Finite Record Effects of the Errors-in-Variables Estimator for Linear Dynamic Systems

2011 ◽  
Vol 60 (2) ◽  
pp. 642-654 ◽  
Author(s):  
Kurt Barbe ◽  
Rik Pintelon ◽  
Gerd Vandersteen
Keyword(s):  
Dynamic Systems ◽  
Errors In Variables ◽  
Linear Dynamic Systems ◽  
Linear Dynamic

scholarly journals Identification of linear dynamic systems of fractional order with errors in variables based on an augmented system of equations

2021 ◽  
Vol 25 (3) ◽  
pp. 508-518
Author(s):  
Dmitriy Vladimirovich Ivanov
Keyword(s):  
Fractional Order ◽  
Dynamic Systems ◽  
System Of Equations ◽  
Errors In Variables ◽  
Linear Dynamic Systems ◽  
Linear Dynamic ◽  
Augmented System

Уравнения с производными и разностями дробного порядка находят широкое применение для описания различных процессов и явлений. В настоящее время активно развиваются методы идентификации систем, описываемых уравнениями с разностями дробного порядка. Статья посвящена идентификации дискретных динамических систем, описываемых уравнениями с разностями дробного порядка с ошибками в переменных. Задачи идентификации систем с ошибками в переменных часто бывают плохо обусловленными. В статье предложен алгоритм, использующий представление нормальной смещенной системы в виде расширенной эквивалентной системы. Данное представление позволяет уменьшить число обусловленности решаемой задачи. Тестовые примеры показали, что предложенный алгоритм обладает более высокой точностью по сравнению с алгоритмами на основе разложения Холецкого и минимизации обобщенного отношения Релея.

scholarly journals On the Uncertainty Identification for Linear Dynamic Systems Using Stochastic Embedding Approach with Gaussian Mixture Models

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3837
Author(s):  
Rafael Orellana ◽  
Rodrigo Carvajal ◽  
Pedro Escárate ◽  
Juan C. Agüero
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Dynamic Systems ◽  
Gaussian Mixture ◽  
Error Model ◽  
Fault Detection And Diagnosis ◽  
Deterministic Models ◽  
Linear Dynamic Systems ◽  
Linear Dynamic

In control and monitoring of manufacturing processes, it is key to understand model uncertainty in order to achieve the required levels of consistency, quality, and economy, among others. In aerospace applications, models need to be very precise and able to describe the entire dynamics of an aircraft. In addition, the complexity of modern real systems has turned deterministic models impractical, since they cannot adequately represent the behavior of disturbances in sensors and actuators, and tool and machine wear, to name a few. Thus, it is necessary to deal with model uncertainties in the dynamics of the plant by incorporating a stochastic behavior. These uncertainties could also affect the effectiveness of fault diagnosis methodologies used to increment the safety and reliability in real-world systems. Determining suitable dynamic system models of real processes is essential to obtain effective process control strategies and accurate fault detection and diagnosis methodologies that deliver good performance. In this paper, a maximum likelihood estimation algorithm for the uncertainty modeling in linear dynamic systems is developed utilizing a stochastic embedding approach. In this approach, system uncertainties are accounted for as a stochastic error term in a transfer function. In this paper, we model the error-model probability density function as a finite Gaussian mixture model. For the estimation of the nominal model and the probability density function of the parameters of the error-model, we develop an iterative algorithm based on the Expectation-Maximization algorithm using the data from independent experiments. The benefits of our proposal are illustrated via numerical simulations.

Sign in / Sign up

Export Citation Format

Share Document