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考虑刚度和质量耦合效应的结构弹性成像方法

STRUCTURAL ELASTOGRAPHY METHOD CONSIDERING THE COUPLING EFFECT OF STIFFNESS AND MASS

  • 摘要: 弹性成像是一种医学影像技术, 可以把生物体组织的弹性模量信息转换为可视化图像. 为了将弹性成像用于机械结构的损伤识别, 实现机械结构缺损、夹杂、结冰和积水多种损伤类型的全局识别, 提出一种考虑刚度和质量耦合效应的结构弹性成像方法. 弹性模量仅能反映结构刚度变化, 单一的弹性模量不足以表征多种损伤类型, 因而还需引入能反映结构质量变化的参数. 受结构拓扑优化理论启发, 以结构离散单元的弹性模量系数和材料密度系数作为成像参数, 将成像参数与弹性模量和材料密度关联, 构建考虑结构刚度和质量耦合效应的损伤表征. 基于无阻尼自由振动系统的有限元模型, 构建损伤表征、力学模型和特征值响应之间的映射关系. 以数字模型和真实结构模型的特征值响应变化率的平方和为目标函数, 以有限元平衡方程和成像参数上下限为约束条件, 建立基于特征值响应的结构弹性成像模型, 推导弹性成像目标函数关于成像参数的导数, 采用基于梯度的优化算法求解弹性成像模型. 数值算例表明, 针对结构缺损、夹杂、结冰、积水等损伤, 该方法无需先验信息, 可有效实现结构损伤位置、数量和形状的精确量化, 并通过三维结构弹性成像算例验证了该方法的通用性.

     

    Abstract: Elastography is a medical imaging technology that can convert the elastic modulus information of biological tissues into visual images. In order to use elastography for damage identification of mechanical structures and achieve global identification of various damage types such as mechanical structural defects, inclusions, ice, and water accumulation. A structural elastography method considering the coupling effect of both stiffness and mass is proposed. The elastic modulus can only reflect the change in structural stiffness and is not enough to characterize various damage types. It is also necessary to introduce parameters that reflect the change in the mass of the structure. Inspired by the structural topology optimization theory, the proposed method takes the elastic modulus coefficients and material density coefficients of the discrete elements of the structure as the imaging parameters. The imaging parameters are correlated with the elastic modulus and material density to construct a damage characterization considering the coupling effect of structural stiffness and mass. The mapping relationship between damage characterization, mechanical model, and eigenvalue response is constructed based on the finite element model of the undamped free vibration system. The sum of the squares of the eigenvalue response change rates of the digital model and the real structural model is used as the objective function. The finite element equilibrium equation as well as the upper and lower limits of the imaging parameters are used as constraints. Eigenvalue response-based structural elastography model is established based on the objective function and constraints. The derivatives of the elastography objective function with respect to the imaging parameters are derived. The elastography model is solved using a gradient-based optimization algorithm. Numerical examples show that this method can effectively achieve accurate quantification of structural damage location, quantity, and shape without any prior information for damages such as structural defects, inclusions, ice, and water accumulation. The generality of this method is further verified by three-dimensional structural elastography examples.

     

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