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2. IMPEDANCE METHODS WITH FEATURE EXTRACTION
The impedance-based health monitoring technique has been applied to a wide variety of structures as a promising tool
for real-time structural damage assessments (Park et al. 2000; Giurgiutiu et al., 2002; Park et al., 2003). The basic
concept of this technique is to monitor the variations in the structural mechanical impedance caused by the presence of
damage. Because mechanical impedance measurements can be difficult to obtain, the technique utilizes the electro-
mechanical coupling property of PZT. The PZT's electrical impedance is directly related to the mechanical impedance
and, hence, will also be affected by the presence of damage. In order to ensure high sensitivity to incipient damage, the
electrical impedance is measured at high frequencies (typically greater than 20 kHz), at which the wavelength of the
excitation is smaller than the characteristic length of the damage in a structure. A more detailed description of the
technique can be found in the references.
2.1. Impedance methods and linear feature extraction
In structural health monitoring, the process of feature extraction is required for the selection of the key information from
the measured data that distinguishes between a damaged and an undamaged structure. The extractions also accomplish
the condensation of large amount of available data into a much smaller data set that provides concise damage indication.
In impedance methods, damage sensitive features are traditionally employed with the use of a scalar damage metric. In 7
earlier work (Park et al 2000), simple statistical algorithm, which is based on frequency-by-frequency comparisons and ~
referred to as 'Root Mean Square Deviation' (RMSD) has been used,
M " [Re(Zr ,) - Re(Zigz )]2
i=1 [Re(Z )]2
where M represents the damage metric, Zij is the impedance of the PZT measured at healthy conditions, and Z,2 is the
impedance for the comparison with the baseline measurement at frequency interval i. In a RMSD damage metric chart,
the greater numerical value of the metric, the larger the difference between the baseline and the impedance measurement
of interest indicating the presence of damage in a structure.
Another scalar damage metric, referred to as the 'Cross-Correlation' metric, can also be used to interpret and quantify
information from different data sets. The correlation coefficient between two impedance data sets determines the linear
relationship between the two signatures
1 Z (Re(Z;,) - Re(Z,))(Re(Z,2) - Re(Z2))
n-1 sz s~z
where p is the correlation coefficient, Z1 and Zi2 are as described above, Z and 2 are the means of the signals and
the s terms are the standard deviations. For convenience, the feature examined in this case is typically (1- p); this is done
merely to ensure that with increasing damage or change in structural integrity, the metric values also increase. This
provides an aesthetic metric chart and is consistent with other metrics, such as RMSD, in which metric values increase
when there is an increase in damage. The cross-correlation metric account for vertical and horizontal shift of entire
impedance signature, usually associated with temperature changes. In most cases, the results with the correlation metric
are consistent with those of RMSD. Zagrai and Giurgiutiu (2001) investigate several statistics-based damage metrics,
including RMSD, mean absolute percentage deviation, covariance change, and correlation coefficient deviation. It has
been found that the third power of the correlation coefficient deviation, (1- p)3, is the most successful damage indicator,
which tends to linearly decrease as the crack in a thin plate moves away from the sensor.
2.2. Impedance methods and nonlinear feature extraction
The linear features described above are well suited to situations in which one structural state is to be discriminated from
another in a linear sense, but they would not be able to quantify any nonlinear changes. Because the frequency ranges of
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Chen, Bin; Lin, Jung-Fu; Chen, Jiuhua; Zhang, Hengzhong & Zeng, Qiaoshi. Synchrotron-based high-pressure research in materials science, article, June 1, 2016; (digital.library.unt.edu/ark:/67531/metadc927636/m1/3/: accessed January 18, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.