arXiv subjects

Johan Schoukens

Publications and source records attributed to Johan Schoukens.

At least 19 recordsLinked to original sources

arXiv2022

Decoupling multivariate functions using a nonparametric filtered tensor decomposition

Multivariate functions emerge naturally in a wide variety of data-driven models. Popular choices are expressions in the form of basis expansions or neural networks. While highly effective, the resulting functions tend to be hard to interpret, in part because of the large number of required parameters. Decoupling techniques aim at providing an alternative representation of the nonlinearity. The so-called decoupled form is often a more efficient parameterisation of the relationship while being highly structured, favouring interpretability. In this work two new algorithms, based on filtered tensor decompositions of first order derivative information are introduced. The method returns nonparametric estimates of smooth decoupled functions. Direct applications are found in, i.a. the fields of nonlinear system identification and machine learning.

stat.ML↗

arXiv2022

Applying Polynomial Decoupling Methods to the Polynomial NARX Model

System identification uses measurements of a dynamic system's input and output to reconstruct a mathematical model for that system. These can be mechanical, electrical, physiological, among others. Since most of the systems around us exhibit some form of nonlinear behavior, nonlinear system identification techniques are the tools that will help us gain a better understanding of our surroundings and potentially let us improve their performance. One model that is often used to represent nonlinear systems is the polynomial NARX model, an equation error model where the output is a polynomial function of the past inputs and outputs. That said, a major disadvantage with the polynomial NARX model is that the number of parameters increases rapidly with increasing polynomial order. Furthermore, the polynomial NARX model is a black-box model, and is therefore difficult to interpret. This paper discusses a decoupling algorithm for the polynomial NARX model that substitutes the multivariate polynomial with a transformation matrix followed by a bank of univariate polynomials. This decreases the number of model parameters significantly and also imposes structure on the black-box NARX model. Since a non-convex optimization is required for this identification technique, initialization is an important factor to consider. In this paper the decoupling algorithm is developed in conjunction with several different initialization techniques. The resulting algorithms are applied to two nonlinear benchmark problems: measurement data from the Silver-Box and simulation data from the Bouc-Wen friction model, and the performance is evaluated for different validation signals in both simulation and prediction.

eess.SY↗

arXiv2021

A frequency domain approach for local module identification in dynamic networks

In classical approaches of dynamic network identification, in order to identify a system (module) embedded in a dynamic network, one has to formulate a Multi-input-Single-output (MISO) identification problem that requires identification of a parametric model for all the modules constituting the MISO setup including (possibly) the noise model, and determine their model order. This requirement leads to model order selection steps for modules that are of no interest to the experimenter which increases the computational complexity for large-sized networks. Also, identification using a parametric noise model (like BJ method) can suffer from local minima, however neglecting the noise model has its impact on the variance of the estimates. In this paper, we provide a two-step identification approach to avoid these problems. The first step involves performing a non-parametric indirect approach for a MISO identification problem to get the non-parametric frequency response function (FRF) estimates and its variance as a function of frequency. In the second step, the estimated non-parametric FRF of the target module is smoothed using a parametric frequency domain estimator with the estimated variance from the previous step as the non-parametric noise model. The developed approach is practical with weak assumptions on noise, uses the available toolbox, requires a parametric model only for the target module of interest, and uses a non-parametric noise model to reduce the variance of the estimates. Numerical simulations illustrate the potentials of the introduced method in comparison with the classical identification methods.

eess.SY↗

arXiv2021

Decoupling multivariate functions using a non-parametric Filtered CPD approach

Black-box model structures are dominated by large multivariate functions. Usually a generic basis function expansion is used, e.g. a polynomial basis, and the parameters of the function are tuned given the data. This is a pragmatic and often necessary step considering the black-box nature of the problem. However, having identified a suitable function, there is no need to stick to the original basis. So-called decoupling techniques aim at translating multivariate functions into an alternative basis, thereby both reducing the number of parameters and retrieving underlying structure. In this work a filtered canonical polyadic decomposition (CPD) is introduced. It is a non-parametric method which is able to retrieve decoupled functions even when facing non-unique decompositions. Tackling this obstacle paves the way for a large number of modelling applications.

eess.SY↗

arXiv2021

Decoupling P-NARX models using filtered CPD

Nonlinear Auto-Regressive eXogenous input (NARX) models are a popular class of nonlinear dynamical models. Often a polynomial basis expansion is used to describe the internal multivariate nonlinear mapping (P-NARX). Resorting to fixed basis functions is convenient since it results in a closed form solution of the estimation problem. The drawback, however, is that the predefined basis does not necessarily lead to a sparse representation of the relationship, typically resulting in very large numbers of parameters. So-called decoupling techniques were specifically designed to reduce large multivariate functions. It was found that, often, a more efficient parameterisation can be retrieved by rotating towards a new basis. Characteristic to the decoupled structure is that, expressed in the new basis, the relationship is structured such that only single-input single-output nonlinear functions are required. Classical decoupling techniques are unfit to deal with the case of single-output NARX models. In this work, this limitation is overcome by adopting the filtered CPD decoupling method of Decuyper et al. (2021b). The approach is illustrated on data from the Sliverbox benchmark: measurement data from an electronic circuit implementation of a forced Duffing oscillator.

stat.ME↗

arXiv2021

PNLSS Toolbox 1.0

This is a demonstration of the PNLSS Toolbox 1.0. The toolbox is designed to identify polynomial nonlinear state-space models from data. Nonlinear state-space models can describe a wide range of nonlinear systems. An illustration is provided on experimental data of an electrical system mimicking the forced Duffing oscillator, and on numerical data of a nonlinear fluid dynamics problem.

eess.SY↗

arXiv2020

A nonlinear model of vortex-induced forces on an oscillating cylinder in a fluid flow

A nonlinear model relating the imposed motion of a circular cylinder, submerged in a fluid flow, to the transverse force coefficient is presented. The nonlinear fluid system, featuring vortex shedding patterns, limit cycle oscillations and synchronisation, is studied both for swept sine and multisine excitation. A nonparametric nonlinear distortion analysis (FAST) is used to distinguish odd from even nonlinear behaviour. The information which is obtained from the nonlinear analysis is explicitly used in constructing a nonlinear model of the polynomial nonlinear state-space (PNLSS) type. The latter results in a reduction of the number of parameters and an increased accuracy compared to the generic modelling approach where typically no such information of the nonlinearity is used. The obtained model is able to accurately simulate time series of the transverse force coefficient over a wide range of the frequency-amplitude plane of imposed cylinder motion.

physics.flu-dyn↗

arXiv2020

Retrieving highly structured models starting from black-box nonlinear state-space models using polynomial decoupling

Nonlinear state-space modelling is a very powerful black-box modelling approach. However powerful, the resulting models tend to be complex, described by a large number of parameters. In many cases interpretability is preferred over complexity, making too complex models unfit or undesired. In this work, the complexity of such models is reduced by retrieving a more structured, parsimonious model from the data, without exploiting physical knowledge. Essential to the method is a translation of all multivariate nonlinear functions, typically found in nonlinear state-space models, into sets of univariate nonlinear functions. The latter is computed from a tensor decomposition. It is shown that typically an excess of degrees of freedom are used in the description of the nonlinear system whereas reduced representations can be found. The method yields highly structured state-space models where the nonlinearity is contained in as little as a single univariate function, with limited loss of performance. Results are illustrated on simulations and experiments for: the forced Duffing oscillator, the forced Van der Pol oscillator, a Bouc-Wen hysteretic system, and a Li-Ion battery model.

eess.SY↗

arXiv2019

Nonlinear System Identification: A User-Oriented Roadmap

The goal of this article is twofold. Firstly, nonlinear system identification is introduced to a wide audience, guiding practicing engineers and newcomers in the field to a sound solution of their data driven modeling problems for nonlinear dynamic systems. In addition, the article also provides a broad perspective on the topic to researchers that are already familiar with the linear system identification theory, showing the similarities and differences between the linear and nonlinear problem. The reader will be referred to the existing literature for detailed mathematical explanations and formal proofs. Here the focus is on the basic philosophy, giving an intuitive understanding of the problems and the solutions, by making a guided tour along the wide range of user choices in nonlinear system identification. Guidelines will be given in addition to many examples, to reach that goal.

eess.SY↗

arXiv2018

Data-Driven Nonlinear Identification of Li-Ion Battery Based on a Frequency Domain Nonparametric Analysis

Lithium ion batteries are attracting significant and growing interest, because their high energy and high power density render them an excellent option for energy storage, particularly in hybrid and electric vehicles. In this brief, a data-driven polynomial nonlinear state-space model is proposed for the operating points at the cusp of linear and nonlinear regimes of the battery's electrical operation, based on the thorough nonparametric frequency domain characterization and quantification of the battery's behavior in terms of its linear and nonlinear behavior at different levels of the state of charge.

eess.SY↗

arXiv2018

Data driven discrete-time parsimonious identification of a nonlinear state-space model for a weakly nonlinear system with short data record

Many real world systems exhibit a quasi linear or weakly nonlinear behavior during normal operation, and a hard saturation effect for high peaks of the input signal. In this paper, a methodology to identify a parsimonious discrete-time nonlinear state space model (NLSS) for the nonlinear dynamical system with relatively short data record is proposed. The capability of the NLSS model structure is demonstrated by introducing two different initialisation schemes, one of them using multivariate polynomials. In addition, a method using first-order information of the multivariate polynomials and tensor decomposition is employed to obtain the parsimonious decoupled representation of the set of multivariate real polynomials estimated during the identification of NLSS model. Finally, the experimental verification of the model structure is done on the cascaded water-benchmark identification problem.

eess.SY↗

arXiv2018

A Local Polynomial Approach to Nonparametric Estimation of the Best Linear Approximation of Lithium-Ion Battery From Multiple Datasets

Battery short-term electrical impedance behavior varies between linear, linear time-varying, or nonlinear at different operating conditions. Data-based electrical impedance modeling techniques often model the battery as a linear time-invariant system at all operating conditions. In addition, these techniques require extensive and time consuming experimentation. Often due to sensor failures during experiments, constraints in data acquisition hardware, varying operating conditions, and the slow dynamics of the battery, it is not always possible to acquire data in a single experiment. Hence, multiple experiments must be performed. In this letter, a local polynomial approach is proposed to estimate nonparametrically the best linear approximation of the electrical impedance affected by varying levels of nonlinear distortion, from a series of input current and output voltage data subrecords of arbitrary length.

eess.SY↗

arXiv2018

Recursive Discrete-Time Models for Continuous-Time Systems Under Band-Limited Assumptions

Discrete-time models are very convenient to simulate a nonlinear system on a computer. In order to build the discrete-time simulation models for the nonlinear feedback systems (which is a very important class of systems in many applications) described as y(t) = g1(u(t), y(t)), one has to solve at each time step a nonlinear algebraic loop for y(t). If a delay is present in the loop, i.e., y(t) = g2(u(t), y(t -1)), fast recursive simulation models can be developed and the need to solve the nonlinear differential-algebraic equations is removed. In this paper, we use the latter to model the nonlinear feedback system using recursive discrete-time models. Theoretical error bounds for such kind of approximated models are provided in the case of band-limited signals, and furthermore, a measurement methodology is proposed for quantifying and validating the output error bounds experimentally.

eess.SY↗

arXiv2018

Using the Best Linear Approximation With Varying Excitation Signals for Nonlinear System Characterization

Block oriented model structure detection is quite desirable since it helps to imagine the system with real physical elements. In this work we explore experimental methods to detect the internal structure of the system, using a black box approach. Two different strategies are compared and the best combination of these is introduced. The methods are applied on two real systems with a static nonlinear block in the feedback path. The main goal is to excite the system in a way that reduces the total distortion in the measured frequency response functions to have more precise measurements and more reliable decision about the structure of the system.

eess.SY↗

arXiv2018

Improved Tactile Resonance Sensor for Robotic Assisted Surgery

This paper presents an improved tactile sensor using a piezoelectric bimorph able to differentiate soft materials with similar mechanical characteristics. The final aim is to develop intelligent surgical tools for brain tumour resection using integrated sensors in order to improve tissue tumour delineation and tissue differentiation. The bimorph sensor is driven using a random phase multisine and the properties of contact between the sensor's tip and a certain load are evaluated by means of the evaluation of the nonparametric FRF. An analysis of the nonlinear contributions is presented to show that the use of a linear model is feasible for the measurement conditions. A series of gelatine phantoms were tested. The tactile sensor is able to identify minimal differences in the consistency of the measured samples considering viscoelastic behaviour. A variance analysis was performed to evaluate the reliability of the sensors and to identify possible error sources due to inconsistencies in the preparation method of the phantoms. The results of the variance analysis are discussed showing that ability of the proposed tactile sensor to perform high quality measurements.

physics.med-ph↗

arXiv2018

Measuring the Noise Cumulative Distribution Function Using Quantized Data

This paper considers the problem of estimating the cumulative distribution function and probability density function of a random variable using data quantized by uniform and non-uniform quantizers. A simple estimator is proposed based on the empirical distribution function that also takes the values of the quantizer transition levels into account. The properties of this estimator are discussed and analyzed at first by simulations. Then by removing all assumptions that are difficult to apply, a new procedure is described that does not require neither the transition levels nor the input sequence used to source the quantizer to be known. The experimental results obtained using a commercial 12-b data acquisition system show the applicability of this estimator to real-world type of problems.

eess.SP↗

arXiv2018

Grey-box state-space identification of nonlinear mechanical vibrations

The present paper deals with the identification of nonlinear mechanical vibrations. A grey-box, or semi-physical, nonlinear state-space representation is introduced, expressing the nonlinear basis functions using a limited number of measured output variables. This representation assumes that the observed nonlinearities are localised in physical space, which is a generic case in mechanics. A two-step identification procedure is derived for the grey-box model parameters, integrating nonlinear subspace initialisation and weighted least-squares optimisation. The complete procedure is applied to an electrical circuit mimicking the behaviour of a single-input, single-output (SISO) nonlinear mechanical system and to a single-input, multiple-output (SIMO) geometrically nonlinear beam structure.

eess.SY↗

arXiv2018

Accurate Sine-Wave Amplitude Measurements Using Nonlinearly Quantized Data

The estimation of the amplitude of a sine wave from the sequence of its quantized samples is a typical problem in instrumentation and measurement. A standard approach for its solution makes use of a least squares estimator (LSE) that, however, does not perform optimally in the presence of quantization errors. In fact, if the quantization error cannot be modeled as an additive noise source, as it often happens in practice, the LSE returns biased estimates. In this paper, we consider the estimation of the amplitude of a noisy sine wave after quantization. The proposed technique is based on a uniform distribution of signal phases and it does not require that the quantizer has equally spaced transition levels. The experimental results show that this technique removes the estimation bias associated with the usage of the LSE and that it is sufficiently robust with respect to small uncertainties in the known values of transition levels.

eess.SP↗