Recursive State-space Model Identification of Non-uniformly Sampled Systems Using Singular Value Decomposition

In this paper a recursive state-space model identification method is proposed for non-uniformly sampled systems in industrial applications. Two cases for measuring all states and only output(s) of such a system are considered for identification. In the case of state measurement, an identification algorithm based on the singular value decomposition(SVD) is developed to estimate the model parameter matrices by using the least-squares fitting. In the case of output measurement only, another identification algorithm is given by combining the SVD approach with a hierarchical identification strategy. An example is used to demonstrate the effectiveness of the proposed identification method.

RECURSIVE SYSTEM IDENTIFICATION

Most of existing methods in system identification with possible exception of those for linear systems are off-line in nature, and hence are nonrecursive. This paper demonstrates the recent progress in recursive system identification. The recursive identification algorithms are presented not only for linear systems （multivariate ARMAX systems） but also for nonlinear systems such as the Hammerstein and Wiener systems, and the nonlinear ARX systems. The estimates generated by the algorithms are online updated and converge a.s. to the true values as time tends to infinity.

Identification of time-varying system and energy-based optimization of adaptive control in seismically excited structure

The combination of structural health monitoring and vibration control is of great importance to provide components of smart structures.While synthetic algorithms have been proposed,adaptive control that is compatible with changing conditions still needs to be used,and time-varying systems are required to be simultaneously estimated with the application of adaptive control.In this research,the identification of structural time-varying dynamic characteristics and optimized simple adaptive control are integrated.First,reduced variations of physical parameters are estimated online using the multiple forgetting factor recursive least squares(MFRLS)method.Then,the energy from the structural vibration is simultaneously specified to optimize the control force with the identified parameters to be operational.Optimization is also performed based on the probability density function of the energy under the seismic excitation at any time.Finally,the optimal control force is obtained by the simple adaptive control(SAC)algorithm and energy coefficient.A numerical example and benchmark structure are employed to investigate the efficiency of the proposed approach.The simulation results revealed the effectiveness of the integrated online identification and optimal adaptive control in systems.

Experimental and Numerical Study of Structural Identification Using Non-Linear Resonant Decay Method

One of the practical approaches in identifying structures is the non-linear resonant decay method which identifies a non-linear dynamic system utilizing a model based on linear modal space containing the underlying linear system and a small number of extra terms that exhibit the non-linear effects.In this paper,the method is illustrated in a simulated system and an experimental structure.The main objective of the non-linear resonant decay method is to identify the non-linear dynamic systems based on the use of a multi-shaker excitation using appropriated excitation which is obtained from the force appropriation approach.The experimental application of the method is indicated to provide suitable estimates of modal parameters for the identification of non-linear models of structures.

SYSTEM IDENTIFICATION METHOD OF LINEAR AND NON-LINEAR LIQUID PREPARATIVECHROMATOGRAPHIC SEPARATION

The paper proposes the identification method of linear and non-linear chromatographic system. Isotherms and lumped mass transfer coefficients of chromatography separating isomer sorbitol and mannitol on D80 adsorbent are determined. The analyses of root mean square error of chromatography elution curves are carried out. The results show that the system studied is non-linear and the theoretical elution curves of the non-linear chromatographic model are more accurate than those of the linear chromatographic model. Results of parameter sensitivity analyses show that elution curves of non-linear chromatographic separation are more sensitive to the variation of parameter "ai" in the adsorption isotherms than to the variation of parameter "bi" as well as lumped mass transfer coefficients.

Nonlinear Modeling and Identification of the Electro-hydraulic Control System of an Excavator Arm Using BONL Model

Electro-hydraulic control systems are nonlinear in nature and their mathematic models have unknown parameters. Existing research of modeling and identification of the electro-hydraulic control system is mainly based on theoretical state space model, and the parameters identification is hard due to its demand on internal states measurement. Moreover, there are also some hard-to-model nonlinearities in theoretical model, which needs to be overcome. Modeling and identification of the electro-hydraulic control system of an excavator arm based on block-oriented nonlinear（BONL） models is investigated. The nonlinear state space model of the system is built first, and field tests are carried out to reveal the nonlinear characteristics of the system. Based on the physic insight into the system, three BONL models are adopted to describe the highly nonlinear system. The Hammerstein model is composed of a two-segment polynomial nonlinearity followed by a linear dynamic subsystem. The Hammerstein-Wiener（H-W） model is represented by the Hammerstein model in cascade with another single polynomial nonlinearity. A novel Pseudo-Hammerstein-Wiener（P-H-W） model is developed by replacing the single polynomial of the H-W model by a non-smooth backlash function. The key term separation principle is applied to simplify the BONL models into linear-in-parameters struc^tres. Then, a modified recursive least square algorithm（MRLSA） with iterative estimation of internal variables is developed to identify the all the parameters simultaneously. The identification results demonstrate that the BONL models with two-segment polynomial nonlinearities are able to capture the system behavior, and the P-H-W model has the best prediction accuracy. Comparison experiments show that the velocity prediction error of the P-H-W model is reduced by 14%, 30% and 75% to the H-W model, Hammerstein model, and extended auto-regressive （ARX） model, respectively. This research is helpful in controller design, system monitoring and diagnosis.

RECURSIVE STRUCTURE AND QUASI-RECURSIVE STRUCTURE OF ADAPTIVE VOLTERRA FILTER AND THEIR ALGORITHMS AND APPLICATIONS

The recursive structure and quasi-recursive structure of Adaptive Volterra Fil-ter(AVF) are put forward, their algorithms are given, and their characteristics and applications are discussed. The introduction of recursive structure can remarkably reduce the parameters and computational cost of AVF.

Identification of Fuzzy System Via Fuzzy Competitive Learning Method

The paper presents an approach to identfying a fhzzy model composed of fuzzy-logic rules for a multi-in-put/single outpu system. The ther of fuzzy rules and membership functions of input variables are obtained by means of a fuzzy competitive lerning method with a validity criterion. This method avoids the complexity of system structure identilication and decreases the number of fuzzy rules. Recareive least square algorithm can be used to iden-tify the parameters of conclusion polynomials .The proposed method is used to identify the well-known Box-Jenkins da-ta set with the result shawn at the end of the paper to demonstrae its advanages.

CONVERGENCE AND STABILITY OF RECURSIVE DAMPED LEAST SQUARE ALGORITHM

The recursive least square is widely used in parameter identification. But if is easy to bring about the phenomena of parameters burst-off. A convergence analysis of a more stable identification algorithm-recursive damped least square is proposed. This is done by normalizing the measurement vector entering into the identification algorithm. rt is shown that the parametric distance converges to a zero mean random variable. It is also shown that under persistent excitation condition, the condition number of the adaptation gain matrix is bounded, and the variance of the parametric distance is bounded.

Research of internet worm warning system based on system identification

The frequent explosion of Internet worms has been one of the most serious problems in cyberspace security. In this paper, by analyzing the worm＇s propagation model, we propose a new worm warning system based on the method of system identification, and use recursive least squares algorithm to estimate the worm＇s infection rate. The simulation result shows the method we adopted is an efficient way to conduct Internet worm warning.

QRD-BASED MULTICHANNEL ADAPTIVE LATTICEALGORITHMS FOR THE PARAMETERIDENTIFICATION PROBLEM

A pair of multichannel recursive least squares (RLS) adaptive lattice algorithms based on the order recursive of lattice filters and the superior numerical properties of Givens algorithms is derived in this paper. The derivation of the first algorithm is based on QR decomposition of the input data matrix directly, and the Givens rotations approach is used to compute the QR decomposition. Using first a prerotation of the input data matrix and then a repetition of the single channel Givens lattice algorithm, the second algorithm can be obtained. Both algorithms have superior numerical properties, particularly the robustness to wordlength limitations. The parameter vector to be estimated can be extracted directly from internal variables in the present algorithms without a backsolve operation with an extra triangular array. The results of computer simulation of the parameter identification of a two-channel system are presented to confirm efficiently the derivation.

Improved fuzzy identification method based on Hough transformation and fuzzy clustering

This paper presents an approach that is useful for the identification of a fuzzy model in SISO system. The initial values of cluster centers are identified by the Hough transformation, which considers the linearity and continuity of given input-output data, respectively. For the premise parts parameters identification, we use fuzzy-C-means clustering method. The consequent parameters are identified based on recursive least square. This method not only makes approximation more accurate, but also let computation be simpler and the procedure is realized more easily. Finally, it is shown that this method is useful for the identification of a fuzzy model by simulation.

Online battery model parameters identification approach based on bias-compensated forgetting factor recursive least squares

Accuracy of a lithium-ion battery model is pivotal in faithfully representing actual state of battery,thereby influencing safety of entire electric vehicles.Precise estimation of battery model parameters using key measured signals is essential.However,measured signals inevitably carry random noise due to complex real-world operating environments and sensor errors,potentially diminishing model estimation accuracy.Addressing the challenge of accuracy reduction caused by noise,this paper introduces a Bias-Compensated Forgetting Factor Recursive Least Squares(BCFFRLS)method.Initially,a variational error model is crafted to estimate the average weighted variance of random noise.Subsequently,an augmentation matrix is devised to calculate the bias term using augmented and extended parameter vectors,compensating for bias in the parameter estimates.To assess the proposed method's effectiveness in improving parameter identification accuracy,lithium-ion battery experiments were conducted in three test conditions—Urban Dynamometer Driving Schedule(UDDS),Dynamic Stress Test(DST),and Hybrid Pulse Power Characterization(HPPC).The proposed method,alongside two contrasting methods—the offline identification method and Forgetting Factor Recursive Least Squares(FFRLS)—was employed for battery model parameter identification.Comparative analysis reveals substantial improvements,with the mean absolute error reduced by 25%,28%,and 15%,and the root mean square error reduced by 25.1%,42.7%,and 15.9%in UDDS,HPPC,and DST operating conditions,respectively,when compared to the FFRLS method.

Recursive modeling and online identification of lithium-ion batteries for electric vehicle applications

For safe and reliable operation of lithium-ion batteries in electric vehicles,the real-time monitoring of their internal states is important.The purpose of our study is to find an easily implementable,online identification method for lithium-ion batteries in electric vehicles.In this article,we propose an equivalent circuit model structure.Based on the model structure we derive the recursive mathematical description.The recursive extended least square algorithm is introduced to estimate the model parameters online.The accuracy and robustness are validated through experiments and simulations.Real-road driving cycle experiment shows that the proposed online identification method can achieve acceptable accuracy with the maximum error of less than 5.52%.In addition,it is proved that the proposed method can also be used to estimate the real-time SOH and SOC of the batteries.

Non-linear Chemical Process Modelling and Application in Epichlorhydrine Production Plant Using Wavelet Networks

A type of wavelet neural network, in which the scale function isadopted only, is proposed in this paper for non-linear dynamicprocess modelling. Its network size is decreased significantly andthe weight coefficients can be estimated by a linear algorithm. Thewavelet neural network holds some advantages superior to other typesof neural networks. First, its network structure is easy to specifybased on its theoretical analysis and intuition. Secondly, networktraining does not rely on stochastic gradient type techniques andavoids the problem of poor convergence or undesirable local minima.

Recursive identification for EIV ARMAX systems

The input uk and output yk of the multivariate ARMAX system A（x）yk = B（z）uk ＋ C（z）wk are observed with noises： uk^ob△=uk ＋ εk^u and yk^ob △=yk＋ εk^y, where εk^u and εk^y denote the observation noises. Such kind of systems are called errors-in-variables （EIV） systems. In the paper, recursive algorithms based on observations are proposed for estimating coefficients of A（z）, B（z）, C（z）, and the covariance matrix Rw of wk without requiring higher than the second order statistics. The algorithms are convenient for computation and are proved to converge to the system coefficients under reasonable conditions. An illustrative example is provided, and the simulation results are shown to be consistent with the theoretical analysis.

Distributed and recursive blind channel identification to sensor networks

In this paper, the distributed and recursive blind channel identification algorithms are proposed for single-input multi-output （SIMO） systems of sensor networks （both time-invariant and time-varying networks）. At any time, each agent updates its estimate using the local observation and the information derived from its neighboring agents. The algorithms are based on the truncated stochastic approximation and their convergence is proved. A simulation example is presented and the computation results are shown to be consistent with theoretical analysis.

Recursive least squares identification for piecewise affine Hammerstein models

Purpose-The purpose of this paper is to probe the recursive identification of piecewise affine Hammerstein models directly by using input-output data.To explain the identification process of a parametric piecewise affine nonlinear function,the authors prove that the inverse function corresponding to the given piecewise affine nonlinear function is also an equivalent piecewise affine form.Based on this equivalent property,during the detailed identification process with respect to piecewise affine function and linear dynamical system,three recursive least squares methods are proposed to identify those unknown parameters under the probabilistic description or bounded property of noise.Design/methodology/approach-First,the basic recursive least squares method is used to identify those unknown parameters under the probabilistic description of noise.Second,multi-innovation recursive least squares method is proposed to improve the efficiency lacked in basic recursive least squares method.Third,to relax the strict probabilistic description on noise,the authors provide a projection algorithm with a dead zone in the presence of bounded noise and analyze its two properties.Findings-Based on complex mathematical derivation,the inverse function of a given piecewise affine nonlinear function is also an equivalent piecewise affine form.As the least squares method is suited under one condition that the considered noise may be a zero mean random signal,a projection algorithm with a dead zone in the presence of bounded noise can enhance the robustness in the parameter update equation.Originality/value-To the best knowledge of the authors,this is the first attempt at identifying piecewise affine Hammerstein models,which combine a piecewise affine function and a linear dynamical system.In the presence of bounded noise,the modified recursive least squares methods are efficient in identifying two kinds of unknown parameters,so that the common set membership method can be replaced by the proposed methods.

Process data compression based on recursive identification of nonuniformly sampled systems

A recursive identification method is proposed to obtain continuous-time state-space models in systems with nonuniformly sampled （NUS） data. Due to the nonuniform sampling feature, the time interval from one recursion step to the next varies and the parameter is always updated partially at each step. Furthermore, this identification method is applied to form a combined data compression method in NUS processes. The data to be compressed are first classified with respect to a series of potentially existing （possibly time-varying） models, and then modeled by the NUS identification method. The model parameters are stored instead of the identification output data, which makes the first compression. Subsequently, as the second step, the conventional swinging door trending method is carried out on the data from the first step. Numeric results from simulation as well as practical data are given, showing the effectiveness of the proposed identification method and fold increase of compression ratio achieved by the combined data compression method.

滤波辨识(10):多变量Box-Jenkins系统的滤波辅助模型递阶广义增广参数辨识

针对多变量Box-Jenkins模型,即多变量输出误差自回归滑动平均(M-OEARMA)系统,利用滤波辨识理念和辅助模型辨识思想,研究和提出了滤波辅助模型递阶广义增广随机梯度辨识方法、滤波辅助模型递阶多新息广义增广随机梯度辨识方法、滤波辅助模型递阶广义增广递推梯度辨识方法、滤波辅助模型递阶多新息广义增广递推梯度辨识方法、滤波辅助模型递阶广义增广最小二乘辨识方法、滤波辅助模型递阶多新息广义增广最小二乘辨识方法。这些滤波辅助模型递阶广义增广辨识方法可以推广到其他有色噪声干扰下的线性和非线性多变量随机系统中。