Uncertainty quantification for the modal shape sensing of structures undergoing geometrically non-linear deformation

IF 8.9 1区 工程技术 Q1 ENGINEERING, MECHANICAL
Janto Gundlach , Marc Böswald , Jurij Sodja
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引用次数: 0

Abstract

Shape sensing techniques allow for the time-efficient reconstruction of displacements based on measured strain data. There are technical applications, where the structure of interest is deformed in the geometrically non-linear domain. In aeronautics, this is the case for high-aspect-ratio wings, which are more frequently found in future designs. Only shape sensing methods that specifically take the non-linearity into account, can deliver appropriate displacement estimates for such application. A shape sensing method based on the linear modal approach can be utilised incrementally to capture the geometric non-linearity; it has therefore been denoted incremental modal method (IMM). This paper presents analytical relations for the uncertainty propagation for the various input quantities of the method, specifically strain mode shapes, displacement mode shapes, and measured strain. Deterministic shape sensing and uncertainty propagation are demonstrated using data obtained with a finite element model of a high-aspect-ratio wing experiencing geometric non-linear deflections in flapwise bending. Virtual strain and acceleration sensors are assumed for this setup, imitating the instrumentation conceivable for experimental work. The results obtained by analytical propagation are compared to Monte Carlo simulations for the purpose of validation. The derived propagation formulas make it possible to follow the evolution of the uncertainties over the number of increments. Given that the variability of the input quantities is known, the number of increments that minimise uncertainties can be determined for a model-free application of the shape sensing. Together with the deterministic estimates provided by an FE model, it is possible to determine the ideal number of increments for a specific shape sensing application in the geometrically non-linear domain.
几何非线性变形结构模态振型感知的不确定性量化
形状传感技术允许基于测量应变数据的位移的时间高效重建。有一些技术应用,其中感兴趣的结构在几何非线性域中变形。在航空学中,这是高展弦比机翼的情况,这在未来的设计中更常见。只有特别考虑非线性的形状传感方法,才能为这种应用提供适当的位移估计。基于线性模态方法的形状感知方法可以增量地捕捉几何非线性;因此,它被称为增量模态法(IMM)。本文给出了该方法的各种输入量,特别是应变模态振型、位移模态振型和实测应变的不确定性传播的解析关系。利用高展弦比机翼在扑翼弯曲中经历几何非线性偏转的有限元模型获得的数据,证明了确定性形状感知和不确定性传播。该装置假定虚拟应变和加速度传感器,模仿实验工作中可以想象的仪器。为了验证,将解析传播得到的结果与蒙特卡罗模拟进行了比较。推导出的传播公式使得跟踪不确定性随增量数的变化成为可能。考虑到输入量的可变性是已知的,对于无模型的形状传感应用,可以确定将不确定性最小化的增量数量。结合有限元模型提供的确定性估计,可以确定几何非线性领域中特定形状传感应用的理想增量数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Mechanical Systems and Signal Processing
Mechanical Systems and Signal Processing 工程技术-工程:机械
CiteScore
14.80
自引率
13.10%
发文量
1183
审稿时长
5.4 months
期刊介绍: Journal Name: Mechanical Systems and Signal Processing (MSSP) Interdisciplinary Focus: Mechanical, Aerospace, and Civil Engineering Purpose:Reporting scientific advancements of the highest quality Arising from new techniques in sensing, instrumentation, signal processing, modelling, and control of dynamic systems
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