DSpace Collection:
https://dspace.lboro.ac.uk/2134/3610
Mon, 02 Mar 2015 03:50:08 GMT
20150302T03:50:08Z

Limit cycles in Lienard equations
https://dspace.lboro.ac.uk/2134/16251
Title: Limit cycles in Lienard equations
Authors: Tosi, Giovanni; Wang, Simon
Abstract: An analytical estimation of the existence and characteristics of limit cycles in a given planar polynomial vector field represents a significant progress towards the complete answer to the second part of Hilbert’s 16th problem. In a very recent work [1], the second author of this present paper has developed a theory to fulfil this purpose. One major conclusion of the theory is that the number of limit cycles nested around a critical point in a general planar polynomial vector field is bounded by the Hilbert number where n is the order of the vector field. It is well known that linear vector fields have no limit cycles and this, of course agrees with the conclusion. Shi [2] shows that there are maximum three limit cycles nested around a critical point in quadratic vector fields. Again, it is in an agreement with the conclusion. For cubic vector fields results from previous studies [3,4,5] are also in an agreement with the conclusion whilst the result from the work [6] is in a disagreement although there exists some doubt about the result. In this present work, a detailed study is given to the limit cycles in a fifteenth order Liénard equation by using both the theory [1] and numerical simulations to check the validity of the theory. The method of analysis is briefly given in Section 2. An application example and conclusions are presented in Section 3 and 4, respectively.
Description: This is a conference paper.
Sat, 01 Jan 2005 00:00:00 GMT
https://dspace.lboro.ac.uk/2134/16251
20050101T00:00:00Z

Sound source contributions for the prediction of vehicle passby noise
https://dspace.lboro.ac.uk/2134/16170
Title: Sound source contributions for the prediction of vehicle passby noise
Authors: Braun, Michael E.; Walsh, Stephen J.; Horner, Jane L.
Abstract: Road traffic noise contributes to environmental noise, which can result in cardiovascular disease,
sleep disturbance or annoyance for the exposed population1. The reduction of road traffic noise
aims to increase health and life quality. Therefore, the vehicle passby noise emission, which is
determined in a standardised test situation, was limited by legislation. First introduced in the 1970s,
vehicle passby noise limits have been gradually reduced for all vehicle classes. However, road
traffic noise was not as significantly reduced as the passby noise limits.
Description: This is a conference paper, it was published in the Proceedings of The Institute of Acoustics [© Institute of Acoustics].
Wed, 01 Jan 2014 00:00:00 GMT
https://dspace.lboro.ac.uk/2134/16170
20140101T00:00:00Z

Estimation of time to point of closest approach for collision avoidance and separation systems
https://dspace.lboro.ac.uk/2134/16078
Title: Estimation of time to point of closest approach for collision avoidance and separation systems
Authors: Dunthorne, James; Chen, WenHua; Dunnett, Sarah J.
Abstract: This paper proposes a method for estimating the amount of time until the point of closest approach (TPCA) between two aircraft. A range of simple methods which use derivatives to estimate the time to collision are analysed. These methods are only accurate when the angle subtended between the direction of the relative velocity vector, and the bearing of the intruder aircraft is small. An extended method is developed which calculates the exact TPCA from relative distance and bearing measurements. Representative levels of Gaussian white noise are introduced to the core equation variables for both the derivative and extended methods. It is found that as we increase the value of θ, the extended method's accuracy increases beyond that of the derivative method. A fusion algorithm is developed to switch between methods and is shown to perform well for a range of conflicts. When the relative velocity between the two aircraft is small, the signal to noise ratio on the relative velocity variable reduces causing large errors to the TPCA estimation. It is therefore concluded that at a certain relative velocity threshold, Vk (dependant on sensor and filter performance) both the derivative and extended TPCA estimation methods would become undesirable as risk estimators. It is suggested that in these situations distance could be better to use since it can be measured directly.
Description: This is a conference paper [© 2014 IEEE]. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Wed, 01 Jan 2014 00:00:00 GMT
https://dspace.lboro.ac.uk/2134/16078
20140101T00:00:00Z

Failure boundary estimation for lateral collision avoidance manoeuvres
https://dspace.lboro.ac.uk/2134/16050
Title: Failure boundary estimation for lateral collision avoidance manoeuvres
Authors: Dunthorne, James; Chen, WenHua; Dunnett, Sarah J.
Abstract: This paper proposes a method for predicting the
point at which a simple lateral collision avoidance manoeuvre
fails. It starts by defining the kinematic failure boundary
for a range of conflict geometries and velocities. This relies
on the assumption that the ownship aircraft is able to turn
instantaneously. The dynamics of the ownship aircraft are
then introduced in the form of a constant rate turn model.
With knowledge of the kinematic boundary, two optimisation
algorithms are used to estimate the location of the real
failure boundary. A higher fidelity simulation environment
is used to compare the boundary predictions. The shape of
the failure boundary is found to be heavily connected to the
kinematic boundary prediction. Some encounters where the
ownship aircraft is travelling slower than the intruder were
found to have large failure boundaries. The optimisation
method is shown to perform well, and with alterations to
the turn model, its accuracy can be improved. The paper
finishes by demonstrating how the failure boundary is used to
determine accurate collision avoidance logic. This is expected to
significantly reduce the size and complexity of the verification
problem.
Description: This is a conference paper [© 2014 IEEE]. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Wed, 01 Jan 2014 00:00:00 GMT
https://dspace.lboro.ac.uk/2134/16050
20140101T00:00:00Z