scholarly journals Stability analysis of real-time dynamic substructuring using delay differential equation models

2005 ◽  
Vol 34 (15) ◽  
pp. 1817-1832 ◽  
Author(s):  
M. I. Wallace ◽  
J. Sieber ◽  
S. A. Neild ◽  
D. J. Wagg ◽  
B. Krauskopf
Keyword(s):  
Differential Equation ◽  
Stability Analysis ◽  
Real Time ◽  
Delay Differential Equation ◽  
Time Dynamic ◽  
Dynamic Substructuring ◽  
Differential Equation Models ◽  
Delay Differential

scholarly journals Delay Differential Equation Models for Real-Time Dynamic Substructuring

2005 ◽  
Author(s):  
Max Wallace ◽  
Jan Sieber ◽  
Simon Neild ◽  
David Wagg ◽  
Bernd Krauskopf
Keyword(s):  
Differential Equation ◽  
Real Time ◽  
Delay Differential Equation ◽  
Software Tool ◽  
Test System ◽  
System Stability ◽  
Delay Compensation ◽  
Time Dynamic ◽  
Dynamic Substructuring ◽  
Delay Differential

Real-time dynamic substructuring is a testing technique that models an entire system through the combination of an experimental test piece, representing part of the system, with a numerical model of the rest of the system. Delays can have a significant effect on the technique, as signals are passed between the two parts of the system in real-time. The focus of this paper is the influence of the delay on the dynamics of the substructured system. This is addressed using a linear example which may be described by a delay differential equation (DDE) model. This type of analysis allows critical delay values for system stability to be computed, which in turn can be used to help design the substructuring test system. Two methods are presented for the example considered. The first makes use of an analytical approach and the second of a numerical software tool, DDE-BIFTOOL. Normally, in substructuring tests, the actuator’s response time exceeds the critical delay time and the substructured system is unstable. It is demonstrated that the system can be stabilized using an adaptive delay compensation technique based on forward polynomial prediction. Finally we outline how these techniques may be applied to an industrial example of modelling a nonlinear spring.

scholarly journals Maximum Likelihood Inference for Univariate Delay Differential Equation Models with Multiple Delays

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Ahmed A. Mahmoud ◽  
Sarat C. Dass ◽  
Mohana S. Muthuvalu ◽  
Vijanth S. Asirvadam
Keyword(s):  
Differential Equation ◽  
Maximum Likelihood ◽  
Delay Differential Equation ◽  
Information Matrix ◽  
Likelihood Inference ◽  
Multiple Delays ◽  
Unknown Parameters ◽  
Differential Equation Models ◽  
Delay Differential ◽  
Initial Starting

This article presents statistical inference methodology based on maximum likelihoods for delay differential equation models in the univariate setting. Maximum likelihood inference is obtained for single and multiple unknown delay parameters as well as other parameters of interest that govern the trajectories of the delay differential equation models. The maximum likelihood estimator is obtained based on adaptive grid and Newton-Raphson algorithms. Our methodology estimates correctly the delay parameters as well as other unknown parameters (such as the initial starting values) of the dynamical system based on simulation data. We also develop methodology to compute the information matrix and confidence intervals for all unknown parameters based on the likelihood inferential framework. We present three illustrative examples related to biological systems. The computations have been carried out with help of mathematical software: MATLAB® 8.0 R2014b.

Stability Switches in a Neutral Delay Differential Equation with Application to Real-Time Dynamic Substructuring

2006 ◽  
Vol 5-6 ◽  
pp. 79-84 ◽  
Author(s):  
Y.N. Kyrychko ◽  
K.B. Blyuss ◽  
A. Gonzalez-Buelga ◽  
S.J. Hogan ◽  
David J. Wagg
Keyword(s):  
Real Time ◽  
Closed Loop ◽  
Numerical Models ◽  
Closed Loop System ◽  
Neutral Delay ◽  
Time Dynamic ◽  
Dynamic Substructuring ◽  
Delay Differential ◽  
Mass Spring ◽  
Theoretical Results

In this paper delay differential equations approach is used to model a real-time dynamic substructuring experiment. Real-time dynamic substructuring involves dividing the structure under testing into two or more parts. One part is physically constructed in the lab- oratory and the remaining parts are being replaced by their numerical models. The numerical and physical parts are connected via an actuator. One of the main difficulties of this testing technique is the presence of delay in a closed loop system. We apply real-time dynamic sub- structuring to a nonlinear system consisting of a pendulum attached to a mass-spring-damper. We will show how a delay can have (de)stabilising effect on the behaviour of the whole system. Theoretical results agree very well with experimental data.

Delay-Differential Equation Models for Fisheries

1973 ◽  
Vol 30 (7) ◽  
pp. 939-945 ◽  
Author(s):  
Gilbert G. Walter
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Growth Curves ◽  
Fishing Effort ◽  
Oscillatory Behavior ◽  
The Other ◽  
Differential Equation Models ◽  
New Models ◽  
Delay Differential

Two new "simple" fishery models based on delay-differential equations are introduced and compared to three currently used differential equation models. These new models can account for reproductive lag and allow oscillatory behavior of population biomass, but require only catch and effort data for their application. Equilibrium levels are calculated for both models and examples of various types of growth curves are given. Levels of fishing effort which maximize yield are calculated and found in one case to depend on the previous population and in the other to be constant.

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