scholarly journals Uncertainty propagation in model extraction by system identification and its implication for control design

2016 ◽  
Vol 791 ◽  
pp. 214-236 ◽  
Author(s):  
Nicolas Dovetta ◽  
Peter J. Schmid ◽  
Denis Sipp
Keyword(s):  
Monte Carlo ◽  
System Identification ◽  
Error Bounds ◽  
Control Design ◽  
Design System ◽  
Input Output ◽  
Input Space ◽  
System Parameters ◽  
System Representation ◽  
Low Dimensional

In data-based control design, system-identification techniques are used to extract low-dimensional representations of the input–output map between actuators and sensors from observed data signals. Under realistic conditions, noise in the signals is present and is expected to influence the identified system representation. For the subsequent design of the controller, it is important to gauge the sensitivity of the system representation to noise in the observed data; this information will impact the robustness of the controller and influence the stability margins for a closed-loop configuration. Commonly, full Monte Carlo analysis has been used to quantify the effect of data noise on the system identification and control design, but in fluid systems, this approach is often prohibitively expensive, due to the high dimensionality of the data input space, for both numerical simulations and physical experiments. Instead, we present a framework for the estimation of statistical properties of identified system representations given an uncertainty in the processed data. Our approach consists of a perturbative method, relating noise in the data to identified system parameters, which is followed by a Monte Carlo technique to propagate uncertainties in the system parameters to error bounds in Nyquist and Bode plots. This hybrid approach combines accuracy, by treating the system-identification part perturbatively, and computational efficiency, by applying Monte Carlo techniques to the low-dimensional input space of the control design and performance/stability evaluation part. This combination makes the proposed technique affordable and efficient even for large-scale flow-control problems. The ARMarkov/LS identification procedure has been chosen as a representative system-identification technique to illustrate this framework and to obtain error bounds on the identified system parameters based on the signal-to-noise ratio of the input–output data sequence. The procedure is illustrated on the control design for flow over an idealized aerofoil with a trailing-edge splitter plate.

SYSTEM IDENTIFICATION IN TUMOR GROWTH MODELING USING SEMI-EMPIRICAL EIGENFUNCTIONS

2012 ◽  
Vol 22 (06) ◽  
pp. 1250003 ◽  
Author(s):  
THIERRY COLIN ◽  
ANGELO IOLLO ◽  
DAMIANO LOMBARDI ◽  
OLIVIER SAUT
Keyword(s):  
System Identification ◽  
Tumor Growth ◽  
Solution Space ◽  
Cellular Division ◽  
Volume Increase ◽  
Tumor Growth Model ◽  
Species Population ◽  
Tumor Growth Modeling ◽  
Low Dimensional ◽  
Semi Empirical

A tumor growth model based on a parametric system of partial differential equations is considered. The system corresponds to a phenomenological description of a multi-species population evolution. A velocity field taking into account the volume increase due to cellular division is introduced and the mechanical closure is provided by a Darcy-type law. The complexity of the biological phenomenon is taken into account through a set of parameters included in the model that need to be calibrated. To this end, a system identification method based on a low-dimensional representation of the solution space is introduced. We solve several idealized identification cases corresponding to typical situations where the information is scarce in time and in terms of observable fields. Finally, applications to actual clinical data are presented.

scholarly journals Data Augmentation Through Monte Carlo Arithmetic Leads to More Generalizable Classification in Connectomics

2020 ◽  
Author(s):  
Gregory Kiar ◽  
Yohan Chatelain ◽  
Ali Salari ◽  
Alan C. Evans ◽  
Tristan Glatard
Keyword(s):  
Monte Carlo ◽  
Data Augmentation ◽  
Learning Models ◽  
Reduction Techniques ◽  
Numerical Noise ◽  
Numerical Instabilities ◽  
Dimensionality Reduction Techniques ◽  
Improved Performance ◽  
Low Dimensional ◽  
Machine Learning Models

AbstractMachine learning models are commonly applied to human brain imaging datasets in an effort to associate function or structure with behaviour, health, or other individual phenotypes. Such models often rely on low-dimensional maps generated by complex processing pipelines. However, the numerical instabilities inherent to pipelines limit the fidelity of these maps and introduce computational bias. Monte Carlo Arithmetic, a technique for introducing controlled amounts of numerical noise, was used to perturb a structural connectome estimation pipeline, ultimately producing a range of plausible networks for each sample. The variability in the perturbed networks was captured in an augmented dataset, which was then used for an age classification task. We found that resampling brain networks across a series of such numerically perturbed outcomes led to improved performance in all tested classifiers, preprocessing strategies, and dimensionality reduction techniques. Importantly, we find that this benefit does not hinge on a large number of perturbations, suggesting that even minimally perturbing a dataset adds meaningful variance which can be captured in the subsequently designed models.

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