Piezoelectric Transducers Applied in Structural Health Monitoring: Data Acquisition and Virtual Instrumentation for Electromechanical Impedance Technique

There is a growing interest in systems able to continuously monitor a structure and timely detect incipient damage, ensuring a high level of safety and reducing maintenance costs. This concept is commonly known as Structural Health Monitoring (SHM) in the literature. Many techniques can be used to develop SHM systems, but the electromechanical impedance (EMI) technique has the advantage of using small and very thin piezoelectric patches, with thickness on the order of a few tenths of millimeters. Thus, these devices are like adhesives bonded to the monitored structure, allowing a large area of the structure to be monitored with negligible effects on its mechanical properties. Due to the piezoelectric effect, when a piezoelectric transducer is bonded to the structure to me monitored, there is an interaction between the mechanical impedance of the host structure and the electrical impedance of the transducer. Therefore, changes in the mechanical impedance of the host structure caused by damage, such as cracks or corrosions, can be detected simply by measuring the electrical impedance of the transducer in a suitable frequency range, which is easier to measure than the mechanical impedance.

Among the various fields of application, we can cite the large civil infrastructures (bridges, buildings, roads, oil rigs, etc.), the aeronautical and aerospace structures (aircraft, helicopters, satellites, space stations, etc.), and large marine structures (submarines and ships).There are both scientific and economic motivations for the use of an SHM system.From the scientific point of view, the monitoring and detection of structural damage mean to achieve a high level of safety.From the economic point of view, systems with this capability allow a significant reduction in maintenance costs.For example, Cawley (1997) suggested the use of an SHM system to identify corrosion in pipelines of chemical and petrochemical industries, in which the costs associated with the removal of these pipelines for inspection is prohibitive.The Federal Highway Administration estimates that nearly 35% of all bridges in the United States are either structurally or functionally deficient (Wang et al., 1997).The cost of repair or rebuilding lies in the billions of dollars Therefore, SHM systems could reduce this cost while providing high level of safety for users during repair or assessment.
Currently, the aviation industry is one of most focused fields of application.Although the design and criterions for certification of an aircraft already guarantee a high level of security, an SHM system could significantly reduce the repair and maintenance costs, which represent 27% of the cost of its life cycle (Kessler et al., 2002).The direct costs related to the repair could be reduced by detecting damage in an early stage.In addition, the indirect costs could be reduced by a lower frequency at which the aircraft would be shut down for maintenance.
The definition of damage is important in SHM systems.Damage is any change in the structure that may affect its performance and safety.Implicit in this definition is the concept that damage detection is based on the comparison between two states of the structure.In a first state, the structure is considered healthy and it is used as a reference for comparison with an updated state after a probable occurrence of damage.Damage such as cracks and corrosion can change various properties of the monitored structure as, for example, mass, www.intechopen.comPiezoelectric Transducers Applied in Structural Health Monitoring: Data Acquisition and Virtual Instrumentation for Electromechanical Impedance Technique 107 stiffness, energy dissipation, mechanical impedance and its cross-section area.In addition, these changes alter the dynamic properties of the structure.From this concept, there are the techniques based on the frequency response function (FRF).In these techniques, the data for the evaluation of the structure are collected while the structure is in dynamic condition using one of two methods: ambient excitation and forced-excitation.In the ambient excitation, the vibration produced by the structure during its normal operation is utilized.The vibration of a bridge due to the vehicular traffic is an example of ambient excitation.On the other hand, the forced-excitation is controlled using actuators, such as shakers and piezoelectric transducers.
There are many techniques for developing SHM systems.Several techniques are based on non-destructive evaluation (NDE) methods, such as acoustic emission, comparative vacuum, magnetic particle inspection, Eddy current, and methods based on optical fibre sensors.In this chapter, we aim to analyze the electromechanical impedance (EMI) technique, which is a method based on forced-excitation.In this technique, low-cost and thin piezoelectric patches are bonded to the host structure and combine both the functions of actuator and sensor.The EMI technique is presented in the next section.

Basic concept
The EMI technique is a form of nondestructive evaluation based on the FRF which has the advantages of its simplicity and using thin and low-cost piezoelectric transducers.The most widely used piezoelectric transducers are the PZT (Pb-lead Zirconate Titanate) ceramics and MFC (Macro-Fiber Composite), which have thickness on the order of a few tenths of millimeters.These characteristics make the EMI technique especially attractive for the monitoring of aircraft structures, which is one of the most prominent application fields nowadays.The EMI technique is the only PZT-based technique that has characteristics for the development of a real-time and in-situ SHM system in aircrafts (Gyekenyesi et al., 2005).These devices are bonded to the structure to be monitored through a high-strength adhesive that can be instantaneous glue based on cyanoacrylate or epoxy resin.Due to the piezoelectric effect, there is a relationship between the mechanical properties of the structure and the electrical impedance of the transducer.Therefore, it is possible to monitor variations in these mechanical properties by measuring the electrical impedance.For example, Figure 1 shows a PZT patch from Piezo Systems bonded to an aluminum beam.Fig. 1.A PZT patch bonded to an aluminum beam for damage detection.
In Figure 1, both sides of the PZT ceramic are coated by a thin metal layer, where wires are soldered to connection.Through these wires, the patch is excited and, simultaneously, its electrical impedance is measured in an appropriate frequency range.As a result, these ceramics combine the functions of sensor (direct piezoelectric effect) and actuator (reverse piezoelectric effect.
In order to obtain the relationship between the electrical impedance of the transducer and the mechanical impedance of the structure, we should analyze the wave propagation in the structure when the transducer is excited.For this analysis we consider the representation of a square PZT patch bonded to a host structure, as shown in Figure 2. Fig. 2. Principle of the EMI technique; a square PZT patch is bonded to the structure to be monitored.
In Figure 2, a square PZT patch with side  and thickness t is bonded to a rectangular structure with cross-sectional area S A , which is perpendicular to the direction of its length.An alternating voltage U is applied to the transducer through the bottom and top electrodes, and the response is a current with intensity I.If the PZT patch has small thickness, a wave propagating at velocity a v in the host structure reaches the patch side with coordinate a x and surface area T A causing the force a F .Similarly, in the side of coordinate b x there is a force b F due to the incoming wave propagating at velocity b v .
To find an equivalent circuit that represents the behavior of the PZT patch bonded to the structure, we need to determine the relationship between the mechanical quantities ) and the electrical quantities (U, I), as shown in the next section.

Theoretical analysis
The theory developed in this section is based on analysis presented by Royer & Dieulesaint (2000).
As the thickness of the transducer is much smaller than the other dimensions, the deformation in its thickness direction (z-axis) due to the applied electric field is negligible.In general, for PZT patches of 5A and 5H type with thickness ranging from 0.1 to 0.3 mm, the deformation in the thickness direction is on the order of nanometers.On the other hand, the deformations in the sides  (transverse direction) are on the order of micrometers.Therefore, the vibration mode is predominantly transverse to the direction of the applied electric field.In addition, if the applied voltage U is low in the order of a few volts and hence the resultant electric field is also low, the piezoelectric effect is predominantly linear and the non-linearities can be neglected.From this assumption and considering the class 6mm for PZT ceramics (Meitzler, 1987), the basic piezoelectric equations for this case are given by Although the transducer is square and the deformations in both sides are approximately the same, only the deformation along the length of the structure is considered for the onedimensional (1D) assumption.Thus, the main propagation direction is considered along the length direction (x-axis) perpendicular to the cross-section area S A of the host structure, as shown in Figure 2. Therefore, for 1-D assumption, it is correct to consider 2 T = 3 T = 2 S = 0. Hence, the Equations ( 1) to (3) can be rewritten as follows The patch is essentially a capacitor.Thus, due to the voltage source, there is a charge density ( e  ) on the electrodes of the patch and according to the Poisson equation we have This results in a current of intensity C jt Ie  .If the current is uniform over the entire area of the electrodes, the charge conservation requires where   Jt is the current density and E A is the area of each electrode.
It is appropriate to put the stress 1 T in function of the electric displacement 3 D .So, from Equation (5) and considering the following relation where x u is the displacement in the x direction, we can obtain where T  is the mass density of the piezoelectric material.The general solution for Equation ( 13) is the sum of two waves propagating in opposite directions, as shown in Figure 2. In steady state, we have where m and n are constants and k is the wave number given by where V is the velocity of propagation given by 11 1 Substituting the velocity given in Equation ( 14) into the stress in Equation ( 12) and integrating with respect to time, we have The forces acting on each face of the transducer can be calculated by 1 () Thus, replacing Equation (20) into Equations ( 21) and ( 22) and considering the mechanical impedance of the transducer given by 11  26) and ( 27) can be computed as follows 2( ) Replacing Equations ( 28) and ( 29) into Equations ( 24) and ( 25) and considering the trigonometric identify , the expressions for the forces a F and b F can be rewritten as We need to determine the total current, which is the response of the transducer due to changes in the mechanical properties of the monitored structure.The total current can be obtained from the electric displacement.
The electric displacement in Equation ( 4) can be rewritten as The electric charge Q can be obtained from the electric displacement integrating Equation ( 32) with respect to area of the electrodes Since the PZT patch is very thin, the electric field is practically constant in the z-axis direction and it can be calculated as follows In addition, the static capacitance 0 C of the patch is given by Substituting Equations ( 34) and ( 35) into Equation ( 33), we obtain From Equations ( 38) and ( 39) we obtain According to Equation ( 40), besides the current C I due to the capacitance 0 C , there is a current related to the velocities a v and b v .
Thus, the voltage U at the terminals of the transducer is given by Or we can also write Finally, equations ( 30), ( 31) and ( 42) can be rewritten in matrix form, as follows The matrix in Equation ( 43) is known as the electromechanical impedance matrix and defines the piezoelectric transducer as a hexapole, as shown in Figure 3.According to Figure 3, the transducer is represented by a hexapole with one electrical port and two acoustic ports.Therefore, there is an electromechanical coupling with the monitored structure.Through the acoustic ports the structure is excited so that the dynamic properties can be assessed.Any variation in the dynamic properties of the structure caused by damage changes the mechanical quantities ( a F , b F , a v , b v ) and, due to the electromechanical coupling, also changes the electrical quantities (U, I).Therefore, the structural health can be monitored by measuring the current ( T I ) and voltage (U) of the transducer.
In practice, the electrical impedance of the transducer is measured.The electrical impedance ( E Z ) of the transducer is given by Thus, it is useful to find an equivalent electromechanical circuit that relates the electrical impedance of the transducer to the mechanical properties of the structure.The equivalent circuit is presented in the next section.

Equivalent electromechanical circuit
An electromechanical circuit makes it easy to analyze the electrical impedance of the transducer in relation to the dynamic properties of the structure, which are directly related to its mechanical impedance.Thus, we should obtain a circuit that establishes a relationship between the electrical impedance of the transducer and the mechanical impedance of the host structure.
Given the following trigonometric identify  11 tan tan( ) 2 And considering the following manipulation We can rewrite Equations ( 30) and (31) as follows From Equations ( 41), ( 42), (47), and (48), we can easily obtain the circuit shown in Figure 4 (a).The mechanical and electrical quantities are related through the electromechanical transformer with ratio (TR) given by The circuit in Figure 4 (a) is not suitable for analysis of structural damage detection because it does not consider the monitored structure as a propagation media in each acoustic port of the transducer.Both the sides of the circuit, which corresponds to the acoustic ports, must be loaded by the mechanical impedance of the structure, as shown in Figure 4 (b).
The mechanical impedance ( S Z ) is given by (Kossoff, 1966) 22 11 where S  is the mass density of the structure, S A is the cross-sectional area of the structure, as shown in Figure 2, orthogonal to the wave propagating at velocity v and  is the damping, i.e., the loss factor in nepers.
According to Equation ( 51), there is a relationship between the mechanical impedance of the monitored structure and the electrical impedance of the piezoelectric transducer.Changes in the mechanical impedance of the structure due to damage result in a corresponding change in the electrical impedance of the transducer.Therefore, structural damage can be characterized by measuring the electrical impedance in an appropriate frequency range.This is the basic principle of damage detection discussed in the next section.

Damage detection
The comparison between the electrical impedance signatures of a PZT transducer unbonded and bonded to an aluminum beam in a frequency range of 10-40 kHz is shown in Figure 5.
When the transducer is bonded to the structure, several peaks are observed in both the real part and the imaginary part signatures.Usually, the characterization of damage is performed through metric indices by comparing two impedance signatures, where one of these is previously acquired when the structure is considered healthy and used as reference, commonly called the baseline.Thus, the electrical impedance is repetitively acquired and compared with the baseline signature.
Various indices have been proposed in the literature for damage detection, but the most widely used is the root mean square deviation (RMSD) which is based on Euclidian norm (Giurgiutiu & Rogers, 1998).Some changes in this index have been suggested by several researchers.One of the most used is given by    and M is the total number of frequency components, which is related to the frequency resolution of the measurement system.
The index in Equation ( 52) should be calculated within an appropriate frequency range, which provides good sensitivity for damage detection.Generally, the suitable frequency range is selected experimentally by trial and error methods, but recently some researchers have proposed more efficient methodologies (Peairs et al., 2007;Baptista & Vieira Filho, 2010).In addition to selecting the appropriate frequency range, it is essential that the measurement system has a good sensitivity and repeatability to avoid either false negative or false positive diagnosis in detecting damage.The measurement systems based on virtual instrumentation are presented in the next section.

Electrical impedance measurement
Normally, the measurement of the electrical impedance, which is the basic stage of the EMI technique, is performed by commercial impedance analyzers such as the 4192A and 4294A from Hewlett Packard / Agilent, for example.Besides the high costs, these instruments are slow, making it difficult to use the technique in real-world applications, where it is required to use multiple sensors and to diagnose the structure in real-time.The conventional impedance analyzers use a pure sinusoidal wave at each frequency step, making a stepwise measurement under steady-state condition within an appropriate frequency range.Based on this principle, many researchers have developed alternative and low-cost systems for general impedance measurements.Usually, these systems are based on the volt-ampere method (Ramos et al., 2009) where the sinusoidal signal at each frequency step is supplied by a function generator or a direct digital synthesizer -DDS (Radil et al., 2008).
Steady-state measurement systems for specific applications in SHM have also been proposed.In the system proposed by Panigrahi et al. (2010), a function generator was used to excite gradually the piezoelectric transducer with pure sinusoidal signals at each frequency step and an oscilloscope was employed to measure the output response at each excitation frequency.This system is an improvement from a previous work developed by Peairs et al., (2004) where a fast Fourier transform (FFT) analyzer was used to obtain the electrical impedance in the frequency domain.Recently, Analog Devices developed a miniaturized high precision impedance converter, which includes a frequency generator, a DDS core, analog-to-digital converter (ADC) and digital-to-analog converter (DAC), a digital-signal-processor (DSP) integrated in a single chip (AD5933).This chip is used with a microcontroller and other required devices and can provide electrical impedance measurements with high accuracy.This chip has been used in SHM to develop compact and low-cost measurement systems.These new systems support wireless communication and several sensors through analog multiplexer, and can process data locally (Min et al., 2010;Park et al., 2009).
Although steady-state measurement systems provide results with high accuracy, the measurements usually take a long time because the frequency of the pure sinusoidal signal should be gradually increased step-by-step within the suitable range for damage detection.The time consumption may be very significant if a wide frequency range with many steps is required.Accordingly, in these new portable systems a wide frequency range with a narrow frequency step demands a large amount of data that can be difficult to be stored and processed locally or transmitted in a wireless mode.Moreover, these systems are difficult to assemble or require specific evaluation boards, which make them attractive mainly for specific SHM applications.For research and general applications, a simpler system should be developed.
We can design fast and easy to assemble measurement systems if the piezoelectric transducer is excited with a sweep signal and using virtual instrumentation.The concept of virtual instrumentation is shown in Figure 6.The virtual instrumentation presented in this chapter is mainly based on LabVIEW (Laboratory Virtual Instrument Engineering Workbench), a graphical programming environment from National Instruments.However, other programming platforms can be used, such as Matlab from Mathworks that provides tools for data acquisition and is commonly found in research laboratories.
A basic LabVIEW program for signal acquisition and generation using a DAQ device is shown in Figure 7.The program sets through virtual channels the analog output (AO) and the analog input (AI) used for the excitation of the transducer and the acquisition of the corresponding response signal, respectively.The excitation is performed by a linear chirp signal, which makes a sweep from an initial frequency to a final frequency.The synchronization between the signal generation and acquisition is essential to ensure excellent repeatability between the measurements, which is an important feature in SHM to avoid incorrect diagnosis.The loop structure allows various cycles of excitation and response in applications where is required an average between the measurements for high accuracy.
The characterization of damage can be carried out by analyzing the electrical impedance signatures in the frequency domain or directly the response signal from the transducer in the time domain, as presented in the next sections.

Frequency domain analysis
The analysis in the frequency domain is the usual way to characterize damage and it is usually based on the FRF, as mentioned in the Section 2. The FRF is obtained from the excitation and response signals considered as input and output, respectively, of the system under test containing the structure and the transducer.Thus, from the FRF, we can calculate the electrical impedance in an appropriate frequency range.
The measurement system proposed by Baptista & Vieira Filho (2009) is based on the concept shown in Figure 6 and uses a low-cost DAQ device with maximum sampling rate of 250 kS/s, limiting the impedance measurement up to 125 kHz, limiting the impedance measurement up to frequency of 125 kHz, although other devices with higher sampling rate can be used without significant changes in the software.The software was developed in LabVIEW with the basic configuration shown in Figure 7.Besides the software, the hardware is very simple and uses only a common resistor in addition to DAQ device to connect the transducer.The system diagram is shown in Figure 8.
where the resistor S R is a current limiter, r is the resistance of the cable used to connect the DAQ device and the PZT sensor, and in Z is the input impedance of the DAQ device and n is de frequency of the chirp signal ranging from an initial low value to a final high value as defined in the basic program shown in Figure 7.
This system was tested in a PZT transducer bonded to an aluminum beam and the results were compared with the measurements obtained using a conventional impedance analyzer 4192A from Hewlett Packard.The comparison between the two electrical impedance signatures in a frequency range of 30-50 kHz is shown in Figure 9.The similarity between the two signatures indicates the accuracy and feasibility of the system based on virtual instrumentation.The discrepancy between the two measures is less than 4%.Besides the good accuracy, the measurement system provides fast measurements, versatility and lowcost compared to the conventional impedance analyzers.
Improvements such as multiple sensors and real-time diagnosis can be easily included.The system diagram shown in Figure 10 has these features (Baptista et al., 2011).As in the    (Baptista et al., 2011).
Typically, the output impedance R out is very low on the order of tenths of Ohm.If the resistances R L are much higher than the output impedance, i.e., R L >> R out , the excitation signal x(t) in the analog output of the DAQ device can be considered constant in relation to the variations in the electrical impedance of the sensors.Consequently, any mutual interference between the acquisition channels can be neglected and the variations in the response signals y 1 (t), y 2 (t), …, y n (t) from each sensor are caused only by the mechanical properties of the host structure or other environmental conditions.The piezoelectric transducers, especially those made of thin PZT ceramics, require low voltage and low current for the excitation signal, so that the piezoelectric effect is linear (Sun et al., 1995;Baptista et al., 2010).Thus, the resistance R L may be on the order of some thousands of Ohm and the condition R L >> R out is easily satisfied.
As in the previous system, the software was implemented in LabVIEW. Figure 11 shows a user-friendly interface that allows the adjustment of the parameters of the signal generation and signal acquisition.A display shows the baseline and the current impedance signatures of the selected sensor and vertical bars indicate the level of damage.In addition, a panel displays a 3D model of the host structure, a LabVIEW tool known as sensor mapping.In this 3D model, virtual sensors are placed in the same positions that they have in the real-world structure, changing the color of the model according to the intensity and in the regions indicated by the metric indices.This feature gives a reasonable suggestion of the damage location, especially in large structures with many sensors.Note instead of the RMDD index, it was used the CCDM index, which is based on the correlation coefficient.Fig. 11.User-friendly interface of the measurement system (Baptista et al., 2011).
The system was evaluated in an aluminum plate with nine transducers and the DAQ device used was the model USB-6259 from National Instruments.This model has 16 differential analog inputs and a maximum sampling rate of 1.00 MS/s in the aggregated mode.Thus, for the acquisition of the signals from the nine sensors the sampling rate was set to 110 kS/s with 32768 samples.The results show conclusively that the system has good repeatability, sensitivity to detect damage and provides fast measurements.For this configuration, the measurement of the nine sensors and the presentation of the results are completed in less than 2 seconds in a PC laptop with medium performance.
The systems presented previously are based on the FRF, where structural damage is detected by analyzing the electrical impedance signatures in the frequency domain.However, the characterization of damage can be performed in a simpler method directly in the time domain, as discussed in the next section.

Time domain analysis
In this section, we show that the time response of a piezoelectric transducer provides information on the electromechanical impedance variation when a monitored structure is damaged (Vieira Filho et al., 2011).The time domain approach changes the paradigm of SHM systems based on EMI and the results are similar to those obtained using electrical impedance measurements in the frequency domain.The efficiency of the time domain approach was demonstrated through experiments using an aluminum plate.The results using both the FRF and the time response were obtained and compared.
In the time domain approach, the analysis of only the time response y(t) of the transducer using the system presented in Figure 8 is sufficient to detect damage.From Figure 8, the time response of the transducer y(t) in relation to the excitation signal x(t) can be obtained through an inverse Fourier or Laplace transform according to the following equation where E Z is the electrical impedance of the transducer.
From a practical point of view, the inverse transform is not necessary because the time response is directly obtained.However, the response signal y(t) changes according to the electrical impedance E Z and the input signal x(t).Considering an input signal with constant amplitude and frequency, the response signal y(t) will change only if the electrical impedance E Z changes, which according to Equation (51) occurs when the structure suffers any type of damage and its mechanical impedance S Z changes .In this case, the signal y(t) could be directly related to the health condition of the monitored structure.If x(t) is a pure sine wave signal with peak amplitude V px and fixed frequency ω x , it can be shown (Radil et al., 2008) that the approximate magnitude of the electrical impedance E Z is given by where V py represents the amplitude peak of the response signal y(t).
For a complete characterization of E Z , it is possible to compute both the real and the imaginary parts.This is quite direct if the phase difference between x(t) and y(t) is known.124 However, the magnitude of the impedance might assure good sensitivity as well and this will be shown in the example results.So, considering a constant peak value of x(t), the response y(t) will be modified according to any variation of E Z , which affirms that y(t) is function of E Z .This approach is enough to detect damage because it is sensitive to any structural change.Furthermore, an efficient SHM method based on the EMI does not have to measure the electrical impedance itself, but just measure its variation.This new methodology is called here the time electrical impedance (TEI).
An experiment using an aluminum plate of 500 x 300 x 2 mm with four PZT transducers was carried out to validate the TEI method (Vieira Filho et al., 2011).Figure 12 presents the time response signal y(t) in both healthy and damage conditions.We can observe that both responses are close.However, a significant difference can be observed if a subtraction between time responses (y b [n]-y m [n]) is carried out, where y b is the baseline, y m is the updated time response and n is the sample.This operation was carried out first between the baseline and the time response in the healthy condition and then between the baseline and the time response in the damaged condition.The results are presented in Figure 13 and they show that this operation gives suitable information on the structure's condition.As a result, it is expected that these differences could be detected using metric indices, such as RMSD.
The TEI method was implemented and the results were compared to the ones obtained using the traditional EMI based on the FRF.Thus, the RMSD values were obtained for both TEI and FRF.It is important to observe that although the absolute values of the indices are not the best method for comparing the results, they are interesting for the purpose of evaluating each method separately.However, since the goal is to compare TEI and FRF, the indices are presented using the ones obtained in healthy condition as reference (called normalized here).Figure 14    Therefore, the results indicate conclusively that the characterization of damage in the time domain is feasible and has excellent sensitivity.Since the analysis is carried out directly from the time response signal and it is not required to compute the DFT, the TEI is simpler than the conventional EMI method.

Conclusion
In this chapter, we have presented the basic principle of the electromechanical impedance technique for detecting damage in structural health monitoring.The measurement of the electrical impedance of piezoelectric transducers, which is the basic stage of the technique, was addressed focusing the virtual instrumentation.The analysis in the frequency domain and the time domain were presented.The experimental results show conclusively that the measurement systems based on virtual instrumentation are feasible and efficient for both methods of analysis.
It is important to note that the equivalent electromechanical circuit and the experimental results presented here were obtained for the PZT ceramics.However, these ceramics are brittle and in some applications it is advantageous to use MFC transducers, which are more flexible.In addition, the electromechanical impedance signatures are significantly sensitive to temperature variations.Therefore, the measurements systems should include some compensation method to correct the changes in the impedance signatures for practical applications under temperature variations.

(
ba xx   , as shown in Figure2, the terms m and n in Equations (

Fig. 3 .
Fig. 3. Piezoelectric transducers can be represented as a hexapole with one electrical port and two acoustic ports.

Fig. 4 .
Fig. 4. (a) Piezoelectric transducer represented by an equivalent electromechanical circuit and (b) both acoustic ports loaded by the mechanical impedance of the host structure.Analyzing the circuit in Figure 4 (b), we can obtain the equivalent electrical impedance between the terminals of the transducer, which is given by

Fig. 5 .
Fig. 5. Real part and imaginary part of the electrical impedance signatures in a frequency range of 10-40 kHz for a PZT transducer unbonded and bonded to an aluminum beam.These peaks are related to the natural frequencies of the monitored structure.Changes in the natural frequencies either in frequency shifts or variations in the amplitude may indicate structural damage. 117

Fig. 6 .
Fig. 6.Data acquisition and virtual instrumentation for structural health monitoring based on EMI methods.The hardware consists mainly of ADC and DAC converters, multiplexer and bus interface, generally integrated into a single data acquisition (DAQ) device.The DAC generates the excitation signal in a frequency range selected by the user.The response signal of the transducer with information related to the structural health is acquired by the ADC, which must have a sampling rate of at least twice the maximum frequency in the excitation signal.The multiplexer allows the connection of multiple transducers and the bus interface provides the connection with a personal computer.The control of the DAQ device and the signal processing is done through software.The graphical user interface (GUI) provides knobs and displays for adjusting the parameters of

Fig. 7 .
Fig. 7. Basic LabVIEW program for signal acquisition and generation.

Fig. 8 .
Fig.8.Example of measurement system based on DAQ device and virtual instrumentation(Baptista & Vieira Filho, 2009).In Figure8, () xt and () y t represent the analog signals of excitation and response, respectively, and () xn and () y n represent the digital signals.The measurements are based on averaged FRF ( H ) obtained from discrete Fourier transform (DFT) of the excitation and response signals.Thus, the electrical impedance ( E Z ) in the frequency domain is given by www.intechopen.comPiezoelectric Transducers Applied in Structural Health Monitoring: Data Acquisition and Virtual Instrumentation for Electromechanical Impedance Technique 121 previous system, the excitation signal x(t) is generated by the DAC which has a output impedance R out and the corresponding response signal y(t) from each PZT sensor is acquired by the ADC which has a input impedance Z IN constituted by a high resistance connected in parallel with a capacitance.The low cost DAQ devices have only one ADC and each analog input is routed through an onboard multiplexer (MUX).The samples n of the excitation and the response signals in the discrete form (x[n] and y[n]) are synchronized by software through the onboard clock.

Fig. 9 .
Fig. 9. Comparison between the electrical impedance signatures obtained with a conventional impedance analyzer and the system based on virtual instrumentation.The resistors R L are current limiters and are connected in series with the sensors.The sensors have common ground, which facilitates the installation of multiple sensors in metallic structures.This common ground should be connected to the DAQ ground.

Fig. 12 .
Fig. 12.Time response signal y(t) in health and damage conditions.
shows the normalized RMSD values for (a) TEI and (b) for FRF obtained using a plate with four PZT patches and damage simulated at three different positions.According to the experimental results, the RMSD values obtained in the time www.intechopen.comPiezoelectric Transducers Applied in Structural Health Monitoring: Data Acquisition and Virtual Instrumentation for Electromechanical Impedance Technique 125domain are significantly higher than those obtained from FRF.In the time domain, the variation in these values for the damaged structure in relation to the healthy condition reaches a factor of 45 times greater.On the other hand, in the frequency domain this variation is only about 12 times greater.

Fig. 13 .
Fig. 13.Difference between the baseline and updated time response signals.