63 research outputs found
Parameter reduction in nonlinear state-space identification of hysteresis
Hysteresis is a highly nonlinear phenomenon, showing up in a wide variety of
science and engineering problems. The identification of hysteretic systems from
input-output data is a challenging task. Recent work on black-box polynomial
nonlinear state-space modeling for hysteresis identification has provided
promising results, but struggles with a large number of parameters due to the
use of multivariate polynomials. This drawback is tackled in the current paper
by applying a decoupling approach that results in a more parsimonious
representation involving univariate polynomials. This work is carried out
numerically on input-output data generated by a Bouc-Wen hysteretic model and
follows up on earlier work of the authors. The current article discusses the
polynomial decoupling approach and explores the selection of the number of
univariate polynomials with the polynomial degree, as well as the connections
with neural network modeling. We have found that the presented decoupling
approach is able to reduce the number of parameters of the full nonlinear model
up to about 50\%, while maintaining a comparable output error level.Comment: 24 pages, 8 figure
On the smoothness of nonlinear system identification
We shed new light on the \textit{smoothness} of optimization problems arising
in prediction error parameter estimation of linear and nonlinear systems. We
show that for regions of the parameter space where the model is not
contractive, the Lipschitz constant and -smoothness of the objective
function might blow up exponentially with the simulation length, making it hard
to numerically find minima within those regions or, even, to escape from them.
In addition to providing theoretical understanding of this problem, this paper
also proposes the use of multiple shooting as a viable solution. The proposed
method minimizes the error between a prediction model and the observed values.
Rather than running the prediction model over the entire dataset, multiple
shooting splits the data into smaller subsets and runs the prediction model
over each subset, making the simulation length a design parameter and making it
possible to solve problems that would be infeasible using a standard approach.
The equivalence to the original problem is obtained by including constraints in
the optimization. The new method is illustrated by estimating the parameters of
nonlinear systems with chaotic or unstable behavior, as well as neural
networks. We also present a comparative analysis of the proposed method with
multi-step-ahead prediction error minimization
Memory-element based hysteresis:Identification and compensation of a piezoelectric actuator
Hysteresis phenomena can significantly deteriorate the performance when performing servo tasks with piezoelectric actuators. The aim of this brief is to model this nonlinear hysteresis effect and use this model to develop a feedforward controller that compensates for the hysteretic behavior. Exploiting the dual-pair concept, a connection is established between hysteresis models and general memory (MEM) elements examplified by the Ramberg–Osgood model. This facilitates both a straightforward identification procedure of a hysteresis model and a feedforward controller design. Both the identification procedure and the feedforward controller are implemented on a piezoelectric actuator indicating a performance improvement by a factor 3.5
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.Comment: submitted to Mechanical Systems and Signal Processin
Polynomial Nonlinear State Space Identification of an Aero-Engine Structure
Most nonlinear identification problems often require prior knowledge or an initial assumption of the mathematical law (model structure) and data processing to estimate the nonlinear parameters present in a system, i.e. they require the functional form or depend on a proposition that the measured data obey a certain nonlinear function. However, obtaining prior knowledge or performing nonlinear characterisation can be difficult or impossible for certain identification problems due to the individualistic nature of practical nonlinearities. For example, joints between substructures of large aerospace design frequently feature complex physics at local regions of the structure, making a physically motivated identification in terms of nonlinear stiffness and damping impossible. As a result, black-box models which use no prior knowledge can be regarded as an effective method. This paper explores the pragmatism of a black-box approach based on Polynomial Nonlinear State Space (PNLSS) models to identify the nonlinear dynamics observed in a large aerospace component. As a first step, the Best Linear Approximation (BLA), noise and nonlinear distortion levels are estimated over different amplitudes of excitation using the Local Polynomial Method (LPM). Next, a linear state space model is estimated on the non-parametric BLA using the frequency domain subspace identification method. Nonlinear model terms are then constructed in the form of multivariate polynomials in the state variables while the parameters are estimated through a nonlinear optimisation routine. Further analyses were also conducted to determine the most suitable monomial degree and type required for the nonlinear identification procedure. Practical application is carried out on an Aero-Engine casing assembly with multiple joints, while model estimation and validation is achieved using measured sine-sweep and broadband data obtained from the experimental campaign
Identification of Linear State-Space Models Subject to Truncated Gaussian Disturbances
Within Bayesian state estimation, an important effort has been put to incorporate constraints into state estimation for process optimization, state monitoring, fault detection and control. Nonetheless, in the domain of state-space system identification, the prevalent practice entails constructing models under Gaussian noise assumptions, which suffer from inaccuracies when the noise follows bounded distributions. This poster introduces a novel data-driven method rooted in maximum likelihood principles, aimed at identifying linear state-space models subject to truncated Gaussian noise. This approach enables the concurrent estimation of model parameters, noise statistics, and noise truncation bounds, by solving a series of quadratic programs and nonlinear sets of equations
Beyond exploding and vanishing gradients: analysing RNN training using attractors and smoothness
The exploding and vanishing gradient problem has been the major conceptual
principle behind most architecture and training improvements in recurrent
neural networks (RNNs) during the last decade. In this paper, we argue that
this principle, while powerful, might need some refinement to explain recent
developments. We refine the concept of exploding gradients by reformulating the
problem in terms of the cost function smoothness, which gives insight into
higher-order derivatives and the existence of regions with many close local
minima. We also clarify the distinction between vanishing gradients and the
need for the RNN to learn attractors to fully use its expressive power. Through
the lens of these refinements, we shed new light on recent developments in the
RNN field, namely stable RNN and unitary (or orthogonal) RNNs.Comment: To appear in the Proceedings of the 23rd International Conference on
Artificial Intelligence and Statistics (AISTATS), 2020. PMLR: Volume 108.
This paper was previously titled "The trade-off between long-term memory and
smoothness for recurrent networks". The current version subsumes all previous
version
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