scholarly journals Parameter Estimation of Joint Models Using Global Optimization

Author(s):  
Robert J. Kuether ◽  
David A. Najera
2009 ◽  
Vol 63 (3) ◽  
Author(s):  
Michal Čižniar ◽  
Marián Podmajerský ◽  
Tomáš Hirmajer ◽  
Miroslav Fikar ◽  
Abderrazak Latifi

AbstractThe estimation of parameters in semi-empirical models is essential in numerous areas of engineering and applied science. In many cases, these models are described by a set of ordinary-differential equations or by a set of differential-algebraic equations. Due to the presence of non-convexities of functions participating in these equations, current gradient-based optimization methods can guarantee only locally optimal solutions. This deficiency can have a marked impact on the operation of chemical processes from the economical, environmental and safety points of view and it thus motivates the development of global optimization algorithms. This paper presents a global optimization method which guarantees ɛ-convergence to the global solution. The approach consists in the transformation of the dynamic optimization problem into a nonlinear programming problem (NLP) using the method of orthogonal collocation on finite elements. Rigorous convex underestimators of the nonconvex NLP problem are employed within the spatial branch-and-bound method and solved to global optimality. The proposed method was applied to two example problems dealing with parameter estimation from time series data.


2018 ◽  
Vol 26 (1) ◽  
pp. 51-66 ◽  
Author(s):  
Valeriya V. Zheltkova ◽  
Dmitry A. Zheltkov ◽  
Zvi Grossman ◽  
Gennady A. Bocharov ◽  
Eugene E. Tyrtyshnikov

AbstractThe development of efficient computational tools for data assimilation and analysis using multi-parameter models is one of the major issues in systems immunology. The mathematical description of the immune processes across different scales calls for the development of multiscale models characterized by a high dimensionality of the state space and a large number of parameters. In this study we consider a standard parameter estimation problem for two models, formulated as ODEs systems: the model of HIV infection and BrdU-labeled cell division model. The data fitting is formulated as global optimization of variants of least squares objective function. A new computational method based on Tensor Train (TT) decomposition is applied to solve the formulated problem. The idea of proposed method is to extract the tensor structure of the optimized functional and use it for optimization. The method demonstrated a better performance in comparison with some other broadly used global optimization techniques.


2021 ◽  
Vol 54 (7) ◽  
pp. 391-396
Author(s):  
Meaghan Podlaski ◽  
Luigi Vanfretti ◽  
Tetiana Bogodorova ◽  
Tin Rabuzin ◽  
Maxime Baudette

2014 ◽  
Vol 10 (6) ◽  
pp. 1385-1392 ◽  
Author(s):  
Ziwei Dai ◽  
Luhua Lai

DSA outperformed five other algorithms in parameter estimation of 95 biological networks and showed significant advantage in large networks.


Author(s):  
Stig Moberg ◽  
Erik Wernholt ◽  
Sven Hanssen ◽  
Torgny Brogårdh

This paper considers the problem of dynamic modeling and identification of robot manipulators with respect to their elasticities. The so-called flexible joint model, modeling only the torsional gearbox elasticity, is shown to be insufficient for modeling a modern industrial manipulator accurately. Another lumped parameter model, called the extended flexible joint model, is therefore used to improve the model accuracy. In this model, nonactuated joints are added to model the elasticity of the links and bearings. The unknown elasticity parameters are estimated using a frequency-domain gray-box identification method. The conclusion is that the obtained model describes the movements of the motors and the tool mounted on the robot with significantly higher accuracy than the flexible joint model. Similar elasticity model parameters are obtained when using two different output variables for the identification, the motor position and the tool acceleration.


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