基于MSVAR模型的非线性损伤识别方法

实际工程中出现的损伤往往具有非线性特征，比如裂缝开合导致结构刚度呈现明显的双线性特性。采用简单的线性模型会遗漏与损伤相关的非线性信息，进而影响到损伤识别结果的可靠性。为解决上述问题，该文提出基于马尔科夫状态转移向量自回归模型(MSVAR)的非线性损伤识别方法。该方法假定损伤会导致结构振动响应出现非线性特征，利用MSVAR模型隐状态平滑概率能够反映数据非线性变化的特点，构造信息熵作为损伤预警指标监测结构损伤状态。MSVAR模型的自回归系数包含损伤位置信息，可据此构造损伤定位向量确定裂缝位置，以裂缝位置处的层间位移(平滑概率由0突变到100%时)表征裂缝宽度。最后通过数值算例和模型试验验证该文所提方法在裂缝类型损伤识别的有效性。

NOLINEAR DAMAGE IDENTIFICATION BASED ON MSVAR MODEL

Damage in real engineering often exhibits nonlinear characteristics. For example, crack opening and closing can lead to bilinear stiffness of structures. Using simple linear model will miss the nonlinear information related to damage, and reduce the damage identification reliability. To solve this problem, a new nonlinear damage identification method based on the Markov-Switching Vector Auto-Regression (MSVAR) model is proposed. This method assumes that the damage will cause nonlinear characteristics in the structural responses. Since the hidden state smooth probability of the MSVAR model can reflect nonlinear changes in the data, the smooth probability-based information entropy is used as the damage warning indicator to monitor the damage state of the structure. For cracks, their locations can be infered using the damage location vector constructed by autoregressive coefficients of the MSVAR model. The crack width is represented as the interlayer displacement at the crack location (when the smooth probability switches from 0 to 100%). A numerical example and an experimental test are introduced to verify the effectiveness of the proposed method in the identification of crack damage.