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Control-based bifurcation analysis for experiments

基于控制的实验分岔分析

基本信息

批准号：
EP/J010820/1
负责人：
Jan Sieber
金额：
$ 10.83万
依托单位：
UNIVERSITY OF EXETER
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2012
资助国家：
英国
起止时间：
2012 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FJ010820%2F1
关键词：
Control based bifurcation analysis experiments

项目摘要

Many phenomena that are predicted to exist by mathematical theoryremain invisible in real life. Yet, mathematical theory also predictsthat these hidden phenomena determine our fate when real life is "onthe edge". For example, a small increase of wind strength can abruptlycause a bridge cable to start swinging violently. Still more puzzling,the bridge cable may continue to swing strongly even if the windstrength decreases again. Mathematical theory reveals that themechanisms behind these striking sudden changes (often catastrophesfrom the point of view of engineering) are universal: they apply to abridge cable as well as to an ocean current or a neuron. The observedchange is abrupt only because the missing link between the twodifferent visible behaviours is typically a phenomenon that isunstable or too sensitive to be visible. This insight enablesengineers and scientists to predict, and avoid or control, suddenchanges whenever they can rely on a set of equations describing themotion.This research will develop a method, "control-based continuation",that enables experimenters to observe unstable phenomena directly incontrolled laboratory experiments. Control-based continuation usescontrol to convert the relation between experimental inputs andoutputs into an equation that can be solved computationally. Everyphenomenon that is natural in the uncontrolled experiment can be foundas a solution of this equation. Mechanical prototype experiments(using, for example, pendula and beam-magnet arrangements) have shownthat the method is indeed feasible. This project aims to makecontrol-based continuation applicable to more complex experiments andmore complex phenomena.The PI will collaborate with experimenters at the Technical Universityof Denmark (Lyngby) who investigate vibrations in fast rotatingmachinery. One specific objective of the project is to develop and test the continuationof the exact boundaries between stability and instability (so-calledbifurcations). Traditional computational methods for determiningbifurcations are not applicable to equations extracted frommeasurements because they rely on the ability to solve the equationwith high accuracy (8-16 significant digits), which is not achievablein most experiments.

许多被数学理论预言存在的现象在真实的生活中是看不见的。然而，数学理论也预测，当真实的生活处于“边缘”时，这些隐藏的现象决定了我们的命运。例如，风力的小幅增加可能会导致桥梁缆索开始剧烈摆动。更令人费解的是，即使风力再次减弱，大桥缆索仍可能继续强烈摆动。数学理论表明，这些惊人的突变（从工程学的角度来看，通常是灾难）背后的机制是普遍的：它们适用于桥梁电缆，也适用于洋流或神经元。这种变化之所以突然，只是因为两种不同的可见行为之间的缺失环节通常是一种不稳定或过于敏感而不可见的现象。这种洞察力使工程师和科学家能够预测、避免或控制突然的变化，只要他们可以依靠一组描述运动的方程。这项研究将开发一种方法，“基于控制的延续”，使实验人员能够直接观察受控实验室实验中的不稳定现象。基于控制的延续使用控制来将实验输入和输出之间的关系转换为可以通过计算求解的方程。在不受控制的实验中的每一个自然现象都可以作为这个方程的一个解来发现。机械原型实验（使用，例如，摆和梁磁铁安排）表明，该方法确实是可行的。该项目旨在使基于控制的延续适用于更复杂的实验和更复杂的现象。PI将与丹麦技术大学（Lyngby）的实验人员合作，研究快速振动机械中的振动。该项目的一个具体目标是开发和测试稳定性和不稳定性（所谓的分叉）之间的精确边界的延续。传统的确定分叉的计算方法不适用于从测量中提取的方程，因为它们依赖于高精度（8-16位有效数字）求解方程的能力，这在大多数实验中是不可行的。