Research On Inverse Force Identification Methods Of Structures Under Multiple Vibration Excitation

The force identification,as an effective way to obtain the vibration excitation source, is of importance to predict the vibration and acoustics radiation of structures. Due to the complexity of engineering structures,it is generally difficult or impossible to directly measure the force in lots of engineering problems. In practice, the inverse problem is usually employed to identify the structural equivalent excitation force. However, there exists ill-posed problem resulting in serious instability of method. Regularization method can be used to effectively deal with ill-posed problem. Obviously, it is significant to study pathological characteristics of systems and select appropriate solution which is useful to improve the accuracy and efficiency of the force identification. In this thesis, a combination of numerical simulation and measurements approach is proposed. This method is capable of identifying forces of structures under multiple vibration excitations in a wide frequency range which fully cover both low and high modal overlap.Firstly, the characteristics and causes of the ill-posed problem are discussed. Several methods which can overcome ill-posed problems such as singular value decomposition and least squares method are introduced. Since the essential distinction between different regularization methods is filtering factor, the regularization parameter selection method which strongly depend on the filtering factor is discussed in detail. At the same time,the numerical model is built and validated. The noise is added to the transfer function and responses to simulate actual environment which can be serve as reference for numerical simulation.In order to compare the performance of the threshold based on estimates of error in transfer functions and operational response, the generalized cross-validation, L curve and so on, a simply-supported rectangular plate is analyzed. The influence of signal-to-noise ratios,point numbers of excitation and response and geometrical parameters of plates on the accuracy of force identification is investigated. To deal with unknown error proportion of transfer functions and responses,a modified singular value method is proposed.The basic principles of the Tikhonov regularization are presented. The effects of signal-to-noise ratio of the transfer function and response as well as the relative positions of the force and response are studied in detail. It is observed that full-rank pseudo-inversion give better results than Tikhonov regularization in some cases, particularly mild ill-conditioned problems. In this thesis,the threshold condition number of rectangular plate structures is identified by the error of force identification. The results reveal that the full-rank pseudo-inversion in conjunction with the Tikhonov regularization method can improve the accuracy of the force identification.A verification experiment about actual complex structures is given,and a modified finite element model is adopted to achieve the transfer function between the force and response point which can solve difficulty in direct measuring transfer function of complex structure.The results indicate that multiple regularization load identification method is effective and stable which can meet the engineering precision requirements.