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Abstract:
In view of the demand for accurate modal identification, and based on the characteristics of free vibration response, this paper introduces a new window function for Fourier Transform called the Power–Exponential window. The Power–Exponential window addresses the characteristics of free vibration response. It significantly enhances the accuracy of modal identification by improving the spectral properties of structural response. The proposed window function consists of exponential and power terms. This study focuses on the additional damping and frequency-domain differentiation introduced by the Power–Exponential window function. The exponential term weakens the boundary effect related to the time-domain truncation and suppresses the spectral leakage. Moreover, it can be interpreted in clear physical terms as providing additional damping to the signal. The power term in the window function corresponds to frequency domain differentiation, and it alleviates the spectral broadening that arises due to the additional damping. Furthermore, the analytical expression for the response spectrum confirms that the Power–Exponential window not only aligns the peak response frequency with the damped natural frequency but also establishes an explicit linear relationship between the actual structural damping ratio and the identification result from the half power bandwidth method. Both contribute to an improved accuracy and usability of certain frequency-domain modal identification methods. The influence of the Power–Exponential window parameters on modal parameter identification is analyzed, and the optimal selection principle and suggested parameter values are proposed. Finally, numerical simulations and an experimental frame model test are conducted to verify the accuracy and validity of modal parameter identification based on the Power–Exponential window.

Keywords:
Modal identification, Window function, Frequency domain, Spectrum leakage, Fourier Transform (FT)

Abstract:
Many mode decomposition methods suffer from aliasing effects and modal distortion. This paper proposes a constrained mode decomposition (CMD) method that directly addresses these problems. The CMD is based on a linear combination of structural-free responses. The decomposed response is thus ensured to have a physical meaning and to satisfy the structural equation of motion, which improves the accuracy of mode decomposition and identification. The decomposition aim is to obtain a single-mode response. The CMD defines the corresponding natural frequency as the target frequency, while other natural frequencies are defined as constrained frequencies. The proposed method combines the measured physical responses in such a way that the constrained frequency components are selectively suppressed, while the amplitude of the target frequency component is selectively retained above a predefined level. The result is the intended single-mode free response, which can be used to clearly extract the corresponding modal parameters. For well-separated modes, the criterion for selective suppression is based on the fast Fourier transform (FFT) peak amplitude. For separation of closely spaced modes, a criterion based on FFT derivative is proposed to avoid modal distortion. The accuracy and applicability of the CMD method is tested in a numerical simulation and using a four-story lab frame structure. The experimental data are used to verify the effectiveness of the proposed CMD method and to compare it with two other widely used mode decomposition methods.

Keywords:
frequency-domain response, linear combination, mode decomposition, peak characteristics, structural health monitoring (SHM)

Abstract:
Damage identification methods based on structural modal parameters are influenced by the structure form, number of measuring sensors and noise, resulting in insufficient modal data and low damage identification accuracy. The additional virtual mass method introduced in this study is based on the virtual deformation method for deriving the frequency-domain response equation of the virtual structure and identify its mode to expand the modal information of the original structure. Based on the initial condition assumption that the structural damage was sparse, the damage identification method based on sparsity with l1 and l2 norm of the damage-factor variation and the orthogonal matching pursuit (OMP) method based on the l0 norm were introduced. According to the characteristics of the additional virtual mass method, an improved OMP method (IOMP) was developed to improve the localization of optimal solution determined using the OMP method and the damage substructure selection process, analyze the damage in the entire structure globally, and improve damage identification accuracy. The accuracy and robustness of each damage identification method for multi-damage scenario were analyzed and verified through simulation and experiment.

Keywords:
structural health monitoring (SHM), damage identification, virtual mass, sparse constraint, IOMP method

Abstract:
Damage identification for liquid–solid coupling structures remains a challenging topic due to the influence of liquid and the limitation of experimental conditions. Therefore, the adding mass method for damage identification is employed in this study. Adding mass to structures is an effective method for damage identification, as it can increase not only the experimental data but also the sensitivity of experimental modes to local damage. First, the fundamental theory of the adding mass method for damage identification is introduced. After that, the method of equating the liquid to the attached mass is proposed by considering the liquid–solid coupling. Finally, the effectiveness and reliability of damage identification, based on adding mass for liquid–solid coupling structures, are verified through experiments of a submerged cantilever beam and liquid storage tank.

Keywords:
structural health monitoring, damage identification, liquid-solid coupling, adding mass, sensitivity

Abstract:
This contribution presents, discusses and illustrates the constrained mode decomposition (CMD) method. The CMD is a recently proposed method that extracts single mode components from measured multimodal free structural responses. These components can be then processed, in time domain or in frequency domain, for identification of modal parameters, and ultimately, for structural health monitoring. The aim of the CMD is thus similar to the aims of other well-known mode decomposition approaches, such as the empirical mode decomposition (EMD) or the variational mode decomposition (VMD). However, in contrast to the EMD, the CMD-processed responses retain the characteristics of the free response (satisfy the equation of motion of the same structure) and they have thus a clear, well-defined physical meaning. In comparison to the VMD, the formulation of the CMD is much simpler: the CMD combines linearly recorded structural responses in a way that simultaneously (1) amplifies the selected modal component and (2) constrains/suppresses other components. The amplification/suppression process is quantified in terms of the FRF peaks or, in case of closely spaced modes, in terms of FRF derivatives.

Keywords:
mode decomposition, frequency domain, linear combination, FRF peak, structural health monitoring, modal identification