caa a22 4500 606159029 CHVBK 20210128100622.0 cr unu---uuuuu 210128e20150101xx s 000 0 eng 10.1007/s00521-014-1716-8 doi (NATIONALLICENCE)springer-10.1007/s00521-014-1716-8 Balanced simplicity-accuracy neural network model families for system identification [Elektronische Daten] [Hector Romero Ugalde, Jean-Claude Carmona, Juan Reyes-Reyes, Victor Alvarado, Christophe Corbier] Nonlinear system identification tends to provide highly accurate models these last decades; however, the user remains interested in finding a good balance between high-accuracy models and moderate complexity. In this paper, four balanced accuracy-complexity identification model families are proposed. These models are derived, by selecting different combinations of activation functions in a dedicated neural network design presented in our previous work (Romero-Ugalde et al. in Neurocomputing 101:170-180. doi: 10.1016/j.neucom.2012.08.013 , 2013). The neural network, based on a recurrent three-layer architecture, helps to reduce the number of parameters of the model after the training phase without any loss of estimation accuracy. Even if this reduction is achieved by a convenient choice of the activation functions and the initial conditions of the synaptic weights, it nevertheless leads to a wide range of models among the most encountered in the literature. To validate the proposed approach, three different systems are identified: The first one corresponds to the unavoidable Wiener-Hammerstein system proposed in SYSID2009 as a benchmark; the second system is a flexible robot arm; and the third system corresponds to an acoustic duct. The Natural Computing Applications Forum, 2014 Nonlinear system identification nationallicence Black box nationallicence Neural networks nationallicence Model reduction nationallicence Estimation quality nationallicence $$J_{u} \in R^{1\times n_b}$$ J u ∈ R 1 × n b : Input regressor vector nationallicence $$J_{\hat{y}} \in R^{1\times n_a}$$ J y ^ ∈ R 1 × n a : Output regressor vector nationallicence $$n_a \in R^{1\times 1}$$ n a ∈ R 1 × 1 : Number of pass outputs of the system nationallicence $$n_b \in R^{1\times 1}$$ n b ∈ R 1 × 1 : Number of pass inputs of the system nationallicence $$X \in R^{1\times 1}$$ X ∈ R 1 × 1 : Synaptic weight nationallicence $$Z_{b} \in R^{1\times 1}$$ Z b ∈ R 1 × 1 : Synaptic weight nationallicence $$Z_{a} \in R^{1\times 1}$$ Z a ∈ R 1 × 1 : Synaptic weight nationallicence $$V_{b_i} \in R^{1\times 1}$$ V b i ∈ R 1 × 1 : Synaptic weight nationallicence $$V_{a_i} \in R^{1\times 1}$$ V a i ∈ R 1 × 1 : Synaptic weight nationallicence $$Z_h \in R^{1\times 1}$$ Z h ∈ R 1 × 1 : Synaptic weight nationallicence $$W_{b_{i}} \in R^{1\times n_b}$$ W b i ∈ R 1 × n b : Synaptic weight nationallicence $$W_{a_i} \in R^{1\times n_a}$$ W a i ∈ R 1 × n a : Synaptic weight nationallicence $$W_{B} \in R^{1\times n_b}$$ W B ∈ R 1 × n b : Synaptic weight nationallicence $$W_{A} \in R^{1\times n_a}$$ W A ∈ R 1 × n a : Synaptic weight nationallicence $$V_{B} \in R^{1\times 1}$$ V B ∈ R 1 × 1 : Synaptic weight nationallicence $$V_{A} \in R^{1\times 1}$$ V A ∈ R 1 × 1 : Synaptic weight nationallicence $$Z_H \in R^{1\times 1}$$ Z H ∈ R 1 × 1 : Synaptic weight nationallicence $$X^* \in R^{1\times 1}$$ X ∗ ∈ R 1 × 1 : Synaptic weight after training nationallicence $$Z_{b}^* \in R^{1\times 1}$$ Z b ∗ ∈ R 1 × 1 : Synaptic weight after training nationallicence $$Z_{a}^* \in R^{1\times 1}$$ Z a ∗ ∈ R 1 × 1 : Synaptic weight after training nationallicence $$V_{b_i}^* \in R^{1\times 1}$$ V b i ∗ ∈ R 1 × 1 : Synaptic weight after training nationallicence $$V_{a_i}^* \in R^{1\times 1}$$ V a i ∗ ∈ R 1 × 1 : Synaptic weight after training nationallicence $$Z_h^* \in R^{1\times 1}$$ Z h ∗ ∈ R 1 × 1 : Synaptic weight after training nationallicence $$W_{b_{i}}^* \in R^{1\times n_b}$$ W b i ∗ ∈ R 1 × n b : Synaptic weight after training nationallicence $$W_{a_i}^* \in R^{1\times n_a}$$ W a i ∗ ∈ R 1 × n a : Synaptic weight after training nationallicence $$W_{B}^* \in R^{1\times n_b}$$ W B ∗ ∈ R 1 × n b : Synaptic weight after training nationallicence $$W_{A}^* \in R^{1\times n_a}$$ W A ∗ ∈ R 1 × n a : Synaptic weight after training nationallicence $$V_{B}^* \in R^{1\times 1}$$ V B ∗ ∈ R 1 × 1 : Synaptic weight after training nationallicence $$V_{A}^* \in R^{1\times 1}$$ V A ∗ ∈ R 1 × 1 : Synaptic weight after training nationallicence $$Z_H^* \in R^{1\times 1}$$ Z H ∗ ∈ R 1 × 1 : Synaptic weight after training nationallicence $$\varphi _{1}$$ φ 1 : Activation function (linear or nonlinear) nationallicence $$\varphi _{2}$$ φ 2 : Activation function (linear or nonlinear) nationallicence $$\varphi _{3}$$ φ 3 : Activation function (linear or nonlinear) nationallicence $$nn \in R^{1\times 1}$$ n n ∈ R 1 × 1 : Number of neurons nationallicence $$e_{{\mathrm{sim}}}$$ e sim : Simulation error nationallicence $$\mu _t$$ μ t : Mean value of the simulation error nationallicence $$s_t$$ s t : Standard deviation of the error nationallicence $$e_{{\mathrm{RMS}}t}$$ e RMS t : Root mean square (RMS) of the error nationallicence $$u$$ u : Input of the neural network nationallicence $$\hat{y}$$ y ^ : Output of the neural network nationallicence Romero Ugalde Hector Laboratoire Traitement du Signal et de l'Image, LTSI, Université de Rennes 1, INSERM U1099, 35042, Rennes, France aut Carmona Jean-Claude Laboratoire des Sciences de l'Information et des Systemes, UMR CNRS 7296, ENSAM, 13100, Aix en Provence, France aut Reyes-Reyes Juan Centro Nacional de Investigacion y Desarrollo Tecnologico, CENIDET, 62490, Cuernavaca, Morelos, Mexico aut Alvarado Victor Centro Nacional de Investigacion y Desarrollo Tecnologico, CENIDET, 62490, Cuernavaca, Morelos, Mexico aut Corbier Christophe LASPI, F-42334 IUT de Roanne, Université de Saint Etienne, Jean Monnet, 42334, Roanne, France aut Neural Computing and Applications Springer London 26/1(2015-01-01), 171-186 0941-0643 26:1<171 2015 26 521 https://doi.org/10.1007/s00521-014-1716-8 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00521-014-1716-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Romero Ugalde Hector Laboratoire Traitement du Signal et de l'Image, LTSI, Université de Rennes 1, INSERM U1099, 35042, Rennes, France aut NATIONALLICENCE 700 1- Carmona Jean-Claude Laboratoire des Sciences de l'Information et des Systemes, UMR CNRS 7296, ENSAM, 13100, Aix en Provence, France aut NATIONALLICENCE 700 1- Reyes-Reyes Juan Centro Nacional de Investigacion y Desarrollo Tecnologico, CENIDET, 62490, Cuernavaca, Morelos, Mexico aut NATIONALLICENCE 700 1- Alvarado Victor Centro Nacional de Investigacion y Desarrollo Tecnologico, CENIDET, 62490, Cuernavaca, Morelos, Mexico aut NATIONALLICENCE 700 1- Corbier Christophe LASPI, F-42334 IUT de Roanne, Université de Saint Etienne, Jean Monnet, 42334, Roanne, France aut NATIONALLICENCE 773 0- Neural Computing and Applications Springer London 26/1(2015-01-01), 171-186 0941-0643 26:1<171 2015 26 521