系统辨识(7)：递阶辨识原理与方法

递阶辨识是系统辨识的一个重要分支.递阶辨识原理是在大系统递阶控制的"分解-协调原理"基础上发展起来的,它不仅能够解决参数数目多、维数高、大规模系统辨识算法计算量大的问题,而且能够解决结构复杂的双线性参数系统、多线性参数系统以及非线性系统的辨识问题.首先介绍递阶辨识原理和线性方程组Ax=b的著名雅可比迭代和高斯-赛德尔迭代,给出了线性方程组的迭代方法族;其次将雅可比迭代思想和递阶辨识原理用于研究一般矩阵方程和耦合矩阵方程的递阶梯度迭代求解方法和递阶最小二乘迭代求解方法;再次介绍了方程误差模型的两阶段最小二乘辨识方法(一个简单的递阶辨识方法)和线性回归模型的递阶最小二乘辨识方法;最后研究了类多变量CARMA系统的递阶辨识方法.     

系统辨识(5):迭代搜索原理与辨识方法

递推辨识与迭代辨识构成了两类重要的参数估计方法.递推辨识的递推变量与时间有关,因而可以用于在线估计系统参数;迭代辨识的迭代变量是自然数,与客观世界的时间无关,通常用于离线估计系统参数.基于辅助模型辨识思想、多新息辨识理论、递阶辨识原理、耦合辨识概念等辨识方法都可以用递推算法和迭代算法实现.迭代方法渊源很早,如求解矩阵方程Ax=b的雅可比迭代、高斯-赛德尔迭代等.迭代辨识方法主要使用梯度搜索、最小二乘搜索、牛顿搜索原理来实现.为此主要研究了CARMA系统和Box-Jenkins系统的最小二乘迭代辨识方法与梯度迭代辨识方法.这些方法也可推广到其他所有方程误差类系统和输出误差类系统,以及非线性系统.迭代辨识方法通常用于有限量测数据的系统辨识,其收敛性证明是辨识领域极具挑战性的研究课题.     

辅助模型辨识方法(2):输入非线性输出误差系统

针对具有已知基的输入非线性输出误差系统,提出了基于过参数化模型的辅助模型递推辨识方法和辅助模型递阶辨识方法,提出了基于关键项分离的辅助模型递推辨识方法、基于关键项分离的辅助模型两阶段辨识方法和辅助模型三阶段辨识方法,提出了基于双线性参数模型分解的辅助模型随机梯度算法和基于双线性参数模型分解的辅助模型递推最小二乘算法,并给出了几个典型辨识算法的计算量、计算步骤.这些算法的收敛性分析都是需要研究的辨识课题.     

线性参数系统的多新息辨识方法

系统有线性和非线性之分.线性系统有统一的描述形式,非线性系统因类别无数,不可能有统一描述.线性参数系统是一类特殊的非线性系统,它在参数空间上呈现线性特征,介于线性系统与非线性系统之间.针对伪线性参数系统,讨论了基于辅助模型的多新息辨识方法、基于滤波的辅助模型多新息辨识方法、基于模型分解的辅助模型多新息辨识方法、基于滤波的分解多新息辨识方法,并给出了几个典型辨识算法的计算量、计算步骤和流程图.     

输出非线性方程误差类系统递推最小二乘辨识方法

随着控制技术的发展,控制对象的规模越来越大,使得辨识算法的计算量也越来越大.对于结构复杂的非线性系统,特别是包含未知参数乘积的非线性系统,使得过参数化辨识方法的参数数目大幅度增加,辨识算法的计算量也急剧增加,因此探索计算量小的参数估计方法势在必行.针对输出非线性方程误差类系统,讨论了基于过参数化模型的递推最小二乘类辨识方法;为减小过参数化辨识算法的计算量和提高辨识精度,分别利用分解技术和数据滤波技术,研究和提出了基于模型分解的递推最小二乘辨识方法和基于数据滤波的递推最小二乘辨识方法.最后给出了几个典型辨识算法的计算量、计算步骤、流程图.     

输入非线性方程误差系统的多新息辨识方法

针对输入非线性方程误差系统,即输入非线性受控自回归系统,研究了基于过参数化模型的多新息辨识方法和基于过参数化模型的递阶多新息辨识方法;研究了基于关键项分离原理的多新息辨识方法;使用辨识模型分解技术,研究了基于关键项分离原理的两阶段多新息辨识方法和三阶段多新息辨识方法.这些方法可以推广到其他输入非线性方程误差系统、输入非线性输出误差类系统、输出非线性方程误差类系统、输出非线性输出类系统、反馈非线性系统等.同时,给出了几个典型辨识算法的计算量、计算步骤和流程图.     

辅助模型辨识方法(3):输入非线性输出误差自回归系统

输入非线性系统包括输入非线性方程误差类系统和输入非线性输出误差类系统.针对输入非线性输出误差自回归系统,分别基于过参数化模型,基于关键项分离原理,基于数据滤波技术,研究了相应的基于过参数化模型的辅助模型递推辨识方法、基于关键项分离的辅助模型递推辨识方法、基于数据滤波的辅助模型递推辨识方法.这些方法可以推广到其他输入非线性输出误差系统、输出非线性输出误差系统、反馈非线性系统等.并给出了几个典型辨识算法的计算步骤、流程图和计算量.     

系统辨识(8):耦合辨识概念与方法

耦合辨识是系统辨识的一个重要分支,是新近发展和提炼形成的一种辨识概念,主要用于研究结构复杂的参数耦合线性和非线性多变量系统的辨识问题.辅助模型辨识思想、多新息辨识理论、递阶辨识原理、耦合辨识概念是本文作者提出的一些新的辨识研究思路、理念和方法,分别能够用于研究存在未知过程变量的不可测系统的辨识,能够提高辨识方法的收敛速度和参数估计精度,能够解决结构复杂、大规模多变量系统及参数耦合多变量系统的辨识问题、减小辨识算法的计算量.首先介绍多变量系统耦合辨识概念,在此基础上讨论多变量系统的几种(全)耦合最小二乘辨识方法、(全)耦合随机梯度辨识方法、部分耦合随机梯度辨识方法、部分耦合最小二乘辨识方法等,最后说明耦合辨识方法可推广用于有色噪声干扰多变量系统的辨识,并列出了一些多变量系统模型结构,阐述了耦合辨识概念可以结合辅助模型辨识思想、多新息辨识理论、递阶辨识原理、迭代搜索原理(梯度迭代、最小二乘迭代、牛顿迭代)等来研究线性或非线性多变量系统的辨识问题.     

规范状态空间系统辨识方法

因为状态空间模型既包含了未知状态,又包含了未知参数,且二者是非线性乘积关系,使得辨识问题变得复杂.针对这一问题,详细研究了规范状态空间系统的状态与参数联合估计方法.采用交互估计理论,即采用递推方法或迭代方法实现系统状态与参数的交互估计.基本思路是在计算参数估计时,辨识算法信息向量中的未知状态用其估计值代替,然后利用获得的参数估计,设计基于参数估计的状态观测器或基于参数估计的Kalman滤波算法估计系统的状态,二者形成一个交互计算过程(递阶计算过程).沿着这条思路,分别从递推方案和迭代方案,研究和提出了基于状态观测器和基于Kalman滤波状态估计的随机梯度辨识算法、递推最小二乘辨识算法、多新息随机梯度辨识算法、多新息最小二乘辨识算法,以及模型分解的辨识算法,并给出了几个典型算法的计算步骤、流程图和计算量.     

类多变量输出误差系统的耦合多新息辨识方法

辅助模型辨识思想、多新息辨识理论、耦合辨识概念是研究复杂多变量系统辨识的新理念和原理.将它们结合起来研究类多变量输出误差系统的辨识问题,提出了多元辅助模型辨识方法、多元辅助模型多新息辨识方法、变递推间隔多元辅助模型多新息辨识方法.为减小算法的计算量和提高参数估计精度,将系统模型分解为一些子辨识模型,应用辅助模型辨识思想、多新息辨识理论、耦合辨识概念,研究和推导了部分耦合辅助模型辨识方法、部分耦合辅助模型多新息辨识方法.讨论了几个典型辨识算法的计算量,给出了参数估计的计算步骤和计算流程图.     

An Adaptive Estimation of Forecast Error Covariance Parameters for Kalman Filtering Data Assimilation

An adaptive estimation of forecast error covariance matrices is proposed for Kalman filtering data assimilation. A forecast error covariance matrix is initially estimated using an ensemble of perturbation forecasts. This initially estimated matrix is then adjusted with scale parameters that are adaptively estimated by minimizing -2log-likelihood of observed-minus-forecast residuals. The proposed approach could be applied to Kalman filtering data assimilation with imperfect models when the model error statistics are not known. A simple nonlinear model (Burgers' equation model) is used to demonstrate the efficacy of the proposed approach.     

Estimation methods for monthly humidity from dynamical downscaling data for quantitative assessments of climate change impacts

Methods are proposed to estimate the monthly relative humidity and wet bulb temperature based on observations from a dynamical downscaling coupled general circulation model with a regional climate model (RCM) for a quantitative assessment of climate change impacts. The water vapor pressure estimation model developed was a regression model with a monthly saturated water vapor pressure that used minimum air temperature as a variable. The monthly minimum air temperature correction model for RCM bias was developed by stepwise multiple regression analysis using the difference in monthly minimum air temperatures between observations and RCM output as a dependent variable and geographic factors as independent variables. The wet bulb temperature was estimated using the estimated water vapor pressure, air temperature, and atmospheric pressure at ground level both corrected for RCM bias. Root mean square errors of the data decreased considerably in August.     

EOF分解与GA优化的热带太平洋海温场动力预报模型反演

基于NCEP/NCAR提供的1950-2000年月平均海温场资料,首先用EOF方法对海温场序列进行时、空分解,在考虑相邻时段位势场空间模态基本稳定的前提下,引入动力系统重构思想,以EOF分解的空间模态时间系数序列作为动力模型变最,用遗传算法全局搜索和并行计算优势,进行了模型参数的优化反演,建立了EOF分解时间系数的非线性预报模型。通过模型积分和EOF时、空重构,实现了海温场的中长期预报。试验结果表明,在1—6月时效预报上,模型预报海温场与实际海温场非常吻合;对于7 15月时效的预报,尽管模型预报的海温场与实际海温场存在一些出入,但基本构型大致相符,特别是对12月以上的海温场形态和范围仍然能较为准确地描述。所有时效的预报结果均能对1997年的El Nino事件特征有不同程度的描述。该研究方法为海温场以及El Nino/La Nina事件的预报提供了一种新的思路,文中提出的反演热带太平洋海温场与El Nino/LaNina的动力统计模型的研究思想和技术途径,在热带太平洋海温场的预测试验中(特别是中、长期预报)表现出良好的预报效果,为热带太平洋海温场及其异常的El Nino/La Nina事件的中、长期预报提供了有益的研究和参考方法。     

A Medium/Long-Range Forecast of Paci c Subtropical High Based on Dynamic Statistic Model Reconstruction

Based on the 500-hPa geopotential height eld series of T106 numerical forecast products, by empirical rthogonal function (EOF) time-space separation, and on the hypotheses of EOF space-models being stable,he EOF time coe cient series were taken as dynamical statistic model variables. The dynamic system econstruction idea and genetic algorithm were introduced to make the dynamical model parameters optimized, and a nonlinear dynamic statistic model of EOF separating time coefficient series was established. By he model time integral and EOF time-space reconstruction, a medium/long-range forecast of subtropical high was carried out. The results show that the dynamical model forecast and T106 numerical forecast were approximately similar in the short-range forecast (65 days), but in the medium/long-range forecast>5 days), the forecast results of dynamical model was superior to that of T106 numerical products. A new method and idea were presented for diagnosing and forecasting complicated weathers such as subtropical high, and showed a better application outlook.     

Progress in Predictability Studies in China （2003-2006）

Since the last International Union of Geodesy and Geophysics General Assembly(2003),predictability studies in China have made significant progress.For dynamic forecasts,two novel approaches of conditional nonlinear optimal perturbation and nonlinear local Lyapunov exponents were proposed to cope with the predictability problems of weather and climate,which are superior to the corresponding linear theory.A possible mechanism for the"spring predictability barrier"phenomenon for the El Ni(?)o-Southern Oscillation (ENSO)was provided based on a theoretical model.To improve the forecast skill of an intermediate coupled ENSO model,a new initialization scheme was developed,and its applicability was illustrated by hindcast experiments.Using the reconstruction phase space theory and the spatio-temporal series predictive method, Chinese scientists also proposed a new approach to improve dynamical extended range(monthly)prediction and successfully applied it to the monthly-scale predictability of short-term climate variations.In statistical forecasts,it was found that the effects of sea surface temperature on precipitation in China have obvious spatial and temporal distribution features,and that summer precipitation patterns over east China are closely related to the northern atmospheric circulation.For ensemble forecasts,a new initial perturbation method was used to forecast heavy rain in Guangdong and Fujian Provinces on 8 June 1998.Additionally, the ensemble forecast approach was also used for the prediction of a tropical typhoons.A new downscaling model consisting of dynamical and statistical methods was provided to improve the prediction of the monthly mean precipitation.This new downsealing model showed a relatively higher score than the issued operational forecast.     

Statistical-dynamical analysis of wind observations usinga variational approach

Summary  In this paper, we present a variational analysis of wind and pressure data which takes into account statistical characteristics of the data and a linear model describing the dynamical relations between the analysed variables. The variational approach is used to adjust the given data to the dynamical model and it will be shown that this adjustment process can be controlled in an uncomplicated, comprehensible, and reproducible way by very few parameters only. The dependence of the analysis results on these parameters is investigated in theory and this theoretical conclusions are tested by an application. It is studied how effectively this method can be used to correct erroneous data. We apply the analysis to the COADS (Comprehensive Ocean-Atmosphere Data Set) wind and pressure data of the Januaries 1951–1993 over the North Atlantic and introduce the Ekman balance as a weak dynamical constraint. This specific data set is chosen because several previous investigations suggested that there is a spurious trend in the COADS wind speed of ∼ 1 ms⁻¹ since the mid-century. The results show that the control parameters can be effectively used to shift the wind field continuously between the identity with the input data and the exact consistency with the dynamical model. But it has to be admitted that the Ekman balance is inadequate in the tropics and that it overestimates the magnitude of the horizontal vector wind although this dynamical model is more suitable than the frequently used geostrophic balance. Received January 20, 2000 Revised April 10, 2000     

关于发展人工影响天气数值模式的一些问题

人工影响天气的学科基础是中小尺度天气动力学与云降水物理学,需要将天气-动力-云降水物理耦合为一体。考虑到目前将天气动力学性质的基础数值模式用于人工影响天气中的问题,从数值模式动力方程、模式分辨率、云物理过程、数值求解方案、初边值条件等方面系统地探索了发展人工影响天气数值模式中一些需要重点解决、且不可忽视的特色问题,并举例对相关问题提出了解决思路和方法。期望提出的问题有助于构思更适合于人工影响天气数值模式,使数值模式功能真正向满足人工影响天气的要求靠近一步。     

Experiments of DSAEF_LTP Model with Two Improved Parameters for Accumulated Precipitation of Landfalling Tropical Cyclones over Southeast China

The Dynamical-Statistical-Analog Ensemble Forecast model for landfalling tropical cyclones (TCs) precipitation (DSAEF_LTP) utilises an operational numerical weather prediction (NWP) model for the forecast track, while the precipitation forecast is obtained by finding analog cyclones, and making a precipitation forecast from an ensemble of the analogs. This study addresses TCs that occurred from 2004 to 2019 in Southeast China with 47 TCs as training samples and 18 TCs for independent forecast experiments. Experiments use four model versions. The control experiment DSAEF_LTP_1 includes three factors including TC track, landfall season, and TC intensity to determine analogs. Versions DSAEF_LTP_2, DSAEF_LTP_3, and DSAEF_LTP_4 respectively integrate improved similarity region, improved ensemble method, and improvements in both parameters. Results show that the DSAEF_LTP model with new values of similarity region and ensemble method (DSAEF_LTP_4) performs best in the simulation experiment, while the DSAEF_LTP model with new values only of ensemble method (DSAEF_LTP_3) performs best in the forecast experiment. The reason for the difference between simulation (training sample) and forecast (independent sample) may be that the proportion of TC with typical tracks (southeast to northwest movement or landfall over Southeast China) has changed significantly between samples. Forecast performance is compared with that of three global dynamical models (ECMWF, GRAPES, and GFS) and a regional dynamical model (SMS-WARMS). The DSAEF_LTP model performs better than the dynamical models and tends to produce more false alarms in accumulated forecast precipitation above 250 mm and 100 mm. Compared with TCs without heavy precipitation or typical tracks, TCs with these characteristics are better forecasted by the DSAEF_LTP model.     

How dynamical models can learn from the data��an example with a simplified ENSO model

Most dynamical models of the natural system contain a number of empirical parameters which reflect our limited understanding of the simulated system or describe unresolved subgrid-scale processes. While the parameterizations basically introduce some uncertainty to the model results, they also hold the prospect of tuning the model. In general, a deterministic tuning is related to an inversion of the model which is often impossible or requires considerable computing effort for most climate models. Another way to adjust the model parameters to a specific observed process is stochastic fitting where a set of parameters and model output are taken as random variables. Here, we present a dynamical?Cstatistical approach with a simplified model of the El Ni?o?CSouthern Oscillation (ENSO) cycle whose parameters are adjusted to simulated and observed data by means of Bayesian statistics. As ENSO model, we employ the Schop?CSuarez delay oscillator model. Monte Carlo experiments highlight the large sensitivity of the model results to varied model parameters and initial values. The statistical adjustment is done by Bayesian model averaging of the Monte Carlo experiments. Applying the method to simulated data, the posterior ensemble mean is much closer to the reference data than the prior ensemble mean. The learning effect of the model is evident in the leading empirical orthogonal functions and statistically significant in the mean state. When the method is applied to the observed ENSO time series, the ENSO model in its classical setup is not able to account for the temporally varying periodicity of the observed ENSO phenomenon. An improved setup with continuous adjustment periods and extended parameter range is developed in order to allow the model to learn from the data gradually. The improved setup leads to promising results during the twentieth century and even a weak forecast skill over 6?months. Thus, the described method offers a promising tool for data assimilation in dynamical weather and climate models. However, the simplified ENSO model is barely appropriate for operational ENSO forecasts owing to its limited physical complexity.     

GRAPES业务全球集合控制预报初值的动力升尺度方法

以生成GRAPES全球集合预报业务系统的控制预报初值为目的,基于GRAPES全球模式,开展了控制预报初值生成方法研究,发展了高分辨率初值动力升尺度方法,并检验了不同方法的可行性。通过对比不同方法产生的初始场形态,证实了仅仅对高分辨率初始场进行二维水平插值存在不足,基于静力学方程对Exner气压变量进行三维插值至关重要。结果表明,动力升尺度方法利用静力平衡关系,对全场的温压场进行调整,使之协调平衡,可以改善二维水平插值方法导致的初始位势高度场和温度场的噪音问题,产生适用于GRAPES全球集合预报业务系统的控制预报初值。