基于频率等高线与粒子群优化的悬臂梁裂纹识别方法

A crack identification method for cantilever beam based on frequency contours and particle swarm optimization

摘要

利用频率响应曲面和固有频率获得的频率等高线交点，可用于确定梁结构的裂纹位置与深度，但传统的频率等高线法需要求解大量的二元超越方程，随着频率等高线的增多及测试噪声的干扰，绘制并寻找损伤交点位置耗时长且准确率低。针对上述问题，建立含单一贯穿裂纹悬臂梁的动力学损伤模型，采用固有频率和振型曲率函数求解结构的频率等高线，提出基于固有频率数据的两步粒子群算法自主搜索确定最优交点位置，依次识别出悬臂梁结构的裂纹位置与深度。数值算例与试验测试结果表明，该方法免于计算大量二元超越方程来绘制频率等高线，可有效提高裂纹识别的计算效率；在环境噪声干扰下，也能够准确判别裂纹位置。

Abstract

The intersection points of frequency contours obtained from the frequency response surfaces and natural frequencies can be used to determine the location and depth of crack in beam structure. However，the traditional frequency contour method requires solving a large number of binary transcendental equations，and it takes time and low accuracy to plot and find the intersection region with the increase of frequency contours and the interference of test noise. To address the above problems，a dynamic model of cantilever beam with a penetrated crack is established，natural frequencies and mode curvature functions are used to solve the frequency contours of the structure，and a two-step particle swarm optimization algorithm based on the natural frequency data is proposed to autonomously search and determine the optimal intersection point，and then the location and depth of crack in cantilever beam are sequentially identified. Numerical simulations and experimental tests show that the proposed method can effectively improve the computational efficiency of crack identification without calculating a large number of binary transcendental equations to plot frequency contours. Under the interference of environmental noise，the crack location can be accurately identified.

关键词

悬臂梁 / 裂纹识别 / 单裂纹 / 固有频率 / 频率等高线 / 粒子群优化

Key words

cantilever beam / crack identification / single crack / natural frequency / frequency contours / particle swarm optimization

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基金资助

国家自然科学基金资助项目(52175108)

山西省重点研发资助项目(202102010101009)