Intelligent modeling, observation, and control for nonlinearsystems

We present identification methods for nonlinear mechatronic systems. First, we consider a system consisting of a known linear part and an unknown static nonlinearity. With this approach, using an intelligent observer, it is possible to identify the nonlinear characteristic and to estimate all unmeasurable system states. The identification result of the nonlinearity and the estimated system states are used to improve the controller performance. Secondly, the first approach is extended to systems where both the linear parameters and the nonlinear characteristic are unknown. This is achieved by implementing the intelligent observer as a structured recurrent neural network     

Auxiliary Model-Based Forgetting Factor Stochastic Gradient Algorithm for Dual-Rate Nonlinear Systems and its Application to a Nonlinear Analog Circuit

This paper studies the identification problem of dual-rate Hammerstein nonlinear systems. By means of the key-term separation principle, we develop a regression identification model with different input and output sampling rates. In order to promote the convergence rate of the stochastic gradient (SG) algorithm, an auxiliary model-based forgetting factor SG algorithm is derived. Finally, the proposed algorithm is applied to model a nonlinear analog circuit with dual-rate sampling and the simulation result shows the effectiveness of the algorithm.     

Nonlinear Noise-Induced Transitions in Active Rotator Model

We investigate noise-induced transitions in active rotator model with a fluctuating threshold in the presence of an additive noise. The fluctuation of the threshold depends on the additive noise in a nonlinear fashion. In the white-noise limit of the fluctuation, the Fokker-Planck equation of the system reduces to that of the system with correlated linear fluctuation implying that the nonlinearity may be transformed into the correlation of linear noises. We also investigate the system with a nonlinear colored noise which depends on the additive noise as its square. The system shows a single peak, two peaks, and three peaks in its steady state probability distribution according to the noise intensities and the correlation time whose change leads to peak-creating, peak-splitting, and peak-merging transitions.     

Nonlinear system identification

This paper provides an overview of nonlinear system identification methodologies. The theory and application of nonlinear system identification is vast, and this overview is not intended to be comprehensive. Rather, the attempt here is to illustrate some of the salient features and key aspects of nonlinear system identification, especially those most relevant to the practitioner. In particular, this overview focuses on important issues in nonlinear system idenfication that differ from those encountered in linear system identification, including tests for nonlinearity, model selection, and input signal considerations.     

Identification of nonlinear systems using the Wiener model

An algorithm for the identification of nonlinear systems which can be described by a Wiener model consisting of a linear system followed by a single-valued nonlinearity is presented. Crossconolation techniques are employed to decouple the identification of the linear dynamics from the characterisation of the nonlinear element.     

Acoustic Echo Cancellation Using a Pseudocoherence Function in the Presence of Memoryless Nonlinearity

Acoustic echo cancellation (AEC) is critical for telecommunication applications involving two or more locations such as teleconferencing. It is also challenging because of loudspeaker's nonlinearity, real-time implementation requirement, and multipath effects of indoor environments. This paper addresses the nonlinear AEC problem. We use a Hammerstein model to describe the memoryless nonlinearity of loudspeaker concatenated with a linear room impulse response. We propose a method using a pseudo magnitude squared coherence (MSC) function to identify the nonlinearity in the Hammerstein system and develop an on-line AEC algorithm. Our method identifies nonlinearity without knowing the linear block in the Hammerstein system, which guarantees the stability of the algorithm and leads to a faster convergence rate. Moreover, several alternative criteria based on the MSC function are also proposed for nonlinearity identification. Effectiveness of the proposed algorithms is demonstrated through computer simulations.      

On Nonparametric Identification of Wiener Systems

In this paper, a new method for the identification of the Wiener nonlinear system is proposed. The system, being a cascade connection of a linear dynamic subsystem and a nonlinear memoryless element, is identified by a two-step semiparametric approach. The impulse response function of the linear part is identified via the nonlinear least-squares approach with the system nonlinearity estimated by a pilot nonparametric kernel regression estimate. The obtained estimate of the linear part is then used to form a nonparametric kernel estimate of the nonlinear element of the Wiener system. The proposed method permits recovery of a wide class of nonlinearities which need not be invertible. As a result, the proposed algorithm is computationally very efficient since it does not require a numerical procedure to calculate the inverse of the estimate. Furthermore, our approach allows non-Gaussian input signals and the presence of additive measurement noise. However, only linear systems with a finite memory are admissible. The conditions for the convergence of the proposed estimates are given. Computer simulations are included to verify the basic theory     

Stochastic analysis of gradient adaptive identification ofnonlinear systems with memory for Gaussian data and noisy input andoutput measurements

This paper investigates the statistical behavior of two gradient search adaptive algorithms for identifying an unknown nonlinear system comprised of a discrete-time linear system H followed by a zero-memory nonlinearity g(·). The input and output of the unknown system are corrupted by additive independent noises. Gaussian models are used for all inputs. Two competing adaptation schemes are analyzed. The first is a sequential adaptation scheme where the LMS algorithm is first used to estimate the linear portion of the unknown system. The LMS algorithm is able to identify the linear portion of the unknown system to within a scale factor. The weights are then frozen at the end of the first adaptation phase. Recursions are derived for the mean and fluctuation behavior of the LMS algorithm, which are in excellent agreement with Monte Carlo simulations. When the nonlinearity is modeled by a scaled error function, the second part of the sequential gradient identification scheme is shown to correctly learn the scale factor and the error function scale factor. Mean recursions for the scale factors show good agreement with Monte Carlo simulations. For slow learning, the stationary points of the gradient algorithm closely agree with the stationary points of the theoretical recursions. The second adaptive scheme simultaneously learns both the linear and nonlinear portions of the unknown channel. The mean recursions for the linear and nonlinear portions show good agreement with Monte Carlo simulations for slow learning. The stationary points of the gradient algorithm also agree with the stationary points of the theoretical recursions     

Estimating second-order Volterra system parameters from noisy measurements based on an LMS variant or an errors-in-variables method

This paper deals with the identification of a nonlinear SISO system modelled by a second-order Volterra series expansion when both the input and the output are disturbed by additive white Gaussian noises. Two methods are proposed. Firstly, we present an unbiased on-line approach based on the LMS. It includes a bias correction scheme which requires the variance of the input additive noise. Secondly, we suggest solving the identification problem as an errors-in-variables issue, by means of the so-called Frisch scheme. Although its computational cost is high, this approach has the advantage of estimating the Volterra kernels and the variances of both the additive noises and the input signal, even if the signal-to-noise ratios at the input and the output are low.     

Nonlinear Modeling of DC/DC Converters Using the Hammerstein's Approach

This paper deals with the modelling of highly nonlinear switching power-electronics converters using black-box identification methods. The duty cycle and the output voltage are chosen, respectively, as the input and the output of the model. A nonlinear Hammerstein-type mathematical model, consisting of a static nonlinearity and a linear time-invariant model, is considered in order to cope with the well-known limitations of the more common small-signal models, i.e. the entity of the variations of the variables around a well-defined steady-state operating point and the incorrect reproduction of the steady-state behavior corresponding to input step variations from the above steady-state operating point. The static nonlinearity of the Hammerstein model is identified from input-output couples measured at steady state for constant inputs. The linear model is identified from input-output data relative to a transient generated by a suitable pseudorandom binary sequence constructed with two input values used to identify the nonlinearity. The identification procedure is, first, illustrated with reference to a boost DC/DC converter using results of simulations carried out in the PSpice environment as true experimental results. Then, the procedure is experimentally applied on a prototype of the above converter. In order to show the utility of the Hammerstein models, a PI controller is tuned for a nominal model. Simulation and experimental results are displayed with the aim of showing the peculiarities of the approach that is followed.     

Statistical analysis of neural network modeling and identificationof nonlinear systems with memory

The paper presents a statistical analysis of neural network modeling and identification of nonlinear systems with memory. The nonlinear system model is comprised of a discrete-time linear filter H followed by a zero-memory nonlinear function g(.). The system is corrupted by input and output independent Gaussian noise. The neural network is used to identify and model the unknown linear filter H and the unknown nonlinearity g(.). The network architecture is composed of a linear adaptive filter and a two-layer nonlinear neural network (with an arbitrary number of neurons). The network is trained using the backpropagation algorithm. The paper studies the MSE surface and the stationary points of the adaptive system. Recursions are derived for the mean transient behavior of the adaptive filter coefficients and neural network weights for slow learning. It is shown that the Wiener solution for the adaptive filter is a scaled version of the unknown filter H. Computer simulations show good agreement between theory and Monte Carlo estimations     

Artificial neural networks for nonlinear time-domain filtering ofspeech

A multilayer perceptron (MLP) is applied as a time domain nonlinear filter to two classes of degraded speech, namely Gaussian white noise and nonlinear system degradation introduced by a low bit-rate CELP coder. The goal of the study is to examine the influence of the inherent nonlinearity within the MLP, and this is achieved by varying the levels of nonlinearity within the structure. Direct comparisons of MLPs and linear filters show that with CELP degradation the SNR improvements achieved by the MLP is measurably better than with an equivalent linear structure (3 dB cf 1.5 dB) but when the degradation is additive noise the two structures perform equally well. The study highlights the importance of scaling to achieve optimum performance, and of matching the enhancer to the degradation     

Blind identification of linear subsystems of LTI-ZMNL-LTI modelswith cyclostationary inputs

Discrete-time nonlinear models consisting of two linear time invariant (LTI) filters separated by a finite-order zero memory nonlinearity (ZMNL) of the polynomial type (the LTI-ZMNL-LTI model) are appropriate in a large number of practical applications. We discuss some approaches to the problem of blind identification of such nonlinear models, It is shown that for an Nth-order nonlinearity, the (possibly non-minimum phase) finite-memory linear subsystems of LTI-ZMNL and LTI-ZMNL-LTI models can be identified using the N+1th-order (cyclic) statistics of the output sequence alone, provided the input is cyclostationary and satisfies certain conditions. The coefficients of the ZMNL are not needed for identification of the linear subsystems and are not estimated. It is shown that the theory presented leads to analytically simple identification algorithms that possess several noise and interference suppression characteristics     

A stable adaptive Hammerstein filter employing partial orthogonalization of the input signals

This paper presents an algorithm that adapts the parameters of a Hammerstein system model. Hammerstein systems are nonlinear systems that contain a static nonlinearity cascaded with a linear system. In this paper, the static nonlinearity is modeled using a polynomial system, and the linear filter that follows the nonlinearity is an infinite-impulse response (IIR) system. The adaptation of the nonlinear components is improved by orthogonalizing the inputs to the coefficients of the polynomial system. The step sizes associated with the recursive components are constrained in such a way as to guarantee bounded-input bounded-output (BIBO) stability of the overall system. This paper also presents experimental results that show that the algorithm performs well in a variety of operating environments, exhibiting stability and global convergence of the algorithm.     

A novel fuzzy friction compensation approach to improve theperformance of a DC motor control system

The compensation of friction nonlinearities for servomotor control has received much attention due to undesirable and disturbing effects that the friction often has on conventional control systems. Compensation methods have generally involved selecting a friction model and then using model parameters to cancel the effects of the nonlinearity. In this paper, a method using fuzzy logic for the compensation of nonlinear friction is developed for the control of a DC motor. The method is unique in that a single fuzzy rule is used to compensate directly for the nonlinearity of the physical system. As a result, the method introduces fewer adjustable parameters than a typical fuzzy logic approach while still incorporating many advantages of using fuzzy logic such as the incorporation of heuristic knowledge, ease of implementation and the lack of a need for an accurate mathematical model. The general approach, analysis and experimental results obtained for an actual DC motor system with nonlinear friction characteristics are presented and the effectiveness of the fuzzy friction compensation control technique is discussed. The smoothness of response, response times and disturbance rejection of a PI control system with and without the proposed fuzzy compensator are analyzed and discussed to illustrate the effectiveness of the proposed method     

Adaptive sigmoidal plant identification using reduced sensitivity recursive least squares

Logistic models, comprising a linear filter followed by a nonlinear memoryless sigmoidal function, are often found in practice in many fields, e.g., biology, probability modelling, risk prediction, forecasting, signal processing, electronics and communications, etc., and in many situations a real time response is needed. The online algorithms used to update the filter coefficients usually rely on gradient descent (e.g., nonlinear counterparts of the Least Mean Squares algorithm). Other algorithms, such as Recursive Least Squares, although promising improved characteristics, cannot be directly used due to the nonlinearity in the model. We propose here a modified Recursive Least Squares algorithm that provides better performance than competing state of the art methods in an adaptive sigmoidal plant identification scenario.     

Three-level m sequences

Those properties of 3-level m sequences which are likely to prove useful in the crosscorrelation method of system dynamic analysis are listed. The use of 3-level m sequence signals in the identification of nonlinear systems is discussed, and it is shown that the number of crosscorrelation experiments required to determine the impulse response of the linear channel of a system with an amplitude nonlinearity is reduced by the use of these signals.     

Nonlinear Devices Acting as SNR Amplifiers for a Harmonic Signal in Noise

A harmonic signal corrupted by an additive white noise is processed by an arbitrary memoryless nonlinear device. The transformation of the signal-to-noise ratio (SNR) by the nonlinearity is explicitly computed and analyzed for Gaussian and non-Gaussian noise. Simple nonlinearities, easily implementable as electronic circuits, are shown capable of producing an amplification of the SNR. Such an amplification is not obtainable with linear filters, whatever their complexity or high order, but becomes easily accessible with simple nonlinear devices.     

CDKF在GPS/SINS组合导航系统非线性模型中的应用

GPS/SINS组合导航系统模型的非线性会导致扩展卡尔曼滤波（EKF）的估计精度降低。而中心差分卡尔曼滤波（CDKF）的新型非线性滤波方法,则利用插值公式对非线性系统的状态估计进行逼近,从而减小线性化误差对系统精度的影响。针对GPS/SINS导航系统的特点,建立了一种非线性误差模型,并将EKF与CDKF分别应用于组合导航系统模型中进行仿真比较。仿真结果表明,该算法简单易实现,且能满足系统在非线性模型下的导航要求,并具有较高的精度和收敛性。     

Quantifying and cancelation memory effects in high power amplifier for OFDM systems

A modeling approach to power amplifier design for implementation in OFDM radio units is presented. The power amplifier model assesses the impact of linear memory effects within the system using a Wiener representation, and employs a linear novel parametric estimation technique using Hilbert space. In addition, in order to model the nonlinear memory effects the previous topology is generalized by inserting the truncated Volterra filter before the static nonlinearity. Predistortion based on the Hammerstein model is introduced to deal with the nonlinear response. The new general algorithm is proposed to evaluate the Hammerstein model parameters for an OFDM system. A representative test bed was designed and implemented. The assessment of the new methods for PA and PD modeling are confirmed by experimental measurements. The measurement results reveal the preference of the new techniques over the existing approaches.