On embedded FIR filter models for identifying continuous-time and discrete-time transfer functions: the RPM approach

For identifying a continuous-time (CT) transfer function model, data filtering is a solution which provides the necessary unmeasurable input--output derivative approximations. In discrete-time (DT) system identification, the well-known ARX model can be used successfully if the estimate is performed with suitable prefiltered data. This article describes the reinitialised partial moment (RPM) model which embeds implicitly a finite impulse response filter in both CT and DT domains. With knowledge of the important role of data prefiltering in standard methods, this RPM model embedded filter gives particular properties to this original tool. Although both the CT RPM model and the DT RPM model present an embedded filter, the formulation and the implementation in the CT and the DT domains are different. Therefore, the aim of this article is to present a tutorial on the RPM models and to give an overview of all the applications.     

Instrumental variable methods for identifying partial differential equation models

This paper presents a refined instrumental variable method for identifying partial differential equation models of distributed parameter systems directly from discrete-time sampled input–output data. The proposed method is compared with conventional least-squares and other instrumental variable-based techniques. Monte Carlo simulation analysis results are presented to illustrate the effectiveness and superiority of the proposed method in the presence of additive output measurement noise and under different spatio-temporal sampling conditions.     

Identification of continuous-time models for nonlinear dynamic systems from discrete data

A new iOFR-MF (iterative orthogonal forward regression--modulating function) algorithm is proposed to identify continuous-time models from noisy data by combining the MF method and the iOFR algorithm. In the new method, a set of candidate terms, which describe different dynamic relationships among the system states or between the input and output, are first constructed. These terms are then modulated using the MF method to generate the data matrix. The iOFR algorithm is next applied to build the relationships between these modulated terms, which include detecting the model structure and estimating the associated parameters. The relationships between the original variables are finally recovered from the model of the modulated terms. Both nonlinear state-space models and a class of higher order nonlinear input–output models are considered. The new direct method is compared with the traditional finite difference method and results show that the new method performs much better than the finite difference method. The new method works well even when the measurements are severely corrupted by noise. The selection of appropriate MFs is also discussed.     

Identification of continuous-time models with slowly time-varying parameters

The off-line estimation of the parameters of continuous-time, linear, time-invariant transfer function models can be achieved straightforwardly using linear prefilters on the measured input and output of the system. The on-line estimation of continuous-time models with time-varying parameters is less straightforward because it requires the updating of the continuous-time prefilter parameters. This paper shows how such on-line estimation is possible by using recursive instrumental variable approaches. The proposed methods are presented in detail and also evaluated on a numerical example using both single experiment and Monte Carlo simulation analysis. In addition, the proposed recursive algorithms are tested using data from two real-life systems.     

Projection-based identification algorithm for grey-box continuous-time models

In this paper, a new identification method for continuous-time models, which can handle various grey-box structures and has strong robustness, is presented. The proposed method is based on an incremental model update scheme and the projection onto the subspace which reflects the model structure. By utilising these schemes, robustness of other continuous-time system identification methods and versatility of generic optimisation algorithms can be integrated into the proposed method. The effectiveness of the proposed method is demonstrated through numerical examples related to a grey-box model in closed-loop system and systems with unknown time-delay.     

Subspace-based continuous-time identification of fractional order systems from non-uniformly sampled data

This work focuses on the identification of fractional commensurate order systems from non-uniformly sampled data. A novel scheme is proposed to solve such problem. In this scheme, the non-uniformly sampled data are first complemented by using fractional Laguerre generating functions. Then, the multivariable output error state space method is employed to identify the relevant system parameters. Moreover, an in-depth property analysis of the proposed scheme is provided. A numerical example is investigated to illustrate the effectiveness of the proposed method.     

反馈未知闭环系统的MRIV法辨识

本文提出了一种改进的精致辅助变量法.这种方法适合于反馈未知的闭环系统的参数估计.本文在理论上分析了此方法的一致性,并通过Monte Carlo仿真实验证实了方法的有效性.     

Efficient parameterisation of nonlinear system models: a comment on Nöel and Schoukens (2018)

Abstract

Nöel, J. P., & Schoukens, J. [2018. Grey-box state-space identification of nonlinear mechanical vibrations. International Journal of Control, 91, 1–22] discuss a methodology for the discrete-time state-space identification of nonlinear systems and apply this to experimental data from the well known Silverbox nonlinear circuit, producing a model characterised by 13 parameters. This model explains the data very well but the parameter estimates are not well defined in the optimisation results, with the very large confidence bounds suggesting that the model is over-parameterised. This comment shows that this is indeed the case and that the data can be explained equally well by an alternative continuous-time, State-Dependent Parameter (SDP) transfer function model with only 6 parameters, the estimates of which are well defined with very tight confidence bounds. The comment also raises questions about how the model form for nonlinear systems such as the Silverbox should be identified and suggests that the Data-Based Mechanistic (DBM) approach to modelling has some advantages in this regard.     

舰艇发电机励磁系统参数辨识研究

介绍辅助变量法与粒子群优化算法在舰艇发电机励磁系统辨识中的应用,并在Labview软件中编写了相应的计算程序。以某舰艇发电机励磁系统为例,在Matlab/Simulink中搭建该励磁系统仿真模型,将采样获得的输入输出数据,输入Labview辨识软件中,估计各参数值。实验分别采用+10%、+50%阶跃响应,辨识系统线性模型和非线性模型,并比较不同噪声幅值情况下的PSO辨识结果。实验结果证明PSO算法在励磁系统参数估计中的有效性。     

Determination of model order for NARX models directly from input-output data

Nonlinear auto-regressive models with exogenous inputs (NARX models) have proved to be versatile and useful empirical models for industrial processes. There are a wide variety of identification methods and model structures from which to choose; in all methods, however, key parameters are the model orders, which are the number of past outputs and inputs used in the model. In this paper the methods of Lipschitz numbers and false nearest neighbors are evaluated as a means of estimating the model orders of dynamic, discrete-time NARX models. No specific model structure is assumed and the model orders are estimated directly from input-output data using only geometric concerns and the continuity property. The two methods are applied to several dynamic systems, including realistic process simulations and experimental data from the UCSB pH neutralization process, and the consistency and accuracy of these methods are examined. The usefulness of these methods of model order determination for radial basis function network (RBFN) identification is examined.     

Robust identification of continuous-time low-order models using moments of a single rectangular pulse response

This paper presents a simple method for identifying first- and second-order processes with dead-time by using moments of a single rectangular pulse response in an open-loop system. A closed-form formula is proposed to determine all parameters of four types of process models for a stable linear time-invariant process. It is shown that the same approach can be extended to the identification of multi-input, multi-output linear processes. It is demonstrated through a comparative analysis that the proposed identification method results in good accuracy with a noisy output, and is also able to closely approximate various high-order processes in those low-order models.     

A practical approach to data modelling in spatial applications

The storage and manipulation of spatial data requires a different style of support from that normally found in commercial database systems. This paper explores the use of the functional data model and the high level language Daplex to provide an integrated tool for the conceptual modelling of spatial data and the manipulation of data values. Importance is attached to allowing dynamic schema definition and to the provision of abstract data types to support spatial objects. The implementation comprises three separate modules and uses an underlying relational DBMS to store all metadata and data values. This modular design has enabled the user interface, Daplex language and storage aspects of the software to be developed independently, creating a system which has already proved to be easily portable. Consideration has also been given to ways of improving system performance.     

Refined instrumental variable methods for identification of LPV Box-Jenkins models

The identification of linear parameter-varying systems in an input-output setting is investigated, focusing on the case when the noise part of the data generating system is an additive colored noise. In the Box-Jenkins and output-error cases, it is shown that the currently available linear regression and instrumental variable methods from the literature are far from being optimal in terms of bias and variance of the estimates. To overcome the underlying problems, a refined instrumental variable method is introduced. The proposed approach is compared to the existing methods via a representative simulation example.     

Uncertainty of transfer function modelling using prior estimated noise models

Assuming “small” model errors (unmodelled dynamics and/or nonlinear distortions) and “large” signal-to-noise ratios we derive in this paper explicit expressions for the covariance matrix of a frequency domain estimator using prior estimated noise models. These analytic expressions (i) give a clear insight in the behaviour of the covariance matrix as a function of the signal-to-noise ratio, the unmodelled dynamics and the nonlinear distortions, and (ii) allow to predict accurately the order of magnitude of the actual uncertainty of the estimates. The link with the classical prediction error approach is also established.     

A mixture of generalized latent variable models for mixed mode and heterogeneous data

In the behavioral, biomedical, and social-psychological sciences, mixed data types such as continuous, ordinal, count, and nominal are common. Subpopulations also often exist and contribute to heterogeneity in the data. In this paper, we propose a mixture of generalized latent variable models (GLVMs) to handle mixed types of heterogeneous data. Different link functions are specified to model data of multiple types. A Bayesian approach, together with the Markov chain Monte Carlo (MCMC) method, is used to conduct the analysis. A modified DIC is used for model selection of mixture components in the GLVMs. A simulation study shows that our proposed methodology performs satisfactorily. An application of mixture GLVM to a data set from the National Longitudinal Surveys of Youth (NLSY) is presented.     

非参数回归模型均值函数结构变点的检测与应用

本文将一类系统参数变点检测问题转化为非参数回归模型均值函数结构变点的检测问题.针对当非参数模型均值函数跃度的长期均值为零时,残量累积和(cumulative sum,CUSUM)统计量无效的问题,首先利用均值函数的核估计构造新统计量,给出了原假设和备择假设下统计量的极限分布;进一步构造Bootstrap检验,证明了Bootstrap检验的一致性;最后以模拟结果表明新方法明显优于已有的方法,并应用于两类实际数据分析,说明方法的有效性.     

Identification of nonlinear errors-in-variables models

The paper is about a generalization of a classical eigenvalue-decomposition method originally developed for errors-in-variables linear system identification to handle an important class of nonlinear problems. A number of examples are presented to call the attention to the most critical part of the procedure turning the identification problem to a generalized eigenvalue–eigenvector calculation problem with symmetrical matrices. The elaborated method generates consistent parameter estimation. Simulation results demonstrate the effectiveness of the proposed algorithm.     

On optimal experiment design for identifying premise and conclusion parameters of Takagi-Sugeno models: Nonlinear regression case

Optimal Experiment Design (OED) is a well-developed concept for regression problems that are linear-in-the-parameters. In case of experiment design to identify nonlinear Takagi-Sugeno (TS) models, non-model-based approaches or OED restricted to the local model parameters (assuming the partitioning to be given) have been proposed. In this article, a Fisher Information Matrix (FIM) based OED method is proposed that considers local model and partition parameters. Due to the nonlinear model, the FIM depends on the model parameters that are subject of the subsequent identification. To resolve this paradoxical situation, at first a model-free space filling design (such as Latin Hypercube Sampling) is carried out. The collected data permits making design decisions such as determining the number of local models and identifying the parameters of an initial TS model. This initial TS model permits a FIM-based OED, such that data is collected which is optimal for a TS model. The estimates of this first stage will in general not be ideal. To become robust against parameter mismatch, a sequential optimal design is applied. In this work the focus is on D-optimal designs. The proposed method is demonstrated for three nonlinear regression problems: an industrial axial compressor and two test functions.     

新旧系统切换中数据转换的研究与实现

数据转换是信息系统升级、新旧信息系统切换过程中的重要工作。按照软件工程的方法,对数据转换过程中的各个环节进行定义,保证通过有效的数据转换工作使历史数据资源在新系统中得以利用。