| 1. |
- Barbe, Kurt, et al.
(författare)
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Fractional models for modeling complex linear systems under poor frequency resolution measurements
- 2013
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Ingår i: Digital signal processing (Print). - : Elsevier BV. - 1051-2004 .- 1095-4333. ; 23:4, s. 1084-1093
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Tidskriftsartikel (refereegranskat)abstract
- When modeling a linear system in a parametric way, one needs to deal with (i) model structure selection, (ii) model order selection as well as (iii) an accurate fit of the model. The most popular model structure for linear systems has a rational form which reveals crucial physical information and insight due to the accessibility of poles and zeros. In the model order selection step, one needs to specify the number of poles and zeros in the model. Automated model order selectors like Akaikeʼs Information Criterion (AIC) and the Minimum Description Length (MDL) are popular choices. A large model order in combination with poles and zeros lying closer to each other in frequency than the frequency resolution indicates that the modeled system exhibits some fractional behavior. Classical integer order techniques cannot handle this fractional behavior due to the fact that the poles and zeros are lying to close to each other to be resolvable and not enough data is available for the classical integer order identification procedure. In this paper, we study the use of fractional order poles and zeros and introduce a fully automated algorithm which (i) estimates a large integer order model, (ii) detects the fractional behavior, and (iii) identifies a fractional order system.
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| 2. |
- 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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| 3. |
- 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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| 4. |
- Sjöberg, Jonas, 1964, et al.
(författare)
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Identification of Wiener–Hammerstein models: Two algorithms based on the best split of a linear model applied to the SYSID'09 benchmark problem
- 2012
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Ingår i: Control Engineering Practice. - : Elsevier BV. - 0967-0661. ; 20:11, s. 1119-1125
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Tidskriftsartikel (refereegranskat)abstract
- This paper describes the identification of Wiener–Hammerstein models and two recently suggested algorithms are applied to the SYSID'09 benchmark data. The most difficult step in the identification process of such block-oriented models is to generate good initial values for the linear dynamic blocks so that local minima are avoided. Both of the considered algorithms obtain good initial estimates by using the best linear approximation (BLA) which can easily be estimated from data. Given the BLA, the two algorithms differ in the way the dynamics are separated into two linear parts. The first algorithm simply considers all possible splits of the dynamics. Each of the splits is used to initialize one Wiener–Hammerstein model using linear least-squares and the best performing model is selected. In the second algorithm, both linear blocks are initialized with the entire BLA model using basis function expansions of the poles and zeros of the BLA. This gives over-parameterized linear blocks and their order is decreased in a model reduction step. Both algorithms are explained and their properties are discussed. They both give good, comparable models on the benchmark data.
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