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best linear approximation of nonlinear and nonstationary systems using Operational Modal Analysis

MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2021年 152卷 107395-107395页

作者： Friis, Tobias Tarpo, Marius Katsanos, Evangelos I. Brincker, Rune Tech Univ Denmark Dept Civil Engn Brovej B-118 Lyngby Denmark Aarhus Univ Dept Engn Inge Lehmanns Gade 10 Aarhus Denmark

Operational Modal Analysis (OMA) is a widely used class of tools to identify the modal properties of existing civil engineering structures and mechanical systems under ambient vibrations or normal operating conditions by only employing measured responses. The OMA techniques, however, are confined to estimate modal properties of linear and time invariant systems, which do not always comply with real life applications. Additionally, even though structures are found to be nonlinear and nonstationary (i.e., time-varying), it is often engineering practice to apply linear models due to their straightforward insight into the dynamic behaviour of the considered system and mathematical properties when compared to more time consuming consideration of nonlinearities and nonstationarities. With that point of view, the concept of evaluating a best linear approximation of a nonlinear response is well established within Experimental Modal Analysis, i.e., deterministic modal analysis where both the system excitation and the corresponding response are measured. Along these lines, the paper takes the first step towards extending the concept of a best linear approximation to correlation-driven OMA in terms of estimated natural frequencies, damping ratios, and mode shapes. This paper proves that the correlation function matrix calculated from the measured response of a nonlinear and nonstationary system can be approximated by a set of free decays of the best linear approximation. In other words, the paper derives and shows through appropriately designed numerical simulations that the linear modal model, estimated using the output-only framework of conventional correlation-driven (i.e., covariance-driven) OMA, leads to suboptimal minimisation of the difference between the true response of a nonlinear and/or nonstationary system and the response of the linear modal model in a least squares sense. Moreover, the paper demonstrates, using an additional numerical simulation case study, that

关键词： Operational Modal Analysis Nonlinear dynamics Nonstationary systems best linear approximation Output-only identification

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On the Initialization of Nonlinear LFR Model Identification with the best linear approximation 21st

On the Initialization of Nonlinear LFR Model Identification ...

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21st IFAC World Congress on Automatic Control - Meeting Societal Challenges

作者： Schoukens, Maarten Toth, Roland Eindhoven Univ Technol Dept Elect Eng Control Syst Grp Postbus 513 NL-5600 MB Eindhoven Netherlands

Balancing the model complexity and the representation capability towards the process to be captured remains one of the main challenges in nonlinear system identification. One possibility to reduce model complexity is to impose structure on the model representation. To this end, this work considers the linear fractional representation framework. In a linear fractional representation the linear dynamics and the system nonlinearities are modeled by two separate blocks that are interconnected with one another. This results in a structured, yet flexible model structure. Estimating such a model directly from input-output data is not a trivial task as the involved optimization is nonlinear in nature. This paper proposes an initialization scheme for the model parameters based on the best linear approximation of the system and shows that this approach results in high quality models on a set of benchmark data sets. Copyright (C) 2020 The Authors.

关键词： Nonlinear Identification Neural Network linear Fractional Representation best linear approximation

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On the Initialization of Nonlinear LFR Model Identification with the best linear approximation

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IFAC-PapersOnLine 2020年第2期53卷 310-315页

作者： Maarten Schoukens Roland Tóth Control Systems Group Dept. of Electrical Eng. Eindhoven University of Technology Postbus 513 5600 MB Eindhoven The Netherlands.

关键词： Nonlinear Identification Neural Network linear Fractional Representation best linear approximation

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Distortion Contribution Analysis With the best linear approximation

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS 2018年第12期65卷 4133-4146页

作者： Cooman, Adam Bronders, Piet Peumans, Dries Vandersteen, Gerd Rolaing, Yves INRIA FACTAS F-06902 Valbonne France Vrije Univ Brussel Dept Fundamental Elect & Instrumentat B-1050 Brussels Belgium

A distortion contribution analysis (DCA) obtains the distortion at the output of an analog electronic circuit as a sum of distortion contributions of its subcircuits. Similar to a noise analysis, a DCA helps a designer to pinpoint the actual source of the distortion. Classically, the DCA uses the Volterra theory to model the circuit and its subcircuits. This DCA has been proven useful for small circuits or heavily simplified examples. In more complex circuits, however, the amount of contributions increases quickly, making the interpretation of the results difficult. In this paper, the best linear approximation (BLA) is used to perform the DCA instead. The BLA represents the behavior of a subcircuit as a linear circuit with the unmodeled distortion represented by a noise source. Combining the BLA with a classical noise analysis yields a DCA which is simple to understand, yet capable to handle complex excitation signals and complex strongly nonlinear circuits.

关键词： Non-linear distortion distortion contribution analysis best linear approximation

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Hammerstein system identification through best linear approximation inversion and regularisation

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INTERNATIONAL JOURNAL OF CONTROL 2018年第8期91卷 1757-1773页

作者： Castro-Garcia, Ricardo Tiels, Koen Agudelo, Oscar Mauricio Suykens, Johan A. K. Katholieke Univ Leuven ESAT STADIUS Leuven Belgium Vrije Univ Brussel Fac Engn Dept Fundamental Elect & Instrumentat Brussels Belgium

Hammerstein systems are composed by the cascading of a static nonlinearity and a linear system. In this paper, a methodology for identifying such systems using a combination of least squares support vector machines (LS-SVM) and best linear approximation (BLA) techniques is proposed. To do this, a novel method for estimating the intermediate variable is presented allowing a clear separation of the identification steps. First, an approximation to the linear block is obtained through the BLA of the system. Then, an approximation to the intermediate variable is obtained using the inversion of the estimated linear block and the known output. Afterwards, a nonlinear model is calculated through LS-SVM using the estimated intermediate variable and the known input. To do this, the regularisation capabilities of LS-SVM play a crucial role. Finally, a parametric re-estimation of the linear block is made. The method was tested in three examples, two of them with hard nonlinearities, and was compared with four other methods showing very good performance in all cases. The obtained results demonstrate that also in the presence of noise, the method can effectively identify Hammerstein systems. The relevance of these findings lies in the fact that it is shown how the regularisation allows to bypass the usual problems associated with the noise backpropagation when the inversion of the estimated linear block is used to compute the intermediate variable.

关键词： best linear approximation frequency domain Hammerstein systems least squares support vector machines nonlinear system identification linear block inversion

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Measuring the best linear approximation of Wiener Systems Using Multilevel Sequences

Measuring the Best Linear Approximation of Wiener Systems Us...

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IEEE International Instrumentation and Measurement Technology Conference (I2MTC)

作者： De Angelis, A. Schoukens, J. Godfrey, K. R. Carbone, P. Univ Perugia Dept Engn Via G Duranti 93 I-06125 Perugia Italy Vrije Univ Brussel Dept ELEC Pl Laan 2 B-1050 Brussels Belgium Univ Warwick Sch Engn Coventry CV4 7AL W Midlands England

ISBN: (纸本)9781509035960

The problem of measuring the best linear approximation of a nonlinear system by means of multilevel excitation sequences is analyzed. A comparison between different types of sequences applied at the input of Wiener systems is provided by numerical simulations. The performance of the sequences is compared with a white Gaussian noise signal for reference purposes. It is shown that the randomized constrained approach for designing ternary sequences has a low sensitivity to even and odd order nonlinearity, resulting in a response close to the actual response of the underlying linear system.

关键词： Nonlinear systems best linear approximation ternary sequences binary pseudorandom sequences

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Estimation of best linear approximation from Varying Operating Conditions for the Identification of a Li-ion Battery Model

Estimation of Best Linear Approximation from Varying Operati...

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20th World Congress of the International-Federation-of-Automatic-Control (IFAC)

作者： Relan, Rishi Tiels, Koen Timmermans, Jean-Marc Schoukens, Johan Vrije Univ Brussel Dept ELEC B-1050 Brussels Belgium Vrije Univ Brussel Dept ETEC MOBI B-1050 Brussels Belgium

The short term dynamic response of the battery varies with varying operating conditions. Hence, even before proceeding towards the modelling step, it is important to fully characterise and understand the dynamic behaviour of the battery at varying operating conditions. In this paper, a data-driven methodology for characterising the battery's short term electrical response at varying operating conditions e.g. at different levels of SoC and different temperature levels is discussed. Furthermore, a novel way to estimate the best linear approximation from the data acquired at these operating conditions with varying levels of noise and nonlinear distortions is proposed. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： System identification Multiple experiments Nonlinear models Li-ion battery best linear approximation

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Estimation of best linear approximation from Varying Operating Conditions for the Identification of a Li-ion Battery Model

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IFAC-PapersOnLine 2017年第1期50卷 4739-4744页

作者： Relan R. Tiels K. Timmermans J.-M. Schoukens J. Department ELEC Belgium Department ETEC-MOBI Vrije Universiteit Brussel Brussels 1050 Belgium

关键词： best linear approximation Li-ion battery Multiple experiments Nonlinear models System identification

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Analysis of Phase-Locked Loops using the best linear approximation 13

Analysis of Phase-Locked Loops using the Best Linear Approxi...

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13th International Conference on Synthesis, Modeling, Analysis and Simulation Methods and Applications to Circuit Design (SMACD)

作者： Peumans, Dries Cooman, Adam Vandersteen, Gerd

ISBN: (纸本)9781509004904

During the early design stage of Phase-Locked Loops, linear models are thoroughly used to analyse the steady-state behaviour. In reality, the envisioned linear performance is degraded due to nonlinearities present in the actual implementation. Lately, a nonlinear modelling technique based on the best linear approximation has been developed which allows to verify the validity of this linear model and, in addition, permits to characterise the nonlinear distortions present in the system. Incorporating this best linear approximation in the design stage allows to intuitively analyse the nonlinear behaviour of the Phase Locked Loop.

关键词： Terms Phase-Locked Loop nonlinear distortions best linear approximation

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Identification of Rate Saturation From best linear approximation 1

Identification of Rate Saturation From Best Linear Approxima...

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IEEE Conference on Energy Conversion (CENCON)

作者： Yong, Alex Yean Keong Tan, Ai Hui Cham, Chin Leei Multimedia Univ Fac Engn Cyberjaya Malaysia

ISBN: (纸本)9781479948482

This paper considers the identification of rate saturation nonlinearity. A method to estimate the rate saturation limits from the best linear approximation is proposed and applied to the model in discrete-time. The approach has the advantages that it can be easily extended to the identification of Wiener-Hammerstein models whereby the rate saturation block is cascaded in a Wiener-Hammerstein structure and identification can also be carried out across the frequency bandwidth of interest. Simulation results are presented to show the effectiveness of the proposed technique.

关键词： best linear approximation identification nonlinear systems rate saturation

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