Showing papers on "System identification published in 1987"

Water quality modeling: A review of the analysis of uncertainty

Abstract: This paper reviews the role of uncertainty in the identification of mathematical models of water quality and in the application of these models to problems of prediction. More specifically, four problem areas are examined in detail: uncertainty about model structure, uncertainty in the estimated model parameter values, the propagation of prediction errors, and the design of experiments in order to reduce the critical uncertainties associated with a model. The review is rather lengthy, and it has therefore been prepared in effect as two papers. There is a shorter, largely nontechnical version, which gives a quick impression of the current and future issues in the analysis of uncertainty in water quality modeling. Enclosed by this shorter discussion is the main body of the review dealing in turn with (1) identifiability and experimental design, (2) the generation of preliminary model hypotheses under conditions of sparse, grossly uncertain field data, (3) the selection and evaluation of model structure, (4) parameter estimation (model calibration), (5) checks and balances on the identified model, i.e., model “verification” and model discrimination, and (6) prediction error propagation. Much time is spent in discussing the algorithms of system identification, in particular, the methods of recursive estimation, and in relating these algorithms and the subject of identification to the problems of prediction uncertainty and first-order error analysis. There are two obvious omissions from the review. It is not concerned primarily with either the development and solution of stochastic differential equations or the issue of decision making under uncertainty, although clearly some reference must be made to these topics. In brief, the review concludes (not surprisingly) that much work has been done on the analysis of uncertainty in the development of mathematical models of water quality, and much remains to be done. A lack of model identifiability has been an outstanding difficulty in the interpretation and explanation of past observed system behavior, and there is ample evidence to show that the “larger,” more “comprehensive” models are easily capable of generating highly uncertain predictions of future behavior. For the future of the subject, it is speculated that there is the possibility of progress in the development of novel algorithms for model structure identification, a need for new questions to be posed in the problem of prediction, and a distinct challenge to the conventional views of this review in the new forms of knowledge representation and manipulation now emerging from the field of artificial intelligence.

Linear stochastic systems

Abstract: Stochastic Processes Linear Stochastic Systems Estimation Theory Stochastic Realization Theory System Identification: Foundations and Basic Concepts Least Squares Parameter Estimation Maximum Likelihood Estimation of Gaussian Armax and State-Space System Minimum Prediction Error Identification Methods Non-Stationary System Identification Feedback, Causality, and Closed Loop System Identification Linear-Quadratic Stochastic Control Stochastic Adaptive Control Appendix 1: Probability Theory Appendix 2: System Theory Appendix 3: Harmonic Analysis.

Identification of linear stochastic systems via second- and fourth-order cumulant matching

Abstract: The identification problem for time-invariant single-input single-output linear stochastic systems driven by non-Gaussian white noise is considered The system is not restricted to be minimum phase, and it is allowed to contain all-pass components A least-squares criterion that involves matching the second- and the fourth-order cumulant functions of the noisy observations is proposed Knowledge of the probability distribution of the driving noise is not required An order determination criterion that is a modification of the Akaike information criterion is also proposed Strong consistency of the proposed estimator is proved under certain sufficient conditions Simulation results are presented to illustrate the method

Identification of continuous systems

Abstract: Introduction. Continuous-Time Models of Dynamical Systems. Nonparametric Models. Parametric Models. Stochastic Models of Linear Time-Invariant Systems. Models of Distributed Parameter Systems (DPS). Signals and their Representations. Functions in the Ordinary Sense. Distribution or Generalized Functions. Identification of Linear Time-Invariant (LTIV) Systems via Nonparametric Models. The Role of Nonparametric Models in Continuous System Identification. Test Signals for System Identification. Identification of Linear Time-Invariant Systems - Time-Domain Approach. Frequency-Domain Approach. Methods for Obtaining Transfer Functions from Nonparametric Models. Numerical Transformations between Time- and Frequency-Domains. Parameter Estimation for Continuous-Time Models. The Primary Stage. The Secondary Stage: Parameter Estimation. Identification of Linear Systems Using Adaptive Models. Gradient Methods. Frequency-Domain. Stability Theory. Linear Filters. Identification of Multi-Input Multi-Output (MIMO) Systems, Distributed Parameter Systems (DPS) and Systems with Unknown Delays and Nonlinear Elements. MIMO Systems. Time-Varying Parameter Systems (TVPS). Lumped Systems with Unknown Time-Delays. Identification of Systems with Unknown Nonlinear Elements. Identification of Distributed Parameter Systems. Determination of System Structure. Index.

The asymptotic local approach to change detection and model validation

Abstract: We present a systematic approach for the design of change detection and model validation algorithms for dynamical systems. We show how to associate to any identification algorithm a change detection and a model validation procedure, which are optimal in some asymptotic sense. The foundations of our method go back to the asymptotic local approach in statistics, and our method generalizes this approach.

Optimum approximation for residual stiffness in linear system identification

Abstract: A new method of system identification uti 1 i zes projector m atrix theory and the MoorePenrose generalized inverse to derive an analytical stiffness matrix which, when combined with the analytical mass matrix, will more closely p redict modal test results. Weighting matrices a re used to enforce connectivity and make weighted corrections to the original analytical stiffness matrix. A simple and straightforward mathematical formulation is obtained. The method is compared and contrasted with other methods found in the literature, and a simple numerical example is presented.

Recursive identification of bilinear systems

Abstract: Methods of identifying bilinear systems from recorded input-output data are discussed in this article A short survey of the existing literature on the topic is given ‘Standard’ methods from linear systems identification, such as least squares, extended least squares, recursive prediction error and instrumental variable methods are transferred to bilinear, input-output model structures and tested in simulation Special attention is paid to problems of stabilizing the model predictor, and it is shown how a time-varying Kalman filter and associated parameter estimation algorithm can deal with this problem

An experimental procedure for simulation response surface model identification

Abstract: An experimental method for identifying an appropriate model for a simulation response surface is presented. This technique can be used for globally identifying those factors in a simulation that have a significant influence on the output. The experiments are run in the frequency domain. A simulation model is run with input factors that oscillate at different frequencies during a run. The functional form of a response surface model for the simulation is indicated by the frequency spectrum of the output process. The statistical significance of each term in a prospective response surface model can be measured. Conditions are given for which the frequency domain approach is equivalent to ranking terms in a response surface model by their correlation with the output. Frequency domain simulation experiments typically will require many fewer computer runs than conventional run-oriented simulation experiments.

On the Identification and Approximation of Linear Systems

Abstract: This thesis consists of four parts. In the first one, the connections between system identification and model reduction are discussed. The second part deals with the problem of estimating ARMA models for narrow band processes. In the third part we study how to build models of continuous time dynamical models form discrete time measurements, and in the fourth part we show how to affect the bias distribution in transfer function estimation.No mathematical models are perfect descriptions of physical systems. Recently there has been a growing interest in how approximate models will affect the results, in e.g. control design. System identification deals with the problem of building mathematical models of dynamical systems based on observed data from the system. The theme of this thesis is to study how the fact that the physical system cannot be exactly represented within the chosen model set will influence the identified model.In parts I and II the application of model reduction in system identification is investigated. It is showed how the fact that the high order model is obtained from an identification experiment will affect the choice of model reduction procedure. A by-product will be an identification algorithm based on an high order ARX estimate and model reduction.In part III the problem of building models of continuous time linear dynamical systems based on discrete time observations of the system is considered. By studying continuous time prediction error methods it is shown how the choice of model structure and sampling interval will affect the resulting estimate in case of fast sampling.In part IV it is shown how the use of prefilters, noise model, sampling interval and prediction horizon will affect the distribution of bias transfer function estimation. An important aspect is that the true sytem is not assumed to be exactly represented within the chosen model set. It is shown how the distribution of bias in the frequency domain is governed by a weighting function that emphasizes different frequency bands.

Hammerstein system identification by non-parametric regression estimation

Abstract: A discrete-time, multiple-input non-linear Hammerstein system is identified. The dynamical subsystem is recovered using the standard correlation method. The main results concern estimation of the non-linear memoryless subsystem. No conditions concerning the functional form of the transform characteristic of the subsystem are made and an algorithm for estimation of the characteristic is given. The algorithm is simply a non-parametric kernel estimate of the regression function calculated from the dependent data. It is shown that the algorithm converges to the characteristic of the subsystem in the pointwise as well as the global sense. For sufficiently smooth characteristics, the rate of convergence is o(n-1/(2+d in probability, where d is the dimension of the input variable.

Integral-equation approach to system identification

Abstract: This paper presents an integral-equation approach to the problem of parameter identification in continuous linear SISO, MIMO and linear-in-parameters nonlinear systems. Parameter estimates are deduced from an appropriate set of overdetermined equations, which are solved in a least-squares sense. The effects of deterministic disturbances at system input and output are also included in the analysis.

Modeling and Identification in Structural Dynamics

Abstract: Analytical modeling of structures subjected to ground motions is an important aspect of fully dynamic earthquake-resistant design. In general, linear models are only sufficient to represent structural responses resulting from earthquake motions of small amplitudes. However, the response of structures during strong ground motions is highly nonlinear and hysteretic. System identification 1s an effective tool for developing analytical models from experimental data. Testing of full-scale prototype structures remains the most realistic and reliable source of inelastic seismic response data. Pseudo-dynamic testing is a recently developed quasi-static procedure for subjecting full-scale structures to simulated earthquake response. The present study deals with structural modeling and the determination of optimal linear and nonlinear models by applying system identification techniques to elastic and inelastic pseudo-dynamic data from a full-scale, six-story steel structure. It is shown that the feedback of experimental errors during the pseudo-dynamic tests significantly affected the higher modes and led to an effective negative damping for the third mode. The contributions of these errors are accounted for and the small-amplitude modal properties of the test structure are determined. These properties are in agreement with the values obtained from a shaking table test of a 0.3 scale model. The nonlinear hysteretic behavior of the structure during strong ground motions is represented by a general class of Masing models. A simple model belonging to this class is chosen. with parameters which can be estimated theoretically, thereby making this type of model potentially useful during the design stages. The above model is identified from the experimental data and then its prediction capability and application in seismic design and analysis are examined.

Adaptive Uncertainty Modeling: On-Line Robust Control Design

Abstract: An approach is presented to the problem of designing a robust control using on-line measurements The idea is to use standard methods of parametric system identification to obtain a nominal estimate of the plant transfer function Non-parametric spectral methods are then used to obtain a frequency domian expression for model uncertainty If the model uncertainty exceeds a specified frequency bound, which has been predetermined from the nominal model and the performance criteria, then data filters used in the system identification are modified and the proceedure is repeated An analysis is presented which establishes conditions under which the proceedure will actually converge to a satisfactory robust design An example is provided which illustrates the method and supporting analysis

Identification of a linear system observed through zero-memory non-linearity

Abstract: The paper deals with the identification problem for the Wiener-type system, where the memoryless output non-linearity is known but is not necessarily one-to-one or even monotonic. First, the deterministic identifiability test for the linear dynamic segment is derived assuming that the respective segment outputs are accessible for direct measurements. Next, using the results by Masry and Cambanis (1980), a least-squares type parameter estimation algorithm for linear dynamics is proposed for the case where only the noise-corrupted outputs of the overall non-linear tandem can be gained. A convergence with probability one is shown of the parameter estimate to the true value of the system parameter vector and some computational aspects of the proposed algorithm are discussed.

Identification of an industrial process : a Markov parameter approach

Abstract: • A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers.

A Microcomputer Based On-Line Identification Approach to Power System Dynamic Load Modelling

Abstract: An on-line method for the development of power system load models using system identification techniques is presented. The modelling procedure involves the selection of the load model structure as well as the estimation of the load model parameters. A load model structure selection technique based on the model reference error cost function is used and a square root based least squares estimator is developed. The collection of large volumes of data, for later off-line analysis, is avoided by using an online microcomputer system for the acquisition and analysis of perturbed load data. Load tests were carried out for both agricultural and industrial/commercial loads and typical results obtained are also presented in this paper.

Determination of Loudspeaker Driver Parameters Using a System Identification Technique

Abstract: A time-domain method for measuring the parameters of linear models of loudspeaker drivers is described. The loudspeaker is excited by a low-pass filtered square-wave voltage or current input. In addition to voltage and current, the cone displacement is measured and recorded by a personal computer. From these data the parameters are estimated by system identification techniques, in particular the least-squares and the instrumental-variable algorithms

Structural Parameter Identification in the Frequency Domain: The Use of Overdetermined Systems

Abstract: This paper deals with the fitting of a rational function to an experimentally determined frequency domain transfer function. Examples show that the use of overdetermined fitted systems improve the identification in noisy situations. A method is presented, enabling the determination of the number of zero/poles of the system, and the relation to the rank of the matrix used in a least square identification method.

Qualitative simulation of technical systems using the general system problem solving framework

Abstract: In this paper, it is discussed how the General System Problem Solving (GSPS) Framework1 can be applied to the identification of technical systems for the purpose of a qualitative simulation of such systems. Both advantages and severe shortcomings of this identification technique are demonstrated, and it is discussed under what circumstances this technique may eventually lead to good results. Major emphasis is devoted to the design of multi-layered hierarchical control systems.

Induction Motor Identification by a Microcomputer-Based Structure

Abstract: The paper deals with the parameter estimation of an induction motor performed through a microcomputer-based data acquisition system and recursive identification algorithms (RLS and RGLS) implemented by means of a general purpose computer The microcomputer-based data acquisition system is essentially made by connecting the Z80 CPU with its peripherals and auxiliary memories through a bus standard The motor is represented by a classical fifth-order model linearized around a usual working point; an approximate third-order model, obtained via balanced realization, is in good correlation with the original one according to the identification aims and to the measurement set efficiency An original CAD procedure is utilized to determine the electrical parameters

Identification of ARX models with markovian parameters

Abstract: Many different recursive identification methods for time-varying systems have been suggested in the literature. An assumption that the variations in the system parameters are slow is common for all the methods. When using the methods on systems with faster variations, one is forced to compromise between alertness to parameter variations on one hand and noise sensitivity on the other. The topic of this paper is to investigate if this compromise can be avoided for a special class of systems. The systems considered are such that their dynamic changes between some different typical modes. The philosophy behind the approach taken in the paper is to separate the observations into different sets corresponding to the different modes. The parameters of the different modes can then be estimated using the separated data sets. Technically, this parallel modelling is achieved by describing the system parameters as the realizations of a Markov chain. A parameter-identification algorithm for time-varying ARX mo...