Identification Of Nonlinear Dynamic Systems Research Articles

Kernel Identification of Non-Linear Systems with General Structure

In the paper we deal with the problem of non-linear dynamic system identification in the presence of random noise. The class of considered systems is relatively general, in the sense that it is not limited to block-oriented structures such as Hammerstein or Wiener models. It is shown that the proposed algorithm can be generalized for two-stage strategy. In step 1 (non-parametric) the system is approximated by multi-dimensional regression functions for a given set of excitations, treated as representative set of points in multi-dimensional space. ‘Curse of dimensionality problem’ is solved by using specific (quantized or periodic) input sequences. Next, in step 2, non-parametric estimates can be plugged into least squares criterion and support model selection and estimation of system parameters. The proposed strategy allows decomposition of the identification problem, which can be of crucial meaning from the numerical point of view. The “estimation points” in step 1 are selected to ensure good task conditioning in step 2. Moreover, non-parametric procedure plays the role of data compression. We discuss the problem of selection of the scale of non-parametric model, and analyze asymptotic properties of the method. Also, the results of simple simulation are presented, to illustrate functioning of the method. Finally, the proposed method is successfully applied in Differential Scanning Calorimeter (DSC) to analyze aging processes in chalcogenide glasses.

A novel pipelined neural FIR architecture for nonlinear adaptive filter

This paper presents a novel adaptive pipelined neural finite impulse response (PNFIR) filter for nonlinear signal processing. Unlike traditional pipelined recurrent neural network (PRNN), each module of the PNFIR filter is a simple architecture that includes a standard FIR filter followed by a nonlinear activation function. The complete design of proposed filter includes two subsections: The nonlinear part consists of neural FIR (NFIR) modules which is interconnected in a chained form and simultaneously executed in a parallel fashion; the linear subsection is a tapped-delay-line (TDL) linear combiner. Based on convex combination architecture, the adaptive algorithm derived from the gradient descent approach is utilized to update weights of the nonlinear and linear parts. Moreover, the analysis of stability conditions and computational complexity is also presented. Numerous simulation experimental results on nonlinear dynamic systems identification, speech signal and chaotic time series prediction show that the proposed PNFIR filter has simpler architecture, faster convergence rate, and lower computation complexity than the PRNN and joint process filter using pipelined feedforward second-order Volterra architecture (JPPSOV).

Data-driven modeling to predict the load vs. displacement curves of targeted composite materials for industry 4.0 and smart manufacturing

This work presents an approach for smart manufacturing focusing on Industry 4.0 to predict the load vs. displacement curve of targeted cotton fiber/Polypropylene (PP) composite materials while complying with the required intended properties. Experimental data for varying composite fiber percentage to characteristic load and earlier built artificial neural network (ANN) models are used as the feed. A newly built ANN model is being trained and tested on the TensorFlow backend using the Keras library in Python to predict the load vs. displacement curves for any in-between values of the experimental range (e.g., 0–50% cotton fiber filler content in PP) without doing any further experiment. Finally, a Python package for the sparse identification of nonlinear dynamical (PySINDy) systems is used to identify the exact data-driven ANN model through the system identification, which will facilitate the effective implementation of the control algorithms, smart internet of things (IoT), and high-tech automated system.

Data-driven modeling of the chaotic thermal convection in an annular thermosyphon

dentifying accurate and yet interpretable low-order models from data has gained a renewed interest over the past decade. In the present work, we illustrate how the combined use of dimensionality reduction and sparse system identification techniques allows us to obtain an accurate model of the chaotic thermal convection in a two-dimensional annular thermosyphon. Taking as guidelines the derivation of the Lorenz system, the chaotic thermal convection dynamics simulated using a high-fidelity computational fluid dynamics solver are first embedded into a low-dimensional space using dynamic mode decomposition. After having reviewed the physical properties the reduced-order model should exhibit, the latter is identified using SINDy, an increasingly popular and flexible framework for the identification of nonlinear continuous-time dynamical systems from data. The identified model closely resembles the canonical Lorenz system, having a similar structure and exhibiting the same physical properties. Finally, extensions to other flow configurations with or without control are discussed.

S-synchronization Structural Identifiability and Identification of Nonlinear Dynamic Systems

An approach to the structural identifiability analysis of nonlinear dynamic systems under uncertainty is proposed. We have shown that S-synchronization is the necessary condition for the structural identifiability of a nonlinear system. Conditions are obtained for the design of a model which identifies the nonlinear part of the system. The method is proposed for the obtaining of a set which contains the information on the nonlinear part. A class of geometric frameworks which reflect the state of the system nonlinear part is introduced. Geometrical frameworks are defined on the synthesized set. The conditions are given for the structural indistinguishability of geometric frameworks on the set of S-synchronizing inputs. Local identifiability conditions are obtained for the nonlinear part. We are shown that a non-synchronizing input gives an insignificant geometric framework. This leads to a structural non-identifiability of the system nonlinear part. The method is proposed for the estimation of the structural identifiability the nonlinear part of the system. Conditions for parametric identifiability of the system linear part are obtained. We show that the structural identifiability is the basis for the structural identification of the system. The hierarchical immersion method is proposed for the estimation of nonlinear system structural parameters. The method is used for the structural identification of a system with Bouc-Wen hysteresis.

PySINDy: A Python package for the sparse identification of nonlinear dynamical systems from data

Scientists have long quantified empirical observations by developing mathematical models that characterize the observations, have some measure of interpretability, and are capable of making predictions. Dynamical systems models in particular have been widely used to study, explain, and predict system behavior in a wide range of application areas, with examples ranging from Newton’s laws of classical mechanics to the Michaelis-Menten kinetics for modeling enzyme kinetics. While governing laws and equations were traditionally derived by hand, the current growth of available measurement data and resulting emphasis on data-driven modeling motivates algorithmic approaches for model discovery. A number of such approaches have been developed in recent years and have generated widespread interest, including Eureqa (Schmidt & Lipson, 2009), sure independence screening and sparsifying operator (Ouyang, Curtarolo, Ahmetcik, Scheffler, & Ghiringhelli, 2018), and the sparse identification of nonlinear dynamics (SINDy) (Brunton, Proctor, & Kutz, 2016). Maximizing the impact of these model discovery methods requires tools to make them widely accessible to scientists across domains and at various levels of mathematical expertise.

The Use of Kalman Filter Techniques for Ship Track Estimation

Unscented Kalman Filter (UKF) is a technique used in non-linear applications and dynamic systems identification (e.g. tracking marine vessels and ships) that require state and parameter estimation. This paper studies Kalman Filter (KF) based techniques for tracking ships using Global Positioning System (GPS) data. The present work proposes to exploit information from GPS sensors in order to track a ship in real-time. The absence and presence problem of a ship is handled by a applying KF theory to analyze GPS coordinates and compare current marine vessel routes to previously recorded ones. To study tracking performance, the system was implemented in C++ and simulation results demonstrate the feasibility and high accuracy of the proposed tracking method

A review on computational intelligence for identification of nonlinear dynamical systems

This work aims to provide a broad overview of computational techniques belonging to the area of artificial intelligence tailored for identification of nonlinear dynamical systems. Both parametric and nonparametric identification problems are considered. The examined computational intelligence techniques for parametric identification deal with genetic algorithm, particle swarm optimization, and differential evolution. Special attention is paid to the parameters estimation for a rich class of nonlinear dynamical models, including the Bouc–Wen model, chaotic systems, the Jiles–Atherton model, the LuGre model, the Prandtl–Ishlinskii model, the Preisach model, and the Wiener–Hammerstein model. On the other hand, genetic programming and artificial neural networks are discussed for nonparametric identification applications. Once the identification problem is formulated, a detailed illustration of the considered computational intelligence techniques is provided, together with a comprehensive examination of relevant applications in the fields of structural mechanics and engineering. Possible directions for future research are also addressed.

Fuzzy Identification of Nonlinear Dynamic System Based on Input Variable Selection and Particle Swarm Optimization Parameter Optimization

Input variable selection is an essential step in the development of data-driven models. In order to establish a fuzzy model with high identification accuracy for complex nonlinear systems (such as variable load pneumatic loading system) in engineering, a novel fuzzy identification method is proposed, which is based on the selection of important input variables. Firstly, the simplified Two Stage Fuzzy Curves and Surfaces method is used to rank the original input variables according to their significance, and the variables which are most relevant to the output are selected as the input of the T-S fuzzy model. Then, the Fuzzy c-Means clustering algorithm and Particle Swarm Optimization algorithm are used to identify the antecedent parameters, and the Recursive Least Square method is used to identify the consequent parameters. The validity of the proposed fuzzy identification method is verified by two benchmark problems, and the results show that the accuracies of identified models have been improved significantly compared with the other existing models. Finally, the proposed approach is implemented to the practical data of an actual variable load pneumatic loading system, and preponderant trajectory matching performance is achieved.

Parameter Identification of Block-Oriented Nonlinear Systems in the Frequency Domain

Abstract A problem of parameter identification of nonlinear dynamic systems of manufacturing processes on the set of block-oriented models in the frequency domain is considered. Method of parameter identification in steady state at the input sinusoidal influences is proposed. The solution of the problem of parameter identification is reduced to the solution of the systems of algebraic equations by using the Fourier approximation. The parameters estimations are received by the least squares method. The identification method is investigated by theoretical analysis and computer modelling.

Nonlinear dynamic system identification with a cooperative population-based algorithm featuring a restart metaheuristic

Dynamic system identification is commonly reduced to an optimization problem which is complex and multimodal. To find a global optimum of this problem, evolutionary algorithms are often applied. However, as it was shown in many studies, conventional evolution-based algorithms do not demonstrate the acceptable performance for this class of problems, therefore, some effective modifications have been proposed so far. In our study, we combine two approaches which were previously used in linear dynamic system identification and allowed their accurate identification. More specifically, we present a cooperative evolutionary algorithm with a restart metaheuristic and apply it for the parameter identification of a nonlinear cascaded system. The experimental results prove the effectiveness of the proposed evolution-based identification compared to other known solutions of this problem.

Approximate GP Inference for Nonlinear Dynamical System Identification Using Data-Driven Basis Set

We address the problem of nonlinear dynamical system identification in state space formulation using an approximate Gaussian process (GP) regression framework where the basis for GP are learned from data. Approximate GP inference is used to address the high computational cost of exact GP frameworks, and is based on basis function expansion concept. We address the design of these basis functions using data and eigenvalue decomposition framework. The need for such design arises in practical applications where the collected data has outliers, discontinuities and other non-stationary characteristics which limit not only the applicability but also the performance of traditional GP framework with inherent stationary assumptions. Using the available data set, a kernel eigenvalue problem is formulated which is solved using Monte Carlo techniques to construct basis functions. Then, a low-rank approximation to the exact GP is obtained by an approach similar to kernel principle component analysis (k-PCA). The coefficients in the basis function expansion and other unknown parameters are learned from data using sequential Monte Carlo technique. The proposed GP framework for dynamical system identification is tested and validated against fixed basis framework using simulations and experimental data.

Optimal feedback input design for dynamic nonlinear systems

An optimal feedback input design method for active parameter identification of dynamic nonlinear systems is presented. The problem is formulated in a receding horizon framework where extended Kalman filter is used for system identification and the optimal input is designed in a nonlinear model predictive control framework. Towards this end, a suitable optimality criterion related to the unknown parameters is proposed and motivated as an information measure. The aim of the optimal input design is to yield maximal information from the unknown system by minimising the cost related to the unknown parameters while maintaining some process performance and satisfying the possible constraints. Simulations are performed to show the effectiveness of the proposed algorithm.

Fuzzy jump wavelet neural network based on rule induction for dynamic nonlinear system identification with real data applications.

AimFuzzy wavelet neural network (FWNN) has proven to be a promising strategy in the identification of nonlinear systems. The network considers both global and local properties, deals with imprecision present in sensory data, leading to desired precisions. In this paper, we proposed a new FWNN model nominated “Fuzzy Jump Wavelet Neural Network” (FJWNN) for identifying dynamic nonlinear-linear systems, especially in practical applications.MethodsThe proposed FJWNN is a fuzzy neural network model of the Takagi-Sugeno-Kang type whose consequent part of fuzzy rules is a linear combination of input regressors and dominant wavelet neurons as a sub-jump wavelet neural network. Each fuzzy rule can locally model both linear and nonlinear properties of a system. The linear relationship between the inputs and the output is learned by neurons with linear activation functions, whereas the nonlinear relationship is locally modeled by wavelet neurons. Orthogonal least square (OLS) method and genetic algorithm (GA) are respectively used to purify the wavelets for each sub-JWNN. In this paper, fuzzy rule induction improves the structure of the proposed model leading to less fuzzy rules, inputs of each fuzzy rule and model parameters. The real-world gas furnace and the real electromyographic (EMG) signal modeling problem are employed in our study. In the same vein, piecewise single variable function approximation, nonlinear dynamic system modeling, and Mackey–Glass time series prediction, ratify this method superiority. The proposed FJWNN model is compared with the state-of-the-art models based on some performance indices such as RMSE, RRSE, Rel ERR%, and VAF%.ResultsThe proposed FJWNN model yielded the following results: RRSE (mean±std) of 10e-5±6e-5 for piecewise single-variable function approximation, RMSE (mean±std) of 2.6–4±2.6e-4 for the first nonlinear dynamic system modelling, RRSE (mean±std) of 1.59e-3±0.42e-3 for Mackey–Glass time series prediction, RMSE of 0.3421 for gas furnace modelling and VAF% (mean±std) of 98.24±0.71 for the EMG modelling of all trial signals, indicating a significant enhancement over previous methods.ConclusionsThe FJWNN demonstrated promising accuracy and generalization while moderating network complexity. This improvement is due to applying main useful wavelets in combination with linear regressors and using fuzzy rule induction. Compared to the state-of-the-art models, the proposed FJWNN yielded better performance and, therefore, can be considered a novel tool for nonlinear system identification.

Lyapunov Theory-Based Fusion Neural Networks for the Identification of Dynamic Nonlinear Systems.

This paper introduces a novel fusion neural architecture and the use of a novel Lyapunov theory-based algorithm, for the online approximation of the dynamics of nonlinear systems. The proposed neural system, in combination with the proposed update rule of the neural weights, achieves fast convergence of the identification process, ensuring at the same time stability of the error system in the sense of Lyapunov theory. The fusion neural system combines the features that are extracted from two-independent neural streams, a feedforward and a diagonal recurrent one, satisfying different design criteria of the identification task. Simulation results for five cases reveal the approximation strength of both proposed fusion neural architecture and proposed learning algorithm. Also, additional experiments demonstrate the effectiveness in cases of parameter variations and additive noise.

Discovering time-varying aerodynamics of a prototype bridge by sparse identification of nonlinear dynamical systems.

Vortex-induced vibrations (VIVs) have been observed on a long-span suspension bridge. The nonstationary wind in the field characterized by the time-varying mean wind speed is likely to lead to time-varying aerodynamics of the wind-bridge system during VIVs, which is different from VIVs induced by stationary or even steady wind in wind tunnels. In this paper, data-driven methods are proposed to reveal the time-varying aerodynamics of the wind-bridge system during VIV events based on field measurements on a long-span suspension bridge. First, a variant of the sparse identification of nonlinear dynamics algorithm is proposed to identify parsimonious, time-varying aerodynamical systems that capture VIV events of the bridge. Thus we are able to posit new, data-driven, and interpretable models highlighting the aeroelastic interactions between the wind and bridge. Second, a density-based clustering algorithm is applied to discovering the potential modes of dynamics during VIV events. As a result, the time-dependent model is obtained to reveal the evolution of the aerodynamics of the wind-bridge system over time during an entire VIV event. It is found that the level of self-excited effects of the wind-bridge system is significantly time varying with the real-time wind speed and bridge motion state. The simulations of VIVs by the obtained time-dependent models show high accuracies of the models with an averaged normalized mean-square error of 0.0023. The clustering of obtained models shows underlying distinct dynamical regimes of the wind-bridge system, which are distinguished by the level of self-excited effects.

Nonlinear system identification model of the spread of TB disease using the genetic algorithm and multilayer perceptron

System identification is the process of building a mathematical model of a dynamic system based on the observed input-output data. Artificial neural networks have been shown to complete the identification of nonlinear systems with various learning algorithms. Identification of nonlinear dynamic systems in the model of TB disease spread is needed to predict the spread of TB disease. The model for the spread of TB disease has three compartments and six parameters. The process of identifying models for the spread of TB disease by estimating parameters using the genetic algorithm and validation of the model using multilayer perceptron. The choice of multilayer perceptron architecture determines the minimum error in the nonlinear system identification process for the model of TB disease spread. From the results of the trial, it was shown that the multilayer perceptron and genetic algorithm were able to identify the spread model of TB disease with MMRE of 0.00347

Data driven nonlinear dynamical systems identification using multi-step CLDNN

In many cases, the equations that dynamical systems are based on are unknown and hard to model and predict. On the other hand, machine learning algorithms are based on the data of a solution as it evolves and do not need equations. In the era of abundant data, using machine learning technology to discover accurate mathematical models of dynamical systems directly from time series data becomes increasingly important. Recently, a multi-step deep neural networks (multi-step DNN) model without need of direct access to temporal gradients is proposed, which can accurately learn the evolution from a given set of observed data, identify nonlinear dynamical systems, and forecast future states. However, the architecture lacks the capability to capture long term temporal dependencies from dynamical time-series data. In the paper, based on the multi-step time-stepping schemes, we proposed a new CLDNN model which combine convolutional layer, long short-term memory layer and fully connected layer, to address the aforementioned weakness. The effectiveness of our model is tested for several benchmark problems involving the identification and prediction of complex, nonlinear and chaotic dynamics. The experiment results show that the multi-step CLDNN has better identification and prediction performance than the multi-step DNN. The research provides possible corroboration for developing new deep learning based algorithms for nonlinear system identification.

Evolving Neural Network CMAC and its Applications

The conventional CMAC (Cerebellar Model Articulation Controller) neural network (NN) can be applied in many real-world applications thanks to its high learning speed and good generalization capability. In this paper it is proposed to utilize a neuro-evolutional approach to adjust CMAC parameters and construct mathematical models of nonlinear objects in the presence of the gaussian noise. The general structure of the evolving CMAC NN is considered. The paper demonstrates that the evolving CMAC NN can be used effectively for the identification of nonlinear dynamical systems. The simulation of the proposed approach for various nonlinear objects is performed. The results proved the effectiveness of the developed methods.

NARX Model Identification Using Correntropy Criterion in the Presence of Non-Gaussian Noise

In past years, the system identification area has emphasized the identification of nonlinear dynamic systems. In this field, polynomial nonlinear autoregressive with exogenous (NARX) models are widely used due to flexibility and prominent representation capabilities. However, the traditional identification algorithms used for model selection and parameter estimation with NARX models have some limitation in the presence of non-Gaussian noise, since they are based on second-order statistics that tightly depend on the assumption of Gaussianity. In order to solve this dependence, a novel identification method called simulation correntropy maximization with pruning (SCMP) based on information theoretic learning is introduced by this paper. Results obtained in non-Gaussian noise environment in three experiments (numerical, benchmark data set and measured data from a real plant) are presented to validate the performance of the proposed approach when compared to other similar algorithms previously reported in the literature, e.g., forward regression with orthogonal least squares and simulation error minimization with pruning. The proposed SCMP method has shown increased accuracy and robustness for three different experiments.