## Abstract

This paper presents an overview and recent advances in impedance-based structural health monitoring. The basic principle behind this technique is to apply high-frequency structural excitations (typically greater than 30 kHz) through surface-bonded piezoelectric transducers, and measure the impedance of structures by monitoring the current and voltage applied to the piezoelectric transducers. Changes in impedance indicate changes in the structure, which in turn can indicate that damage has occurred. An experimental study is presented to demonstrate how this technique can be used to detect structural damage in real time. Signal processing methods that address damage classifications and data compression issues associated with the use of the impedance methods are also summarized. Finally, a modified frequency-domain autoregressive model with exogenous inputs (ARX) is described. The frequency-domain ARX model, constructed by measured impedance data, is used to diagnose structural damage with levels of statistical confidence.

## 1. Introduction

To date, extensive analysis and investigations have been focused on integrating smart material technology into health monitoring systems (Inman 1998). The ‘smart structures’ or ‘intelligent material systems’ refers to the integrated use of structures, actuators, sensors and control systems allowing them to adaptively change or respond to external conditions. Smart materials, for instance piezoelectric materials (piezo-impedance transducers, PZT), are keenly suited for integrating into health monitoring and fault detection systems based on vibration signals. They are small and unobtrusive and come in a variety of sizes and abilities, allowing them to be placed almost anywhere. However, the most interesting aspect of smart materials is that they can also serve as actuators to provide driving signals as well as sensing, for systems that do not contain natural excitation forces or for diagnostic algorithms that require a known, well-controlled excitation. Thus, by combining smart structures technology with diagnostics, one can imagine structural systems that have self-contained and self-diagnostic components minimizing maintenance and inspection cycles.

Impedance-based structural health monitoring techniques have been developed by using the variety of smart material technologies and form a new non-destructive evaluation (NDE) method. A key aspect of impedance-based structural health monitoring is the use of PZT as collocated sensors and actuators. The basis of this active sensing technology is the energy transfer between the actuator and its host mechanical system. It has been shown that the electrical impedance of the PZT can be directly related to the mechanical impedance of host structural component where the PZT patch is attached. Using the same material for both actuation and sensing not only reduces the number of sensors and actuators, but also reduces the electrical wiring and associated hardware. Furthermore, the size and weight of the PZT patch are negligible compared with those of host structures so that its attachment to the structure introduces little impact on dynamic characteristics of the structure.

This paper is intended to provide a brief overview on research work on the impedance method from both hardware and software standpoints. By integrating the technique with the concept of self-sensing actuation (Dosch *et al*. 1992) and with signal processing procedures based on statistically rigorous algorithms, it has been demonstrated that the impedance method is suitable for monitoring of various structures.

## 2. Electro-mechanical principle

The application of impedance measurements to structure health monitoring was first proposed by Liang *et al*. (1994) and subsequently developed by Chaudhry *et al*. (1995), Sun *et al*. (1995), Park *et al*. (1999, 2000*a*,*b*, 2001, 2003), Soh *et al*. (2000), Bhalla & Soh (2003, 2004*a*,*b*), Peairs *et al*. (2004) and their co-workers. The method uses high-frequency structural excitations, which are typically higher than 30 kHz through surface-bonded PZT patches to monitor changes in structural mechanical impedance. The PZT patches require very low-level voltage, typically less than 1 V, to produce a useful impedance excitation in the host structure.

Piezoceramic transducers acting in the ‘direct’ manner produce an electrical charge when stressed mechanically. Conversely, a mechanical strain is produced when an electrical field is applied. For a linear piezoelectric material, the relation between the electrical and the mechanical variables can be described by linear relations (Crawley & Anderson 1990)(2.1)where *S* is the mechanical strain; *T* is the mechanical stress; *E* is the electric field; *D* is the charge density; *s* is the mechanical compliance; *d* is the piezoelectric strain constant; and *ϵ* is the permittivity. The superscripts *E* and *T* indicate that those quantities are measured with electrodes connected together and zero stress, respectively, and the subscript t indicates transpose. The first equation describes the converse piezoelectric effect and the second describes the direct piezoelectric effect.

The process to be used with the impedance-based monitoring method uses both the direct and the converse versions of the piezoelectric effect simultaneously to obtain an impedance signature. An electromechanical model which quantitatively describes the process of the impedance methods is detailed in Liang *et al*. (1994) and Bhalla & Soh (2003). In their electromechanical model, they showed that the electrical impedance, or electrical admittance, is directly related to the mechanical impedance of a host structure, thereby allowing the monitoring of the host structure's mechanical properties using the measured electrical impedance. A simplified electrical circuit analysis can also be used to illustrate the coupling properties of PZT electrical impedances. A PZT can be modelled as a pure capacitor (*C*_{p}) and a voltage source (*V*_{p}) caused by applied voltage (*V*_{in}) as in the case of self-sensing actuation, shown in figure 1. Because both *V*_{in} and *V*_{p} are considered AC sources of unknown frequencies, the output voltage (*V*_{out}) has two components; the first caused by *V*_{in} and the second component caused by *V*_{p}. As such, *V*_{out} can be obtained by the following equation:(2.2)where *ω* is frequency; *Z*_{R} is the electrical impedance of the sensing resister; and *Z*_{p} is electrical impedance of PZT. Then, the electrical impedance of PZT can be written as(2.3)Equation (2.3) clearly indicates that the electrical impedance of the PZT is a function of sensing voltage *V*_{p} (caused by *V*_{in}). The sensing voltage, *V*_{p}, is a function of structural mass, stiffness or damping as confirmed by numerous researchers. Therefore, equation (2.3) indicates that the electrical impedance of the PZT contains the unique nature of the structural responses. Considering the capacitive nature of PZT electrical impedances, the imaginary part of the impedance plays a dominant role in equation (2.3) because, without the component of *V*_{p}, the electrical impedance (*Z*_{p}) is equivalent to 1/*C*_{p}*jω*. Therefore, the sensing voltage, *V*_{p}, would show up more clearly in the real part of the impedance. For that reason, the real part of the impedance is mainly used for health monitoring applications. The variation in the PZT electrical impedance over a range of frequencies is analogous to that of the frequency response functions (FRFs) of a structure, which contains vital information regarding the health of the structure.

The impedance methods usually involve recording impedance signatures of the structure in a healthy condition, and then evaluating the state of the structure by comparing the electrical impedance taken at various times during the lifespan of the structure, which follows the same philosophy of traditional vibration-based methods. The foremost difference is the frequency range that is used to detect the changes in structural integrity. In order to ensure high sensitivity to incipient damage, the electrical impedance is measured at high frequencies in the range of 30–400 kHz. Under this high-frequency range, the wavelength of the excitation is small and sensitive enough to detect minor changes in the structural integrity.

## 3. Comparison with other NDE approaches

Traditional NDE techniques include ultrasonic technology, acoustic emission, magnetic field analysis, penetrant testing, eddy current techniques, X-ray analysis, impact-echo testing, global structural response analysis and visual inspections. Detailed comparisons between the impedance method and other NDE approaches can be found in the literature (Park *et al*. 2000*a*, 2003; Giurgiutiu *et al*. 2002).

As described in the previous section, the impedance method tracks changes in the dynamic properties or response of structures as in global structural response methods. However, the impedance measurements are made at much higher frequencies than those used in global structural methods, which greatly improves the sensitivity to damage. Ultrasonic methods, acoustic emission, eddy current or any other high-frequency testing methods may provide detailed information on anomalies in some structures, but these methods usually require complicated instruments and professional skills to interpret the measured data. Most of these methods require out of service periods, or can be applied only at certain time intervals, which may not be suitable for autonomous on-line structural health monitoring. The sensitivity of the impedance method to minor defects is comparable with that of ultrasonic methods, but the method does not require experienced technicians to discern details. The cost required for hardware and sensors/actuators would be much lower than that of ultrasonic, or any other NDE techniques, with the development and the implementation of low-cost impedance measuring circuits (Peairs *et al*. 2004). The sensing regions of the impedance sensors are much larger than those of local ultrasonic or eddy current sensors, which are usually moved to scan over certain areas to detect damage in a structure.

Impedance-based structural health monitoring provides a compromise between global structural methods and traditional ultrasonic techniques. With a limited number of sensors and actuators, critical areas of a structure can be monitored which is one of the advantages of the global structural methods. Damage in an incipient stage can be accurately identified, which prior to the impedance methods, only local inspection techniques could possibly detect. In addition, by using the actuation and sensing capabilities of PZT, the impedance sensors can also be used to measure global or ultrasonic vibrational response if a proper signal conditioning circuit is implemented, which makes the method attractive for integrated uses of several NDE approaches.

## 4. Proof-of-concept application

The impedance-based health monitoring technique has been successfully applied to several structural systems. Damage detection on composite reinforced concrete walls is presented to illustrate the potential of the impedance-based method for locating local damage in civil structures. Applications to a wide variety structures, including civil, aero and mechanical systems, are summarized in Park *et al*. (2003).

For composite reinforced structures, the integrity of the bonding between the base structures and the reinforced composite patches must be maintained throughout their service lives. In addition, crack growth, which is hidden by the composite patches, needs to be monitored to ensure the integrity of the structure. In this section, an experimental verification that the impedance method can be adapted and applied to damage detection in masonry walls is reported.

### (a) Experimental set-up

Four masonry walls, each of them with a different type of composite reinforcement, were considered. Only the result of one wall is presented in this paper. The results of the other three walls are similar and further experimental results are detailed in Raju *et al*. (1998). The structures were incrementally loaded and PZT patches were used to interrogate the structure. The size of PZT patches was 30×30×0.25 mm. This size makes the PZT actuators/sensors small enough not to be intrusive, i.e. they do not significantly affect the structural properties of the composite walls. Five PZT patches were attached to one side of the wall. Four PZT patches were bonded in the corners and an additional PZT patch in the centre. The loading was applied diagonally to promote early failure. If the walls were to be loaded along the sides, instead of across two opposite corners, failure would occur at much higher loads. Specially designed test fixtures that fit onto the corners of the walls were used. The experimental set-up is shown in figure 2. An HP4194 electrical impedance analyser was used for the measurement of the PZTs' electrical impedance at each step of loading in the frequency range of 45–65 kHz.

### (b) Test observations and analysis

The structure–composite combination was loaded up to 50 000 lbs in steps of 5000 lbs, at which point failure along the top-line occurred. The top length of the wall failed sideways and a visible crack appeared at this load level as shown in figure 3. Then, the load was reduced to 40 000 lbs to observe if it could still withstand load. The loading was then increased and finally stopped at 60 000 lbs at which point a centre-line fracture along with multiple cracks at the lower corner of the wall appeared. The impedance readings were taken at each step of loading. Figure 3 shows the loading configuration and the placement of the PZTs and their numbering scheme, employed on this wall. The position of the cracks is also shown.

The real part of the impedance measurements of PZT 2 is shown in figure 4. Only the real portion of the electrical impedance is analysed to predict the existence and location of damage. The location of both the top and centre-line cracks is within the sensing range of PZT 2. It can be seen that measurement R6, at which stage the top crack occurred, is significantly different from the previous readings. All measurement readings taken after R6 also follow a similar pattern (as that of R6). Measurement R14, at which stage the centre-line crack appeared, shows a significant difference in the signature pattern. It can also be noted that R13 also shows a significant change in the signature pattern as compared with the previous readings; this is indicative of imminent damage. The centre-line crack appeared within the next 2000 lbs load increase.

The impedance measurements of PZT 3 are shown in figure 5. The location of the top crack is well out of the sensing range of PZT 3. Hence, there is little change in measurement R6, at which stage the top crack occurred. PZT 3 is right in the path of the centre-line crack. Measurement R14, at which stage the centre-line crack appeared, shows a significant change in the signature pattern.

By looking for variations in the impedance measurements, structural damage can be detected. However, the visual analysis of the impedance measurement graph is not suitable for on-line implementation of the impedance-based health monitoring technique. To simplify the interpretation of the impedance variations, a scalar damage metric, referred to as correlation coefficients between two impedance measurements, is used to analyse the information from each PZT. A number of different possible damage metrics that are used with impedance methods are summarized and discussed in §5. The damage metric chart is constructed after each measurement has been taken in order to give some indication of the conditions of a structure through comparison with the reference measurement.

As can be seen in figure 6, at 50 000 lbs when top-line fracture occurred, there is a large increase in the damage metric values for PZT 1, 2 and 5. PZT 3 and 4 show a small increase; this is because they are distant from the damage. The area covered by each sensor is estimated as having about a 0.4 m radius. At 60 000 lbs, at which stage the centre-line crack appeared, there is a large increase in the damage metric for all PZTs except PZT 4. PZTs 5 and 3 are located right in the path of this centre-line crack and show a large increase in the damage metric. PZT 2 also shows a large increase for this damage since it is close to the crack. PZT 1 shows an increase possibly because the delamination became more pronounced in the vicinity. PZT 4 is distant from the damage and does not show a large increase in the damage metric.

This structure provided an excellent opportunity to study the detection of imminent damage. Twice during the tests on four walls, a PZT sensor picked up the damage to the structure, even before the cracks were physically visible, demonstrating the extreme sensitivity to the presence of damage. In addition, it can be seen from the observations and charts that the location of the damage can be approximately predicted. Multiple cracks in different areas at different periods of time are picked up accurately. Furthermore, relatively large sensing regions of each PZT sensor, compared with ultrasonics- or eddy current-based damage detection methods, were observed.

## 5. Signal processing in impedance-based structural health monitoring

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 dataset that provides concise damage indication. In impedance methods, the damage sensitive features traditionally employed are based on a scalar damage metric. In earlier work (Park *et al*. 2000*a*,*b*), a simple statistical algorithm, which is based on frequency-by-frequency comparisons and referred to as ‘root mean square deviation’ (RMSD) has been used.(5.1)where *M* represents the damage metric; *Z*_{i,1} is the impedance of the PZT measured at healthy conditions; and *Z*_{i,2} is the impedance for the comparison with the baseline measurement at frequency interval *i*. In a RMSD damage metric chart, the greater the 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 datasets. The correlation coefficient between two impedance datasets determines the linear relationship between the two signatures(5.2)where *ρ* is the correlation coefficient, *Z*_{i,1} and *Z*_{i,2} are as described earlier, and 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−*ρ*); this is done merely to ensure that, with increasing damage or change in structural integrity, the metric values also increase. This provides a metric chart that is consistent with other metrics, such as RMSD, in which metric values increase when there is an increase in levels of damage. The cross-correlation metric accounts for vertical and horizontal shifts of impedance signatures usually associated with temperature changes. In most cases, the results with the correlation metric are consistent with those of RMSD. Zagrai & 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−*ρ*)^{3}, is the most successful damage indicator, which tends to linearly decrease as the crack in a thin plate moves away from the sensor. Tseng & Naidu (2002) also investigate the performance of RMSD, mean absolute percentage deviation (MAPD), covariance and correlation coefficients as indicators of damage. The RMSD and the MAPD were found to be suitable for characterizing the growth and the location of damage, whereas the covariance and the correlation coefficient are efficient in quantifying the increase in damage size at a fixed location.

Temperature changes, among all other ambient conditions, significantly affect the electric impedance signatures measured by a PZT. Some of PZT material parameters, such as the dielectric and strain constant, are strongly dependent on temperature. Generally speaking, the increase in temperature causes the decrease in the magnitude of electric impedance and leftward shifting of the real part (decreases in resonant frequencies) of the electric impedances. Krishnamurthy *et al*. (1996) developed a software-based correction technique, which eliminates the effects of temperature on the PZT while not eliminating the effects on the structures. This method, however, requires prior measurements of the temperature to obtain the temperature coefficient of the PZT, which is not trivial in some cases. Park *et al*. (1999) use a modified RMSD metric, which compensates for horizontal and vertical shifts of the impedance in order to minimize the impedance signature drifts caused by the temperature or normal variations.

Lopes *et al*. (2000) incorporate neural network features with the impedance method for somewhat quantitative damage analysis. The authors proposed a two-step damage identification scheme. In the first step, the impedance-based method detects and locates structural damage and provides damage indication in a green/red light form with the use of the modified RMSD. When damage is identified, the neural networks, which are trained for each specific damage, are then used to estimate the severity of damage. Naidu & Soh (2004) present the integration of Bayesian networks with impedance methods for identifying damage locations in structures.

One of the main limitations of using a traditional damage index is how to establish appropriate decision limits or thresholds values to indicate the presence of structural damage. Damage metric charts are useful only when a qualitative comparison between datasets needs to be made. Since the impedance-based method relies on experimental data with inherent uncertainties, statistical analysis procedures are inevitable if one is to state in a quantifiable manner that changes in the impedance of a structural system are indicative of damage as opposed to operational and environmental variability. Therefore, in recent studies, statistical pattern recognition paradigms have been implemented into impedance methods for more effective structural health monitoring.

### (a) Impedance methods with statistical classifiers

Statistically rigorous algorithms are beginning to be employed in impedance methods to assess the variation of the impedance signature patterns caused by structural damage. An autoregressive model with exogenous inputs (AR–ARX) in the frequency domain is incorporated into the impedance methods for nonlinear damage discrimination (Fasel *et al*. 2005). Since nonlinear feature identification requires separate input and output measurements, which are not possible with the traditional impedance analysers, a modified frequency AR–ARX model is proposed (Park *et al*. 2005).

Statistical process control methods (Sohn *et al*. 2001) consist of using a baseline measurement of a healthy system. In a time-domain framework, a two-stage prediction model, that is a combination of an autoregressive (AR) model and autoregressive model with exogenous inputs (ARX), is constructed in accordance with the healthy signals. The model is then used to predict the response of the structure. The predicted response is compared as a baseline to the current response and the residual errors between the two signals are computed. If the system experiences damage that alters the dynamic response, the reference ARX model is not able to adequately predict the response, resulting in significant variations in residual errors. This variation will be indicated by an unusual number of residual error terms exceeding predetermined limits (called control limits). A statistically significant number of residual error terms outside the control limits indicate a system anomaly.

The features that are analysed in the impedance methods are mainly drawn from the frequency domain. In a traditional time-series analysis, an ARX model attempts to predict output at the current time-point based on its own past time-point outputs, as well as the present and past inputs to the system. A frequency domain ARX model attempts to predict the output at a particular frequency based on the input at that frequency, as well as outputs at surrounding frequencies. The outputs at the surrounding frequencies are included as inputs to the model to account for subharmonics and superharmonics introduced to the system through nonlinear feedback. A first-order ARX model, among many possible forms of models in the frequency domain, is as follows (Adams 2001):(5.3)where **Y**(*ω*) is the response at frequency *ω*; **U**(*ω*) is the input; **Y**(*ω*−Δ*ω*) and **Y**(*ω*+Δ*ω*) are the responses at frequencies *ω*−Δ*ω* and *ω*+Δ*ω*, respectively; **A**_{1}(*ω*) and **A**_{−1}(*ω*) are the frequency domain autoregressive coefficients; and **B**(*ω*) is the exogenous coefficient. These terms are then determined by minimizing the sum of the squared error associated with how well the model in equation (5.3) describes the measured data. If the nonlinear terms are set to 0, the exogenous coefficient is equivalent to frequency response estimates.

With the traditional impedance measurement approach, using an analyser such as HP4194A, the measurement of the nonlinear terms, **Y**(*ω*−Δ*ω*)/**U**(*ω*) and **Y**(*ω*+Δ*ω*)/**U**(*ω*), is not currently available, making it difficult to use a frequency domain ARX model with impedance methods. To obtain these nonlinear terms, separate input and output data in the time domain and an appropriate data-processing procedure are required (Adams 2001). Therefore, Park *et al*. (2005) propose to use a modified frequency domain ARX model by replacing the nonlinear terms in equation (5.3) with curvatures of measured impedance data, defined as follows:(5.4)

In equation (5.4), the curvature of impedance was obtained numerically by using a central difference approximation as(5.5)where *Z*(*ω*) is the measured impedance. It should be noted that this modified ARX model does not explicitly consider the nonlinearity, or strain, displacement or velocity relationship. Instead, by considering the coupling terms in the curvatures before and after the frequency components of interest, the proposed ARX model can be considered as an empirical data-driven model that is able to predict the output at the specific frequency and allow the extraction of the unique characteristics of measured impedance data.

Once the coefficients of **B**(*ω*), **C**_{1}(*ω*) and **C**_{-1}(*ω*) are obtained with the several baseline impedance measurements in the least square sense, the model is used to predict the response of a newly measured signal. As the time domain AR–ARX model, this prediction model should be able to appropriately predict the new signal if the new signal is close to the reference signal. On the other hand, if the new signal is recorded under a structural condition different from the conditions where reference signals were obtained, the ARX model would not reproduce the new signal well. Thus, the residual error is adopted as a damage sensitive feature in this method as in time domain analysis, casting the impedance-based approach into an outlier detection framework.

When analysing the residual error, extreme value statistics (EVS) is employed. The major problem in statistical analysis is that the functional form of the distribution is often unknown and there are an infinite number of candidate distributions. However, there are only three types of distributions for the extreme (maximum or minimum) values regardless of the distribution type of the parent data. Since there are only three distributions (Gumbel, Weibull and Frechet distributions) to choose from, the distribution selection and parameter estimation becomes much easier. EVS is a powerful tool if the data of interest are in the tails (extremes) of the damage sensitive feature distribution. Control limits for the outlier analysis can be accurately established by employing EVS from the reference impedance signals measured from the health structure. More information on the application of structural health monitoring based on EVS can be found in Sohn *et al*. (2003). With statistical process control, the impedance-based health monitoring can be broken into impedance data acquisition, construction of the frequency domain ARX model, establishment of the control limit coupled with EVS and the discrimination between features from the undamaged and damaged structures with statistical confidence.

Experimental results are presented to illustrate how the approach can be used in real structures. The structure being considered is a simulated three-story moment-resisting frame structure, constructed of unistrut columns and aluminium floor plates, shown in figures 7 and 8. The floors are 1.3 cm thick aluminium plates with two-bolt connections to brackets on the unistrut columns. Support brackets for the columns are bolted to this 3.8 cm thick aluminium base plate.

Four PSI-5A PZT patches (2.5×2.5×0.025 cm) are bonded to the brackets that affix the second floor to the unistrut columns for acquiring electrical impedances, as shown in figure 9. The impedance measurements were made using a Dactron FFT analyser with an impedance sensing circuit in the frequency range of 5–20 kHz.

After measuring the several baseline impedance signatures, damage was introduced by loosening a bolt over selected locations. Two conditions were imposed on this structure in sequence, as shown below.

Damage I: loosening a bolt at Joint 1.

Damage II: loosening a bolt at Joint 3.

A total of 13 impedance measurements were taken over a three-week period (seven baseline measurements, one measurement under Damage I and five measurements under Damage II condition). The measurements were taken at different times on different days. This is because the impedance signatures are expected to show relatively large variations owing to the presence of bolted joints in the structure and slight changes in room temperature during the test. When designing and planning long-term health monitoring systems, these ambient effects should be taken into account. In the impedance-based technique, analysing impedance signatures before and after damage would produce measurable changes in most cases. However, the variation in the impedance measurements due to the induced damage must be larger than that caused by these boundary or ambient condition changes.

The real part of impedance measurements of the PZT at Joint 1 is shown in figures 10–12. Figure 10 shows all seven undamaged impedance curves. It can be seen that the essential pattern of the impedance signatures remains the same over time when damage was not induced. There are small random variations along the curves over the days of testing. However, the variations are relatively small and the measurements are repeatable. No noticeable degradation in the impedance signature is observed. After the damage is induced (completely loosening one bolt), a significant change occurs in the signature pattern of the impedance curve over the entire frequency range, shown in figure 11. This is because the damage causes changes in stiffness or damping resulting in changes in mechanical impedance of the joint. All measurement readings taken after Damage II also follow a similar pattern as that of Damage I and are shown in figure 12. This is because the Joint 1 is distant from Damage II (introduced at Joint 3), hence only a small change, if any, has been observed. The remaining three PZTs show the same pattern. A complete change occurs in the signature pattern of the curve over the entire frequency range when the damage is introduced close to the sensor location. If the damage is distant, there are only minor variations of the existing signature pattern.

In order to apply the outlier analysis framework, the first five baseline measurements were used to obtain autoregressive coefficients and exogenous coefficients of the modified ARX model. Once the coefficients are identified, the residual errors are extracted as a damage sensitive feature by differentiating the measured impedance and output of the ARX model. EVS is employed to establish the statistical confidence limit of 99.5%, and it is determined that the Frechet distribution is the most appropriate extreme value distribution for use in the analysis. If the normality assumption is used, there are many false positives with the inflated number of outliers. The selection of the decision limit depends on the specific structure and type of damage to be monitored. The 99.5% was chosen because it provides acceptable risk. For a sample size of 1020 points and a 99.5% confidence interval, 5 or 6 outliers beyond the confidence interval for an undamaged case are expected. However, as many as 10–12 outliers could be considered undamaged, because the established confidence is based on statistical limits not true limits. Such results would be less likely to occur with a larger amount of baseline data to establish the EVS confidence limits.

The number of outliers of Joint 1 and 3 for each damage case is shown in figures 13 and 14. The traditional damage metric based on RMSD is also shown for comparison. Although there is an increase in RMSD if damage is located close to the sensor and normal variations are relatively small, the RMSD does not establish threshold values or statistical confidence intervals of the structures' condition. On the other hand, two damage conditions can be correctly identified with the statistical confidence from the outlier analysis, and no false positive indication of damage is observed from all joints. This result shows that the proposed algorithm coupled with impedance methods can clearly detect and locate a state of structural damage with statistical confidence.

It has been found that the frequency domain ARX coefficients are sensitive to leakage in the frequency response measurements. In this study, a prior curve fitting on the impedance data was performed before constructing the ARX model in order to minimize this effect. In addition, the feature extraction in this method involves the process of differentiating a frequency domain spectrum as a function of frequency using a central difference curvature expansion. This differentiation often leads to amplifications of existing noise in data. Therefore, a study is needed to identify and quantify the effects of leakage and noise in experimental data on the proposed algorithm.

The inclusion of a statistical framework provides a distinct advantage to traditional impedance-based health monitoring approaches. The method enables a more quantitative assessment of the damaged and undamaged conditions. As stated, the main limitation of previous impedance-based approaches was ‘how to establish appropriate control limits or threshold values for damage indication’. The decision was typically made based on arbitrary values, i.e. ‘small variations’ for undamaged cases and ‘large variations’ for damaged cases. In this approach, the undamaged condition can be quantitatively assessed by tracking the number of outliers. The numbers within or below the control limit can be considered as an undamaged state. In the case of damage present, the proposed algorithm shows a statistically significant number of outliers outside the control limits that allows a diagnosis of the damage state in a more conclusive manner.

## 6. Summary

A brief overview of the impedance-based structural health monitoring method has been presented. The basic concept of this technique is to monitor the variations in the structural mechanical impedance caused by the presence of damage, using the electromechanical coupling properties of piezoelectric materials at high-frequency ranges. The feasibility of implementing the technique to detect real-time damage on composite reinforced concrete walls was demonstrated. New pattern recognition approaches that capitalize on the features of impedance signals were also summarized. While several successful examples of the use of impedance methods have been presented, it is important to note that there are several research issues that remain. These include (i) developing miniaturized and portable impedance measurement equipment, (ii) packaging of the sensors to facilitate installation, (iii) integrating this method with other NDE techniques, such as wave propagation methods, acoustic emissions and ultrasonics, and (iv) investigating the possibility of wireless communication between the sensor and the signal processing equipment. Extensive efforts are being devoted to study these implementation issues in order to handle real-life field applications.

## Acknowledgments

This work was sponsored by the Department of Energy through the internal funding program (LDRD-DR) at Los Alamos National Laboratory, partially by National Science Foundation and by the US Army Corps of Engineers' Construction Engineering Research Laboratory. The authors also would like to thank Dr Harley H. Cudney for providing expert guidance and experimental results for composite testing.

## Footnotes

One contribution of 15 to a Theme Issue ‘Structural health monitoring’.

- © 2006 The Royal Society