Vibration-Based Damage Features from Non-Parametric

Parametric Methods

1.3.3.1

Modal Parameters

Peak picking and the frequency domain decomposition (FDD) are two of the simplest methods employed for the identification of the modal parameters. In peak picking, the frequency response function (FRF) of the system is calculated and the peaks of the frequency spectrum are identified as the natural frequencies. Damping can be estimated by the half-power method, while the mode shapes are obtained from the amplitudes and phase angles for different degrees of freedom (DOFs). A disadvantage of peak picking is that the input of the system has to be measured in order to build the FRF. On the other hand, FDD is an output-only method that computes the power spectral density (PSD) of the signals and then applies singular value decomposition (SVD) to extract the natural frequencies and mode shapes. EFDD is an enhanced version of FDD which allows for the estimation of damping ratios. FDD assumes an independent white-noise input, i.e., constant PSD for the input. FDD was introduced in 2000 by Brincker et. al. and verified on a two-story building model [40]. In [41], FDD is employed to identify the modal parameters of a bridge.

Stiffness reduction due to damage causes decrease of the natural frequencies and changes in the mode shapes. Monitoring the changes of the identified mode shapes is among the most commonly used approaches for detecting damage in structures. In particular, mode shapes, curvature mode shapes and strain energy mode shapes are often used for damage localization. A disadvantage of these approaches is that a large number of sensors is required in order to capture the mode shapes. In [42], changes in curvature mode shapes are used for damage localization and are compared to displacement mode shapes.

Damping is also employed for damage detection. However, inaccuracies and er- rors are introduced during the estimation of damping values as well as in the definition of damping in the first place [43].

Another metric for damage identification, which belongs to the non-parametric approaches is the accumulated energy. Accumulated energy refers to the integral of power spectral densities over the measured frequency range. It serves as an indicator of energy distribution within a signal and takes into account changes in the entire frequency range instead of just single peaks. In [16], the mean frequency for 90-100% of accumulated energy of a single sensor is used as a damage feature for monitoring an offshore wind turbine.

system dynamics and exhibit sensitivity to structural changes, they also exhibit vari- ability to EOC changes. The variability of the natural frequencies and mode shapes of the Alamosa Canyon bridge, which are caused by EOC changes, are discussed in [44]. This work shows that changes in the enviromental and service conditions, such as thermal gradients and traffic loads, introduce significant variability of the modal parameters and suggest that the effect of these variability sources to the modal pa- rameters be quantified prior to the damage identification process. As a result, special attention has to be paid when employing the modal parameters as a damage indicator, in order to identify changes that are caused by effects other than damage.

1.3.3.2

Transmissibility Measures

Transmissibility functions are defined as the ratio between two response spectra. They are employed to extract damage-sensitive features, especially when the excitation of a structure is not available or cannot be measured. Johnson et. al. use auto- and cross- power spectral densities to compute the transmissibility functions between different degrees of freedom (DOFs) of the structure [45]. The transmissibilities are further normalized by computing their logarithms. Relative changes in both the transmis- sibility functions and their logarithms are computed for the baseline state and for the current datasets. Relative changes in all DOFs are then summed up to build a damage index for damage detection and localization on the example of the LANL three-story building. Furthermore, it is proven that the transmissibility functions are insensitive to nonlinearities at the structural boundaries as the operational conditions change. In [46], the ratio of two response spectra is used to build a transmissibility function and the difference between the transmissibility functions of different DOFs is used to calculate the system zeros and their properties. It is shown that the modal parameters of a system can be obtained from the suggested approach, i.e., by com- bining transmissibility measurements from different loading conditions. Devriendt et al. [46] employ the logarithm-related damage index of Johnson et al. [45] along with the comparison of transmissibility functions of different states to show that damage indicators based on transmissibility measurements can also be used for the challeng- ing case of changing loading conditions. In particular, this is achieved by considering small frequency bands around the resonance frequencies of the structure. Similarly, the ratio of frequency responses is used in [47] to detect and localize damage on a 40 m rotor blade. FRFs are used in [48] to build transmissibilities on a plate with stiffeners that simulates a metallic aircraft wingbox. The transmissibilities are eval- uated by three novelty detection algorithms: outlier analysis, density estimation and an auto-associative neural network (AANN).

1.3.3.3

Residues

Some direct ways for calculating residues for damage detection can be defined by the comparison of distances, FRF and frequency spectra. For example, in [49], FRFs

are compared for damage detection on a truss structure. Furthermore, in [24], the amplitude of FRF is used to build characteristic vectors, which are arranged in a matrix. Singular value decomposition (SVD) is used to obtain the matrix singular values and matrix rank, which are used to build a damage index. The residual nature of the damage index is due to the fact that the matrix rank is related to the undamaged structure.