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Further development and experimental verification of wavelet deconvolution technique for impact force reconstruction

机译：冲击力重建小波碎屑卷积技术的进一步发展与实验验证

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摘要

Reconstruction or deconvolution has widely been known as a useful indirect method to determine impact force which is often difficult to be directly measured in reality. This paper deals with the deconvolution technique using wavelet approach for impact force reconstruction. Based on the ability of wavelet transform in representing arbitrary signal using different scaled and shifted versions of a certain wavelet, impact force reconstruction is formulated and deployed through its wavelet expansion coefficients with controlling scale and shift components. Controlling both scale and shift components can be regarded as a kind of regularization in order to mitigate the ill-posed nature which often undermines or destabilizes reconstructed result. In the author's previous publication, the theoretical analysis of wavelet deconvolution technique for impact force reconstruction was proposed and numerically verified with controlling only shift components at a particular scale after removing some small scales. Although this technique has been verified to be successful and effective, the elimination of some smaller scales (i.e., ignoring all shift components at these scales) can also cause loss of high frequency information. Therefore, in the current work, controlling shifts is further operated not only at a particular scale but at all scales with the aim of limiting the loss of important high frequency information. This task can be considered as a further development of the previous work so as to improve the accuracy of reconstructed result, especially the peak force which often contains important high frequency information. This paper also experimentally verifies the applicability of the proposed technique by reconstructing various actual forces acting on a polycarbonate plate produced by different impactors. Results first show that the impact force reconstruction is affected by the ill-posedness if the scales or shifts of wavelets are not controlled. After applying the control of shift components at all scales, results revealed that the proposed technique is actually more efficient in improving reconstruction in comparison with the technique presented in the previous paper.
机译：被广泛的重建或去卷积被称为有用的间接方法，以确定通常难以直接测量的冲击力。本文涉及采用小波法进行冲击力重建的解卷积技术。基于小波变换在使用不同小波的不同缩放和移位版本的任意信号的能力，通过控制刻度和移位组件的小波膨胀系数配制并展开冲击力重建。控制两个比例和移位组件都可以被视为一种正规化，以便减轻经常破坏或破坏重建结果的不良性性质。在提交人以前的出版物中，提出了对冲击力重建的小波碎片卷积技术的理论分析，并在除去一些小尺度后仅在特定刻度下进行移动组件进行数值验证。虽然这种技术已经被验证成功而有效，但消除了一些较小的尺度（即，忽略这些比例的所有移位组件）也可能导致高频信息的损失。因此，在当前的工作中，控制换档不仅在特定规模处进一步运行，而是在所有尺度上，目的是限制重要的高频信息的损失。该任务可以被视为前一项工作的进一步发展，以提高重建结果的准确性，尤其是通常包含重要高频信息的峰值力。本文还通过重建在不同撞击件产生的聚碳酸酯板上的各种实际力来实验验证所提出的技术的适用性。结果首先表明，如果没有控制小波的尺度或偏移，则冲击力重建受到不良呈现的影响。在所有尺度处应用转移组分的控制后，结果表明，与前一篇论文中呈现的技术相比，该技术实际上在改善重建方面更有效。

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