Identification Of Nonlinear Dynamic Systems Research Articles

Nonlinear system identification via data augmentation

This paper presents a novel nonparametric approach to the identification of nonlinear dynamical systems. The proposed methodology exploits the potential of manifold learning on an artificially augmented dataset, obtained without running new experiments on the plant. The additional data are employed for approximating the manifold where input regressors lie. The knowledge of the manifold acts as a prior information on the system, that induces a proper regularization term on the identification cost. The new regularization term, as opposite to the standard Tikhonov one, enforces local smoothness of the function along the manifold. A graph-based algorithm tailored to dynamical systems is proposed to generate the augmented dataset. The hyperparameters of the method, along with the order of the system, are estimated from the available data. Numerical results on a benchmark Nonlinear Finite Impulse Response (NFIR) system show that the proposed approach may outperform the state of the art nonparametric methods.

Detection of reaching intention using EEG signals and nonlinear dynamic system identification

Background and objectivesLow frequency electroencephalography (EEG) signals are associated with preparation of movement and thus provide valuable information for brain-machine interface applications. The purpose of this study was to detect movement intention from EEG signals before execution of self-paced arm reaching movements. MethodsTen healthy individuals were recruited. Movement onset was determined from surface electromyography recordings time-locked with EEG signals. Unlike previous studies, which employed feature extraction and classification for decoding, a nonlinear dynamic multiple-input/single output (MISO) model was developed. The MISO model consisted of a cascade of Volterra structures and a threshold block, generating the binary output corresponding to intention/no-intention. The modeling process included input selection from a pool of different EEG channels. The predictive performance of the model was evaluated using the receiver operating characteristics curve, from which the optimum threshold was also selected. The Mann–Whitney statistics was employed to select the significant EEG channels for the output by examining the statistical significance of improvement in the predictive capability of the model when the respective channels were included. ResultsWith the proposed approach, movement intention was detected approximately 500 ms before the movement onset and on average, with an accuracy of 96.37 ± 0.94%, a sensitivity of 77.93 ± 4.40% and a specificity of 98.52 ± 1.19%. ConclusionsThe model output can be converted to motion commands for neuroprosthetic devices and exoskeletons in future applications.

Identification of nonlinear block-oriented systems with backlash and saturation

Abstract A new approach to modeling and identification of discrete-time nonlinear dynamic systems with input backlash and output saturation nonlinearities is presented. The proposed three-block cascade mathematical model results from successive applications of the key-term separation principle. This provides special nonlinear model description that is linear in parameters. An iterative technique with internal variable estimation is proposed for estimation of all the model parameters based on measured input/output data and minimizing the least-squares criterion. Illustrative example of cascade system identification with backlash and saturation is included.

Recovery of the Input Signals of Eddy-Current Displacement Transducers Under Thermal-Shock Actions

We propose a method for the recovery of input signals of eddy-current displacement transducers under thermal-shock action. The recovery of the input signals was performed with correction of the output data of a primary measuring transducer. The procedure of correction is based on the methods of identification of nonlinear dynamic systems described by the discrete Volterra series.

Using self-constructing recurrent fuzzy neural networks for identification of nonlinear dynamic systems

In this paper, the self-constructing recurrent fuzzy neural network (SCRFNN) is applied for nonlinear dynamical system identification (NDSI). The SCRFNN is a novel fuzzy neural network (FNN) by adding a recurrent path in each node of the hidden layer of self-constructing FNN, which contains two learning phases. Specifically, the structure learning is based on partition of the input space and the parameter learning is based on the supervised gradient descent method using a delta adaptation law. The SCRFNN can decrease the minimum firing strength in each learning cycle and the number of hidden neurons which is an FNN with high accuracy and compact structure compared with several other neural networks. The performance of SCRFNN in NDSI is further verified in simulation.

Structure Identification of Continuous-Time Block-Oriented Nonlinear Systems in the Frequency Domain

Abstract A problem of structure identification of nonlinear dynamic systems on the set of continuous block-oriented models with nonlinear elements in the form of polynomial functions of finite degree and stable linear elements in the frequency domain is considered. Method of structure identification in steady state based on the observation of the system’s input and output variables at the input sinusoidal influences is proposed. The problem of the structure identification is considered according to the classical definition of identification of Zadeh. The structure definition criterion of the model is developed. The identification method is investigated by theoretical analysis and computer modelling.

Using self-constructing recurrent fuzzy neural networks for identification of nonlinear dynamic systems

Using self-constructing recurrent fuzzy neural networks for identification of nonlinear dynamic systems

Discovery of Nonlinear Multiscale Systems: Sampling Strategies and Embeddings

A major challenge in the study of dynamical systems is that of model discovery: turning data into models that are not just predictive, but provide insight into the nature of the underlying dynamical system that generated the data. This problem is made more difficult by the fact that many systems of interest exhibit diverse behaviors across multiple time scales. We introduce a number of data-driven strategies for discovering nonlinear multiscale dynamical systems and their embeddings from data. We consider two canonical cases: (i) systems for which we have full measurements of the governing variables, and (ii) systems for which we have incomplete measurements. For systems with full state measurements, we show that the recent sparse identification of nonlinear dynamical systems (SINDy) method can discover governing equations with relatively little data and introduce a sampling method that allows SINDy to scale efficiently to problems with multiple time scales. Specifically, we can discover distinct governing equations at slow and fast scales. For systems with incomplete observations, we show that the Hankel alternative view of Koopman (HAVOK) method, based on time-delay embedding coordinates, can be used to obtain a linear model and Koopman invariant measurement system that nearly perfectly captures the dynamics of nonlinear quasiperiodic systems. We introduce two strategies for using HAVOK on systems with multiple time scales. Together, our approaches provide a suite of mathematical strategies for reducing the data required to discover and model nonlinear multiscale systems.

Identification and robustness analysis of nonlinear hybrid dynamical system of genetic regulation in continuous culture

In this paper, we present a framework to infer the possible transmembrane transport of intracellular substances. Considering four key enzymes, a modified fourteen-dimensional nonlinear hybrid dynamic system is established to describe the microbial continuous culture with enzyme-catalytic and genetic regulation. A novel quantitative definition of biological robustness is proposed to characterize the system's resilience when system parameters were perturbed. It not only considers the expectation of system output data after parameter disturbance but also considers the influence of the variance of these data. In this way, the definition can be used as an objective function of the system identification model due to the lack of data on the concentration of intracellular substances. Then, we design a parallel computing method to solve the system identification model. Numerical results indicate that the most likely transmembrane mode of transport is active transport coupling with passive diffusion for glycerol and 1, 3-propanediol.

India: IG Petrochemicals & Thirumalai – phthalic anhydride

This paper presents a new method for the identification of nonlinear dynamical systems employing a wavelet neural network (wavenet) coupled to an infinite impulse response filter (WIIR). It is well known that a neural network trained by a gradient method is susceptible to fall in a minimum local. In order to solve this problem, we train the wavenet with a modified particle swarm optimization (mPSO) evolutionary algorithm, which integrates an elitist selection in order to conserve the best qualified particles. This approach is called mPSOWIIR algorithm. Basically, the idea is that the mPSO generates different sets of parameters that are evaluated in the dynamical system to be identified in order to obtain the fitness of every set. The best one and the best historical values of every set are taken into account to improve the set of parameters, keeping the diversity of new solutions and training the wavenet only with the first time steps of the dynamical system. This approach is able to reduce the number of possible solutions, avoid local minima and extend the search space of the wavenet; eluding the problem of finding good initial parameters by trial and error. One of the main features of the proposed method is that the number of parameters remains constant in all the training process. The mPSOWIIR algorithm is applied to identify nonlinear dynamical systems commonly used in specialized literature, obtaining satisfactory results.

Identification and control of dynamical systems using different architectures of recurrent fuzzy system

Fuzzy logic based systems are very widely used for modeling and control of complex non-linear, plants. Fuzzy systems require the knowledge about the structure of the dynamic plant in order to achieve fruitful results. Recurrent Fuzzy systems (RFS) are a variation of fuzzy systems and have the ability to model and control dynamic plants without using the information about the structure of the plant. This paper presents identification and control of non-linear dynamical systems using two different architectures of recurrent fuzzy system (RFS). It highlights the importance of RFS over the conventional type-1 fuzzy based system. The objective of system identification as well as control has been achieved using both the architectures of RFS and the simulation results clearly show their efficiency. This paper also highlights yet another advantage of RFS over the conventional type-1 fuzzy systems which comes into light when dealing with higher order systems. The paper explains how the computational complexity can be greatly reduced by using RFS for higher order dynamical systems. A comparative analysis between the conventional type-1 fuzzy system and the two recurrent fuzzy systems has also been performed.

Modelling and identification of nonlinear cascade systems with backlash input and static output nonlinearities

ABSTRACTA new approach to the parameter identification of nonlinear dynamic systems using cascade models with nonlinear dynamic, linear dynamic and nonlinear static blocks is presented. Application of the key-term separation principle provides special expressions for the corresponding nonlinear model description that are linear in parameters. A least-squares-based iterative technique is proposed allowing estimation of all the model parameters based on measured input/output data. Illustrative examples of nonlinear cascade systems identification with input backlash and nonlinear static output characteristics are included.

Excitation signal design for nonlinear dynamic systems with multiple inputs – A data distribution approach

Abstract A methodology to generate excitation signals that can be used for the identification of nonlinear dynamic systems is proposed. In contrast to traditional approaches which are based on specific signal types, the objective here is the homogeneous distribution of the data points in the input space of the model. A space-filling data distribution in the whole input space is a necessity for gathering information about the nonlinearities of the system and minimizes the risk of extrapolation. The methodology can be extended to multiple inputs with moderate increase in complexity which is a key feature for most real-world applications. The quality of the excitation signal is demonstrated with simulations and on a high pressure fuel supply system.

DETERMINISTIC IDENTIFICATION METHODS FOR NONLINEAR DYNAMICALSYSTEMS BASED ON THEVOLTERRA MODEL

The paper solves an important scientific and practical problem, which is to improve the accuracy and computational stability of the methods of deterministic identification of nonlinear dynamic systems in the form of Volterra model based on experimental data of observations ”input-output” taking. On the base of theoretical and experimental studies created effective instrumental algorithmic and software tools for estimating Volterra kernels in the time domain Into account measurement errors. Results of the further development of methods of deterministic identification of nonlinear dynamic systems based on Volterra models using irregular pulse sequences show. The methods are based on the use of the Tikhonov regularization procedure. The amplitude of test impulses is used as a regularization parameter. In the identification, procedure applies wavelet filtering for smooth the estimates of the Volterra kernels apply. This gives increase the accuracy and noise immunity of identification methods. The approximation method of identification of the nonlinear dynamic systems based on Volterra models is improved. Method is consists in the choice of amplitudes of test signals and of coefficients scaling of the partial components of responses a nonlinear system in procedure of processing of signals-responses. The improvement is reduced to minimizing the methodological error in the allocation of partial components from the response of the identification object and allows obtaining more accurate estimates of Volterra nuclei. To improve the computational stability of the developed identification algorithms and for noise reduction in the obtained estimates of multidimensional Volterra kernels the wavelet filtration is used. This allows obtaining smoothed solutions and decreases error of the identification by 1,5-2,5 times. A new robust method of deterministic identification of nonlinear dynamic systems based on Volterra models in the time domain is developed. In contrast to the interpolation method, where finite difference formulas with a predetermined number of experimental studies of the object of identification are used for numerical differentiation. It is proposed to solve the corresponding Volterra integral equations of the first kind, for the numerical implementation of which an unlimited number of experiments can be used. This makes it possible to increase the accuracy of the calculation of derivatives, and consequently, the accuracy of identification. Software tools on the system Matlab platform have been developed to implement the developed computational algorithms for deterministic identification of nonlinear dynamic systems in the form of Volterra kernels.

Self‐recurrent wavelet neural network–based identification and adaptive predictive control of nonlinear dynamical systems

SummaryIn this paper, the problem of simultaneous identification and predictive control of nonlinear dynamical systems using self‐recurrent wavelet neural network (SRWNN) is addressed. The structure of the SRWNN is a modification of the wavelet neural network (WNN). Unlike WNN, the neurons present in the hidden layer of SRWNN contain the weighted self‐feedback loops. Dynamic back‐propagation algorithm is employed to derive the necessary parameter update equations. To further improve the convergence speed of the parameters, a time‐varying (adaptive) learning rate is used. Four simulation examples are considered for testing the effectiveness of the proposed method. Furthermore, some disturbance rejection tests are also performed on the proposed method. The results obtained through the simulation study confirm the effectiveness of the proposed method.

Online Identification of Nonlinear Stochastic Spatiotemporal System With Multiplicative Noise by Robust Optimal Control-Based Kernel Learning Method.

In this paper, we propose a novel kernel method for the online identification of stochastic nonlinear spatiotemporal dynamical systems using the robust control approach. By the difference method, the stochastic spatiotemporal (SST) systems driven by multiplicative noise are first transformed into a class of multi-input-multi-output-partially linear kernel models (PLKMs) with heterogeneous random terms. With the help of techniques established for reproducing kernel Hilbert space, the online learning problem is reasonably considered as an output feedback control problem for a group of time varying linear dynamical systems. We develop an effective algorithm to address the learning problem of PLKM and SST systems by employing the model predictive control theory. Compared with the existing learning methods, the new one can achieve adaptive, robust, and fast convergent online modeling performance for the spatiotemporal dynamics with multiplicative noise, which greatly facilitates the characterization of physical characteristics of the system. Moreover, this investigation for the first time addresses the learning problems for SST systems with novel robust control techniques, which can provide some novel insights into the design of kernel machine learning methods from the perspective of optimal control theory. Numerical studies for benchmark systems are presented to illustrate the effectiveness and efficiency of our new method.

Wavenet identification of dynamical systems by a modified PSO algorithm

This paper presents a new method for the identification of nonlinear dynamical systems employing a wavelet neural network (wavenet) coupled to an infinite impulse response filter (WIIR). It is well known that a neural network trained by a gradient method is susceptible to fall in a minimum local. In order to solve this problem, we train the wavenet with a modified particle swarm optimization (mPSO) evolutionary algorithm, which integrates an elitist selection in order to conserve the best qualified particles. This approach is called mPSOWIIR algorithm. Basically, the idea is that the mPSO generates different sets of parameters that are evaluated in the dynamical system to be identified in order to obtain the fitness of every set. The best one and the best historical values of every set are taken into account to improve the set of parameters, keeping the diversity of new solutions and training the wavenet only with the first time steps of the dynamical system. This approach is able to reduce the number of possible solutions, avoid local minima and extend the search space of the wavenet; eluding the problem of finding good initial parameters by trial and error. One of the main features of the proposed method is that the number of parameters remains constant in all the training process. The mPSOWIIR algorithm is applied to identify nonlinear dynamical systems commonly used in specialized literature, obtaining satisfactory results.

Adaptive control over non­linear objects using the robust neural network FCMAC

The paper explores issues related to the application of artificial neural networks (ANN) when solving the problems on identification and control of nonlinear dynamic systems. We have investigated characteristics of the network, which is a result of the application of the apparatus of fuzzy logic in a classical СМАС neural network, which is titled FCMAC ‒ Fuzzy Cerebral Model Arithmetic Computer. We studied influence of the form of receptive fields of associative neurons on the accuracy of identification and control; various information hashing algorithms that make it possible to reduce the amount of memory required for the implementation of a network; robust learning algorithms are proposed allowing the use of a network in systems with strong perturbations. It is shown that the FСМАС network, when selecting appropriate membership functions, can be applied in order to synthesize indirect control systems with and without a reference model; it is more efficient to use it in control systems with the reference model. This sharply reduces the quantity of training pairs and simplifies the coding due to the narrower range of the applied values of input signals. The results obtained are confirmed by simulation modeling of the processes of identification of and control over nonlinear dynamical systems

Identification of Parameters of Nonlinear Dynamical Systems Simulated by Volterra Polynomials

We study the identification methods for the nonlinear dynamical systems described by Volterra series. One of the main problems in the dynamical system simulation is the problem of the choice of the parameters allowing the realization of a desired behavior of the system. If the structure of the model is identified in advance, then the solution to this problem closely resembles the identification problem of the system parameters. We also investigate the parameter identification of continuous and discrete nonlinear dynamical systems. The identification methods in the continuous case are based on application of the generalized Borel Theorem in combination with integral transformations. To investigate discrete systems, we use a discrete analog of the generalized Borel Theorem in conjunction with discrete transformations. Using model examples, we illustrate the application of the developed methods for simulation of systems with specified characteristics.

Block-oriented identification of non-linear systems with input time delay in presence of measurement noise: a Laguerre–neural network approach

This paper proposes an approach for identification of non-linear dynamic systems with input time delay into the block-oriented Wiener model in the presence of measurement noise. The model comprised a linear dynamic subsystem (LDS) at the input side that is cascaded with a non-linear static subsystem (NSS). The LDS comprised Laguerre filters, whereas the NSS is constructed using committee neural networks (CNNs). The Laguerre filter compensates for the input time delay, whereas the CNN finds an appropriate non-linear mapping between its input and output with the useful property of the measurement noise attenuation. The parameters of the Laguerre filters as well as those of the CNN are determined using offline training algorithms. In order to find the optimal values of the weights of the CNN, a noise analysis is conducted. The proposed method is applied to a simulated continuous-stirred tank reactor (CSTR) with input time delay and measurement noise. The results indicate substantial benefits of the proposed method compared with the similar methods proposed in the literature for system identification.