models for the Extraction of Bioactive Compounds from Plant Sources

This article focuses on the mathematical modelling of the extraction process of bioactive compounds from grape marc and berries (Aronia, rosehip, rowan, and hawthorn). The composition of the extraction medium (the concentration of the ethyl alcohol) served as a factor of influence. Furthermore, 8 experimental measured parameters were used as variables. The experimental results were processed using Hermite polynomials. In order to adapt the degree of the polynomial, the following conditions were imposed: high precision of the mathematical model by appealing to models on interval;obtaining a nominal model and two uncertain models (upper and lower);deduction of two predictive models, one superior and one inferior. It was found that the mathematical models based on Hermite polynomials do not provide explicit analytical expressions, although they allow the establishment of parameter values for any concentration of the extraction medium. In some cases, only high-grade polynomial models ensure the modelling error below 2%. Uncertain models (upper and lower 95%) include all experimental data. Predictive mathematical models (upper and lower) were established for a high prediction. The analytical expressions of the mathematical models on intervals are non-gaps, the coefficients having non-zero values. Dependencies between the measured parameters and the composition of the extraction solvent were analyzed, the results being presented through the calculation of a surface, with all the experimental values and their average values. Thus, it was found that polynomial mathematical models provide complete information for modelling the extraction processes of bioactive compounds of plant origin.

考虑多源误差影响的谐波减速器传动误差建模与分析

为解决现有谐波减速器传动误差建模方法的不足,提出一种考虑装配误差、齿面误差的综合误差建模方法。该方法首先建立装配误差和齿面误差数学模型,并进行误差影响参数分析。其次,测量实验样机装配偏心量和歪斜角度,基于模型得到对应偏心误差、歪斜误差模型理论值,齿面加工误差幅值按一般加工工况大小代入模型,得到对应加工误差模型理论值;然后,分别进行500 h、1500 h、3000 h时长的磨损实验,磨损后进行齿面形貌扫描和数据分析,得到对应的齿面形貌参数,基于模型得到对应的磨损误差模型理论值。最后,综合考虑多源误差影响,设置3组同型号样机,进行传动误差实验。实验结果表明:考虑装配偏心、歪斜和齿面加工等影响因素,传动误差的实验测量值与模型理论值误差在1.7~3.3%之间;综合考虑装配偏心、歪斜、齿面加工、齿面磨损等影响因素,在磨损500 h、1500 h、3000 h后传动误差的实验测量值与模型理论值误差分别在-3.45~2.07%、-5.88~-2.94%、1.33~5.33%之间。

机器人几何参数标定误差模型对定位精度影响研究

机器人几何参数误差是影响机器人定位精度的主要因素,通过对几何参数标定能够有效提高机器人定位精度。为了解决机器人在标定过程中的奇异性问题,采用改进的Denavit-Hartenberg(MDH)方法建立机器人几何参数模型,根据微分误差原理分别建立了机器人几何参数标定位姿误差和位置误差及姿态误差模型,并通过对几何参数冗余性分析及采用Levenberg-Marquardt(LM)算法辨识几何参数误差,研究不同误差模型对机器人定位精度影响。实验结果表明:采用位姿误差模型对机器人几何参数标定后其末端位置和姿态精度均能提升约75%,适于在有高精度定位要求的机器人中推广应用。

Incorporating Linguistic Rules in Statistical Chinese Language Model for Pinyin-to-character Conversion

An N-gram Chinese language model incorporating linguistic rules is presented. By constructing elements lattice, rules information is incorporated in statistical frame. To facilitate the hybrid modeling, novel methods such as MI-based rule evaluating, weighted rule quantification and element-based n-gram probability approximation are presented. Dynamic Viterbi algorithm is adopted to search the best path in lattice. To strengthen the model, transformation-based error-driven rules learning is adopted. Applying proposed model to Chinese Pinyin-to-character conversion, high performance has been achieved in accuracy, flexibility and robustness simultaneously. Tests show correct rate achieves 94.81% instead of 90.53% using bi-gram Markov model alone. Many long-distance dependency and recursion in language can be processed effectively.

基于MPC的光电热联合系统建模与控制优化

为解决我国北方地区冬季采暖产生的能源消耗与环境污染问题,改善光资源丰富、较丰富地区光能利用率不足的现状,充分利用谷电和日照优势,针对太阳能利用与建筑采暖相结合的分布式能源系统性问题,提出一种基于TRNSYS动态建模与数值建模相结合的光电热联合供暖系统。综合考虑小范围内供暖温度的时滞性以及系统各设备的出力情况,联合Matlab搭建模型预测控制器(MPC),提出一种基于MPC的误差实时校正优化控制策略。分析表明:采用MPC的控制优化,在热负荷跟踪方面,最大误差降低4.16%,平均误差降低2.79%;在室内温度控制方面,最大偏差降低1.2℃,平均偏差降低0.2℃;在太阳能利用占比方面,太阳辐射强度趋近于800 W/m^(2)时,太阳能利用占比差距达最大8.9%。分析结果说明该系统可以更快速、更准确地跟踪建筑热负荷波动,并且有效抑制室内温度波动,提高清洁能源的利用率。

贵州喀斯特地貌地区GNSS站坐标时间序列特性研究

使用GAMIT/GLOBK10.71软件解算贵州省北斗卫星导航定位基准站网(GZCORS)25个基准站数据,获得各站单天解坐标时间序列。利用主成分分析法提取站坐标共模误差,利用谱分析法分析共模误差基本特性,采用极大似然估计法确定站点最优噪声模型及其运动速度。结果表明,GZCORS坐标序列共模误差中包含有周期项,N方向最大振幅周期分别出现在0.2周/a、1.2周/a、3.2周/a和4.2周/a;GZCORS站点最优噪声模型以WN+FN和WN+GM为主,剔除共模误差后,36%的测站分量噪声特性发生变化;剔除共模误差后,坐标时间序列噪声水平明显降低,各坐标分量速度参数的估计精度均有明显提升,其中N、E、U分量分别提高52%、56%和50%。

基于隧道三台阶铣挖定额施工组织模型的数据误差处理研究

针对我国铁路建设过程中出现的复杂地质和特殊工况问题,铁路建设者提出了各种新工艺新工法,随之而来的挑战是测定新型工艺工法的补充定额,以便完善铁路工程造价体系。如何提高定额数据的准确性和定额测定的稳健性是铁路造价人员需要解决的问题。本文运用误差理论和数理分析的方法,通过建立系统误差、粗大误差和随机误差数据处理模型,对现场测定数据进行计算分析和降噪处理,准确剔除了异常值,提高了定额测定工作的技术高度和深度。