System Identification Framework Research Articles

Frequency Domain Identification of Linear, Deterministically Time-Varying Systems

This paper proposes an extension of the framework of linear time invariant system identification to linear slowly time-varying system identification. The class of systems considered is described by ordinary differential equations with coefficients varying piecewise polynomially with time. The estimation is performed in the frequency domain using multisine excitation signals within an errors-in-variables framework. It is also discussed how multisine excitations provide estimates of, on the one hand, the speed of variation of the system and, on the other hand, an estimation of a non-parametric noise model.

222 LMIに基づくシステム同定法 : 台湾NCREEベンチマーク構造物の同定

A method for system identification with Linear Matrix Inequalities (LMIs) is proposed in this report. We show that system identification problems for various types of systems, e.g., an identification problem of LTI discrete time systems, continuous time systems and time varying systems etc., can be formulated as an LMI optimization problem. With the present problem formulation we can easily incorporate inequality constraints on identified parameters, e.g., a constraint on the upper and the lower bounds and/or quadratic constraints, etc.. This property helps us to get the mathematical model that is physically valid, such as the damping and the stiffness matrix of mechanical systems generally take positive value. Furthermore, the proposed LMI formulation for system identification can be applied to a framework of iterative system identification and controller design. The effectiveness the present identification methodology is experimentally examined with a system identification for a 3-story benchmark building of NCREE, Taiwan.

Practical estimation of Volterra filters of arbitrary degree

Generalized Fock spaces (GFS) were proposed some time ago as a general framework for non-linear system identification and signal analysis. Corresponding to a particular class of reproducing kernel Hubert spaces (RKHS) they provide a natural framework for the estimation of continuous- and discrete-time Volterra filters (VF). Whilst both finite and infinite degree VF are treated in a single framework using GFS an open question is the practical estimation of infinite degree VF. In this paper this problem is resolved and it is shown how VF of arbitrary degree (including infinite) can be computed with finite resources. The solutions are global best approximations to the entire VF based on the available data. Use is made of recent advances in the machine learning community, such as the support vector machine, which make extensive use of RKHS ideas. This paper also highlights the importance of this work to the system identification community. A number of particular contributions are made including a derivation of a particular GFS for VF which permits a simply computable reproducing kernel, derivations of the associated mappings between Volterra parameter space and RKHS parameter space which permit the extraction of the Volterra parameters from the RKHS approximation and solve a set of “free” parameters, extending the GFS framework to include regularization and a detailed simulation-based comparison of the estimation of VF.

Linear Predictor-Based Lossless Compression of Vibration Sensor Data: Systems Approach

This paper presents a novel systems approach to compressing sensor network data. Unlike previous data compression methods, the proposed lossless linear predictor-based sensor data compression method utilizes structural system information to minimize the signal correlation in sensor network data. In the proposed method, linear predictor is derived in a system identification framework in which auto-regressive (AR) model is used as its model structure and the instrumental variables (IV) method is used to calculate the predictor parameters. A parametric study was carried out to study the effects of changes in system property, number of sensors, and sensor noise level on the compression performance of the proposed method. Both numerical simulation and experimental results show that the proposed sensor data compression method has a better compression performance than conventional linear predictor-based data compression method for single sensor.

Efficient seismic response data storage and transmission using ARX model-based sensor data compression algorithm

This paper presents a linear predictor (LP)-based lossless sensor data compression algorithm for efficient transmission, storage and retrieval of seismic data. Auto-Regressive with eXogenous input (ARX) model is selected as the model structure of LP. Since earthquake ground motion is typically measured at the base of monitored structures, the ARX model parameters are calculated in a system identification framework using sensor network data and measured input signals. In this way, sensor data compression takes advantage of structural system information to maximize the sensor data compression performance. Numerical simulation results show that several factors including LP order, measurement noise, input and limited sensor number affect the performance of the proposed lossless sensor data compression algorithm concerned. Generally, the lossless data compression algorithm is capable of reducing the size of raw sensor data while causing no information loss in the sensor data. Copyright © 2005 John Wiley & Sons, Ltd.

Sensor fusion of a railway bridge load test using neural networks

Field testing of bridge vibrations induced by passage of vehicle is an economic and practical form of bridge load testing. Data processing of this type of tests are usually carried out in a system identification framework using output measurements techniques which are categorized as parametric or nonparametric methods. These methods are based on the theory of probability. Learning theory which stems its origin from two separate disciplines of statistical learning theory and neural networks, presents an efficient and robust framework for data processing of such tests. In this article, the linear two layer feed forward neural network (NN) with back propagation learning rule has been adapted for strain and displacement sensors fusion of a railway bridge load test. The trained NN has been used for structural analysis and finite element (FE) model updating.

Subspace system identification framework for the analysis of multimoded propagation of THz-transient signals

We provide a system identification framework for the analysis of THz-transient data. The subspace identification algorithm for both deterministic and stochastic systems is used to model the time-domain responses of structures under broadband excitation. Structures with additional time delays can be modelled within the state-space framework using additional state variables. We compare the numerical stability of the commonly used least-squares ARX models to that of the subspace N4SID algorithm by using examples of fourth-order and eighth-order systems under pulse and chirp excitation conditions. These models correspond to structures having two and four modes simultaneously propagating respectively. We show that chirp excitation combined with the subspace identification algorithm can provide a better identification of the underlying mode dynamics than the ARX model does as the complexity of the system increases. The use of an identified state-space model for mode demixing, upon transformation to a decoupled realization form is illustrated. Applications of state-space models and the N4SID algorithm to THz transient spectroscopy as well as to optical systems are highlighted.

On the Parameter Estimation and Modeling of Aggregate Power System Loads

This paper addressed some theoretical and practical issues relevant to the problem of power system load modeling and identification. Two identification techniques are developed in the theoretical framework of stochastic system identification. The identification techniques presented in this paper belong to the family of output error models; both techniques are based on well-established equations describing load recovery mechanisms having a commonly recognized physical appeal. Numerical experiments with artificially created data were first performed on the proposed techniques and the estimates obtained proved to be asymptotically unbiased and achieved the corresponding Crame/spl acute/r-Rao lower bound. The proposed techniques were then tested using actual field measurements taken at a paper mill, and the corresponding results were used to validate a commonly used aggregate load model. The results reported in this paper indicate that the existing load models satisfactorily describe the actual behavior of the physical load and can be reliably estimated using the identification techniques presented herein.

A unified wavelet-based modelling framework for non-linear system identification: the WANARX model structure

A new unified modelling framework based on the superposition of additive submodels, functional components, and wavelet decompositions is proposed for non-linear system identification. A non-linear model, which is often represented using a multivariate non-linear function, is initially decomposed into a number of functional components via the well-known analysis of variance (ANOVA) expression, which can be viewed as a special form of the NARX (non-linear autoregressive with exogenous inputs) model for representing dynamic input–output systems. By expanding each functional component using wavelet decompositions including the regular lattice frame decomposition, wavelet series and multiresolution wavelet decompositions, the multivariate non-linear model can then be converted into a linear-in-the-parameters problem, which can be solved using least-squares type methods. An efficient model structure determination approach based upon a forward orthogonal least squares (OLS) algorithm, which involves a stepwise orthogonalization of the regressors and a forward selection of the relevant model terms based on the error reduction ratio (ERR), is employed to solve the linear-in-the-parameters problem in the present study. The new modelling structure is referred to as a wavelet-based ANOVA decomposition of the NARX model or simply WANARX model, and can be applied to represent high-order and high dimensional non-linear systems.

Mathematical foundations of qualitative reasoning

We examine different formalisms for modeling qualitatively physical systems and their associated inferential processes that allow us to derive qualitative predictions from the models. We highlight the mathematical aspects of these processes along with their potential and limitations. The article then bridges to quantitative modeling, highlighting the benefits of qualitative reasoning-based approaches in the framework of system identification, and discusses open research issues.

Identification of Linear Systems with Nonlinear Distortions

In this paper the impact of nonlinear distortions on the linear system identification framework is studied. In the first part the nonlinear system is replaced by a linear model plus a nonlinear noise source. The properties of this representation are studied. Next a method to detect, qualify and quantify the nonlinear distortions is presented. In the second part, the (non)-parametric identification of the best linear approximation is studied. In the last part, the linear modelling approach is extended towards nonlinear modelling. A fast approximate nonlinear modelling framework is set up that is a natural extension of the linear framework, and bridges the gap between the linear and the nonlinear identification approaches.

Neural networks for process control and optimization: Two industrial applications

Abstract The two most widely used neural models, multilayer perceptron (MLP) and radial basis function network (RBFN), are presented in the framework of system identification and control. The main steps for building such nonlinear black box models are regressor choice, selection of internal architecture, and parameter estimation. The advantages of neural network models are summarized: universal approximation capabilities, flexibility, and parsimony. Two applications are described in steel industry and water treatment, respectively, the control of alloying process in a hot dipped galvanizing line and the control of a coagulation process in a drinking water treatment plant. These examples highlight the interest of neural techniques, when complex nonlinear phenomena are involved, but the empirical knowledge of control operators can be learned.

Genetic programming based approaches to identification and fault diagnosis of non-linear dynamic systems

System identification is one of the most important research directions. It is a diverse field which can be employed in many different areas. One of them is the model-based fault diagnosis. Thus, the problems of system identification and fault diagnosis are closely related. Unfortunately, in both cases, the research is strongly oriented towards linear systems, while the problem of identification and fault diagnosis of non-linear dynamic systems still remains open. There are, of course, many more or less sophisticated approaches to this problem, although they are not as reliable and universal as those related to linear systems, and the choice of the method to be used depends on the application. The purpose of this paper is to provide a new system identification framework based on a genetic programming technique. Moreover, a fault diagnosis scheme for non-linear systems is proposed. In particular, a new fault detection observer is presented, and the Lyapunov approach is used to show that the proposed observer is convergent under certain conditions. It is also shown how to use the genetic programming technique to increase the convergence rate of the observer. The final part of this paper contains numerical examples concerning identification of chosen parts of the evaporation station at the Lublin Sugar Factory S.A., as well as state estimation and fault diagnosis of an induction motor.

Persistent identification of systems with unmodeled dynamics and exogenous disturbances

In this paper, a novel framework of system identification is introduced to capture the hybrid features of systems subject to both deterministic unmodeled dynamics and stochastic observation disturbances. Using the concepts of persistent identification, control-oriented system modeling and stochastic analysis, we investigate the central issues of irreducible identification errors and time complexity in such identification problems. Upper and lower bounds on errors and speed of persistent identification are obtained. The error bounds are expressed as functions of observation lengths, sizes of unmodeled dynamics, and probability distributions of disturbances. Asymptotic normality and complexity lower bounds are investigated when periodic inputs and LS estimation are applied. Generic features of asymptotic normality are further explored to extend the asymptotic lower bounds to a wider range of signals and identification mappings.

Generic Metallurgical Quality Control Methodology for Furnaces on the Basis of Thermodynamics and Dynamic System Identification Techniques

A generic non-linear dynamic modelling approach for the quality control of metallurgical furnaces is discussed, in this paper focusing on furnaces with long time constants (e.g. blast furnaces, submerged-arc furnaces). Non-linear system identification techniques, including neural networks and rule induction from decision trees, were applied in a classic linear system identification framework. Very importantly, a simple hybrid methodology is described with which the trends in the metallurgical models derived are verified with thermodynamic equilibrium data.

Neural predictive controller for insulin delivery using the subcutaneous route.

A neural predictive controller for closed-loop control of glucose using subcutaneous (s.c.) tissue glucose measurement and s.c. infusion of monomeric insulin analogs was developed and evaluated in a simulation study. The proposed control strategy is based on off-line system identification using neural networks (NN's) and nonlinear model predictive controller design. The system identification framework combines the concept of nonlinear autoregressive model with exogenous inputs (NARX) system representation, regularization approach for constructing radial basis function NN's, and validation methods for nonlinear systems. Numerical studies on system identification and closed-loop control of glucose were carried out using a comprehensive model of glucose regulation and a pharmacokinetic model for the absorption of monomeric insulin analogs from the s.c. depot. The system identification procedure enabled construction of a parsimonious network from the simulated data, and consequently, design of a controller using multiple-step-ahead predictions of the previously identified model. According to the simulation results, stable control is achievable in the presence of large noise levels, for unknown or variable time delays as well as for slow time variations of the controlled process. However, the control limitations due to the s.c. insulin administration makes additional action from the patient at meal time necessary.

A linear regression approach to state-space subspace system identification

Recently, state-space subspace system identification (4SID) has been suggested as an alternative to the more traditional prediction error system identification. The aim of this paper is to analyze the connections between these two different approaches to system identification. The conclusion is that 4SID can be viewed as a linear regression multistep-ahead prediction error method with certain rank constraints. This allows us to describe 4SID methods within the standard framework of system identification and linear regression estimation. For example, this observation is used to compare different cost-functions which occur rather implicitly in the ordinary framework of 4SID. From the cost-functions, estimates of the extended observability matrix are derived and related to previous work. Based on the estimates of the observability matrix, the asymptotic properties of two pole estimators, namely the shift invariance method and a weighted subspace fitting method, are analyzed. Expressions for the asymptotic variances of the pole estimation error are given. From these expressions, difficulties in choosing userspecified parameters are pointed out. Furthermore, it is found that a row-weighting in the subspace estimation step does not affect the pole estimation error asymptotically.

Use of random noise for on-line transducer modeling in an adaptive active attenuation system

Active sound attenuation systems may be described using a system identification framework in which an adaptive filter is used to model the performance of an unknown acoustical plant. An error signal may be obtained from a location following an acoustical summing junction where the undesired noise is combined with the output of a secondary sound source. For the model output to properly converge to a value that will minimize the error signal, it is frequently necessary to determine the transfer function of the secondary sound source and the path to the error signal measurement. Since these transfer functions are unknown and continuously changing in a real system, it is desirable to perform continuous on-line modeling of the output transducer and error path. In this article, the use of an auxiliary random noise generator for this modeling is described. Based on a Galois sequence, this technique is easy to implement, provides continuous on-line modeling, and has minimal effect on the final value of the error signal.

The use of random noise for on‐line transducer modeling in an adaptive active attenuation system

Active sound attenuation systems may be described using a system identification framework in which an adaptive filter is used to model the performance of an unknown acoustical plant. An error signal may be obtained from a location following an acoustical summing junction where the undesired noise is combined with the output of a secondary sound source. In order for the model output to properly converge to a value that will minimize the error signal, it is frequently necessary to determine the transfer function of the secondary sound source and the path to the error signal measurement. Since these transfer functions are continuously changing in a real system, it is desirable to perform continuous on‐line modeling of the output transducer and error path. In this paper, the use of an auxiliary random noise generator for this modeling is described. Based on a Galois sequence, this technique is easy to implement, provides continuous on‐line modeling, and has minimal effect on the final value of the error signal.

Parametric identification of transient electromagnetic systems

Data into and out of a transient eletromagnetic system are considered in the framework of modern system identification. System solutions that take the form of a complex exponential series are discussed. Since the identification of the parameters in the series is non-linear, emphasis shifts to the identification of the parameters in the difference equation whose solution is the exponential series. The subject is cast in the formalism of system identification with generalizations to more complex systems. Two examples are given, one involving an actual electromagnetic experiment.