A new toolbox for the identification of diagonal Volterra kernels allowing the emulation of nonlinear audio devices

Numerous audio systems are nonlinear. It is thus of great importance to study them and understand how they work. Volterra series model and its subclass (cascade Hammerstein-Wiener model) are usual ways to modelize nonlinear systems. However the identification methods of these models are still considered as an open topic. Therefore we have developed a new optimized identification tool ready for use and presented as a Matlab toolbox. This toolbox provides the parameters of the optimized sine sweep needed for the identification method, it is able to calculate the parameters of the Hammerstein model and to emulate the output signal of a nonlinear device for a given input signal. To evaluate the toolbox, we modelize a guitar distortion effect (the Tubescreamer) having a total harmonic distortion (THD) comprised in the range 10-23\%. We report a mean error of less than 0.7\% between the emulated signal and the signal coming from the distortion effect

WH-EA: An Evolutionary Algorithm for Wiener-Hammerstein System Identification

[EN] Current methods to identify Wiener-Hammerstein systems using Best Linear Approximation (BLA) involve at least two steps. First, BLA is divided into obtaining front and back linear dynamics of the Wiener-Hammerstein model. Second, a re tting procedure of all parameters is carried out to reduce modelling errors. In this paper, a novel approach to identify Wiener-Hammerstein systems in a single step is proposed. is approach is based on a customized evolutionary algorithm (WH-EA) able to look for the best BLA split, capturing at the same time the process static nonlinearity with high precision. Furthermore, to correct possible errors in BLA estimation, the locations of poles and zeros are subtly modi ed within an adequate search space to allow a ne-tuning of the model. e performance of the proposed approach is analysed by using a demonstration example and a nonlinear system identi cation benchmark.This work was partially supported by the Spanish Ministry of Economy and Competitiveness (Project DPI2015-71443-R) and Salesian Polytechnic University of Ecuador through a Ph.D. scholarship granted to the first author.Zambrano-Abad, JC.; Sanchís Saez, J.; Herrero Durá, JM.; Martínez Iranzo, MA. (2018). WH-EA: An Evolutionary Algorithm for Wiener-Hammerstein System Identification. Complexity. 2018:1-17. https://doi.org/10.1155/2018/1753262S1172018Mora, L. A., & Amaya, J. E. (2017). Un Nuevo Método de Identificación Basado en la Respuesta Escalón en Lazo Abierto de Sistemas Sobre-amortiguados. Revista Iberoamericana de Automática e Informática Industrial RIAI, 14(1), 31-43. doi:10.1016/j.riai.2016.09.006Liu, T., Wang, Q.-G., & Huang, H.-P. (2013). A tutorial review on process identification from step or relay feedback test. Journal of Process Control, 23(10), 1597-1623. doi:10.1016/j.jprocont.2013.08.003Karnopp, D. C., Margolis, D. L., & Rosenberg, R. C. (2012). System Dynamics. doi:10.1002/9781118152812Bonilla, J., Roca, L., de la Calle, A., & Dormido, S. (2017). Modelo Dinámico de un Recuperador de Gases -Sales Fundidas para una Planta Termosolar Híbrida de Energías Renovables. Revista Iberoamericana de Automática e Informática Industrial RIAI, 14(1), 70-81. doi:10.1016/j.riai.2016.11.003Billings, S. A., & Fakhouri, S. Y. (1982). Identification of systems containing linear dynamic and static nonlinear elements. Automatica, 18(1), 15-26. doi:10.1016/0005-1098(82)90022-xLopes dos Santos, P., A. Ramos, J., & Martins de Carvalho, J. L. (2012). Identification of a Benchmark Wiener–Hammerstein: A bilinear and Hammerstein–Bilinear model approach. Control Engineering Practice, 20(11), 1156-1164. doi:10.1016/j.conengprac.2012.04.002Kalafatis, A., Arifin, N., Wang, L., & Cluett, W. R. (1995). A new approach to the identification of pH processes based on the Wiener model. Chemical Engineering Science, 50(23), 3693-3701. doi:10.1016/0009-2509(95)00214-pJurado, F. (2006). A method for the identification of solid oxide fuel cells using a Hammerstein model. Journal of Power Sources, 154(1), 145-152. doi:10.1016/j.jpowsour.2005.04.005Boubaker, S. (2017). Identification of nonlinear Hammerstein system using mixed integer-real coded particle swarm optimization: application to the electric daily peak-load forecasting. Nonlinear Dynamics, 90(2), 797-814. doi:10.1007/s11071-017-3693-9S Gaya, M. (2017). Estimation of Turbidity in Water Treatment Plant using Hammerstein-Wiener and Neural Network Technique. Indonesian Journal of Electrical Engineering and Computer Science, 5(3), 666. doi:10.11591/ijeecs.v5.i3.pp666-672Bai, E.-W., Cai, Z., Dudley-Javorosk, S., & Shields, R. K. (2009). Identification of a modified Wiener–Hammerstein system and its application in electrically stimulated paralyzed skeletal muscle modeling. Automatica, 45(3), 736-743. doi:10.1016/j.automatica.2008.09.023Haryanto, A., & Hong, K.-S. (2013). Maximum likelihood identification of Wiener–Hammerstein models. Mechanical Systems and Signal Processing, 41(1-2), 54-70. doi:10.1016/j.ymssp.2013.07.008Gómez, J. C., Jutan, A., & Baeyens, E. (2004). Wiener model identification and predictive control of a pH neutralisation process. IEE Proceedings - Control Theory and Applications, 151(3), 329-338. doi:10.1049/ip-cta:20040438Li, S., & Li, Y. (2016). Model predictive control of an intensified continuous reactor using a neural network Wiener model. Neurocomputing, 185, 93-104. doi:10.1016/j.neucom.2015.12.048Zhang, Q., Wang, Q., & Li, G. (2016). Nonlinear modeling and predictive functional control of Hammerstein system with application to the turntable servo system. Mechanical Systems and Signal Processing, 72-73, 383-394. doi:10.1016/j.ymssp.2015.09.011Ławryńczuk, M. (2016). Nonlinear predictive control of dynamic systems represented by Wiener–Hammerstein models. Nonlinear Dynamics, 86(2), 1193-1214. doi:10.1007/s11071-016-2957-0Schoukens, M., Pintelon, R., & Rolain, Y. (2014). Identification of Wiener–Hammerstein systems by a nonparametric separation of the best linear approximation. Automatica, 50(2), 628-634. doi:10.1016/j.automatica.2013.12.027Vanbeylen, L. (2014). A fractional approach to identify Wiener–Hammerstein systems. Automatica, 50(3), 903-909. doi:10.1016/j.automatica.2013.12.013Sjöberg, J., Lauwers, L., & Schoukens, J. (2012). Identification of Wiener–Hammerstein models: Two algorithms based on the best split of a linear model applied to the SYSID’09 benchmark problem. Control Engineering Practice, 20(11), 1119-1125. doi:10.1016/j.conengprac.2012.07.001Westwick, D. T., & Schoukens, J. (2012). Initial estimates of the linear subsystems of Wiener–Hammerstein models. Automatica, 48(11), 2931-2936. doi:10.1016/j.automatica.2012.06.091Tan, A. H., Wong, H. K., & Godfrey, K. (2012). Identification of a Wiener–Hammerstein system using an incremental nonlinear optimisation technique. Control Engineering Practice, 20(11), 1140-1148. doi:10.1016/j.conengprac.2012.04.007Naitali, A., & Giri, F. (2015). Wiener–Hammerstein system identification – an evolutionary approach. International Journal of Systems Science, 47(1), 45-61. doi:10.1080/00207721.2015.1027758Schoukens, J., Lataire, J., Pintelon, R., Vandersteen, G., & Dobrowiecki, T. (2009). Robustness Issues of the Best Linear Approximation of a Nonlinear System. IEEE Transactions on Instrumentation and Measurement, 58(5), 1737-1745. doi:10.1109/tim.2009.2012948Ljung, L., & Singh, R. (2012). Version 8 of the Matlab System Identification Toolbox. IFAC Proceedings Volumes, 45(16), 1826-1831. doi:10.3182/20120711-3-be-2027.0006

From Nonlinear Identification to Linear Parameter Varying Models: Benchmark Examples

Linear parameter-varying (LPV) models form a powerful model class to analyze and control a (nonlinear) system of interest. Identifying a LPV model of a nonlinear system can be challenging due to the difficulty of selecting the scheduling variable(s) a priori, which is quite challenging in case a first principles based understanding of the system is unavailable. This paper presents a systematic LPV embedding approach starting from nonlinear fractional representation models. A nonlinear system is identified first using a nonlinear block-oriented linear fractional representation (LFR) model. This nonlinear LFR model class is embedded into the LPV model class by factorization of the static nonlinear block present in the model. As a result of the factorization a LPV-LFR or a LPV state-space model with an affine dependency results. This approach facilitates the selection of the scheduling variable from a data-driven perspective. Furthermore the estimation is not affected by measurement noise on the scheduling variables, which is often left untreated by LPV model identification methods. The proposed approach is illustrated on two well-established nonlinear modeling benchmark examples

Maternity leave

A numerous off-days which a woman is legally approved to be absent from work in the weeks prenatal and postnatal recovery phase after giving birth defines maternity leave. It is stated that at least 60 consecutive days of paid maternity leave were entitled to all female workers in Malaysia if they have worked at least 90 days with their current employers in four months leading up to their confinement period, except for exempted categories (Employment Act 1955) During the maternity leave, female workers are entitled to be provided with all relevant contractual benefits and paid with full salary as if they are in an active employment excluding the benefits that are tied to active work. The right to resume working upon their return from maternity leave is also protected

A new kernel-based approach for overparameterized Hammerstein system identification

In this paper we propose a new identification scheme for Hammerstein systems, which are dynamic systems consisting of a static nonlinearity and a linear time-invariant dynamic system in cascade. We assume that the nonlinear function can be described as a linear combination of $p$ basis functions. We reconstruct the $p$ coefficients of the nonlinearity together with the first $n$ samples of the impulse response of the linear system by estimating an $np$-dimensional overparameterized vector, which contains all the combinations of the unknown variables. To avoid high variance in these estimates, we adopt a regularized kernel-based approach and, in particular, we introduce a new kernel tailored for Hammerstein system identification. We show that the resulting scheme provides an estimate of the overparameterized vector that can be uniquely decomposed as the combination of an impulse response and $p$ coefficients of the static nonlinearity. We also show, through several numerical experiments, that the proposed method compares very favorably with two standard methods for Hammerstein system identification.Comment: 17 pages, submitted to IEEE Conference on Decision and Control 201