scholarly journals Discussion: “Co-ordinates Which Uncouple the Equations of Motion of Damped Linear Dynamic Systems” (Foss, K. A., 1958, ASME J. Appl. Mech., 25, pp. 361–364)

1959 ◽  
Vol 26 (2) ◽  
pp. 307
Author(s):  
R. W. Traill-Nash
Keyword(s):  
Dynamic Systems ◽  
Equations Of Motion ◽  
Linear Dynamic Systems ◽  
Linear Dynamic

Co-Ordinates Which Uncouple the Equations of Motion of Damped Linear Dynamic Systems

1958 ◽  
Vol 25 (3) ◽  
pp. 361-364 ◽  
Author(s):  
K. A. Foss
Keyword(s):  
Dynamic Systems ◽  
Equations Of Motion ◽  
Continuous Systems ◽  
Present Treatment ◽  
Linear Dynamic Systems ◽  
Linear Dynamic ◽  
Orthogonality Relations ◽  
Lumped Parameters

Abstract Orthogonality relations between the eigenvectors of damped linear dynamic systems with lumped parameters are derived; and from these relations co-ordinates are found in terms of which uncoupled equations of motion can be written. Methods are developed for determining transient stresses in terms of these co-ordinates. The present treatment is extended to systems involving transient damping and to continuous systems.

A Method for Reducing the Number of Degrees of Freedom in Mathematical Models of Damped Linear Dynamic Systems

1962 ◽  
Vol 84 (4) ◽  
pp. 418-421 ◽  
Author(s):  
S. E. Staffeld
Keyword(s):  
Dynamic Systems ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Original System ◽  
Linear Dynamic Systems ◽  
Linear Dynamic ◽  
Limited Frequency ◽  
Damped Systems ◽  
Complex Coefficients ◽  
Better Than

A method is given for systematically operating on the equations of motion of a linear dynamic system to produce the equations of a new system of many fewer degrees of freedom. This reduced system has a multiterminal response as close as desired to the original system in a limited frequency range. The result will always be better than that obtained with the normal mode approach and application to damped systems does not result in complex coefficients.

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.

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