Identification of Nonlinear Systems Structured by Wiener-Hammerstein Model

Wiener-Hammerstein systems consist of a series connection including a nonlinear static element sandwiched with two linear subsystems. The problem of identifying Wiener-Hammerstein models is addressed in the presence of hard nonlinearity and two linear subsystems of structure entirely unknown (asymptotically stable). Furthermore, the static nonlinearity is not required to be invertible. Given the system nonparametric nature, the identification problem is presently dealt with by developing a two-stage frequency identification method, involving simple inputs

Frequency identification of Wiener systems with Backlash operators using separable least squares estimators

This paper deals with the identification of Wiener models that involve backlash operators bordered by possibly noninvertible parametric lines. The latter are also allowed to cross each other making possible to account for general-shape static nonlinearities. The linear dynamic subsystem is not-necessarily parametric but is BIBO stable. A frequency identification method is developed that provides estimates of the nonlinear operator parameters as well as estimates of the linear subsystem frequency gain. The method involves standard and separable least squares estimators that all are shown to be consistent. Backlash operators and memoryless nonlinearities are handled within a unified framework.Preprin

Multi-innovation stochastic gradient algorithms for dual-rate sampled systems with preload nonlinearity

AbstractSince the stochastic gradient algorithm has a slower convergence rate, this letter presents a multi-innovation stochastic gradient algorithm for a class of dual-rate sampled systems with preload nonlinearity. The basic idea is to transform the dual-rate system model into an identification model which can use dual-rate data by using the polynomial transformation technique. A simulation example is provided to verify the effectiveness of the proposed method

Deep Learning for Black-Box Modeling of Audio Effects

Virtual analog modeling of audio effects consists of emulating the sound of an audio processor reference device. This digital simulation is normally done by designing mathematical models of these systems. It is often difficult because it seeks to accurately model all components within the effect unit, which usually contains various nonlinearities and time-varying components. Most existing methods for audio effects modeling are either simplified or optimized to a very specific circuit or type of audio effect and cannot be efficiently translated to other types of audio effects. Recently, deep neural networks have been explored as black-box modeling strategies to solve this task, i.e., by using only input–output measurements. We analyse different state-of-the-art deep learning models based on convolutional and recurrent neural networks, feedforward WaveNet architectures and we also introduce a new model based on the combination of the aforementioned models. Through objective perceptual-based metrics and subjective listening tests we explore the performance of these models when modeling various analog audio effects. Thus, we show virtual analog models of nonlinear effects, such as a tube preamplifier; nonlinear effects with memory, such as a transistor-based limiter and nonlinear time-varying effects, such as the rotating horn and rotating woofer of a Leslie speaker cabinet

Oxygen uptake estimation in humans during exercise using a Hammerstein model

This paper aims to establish a block-structured model to predict oxygen uptake in humans during moderate treadmill exercises. To model the steady state relationship between oxygen uptake (oxygen consumption) and walking speed, six healthy male subjects walked on a motor driven treadmill with constant speed from 2 to 7 km/h. The averaged oxygen uptake at steady state (VO 2) was measured by a mixing chamber based gas analysis and ventilation measurement system (AEI Moxus Metabolic Cart). Based on these reliable date, a nonlinear steady state relationship was successfully established using Support Vector Regression methods. In order to capture the dynamics of oxygen uptake, the treadmill velocity was modulated using a Pseudo Random Binary Signal (PRBS) input. Breath by breath analysis of all subjects was performed. An ARX model was developed to accurately reproduce the measured oxygen uptake dynamics within the aerobic range. Finally, a Hammerstein model was developed, which may be useful for implementing a control system for the regulation of oxygen uptake during treadmill exercises. © 2007 Biomedical Engineering Society