Table 4. Training datasets Natural frequencies of beam using ANSYS

To simulate damage, cracks with a fixed width of 1 mm and a length of 25 mm were introduced, with varying depths of 2 mm, 4 mm, and 6 mm. Crack locations were varied from 0 to 700 mm in 25 mm increments from the fixed end, resulting in 87 damaged states. Including the undamaged state, a total of 88 cases were analyzed using numerical modal analysis in ANSYS. These variations in crack depth and location led to random changes in the beam’s natural frequencies. The bending Modes of Frequencies using ANSYS of Damaged states are tabulated below Table 4.为模拟结构损伤，本次研究引入了宽度固定为1 mm、长度固定为25 mm的裂纹，其深度分别设置为2 mm、4 mm与6 mm。裂纹位置以25 mm为步长，从固定端起在0至700 mm范围内变化，最终得到87种损伤状态。包含无损伤状态在内，共计88组工况通过ANSYS软件完成数值模态分析。裂纹深度与位置的上述变化会导致梁的固有频率产生随机变化。各损伤状态下通过ANSYS求解得到的弯曲模态频率已汇总于下表（表4）。