Fractional order and non-linear system identification algorithms for biomedical applications

We discuss the modelling of dielectric responses of amorphous biological samples. Such samples are commonly encountered in impedance spectroscopy studies as well as in UV, IR, optical and THz transient spectroscopy experiments and in pump-probe studies. In many occasions, the samples may display quenched absorption bands. A systems identification framework may be developed to provide parsimonious representations of such responses. To achieve this, it is appropriate to augment the standard models found in the identification literature to incorporate fractional order dynamics. Extensions of models using the forward shift operator, state space models as well as their non-linear Hammerstein-Wiener counterpart models are highlighted. We also discuss the need to extend the theory of electromagnetically excited networks which can account for fractional order behaviour in the non-linear regime by incorporating nonlinear elements to account for the observed non-linearities. The proposed approach leads to the development of a range of new chemometrics tools for biomedical data analysis and classification.

Nonlinear equalization of Hammerstein OFDM systems

A practical orthogonal frequency-division multiplexing (OFDM) system can generally be modelled by the Hammerstein system that includes the nonlinear distortion effects of the high power amplifier (HPA) at transmitter. In this contribution, we advocate a novel nonlinear equalization scheme for OFDM Hammerstein systems. We model the nonlinear HPA, which represents the static nonlinearity of the OFDM Hammerstein channel, by a B-spline neural network, and we develop a highly effective alternating least squares algorithm for estimating the parameters of the OFDM Hammerstein channel, including channel impulse response coefficients and the parameters of the B-spline model. Moreover, we also use another B-spline neural network to model the inversion of the HPA’s nonlinearity, and the parameters of this inverting B-spline model can easily be estimated using the standard least squares algorithm based on the pseudo training data obtained as a byproduct of the Hammerstein channel identification. Equalization of the OFDM Hammerstein channel can then be accomplished by the usual one-tap linear equalization as well as the inverse B-spline neural network model obtained. The effectiveness of our nonlinear equalization scheme for OFDM Hammerstein channels is demonstrated by simulation results.

Body-centric modelling, identification, and acceleration tracking control of a quadrotor UAV

This paper presents the mathematical development of a body-centric nonlinear dynamic model of a quadrotor UAV that is suitable for the development of biologically inspired navigation strategies. Analytical approximations are used to find an initial guess of the parameters of the nonlinear model, then parameter estimation methods are used to refine the model parameters using the data obtained from onboard sensors during flight. Due to the unstable nature of the quadrotor model, the identification process is performed with the system in closed-loop control of attitude angles. The obtained model parameters are validated using real unseen experimental data. Based on the identified model, a Linear-Quadratic (LQ) optimal tracker is designed to stabilize the quadrotor and facilitate its translational control by tracking body accelerations. The LQ tracker is tested on an experimental quadrotor UAV and the obtained results are a further means to validate the quality of the estimated model. The unique formulation of the control problem in the body frame makes the controller better suited for bio-inspired navigation and guidance strategies than conventional attitude or position based control systems that can be found in the existing literature.

Adaptive B-spline neural network based nonlinear equalization for high-order QAM systems with nonlinear transmit high power amplifier

High bandwidth-efficiency quadrature amplitude modulation (QAM) signaling widely adopted in high-rate communication systems suffers from a drawback of high peak-toaverage power ratio, which may cause the nonlinear saturation of the high power amplifier (HPA) at transmitter. Thus, practical high-throughput QAM communication systems exhibit nonlinear and dispersive channel characteristics that must be modeled as a Hammerstein channel. Standard linear equalization becomes inadequate for such Hammerstein communication systems. In this paper, we advocate an adaptive B-Spline neural network based nonlinear equalizer. Specifically, during the training phase, an efficient alternating least squares (LS) scheme is employed to estimate the parameters of the Hammerstein channel, including both the channel impulse response (CIR) coefficients and the parameters of the B-spline neural network that models the HPA’s nonlinearity. In addition, another B-spline neural network is used to model the inversion of the nonlinear HPA, and the parameters of this inverting B-spline model can easily be estimated using the standard LS algorithm based on the pseudo training data obtained as a natural byproduct of the Hammerstein channel identification. Nonlinear equalisation of the Hammerstein channel is then accomplished by the linear equalization based on the estimated CIR as well as the inverse B-spline neural network model. Furthermore, during the data communication phase, the decision-directed LS channel estimation is adopted to track the time-varying CIR. Extensive simulation results demonstrate the effectiveness of our proposed B-Spline neural network based nonlinear equalization scheme.

Exact Search Directions for Optimization of Linear and Nonlinear Models Based on Generalized Orthonormal Functions

A novel technique for selecting the poles of orthonormal basis functions (OBF) in Volterra models of any order is presented. It is well-known that the usual large number of parameters required to describe the Volterra kernels can be significantly reduced by representing each kernel using an appropriate basis of orthonormal functions. Such a representation results in the so-called OBF Volterra model, which has a Wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a nonlinear static mapping given by the Volterra polynomial series. Aiming at optimizing the poles that fully parameterize the orthonormal bases, the exact gradients of the outputs of the orthonormal filters with respect to their poles are computed analytically by using a back-propagation-through-time technique. The expressions relative to the Kautz basis and to generalized orthonormal bases of functions (GOBF) are addressed; the ones related to the Laguerre basis follow straightforwardly as a particular case. The main innovation here is that the dynamic nature of the OBF filters is fully considered in the gradient computations. These gradients provide exact search directions for optimizing the poles of a given orthonormal basis. Such search directions can, in turn, be used as part of an optimization procedure to locate the minimum of a cost-function that takes into account the error of estimation of the system output. The Levenberg-Marquardt algorithm is adopted here as the optimization procedure. Unlike previous related work, the proposed approach relies solely on input-output data measured from the system to be modeled, i.e., no information about the Volterra kernels is required. Examples are presented to illustrate the application of this approach to the modeling of dynamic systems, including a real magnetic levitation system with nonlinear oscillatory behavior.

A neural network approach for robust nonlinear parameter estimation in presence of unknown-but-bounded errors

Systems based on artificial neural networks have high computational rates due to the use of a massive number of simple processing elements and the high degree of connectivity between these elements. This paper presents a novel approach to solve robust parameter estimation problem for nonlinear model with unknown-but-bounded errors and uncertainties. More specifically, a modified Hopfield network is developed and its internal parameters are computed using the valid-subspace technique. These parameters guarantee the network convergence to the equilibrium points. A solution for the robust estimation problem with unknown-but-bounded error corresponds to an equilibrium point of the network. Simulation results are presented as an illustration of the proposed approach. Copyright (C) 2000 IFAC.

Nitrogen content identification in crop plants using spectral reflectance and artificial neural networks

The accurate identification of the nitrogen content in crop plants is extremely important since it involves economic aspects and environmental impacts. Several experimental tests have been carried out to obtain characteristics and parameters associated with the health of plants and its growing. The nitrogen content identification involves a lot of nonlinear parametes and complexes mathematical models. This paper describes a novel approach for identification of nitrogen content thought spectral reflectance of plant leaves using artificial neural networks. The network acts as identifier of relationships among pH of soil, fertilizer treatment, spectral reflectance and nitrogen content in the plants. So, nitrogen content can be estimated and generalized from an input parameter set. This approach can be form the basis for development of an accurate real time nitrogen applicator.

A neural system to robust Nonlinear optimization subject to disjoint and constrained sets

The ability of neural networks to realize some complex nonlinear function makes them attractive for system identification. This paper describes a novel method using artificial neural networks to solve robust parameter estimation problems for nonlinear models with unknown-but-bounded errors and uncertainties. More specifically, a modified Hopfield network is developed and its internal parameters are computed using the valid-subspace technique. These parameters guarantee the network convergence to the equilibrium points. A solution for the robust estimation problem with unknown-but-bounded error corresponds to an equilibrium point of the network. Simulation results are presented as an illustration of the proposed approach.

Nonlinear parameter estimation in laminar forced convection within a circular sector tube

In this article we examine an inverse heat convection problem of estimating unknown parameters of a parameterized variable boundary heat flux. The physical problem is a hydrodynamically developed, thermally developing, three-dimensional steady state laminar flow of a Newtonian fluid inside a circular sector duct, insulated in the flat walls and subject to unknown wall heat flux at the curved wall. Results are presented for polynomial and sinusoidal trial functions, and the unknown parameters as well as surface heat fluxes are determined. Depending on the nature of the flow, on the position of experimental points the inverse problem sometimes could not be solved. Therefore, an identification condition is defined to specify a condition under which the inverse problem can be solved. Once the parameters have been computed it is possible to obtain the statistical significance of the inverse problem solution. Therefore, approximate confidence bounds based on standard statistical linear procedure, for the estimated parameters, are analyzed and presented.

Harmonic identification using parallel neural networks in single-phase systems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A barrier method for constrained nonlinear optimization using a modified Hopfield network

The ability of neural networks to realize some complex nonlinear function makes them attractive for system identification. This paper describes a novel barrier method using artificial neural networks to solve robust parameter estimation problems for nonlinear model with unknown-but-bounded errors and uncertainties. This problem can be represented by a typical constrained optimization problem. More specifically, a modified Hopfield network is developed and its internal parameters are computed using the valid-subspace technique. These parameters guarantee the network convergence to the equilibrium points. A solution for the robust estimation problem with unknown-but-bounded error corresponds to an equilibrium point of the network. Simulation results are presented as an illustration of the proposed approach.

Harmonic content identification based on neural method for single phase power systems

An alternative method is presented in this paper to identify the harmonic components of non-linear loads in single phase power systems based on artificial neural networks. The components are identified by analyzing the single phase current waveform in time domain in half-cycle of the ac voltage source. The proposed method is compared to the fast Fourier transform. Simulation and experimental results are presented to validate the proposed approach.

Damage detection in nonlinear structures using discrete-time volterra series

Structural damage identification is basically a nonlinear phenomenon; however, nonlinear procedures are not used currently in practical applications due to the complexity and difficulty for implementation of such techniques. Therefore, the development of techniques that consider the nonlinear behavior of structures for damage detection is a research of major importance since nonlinear dynamical effects can be erroneously treated as damage in the structure by classical metrics. This paper proposes the discrete-time Volterra series for modeling the nonlinear convolution between the input and output signals in a benchmark nonlinear system. The prediction error of the model in an unknown structural condition is compared with the values of the reference structure in healthy condition for evaluating the method of damage detection. Since the Volterra series separate the response of the system in linear and nonlinear contributions, these indexes are used to show the importance of considering the nonlinear behavior of the structure. The paper concludes pointing out the main advantages and drawbacks of this damage detection methodology. © (2013) Trans Tech Publications.

Non-parametric identification of a non-linear buckled beam using discrete-time Volterra Series

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Modeling and identification of freeplay nonlinearity

A nonlinear analysis is performed for the purpose of identification of the pitch freeplay nonlinearity and its effect on the type of bifurcation of a two degree-of-freedom aeroelastic system. The databases for the identification are generated from experimental investigations of a pitch-plunge rigid airfoil supported by a nonlinear torsional spring. Experimental data and linear analysis are performed to validate the parameters of the linearized equations. Based on the periodic responses of the experimental data which included the flutter frequency and its third harmonics, the freeplay nonlinearity is approximated by a polynomial expansion up to the third order. This representation allows us to use the normal form of the Hopf bifurcation to characterize the type of instability. Based on numerical integrations, the coefficients of the polynomial expansion representing the freeplay nonlinearity are identified. Published by Elsevier Ltd.