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Two-dimensional modal curvature estimation via Fourier spectral method for damage detection

机译：傅里叶光谱法进行二维模态曲率估计以检测损伤

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摘要

Modal curvature is one of the most important damage indices utilized in the damage identification for composite structures. However, few kinds of sensors can provide the measure for modal curvature directly. The lack of direct measurement method for modal curvature necessitates the use of the central difference estimation, which reduces the stability of the algorithm. Noise is severely amplified by the central difference, and hence limits the damage identification through the use of modal curvature estimation. Instead of numerical differentiation, the two-dimensional Fourier spectral method is employed to conduct the two-dimensional modal curvature estimation in this paper. The use of Fourier spectral method over the conventional central difference operator gives the proposed methodology the following advantages: (1) Spectral calculations for spatial derivatives are implemented in global space, thus noise can be suppressed. The k-domain generated in algorithm provides the space for spatial filtering. (2) The precise estimation for modal curvatures can be obtained by aid of the trigonometric interpolation in spectral method. (3) The proposed method calculates the modal curvatures based on fast Fourier transform, thus the efficiency is ensured. By the numerical and experimental comparisons with the classical central difference method, the suitability of the present method is verified for composite structures. (C) 2016 Elsevier Ltd. All rights reserved.
机译：模态曲率是用于复合结构损伤识别的最重要的损伤指标之一。但是，很少有传感器可以直接提供模态曲率的测量。缺少用于模态曲率的直接测量方法，因此必须使用中心差估计，这会降低算法的稳定性。中心差会严重放大噪声，因此通过使用模态曲率估算来限制损伤识别。本文采用二维傅立叶谱方法代替数值微分方法进行二维模态曲率估计。在传统的中心差分算子上使用傅立叶频谱方法具有以下优点：（1）在全局空间中执行空间导数的频谱计算，因此可以抑制噪声。算法中生成的k域为空间滤波提供了空间。 （2）模态曲率的精确估计可以借助光谱法中的三角插值来获得。 （3）提出的方法基于快速傅里叶变换计算模态曲率，从而保证了效率。通过与经典中心差分方法的数值和实验比较，验证了本方法对复合结构的适用性。 （C）2016 Elsevier Ltd.保留所有权利。

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