基于模态参数灵敏度的损伤方程组求解正则化方法研究

基于模态参数的结构损伤识别方法是振动损伤识别领域中应用最为广泛的方法。利用模态参数灵敏度构建结构损伤方程组,对其进行求解可以识别结构损伤位置和程度。由于实际工程中模态参数不完备性和噪声的影响,结构损伤方程易出现病态问题,直接求解可能产生错误的结果。为了解决这一问题,可以引入正则化方法进行求解。然而,各类正则化方法的基本原理、区别和联系及其在结构损伤识别中的应用没有系统的研究和对比。本文梳理了几类常用的正则化方法,对比分析其在基于模态参数灵敏度的损伤方程组求解中的适用性,讨论损伤程度、噪声水平和测点数目对几类方法识别结果的影响,为结构损伤识别中的正则化方法选择提供依据。通过连续梁和框架结构数值算例分析表明,在求解损伤方程的应用中,L1范数正则化方法鲁棒性较强,贝叶斯正则化方法次之,奇异值截断算法和L2范数正则化方法的鲁棒性较差;L1范数正则化方法能够产生更少的假阳性损伤单元,受噪声和测点数目影响较小,更适合损伤识别的应用。

Regularization methods for solving modal sensitivity-based damage equations: a comparative study

Modal parameters are most widely applied in structural damage identification using vibration responses.Structural damage equations can be established based on the modal sensitivity, and the location and degree of damage can then be obtained by solving the equations.The damage equations are generally ill-conditioned, which may lead to wrong results, because of the incompleteness of modal parameters and noise in practice.To cope with these shortcomings, regularization methods are introduced to guarantee correctness of the solutions of the ill-posed damage equations.However, there is no comprehensive investigation and comparison on the basic principles, differences and connections of various regularization methods and their applications in structural damage identification.This study investigates several commonly-used regularization methods, and compares their applicability for solving modal sensitivity-based damage equations.The effects of the degree of damage, the noise level, and the number of measured points are discussed.This work provides the basis for the selection of regularization methods in structural damage identification.Two numerical case studies of a continuous beam and a frame are carried out.It is demonstrated that L1-norm regularization and Bayesian regularization method are more robust than truncated singular value decomposition and L2-norm regularization method in solving damage equations, and that L1-norm regularization method is more suitable for the application of damage identification, which can produce less false positive damage and is less affected by noise and the number of measurement points.