Showing papers on "System identification published in 1971"

Optimal adaptive estimation: Structure and parameter adaption

Abstract: Optimal structure and parameter adaptive estimators have been obtained for continuous as well as discrete data Gaussian process models with linear dynamics. Specifically, the essentially nonlinear adaptive estimators are shown to be decomposable (partition theorem) into two parts, a linear nonadaptive part consisting of a bank of Kalman-Bucy filters and a nonlinear part that incorporates the adaptive nature of the estimator. The conditional-error-covariance matrix of the estimator is also obtained in a form suitable for on-line performance evaluation. The adaptive estimators are applied to the problem of state estimation with non-Gaussian initial state, to estimation under measurement uncertainty (joint detection-estimation) as well as to system identification. Examples are given of the application of the adaptive estimators to structure and parameter adaptation indicating their applicability to engineering problems.

A noniterative method for identification using Hammerstein model

Abstract: A noniterative method developed by Hsia for the particular case where the transfer function in the Hammerstein model has no zeros is extended to the general case where the transfer function may have zeros. Numerical examples show that the computation time by this method is considerably less than by the iteratire procedure proposed by Narendra and Gallman while the accuracy of the estimates is comparable.

Joint detection, estimation and system identification

Abstract: Recent results of Middleton and Esposito (1968) and Lainiotis (1969) on single-shot joing detection-estimation for discrete data are extended to the single-shot continuous data case and generalized to joint Bayesian detection-estimation-system identification. Moreover, previous results were generalized to the case of causal estimator. Specifically, it is shown that the above problem constitutes a class of nonlinear mse estimation problems, with the attendant difficulties in realizing the optimal nonlinear estimators. However, by utilizing the adaptive approach, closed form integral expressions are given. These are given in terms of the generalized likelihood ratio gλ(t) , which is a sufficient statistic for Bayes-optimal compound detection. The latter in turn is specified by a continuum (for continuous θ ) θ -conditional likelihood ratious λ(t/θ) each of which is the LR for testing for the model specified by the parameter value θ . The latter LR's are, moreover, given in terms of optimal mse causal estimators. In essence then, it has been shown that system identification is equivalent to multihypothesis testing, with a continuum or finite sequence of hypotheses, respectively, for continuous or finite discrete range of θ .

Optimal input signals for nonlinear-system identification

Abstract: The choice of input signal in an identification experiment has a significant bearing on the final result. At one extreme, an input can result in violent system disturbances and the subsequent loss of product or damage to the system. At the other extreme, an input can be so conservative as to yield little or no information about the system's dynamic behaviour. The optimal input signal achieves a compromise between these extremes. This paper describes a design procedure for synthetising optimal input signals. A state-space description of the system is used, and the optimal input is chosen to minimise the variance of the parameter and state estimates. The method applies to both linear and nonlinear systems and the case of both white and coloured output noise has been considered. The optimal input signals are shown to result in a significant improvement in the identification accuracy.

Optimum input test signals for system identification—an information-theoretical approach

Abstract: This paper is concerned with a problem of choosing optimum input test signals for estimating response functions or transfer functions of discrete-time systems. Under the amplitude constraint of signals and some additional appropriate assumptions it is shown that, in the case of identifying response functions, a pseudorandom binary sequence of input signals with as small correlations as possible is optimum in the sense that it maximizes a quantity of information provided by measurements. In the case of estimating unknown coefficients of transfer functions, an optimum scheme of step-by-step choice of input signals is proposed.

On the identification of nonlinear dynamical systems

Abstract: Two classes of nonlinear dynamical systems driven by independent noise on which linear discrete-time scalar measurements are performed also in the presence of additive independent noise are considered. The evolution operators for these classes are described, respectively, by algebraic and trigonometric polynomials in the state variables. Such polynomials frequently appear in equations describing physical systems. On the assumption that certain moments of the noise sources are known, a framework is developed which leads to convergent stochastic approximation algorithms for the identification of system parameters.

Identification of a group of internal signals of zero-memory nonlinear systems

Abstract: The output of a zero-memory nonlinear system can often be considered as the algebraic sum of internal signals corresponding to the actions of separate components of the non-linearity described by a power series. A numerical procedure for determining these signals from recorded outputs is suggested, and their significance to the system identification is indicated.

A simple integral method for system identification

Abstract: A method is described for evaluating the parameters in a differential equation from an experimental solution in the case where the parameters appear as multipliers. By formal integrations a set of linear equations is obtained with coefficients that can be calculated by numerical integrations. The method gives satisfactory results for precise data but loses accuracy when the data are affected by small random errors.

Deterministic approach to a class of nonparametric system identification problems

Abstract: In this paper a class of system identification problems of nonparametric type is considered. Specifically, given an unknown deterministic system, some basic structural aspects related to the problem of estimating its weighting function are discussed. The model adopted for the system input-output relation is general enough to cover a number of situations ranging from problems of identification of linear time-invariant systems to those where the system is nonlinear and time varying. The emphasis is on establishing what, in principle, can be recovered of the system weighting function through a noiseless identification process and the ultimate limitations imposed by the presence of observation or measurement noise.

Representation of sequences

Abstract: In this paper, the space of square summable real sequences is considered. Insight is developed into the structure of the space and a method for representation of its elements is described. The method is shown suitable for on-line implementation and is noniterative; it can be used for wave-form design, signal feature extraction, and discrete-time system identification. The applications are exemplified by three simulation studies.

Test of goodness of fit of impulse response model

Abstract: A method for testing goodness of fit of an impulse response model of a dynamical system has been proposed. This method is also applicable after a slight modification to testing the hypothesis that the system is linear and autonomous. Hotelling's ,T2-test and the sign test are useful tools for these problems. Properties of the method are discussed with results of computer simulation runs.

A Digital Method of Transfer Function Calculation

Abstract: A method is developed that allows the direct calculation of the least-squares estimates of the poles and residues of the transfer function of a linear system when the input and output of the system is represented in a sequential numerical format. The method is particularly adaptable to implementation on a digital computer and is quite efficient for problems of moderate size.

System identification via an extension of the impulse method of Guillemin

Abstract: An extension of the method of Guillemin, as a means of establishing transfer function models of distributed parameter systems from experimental transient response data, is presented

On Utilization of Structural Information to Improve Identification Accuracy

Abstract: The so-called identification problem is that of estimating unknown constant system parameters of dynamic systems. The computation of maximum likelihood is known to be nontrivial and is full of various pitfalls [1]. The Koopmans-Levin algorithm for system identification, which was first discussed in the context of dynamic systems by Levin [2], has been found to be very efficient computationally as compared to the iterative type of algorithms since it only involves the solution of algebraic equations and a very simple eigenvalue problem [3][4]. This method can be motivated through the derivation of the maximum likelihood estimate but is not the true maximum likelihood estimate as claimed by Levin. It has been shown to yield (strongly) consistent estimates under very general conditions on the observation noise and simple restrictions on the systems properties as well as input characteristics. In particular, if the observation noise is Gaussian, then the estimates are known to be close approximations to those obtained via the method of maximum likelihood [3][4].

Computer Generation of Minimally Autocorrelated Aperiodic Binary Signals (for System Identification)

Abstract: An algorithm for the generation of binary signals having an aperiodic autocorrelation function, which is progressively approximated to the unit impulse, are presented. System identification with such a signal for injection and cross-correlation is illustrated and compared with similar identification using pseudorandom binary signals.

System Identifications by a Nonlinear Filter

Abstract: Most system identification problems may be reduced to the state estimation in a nonlinear system. Athans [4] synthesized a filter for nonlinear continuous systems with discrete observations through the Taylor series expansion of nonlinear functions up to the second order term about the estimated state and the minimization of the estimation error covariance under the criterion of unbiased estimate. It has been shown that the Athans’ consideration about the second order term would give the better results compared with the existing methods such as the approximate linearization method. However, in this estimation process there is tedious task to solve the parallel nonlinear differential equations about the state and the estimation error covariance. In this paper the authors have derived a forward recursive algorithm for the nonlinear filter by applying the Taylor series expansion method to the nonlinear discrete systems, in which the computation of the error covariance is simplified due to the discrete form. It has been found that this estimation method is available effectively to the identification of unknown transfer function or the learning of the unknown function in a system. Moreover, it is possible to learn nonstationary functions by expanding into the independent function series with unknown varying coefficients.

Stochastic Approximation Algorithms for System Identification Using Normal Operating Data

Abstract: This paper considers the identification problem of linear control systems by use of stochastic approximation. There are two approaches to constructing models based on stochastic approximation: dynamical model approach and finite memory model one. In the former approach Saridis and Stein [1] have obtained the most general results. And in the latter approach Holmes [2] has established an algorithm giving an unbiased estimate. But it is common with these two works that (i) only white noise sequence is allowed for the input sequence and (ii) the updating of the estimates occurs at every finite time interval.

Modeling and Identification of Power System Components

Abstract: There is a continuing tendency to apply many of the powerful results of modern control theory to various industrial processes. Power systems have been indicated as one area where significant progress can be expected. Practically all results of modern control theory require that models of the processes in terms of state equations are available. The need to obtain such models has been a strong motivation for research in the area of modelling and identification. Some progress and on plant experiments is discussed and compared. Particular emphasis is given to parameter estimation techniques like the maximum likelihood method which offers a possibility of combining physical a priori knowledge with experimental investigations. The formulation of identification problems is discussed, including the choice of criteria and model structures. The techniques are illustrated by applications to data obtained from measurements on various components of a power system. The examples include an electric generator, a nuclear reactor and a drum boiler, and serve to illustrate the potentials and limitations of system identification and modelling techniques when they are applied to real data. (Less)

An Inconsistency between the Rate and the Accuracy of the Learning Method for System Identification and its Tracking Characteristics

Abstract: A learning method for system identification has been proposed [1] which is based on the error-correcting training procedure in learning machines [2] and is an iteration method of identifying the dynamic characteristics of a linear system by use of a sampled weighting function, and detailed investigations have already been made on the fundamental characteristics of the method when an unknown system is a stationary linear one, the output of which is not corrupted by noise. A generalized method has also been proposed [3, 4] which improves the rate of convergence using matrix weight.

Linear and Nonlinear Stochastic Approximation Algorithms for Learning Systems

Abstract: Frequently in the design of on-line learning systems for pattern recognition or system identification, there is a need to construct successive estimates for the unknown parameters of some underlying probability distribution. One of the most widely used methods for this purpose is stochastic approximation. It is well known that stochastic approximation is concerned with the successive estimation algorithms which converge to the true value of some sought (unknown) parameter when, due to the random nature of the system environment, the measurements are inevitably noisy. The algorithms of most interest to on-line pattern recognition or system identification are those which have following properties: (1) they are self-correcting, that is, the error of estimates tends to vanish in the limit, and (2) their convergence to the true value of an unknown parameter is of some specific nature, for example, in mean square or with probability one. This paper will discuss two types of algorithms which have been developed to generate recursive estimates that are linear or nonlinear functions of the past measurements. These algorithms will be discussed in terms of their computational structure as well as their statistical properties such as mean square error. In particular, comparison will be made between linear and nonlinear algorithms on the basis of specific assumptions about the unknown inputs and parameters characterizing the learning environment.

Use of test signals in system identification by quasilinearization

Abstract: Identification of linear systems with unknown input gains and parameters by quasilinearization is studied both by the boundary value method and the performance index method. It is shown that the boundary value method requires a test signal whose order of complexity is proportional to the order of the system. On the other hand, with the performance index method, it is proved that the normal inputs to these systems are sufficient for complete system identification. This is significant because the most important consideration of system identification is to be able to identify the system under normal operation with as little disturbance to the system operation as possible.

Process identification by generalized correlation

Abstract: A generalized cross correlation between two signals in terms of an a priori known linking structure is introduced. This enables the identification of the instantaneous value of time varying parameters, which characterize the process linking these signals. A specific example is given where the identifier reduces to a Wiener filter.