Showing papers on "System identification published in 1973"

Integrated System Identification and Optimization

Abstract: Publisher Summary The modern systems approach in handling large scale problems includes the concepts of system identification and optimization. The coupling relationship between these concepts is inherent in the nature of the desired “optimal solution.” Any mathematical model consists of unknown variables and “known” parameters characterizing the system. These parameters are not known, but are estimated or determined under non-optimal conditions. The solution that is generated from such system models might be non-optimal. The identification of the system's parameters, referred to as system modeling, is essential to obtain an optimal control policy. This chapter discusses the coupling relationship between these concepts and describes the analytical tools and methods for tackling the joint problem. Mathematical models, which aim at representing real physical systems in quantitative form, have become important tools in the design, synthesis, analysis, operation, and control of complex systems.

On joint detection, estimation and system identification: discrete data case†

Abstract: The recent results of Lainiotis (1971 a, b, 1971) on single-shot, as well as multishot, joint detection, estimation and system identification for continuous data and dynamics are extended to multishot, discrete data and discrete dynamical systems. The results are given for the signals generated by the linear dynamical systems with unknown parameter vectors and driven by white gaussian sequences, where the observation contains additive white gaussian noise. Specifically, it is shown that the above problem constitutes a class of non-linear mean-square estimation problems. By utilizing the adaptive approach, closed-form integral expressions are obtained for simultaneously optimal detection, estimation and system identification. In addition, several approximate algorithms that utilize linear Kalman estimators are presented to limit the storage requirement to finite size and reduce computational requirements. The results presented in this paper are applicable to both independent and Markov signalling sources

Optimal test signal design for linear S.I.S.O. system identification

Abstract: A sufficient condition for consistent estimates of parametera in linear S.I.S.O. system identification is that the input signal should be ‘ persistently exciting ’, However,. in practice the exact nature of the test signal has a direct bearing upon the identification accuracy. This paper shows how a-priori knowledge of the approximate system and noise model parameters may be used to design a test signal which will minimize the variance of the parameter estimates. The design procedure is computationally efficient as full advantage is taken of the special structure of linear S.I.S.O. systems. The optimal test signals are shown to result in a significant reduction in the parameter variances. This is of considerable practical importance as either the experiment time may be reduced for the same model accuracy or for fixed experiment time a model of much higher accuracy may be obtained.

On the structure of a class of nonlinear systems

Abstract: Nonlinear systems composed of linear dynamic subsystems in cascade with static power nonlinearities are considered A structure theory is developed based on the representation of input/output behavior by rational functions in several variables An algorithm is given which solves the minimal complete realization problem for two forms of the representation A basis for identification of the representation from input/output experiments is also developed Examples are worked in detail to illustrate the results

Structural Aspects of System Identification

Abstract: The problem of identifying linear dynamical systems is studied by considering structural and deterministic properties of linear systems that have an impact on stochastic identification algorithms. In particular considered is parametrization of linear systems so that there is a unique solution and all systems in appropriate class can be represented. It is assumed that a parametrization of system matrices has been established from a priori knowledge of the system, and the question is considered of when the unknown parameters of this system can be identified from input/output observations. It is assumed that the transfer function can be asymptotically identified, and the conditions are derived for the local, global and partial identifiability of the parametrization. Then it is shown that, with the right formulation, identifiability in the presence of feedback can be treated in the same way. Similarly the identifiability of parametrizations of systems driven by unobserved white noise is considered using the results from the theory of spectral factorization.

A Numerical Algorithm for Identifying Spread Functions of Shift-Invariant Imaging Systems

Abstract: Numerical optimization techniques are applied to the identification of linear, shift-invariant imaging systems in the presence of noise. The approach used is to model the available or measured image of a real known object as the planar convolution of object and system-spread function and additive noise. The spread function is derived by minimization of a spatial error criterion (least squares) and characterized using a matric formalism. The numerical realization of the algorithm is discussed in detail; the most substantial problem encountered being the calculation of a vector-generalized inverse. This problem is avoided in the special case where the object scene is taken to be decomposable.

Identification and modelling of large-scale systems using sensitivity analysis †

Abstract: This paper considers the parametric identification of large-scale systems from noise-corrupted output observations. Computational tractability is achieved using perturbation techniques for decoupling and system-order reduction. The influence of the state variable model assumed for the original system on the performance of the identification system is discussed. Examples are given which demonstrate the effectiveness of the identification techniques.

Hierarchical system identification of models for urban dynamics

Abstract: A critical problem in urban modeling is the validation of system models and identification of system parameters within an assumed structure. This paper applies recent developments in system identification in hierarchical structure to identification of system parameters for two models of urban dynamics.

A new criterion for modeling systems

Abstract: The criterion that is proposed is an expected value of the mean square response error as an alternative to testing a model against new data. Modeling with respect to this new criterion does not change the estimate for a given model format from a maximum likelihood estimate or mean square response error estimate. The new criterion does, however, provide a means of comparing models with different formats and varying complexity. A numerical example is used to illustrate the application of the proposed criteria and the problem of searching for the best model. For all but the most trivial system identification problems, it is shown that a prohibitive number of combinations of terms of the model must be investigated to ensure the final model is best.

Discrete-time system identification by the correlation method

Abstract: The pseudorandom binary sequence is applied to the parameter estimation of discrete-time systems. The proposed method, based on the correlation analysis, gives a computationally simple and effective way of parameter estimation. The estimates of the parameters are shown to be asymptotically unbiased.

Estimation of the parameters of a lung model with clinical applications

Abstract: In a mathematical representation of a physiological system variables of the model usually correspond to particular physiological variables, and model paraemters can be associated with specific quantities in the real system. This paper discusses the application of system identification and parameter estimatiion techniques for estimation of parameters of a lung model. Experimental aspects are outlined and potential clinical applications discussed.

System identification using almost periodic functions: application to non-linearities with memory

Abstract: A method for measuring by crosscorrelation the impulse responses of the linear portions of a system containing a zero-memory non-linearity is shown to be applicable to certain typos of non-linear characteristic with memory. Several situations are analysed and some experimental results presented. A computer programme is given for calculating the parameters of the input signal from a given tabulated non-linear characteristic.

Considerations Related to Ill-Posed and Well-Posed Problems in System Identification.

Abstract: : The authors introduce a class of input/output representations (which are called lambda-representations) for linear, time-invariant systems. For many cases of practical interest the identification of one of these representations is mathematically well-posed. Its determination is thus relatively insensitive to certain experimental uncertainties and rational error-in-identification bounds may be found. Impulse response identification almost always leads to an ill-posed problem, so lambda-representation is often an attractive alternate nonparametric model for physical systems which must be identified from input/output records. Among the practical considerations investigated in this report are the effect of input and output uncertainties (noise) in the identification experiment, and the treatment of the case when only discrete data are available. (Modified author abstract)

System Identification Using Bayesian Estimation.

Abstract: : The problem of identifying a system with a known structure and input is formulated as a nonlinear estimation problem. The problem is solved using equations derived from Bayes' method. The computational burden usually associated with this method is reduced by approximating the conditional density function with Hermite polynomials. A numerical example demonstrates the effectiveness of the proposed technique. (Author)

TIMESBOARD: A Time Series Package.

Abstract: : TIMESBOARD is a collection of subroutines designed to aid the analyst in model identification, parameter estimation and prediction of time series When competing algorithms were available for a particular task, the one with the most favorable numerical characteristics was chosen (Author)

On the determination of the parameters of physical systems

Abstract: The problem of linear time-invarient system identification is investigated. An integral identity which simplifys computation and thereby improves accuracy is introduced in the problem formulation. An analytical example is presented to illustrate the method.

Linear stochastic system identification using correlation techniques

Abstract: The identification of linear, discrete time, scalar output systems which are driven exclusively by white, zero mean, inaccessible noise sequences is discussed. Two principal results are presented. First, two methods (least squares and an autocorrelation technique) for identifying the system characteristic equation coefficients are compared. The least squares approach is shown to be biased except for special cases. In general, the bias cannot be removed. If the state transition matrix is of the phase variable form, bias removal requires a knowledge of the measurement noise variance and all but one of the state driving noise variances. The autocorrelation technique is not biased asymptotically and does not require a knowledge of the noise variances. Secondly, it is shown that the m2 elements of the state transition matrix cannot be identified uniquely from the scalar output sequence autocorrelation coefficients if the system order is higher than one. The implication of this uncertainty in the state transition matrix on optimal filtering of the output sequence is briefly discussed.

System Identification Using Modified Gradient Method

Abstract: This paper describes some methods for identification of linear systems using the input and the output information under operating conditions. The linear system is expressed by an impulse response whose sampled values are to be estimated successively as unknown parameters. These methods are as follows: The same input signal is applied both to the unknown system and to its mathematical model, and the parameters of the model are adjusted succesively so as to minimize the performance criterion, which is the squared difference of the outputs of both systems. And the dynamics of the unknown system is recognized from the model which has approximated sufficiently to the unknown system. As methods for parameter adjustment, this paper proposes three modified gradient methods which use two-valued signals to yield the parameter adjustment signals in order to reduce the quantity of calculation and simplify the structure in making the hardware, that is; (1) a method quantizing the input signal, (2) a method quantizing the output error signal, (3) a method quantizing both the input signal and the output error signal. For each proposed method the authors derive the convergence condition of the estimated parameters and the optimum condition for quick convergence and show the results of the digital simulation, which support the described theory.

Impulse response computer.

Abstract: The Thesis describes the design of a small, portable computer for on-line system identification. The machine generates its own test sequence, monitors, averages and data logs a system's response. On a further command it computes the Cross-correlation Function and displays it on a CRT. Under favourable conditions a valid identification may be obtained in approximately 3 sequence periods. Typical results are given for ideal and real systems.

On an approximation property relevant to non-linear system identification†

Abstract: A separation property for nonlinear functions from R n →R n is indicated. This property, when possessed by the functions constituting the evolution operator of a discrete non-linear dynamical system, is particularly useful in the formulation of stochastic approximation algorithms for system identification in the presence of both dynamic and measurement noise.