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首页> 外文期刊>Mechanical systems and signal processing >A frequency based algorithm for identification of single and double cracked beams via a statistical approach used in experiment
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A frequency based algorithm for identification of single and double cracked beams via a statistical approach used in experiment

机译：一种基于频率的算法，通过实验中使用的统计方法来识别单裂纹和双裂纹梁

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摘要

An algorithm for detecting cracks on the beams and a statistical process for minimising the measurement errors in experiments are presented in this paper. Natural frequencies are determined by using the theoretical model for different depths and locations of single crack. The ratios of cracked and un-cracked beam's natural frequencies constitute the prediction tables scaled in two axes as crack location and crack depth. Frequency contour lines corresponding to measured natural frequency ratios are matched with the interpolated prediction table, called frequency map, and are used for detection of a single crack. However, contour lines do not give any information about the existence of two cracks. The algorithm presented in this paper makes it possible to locate the suitable positions of two cracks searched over the frequency map. The algorithm is tested in the examples employing the frequency map prepared by the theory presented and the input frequency ratios obtained by the commercial finite element program. The algorithm is also verified by using the natural frequencies of cracked and un-cracked cantilever beams employed in several experiments. In measurement, determination of accurate natural frequency ratios is crucial for the success of crack detection. Therefore, this paper also presents a statistical approach called 'recursively scaled zoomed frequencies (RSZF)' for minimising the deviations caused by sensitivity and resolution lack in measured natural frequencies. In this approach, the measured frequencies in spectrum are modified by the mean value of the natural frequencies determined in different frequency scales. Zoomed frequencies are obtained by the cubic spline interpolation method that increases the resolution of frequency spectrum. RSZF comes into further prominence especially when the cracks are needed to be detected by very small sized data. All of the experimental results represent that single crack and double cracks are successfully detected by using the methods presented.
机译：本文提出了一种检测梁裂纹的算法，以及一种将测量中的测量误差降至最低的统计过程。通过使用理论模型针对单个裂纹的不同深度和位置确定固有频率。开裂和未开裂梁的固有频率之比构成了在两个轴上按裂缝位置和裂缝深度缩放的预测表。对应于测得的固有频率比率的频率轮廓线与内插的预测表（称为频率图）匹配，并用于检测单个裂缝。但是，轮廓线不能提供有关两个裂纹的存在的任何信息。本文提出的算法可以在频率图上找到两个裂纹的合适位置。在示例中，使用所介绍的理论准备的频率图和商业有限元程序获得的输入频率比，对算法进行了测试。该算法还通过使用在几个实验中使用的破裂和未破裂的悬臂梁的固有频率进行了验证。在测量中，确定准确的固有频率比对于裂纹检测的成功至关重要。因此，本文还提出了一种统计方法，称为“递归缩放的缩放频率（RSZF）”，用于最小化由测量的固有频率中的灵敏度和分辨率不足引起的偏差。在这种方法中，频谱中的测量频率由在不同频率范围内确定的自然频率的平均值修改。通过三次样条插值方法可以获得放大的频率，从而增加了频谱的分辨率。 RSZF变得更加突出，特别是当需要通过非常小的数据来检测裂缝时。所有的实验结果都表明，使用提出的方法可以成功地检测出单裂纹和双裂纹。

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