This article is concerned with Gaussian process quadratures, which are numerical integration methods based on Gaussian process regression methods, and sigma-point methods, which are used in advanced non-linear Kalman ...
详细信息
This article is concerned with Gaussian process quadratures, which are numerical integration methods based on Gaussian process regression methods, and sigma-point methods, which are used in advanced non-linear Kalman filtering and smoothing algorithms. We show that many sigma-point methods can be interpreted as Gaussian process quadrature based methods with suitably selected covariance functions. We show that this interpretation also extends to more general multivariate Gauss-Hermite integrationmethods and related spherical cubature rules. Additionally, we discuss different criteria for selecting the sigma-point locations: exactness of the integrals of multivariate polynomials up to a given order, minimum average error, and quasi-random point sets. The performance of the different methods is tested in numerical experiments.
Ve své práci se zabývám problematikou užití numerických metod a jejich implementace v objektově orientované simulační knihovně SIMLIB/C++. Navrhnul a realizoval jsem úpra...
详细信息
Ve své práci se zabývám problematikou užití numerických metod a jejich implementace v objektově orientované simulační knihovně SIMLIB/C++. Navrhnul a realizoval jsem úpravu rozhraní a podsystému numerických integračních metod knihovny SIMLIB s cílem umožnit její snadnější rozšiřitelnost o externí integrační metody. Díky tomu jsem mohl simulační knihovnu SIMLIB obohatit o sadu nových metod z knihovny GSL(GNU Scientific Library) a některé zajímavé metody v jazyce Fortran uvedené v databázi Netlib. Nové i existující metody jsem řádně otestoval a porovnal jejich vlastnosti z hlediska efektivity, stability a přesnosti.
Simulátor problému n těles předpovídá pohyb astronomických objektů pomocí numerické integrace pohybových zákonů. Gravitační interakce jsou počítány pomoc...
详细信息
Simulátor problému n těles předpovídá pohyb astronomických objektů pomocí numerické integrace pohybových zákonů. Gravitační interakce jsou počítány pomocí klasické Newtonovy mechaniky, tělesa jsou modelována jako hmotné body a neberou se v úvahu jiné síly než gravitační. Aplikace umožňuje nastavit počáteční polohy a rychlosti těles, animovat jejich pohyb, změnit numerickou metodu a bude dostupná pod licencí GPL. Může být použita při vyučování spojitých simulací na ukázání rozdílu mezi numerickými integrátory s různými časovými kroky. Dále může být použita studenty fyziky jako experimentační nástroj. Jsou dodány základní ukázky jako Sluneční soustava a problém tří těles se Zemí, Měsícem a Sluncem.
In the literature on sensorless control of induction motors, many algorithms have been presented for rotor flux and speed estimation. However, all these algorithms have been developed in the continuous-time domain. Th...
详细信息
In the literature on sensorless control of induction motors, many algorithms have been presented for rotor flux and speed estimation. However, all these algorithms have been developed in the continuous-time domain. The digital realization of the control systems, requires the implementation of those estimation methods in a discrete-time domain. The main goal of this article is comparison of the impact of different numerical integration methods, used in analogue emulation under the digital implementation of the control systems, to the operation of classical Model Reference Adaptive System;CC-based on two current models (MRAS(CC)) speed estimator and its three modified versions developed for the extension of the estimator stability region. In this paper the generalized mathematical model of MRAS(CC) estimator is proposed, which takes into account all known methods for the extension of the stability region of classical speed estimator of this type. After the short discussion of the discretization methods used for the microprocessor implementation of control algorithms the impact of different numerical integration methods on the stable operation range of the classical and modified MRAS(CC) estimators is analyzed and validated in simulation and experimental tests. It is proved that Modified Euler discretization method is much more accurate than forward and backward Euler methods and gives almost as accurate results as Tustin method, however is much less complicated in practical realization.
The optimization of the operation of power systems including steady state and dynamic constraints is efficiently solved by Transient Stability Constrained Optimal Power Flow (TSCOPF) models. TSCOPF studies extend well...
详细信息
The optimization of the operation of power systems including steady state and dynamic constraints is efficiently solved by Transient Stability Constrained Optimal Power Flow (TSCOPF) models. TSCOPF studies extend well-known optimal power flow models by introducing the electromechanical oscillations of synchronous machines. One of the main approaches in TSCOPF studies includes the discretized differential equations that represent the dynamics of the system in the optimization model. This paper analyzes the impact of different implicit and explicit numerical integration methods on the solution of a TSCOPF model and the effect of the integration time step. In particular, it studies the effect on the power dispatch, the total cost of generation, the accuracy of the calculation of electromechanical oscillations between machines, the size of the optimization problem and the computational time.
Gaussian process (GP) models are nowadays considered among the standard tools in modern control system engineering. They are routinely used for model-based control, time- series prediction, modelling and estimation in...
详细信息
Gaussian process (GP) models are nowadays considered among the standard tools in modern control system engineering. They are routinely used for model-based control, time- series prediction, modelling and estimation in engineering applications. While the underlying theory is completely in line with the principles of Bayesian inference, in practice this property is lost due to approximation steps in the GP inference. In this paper we propose a novel inference algorithm for GP models, which relies on adaptive importance sampling strategy to numerically evaluate the intractable marginalization over the hyperparameters. This is required in the case of broad-peaked or multi-modal posterior distribution of the hyperparameters where the point approximations turn out to be insufficient. The benefits of the algorithm are that is retains the Bayesian nature of the inference, has sufficient convergence properties, relatively low computational load and does not require heavy prior knowledge due to its adaptive nature. All the key advantages are demonstrated in practice using numerical examples.
暂无评论