Competitive Modes for the Detection of Chaotic Parameter Regimes in the General Chaotic Bilinear System of Lorenz Type

2015 ◽  
Vol 25 (04) ◽  
pp. 1530012 ◽  
Author(s):  
Kristina Mallory ◽  
Robert A. Van Gorder
Keyword(s):  
Coupled Oscillators ◽  
Chaotic Behavior ◽  
Bilinear System ◽  
Model Parameters ◽  
State Variables ◽  
Third Order ◽  
Lorenz Equation ◽  
Competitive Modes ◽  
Chaotic Parameter ◽  
Special Case

We study chaotic behavior of solutions to the bilinear system of Lorenz type developed by Celikovsky and Vanecek [1994] through an application of competitive modes. This bilinear system of Lorenz type is one possible canonical form holding the Lorenz equation as a special case. Using a competitive modes analysis, which is a completely analytical method allowing one to identify parameter regimes for which chaos may occur, we are able to demonstrate a number of parameter regimes which admit a variety of distinct chaotic behaviors. Indeed, we are able to draw some interesting conclusions which relate the behavior of the mode frequencies arising from writing the state variables for the Celikovsky–Vanecek model as coupled oscillators, and the types of emergent chaotic behaviors observed. The competitive modes analysis is particularly useful if all but one of the model parameters are fixed, and the remaining free parameter is used to modify the chaos observed, in a manner analogous to a bifurcation parameter. Through a thorough application of the method, we are able to identify several parameter regimes which give new dynamics (such as specific forms of chaos) which were not observed or studied previously in the Celikovsky–Vanecek model. Therefore, the results demonstrate the advantage of the competitive modes approach for detecting new parameter regimes leading to chaos in third-order dynamical systems.

scholarly journals State and Parameter Estimation of a Mathematical Carcinoma Model under Chemotherapeutic Treatment

2020 ◽  
Vol 10 (24) ◽  
pp. 9046
Author(s):  
Máté Siket ◽  
György Eigner ◽  
Dániel András Drexler ◽  
Imre Rudas ◽  
Levente Kovács
Keyword(s):  
Parameter Estimation ◽  
Tumor Growth ◽  
Nonlinear Problems ◽  
Model Parameters ◽  
State Variables ◽  
State Estimator ◽  
Third Order ◽  
Tumor Growth Model ◽  
Chemotherapeutic Treatment ◽  
Tumor Growth Modeling

One challenging aspect of therapy optimization and application of control algorithms in the field of tumor growth modeling is the limited number of measurable physiological signals—state variables—and the knowledge of model parameters. A possible solution to provide such information is the application of observer or state estimator. One of the most widely applied estimators for nonlinear problems is the extended Kalman filter (EKF). In this study, a moving horizon estimation (MHE)-based observer is developed and compared to an optimized EKF. The observers utilize a third-order tumor growth model. The performance of the observers is tested on measurements gathered from a laboratory mice trial using chemotherapeutic drug. The proposed MHE is designed to be suitable for closed-loop applications and yields simultaneous state and parameter estimation.

Nearly Exact Bayesian Estimation of Non-linear No-Arbitrage Term-Structure Models*

2021 ◽  
Author(s):  
Marcello Pericoli ◽  
Marco Taboga
Keyword(s):  
Bayesian Estimation ◽  
Term Structure ◽  
Broad Class ◽  
Model Parameters ◽  
State Variables ◽  
Computationally Efficient ◽  
Macroeconomic Factors ◽  
No Arbitrage ◽  
Term Structure Models ◽  
Non Linear

Abstract We propose a general method for the Bayesian estimation of a very broad class of non-linear no-arbitrage term-structure models. The main innovation we introduce is a computationally efficient method, based on deep learning techniques, for approximating no-arbitrage model-implied bond yields to any desired degree of accuracy. Once the pricing function is approximated, the posterior distribution of model parameters and unobservable state variables can be estimated by standard Markov Chain Monte Carlo methods. As an illustrative example, we apply the proposed techniques to the estimation of a shadow-rate model with a time-varying lower bound and unspanned macroeconomic factors.

scholarly journals Determination of synchronous generator nonlinear model parameters based on power rejection tests using a gradient optimization algorithm

2017 ◽  
Vol 65 (4) ◽  
pp. 479-488 ◽  
Author(s):  
A. Boboń ◽  
A. Nocoń ◽  
S. Paszek ◽  
P. Pruski
Keyword(s):  
Parameter Estimation ◽  
Objective Function ◽  
Optimization Algorithm ◽  
Least Squares Method ◽  
Synchronous Generator ◽  
Operating Conditions ◽  
Model Parameters ◽  
State Variables ◽  
Starting Point ◽  
Gradient Optimization

AbstractThe paper presents a method for determining electromagnetic parameters of different synchronous generator models based on dynamic waveforms measured at power rejection. Such a test can be performed safely under normal operating conditions of a generator working in a power plant. A generator model was investigated, expressed by reactances and time constants of steady, transient, and subtransient state in the d and q axes, as well as the circuit models (type (3,3) and (2,2)) expressed by resistances and inductances of stator, excitation, and equivalent rotor damping circuits windings. All these models approximately take into account the influence of magnetic core saturation. The least squares method was used for parameter estimation. There was minimized the objective function defined as the mean square error between the measured waveforms and the waveforms calculated based on the mathematical models. A method of determining the initial values of those state variables which also depend on the searched parameters is presented. To minimize the objective function, a gradient optimization algorithm finding local minima for a selected starting point was used. To get closer to the global minimum, calculations were repeated many times, taking into account the inequality constraints for the searched parameters. The paper presents the parameter estimation results and a comparison of the waveforms measured and calculated based on the final parameters for 200 MW and 50 MW turbogenerators.

Model of the influence of Internet finance on monetary policy based on gibbs sampling and vector autoregression

2020 ◽  
pp. 1-11
Author(s):  
Hui Wang ◽  
Huang Shiwang
Keyword(s):  
Monetary Policy ◽  
Gibbs Sampling ◽  
Posterior Distribution ◽  
Estimation Method ◽  
Financial Supervision ◽  
Var Model ◽  
Model Parameters ◽  
State Variables ◽  
Frequency Data ◽  
Internet Finance

The various parts of the traditional financial supervision and management system can no longer meet the current needs, and further improvement is urgently needed. In this paper, the low-frequency data is regarded as the missing of the high-frequency data, and the mixed frequency VAR model is adopted. In order to overcome the problems caused by too many parameters of the VAR model, this paper adopts the Bayesian estimation method based on the Minnesota prior to obtain the posterior distribution of each parameter of the VAR model. Moreover, this paper uses methods based on Kalman filtering and Kalman smoothing to obtain the posterior distribution of latent state variables. Then, according to the posterior distribution of the VAR model parameters and the posterior distribution of the latent state variables, this paper uses the Gibbs sampling method to obtain the mixed Bayes vector autoregressive model and the estimation of the state variables. Finally, this article studies the influence of Internet finance on monetary policy with examples. The research results show that the method proposed in this article has a certain effect.

Output Adaptive Observers Design for Linear Non-Stationary Systems with Polynomial Parameters

2021 ◽  
Vol 22 (8) ◽  
pp. 404-410
Author(s):  
K. B. Dang ◽  
A. A. Pyrkin ◽  
A. A. Bobtsov ◽  
A. A. Vedyakov ◽  
S. I. Nizovtsev
Keyword(s):  
Linear Time ◽  
State Observer ◽  
Observer Design ◽  
Model Parameters ◽  
Time Varying ◽  
State Variables ◽  
Unknown Constant ◽  
Established Method ◽  
Time Varying Parameters ◽  
True Values

The article deals with the problem of state observer design for a linear time-varying plant. To solve this problem, a number of realistic assumptions are considered, assuming that the model parameters are polynomial functions of time with unknown coefficients. The problem of observer design is solved in the class of identification approaches, which provide transformation of the original mathematical model of the plant to a static linear regression equation, in which, instead of unknown constant parameters, there are state variables of generators that model non-stationary parameters. To recover the unknown functions of the regression model, we use the recently well-established method of dynamic regressor extension and mixing (DREM), which allows to obtain monotone estimates, as well as to accelerate the convergence of estimates to the true values. Despite the fact that the article deals with the problem of state observer design, it is worth noting the possibility of using the proposed approach to solve an independent and actual estimation problem of unknown time-varying parameters.

scholarly journals Robust Position Control of PMSM Using Fractional-Order Sliding Mode Controller

2012 ◽  
Vol 2012 ◽  
pp. 1-33 ◽  
Author(s):  
Jiacai Huang ◽  
Hongsheng Li ◽  
YangQuan Chen ◽  
Qinghong Xu
Keyword(s):  
Fractional Order ◽  
Position Control ◽  
Sliding Mode ◽  
Permanent Magnet Synchronous Motor ◽  
The State ◽  
Sliding Mode Controller ◽  
Sliding Surface ◽  
State Variables ◽  
Nonlinear Load ◽  
Special Case

A new robust fractional-order sliding mode controller (FOSMC) is proposed for the position control of a permanent magnet synchronous motor (PMSM). The sliding mode controller (SMC), which is insensitive to uncertainties and load disturbances, is studied widely in the application of PMSM drive. In the existing SMC method, the sliding surface is usually designed based on the integer-order integration or differentiation of the state variables, while in this proposed robust FOSMC algorithm, the sliding surface is designed based on the fractional-order calculus of the state variables. In fact, the conventional SMC method can be seen as a special case of the proposed FOSMC method. The performance and robustness of the proposed method are analyzed and tested for nonlinear load torque disturbances, and simulation results show that the proposed algorithm is more robust and effective than the conventional SMC method.

Arterial pressure contour analysis for estimating human vascular properties

1976 ◽  
Vol 40 (2) ◽  
pp. 171-176 ◽  
Author(s):  
T. B. Watt ◽  
C. S. Burrus
Keyword(s):  
Cardiac Cycle ◽  
Vascular System ◽  
Model Parameters ◽  
Pressure Curve ◽  
Contour Analysis ◽  
Order Model ◽  
Third Order ◽  
Arterial Blood ◽  
Pressure Contour ◽  
Multiple Measurements

The form of an arterial blood pressure curve during the diastolic portion of the cardiac cycle was here employed to identify parameters in a third-order model of the vascular system. Calculated elastic and intertial characteristics of this fitted model then became clinically accessible indices of corresponding real vascular properties. This technique incurred no risk and little discomfort for the patient. Tested in theory, in animal experimentation, and in human observations, our procedure utilized a Gauss-Newton algorithm via digital computer to provide rapid model solutions from different starting values, from multiple measurements sites, and from normal or diseased patients. Model parameters thus determined defined ranges of normal variation and suggested a less compliant arterial bed in hypertensive than in normotensive patients.

scholarly journals Robust estimation of hydrological model parameters

2008 ◽  
Vol 5 (3) ◽  
pp. 1641-1675 ◽  
Author(s):  
A. Bárdossy ◽  
S. K. Singh
Keyword(s):  
Measurement Errors ◽  
Input Data ◽  
Hydrological Model ◽  
Optimal Parameter ◽  
Model Performance ◽  
Model Parameters ◽  
Geometrical Approach ◽  
State Variables ◽  
Parameter Vector ◽  
Robust Parameter

Abstract. The estimation of hydrological model parameters is a challenging task. With increasing capacity of computational power several complex optimization algorithms have emerged, but none of the algorithms gives an unique and very best parameter vector. The parameters of hydrological models depend upon the input data. The quality of input data cannot be assured as there may be measurement errors for both input and state variables. In this study a methodology has been developed to find a set of robust parameter vectors for a hydrological model. To see the effect of observational error on parameters, stochastically generated synthetic measurement errors were applied to observed discharge and temperature data. With this modified data, the model was calibrated and the effect of measurement errors on parameters was analysed. It was found that the measurement errors have a significant effect on the best performing parameter vector. The erroneous data led to very different optimal parameter vectors. To overcome this problem and to find a set of robust parameter vectors, a geometrical approach based on the half space depth was used. The depth of the set of N randomly generated parameters was calculated with respect to the set with the best model performance (Nash-Sutclife efficiency was used for this study) for each parameter vector. Based on the depth of parameter vectors, one can find a set of robust parameter vectors. The results show that the parameters chosen according to the above criteria have low sensitivity and perform well when transfered to a different time period. The method is demonstrated on the upper Neckar catchment in Germany. The conceptual HBV model was used for this study.

scholarly journals BAYESIAN APPROACH TO THE D-OPTIMAL FOR MIXTURE EXPERIMENTAL DESIGN

2019 ◽  
Vol 3 (2) ◽  
pp. 109
Author(s):  
Uqwatul Alma Wizsa
Keyword(s):  
Optimal Design ◽  
Quadratic Model ◽  
Model Parameters ◽  
Potential Term ◽  
Lattice Design ◽  
Simplex Lattice Design ◽  
Simplex Lattice ◽  
Mixture Experimental Design ◽  
Special Case ◽  
Experimental Region

A mixture experiment is a special case of response surface methodology in which the value of the components are proportions. In case there are constraints on the proportions, the experimental region can be not a simplex. The classical designs such as a simplex-lattice design or a simplex-centroid design, in some cases, cannot fit to the problem. In this case, optimal design come up as a solution. A D-optimal design is seeking a design in which minimizing the covariance of the model parameter.  Some model parameters are important and some of them are less important. As the priority of the parameters, the prior information of parameters is needed in advance. This brings to a Bayesian D-optimal design. This research was focus on a baking experiment in which consisted of three ingredients with lower bounds on the proportion of the ingredients. The assumption model was a quadratic model. Due to the priority of the model parameters, the Bayesian D-optimal design was used to solve the problem. A point-exchange algorithm was developed to find the optimal design. Nineteen candidates is used to choose twelve design points. It found that the potential term is feasible to the actual model and design points represent overall points in the design area.

Exact third-order structure functions for two-dimensional turbulence

2018 ◽  
Vol 851 ◽  
pp. 672-686 ◽  
Author(s):  
Jin-Han Xie ◽  
Oliver Bühler
Keyword(s):  
Structure Functions ◽  
Spectral Energy ◽  
Order Structure ◽  
Two Dimensional ◽  
Third Order ◽  
Transfer Rates ◽  
The Third ◽  
Random Forcing ◽  
Asymptotic Expressions ◽  
Special Case

We derive and investigate exact expressions for third-order structure functions in stationary isotropic two-dimensional turbulence, assuming a statistical balance between random forcing and dissipation both at small and large scales. Our results extend previously derived asymptotic expressions in the enstrophy and energy inertial ranges by providing uniformly valid expressions that apply across the entire non-dissipative range, which, importantly, includes the forcing scales. In the special case of white noise in time forcing this leads to explicit predictions for the third-order structure functions, which are successfully tested against previously published high-resolution numerical simulations. We also consider spectral energy transfer rates and suggest and test a simple robust diagnostic formula that is useful when forcing is applied at more than one scale.

Sign in / Sign up

Export Citation Format

Share Document