Identification Of Dynamic Systems Research Articles

Identification of Errors-in-Variables Models Using Dynamic Iterative Principal Component Analysis

Identification of linear dynamic systems from input–output data has been a subject of study for several decades. A broad class of problems in this field pertain to what is widely known as the errors-in-variables (EIV) class, where both input and output are known with errors, in contrast to the traditional scenario where only outputs are assumed to be corrupted with errors. In this work, we present a novel and systematic approach to the identification of dynamic models for the EIV case in the principal component analysis (PCA) framework. The key contribution of this work is a dynamic iterative PCA (DIPCA) algorithm that has the ability to determine the correct order of the process, handle unequal measurement noise variances (the heteroskedastic case), and provide accurate estimates of the model together with the noise covariance matrix under large sample conditions. The work is presented within the scope of single-input, single-output (SISO) deterministic systems corrupted by white-noise errors. Simulation...

Mode Identification and Fault Detection of Hybrid Dynamical Systems Using Behavior Graphs

Mode Identification and Fault Detection of Hybrid Dynamical Systems Using Behavior Graphs

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.

Maximum likelihood identification of stable linear dynamical systems

This paper concerns maximum likelihood identification of linear time invariant state space models, subject to model stability constraints. We combine Expectation Maximization (EM) and Lagrangian re ...

Algorithms and Performance Analysis for Stochastic Wiener System Identification

We analyze the statistical performance of identification of stochastic dynamical systems with non-linear measurement sensors. This includes stochastic Wiener systems, with linear dynamics, process noise and measured by a non-linear sensor with additive measurement noise. There are many possible system identification methods for such systems, including the maximum likelihood (ML) method and the prediction error method. The focus has mostly been on algorithms and implementation, and less is known about the statistical performance and the corresponding Cramer–Rao lower bound (CRLB) for identification of such non-linear systems. We derive expressions for the CRLB and the asymptotic normalized covariance matrix for certain Gaussian approximations of Wiener systems to show how a non-linear sensor affects the accuracy compared to a corresponding linear sensor. The key idea is to take second order statistics into account by using a common parametrization of the mean and the variance of the output process. This analysis also leads to an ML motivated identification method based on the conditional mean predictor and a Gaussian distribution approximation. The analysis is supported by numerical simulations.

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.

A new approach to identification of input-driven dynamical systems from probability densities

Evolution of probability densities generated by many practical dynamical systems can be more conveniently observed than individual point trajectories. This paper introduces a new method to reconstruct the unknown transformation of a 1D discrete-time dynamical system that is driven by an external control input with a given probability density function, using multiple sequences of converging probability densities generated by the perturbed underlying system. Regardless of different initial conditions the generated densities are demonstrated possessing strong convergence to a unique invariant density. Numerical simulation results validate the applicability of the developed algorithm as well as the performance in the presence of stochastic noise.

Nonparametric identification of linear dynamic errors-in-variables systems

The present work handles the nonparametric identification of linear dynamic systems within an errors-in-variables framework, where the input is arbitrary and both the input and output disturbing noises are white with unknown variances. Using the property that the frequency response function and the system leakage term can be locally approximated very well by a low-order degree polynomial, a frequency domain estimator is developed, which gives consistent estimates for the frequency response function and the input–output noise variances. The consistency and uniqueness of the estimator are theoretically analyzed under mild conditions, and uncertainty bounds are also provided. The proposed method is finally validated on a simulated linear dynamic system.

Adjoint- and Hybrid-Based Hessians for Optimization Problems in System Identification

An adjoint sensitivity-based approach to determine the gradient and Hessian of cost functions for system identification of dynamical systems is presented. The motivation is the development of a computationally efficient approach relative to the direct differentiation (DD) technique and which overcomes the challenges of the step-size selection in finite difference (FD) approaches. An optimization framework is used to determine the parameters of a dynamical system which minimizes a summation of a scalar cost function evaluated at the discrete measurement instants. The discrete time measurements result in discontinuities in the Lagrange multipliers. Two approaches labeled as the Adjoint and the Hybrid are developed for the calculation of the gradient and Hessian for gradient-based optimization algorithms. The proposed approach is illustrated on the Lorenz 63 model where part of the initial conditions and model parameters are estimated using synthetic data. Examples of identifying model parameters of light curves of type 1a supernovae and a two-tank dynamic model using publicly available data are also included.

Comparative study of neural networks for dynamic nonlinear systems identification

In this paper, a comparative study is performed to test the approximation ability of different neural network structures. It involves three neural networks multilayer feedforward neural network (MLFFNN), diagonal recurrent neural network (DRNN), and nonlinear autoregressive with exogenous inputs (NARX) neural network. Their robustness is also tested and compared when the system is subjected to parameter variations and disturbance signals. Further, dynamic back-propagation algorithm is used to update the parameters associated with these neural networks. Four dynamical systems of different complexities including motor-driven robotic link are considered on which the comparative study is performed. The simulation results show the superior performance of DRNN identification model over NARX and MLFFNN identification models.

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.

Training ANFIS structure using simulated annealing algorithm for dynamic systems identification

Abstract In this paper, a new method is presented for the training of the Adaptive Neuro-Fuzzy Inference System (ANFIS). In this work, it is ensured that the best model is created by optimising the premise and consequent parameters of ANFIS by using Simulating Annealing (SA) based on an iterative algorithm. The proposed method was applied to dynamic system identification problems. The simulation results of the proposed method are compared with the Genetic algorithm (GA), Backpropagation (BP) algorithm and different methods from the literature. At the end of this study it was found that the optimisation of ANFIS parameters is more successful by using SA than by GA, BP and the other methods.

Dynamic production system identification for smart manufacturing systems

This paper presents a methodology, called production system identification, to produce a model of a manufacturing system from logs of the system's operation. The model produced is intended to aid in making production scheduling decisions. Production system identification is similar to machine-learning methods of process mining in that they both use logs of operations. However, process mining falls short of addressing important requirements; process mining does not (1) account for infrequent exceptional events that may provide insight into system capabilities and reliability, (2) offer means to validate the model relative to an understanding of causes, and (3) updated the model as the situation on the production floor changes. The paper describes a genetic programming (GP) methodology that uses Petri nets, probabilistic neural nets, and a causal model of production system dynamics to address these shortcomings. A coloured Petri net formalism appropriate to GP is developed and used to interpret the log. Interpreted logs provide a relation between Petri net states and exceptional system states that can be learned by means of novel formulation of probabilistic neural nets (PNNs). A generalized stochastic Petri net and the PNNs are used to validate the GP-generated solutions. The methodology is evaluated with an example based on an automotive assembly system.

Nuclear Norm-Based Recursive Subspace Identification for Wind Turbine Flutter Detection

Commercial wind turbine blades are progressively becoming longer and more flexible; in order to achieve load reduction, the use of shape modifying devices is currently under research. While such modifications facilitate cost reduction, they also render the blade susceptible to the unstable aeroelastic phenomenon of flutter. To be able to detect the onset of flutter, and to modify the load control algorithm accordingly, it is desirable to perform online identification of system dynamics. In this paper, a recursive subspace identification algorithm is augmented with a nuclear norm-based cost function for the rapid identification of changes in the dominant system behavior. The time-consuming singular value thresholding step involved in the identification is replaced by a fast randomized algorithm. The method developed is used to identify the changes in the dynamics of an experimental wind turbine equipped with shape-modifying actuators, and operated under controlled conditions in a wind tunnel. The proposed identification method shows high sensitivity to changes in system dynamics, and is shown capable of stably and rapidly identifying the onset of aeroelastic flutter.

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.

Design of a Generalized Predictive Controller for Temperature Control in a Cement Rotary Kiln

In this paper a generalized predictive controller (GPC) for effective control of clinkerization temperature in a cement rotary kiln is designed. By using methods for identification of dynamic systems a mathematical model of the plant under study is obtained, whose validation results showed a high adequacy degree. The design of the GPC controller is performed based on the mathematical model obtained. It is shown that the designed controller allows controlling the plant under study with a high accuracy considering different real industrial operation scenarios. The comparative simulation results of the control system with PID and GPC controllers showed a better performance when the GPC controller is applied.

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.

Collaborative linear dynamical system identification by scarce relevant/irrelevant observations

In the current paper, linear dynamical system identification by relevant and irrelevant multi-sensor observations is presented. In common system identification methods, it is presumed that observations are related to the system. However, the present study assumes that there are multi-sensor observations, whose sensors may give relevant information related to the system while some others do not. Furthermore, whether or not the sensor data is related or unrelated is unknown. Especially in large dimensions, the scarce observations of sensors pose a problem for estimating parameters. For this scenario, the current work will show that common methods are not appropriate. Therefore, to solve the problem of scarce relevant/irrelevant observations, the collaborative identification method is presented, in which relevant sensors collaborate with each other and, as a result, the estimation of parameters is more accurate. The results of synthetic and real dataset experiments indicate that the proposed model’s performance is superior to common methods.

Improve the Accuracy of Recurrent Fuzzy System Design Using an Efficient Continuous Ant Colony Optimization

This paper proposes a new population-based evolutionary optimization algorithm, elite-mixed continuous ant colony optimization with central initialization (EMCACO-C), for improving the accuracy of Takagi–Sugeno–Kang-type recurrent fuzzy network (TRFN) designs. The EMCACO-C is a stochastic search algorithm. The EMCACO-C initializes the ant solutions on concentrative region around the center of the search range followed by a new designed elite-mixed continuous ant colony optimization to generate new solutions. The EMCACO-C mixes the few best elites to generate the directional solutions for guiding and exploring possible promising regions. Then the EMCACO-C employs the Gaussian random sampling to exploit further the directional solutions for finding better solutions. The methodology similarities and differences between the EMCACO-C and genetic algorithm are analyzed. The performances of the EMCACO-C for TRFN designs are verified in the simulations of five application examples including dynamic system control, dynamic system identification, and chaotic series prediction. The EMCACO-C performance is also compared with other swarm-based evolutionary algorithms in the simulations.