scholarly journals Validation of Simulation Models without Knowledge of Parameters Using Differential Algebra

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Björn Haffke ◽  
Riccardo Möller ◽  
Tobias Melz ◽  
Jens Strackeljan
Keyword(s):  
System Identification ◽  
Numerical Methods ◽  
Nonlinear Systems ◽  
Differential Algebra ◽  
External Validation ◽  
Simulation Models ◽  
Input And Output ◽  
Iterative Numerical Methods

This study deals with the external validation of simulation models using methods from differential algebra. Without any system identification or iterative numerical methods, this approach provides evidence that the equations of a model can represent measured and simulated sets of data. This is very useful to check if a model is, in general, suitable. In addition, the application of this approach to verification of the similarity between the identifiable parameters of two models with different sets of input and output measurements is demonstrated. We present a discussion on how the method can be used to find parameter deviations between any two models. The advantage of this method is its applicability to nonlinear systems as well as its algorithmic nature, which makes it easy to automate.

scholarly journals Data derived NARMAX Dst model

2011 ◽  
Vol 29 (6) ◽  
pp. 965-971 ◽  
Author(s):  
R. J. Boynton ◽  
M. A. Balikhin ◽  
S. A. Billings ◽  
A. S. Sharma ◽  
O. A. Amariutei
Keyword(s):  
Mathematical Model ◽  
Solar Wind ◽  
System Identification ◽  
Nonlinear Systems ◽  
Wide Class ◽  
Geomagnetic Storms ◽  
Output Data ◽  
Dst Index ◽  
Geomagnetic Indices ◽  
Input And Output

Abstract. The NARMAX OLS-ERR methodology is applied to identify a mathematical model for the dynamics of the Dst index. The NARMAX OLS-ERR algorithm, which is widely used in the field of system identification, is able to identify a mathematical model for a wide class of nonlinear systems using input and output data. Solar wind-magnetosphere coupling functions, derived from analytical or data based methods, are employed as the inputs to such models and the outputs are geomagnetic indices. The newly deduced coupling function, p1/2V4/3BTsin6(θ/2), has been implemented as an input to model the Dst dynamics. It was shown that the identified model has a very good forecasting ability, especially with the geomagnetic storms.

scholarly journals Application of hybrid asymptotic methods and modern software for mathematical models developing for nonlinear dynamics of structures with variables in time parameters

2021 ◽  
pp. 66-70
Author(s):  
S. Homeniuk ◽  
S. Grebenyuk ◽  
D. Gristchak
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Methods ◽  
Nonlinear Systems ◽  
Analytical Solution ◽  
Mathematical Models ◽  
Nonlinear Dynamic ◽  
Numerical Solutions ◽  
Hybrid Approach ◽  
Time Dependent ◽  
Forced Oscillations

The relevance. The aerospace domain requires studies of mathematical models of nonlinear dynamic structures with time-varying parameters. The aim of the work. To obtain an approximate analytical solution of nonlinear forced oscillations of the designed models with time-dependent parameters. The research methods. A hybrid approach based on perturbation methods, phase integrals, Galorkin orthogonalization criterion is used to obtain solutions. Results. Nonlocal investigation of nonlinear systems behavior is done using results of analytical and numerical methods and developed software. Despite the existence of sufficiently powerful numerical software systems, qualitative analysis of nonlinear systems with variable parameters requires improved mathematical models based on effective analytical, including approximate, solutions, which using numerical methods allow to provide a reliable analysis of the studied structures at the stage designing. An approximate solution in analytical form is obtained with constant coefficients that depend on the initial conditions. Conclusions. The approximate analytical results and direct numerical solutions of the basic equation were compared which showed a sufficient correlation of the obtained analytical solution. The proposed algorithm and program for visualization of a nonlinear dynamic process could be implemented in nonlinear dynamics problems of systems with time-dependent parameters.

Bayesian robot system identification with input and output noise

2011 ◽  
Vol 24 (1) ◽  
pp. 99-108 ◽  
Author(s):  
Jo-Anne Ting ◽  
Aaron D’Souza ◽  
Stefan Schaal
Keyword(s):  
System Identification ◽  
Robot System ◽  
Input And Output ◽  
Output Noise

Dynamic System Identification Using a Step Input

2005 ◽  
Vol 24 (2) ◽  
pp. 125-134
Author(s):  
Manabu Kosaka ◽  
Hiroshi Uda ◽  
Eiichi Bamba ◽  
Hiroshi Shibata
Keyword(s):  
Steady State ◽  
System Identification ◽  
Transfer Function ◽  
Step Response ◽  
Output Data ◽  
Mass System ◽  
Input And Output ◽  
Rational Transfer ◽  
Line Identification ◽  
The Moment

In this paper, we propose a deterministic off-line identification method performed by using input and output data with a constant steady state output response such as a step response that causes noise or vibration from a mechanical system at the moment when it is applied but they are attenuated asymptotically. The method can directly acquire any order of reduced model without knowing the real order of a plant, in such a way that the intermediate parameters are uniquely determined so as to be orthogonal with respect to 0 ∼ N-tuple integral values of output error and irrelevant to the unmodelled dynamics. From the intermediate parameters, the coefficients of a rational transfer function are calculated. In consequence, the method can be executed for any plant without knowing or estimating its order at the beginning. The effectiveness of the method is illustrated by numerical simulations and also by applying it to a 2-mass system.

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