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Perspectives on system identification
 In Plenary talk at the proceedings of the 17th IFAC World Congress, Seoul, South Korea
, 2008
"... System identification is the art and science of building mathematical models of dynamic systems from observed inputoutput data. It can be seen as the interface between the real world of applications and the mathematical world of control theory and model abstractions. As such, it is an ubiquitous ne ..."
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Cited by 91 (3 self)
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System identification is the art and science of building mathematical models of dynamic systems from observed inputoutput data. It can be seen as the interface between the real world of applications and the mathematical world of control theory and model abstractions. As such, it is an ubiquitous necessity for successful applications. System identification is a very large topic, with different techniques that depend on the character of the models to be estimated: linear, nonlinear, hybrid, nonparametric etc. At the same time, the area can be characterized by a small number of leading principles, e.g. to look for sustainable descriptions by proper decisions in the triangle of model complexity, information contents in the data, and effective validation. The area has many facets and there are many approaches and methods. A tutorial or a survey in a few pages is not quite possible. Instead, this presentation aims at giving an overview of the “science ” side, i.e. basic principles and results and at pointing to open problem areas in the practical, “art”, side of how to approach and solve a real problem. 1.
JustinTime Models with Applications to Dynamical Systems
 Dept. of EE, LinkOping University. S581 83 LinkOping
, 1997
"... System identification deals with the problem of estimating models of dynamical systems given observations from the systems. In this thesis we focus on the nonlinear modeling problem, and, in particular, on the situation that occurs when a very large amount of data is available. Traditional treatmen ..."
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Cited by 24 (3 self)
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System identification deals with the problem of estimating models of dynamical systems given observations from the systems. In this thesis we focus on the nonlinear modeling problem, and, in particular, on the situation that occurs when a very large amount of data is available. Traditional treatments of the estimation problem in statistics and system identification have mainly focused on global modeling approaches, i.e., the model has been optimized using the entire data set. However, when the number of samples becomes large, this approach becomes less attractive mainly because of the computational complexity. We instead assume that all observations are stored in a database, and that models are built dynamically as the actual need arises. When a model is really needed in a neighborhood around an operating point, a subset of the data closest to the operating point is retrieved from the database, and a local modeling operation is performed on that subset. For this concept, the name Jus...
Frequency Domain System Identification Toolbox
, 1994
"... Abstract: System identification often means the determination of linear models from inputoutput data. The behaviour of many systems can be described by an sdomain or zdomain transfer function model, at least for a given excitation amplitude range. The quality of the fit can be assessed by the ana ..."
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Cited by 20 (10 self)
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Abstract: System identification often means the determination of linear models from inputoutput data. The behaviour of many systems can be described by an sdomain or zdomain transfer function model, at least for a given excitation amplitude range. The quality of the fit can be assessed by the analysis of the residuals, that is, of the difference between the measured data and the model. However, even slight nonlinearities can be misleading, by causing part of the residuals nonexplicable by the linear model. We cannot simply tell if the excess residual error is due to undermodelling or to nonlinear system behaviour. This can lead to erroneous overmodelling. Therefore, characterisation of the nonlinear system behaviour is essential in the verification of linear models. The Frequency Domain System Identification Toolbox has been extended with analysis tools of nonlinear system behaviour. Specially designed excitation signals allow the description of nonlinearity levels. By this, model verification becomes possible even if nonlinear error terms excess linear additive noise. Copyright © 2006 IFAC
Some Results on Identifying Linear Systems Using Frequency Domain Data
 In Proc. 32nd IEEE Conference on Decision and Control
, 1993
"... The usefulness of frequency domain interpretations in linear systems is well known. In this contribution the connenctions between frequency domain and time domain expressions will be discussed. In particular, we consider some aspects of using frequency domain data as primary observations. 1 Introduc ..."
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Cited by 13 (1 self)
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The usefulness of frequency domain interpretations in linear systems is well known. In this contribution the connenctions between frequency domain and time domain expressions will be discussed. In particular, we consider some aspects of using frequency domain data as primary observations. 1 Introduction For linear systems the connections and interplay between timedomain and frequency domain aspects have proved to be most fruitful in all applications. We shall in this contribution discuss some aspects in applications to linear system identification. There are two sides of this interplay. One is to consider the primary observation to be in the timedomain, and then to interpret corresponding identification criteria, algorithms and properties in the frequency domain. There are many early results of this character, e.g. [9], [2], [1], [4]. More recently such results have been exploited and developed in [6]. The other side of the interplay is to consider the primary observations to be in th...
On the frequency scaling in continuoustime modeling
 TABLE I ESTIMATED RESONANCE FREQUENCIES AND DAMPING RATIOS OF THE VILLA PASO BRIDGE. (Hz) (%) 1.5761 ± 0.0014 0.67 ± 0.09 2.6650 ± 0.0023 0.95 ± 0.09 3.5098 ± 0.0026 0.74 ± 0.07 3.7775 ± 0.0033 1.03 ± 0.08 f0ζ f0 std f0( )± ζ std ζ
, 2005
"... Abstract When identifying continuoustime systems in the Laplace domain, it is indispensable to scale the frequency axis to guarantee the numerical stability of the normal equations. Without scaling, identification in the Laplace domain is often impossible even for modest model orders of the transf ..."
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Abstract When identifying continuoustime systems in the Laplace domain, it is indispensable to scale the frequency axis to guarantee the numerical stability of the normal equations. Without scaling, identification in the Laplace domain is often impossible even for modest model orders of the transfer function. Although the optimal scaling depends on the system, the model, and the excitation signal, the arithmetic mean of the maximum and minimum angular frequencies in the frequency band of interest is commonly used as a good compromise [13]. In this paper we show (i) that the optimal frequency scaling also strongly depends on the estimation algorithm, and (ii) that the median of the angular frequencies is a better compromise for improving the numerical stability than the arithmetic mean. I. PROBLEM STATEMENT Consider the identification of rational transfer function models in the Laplace variable with (1) starting from measured input/output spectra, or frequency response functions,. The goal is to estimate the numerator and denominator coefficients for a given value of the order of the numerator and denominator polynomials. Since parametrization (1) is not identifiable ( for any nonzero real number), the parameter vector should be constrained, for example, or. From a numerical point of view it is often better to use the full s G s θ, ( ) B s θ, () A s θ, () bns
Frequency Domain Identification with Generalized Orthonormal Basis Functions
 IN PROC. 34TH IEEE CONFERENCE ON DECISION AND CONTROL
, 1995
"... A method is considered for identification of linear parametric models based on a least squares identification criterion that is formulated in the frequency domain. To this end use is made of the empirical transfer function estimate (ETFE), identified from timedomain data. As a parametric model stru ..."
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Cited by 7 (1 self)
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A method is considered for identification of linear parametric models based on a least squares identification criterion that is formulated in the frequency domain. To this end use is made of the empirical transfer function estimate (ETFE), identified from timedomain data. As a parametric model structure use is made of a finite expansion sequence in terms of recently introduced generalized basis functions, being generalizations of the classical pulse, Laguerre and Kautz types of bases. An asymptotic analysis of the estimated models is provided and conditions for consistency are formulated. Explicit and transparent bias and variance expressions are established, the latter ones also valid in a situation of undermodelling.
Identification of Volterra kernels using interpolation
 IEEE Trans. Instrumentation and Measurement
, 2002
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Timedomain Identification of Dynamic Errorsinvariables Systems Using Periodic Excitation Signals
 In Submitted to IFAC Congress
, 1998
"... The use of periodic excitation signals in identification experiments is advocated. With periodic excitation it is possible to separate the driving signals and the disturbances, which for instance implies that the noise properties can be independently estimated. In the paper a nonparametric noise mo ..."
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Cited by 3 (1 self)
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The use of periodic excitation signals in identification experiments is advocated. With periodic excitation it is possible to separate the driving signals and the disturbances, which for instance implies that the noise properties can be independently estimated. In the paper a nonparametric noise model, estimated directly from the measured data, is used in a compensation strategy applicable to both least squares and total least squares estimation. The resulting least squares and total least squares methods are applicable in the errorsinvariables situation and give consistent estimates regardless of the noise. The feasibility of the idea is illustrated in a simulation study. Keywords: System identification; Least squares estimation; Errorsinvariables models. 1 Introduction One of the most important steps in the identification process is the experiment design. This involves, for example, deciding what signals to measure, choosing the sampling interval, and designing the excitation...
Statistical analysis of nonparametric transfer function estimates
 IEEE Trans. Instrum. Meas
, 1996
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ALBENDER, « Impact of nonlinear friction on frequency response function measurements
 Int. Conf. On noise and Vibration Engineering
, 2000
"... measurements ..."