This paper presents numerical and experimental investigations on damage detection of mono-coupled multistory buildings using natural frequency as only diagnostic parameter. Frequency equation of a mono-coupled multistory building is first derived using the transfer matrix method. Closed-form sensitivity equation is established to relate the relative change in the stiffness of each story to the relative changes in the natural frequencies of the building. Damage detection is then performed using the sensitivity equation with its special features and minimizing the norm of an objective function with an inequality constraint. Numerical and experimental investigations are finally conducted on a mono-coupled 3-story building model as an application of the proposed algorithm, in which the influence of modeling error on the degree of accuracy of damage detection is discussed. A mono-coupled 10-story building is further used to examine the capability of the proposed algorithm against measurement noise and incomplete measured natural frequencies. The results obtained demonstrate that changes in story stiffness can be satisfactorily detected, located, and quantified if all sensitive natural frequencies to damaged stories are available. The proposed damage detection algorithm is not sensitive to measurement noise and modeling error.

Many multi-story or highrise buildings consisting of a number of identical stories are usually considered as periodic spring-mass systems. The general expressions of natural frequencies, mode shapes, slopes and curvatures of mode shapes of periodic spring-mass system by utilizing the periodic structure theory are derived in the paper, moreover, the sensitivities of these mode parameters with respect to structural damages, which do not depend on physical parameters of the original structures, are obtained. Based on the sensitivity analysis of these mode parameters, a two-stage method is proposed to localize and quantify damages of multi-story or highrise buildings. The slopes and curvatures of mode shapes, which are highly sensitive to local damages, are used to localize the damages, subsequently, the limited measured natural frequencies, which have a better accuracy than the other mode parameters, are used to quantify the extent of damages within the potential damaged locations. The experimental results of a 3-storey experimental building demonstrate that the single or multiple damages of buildings, either slight or severe, can be correctly localized by using only the slope or curvature of mode shape in one of the lower modes, in which the change of natural frequency is the largest, and can be accurately quantified by the limited measured natural frequencies with noise pollution.

A new structural damage identification method using limited test static displacement based on the grey system theory is proposed in this paper. The grey relation coefficient of displacement curvature is defined and used to locate damage in the structure, and an iterative estimation scheme for solving nonlinear optimization programming problems based on the quadratic programming technique is used to identify the damage magnitude. A numerical example of a cantilever beam with single or multiple damages is used to examine the capability of the proposed grey-theory-based method to localize and identify damages. The factors of measurement noise and incomplete test data are also discussed. The numerical results showed that the damage in the structure can be localized correctly through using the grey-related coefficient of displacement curvature, and the damage magnitude can be identified with a high degree of accuracy, regardless of the number of measured displacement nodes. This proposed method only requires limited static test data, which is easily available in practice, and has wide applications in structural damage detection.

提出了一种基于模态测量参数和神经网络的结构损伤检测方法，建造了两种输入方式的BP神经网络，即自振频率以及结合自振频率与振型，并讨论了不同数量的输入信息对结构损伤检测精度和计算效率的影响。证明了输入的参数越多，神经网络就越聪明，训练的收敛速度越快;以及在保证一定的测量精度的情况下，基于频率与振型的损伤识别结果要好于基于频率的检测结果。最后，通过对3层框架模型的4种损伤工况下的结构损伤检测结果的分析，认为利用模态测量参数和神经网络方法能够准确地识别结构损伤的位置，而且能较精确地识别结构损伤的大小。

An adaptive Fourier Transform (FT) with an optimal window has been proposed for the time-frequency analysis of nonstationary time series. The adaptive optimal window length has been determined by minimizing MSE. The method allows a good estimation of both frequency and amplitude of the spectrum and can be easily applied to the general case of time-varying signals. The evaluation of the proposed approach has been performed on measured time-varying signals from a suspension bridge model and a steel frame model whose data have the typical non-stationary characteristics. The performance of the method has been evaluated by comparing the analyzed modal parameters to the ones from the classic Short-time Fourier Transform (SFT) technique and the calculated values obtained from the finite element model. The numerical results show that the proposed approach can overcome some of the difficulties encountered in the classic Fourier transform technique and can achieve higher computation accuracy.