981 research outputs found
WH-MOEA: A Multi-Objective Evolutionary Algorithm for Wiener-Hammerstein System Identification. A Novel Approach for Trade-Off Analysis Between Complexity and Accuracy
[EN] Several approaches have been presented to identify Wiener-Hammerstein models, most of them starting from a linear dynamic model whose poles and zeros are distributed around the static non- linearity. To achieve good precision in the estimation, the Best Linear Approximation (BLA) has usually been used to represent the linear dynamics, while static non-linearity has been arbitrarily parameterised without considering model complexity. In this paper, identification of Wiener, Hammerstein or Wiener-Hammerstein models is stated as a multiobjective optimisation problem (MOP), with a trade-off between accuracy and model complexity. Precision is quantified with the Mean-Absolute-Error (MAE) between the real and estimated output, while complexity is based on the number of poles, zeros and points of the static non- linearity. To solve the MOP, WH-MOEA, a new multiobjective evolutionary algorithm (MOEA) is proposed. From a linear structure, WH-MOEA will generate a set of optimal models considering a static non-linearity with a variable number of points. Using WH-MOEA, a procedure is also proposed to analyse various linear structures with different numbers of poles and zeros (known as design concepts). A comparison of the Pareto fronts of each design concept allows a more in-depth analysis to select the most appropriate model according to the userÂżs needs. Finally, a complex numerical example and a real thermal process based on a Peltier cell are identified, showing the procedureÂżs goodness. The results show that it can be useful to consider the simultaneously precision and complexity of a block-oriented model (Wiener, Hammerstein or Wiener- Hammerstein) in a non-linear process identification.This work was supported in part by the Ministerio de Ciencia, InnovaciĂłn y Universidades, Spain, under Grant RTI2018-096904-B-I00-AR,
and in part by the Salesian Polytechnic University of Ecuador through a Ph.D. scholarships granted to J. Zambrano.Zambrano, J.; SanchĂs Saez, J.; Herrero DurĂĄ, JM.; MartĂnez Iranzo, MA. (2020). WH-MOEA: A Multi-Objective Evolutionary Algorithm for Wiener-Hammerstein System Identification. A Novel Approach for Trade-Off Analysis Between Complexity and Accuracy. IEEE Access. 8:228655-228674. https://doi.org/10.1109/ACCESS.2020.3046352228655228674
Nonlinear system modeling based on constrained Volterra series estimates
A simple nonlinear system modeling algorithm designed to work with limited
\emph{a priori }knowledge and short data records, is examined. It creates an
empirical Volterra series-based model of a system using an -constrained
least squares algorithm with . If the system
is a continuous and bounded map with a finite memory no longer than some known
, then (for a parameter model and for a number of measurements )
the difference between the resulting model of the system and the best possible
theoretical one is guaranteed to be of order , even for
. The performance of models obtained for and is tested
on the Wiener-Hammerstein benchmark system. The results suggest that the models
obtained for are better suited to characterize the nature of the system,
while the sparse solutions obtained for yield smaller error values in
terms of input-output behavior
Maternity leave
A numerous off-days which a woman is legally approved to be absent from work in the weeks prenatal and postnatal recovery phase after giving birth defines maternity leave. It is stated that at least 60 consecutive days of paid maternity leave were entitled to all female workers in Malaysia if they have worked at least 90 days with their current employers in four months leading up to their confinement period, except for exempted categories (Employment Act 1955) During the maternity leave, female workers are entitled to be provided with all relevant contractual benefits and paid with full salary as if they are in an active employment excluding the benefits that are tied to active work. The right to resume working upon their return from maternity leave is also protected
From Nonlinear Identification to Linear Parameter Varying Models: Benchmark Examples
Linear parameter-varying (LPV) models form a powerful model class to analyze
and control a (nonlinear) system of interest. Identifying a LPV model of a
nonlinear system can be challenging due to the difficulty of selecting the
scheduling variable(s) a priori, which is quite challenging in case a first
principles based understanding of the system is unavailable.
This paper presents a systematic LPV embedding approach starting from
nonlinear fractional representation models. A nonlinear system is identified
first using a nonlinear block-oriented linear fractional representation (LFR)
model. This nonlinear LFR model class is embedded into the LPV model class by
factorization of the static nonlinear block present in the model. As a result
of the factorization a LPV-LFR or a LPV state-space model with an affine
dependency results. This approach facilitates the selection of the scheduling
variable from a data-driven perspective. Furthermore the estimation is not
affected by measurement noise on the scheduling variables, which is often left
untreated by LPV model identification methods.
The proposed approach is illustrated on two well-established nonlinear
modeling benchmark examples
A new kernel-based approach for overparameterized Hammerstein system identification
In this paper we propose a new identification scheme for Hammerstein systems,
which are dynamic systems consisting of a static nonlinearity and a linear
time-invariant dynamic system in cascade. We assume that the nonlinear function
can be described as a linear combination of basis functions. We reconstruct
the coefficients of the nonlinearity together with the first samples of
the impulse response of the linear system by estimating an -dimensional
overparameterized vector, which contains all the combinations of the unknown
variables. To avoid high variance in these estimates, we adopt a regularized
kernel-based approach and, in particular, we introduce a new kernel tailored
for Hammerstein system identification. We show that the resulting scheme
provides an estimate of the overparameterized vector that can be uniquely
decomposed as the combination of an impulse response and coefficients of
the static nonlinearity. We also show, through several numerical experiments,
that the proposed method compares very favorably with two standard methods for
Hammerstein system identification.Comment: 17 pages, submitted to IEEE Conference on Decision and Control 201
Identification of Stochastic Wiener Systems using Indirect Inference
We study identification of stochastic Wiener dynamic systems using so-called
indirect inference. The main idea is to first fit an auxiliary model to the
observed data and then in a second step, often by simulation, fit a more
structured model to the estimated auxiliary model. This two-step procedure can
be used when the direct maximum-likelihood estimate is difficult or intractable
to compute. One such example is the identification of stochastic Wiener
systems, i.e.,~linear dynamic systems with process noise where the output is
measured using a non-linear sensor with additive measurement noise. It is in
principle possible to evaluate the log-likelihood cost function using numerical
integration, but the corresponding optimization problem can be quite intricate.
This motivates studying consistent, but sub-optimal, identification methods for
stochastic Wiener systems. We will consider indirect inference using the best
linear approximation as an auxiliary model. We show that the key to obtain a
reliable estimate is to use uncertainty weighting when fitting the stochastic
Wiener model to the auxiliary model estimate. The main technical contribution
of this paper is the corresponding asymptotic variance analysis. A numerical
evaluation is presented based on a first-order finite impulse response system
with a cubic non-linearity, for which certain illustrative analytic properties
are derived.Comment: The 17th IFAC Symposium on System Identification, SYSID 2015,
Beijing, China, October 19-21, 201
Investigation of the Hammerstein hypothesis in the modeling of electrically stimulated muscle
To restore functional use of paralyzed muscles by automatically controlled stimulation, an accurate quantitative model of the stimulated muscles is desirable. The most commonly used model for isometric muscle has had a Hammerstein structure, in which a linear dynamic block is preceded by a static nonlinear function, To investigate the accuracy of the Hammerstein model, the responses to a pseudo-random binary sequence (PRBS) excitation of normal human plantarflexors, stimulated with surface electrodes, were used to identify a Hammerstein model but also four local models which describe the responses to small signals at different mean levels of activation. Comparison of the local models with the Linearized Hammerstein model showed that the Hammerstein model concealed a fivefold variation in the speed of response. Also, the small-signal gain of the Hammerstein model was in error by factors up to three. We conclude that, despite the past widespread use of the Hammerstein model, it is not an accurate representation of isometric muscle. On the other hand, local models, which are more accurate predictors, can be identified from the responses to short PRBS sequences. The utility of local models for controller design is discussed
Wiener modelling and model predictive control for wastewater applications
The research presented in this paper aims to demonstrate the application of predictive control to an integrated wastewater system with the use of the wiener modeling approach. This allows the controlled process, dissolved oxygen, to be considered to be composed of two parts: the linear dynamics, and a static nonlinearity, thus allowing control other than common approaches such as gain-scheduling, or switching, for series of linear controllers. The paper discusses various approaches to the modelling required for control purposes, and the use of wiener modelling for the specific application of integrated waste water control. This paper demonstrates this application and compares with that of another nonlinear approach, fuzzy gain-scheduled control
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