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Research Papers

Robust Estimation of Balanced Simplicity-Accuracy Neural Networks-Based Models

[+] Author and Article Information
Hector M. Romero Ugalde

INSERM,
U1099;
LTSI,
Université de Rennes 1,
Rennes F-35000, France
e-mail: hector.m.romero.ugalde@gmail.com

Christophe Corbier

Network and Telecommunications,
Université de Lyon,
Saint Etienne F-42023, France;
Network and Telecommunications,
Université de Saint Etienne,
Jean Monnet,
Saint-Etienne F-42000, France;
LASPI,
IUT de Roanne F-42334, France

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received September 2, 2015; final manuscript received January 17, 2016; published online March 3, 2016. Assoc. Editor: Ryozo Nagamune.

J. Dyn. Sys., Meas., Control 138(5), 051001 (Mar 03, 2016) (8 pages) Paper No: DS-15-1413; doi: 10.1115/1.4032687 History: Received September 02, 2015; Revised January 17, 2016

Neural networks are powerful tools for black box system identification. However, their main drawback is the large number of parameters usually required to deal with complex systems. Classically, the model's parameters minimize a L2-norm-based criterion. However, when using strongly corrupted data, namely, outliers, the L2-norm-based estimation algorithms become ineffective. In order to deal with outliers and the model's complexity, the main contribution of this paper is to propose a robust system identification methodology providing neuromodels with a convenient balance between simplicity and accuracy. The estimation robustness is ensured by means of the Huberian function. Simplicity and accuracy are achieved by a dedicated neural network design based on a recurrent three-layer architecture and an efficient model order reduction procedure proposed in a previous work (Romero-Ugalde et al., 2013, “Neural Network Design and Model Reduction Approach for Black Box Nonlinear System Identification With Reduced Number of Parameters,” Neurocomputing, 101, pp. 170–180). Validation is done using real data, measured on a piezoelectric actuator, containing strong natural outliers in the output data due to its microdisplacements. Comparisons with others black box system identification methods, including a previous work (Corbier and Carmona, 2015, “Extension of the Tuning Constant in the Huber's Function for Robust Modeling of Piezoelectric Systems,” Int. J. Adapt. Control Signal Process., 29(8), pp. 1008–1023) where a pseudolinear model was used to identify the same piezoelectric system, show the relevance of the proposed robust estimation method leading balanced simplicity-accuracy neuromodels.

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Figures

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Fig. 1

Recurrent 2nn-2-1 neural network

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Fig. 2

Recurrent 2-1 neural network

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Fig. 3

Recurrent 2nn-1 neural network

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Fig. 4

(a) Experimental piezoelectric system setup, (b) measurements chain, and (c) experimental setup characteristics

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Fig. 5

Frequency response function (mixed L2/L1-norms versus L2-norm)

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Fig. 6

Comparison with nonlinear models in terms of FRF

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Fig. 7

Comparison with pseudolinear models in terms of FRF

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