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Abstract:
A novel criterion, based on additional virtual masses estimated in multiple tests and the Bayesian theory, is proposed in this paper to improve the efficiency and precision of damage identification. Initially, a method is proposed that uses the experimentally measured frequency-domain response and a predetermined target frequency to estimate the required additional virtual mass. The proposed mass estimation method is flexible with respect to the frequency band of excitation, which can be thus selected according to practical engineering constraints. Furthermore, a new objective function based on the residual between the theoretical and experimental virtual masses is proposed. The objective function avoids calculating the structural modes through Eigen decomposition of the structural mass and stiffness matrices, and it thus improves the computational efficiency. Thirdly, based on the theoretical frequency response function of the finite element model, explicit formulas are derived for quick calculation of the additional masses and their sensitivities with respect to damage factors. In the next step, randomness and the influence of measurement noise are considered, and the approach is formulated in the probabilistic Bayesian framework. Finally, numerical simulations of a simply supported beam, a 3D truss structure and a 3D building, as well as an experimental 3-story frame, are used to verify the effectiveness of the proposed methods. The results clearly indicate that identified damage factors are close to real values, and thus acceptable in engineering.

Keywords:
structural health monitoring (SHM), damage identification, additional virtual mass, sensitivity analysis, Bayesian theory

Abstract:
Adding a virtual mass is an effective method for damage identification. It can be used to obtain a large amount of information about structural response and dynamics, thereby improving the sensitivity to local damage. In the current research approaches, the virtual mass is determined first, and then the modal characteristics of the virtually modified structure are identified. This requires a wide frequency band excitation; otherwise the crucial modes of the modified structure might be out of the band, which would negatively influence the modal analysis and damage identification. This paper proposes a method that first determines the target frequency and then estimates the corresponding value of the additional virtual mass. The target frequency refers to the desired value of the natural frequency after the virtual mass has been added to the structure. The virtual masses are estimated by tuning the frequency response peaks to the target frequencies. First, two virtual mass estimation methods are proposed. One is to directly calculate the virtual mass, using the frequency‐domain response at the target frequency point only, whereas the second method estimates the mass using a least‐squares fit based on the frequency‐domain response around the target frequency. Both proposed methods utilize merely a small part of the frequency domain. Therefore, an impulse, a simple harmonic, or a narrow spectral excitation can be used for damage identification. Finally, a numerical simulation of a simply supported beam and experiments of a frame structure and a truss structure are used to verify the effectiveness of the proposed method.

Keywords:
damage identification, frequency response, structural health monitoring (SHM), virtual distortion method (VDM), virtual mass

Abstract:
In practical civil engineering, structural damage identification is difficult to implement due to the shortage of measured modal information and the influence of noise. Furthermore, typical damage identification methods generally rely on a precise Finite Element (FE) model of the monitored structure. Pointwise mass alterations of the structure can effectively improve the quantity and sensitivity of measured data, while the data fusion methods can adequately utilize various kinds of data and identification results. This paper proposes a damage identification method that requires only approximate FE models and combines the advantages of pointwise mass additions and data fusion. First, an additional mass is placed at different positions throughout the structure to collect the dynamic response and obtain the corresponding modal information. The resulting relation between natural frequencies and the position of the added mass is sensitive to local damage, and it is thus utilized to form a new objective function based on the modal assurance criterion (MAC) and l1-based sparsity promotion. The proposed objective function is mostly insensitive to global structural parameters, but remains sensitive to local damage. Several approximate FE models are then established and separately used to identify the damage of the structure, and then the Dempster-Shafer method of data fusion is applied to fuse the results from all the approximate models. Finally, fractional data fusion is proposed to combine the results according to the parametric probability distribution of the approximate FE models, which allows the natural weight of each approximate model to be determined for the fusion process. Such an approach circumvents the need for a precise FE model, which is usually not easy to obtain in real application, and thus enhances the practical applicability of the proposed method, while maintaining the damage identification accuracy. The proposed approach is verified numerically and experimentally. Numerical simulations of a simply supported beam and a long-span bridge confirm that it can be used for damage identification, including a single damage and multiple damages, with a high accuracy. Finally, an experiment of a cantilever beam is successfully performed.

Keywords:
structural health monitoring (SHM), damage identification, adding mass, data fusion, objective function, modal assurance criterion (MAC)

Abstract:
Adding virtual masses to a structure is an efficient way to generate a large number of natural frequencies for damage identification. The influence of a virtual mass can be expressed by Virtual Distortion Method (VDM) using the response measured by a sensor at the involved point. The proper placement of the virtual masses can improve the accuracy of damage identification, therefore the problem of their optimal placement is studied in this paper. Firstly, the damage sensitivity matrix of the structure with added virtual masses is built. The Volumetric Maximum Criterion of the sensitivity matrix is established to ensure the mutual independence of measurement points for the optimization of mass placement. Secondly, a method of sensitivity analysis and error analysis is proposed to determine the values of the virtual masses, and then an improved version of the Particle Swarm Optimization (PSO) algorithm is proposed for placement optimization of the virtual masses. Finally, the optimized placement is used to identify the damage of structures. The effectiveness of the proposed method is verified by a numerical simulation of a simply supported beam structure and a truss structure.

Keywords:
damage identification, sensor optimization, virtual distortion method (VDM), particle swarm optimization (PSO) algorithm, sensitivity