| 1. |
- Enqvist, Martin, 1976-, et al.
(författare)
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Detection of Unmodeled Nonlinearities Using Correlation Methods
- 2007
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Ingår i: Proceedings of the 2007 IEEE Instrumentation and Measurement Technology Conference. - 1424405882 ; , s. 1-6
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Konferensbidrag (refereegranskat)abstract
- This paper concerns the validation of linear models with respect to unmodeled nonlinearities. Two versions of a method for nonlinearity detection based on estimators of higher order cross-correlations are described and evaluated. Unlike many existing approaches, the proposed method seems to be applicable to a wide range of systems and input signals. It can also distinguish between even and odd nonlinearities.
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| 2. |
- Enqvist, Martin, 1976-
(författare)
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Linear Models of Nonlinear Systems
- 2005
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Linear time-invariant approximations of nonlinear systems are used in many applications and can be obtained in several ways. For example, using system identification and the prediction-error method, it is always possible to estimate a linear model without considering the fact that the input and output measurements in many cases come from a nonlinear system. One of the main objectives of this thesis is to explain some properties of such approximate models.More specifically, linear time-invariant models that are optimal approximations in the sense that they minimize a mean-square error criterion are considered. Linear models, both with and without a noise description, are studied. Some interesting, but in applications usually undesirable, properties of such optimal models are pointed out. It is shown that the optimal linear model can be very sensitive to small nonlinearities. Hence, the linear approximation of an almost linear system can be useless for some applications, such as robust control design. Furthermore, it is shown that standard validation methods, designed for identification of linear systems, cannot always be used to validate an optimal linear approximation of a nonlinear system.In order to improve the models, conditions on the input signal that imply various useful properties of the linear approximations are given. It is shown, for instance, that minimum phase filtered white noise in many senses is a good choice of input signal. Furthermore, the class of separable signals is studied in detail. This class contains Gaussian signals and it turns out that these signals are especially useful for obtaining approximations of generalized Wiener-Hammerstein systems. It is also shown that some random multisine signals are separable. In addition, some theoretical results about almost linear systems are presented.In standard methods for robust control design, the size of the model error is assumed to be known for all input signals. However, in many situations, this is not a realistic assumption when a nonlinear system is approximated with a linear model. In this thesis, it is described how robust control design of some nonlinear systems can be performed based on a discrete-time linear model and a model error model valid only for bounded inputs.It is sometimes undesirable that small nonlinearities in a system influence the linear approximation of it. In some cases, this influence can be reduced if a small nonlinearity is included in the model. In this thesis, an identification method with this option is presented for nonlinear autoregressive systems with external inputs. Using this method, models with a parametric linear part and a nonparametric Lipschitz continuous nonlinear part can be estimated by solving a convex optimization problem.
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| 3. |
- Gevers, Michel, et al.
(författare)
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The transient impulse response modeling method and the local polynomial method for nonparametric system identification
- 2012
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Ingår i: 16th IFAC Symposium on System Identification. - : IFAC. - 9783902823069 ; , s. 55-60
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Konferensbidrag (refereegranskat)abstract
- This paper analyzes two recent methods for the nonparametric estimation of the Frequency Response Function (FRF) from input-output data using Prediction Error identification. Such FRF estimate can be the main goal of the identification exercise, or it can be a tool for the computation of a nonparametric estimate of the noise spectrum. We show that the choice of the method depends on the signal to noise ratio and on the objective. The method that delivers the best FRF estimate may not deliver the best estimate of the noise spectrum. Our theoretical analysis is illustrated by simulations.
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| 4. |
- Gillberg, Jonas, et al.
(författare)
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Robust Frequency Domain ARMA Modelling
- 2006
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Ingår i: Proceedings of the 14th IFAC Symposium on System Identification. - 9783902661029 ; , s. 380-385
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Konferensbidrag (refereegranskat)abstract
- In this paper a method for the rejection of frequency domain outliers is proposed. The algorithm is based on the work by Huber on M-estimators and the concept of influence function introduced by Hampel. The estimation takes placein the context of frequency domain continuous-time ARMA modelling, but the method can be also be applied to the discrete time case.
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| 5. |
- Gustafsson, Fredrik, et al.
(författare)
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Fast Calculations of Linear and Nonlinear Least-Squares Estimates for System Identification
- 1998
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Ingår i: Proceedings of the 37th IEEE Conference on Decision and Control. - 0780343948 ; , s. 3408-3410 vol.3
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Konferensbidrag (refereegranskat)abstract
- In this paper an FFT based method is presented to speed-up the calculations of least-squares estimates of d unknown parameters from O(Nd2) to O(Nlog2N) (with N the number of data points) resulting in a significant reduction of the required computation time. The method can be applied to models/methods that are linear or nonlinear-in-the-parameters. Also the memory requirements are significantly reduced, without needing dedicated memory management techniques.
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| 6. |
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| 7. |
- Hong, Mei, et al.
(författare)
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Accuracy Analysis of Time Domain Maximum Likelihood Method and Sample Maximum Likelihood Method for Errors-in-Variables Identification
- 2007
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The time domain maximum likelihood (TML) method and the sample maximum Likelihood (SML) method are two approaches for identifying errors-in-variables models. Both methods may give the optimal estimation accuracy (achieve Cramér-Rao lower bound) but in different senses. In the TML method, an important assumption is that the noise-free input signal is modeled as a stationary process with rational spectrum. For SML, the noise-free input needs to be periodic. It is interesting to know which of these assumptions contain more information to boost the estimation performance. In this paper, the estimation accuracy of the two methods is analyzed statistically. Numerical comparisons between the two estimates are also done under different signal-to-noise ratios (SNRs). The results suggest that TML and SML have similar estimation accuracy at moderate or high SNR.
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| 8. |
- Hong, Mei, et al.
(författare)
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Accuracy comparison of time domain maximum likelihood method and sample maximum likelihood method in errors-in-variables identification
- 2006
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The time domain maximum likelihood (TML) method and the Sample Maximum Likelihood (SML) method are two general approaches for identifying errors-in-variables models. In the TML method, an important assumption is that the noise-free input signal must be a stationary process with rational spectrum. For SML, the noise-free input need to be periodic. In this report, numerical comparisons of these two methods are done under different situations. The results suggest that TML and SML have similar estimation accuracy at moderate or high signal-to-noise ratio (SNR).
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| 9. |
- Lauwers, Lieve, et al.
(författare)
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A Nonlinear Block Structure Identification Procedure using Frequency Response Function Measurements
- 2008
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Ingår i: IEEE Transactions on Instrumentation and Measurement. - : IEEE Instrumentation and Measurement Society. - 0018-9456 .- 1557-9662. ; 57:10, s. 2257-2264
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Tidskriftsartikel (refereegranskat)abstract
- Based on simple Frequency Response Function (FRF) measurements, we give the user some guidance in the selection of an appropriate nonlinear block structure for the system to be modeled. The method consists in measuring the FRF using a Gaussian-like input signal and varying in a first experiment the root-mean-square (rms) value of this signal while maintaining the coloring of the power spectrum. Next, in a second experiment, the coloring of the power spectrum is varied while keeping the rms value constant. Based on the resulting behavior of the FRF, an appropriate nonlinear block structure can be selected to approximate the real system. The identification of the selected block-oriented model itself is not addressed in this paper. A theoretical analysis and two practical applications of this structure identification method are presented for some nonlinear block structures.
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| 10. |
- Lauwers, Lieve, et al.
(författare)
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Nonlinear Structure Analysis Using the Best Linear Approximation
- 2006
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Ingår i: Proceedings of the 2006 International Conference on Noise and Vibration Engineering. ; , s. 2751-2760
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Konferensbidrag (refereegranskat)abstract
- In this paper, we propose a method to distinguish between some nonlinear system structures using the bestlinear approximation (BLA) of the system in order to select an appropriate model structure. The main ideaof the method is to apply a Gaussian input signal and to vary the root mean square (rms) value and thepower spectrum of this signal. Depending on the resulting changes of the amplitude and phasecharacteristics of the BLA, an appropriate model structure for the Device Under Test can be selected. Atheoretical analysis of the method is presented for some block-oriented structures.
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