Identification Of Dynamic Systems Research Articles

System Identification of High-Dimensional Linear Dynamical Systems With Serially Correlated Output Noise Components

We consider identification of linear dynamical systems comprising of high-dimensional signals, where the output noise components exhibit strong serial, and cross-sectional correlations. Although such settings occur in many modern applications, such dependency structure has not been fully incorporated in existing approaches in the literature. In this paper, we explicitly incorporate the dependency structure present in the output noise through lagged values of the observed multivariate signals. We formulate a constrained optimization problem to identify the space spanned by the latent states, and the transition matrices of the lagged values simultaneously , wherein the constraints reflect the low rank nature of the state information, and the sparsity of the transition matrices. We establish theoretical properties of the estimators, and introduce an easy-to-implement computational procedure for empirical applications. The performance of the proposed approach, and the implementation procedure is evaluated on synthetic data, and compared with competing approaches, and further illustrated on a data set involving weekly stock returns of 75 US large financial institutions for the 2001–2017 period.

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.

On the embedding parameters in kernel identification problem of nonlinear dynamical systems

Dynamical models are of fundamental importance in many problems such as simulation, optimization and prediction. In identification problem of dynamical systems an input vector is typically considered as delayed vector of previous outputs. Embedding lag and embedding dimension should be chosen correctly. Identification of nonlinear systems is generally performed using kernel-based methods since they do not require any additional information about system structure. A common question in identification of dynamical system is sensitivity of kernel-based models to selected embedding lag and embedding dimension. The paper presents simulations of the kernel least mean squares algorithm on one-step prediction problem for various values of embedding lag and embedding dimension. It is shown that optimal embedding lag and embedding dimension is dependent on model parameters, while usage of optimal model parameters decreases the value of optimal embedding dimension.

Sparse Wavelet Networks

A wavelet network (WN) is a feed-forward neural network that uses wavelets as activation functions for the neurons in its hidden layer. By predetermining the wavelet positions and dilations, the WN can turn into a linear regression model. The common approach for the construction of these WN families is to use least-squares type algorithms. In this letter, we propose a novel approach by formulating a WN as a sparse linear regression problem, which we call a sparse wavelet network (SWN). In this WN, the problem of calculating the unknown inner parameters of the network becomes that of finding the sparse solution of an under-determined system of linear equations. Our sparse solution algorithm is a non-convex sparse relaxation approach inspired by smoothed L0 (SL0), a distinguished sparse recovery algorithm. The proposed SWN can be applied as a tool for the prediction and identification of dynamical systems.

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.

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.

Modified Elman Spike Neural Network for Identification and Control of Dynamic System

The utilization of conventional modeling strategies in the identification and control of a nonlinear dynamical system suffers from some weaknesses. These include absence of precise, conventional knowledge about the system, a high degree of uncertainty, strongly nonlinear and time-varying behavior. In this paper, a modified training algorithm for the identification and control of a nonlinear system using a soft-computing approach is proposed. Specifically, a modified structure of the Elman neural network with spike neural networks is proposed. This modified structure includes self-feedback, which provides a dynamic trace of the training algorithm. This self-feedback has weights, which can be trained during the training process. The simulation results show that the modified structure with the modified training algorithm is capable of the identification and control of a dynamic system in a more robust manor than when solely applying the other types of neural networks by 70% in terms of minimization of the percentage of error.

Model Structure Identification of Hybrid Dynamical Systems based on Unsupervised Clustering and Variable Selection

This paper proposes a systematic identification process for the hybrid dynamical system (HDS) estimating not only the coefficients but also the structure of the model. Beneficially speaking, the proposed system identification is used for the HDS system that the model structure, the number of modes, and the explanatory variables of the model are unknown. In the proposed method, a quantitative index to evaluate the number of modes is deployed and the optimal number of modes is determined from the measurement. The variable selection method is also introduced to determine the explanatory variables in each mode in a systematic manner. Two of piece-wise linear models which are prepared for the proposed system to identify and the validity of the proposed method is then demonstrated. Finally, the result of the proposed in comparison with the conventional system identification method for HDS is discussed.

Deep Learning Applied to Data-driven Dynamic Characterization of Hysteretic Piezoelectric Micromanipulators

The presence of nonlinearities such as hysteresis and creep increases the difficulty in the dynamic modeling and control of piezoelectric micromanipulators, in spite of the fact that the application of such devices requires high accuracy. Moreover, sensing in the microscale is expensive, making model feedback the only viable option. On the other hand, data-driven dynamic models are powerful tools within system identification that may be employed to construct models for a given plant. Recently, considerable effort has been devoted in extending the huge success of deep learning models to the identification of dynamic systems. In the present paper, we present the results of the successful application of deep learning based black-box models for characterizing the dynamic behavior of micromanipulators. The excitation signal is a multisine spanning the frequency band of interest and the selected model is validated with semi static individual sinusoidal curves. Various architectures are tested to achieve a reasonable result and we try to summarize the best approach for the fine tuning required for such application. The results indicate the usefulness and predictive power for deep learning based models in the field of system identification and in particular hysteresis modeling and compensation in micromanipulation applications.

Simultaneous identification of the all parameters for the Lorenz chaotic system

Drawbacks of the adaptive-searching methods, related with the problem of multi-parameter dynamic system identification are explored and highlighted. New approach, based on “moving regression” method is proposed. New approach is a hybrid method; it combines features of the “moving average” method, linear regression method and differential system representation. This combination allows to simultaneously determining complex dynamic system parameters, in spite of its chaotic behavior and measurement errors. New method possibilities are explored via identification process numerical simulation for the Lorenz chaotic system.

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.

Local and global bifurcations in magnetic resonance force microscopy

The focus of this paper is on the investigation of local and global bifurcations in a continuum mechanics-based resonator model proposed for measurement of electron spin via magnetic resonance force microscopy (MRFM). The resonator model, derived using the extended Hamilton’s principle incorporating the Bloch equations for magnetization, is investigated analytically and numerically. Analysis of both adiabatic and non-adiabatic equilibrium configurations enables formulation of the dynamical system bifurcation structure and identification of the parameter space required for stable MRFM operation. A multiple-scales analysis of the limiting adiabatic model enables estimation of the local bifurcation thresholds for bistable solutions and prediction of the frequency shift that enables spin detection. Orbital instabilities of the adiabatic model reveal a global bifurcation structure where lengthy chaotic transients occur below a homoclinic jump-to-contact threshold which is determined via a Melnikov–Holmes analysis. Both local and global bifurcations are verified numerically in the non-adiabatic model and reveal a dense power spectra for the magnetic moments. The computation of the parameter space governing the model orbital instabilities enables a consistent estimation of robust MRFM operation conditions.

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.

Solvent-based post-combustion CO2 capture for power plants: A critical review and perspective on dynamic modelling, system identification, process control and flexible operation

Solvent-based post-combustion CO2 capture (PCC) appears to be the most effective choice to overcome the CO2 emission issue of fossil fuel fired power plants. To make the PCC better suited for power plants, growing interest has been directed to the flexible operation of PCC in the past ten years. The flexible operation requires the PCC system to adapt to the strong flue gas flow rate change and to adjust the carbon capture level rapidly in wide operating range. In-depth study of the dynamic characteristics of the PCC process and developing a suitable control approach are the keys to meet this challenge. This paper provides a critical review for the dynamic research of the solvent–based PCC process including first-principle modelling, data-driven system/process identification and the control design studies, with their main features being listed and discussed. The existent studies have been classified according to the approaches used and their advantages and limitations have been summarized. Potential future research opportunities for the flexible operation of solvent-based PCC are also given in this review.

Multivariable State-Space Recursive Identification Algorithm Based on Evolving Type-2 Neural-Fuzzy Inference System

In this paper, a novel approach for state-space evolving type-2 neural-fuzzy identification of multivariable dynamic systems is proposed. According to adopted methodology, conditions for creating and merging clusters are used to perform the structural adaptation of the neural-fuzzy model. The center and shape of each cluster are estimated, defining all rules in the interval type-2 neural-fuzzy inference system. The degree of uncertainty on the shape of type-2 membership functions is computed through an extended Kalman filter-based learning mechanism. Once the type-2 membership functions (upper and lower membership values) are estimated, the fuzzy Markov parameters are computed from experimental data, and for each incoming information, the parameters of state-space linear models in the consequent proposition of inference system are recursively estimated. The efficiency and applicability of the proposed methodology are demonstrated through experimental results of modeling of an industrial dryer.

Fuzzy Model Identification and Self Learning with Smooth Compositions

This paper develops a smooth model identification and self-learning strategy for dynamic systems taking into account possible parameter variations and uncertainties. We have tried to solve the problem such that the model follows the changes and variations in the system on a continuous and smooth surface. Running the model to adaptively gain the optimum values of the parameters on a smooth surface would facilitate further improvements in the application of other derivative based optimization control algorithms such as MPC or robust control algorithms to achieve a combined modeling-control scheme. Compared to the earlier works on the smooth fuzzy modeling structures, we could reach a desired trade-off between the model optimality and the computational load. The proposed method has been evaluated on a test problem as well as the non-linear dynamic of a chemical process.

Kinematics model identification and motion control of robot based on fast learning neural network

As a static network, the slow learning of back propagation (BP) neural network is an insurmountable disadvantage facing dynamic system identification. In contrast, dynamic neural network provides a potential choice, representing the development direction of neural network modeling, identification and control. Based on dynamic Elman network, a new learning neural network structure, called fast learning neural network, is proposed in this paper. It not only conforms to the basic characteristics of biological neural network, but also has the advantages of simple algorithm, fast learning convergence and high identification accuracy of linear and non-linear systems. Based on the experimental data, this network is applied to the identification of the motion model of modular robots to obtain the non-linear kinematics model of robots. Therefore, this kind of neural network is very suitable for robot kinematics model identification and motion control. The simulation results show that it is appropriate to identify the kinematics model and control the motion of the robot based on fast learning neural network; and the combination of fast learning and ELM network speeds up the training efficiency.

State space black-box modelling via Markov parameters based on evolving type-2 neural-fuzzy inference system for nonlinear multivariable dynamic systems

In this paper, an approach for state-space interval type-2 neural-fuzzy identification of multivariable dynamic systems, in an evolving and incremental learning context, is proposed. In combination with type-2 fuzzy systems, the adopted methodology regards the following aspects: recursive learning of the footprint of uncertainty, and recursive learning of the rule consequents part by a recursive linear state-space approaches where Markov parameters are incrementally and robustly learnt in sample-wise manner. The efficiency and applicability of the proposed methodology are demonstrated through experimental and computational results and compared with prominent learning algorithms of the literature.