810 research outputs found
Nonlinear structural damage detection based on cascade of Hammerstein models
Structural damages can result in nonlinear dynamical signatures that can significantly enhance their detection. An original nonlinear damage detection approach is proposed that is based on a cascade of Hammerstein models representation of the structure. This model is estimated by means of the Exponential Sine Sweep Method from only one measurement. On the basis of this estimated model, the linear and nonlinear parts of the output are estimated, and two damage indexes (DIs) are proposed. The first DI is built as the ratio of the energy contained in the nonlinear part of an output versus the energy contained in its linear part. The second DI is the angle between the subspaces obtained from the nonlinear parts of two set of outputs after a principal component analysis. The sensitivity of the proposed DIs to the presence of damages as well as their robustness to noise are assessed numerically on spring-mass-damper structures and experimentally on actual composite plates with surface-mounted PZT-elements. Results demonstrate the effectiveness of the proposed method to detect a damage in nonlinear structures and in the presence of noise
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
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
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
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