Showing papers on "System identification published in 1978"

Identification of a class of nonlinear systems using correlation analysis

Abstract: An algorithm is presented for the identification of nonlinear systems which can be described by a model consisting of a linear system in cascade with a nonlinear element followed by another linear system. Cross-correlation techniques are employed to decouple the identification of the linear dynamics from the characterisation of the nonlinear element when the input is a white Gaussian signal. Parameterisation of both the linear and nonlinear component subsystems is discussed and the results of a simulation study are included to illustrate the validity of the algorithm.

Determining models of structures from earthquake records

Abstract: The problem of determining linear models of structures from seismic response data is studied using ideas from the theory of system identification. The investigation employs a general formulation called the output-error approach, in which optimal estimates of the model parameters are obtained by minimizing a selected measure-of-fit between the responses of the structure and the model. The question of whether the parameters can be determined uniquely and reliably in this way is studied for a general class of linear structural models. Because earthquake records are normally available from only a small number of locations in a structure, and because of measurement noise, it is shown that it is necessary in practice to estimate parameters of the dominant modes in the records, rather than the stiffness and damping matrices. Two output-error techniques are investigated. Tests of the first, an optimal filter method, show that its advantages are offset by weaknesses which make it unsatisfactory for application to seismic response. A new technique, called the modal minimization method, is developed to overcome these difficulties. It is a reliable and efficient method to determine the optimal estimates of modal parameters for linear structural models. The modal minimization method is applied to two multi- story buildings that experienced the 1971 San Fernando earthquake. New information is obtained concerning the properties of the higher modes of the taller building and more reliable estimates of the properties of the fundamental modes of both structures are found. The time-varying character of the equivalent linear parameters is also studied for both buildings. It is shown for the two buildings examined that the optimal, time-invariant, linear models with a small number of modes can reproduce the strong-motion records much better than had been supposed from previous work using less systematic techniques.

Structural Identification Concept

Abstract: In this paper, possibilities of identifying important engineering characteristics of the structures using selected inspection and test results are examined. Recently, methods of system identification have been used to obtain a set of differential equations or generalized impulse response functions for the representation of the dynamic behavior of a given structure. It is suggested herein that the characteristics to be thus identified can include such functions as the damage and reliability of the structure at the time of the test and inspection. The general problem of structural identification is formulated and considered. The literature on damage function and reliability functions of structures are reviewed and summarized. Possible applications of various testing procedures including nondestructive and proof-load tests for structural identification purposes are also considered. Finally, the potentially practical implementation of such a methodology is suggested.

System modelling and control

Abstract: Mathematical description of system components * Transient response of systems * System simulation * State space representation and analysis * Frequency response of systems * Statistical methods for system identification * Feedback systems - accuracy and stability * The root locus method * The sampled-data process * Design of closed loop systems * Nonlinearities and dead time * Case studies * Index.

Asymptotic normality of prediction error estimators for approximate system models

Abstract: A general class of parameter estimation methods for stochastic dynamical systems is studied. The class contains the least squares method, output-error methods, the maximum likelihood method and several other techniques. It is shown that the class of estimates so obtained are asymptotically normal and expressions for the resulting asymptotic covariance matrices are given. The regularity conditions that are imposed to obtain these results are fairly weak. It is, for example, not assumed that the true system can be described within the chosen model set, and, as a consequence, the results in this paper form a part of the so-called approximate modeling approach to system identification. It is also noteworthy that arbitrary feedback from observed system outputs to observed system inputs is allowed and that stationarity is not required.

The White-Noise Method in System Identification

Abstract: Early in the study of the dynamics of a physiological system the bioscientist is faced with the task of recognizing the domains of linearity and of nonlinearity of the stimulus-response transformation that the system performs and how these domains compare with the dominant natural variation of the stimuli in the system’s environment. As we saw in the previous chapter, the analytical advantages of linear systems are many, and, therefore, they justify the search for a linear domain in the system’s operational range (if such exists). However, the bioscientist must resist the temptation of being carried away by a natural desire for beautiful and explicit solutions since they often tend to be unrealistic idealizations. We cannot but bow to the evidence that nonlinear system characteristics are abundant in nature and go far beyond the trite admission that every physical system is in some way nonlinear. In much the same way that nonlinearities optimize the design of artificial systems, nonlinearities seem to be necessary for the optimal functioning of physiological systems from the behavioral point of view. There are many such examples: the logarithmic transformation of sensory input in order to accommodate large stimulus ranges, dynamic asymmetries arising from such physiological necessities as sensing direction, and many others.

FIR system modeling and identification in the presence of noise and with band-limited inputs

Abstract: System identification, that is, the modeling and identification of a system from knowledge of its input and output signals, is a subject that is of considerable importance in many areas of signal and data processing. Because of the diversity of applications, a number of different methods for system identification with different advantages and disadvantages have been described and used in the literature. In this paper we investigate the performance of three well-known system identification methods based on an FIR (finite impulse response) model of the system. The methods will be referred to in this paper as the least squares analysis (LSA) method, the least mean squares adaptation algorithm (LMS), and the short-time spectral analysis (SSA) procedure. Our particular interest in this paper concerns the performance of these algorithms in the presence of high noise levels and in situations where the input signal may be band-limited. Both white and nonwhite random noise signals as well as speech signals are used as test signals to measure the performance of each of the system identification techniques as a function of the signal-to-noise ratio of the systems output. Quantitative results in terms of an accuracy measure of system identification are presented and a simple analytical model is used to explain the measured results.

Linear system identification from non-stationary cross-sectional data

Abstract: The identification of time invariant linear stochastic systems from cross-sectional data on non-stationary system behavior is considered. A strong consistency and asymptotic normality result for maximum likelihood and prediction error estimates of the system parameters, system and measurement noise covariances and the initial state covariance is proven. A new identifiability property for the system model is defined and appears in the set of conditions for this result. The non-stationary stochastic realization (i.e., covariance factorization) theorem in [1] describes sufficient conditions for the identifiability property to hold. An application illustrating the use of a computer program implementing the identification method is presented.

Comments on ‘ On model structure testing in system identification’

Abstract: (1978). Comments on ‘ On model structure testing in system identification’. International Journal of Control: Vol. 27, No. 2, pp. 323-324.

Identification and analysis of non-linear systems by tensor techniques

Abstract: A technique based on symmetric tensors is presented for the identification and analysis of a class of multivariable non-linear systems composed of linear subsystems and smooth polynomial type non-linearities. Sufficient conditions for system identification by steady-state sinusoidal analysis are obtained. Expressions for the output response are also developed when the applied input consists of exponentials and sinusoids.

Simulation of Transient Gas-Temperatures in Cylinders of Reciprocating Compressors Using Identification Techniques With a Mathematical Model

Abstract: Results are presented for a theoretical and experimental investigation carried out to create a mathematical model for prediction of transient gas temperatures in cylinders of reciprocating compressors. A method of developing compressor mathematical models using compensating coefficients is discribed. Methods of obtaining the compensating coefficients for the selected mathematical models from experimental data are used. Identification methods for the coefficient are used as in System Identification Parameter and State Estimation, Peter Eykhoff, John Wiley and Sons, 1974.

A sequential regression algorithm for recursive filters

Abstract: A sequential regression (s.e.r.) algorithm is derived for recursive or infinite impulse response (i.i.r.) adaptive filters. Results pertaining to using the algorithm in a system-identification experiment are also included.

On the numerical determination of optimal inputs

Abstract: The design of optimal inputs for linear and nonlinear system identification involves the maximization of a quadratic performance index subject to an input energy constraint. In the classical approach, a Lagrange multiplier is introduced whose value is an unknown constant. In recent papers, the Lagrange multiplier has been determined by plotting a curve of the Lagrange multiplier as a function of the critical interval length or a curve of input energy versus the interval length. A new approach is presented in this paper in which the Lagrange multiplier is introduced as a state variable and evaluated simultaneously with the optimal input. Numerical results are given for both a linear and a nonlinear dynamic system.

General System Identification — Fundamentals and Results

Abstract: The term identification was introduced by Zadeh in a 1956 paper [1] as a generic expression for the problem of “determining the input-output relationships of a black box by experimental means.” He cited the various terminologies then prevalent for the same problem: “characterization,” “measurement,” “evaluation,” “gedanken experiments,” etc., and noted that the term “identification” states “the crux of the problem with greater clarity than the more standard terms above.”

A mathematical model to predict the inelastic response of a steel frame: Formulation of the model

Abstract: The purpose of this research is to use data from experiments to formulate a mathematical model that will predict the non-linear response of a single-storey steel frame to an earthquake input. The process used in this formulation is system identification. The form of the model is a second-order non-linear differential equation with linear viscous damping and Ramberg—Osgood type hysteresis. The damping coefficient and the three parameters in the hysteretic model are to be established. An integral weighted mean squared error function is used to evaluate the [goodness of fit] between the model's response and the structure's response when both are subjected to the same excitation. The function includes errors in displacement and acceleration and is integrated from zero to a time T, which may be the full duration of the recorded response or only a portion of it. The parameters are adjusted using a modified Gauss-Newton method until the error function is minimized. The computer program incorporating these steps in the system identification process is verified with simulated data. Results given in the paper show that in every case the program converges in few iterations to the assigned set of parameters.

Identification of systems driven by nonstationary noise (Corresp.)

Abstract: The system function of an unknown system can be determined in terms of the power spectrum of the output if the

On system identification with and without certainty

Abstract: Information-theoretic concepts are utilized to develop a procedure for identifying a parameter of a stochastic linear discrete time dynamic scalar system based on noisy linear measurements of the system's state. After various simplifying approximations, the derived error entropy identification algorithm reduces to an on-line adaptive identification algorithm that is similar in many respects to well-established identification techniques. Conditions under which the developed on-line adaptive algorithm identifies the system with certainty are presented. Using an error entropy estimation lower bound, which is independent of any estimation procedure, conditions for which identification cannot be made with certainty are also presented. Examples involving non-Gaussian statistics are used to illustrate the efficiency of the error entropy adaptive identification algorithm as well as to compare it with several other identification procedures.

Comparisons of system identification methods in the presence of high noise levels and bandlimited inputs

Abstract: In this paper we investigate the performance of three well known system identification methods based on an FIR (finite impulse response) model of the system The methods will be referred to in this paper as the least squares analysis (LSA) method, the least mean Squares adaptation algorithm (LMS) and the short-time spectral analysis (SSA) procedure Our particular interest in this paper concerns the performance of these algorithms in the presence of high noise levels and in situations where the input signal is bandlimited Both white and nonwhite random noise signals as well as speech signals are used as test signals to measure the performance of the system identification techniques, Quantitative results in terms of an accuracy measure of system identification are presented and a simple analytical model is used to explain the measured results

System Identification: Impulse Response Functions

Abstract: An approach is presented for estimating the impulse response function of a multidegree-of-freedom structural system. The approach discretizes the time axis into contiguous time segments and estimates the structure's impulse response function for each time segment. The identification problem is formulated in the time domain and in matrix form which is solvable using math programming techniques. The solution is a global optimum because the problem is a convex programming problem.

Applied stochastic approximation algorithms in Hilbert space

Abstract: This paper considers the theory of stochastic approximation in a Hilbert space setting for applicable purposes with emphasis in system identification. The algorithms investigated here converge in quadratic mean and with probability 1 and are less restrictive, from the application viewpoint, than the original works on stochastic approximation theory. This approach supplies a suitable class of algorithms satisfying the convergence requirements, without compromising the system identification applicability.

A mathematical model to predict the inelastic response of a steel frame: Establishment of parameters from shaking table experiments

Abstract: The purpose of this research is to use data from experiments to formulate a mathematical model that will predict the non-linear response of a single-storey steel frame to an earthquake input. The process used in this formulation is system identification. In experiments performed on a shaking table, the frame was subjected to two earthquake motions at several intensities. In each case the frame underwent severe inelastic deformation. A computer program which incorporates the concepts of system identification makes use of the recorded data to establish four parameters in a non-linear mathematical model. When different amounts of data are used in the program, parameter sets are established which give the best model response for that amount of test data. The resulting sets of parameters reflect the way in which the properties of the structure change during the excitation. However, when the full durations of the different excitations are used, the sets of parameters are almost identical. For each of these sets of parameters, the correlation of the computed accelerations with the measured is excellent, and the shape of the computed displacement response compares very well with the measured response, although the permanent offset of the displacements is not computed exactly. Suggestions are given on how to overcome this deficiency in the mathematical model.

Some simplified algorithms for the bayesian identification of aircraft parameters

Abstract: The salient features of the bayesian approach for system identification are briefly examined from the numerical viewpoint. The shortcomings of this approach readily suggest the possible simplification which make the technique numerically more attractive. Four such simplifications are proposed, based on three principles, viz. (1) Decomposition of the filter, several schemes are already available and a new scheme is proposed, which is useful when a good number of state equations are noise-free. (2) On-line identification, obtained by estimating the state vector at the present instant only, and then updating the parameters using this state, (3) Simplified gain matrix, based on the idea that not all elements of the gain matrix are equally significant. Two simple gain structures are proposed, based on the structure of the measurement matrix. The stability and control derivatives of Concorde are identified using these algorithms. It is shown that, by a proper combination of these algorithms, it is poss...

System Identification Methodology for Fault Detection and Isolation in Dynamic Systems.

Abstract: : With the availability of inexpensive digital hardware, it has become practical to use advanced analytical techniques to achieve fault tolerance in dynamic systems without significant increase in redundant hardware. Certain analytical techniques based on one or more Kalman filters have been proposed in the past. To achieve the best false/missed alarm probabilities, however, efficient techniques which extract all information from the data must be developed. This report first studies the conditions under which faults are detectable and distinguishable. It then outlines three major considerations in the development of fault detection approaches. These considerations are: (a) statistical criteria, (b) system modeling requirements, and (c) computer architecture. System identification techniques are then specialized to fault detection/isolation applications. In particular, methods for trading-off modeling complexity, statistical optimality and computer architecture are discussed. (Author)

Rotorcraft system identification techniques for handling qualities and stability and control evaluation

Abstract: An integrated approach to rotorcraft system identification is described. This approach consists of sequential application of (1) data filtering to estimate states of the system and sensor errors, (2) model structure estimation to isolate significant model effects, and (3) parameter identification to quantify the coefficient of the model. An input design algorithm is described which can be used to design control inputs which maximize parameter estimation accuracy. Details of each aspect of the rotorcraft identification approach are given. Examples of both simulated and actual flight data processing are given to illustrate each phase of processing. The procedure is shown to provide means of calibrating sensor errors in flight data, quantifying high order state variable models from the flight data, and consequently computing related stability and control design models.