Improvement Of The Methods For Finite Element Model Updating Problems

Finite element model updating problem originated from structural dynamic research, being used widely in engineering structures and signal processing. About finite element model Mu&&( t)+Cu&( t)+Ku(t)=0, where M , C ,K are known as the mass, damping, and stiffness matrices, respectively. Its objective is reducing error between finite element model and the real model through updating, namely, is how to incorporate the measured modal data (Λ, X ) into the finite element model MXΛ~2 + CXΛ+ KX =0 to produce an adjusted finite element model with modal properties M,C,K that closely match the experimental modal data M_a , C_a ,K_a. Besides, different systems have different requires about M , C ,K . Often in most of the systems, M , C ,K are all n×n symmetric, M is assumed to be positive definite (denote by M > 0) and K is positive semi-definite (denote by K≥0), C is positive. From its beginning, finite element model updating problem interested many experts, and many updating procedures have been proposed in recent years.According to recent papers, there are two classes of updating methods: matrix-type methods for undamped systems and damped systems. As to the undamped systems, some references divide the updating procedures into two steps: one step is about the mass matrix updating, the other is about stiffness matrix updating. Many of them use the Lagrange Multiplier method, which will be outlined in this thesis. This thesis discusses some of these procedures and their improvements. For the damped systems, in 1998 Friswell, Inman and Pilkey proposed to incorporate the measured model data into the finite element model to produce an adjusted finite element model on the damping and stiffness so that the experimental modal data is closely match by using the Lagrange Multiplier method. But there are large and dense systems to solve. Recently, Kuo, Lin and Xu developed an efficient algorithm for computing the solutions C and K by differentiating an optimization problem. These methods are general, but have shortcomings. We notice that there are special relations between the two methods: ?F = 0 corresponds to normal equations of the least squares problem. Therefore, differentiation can be substituted by solving the least square problem. This thesis presents two new methods by using the least squares approach, which improves the results of Kuo, Lin and Xu. These new methods simplify the computation process, And the numerical experiments show the effectiveness of the algorithms.The structure of this thesis is as follows: Chapter 0 gives the background, history and the related research problems in the finite element model updating, and at the end introduces the general finite element model updating problems; Chapter 1 summarizes current and existing results. Chapter 2 develops new ideas for improving existing methods. Chapter 3 proposes two new methods to the finite element model updating problems, and presents two examples to illustrate the new methods. Chapter 4 gives conclusions and future works.