基于广义柔度曲率信息熵的梁结构损伤识别方法

广义柔度矩阵具有普通柔度矩阵的基本性质,且仅用一些低阶模态数据就可较为准确地获取,减少了截断高阶模态带来的截断误差。结合广义柔度矩阵对低阶损伤模态的敏感性与信息熵对系统非线性显著的突显作用,提出了广义柔度曲率信息熵指标。新指标以广义柔度曲率矩阵对角向量中每个元素与对角元素之和的比值作为整体概率函数,构造新的信息熵函数识别指标。使用简支梁和连续梁两种不同形式的梁结构算例对所提指标的损伤识别能力进行了分析验证,并采用服从截尾高斯分布的误差模型对所提指标的抗噪性进行分析。结果表明：广义柔度曲率信息熵指标能有效识别结构单处、对称位置处及多处损伤,且在误差不大于10%的情况下具有较好的识别精度。

Damage identification of beam structure based on generalized flexibility curvature information entropy

The Generalized flexibility matrix has the basic properties of general flexibility matrix can be obtained more accurately from low-order modal data and the truncation error caused by truncating higher order modes is reduced. In this paper, Combined the sensitivity of generalized compliance matrix to low-order damage modes with the significant effect of information entropy on system nonlinearity, a new index named generalized flexibility curvature information entropy is proposed, which taking the ratio of each diagonal element to the sum of the total diagonal elements in the generalized flexibility curvature matrix as the probability function. The damage identification capability of the proposed index is verified by using two different types of beam structures: simply supported beam and continuous beam, and the anti-noisy ability of the proposed index is verified by using the error model subject to truncated Gaussian distribution. The results show that the generalized flexibility curvature information entropy index can effectively identify the damage at single, symmetric and multiple locations of beam structures, and has a better identification accuracy under the condition of no more than 10% error.