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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

The electromechanical impedance (EMI) technique is considered to be one of the most promising methods for developing structural health monitoring (SHM) systems. This technique is simple to implement and uses small and inexpensive piezoelectric sensors. However, practical problems have hindered its application to real-world structures, and temperature effects have been cited in the literature as critical problems. In this paper, we present an experimental study of the effect of temperature on the electrical impedance of the piezoelectric sensors used in the EMI technique. We used 5H PZT (lead zirconate titanate) ceramic sensors, which are commonly used in the EMI technique. The experimental results showed that the temperature effects were strongly frequency-dependent, which may motivate future research in the SHM field.

Piezoelectric sensors have been intensively studied in recent years for an important and promising application, the structural health monitoring (SHM) of various types of structures, such as bridges and aircrafts. The main purpose of SHM systems is to monitor a structure and detect incipient damage, thereby increasing safety and reducing maintenance costs. Therefore, SHM systems are an important field of research from both scientific and industrial perspectives [

There are several nondestructive testing (NDT) methods [

This technique is simple to perform. When the sensor is bonded to the structure to be monitored, the piezoelectric effect produces an interaction between the mechanical impedance of the host structure and the electrical impedance of the sensor. Therefore, the mechanical condition of the host structure can be monitored simply by measuring and analyzing the electrical impedance of the piezoelectric sensor.

The EMI method has been studied for decades, and several studies [

This article is organized as follows: in Section 2, we introduce the basic principle of the EMI technique and discuss how structural damage is detected. A preliminary analysis of the temperature effects on the electrical impedance of the piezoelectric sensor is presented in Section 3. The experimental procedure for making measurements at different temperatures is presented in Section 4, and the experimental results are presented and discussed in Section 5. Finally, the paper ends with conclusions in Section 6 and a list of references.

In this section, we discuss the principle on which the EMI method is based and how structural damage is detected.

The EMI technique is based on the electromechanical interaction between the mechanical impedance of the structure to be monitored and the electrical impedance of the piezoelectric sensor that is bonded to the structure. The basic configuration is shown in

_{E}

The patch can be considered as a parallel plate capacitor, whereas the dielectric is a piezoelectric material. The excitation voltage produces an electric field, as well as a mechanical deformation, because of the piezoelectric effect. If the excitation signal voltage is sufficiently small, the piezoelectric effect is approximately linear. Using this consideration, the basic piezoelectric equations can be obtained from the Gibbs free energy [_{mβ}_{βm}_{mk}_{m}_{α}_{k}_{m}_{α}_{β}_{αβ}_{k}_{m}_{m}_{mk}

If we neglect the effect of the temperature and the magnetic field,

_{β}_{m}_{m}_{α}

Typically, the piezoelectric sensors used in the EMI method are very thin, with a thickness on the order of fraction of a millimeter. In this case, the deformation of the piezoelectric material in the direction of the thickness (_{E}_{0} is the static capacitance for a square patch of size _{T}_{S}_{31} is the piezoelectric constant, _{11} is the compliance at a constant electric field, ∥ indicates a parallel connection, and

_{E}_{S}

In the past, impedance measurements have been performed using commercial impedance analyzers, such as the 4192A and 4194A from Agilent Technologies (Santa Clara, CA, USA) and Hewlett-Packard (Palo Alto, CA, USA). These instruments provide highly accurate measurements but are expensive, slow and have many features that are not required in the EMI method. To overcome these drawbacks, several alternative measurement systems have been developed [

Basic damage characterization is accomplished using appropriate metric indices. The most widely used indices are the root mean square deviation (RMSD) and the correlation coefficient deviation metric (CCDM). These indices compare two electrical impedance signatures, where one of the signatures is acquired when the structure is considered to be healthy and is used as a reference, which is commonly called the baseline.

The RMSD index is based on a Euclidean norm [_{E,H}_{E,D}_{I}_{F}

The CCDM index is based on the correlation coefficient [_{C}_{EH}_{E,D}_{E,H}_{E,D}_{I}_{F}

The RMSD and CCDM indices exhibit different behaviors. The RMSD index is more sensitive to variations in the amplitude of the electrical impedance signatures. On the other hand, the CCDM index is more sensitive to changes in the shape of the signatures, such as frequency shifts. However, both indices are significantly affected by temperature variations. The effects of temperature on the electrical impedance of the sensor and the indices are analyzed in the next section.

The effect of the magnetic field can be safely neglected in most applications; however, the same is not true for temperature effects, because the piezoelectric sensors used in the EMI method are also significantly pyroelectric. Thus, temperature changes cause corresponding variations in the electrical impedance of the sensor. Therefore, the temperature can be determined by measuring the electrical impedance of the piezoelectric sensors [

Damage detection is accomplished by comparing two electrical impedance signatures that are obtained at different times: therefore, temperature changes cause variations in the RMSD index. Consequently, the RMSD index can be high even for a healthy structure, leading to a false positive diagnosis.

On the other hand, the CCDM index is insensitive to variations in the amplitude of the electrical impedance and is only sensitive to variations in the shape of the impedance signature. Therefore, if we only consider variations in the amplitude of the electrical impedance resulting from temperature changes, the CCDM index would be a good option for avoiding false diagnoses of the monitored structure from temperature effects. However, the natural frequencies (

Several methods have been developed to compensate for temperature variations. Lim

Bastani

Therefore, the techniques presented above are particularly appropriate and efficient for specific applications and conditions. Simple techniques for general applications can be obtained using modified versions of RMSD and CCDM metric indices. Sun

Although the EFS method is simple, its efficiency decreases if a wide frequency band is used to compute the damage metric indices. The experimental results in this paper show that the frequency shift is not constant, but increases with the excitation frequency, requiring narrow frequency band.

To investigate how temperature affects the sensor impedance signatures, we performed several experiments with an aluminum beam with dimensions of 500 mm × 38 mm × 3 mm and a mass of 179.552 g. A 5H PZT patch with dimensions of 15 mm × 15 mm × 0.267 mm was bonded approximately 30 mm from the end of the specimen using cyanoacrylate glue appropriate for high temperatures.

Structural damage of different intensities was induced in the structure by placing a small nail-head (representing a low damage level) with dimensions of 2 mm × 1 mm and a mass of 0.029 g, a medium steel nut (representing a medium damage level) with dimensions of 5 mm × 2 mm and a mass of 0.312 g, and a large nut (representing a large damage level) with dimensions of 8 mm × 4 mm and a mass of 0.988 g, all at a distance center-to-center of 100 mm from the sensor. The mass loadings of the monitored structure were approximately 0.016%, 0.17%, and 0.5%, respectively, for the low, medium and large damage levels. The mass loading produced variations in the mechanical impedance of the structure and could consequently be related to the structural damage.

The measurement of the electrical impedance of the sensor was performed using a system [

In addition to measuring the electrical impedance, we measured the capacitance of the PZT patch over the same temperature range. _{0}. Thus, it was important to check how the capacitance varied with the temperature. The capacitance was measured with a simple multimeter.

All the measurements were obtained by supporting the specimen on its ends using rubber blocks on a desk.

We have organized the results into three sections. In the first section, we estimate the sensitivity of the system to detect structural damage by calculating the RMSD and CCDM indices for damage with different intensities induced in the aluminum beam. Next, the effects of the temperature on the electrical impedance signatures of the sensor are analyzed in detail. Finally, in the last section, the frequency shifts in the electrical impedance signatures are compensated for by maximizing the correlation coefficient, where we verify that the efficiency of this method decreases as the frequency band increases.

The structural damage was quantified by calculating the RMSD and CCDM indices in an appropriate frequency band. As is well known, frequencies below 100 kHz, particularly in the 0–50 kHz band, produce higher damage indices than other frequency bands. These results have been theoretically and experimentally analyzed in previous studies [

Therefore, the RMSD and CCDM indices were calculated over a 16–40 kHz frequency band and reasonable results were obtained, such that _{I}_{F}

The identification and quantification of damage was simply evaluated using the RMSD and CCDM indices calculated in

The results showed that the system exhibited a high sensitivity for detecting structural damage. Although the nail-head induced a low damage level (

These results are important for estimating the sensitivity of the system to detect damage as well for identifying parameters to evaluate the potential of false positive diagnoses of structural health from temperature effects. Temperature effects are analyzed in the next section.

We performed experiments for temperatures ranging from 25 °C to 102 °C.

The figures show decreases in the amplitude and frequency shifts of the real part, the imaginary part and the magnitude of the impedance signatures. These variations can be analyzed in detail by choosing narrower frequency bands.

The three resonance peaks clearly exhibited left frequency shifts as the temperature increased. However, these shifts were not constant at a given temperature but increased with the frequency of the resonance peak. Therefore, the frequency shifts depended on both the temperature and the frequency. The figures show that increasing the temperature from 25 °C to 102 °C produced a frequency shift of Δ

In addition, the real part, the imaginary part, and the magnitude of the impedance signatures exhibited the same resonance peaks and frequency shifts, although the peaks were more prominent for the real part and resulted in higher damage indices, as shown in

All the frequency shifts (Δ

In addition to being dependent on the temperature, the left frequency shift (

For frequencies above 200 kHz, deformations in the impedance signatures were observed, especially at high temperatures. There were no significant resonance peaks at frequencies below 2 kHz that could enable the frequency shifts to be accurately estimated.

In addition to the frequency shifts in the impedance signatures, variations in the amplitude of the impedance signatures were also observed. _{0}. Therefore, it was important to analyze the variation of the capacitance with temperature.

As previously mentioned, the EFS is a very simple method of compensating for temperature effects, which can be applied to a wide variety of structures under diverse conditions. This method consists of shifting the current impedance signature (after temperature variation) relative to the baseline (reference) impedance signature to maximize the correlation coefficient.

Therefore, before computing the CCDM index, the current impedance signature _{E,D}_{C}_{C}_{f}_{f}_{C}

On the other hand, the impedance signature for a decrease in the temperature must be shifted to the left, as shown below:

Despite the simplicity and feasibility of this approach for a wide variety of structures, the results are only satisfactory if a narrow frequency band (_{I}_{F}_{E,D}_{E,H}

For example,

Consequently, the poor match between the two impedance signatures resulted in a low correlation coefficient. Thus, the maximum correlation coefficient (_{C}_{I}_{F}

The maximum correlation coefficient clearly decreased as both the temperature and frequency band increased. For example, for a narrow frequency band of 2 kHz (_{I}_{F}_{I}_{F}

_{I}_{F}

These results show that a frequency band must be sufficiently narrow for the frequency shift method to effectively compensate for temperature effects and to avoid false positive diagnoses, particularly for detecting low damage levels. On the other hand, wider frequency bands may include more resonance peaks and, consequently, increase the sensitivity of the system to detect structural damage, especially incipient damage. Therefore, the width of the frequency band is a critical issue for compensation techniques based on the frequency shift.

In this study, we investigated the effect of temperature on the electrical impedance signatures of a conventional 5H PZT sensor used in structural health monitoring. The variations in both the amplitude and the frequency were analyzed experimentally by using an aluminum specimen and obtaining impedance signatures at temperatures ranging from 25 °C to 102 °C.

The experimental results showed that the variations in the amplitude of the impedance signatures were related to the temperature-dependence of the capacitance of the piezoelectric sensor. In addition, the frequency shifts of the resonance peaks that resulted from temperature variations were not constant over the entire frequency range but increased with the frequency. Thus, the frequency band used to calculate the damage indices played an important role in compensating for temperature effects by maximizing the correlation coefficient. The results showed that a sufficiently narrow frequency band must be used to avoid a false positive diagnosis of the monitored structure.

Therefore, temperature effects are a critical problem for structural health monitoring based on electromechanical impedance, especially in detecting low damage levels, and efficient compensatory methods for temperature effects remain to be developed.

The authors would like to thank FAPESP–Sao Paulo Research Foundation (grants 2012/10825-4 and 2013/02600-5) and PROPe-UNESP for financial support and the anonymous reviewers for their contributions to the review process.

The authors declare no conflict of interest.

Underlying principle of the EMI method.

Variations in the amplitude and frequency shifts in real part of the electrical impedance resulting from temperature changes.

Aluminum beam with the PZT patch and damage of different intensities.

Experimental configuration.

Variation in (

Normalized (

Real part of the impedance signatures obtained at different temperatures.

Imaginary part of the impedance signatures obtained at different temperatures.

Magnitude of the impedance signatures obtained at different temperatures.

Frequency shifts of the real part of the impedance signatures for resonance peaks at (

Frequency shifts of the imaginary part of the impedance signatures for resonance peaks at (

Frequency shifts of the magnitude of the impedance signatures for resonance peaks at (

Frequency shift (Δ

Capacitance as a function of the temperature.

(

(

Maximum correlation coefficients obtained using the compensation method.

Normalized CCDM indices obtained for the healthy structure after compensating for temperature effects.

Frequency shifts (Δ

| |||||||||||||
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−18 | −30 | −36 | −46 | −56 | −70 | −84 | −92 | −106 | −120 | −134 | |||

−50 | −100 | −120 | −160 | −190 | −230 | −300 | −320 | −370 | −410 | −450 | |||

−400 | −700 | −1,100 | −1,300 | −1,500 | −1,900 | −2,500 | −2,900 | −3,300 | −3,800 | −4,300 |