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Mechanical systems virtual sensing by proportional observer and multi-resolution analysis

机译：通过比例观测器和多分辨率分析的机械系统虚拟感测

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摘要

A technique to reconstruct the displacement field throughout the structure from pointwise measurements under different noise sources is proposed. The developed estimator is a Proportional Observer (PO) that exploits a linear, frequency independent, relation between the estimated state-space vector and the measurements. To improve its accuracy, the PO concept is then extended to the definition of a sequence of proportional observers, each one acting on a signal decomposition provided by wavelet multi-resolution analysis, or a Multi-Resolution Proportional Observer (MR-PO). The considered numerical test case is a straight, uniform beam with an unmodeled stiffness reduction provided by a notch, which allows for characterizing analytically this model uncertainty. The input data is given by virtual strain measurements collected on the top face of the beam, whereas the estimated state variables are the time dependent coordinates of the modal expansion of the vertical displacement along the beam elastic axis. An optimization solver, which minimizes the estimation error, is employed to get the gain matrix of the proposed observers. The effect of different noise sources, like process and measurement noise and unknown excitation, on the estimation accuracy is taken into account with a sensitivity analysis. The obtained results assess the effectiveness of the combination between the PO concept and wavelet multi-resolution analysis as a tool for developing digital twin models based on experimental data.
机译：提出了一种在不同噪声源下从点测量的整个结构中重建位移场的技术。开发的估计器是一种比例观察者（PO），其利用估计的状态空间向量和测量之间的线性，频率独立，与测量之间的关系。为了提高其准确性，然后将PO概念扩展到一系列比例观察者的定义，每一个作用在由小波多分辨率分析或多分辨率比例观察者（MR-PO）提供的信号分解上。所考虑的数值测试壳体是直的，具有由凹口提供的未铭出的刚度减少的梁，其允许分析地表征这种模型不确定性。输入数据由在光束的顶面上收集的虚拟应变测量给出，而估计的状态变量是沿着梁弹性轴的垂直位移的模态扩展的时间相关坐标。最小化估计误差的优化求解器被采用来获取所提出的观察者的增益矩阵。用灵敏度分析考虑了不同噪声源的影响，如过程和测量噪声和未知激发，以估计精度考虑。所获得的结果评估了PO概念与小波多分辨率分析之间的组合的有效性作为基于实验数据开发数字双胞胎模型的工具。

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