Parameter Identification Of Dynamic Systems Research Articles

Parameter identification of dynamical systems based on short-term prediction by the generalized cell mapping method with deep learning

Parameter identification of dynamical systems based on short-term prediction by the generalized cell mapping method with deep learning

Combined Excitation and System Parameter Identification of Dynamic Systems by an Inverse Meta-Model

In the inverse problem, it is common that either the corresponding component parameters or the corresponding input signals are obtained for a given output or response. Most model-based solutions to the inverse problem involve optimization using the so-called forward model. The forward model typically comprises the mechanistic model in some form. Most commonly, inverse problems are formulated in a static setting where a wealth of theoretical results and numerical methods are available. However, there are many important dynamic applications wherein time-dependent information needs to be discerned from time-dependent data. Recently, data-based approaches, or model-free methods, have been invoked whereby feature extraction methods such as Support vector machines (SVM) and artificial neural networks (ANN) are used. Herein we develop an inverse solution for dynamic systems through easy-to-understand least-squares meta-model mathematics. The input and output training data are interchanged, so that a mixed input comprising both component parameters and discrete-time excitations can be found for a given discrete-time output. Single-value decomposition (SVD) makes any matrix inversion tractable. The inverse meta-model is compared to the optimization method and ANN using mechanistic models for fidelity, and is shown to have better accuracy and much increased speed.

A Weight-Generating Approach of a Deep Neural Network for the Parameter Identification of Dynamic Systems

The general learning process of deep learning is extremely time-consuming. Unlike the traditional learning process, a weight-generating approach to quickly generate the weight vectors of a deep neural network model is proposed, which can be used for parameter identification of a dynamic system. Based on the analysis of three trained deep neural network models, which are used to identify the parameters of three different dynamic systems, the statistical relationships between the weight vectors of each hidden layer and its inputs are revealed. Then, the statistical patterns of the weight vectors are imitated by exploiting the statistical patterns of the inputs and these relationships. Then, a weight-generating approach is designed to quickly generate the weight vectors of a deep neural network model. The effectiveness of the weight-generating approach is tested on the tasks of parameter identification for the three dynamic systems. The numerical results are provided to demonstrate the validity and high efficiency of the proposed weight-generating approach.

Coupled extreme learning machine and particle swarm optimization variant for projectile aerodynamic identification

Accurate aerodynamic parameters are the basis for the research of uncontrolled projectile drop point dispersion and precise strike. The traditional methods for aerodynamic parameters rely strongly on the projectile dynamics system. To weaken the influence of kinetic effects, an extreme learning machine (ELM) optimized by particle swarm optimization (PSO) is applied. However, the iterative optimization process of PSO makes the algorithm more complicated and impairs the real-time performance of ELM. To accelerate the convergence of PSO, a new hybrid optimization strategy is proposed. The hybrid optimization strategy combines the advantages of the chaos optimization strategy, the adaptive update strategy, and the mutation strategy. The chaos optimization strategy optimizes the distribution of the initial swarm to improve the optimization efficiency of PSO. The adaptive update strategy tunes the velocity inertia weight based on the value of the evolutionary factor to match the current searching state of the particles. The mutation strategy mutates the particles to break out of the local convergence. Numerical experiments show that the introduction of the hybrid optimization strategy enables ELM to exhibit excellent robustness, real-time performance, and accuracy in noisy environments. The hybrid algorithm has excellent prospects for application and extension for the parameter identification of dynamic systems in complex environments.

Control and Identification Toolbox (CIT): An Android application for teaching automatic control and system identification

AbstractThis article presents a free Android application, named as Control and Identification Toolbox (CIT), for teaching and learning the system response, automatic control, and the parameter identification of dynamic systems. The CIT app performs real‐time experiments and permits tuning a traditional proportional‐integral‐derivative controller, whose performance under constant or noise disturbances, introduced by the app, can be analyzed. Moreover, this app allows estimating the parameters of first‐ and second‐order linear systems by means of the recursive least squares method. The parameter estimates as well as the control system signals produced under common test input signals are displayed by the app. It runs in any Android device supporting a universal serial bus, which is connected with Arduino Uno or Mega boards that carry out data acquisition. Experimental results obtained using first‐ and second‐order low‐pass filters confirm the effectiveness of the proposed application. Moreover, undergraduate students evaluated the CIT app, and their responses are also presented.

Variational Integrators for Parameter Identification of Mechanical Systems

AbstractNumerical methods for parameter identification of dynamical systems are based on matching model outputs to measurements. Computing the model output requires numerical integration techniques, though. In this contribution, we study the role of integration methods for mechanical systems. Since mechanical systems have characteristic properties, using structure‐preserving integration methods suggests itself. First and second order methods are compared in the case study of a damped pendulum.

Simultaneous hybrid modeling of a nosiheptide fermentation process using particle swarm optimization

Hybrid modeling approaches have recently been investigated as an attractive alternative to model fermentation processes. Normally, these approaches require estimation data to train the empirical model part of a hybrid model. This may result in decreasing the generalization ability of the derived hybrid model. Therefore, a simultaneous hybrid modeling approach is presented in this paper. It transforms the training of the empirical model part into a dynamic system parameter identification problem, and thus allows training the empirical model part with only measured data. An adaptive escaping particle swarm optimization (AEPSO) algorithm with escaping and adaptive inertia weight adjustment strategies is constructed to solve the resulting parameter identification problem, and thereby accomplish the training of the empirical model part. The uniform design method is used to determine the empirical model structure. The proposed simultaneous hybrid modeling approach has been used in a lab-scale nosiheptide batch fermentation process. The results show that it is effective and leads to a more consistent model with better generalization ability when compared to existing ones. The performance of AEPSO is also demonstrated.

A new data-driven modeling method for fermentation processes

An accurate model is the premise for successfully implementing fermentation process optimization. Most data-driven models that are widely applied to fermentation processes are unfit for optimization or provide low precision. This paper presents a new data-driven modeling method for directly developing an ANN-based differential model that is fit for optimization. Moreover, this model can provide high precision because it can be discretized using the sampling period of the control variables as the step length. The lack of data pairs is addressed by transforming the model-training problem into a dynamic system parameter identification problem. Further, a particle swarm optimization algorithm with a time-varying escape mechanism (PSOE) is constructed to determine the model parameters. Finally, the uniform design method is used to select the model structure. The results of experiments conducted using practical data for a lab-scale nosiheptide batch fermentation process confirm the effectiveness of the proposed modeling method and PSOE algorithm.

Bayesian parameter identification in dynamic state space models using modified measurement equations

When Markov chain Monte Carlo (MCMC) samplers are used in problems of system parameter identification, one would face computational difficulties in dealing with large amount of measurement data and (or) low levels of measurement noise. Such exigencies are likely to occur in problems of parameter identification in dynamical systems when amount of vibratory measurement data and number of parameters to be identified could be large. In such cases, the posterior probability density function of the system parameters tends to have regions of narrow supports and a finite length MCMC chain is unlikely to cover pertinent regions. The present study proposes strategies based on modification of measurement equations and subsequent corrections, to alleviate this difficulty. This involves artificial enhancement of measurement noise, assimilation of transformed packets of measurements, and a global iteration strategy to improve the choice of prior models. Illustrative examples cover laboratory studies on a time variant dynamical system and a bending–torsion coupled, geometrically non-linear building frame under earthquake support motions.

A time-varying forgetting factor stochastic gradient combined with Kalman filter algorithm for parameter identification of dynamic systems

Parameter estimation problem of a class of observer canonical state-space system is considered in this paper. By means of the property of the shift operator, the space-state model is transformed into the input–output representations. Then, a time-varying forgetting factor stochastic gradient combined with Kalman filter algorithm is proposed. The proposed algorithm is based on interactively estimating unknown parameters to achieve all the parameters identification of the system. A numerical example is provided to verify the effectiveness of the proposed algorithm.

The consideration to the dynamic systems parameter identification

In this paper, a concept for continuous-time dynamic systems parameter identification using modulating function approach is presented. It refers to linear as well as selected non-linear systems. It shows the possibility of direct application without converting differential equation. In particular cases direct application can decrease the amount of computation in non-linear system identification, which generally requires Fourier and Hartley transforms and convolutions. Furthermore, it is shown that parameter identification of dynamic systems might be ambiguous due to the signals used in system identification. This ambiguity should be considered before determining the final mathematical model. During the computation we also focused on the online identification which enables to verify the results obtained consequently from updated data and abort the identification in appropriate moment.

Parameter identification of dynamical systems with regulaization.

Parameter identification of dynamical systems with regulaization.

Global Piecewise Fitting Method for Modal Parameter Identification by Orthogonal Polynomials Based on Dynamic Systems

Global estimation of modal parameters for dynamic Systems using fraction orthogonal polynomials possesses higher precision than the general rational fraction orthogonal polynomials algorithm. The object of this paper is to introduce a new technique to derive the global piecewise fitting method for modal parameter identification of dynamic Systems. Based on the global fraction orthogonal polynomials algorithm, a global piecewise fitting method for eliminating affections of modes outside of fitting bands is proposed. Both lower and higher modes outside of the fitting band are analyzed and processed. The frequency response data are revised by means of modes in two frequency bands close to the fitting band, and a curve fitting model is derived. The proposed method is compared with that of the traditional estimation without regard to the affections of modes outside of the fitting band. For this comparative study, simulated data are used. Simulation research indicates that the processed approach is effective.

Response to “Comment on ‘Adaptive Q-S (lag, anticipated, and complete) time-varying synchronization and parameters identification of uncertain delayed neural networks”’ [Chaos 17, 038101 (2007)

Parameter identification of dynamical systems from time series has received increasing interest due to its wide applications in secure communication, pattern recognition, neural networks, and so on. Given the driving system, parameters can be estimated from the time series by using an adaptive control algorithm. Recently, it has been reported that for some stable systems, in which parameters are difficult to be identified [Li et al., Phys Lett. A 333, 269–270 (2004); Remark 5 in Yu and Cao, Physica A 375, 467–482 (2007); and Li et al., Chaos 17, 038101 (2007)], and in this paper, a brief discussion about whether parameters can be identified from time series is investigated. From some detailed analyses, the problem of why parameters of stable systems can be hardly estimated is discussed. Some interesting examples are drawn to verify the proposed analysis.

Parameter identification of dynamical systems from time series

In this paper, synchronization based parameter identification of dynamical systems from time series is carefully revisited. It is shown, based on rigorous theoretical analysis and concrete counterexamples, that some recent research reports on this issue are incomplete or even incorrect. A linear independence condition is pointed out, which is sufficient for such parameter identification of general dynamical systems.

Neural network algorithm for parameter identification of dynamical systems involving time delays

This paper deals with the problem of identification of unknown parameters and time-delay of dynamical systems. A polynomial function is employed to modify the structure of the system and subsequently suitable algorithms for identifying the parameters of time-lag systems are developed using neural networks. Illustrative examples for identification of time-lag systems and quasi-linear systems with lag have been presented.

An optimal information method for mobile manipulator dynamic parameter identification

High-performance robot-control algorithms often rely on system-dynamic models. For field robots, the dynamic parameters of these models may not be well known. The paper presents a mutual-information-based observability metric for the online dynamic parameter identification of a multibody system. The metric is used in an algorithm to optimally select the external excitation required by the dynamic system parameter identification process. The excitation is controlled so that the identification favors parameters that have the greatest uncertainty at any given time. This algorithm is applied to identify the vehicle and suspension parameters of a mobile-field manipulator, and is found to be computationally more efficient and robust to noise than conventional methods. Issues addressed include the development of appropriate vehicle models, compatible with the onboard sensors. Simulations and experimental results show the effectiveness of this algorithm.

Dynamic System Parameter Identification by Stochastic Realization Methods

Methods for modal parameter identification of random vibrating systems from multi-output data only are presented. These methods use a multivariate state-space model and exploit shift properties of a block Hankel matrix, formed from the covariance matrices of output data and shift properties of the observability matrix. Ordinary least squares, total least squares, and partial least squares algorithms are used to determine the transition matrix of the model, which contains all modal information of the vibrating system. A new iterative procedure is also developed to determine this transition matrix. These methods are compared using numerical examples based on simulations and experimental results.

Sensitivity analysis of ODEs and DAEs — theory and implementation guide

The solution y(t,t 0,y 0) of an initial-value problem (IVP)ẏ(t)=f(t,y,p) with initial value y(t 0)=y 0 at a point t is a differentiable function of the initial value y 0 and the parameter vector p, provided f y and f p are continuous. The computation of y(t,t 0,y 0) and the sensitivity matrix play an important role in the efficient numerical solution of boundary-value problems, optimal-control problems and for parameter identification in dynamical systems. There is a wide variety of algorithms for the solution of IVPs but till now, there are just a few efficient implementations for the computation of , which is the even more important part. Here a number of implementations are introduced, treating non-stiff, stiff and differential algebraic equations. The basic new idea is to regard the numerical approximation of as the solution of the variational differential equation of a linearised IVP with approximation of the linear right-hand side by the difference quotient of the original non-linear f. For further implementations a general guideline is given how integration codes can be extended to the simultaneous efficient and reliable computation of the sensitivity matrix. It may help a numerical software writer who is implementing an integration method to supply the method with an additional option for sensitivity analysis, or even an experienced user of numerical integration software who makes extended use of sensitivity analysis to adapt a routine to his requirements.

Determination of rate constants for butene isomerization by a temporal inversion method

The determination of rate constants for chemical reaction systems is of considerable practical importance. This paper introduces a temporal inversion method for parameter identification of dynamical systems, and butene isomerization is used to illustrate the method. The rate constants are artificially treated as temporal functions and an explicit equation describing the time evolution of the rate constants is obtained by minimizing the error along the reaction course. With appropriate experimental data the unknown rate constants are guided from arbitrary initial values to their best values for the available experiments at the final time. The method leads to an iterative algorithm. Numerical results show that accurate estimates of all the rate constants can be obtained.