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.
Illuminating the Black Box: Interpreting Deep Neural Network Models for Psychiatric Research
