Nonlinear System Identification Problem Research Articles

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.

A Kushner–Stratonovich Monte Carlo filter applied to nonlinear dynamical system identification

A Monte Carlo filter, based on the idea of averaging over characteristics and fashioned after a particle-based time-discretized approximation to the Kushner–Stratonovich (KS) nonlinear filtering equation, is proposed. A key aspect of the new filter is the gain-like additive update, designed to approximate the innovation integral in the KS equation and implemented through an annealing-type iterative procedure, which is aimed at rendering the innovation (observation–prediction mismatch) for a given time-step to a zero-mean Brownian increment corresponding to the measurement noise. This may be contrasted with the weight-based multiplicative updates in most particle filters that are known to precipitate the numerical problem of weight collapse within a finite-ensemble setting. A study to estimate the a-priori error bounds in the proposed scheme is undertaken. The numerical evidence, presently gathered from the assessed performance of the proposed and a few other competing filters on a class of nonlinear dynamic system identification and target tracking problems, is suggestive of the remarkably improved convergence and accuracy of the new filter.

Gradient-based iterative identification for Wiener nonlinear systems with non-uniform sampling

This paper focuses on the identification problem of Wiener nonlinear systems with non-uniform sampling. The mathematical model for the Wiener nonlinear system is established from the non-uniformly sampled input–output data. In order to solve the identification problem of the Wiener nonlinear system with the unmeasurable variables in the information vector, the gradient-based iterative algorithm is presented by replacing the unmeasurable variables with their corresponding iterative estimates. Finally, the simulation results indicate that the proposed algorithm is effective.

Identification of Hammerstein systems using key‐term separation principle, auxiliary model and improved particle swarm optimisation algorithm

The dynamic behaviour of many systems can be approximated by a static non-linearity in series with a linear dynamic part. Systems with static input or output non-linearities are very common in many engineering applications. Such models are known as block-oriented models in the existing literature. The Hammerstein model is a special kind of block-oriented model, where a non-linear block is followed by a linear system. This study investigates the identification of Hammerstein systems with asymmetric two-segment piecewise-linear non-linearities. The basic idea is to employ a key-term separation technique and a corresponding auxiliary model initially. Then, the identification problem of non-linear system is changed into a non-linear function optimisation problem over parameter space. Further, the estimates of all the parameters of the non-linear block, the linear subsystem and the noise part are obtained based on an improved particle swarm optimisation algorithm. Finally, simulation examples are included to demonstrate the effectiveness and robustness of the proposed identification scheme.

A fast learning algorithm for evolving neo-fuzzy neuron

This paper introduces an evolving neural fuzzy modeling approach constructed upon the neo-fuzzy neuron and network. The approach uses an incremental learning scheme to simultaneously granulate the input space and update the neural network weights. The neural network structure and parameters evolve simultaneously as data are input. Initially the space of each input variable is granulated using two complementary triangular membership functions. New triangular membership functions may be added, excluded and/or have their parameters adjusted depending on the input data and modeling error. The parameters of the network are updated using a gradient-based scheme with optimal learning rate. The performance of the approach is evaluated using instances of times series forecasting and nonlinear system identification problems. Computational experiments and comparisons against alternative evolving models show that the evolving neural neo-fuzzy network is accurate and fast, characteristics which are essential for adaptive systems modeling, especially in real-time, on-line environments.

Gradient based iterative parameter identification for Wiener nonlinear systems

This paper focuses on the identification problem of Wiener nonlinear output error systems. The application of the key-term decomposition technique provides a special form of the Wiener model with polynomials, where all the model parameters to be estimated are separated. To solve the identification problem of Wiener nonlinear output error systems with the unmeasurable variables in the information vector, an auxiliary model-based gradient iterative algorithm is presented by replacing the unmeasurable variables with their corresponding iterative estimates. The performances of the proposed algorithm are analyzed and compared by using numerical examples.

On the inference and approximation properties of belief rule based systems

Belief rule based (BRB) system provides a generic inference framework for approximating complicated nonlinear causal relationships between antecedent inputs and output. It has been successfully applied to a wide range of areas, such as fault diagnosis, system identification and decision analysis. In this paper, we provide analytical and theoretical analyses on the inference and approximation properties of BRB systems. We first investigate the unified multi-model decomposition structure of BRB systems, under which the input space is partitioned into different local regions. Then we analyse the distributed approximation process of BRB systems. These analysis results unveil the underlying inference mechanisms that enable BRB systems to have superior approximation performances. Furthermore, by using the Stone–Weierstrass theorem, we constructively prove that BRB systems can approximate any continuous function on a compact set with arbitrary accuracy. This result provides a theoretical foundation for using and training BRB systems in practical applications. Finally, a numerical simulation study on the well-known benchmark nonlinear system identification problem of Box–Jenkins gas furnace is conducted to illustrate the validity of a BRB system and show its inference and approximation capability.

Least-Squares-Based Iterative Identification Algorithm for Wiener Nonlinear Systems

This paper focuses on the identification problem of Wiener nonlinear systems. The application of the key-term separation principle provides a simplified form of the estimated parameter model. To solve the identification problem of Wiener nonlinear systems with the unmeasurable variables in the information vector, the least-squares-based iterative algorithm is presented by replacing the unmeasurable variables in the information vector with their corresponding iterative estimates. The simulation results indicate that the proposed algorithm is effective.

Recursive Least-Squares Estimation for Hammerstein Nonlinear Systems with Nonuniform Sampling

This paper focuses on the identification problem of Hammerstein nonlinear systems with nonuniform sampling. Using the key-term separation principle, we present a discrete identification model with nonuniform sampling input and output data based on the frame period. To estimate parameters of the presented model, an auxiliary model-based recursive least-squares algorithm is derived by replacing the unmeasurable variables in the information vector with their corresponding recursive estimates. The simulation results show the effectiveness of the proposed algorithm.

Variable Sign-Sign Wilcoxon Algorithm: A Novel Approach for System Identification

Behavioral study of a system is an important task. It is mostly used in real world environments and became an emergent research area. Various approaches have been proposed since last two decades. In this paper, we have proposed a Variable Step-Size Sign-Sign Wilcoxon Approach, that is robust against outliers in the desired data and also convergence speed is faster than Wilcoxon norm based approach. In initial stage, Sign-Sign Wilcoxon norm based approach has been verified. Next to it, the proposed approach is verified and compared for the application in Linear and Non-linear system identification problems in presence of outliers. DOI: http://dx.doi.org/10.11591/ijece.v2i4.837

Volterra filter modeling of nonlinear discrete-time system using improved particle swarm optimization

This paper focuses on the identification problem of nonlinear discrete-time systems using Volterra filter series model. Generally, to update the kernels of Volterra model, the most commonly used method is the gradient adaptive algorithm. However, this method probably traps at the local minimum for searching parameter solutions. In this study, a new intelligence swarm computation of the global search is considered. We utilize an improved particle swarm optimization (IPSO) algorithm to design the Volterra kernel parameters. It is somewhat different from the original algorithm due to modifying its velocity updating formula and this can promote the algorithm@?s searching ability for solving the optimization problem. Using the IPSO algorithm to minimize the mean square error (MSE) between the actual output and model output, the identification problem for nonlinear discrete-time systems can be fulfilled. Finally, two different kinds of examples are provided to demonstrate the efficiency of the proposed method. Moreover, some examinations including the Volterra model memory size and algorithm initial condition are further considered.

A comparative study of adaptation algorithms for nonlinear system identification based on second order Volterra and bilinear polynomial filters

Nonlinear filtering techniques have recently become very popular in the field of signal processing. In this study we have considered the modeling of nonlinear systems using adaptive nonlinear Volterra filters and bilinear polynomial filters. The performance evaluation of these nonlinear filter models for the problem of nonlinear system identification has been carried out for several random input excitations and for measurement noise corrupted output signals. The coefficients of the two candidate filter models for are designed using several well known adaptive algorithms, such as least mean squares (LMS), recursive least squares (RLS), least mean p-norm (LMP), normalized LMP (NLMP), least mean absolute deviation (LMAD) and normalized LMAD (NLMAD) algorithms. Detailed simulation studies have been carried out for comparative analysis of Volterra model and bilinear polynomial filter, using these candidate adaptation algorithms, for system identification tasks and the superior solutions are determined.

A species-based improved electromagnetism-like mechanism algorithm for TSK-type interval-valued neural fuzzy system optimization

This paper proposes a novel TSK-type interval-valued neural fuzzy system with asymmetric membership functions (TIVNFS-A) which is optimized by a species-based improved electromagnetism-like mechanism (SIEM) algorithm. The proposed TIVNFS-A uses interval-valued asymmetric fuzzy membership functions and the TSK-type consequent part to improve the approximation performance and to reduce the number of fuzzy rules. In addition, the corresponding type reduction procedure is integrated in the adaptive network layers to reduce the amount of computation in the system. To train the TIVNFS-As, the SIEM combines the advantages of electromagnetism-like mechanism (EM) algorithm and gradient-descent technique to obtain faster convergence and lower computational complexity. Based on a similarity measurement, the swarm of the SIEM has a dynamic population size, and its population is also divided dynamically into subpopulations for optimization. The gradient-descent method is applied to the dominant particle in each species for a neighborhood search. Finally, the nonlinear system identification and classification problems are shown to demonstrate the performance and effectiveness of the proposed TIVNFS-A with the SIEM.

A computationally efficient approach for NN based system identification of a rotary wing UAV

Neural Network (NN) models based on autoregressive structures have long been used for nonlinear system identification problems. Their application for on-line implementations, however require them to be trained within a prescribed time span, which is often related to the sampling time of the system. In this paper, we introduce a NN model that is embedded with a dimensionality reduction mechanism in order to reduce the size of the network. The dimensionality reduction is based on Principal Component Analysis (PCA) and the resulting smaller NN trains faster. The longitudinal and lateral dynamics of a rotary wing Unmanned Aerial Vehicle (UAV) is modelled using flight test data. The results of system identification, error statistics and training times are provided to highlight the benefits of the proposed approach for NN based system identification models.

Discrete-time recurrent high order neural networks for nonlinear identification

This paper focuses on the problem of discrete-time nonlinear system identification via recurrent high order neural networks. It includes the respective stability analysis on the basis of the Lyapunov approach for the NN training algorithm. Applicability of the proposed scheme is illustrated via simulation for a discrete-time nonlinear model of an electric induction motor.

Training algorithm for radial basis function neural network based on quantum-behaved particle swarm optimization

Radial basis function (RBF) networks are widely applied in function approximation, system identification, chaotic time series forecasting, etc. To use a RBF network, a training algorithm is absolutely necessary for determining the network parameters. The existing training algorithms, such as orthogonal least squares (OLS) algorithm, clustering and gradient descent algorithm, have their own shortcomings respectively. In this paper, we propose a training algorithm based on a novel population-based evolutionary technique, quantum-behaved particle swarm optimization (QPSO), to train RBF neural network. The proposed QPSO-trained RBF network was tested on non-linear system identification problem and chaotic time series forecasting problem, and the results show that it can identify the system and forecast the chaotic time series more quickly and precisely than that trained by the particle swarm algorithm.

Improved parameter estimates for non-linear dynamical models using a bootstrap method

It is known that the least-squares (LS) class of algorithms produce unbiased estimates providing certain assumptions are met. There are many practical problems, however, where the required assumptions are violated. Typical examples include non-linear dynamical system identification problems, where the input and output observations are affected by measurement uncertainty and possibly correlated noise. This will result in biased LS estimates and the identified model will exhibit poor generalisation properties. Model estimation for this type of error-in-variables problem is investigated in this study, and a new identification scheme based on a bootstrap algorithm is proposed to improve the model estimates for non-linear dynamical system identification.

Nonlinear System Identification based on Volterra and Laguerre Models

This paper adressed nonlinear system identification problem using Volterra models. First, an approach is established to identify Volterra models using “Plant-friendly” input sequence with define properties. Second, we focus on the parametric complexity problem. As a solution, Volterra kernels are projected onto Laguerre basis resulting a reduced Volterra-Laguerre models. The efficiency of the proposed approach is illustrated according to a real system : the Two Tank System.

A Type-2 Self-Organizing Neural Fuzzy System and Its FPGA Implementation

This paper proposes a type-2 self-organizing neural fuzzy system (T2SONFS) and its hardware implementation. The antecedent parts in each T2SONFS fuzzy rule are interval type-2 fuzzy sets, and the consequent part is of Mamdani type. Using interval type-2 fuzzy sets in T2SONFS enables it to be more robust than type-1 fuzzy systems. T2SONFS learning consists of structure and parameter identification. For structure identification, an online clustering algorithm is proposed to generate rules automatically and flexibly distribute them in the input space. For parameter identification, a rule-ordered Kalman filter algorithm is proposed to tune the consequent-part parameters. The learned T2SONFS is hardware implemented, and implementation techniques are proposed to simplify the complex computation process of a type-2 fuzzy system. The T2SONFS is applied to nonlinear system identification and truck backing control problems with clean and noisy training data. Comparisons between type-1 and type-2 neural fuzzy systems verify the learning ability and robustness of the T2SONFS. The learned T2SONFS is hardware implemented in a field-programmable gate array chip to verify functionality of the designed circuits.

Higher-order spectra for identification of nonlinear modal coupling

Over the past four decades considerable work has been done in the area of power spectrum estimation. The information contained within the power spectrum relates to a signal's autocorrelation or ‘second-order statistics’. The power spectrum provides a complete statistical description of a Gaussian process; however, a problem with this information is that it is phase blind. This problem is addressed if one turns to a system's frequency response function (FRF). The FRF graphs the magnitude and phase of the frequency response of a system; in order to do this it requires information regarding the frequency content of the input and output signals. Situations arise in science and engineering whereby signal analysts are required to look beyond second-order statistics and analyse a signal's higher-order statistics (HOS). HOS or spectra give information on a signal's deviation from Gaussianity and consequently are a good indicator function for the presence of nonlinearity within a system. One of the main problems in nonlinear system identification is that of high modal density. Many modelling schemes involve making some expansion of the nonlinear restoring force in terms of polynomial or other basis terms. If more than one degree-of-freedom is involved this becomes a multivariate problem and the number of candidate terms in the expansion grows explosively with the order of nonlinearity and the number of degrees-of-freedom. This paper attempts to use HOS to detect and qualify nonlinear behaviour for a number of symmetrical and asymmetrical systems over a range of degrees-of-freedom. In doing so the paper also attempts to show that HOS are a more sensitive tool than the FRF in detecting nonlinearity. Furthermore, the object of this paper is to try and identify which modes couple in a nonlinear manner in order to reduce the number of candidate coupling terms, for a model, as much as possible. The bispectrum method has previously been applied to simple low-DOF systems with high symmetry and has been shown to work well in this limited case. The current paper will consider a model of a continuous wing–pylon model with reduced symmetry in order to assess the utility of the method in a more general situation, the analysis is also extended to assess the utility of the trispectrum.