Review of piezoelectric impedance based structural health monitoring: Physics-based and data-driven methods

Abstract

Vibration based structural health monitoring methods are usually dependent on the first several orders of modal information, such as natural frequencies, mode shapes and the related derived features. These information are usually in a low frequency range. These global vibration characteristics may not be sufficiently sensitive to minor structural damage. The alternative non-destructive testing method using piezoelectric transducers, called as electromechanical impedance (EMI) technique, has been developed for more than two decades. Numerous studies on the EMI based structural health monitoring have been carried out based on representing impedance signatures in frequency domain by statistical indicators, which can be used for damage detection. On the other hand, damage quantification and localization remain a great challenge for EMI based methods. Physics-based EMI methods have been developed for quantifying the structural damage, by using the impedance responses and an accurate numerical model. This article provides a comprehensive review of the exciting researches and sorts out these approaches into two categories: data-driven based and physics-based EMI techniques. The merits and limitations of these methods are discussed. In addition, practical issues and research gaps for EMI based structural health monitoring methods are summarized.

Keywords

piezoelectric materials electromechanical impedance technique non-destructive testing data-driven method physics-based method damage quantification

Introduction

In the last decades, the number of civil engineering infrastructure has significantly increased worldwide, especially in the developing countries. There is an increasingly urgent need to satisfy the practical requirements for the safety condition monitoring and management of civil engineering structures. Therefore, structural health monitoring (SHM) techniques have continually attracted the attention of researchers and field engineers in the last several decades. Numerous studies have been carried out to improve the system identification and damage detection techniques. Throughout the years of development and investigation, vibration characteristics, such as natural frequencies and mode shapes, based global SHM techniques have been applied in a wide range (Chatterjee, 2010; Li et al., 2012, 2013; Staszewski and Robertson, 2007; Sung et al., 2013; Xia et al., 2002, 2007). In general, early detection of structural damage can not only prevent catastrophic structural collapse but also minimize the repairing or rehabilitating cost and structural service interruption. Therefore, one of the critical issues in the SHM field is improving the capability to detect minor structural damage at an early stage to prevent progressive structural degradation and potential failure. For instance, the bridge on the Interstate Highway 35W (I-35W, National Bridge Inventory Structure No. 9340) over the Mississippi River in Minneapolis suffered a sudden tragic collapse in 2007. According to the post-accident investigation, a total of 111 vehicles were on the collapsed portion. More than 17 vehicles fell into the water. Thirteen people died, and a hundred and forty-five people were injured because of the collapse. The investigation led by the US National Transportation Safety Board indicated that a damaged gusset plate under a concentrated loading area was the main reason for this collapse and concluded that the regular load rating and annual visual inspections failed to adequately detect the gusset plate conditions (National Transportation Safety Board, 2008). Incipient structural damage is not easy to be detected since it is normally a minor-scale phenomenon and unobservable in structural response at an early stage. The mature global SHM techniques based on the analysis of modal information, such as natural frequencies, mode shapes and the derived indicators, may have an insufficient sensitivity to detect the incipient minor structural damage. For most of the global SHM methods, the defined damage indicators only reflect the global defects of the structure. For this reason, many non-destructive testing (NDT) techniques have been developed, such as ultrasonic technique (Lu and Michaels, 2009), Electrochemical Impedance Spectroscopy Measurements (EISM) (Encinas-Sánchez et al., 2019), and impact echo testing (Epasto et al., 2010). Nevertheless, the obvious drawbacks of such techniques include the high operation and equipment cost and limited inspection range, which may limit the extensive applications of NDT techniques.

On the other hand, developments in the application of smart material based SHM systems have attracted the interest of many researchers in the past decades. Lead zirconate titanate (PZT) is a kind of piezoelectric material that has been commonly used for SHM of aerospace, mechanical and civil engineering structures. PZT transducer is capable of generating a voltage output when a compressive force is applied. Conversely, an applied electric field can be transferred to a mechanical strain on a PZT transducer. Taking the advantages of PZT materials, for example, light weight, robust to environment and cost-effective, it has been widely used as a transducer patch that can be bonded to the structural surface to monitor structural health conditions. Meanwhile, researchers have intensively explored the potential of using PZT based methods in replacing the currently available local damage detection techniques. In the recent years, SHM methods have been developed by using PZT transducer to interact with the host structure using high frequency excitations to obtain the sensitive signatures for health monitoring, which is termed as the electromechanical impedance (EMI) technique. PZT patches are bonded onto the surfaces of the monitored structures in EMI based SHM methods. An alternating voltage sweep signal is applied as the input using signal generator or an impedance analyser. Although the first-hand measurement of the mechanical properties of the host structure is difficult to obtain, the electrical impedance of a PZT transducer can directly reflect the changes in the mechanical impedance of the monitored structure. Recent applications of the EMI based SHM methods have shown promising successes in detecting the local damage of structures (Annamdas, 2012; Peairs et al., 2004; Yang et al., 2008).

In EMI techniques, impedance response in the frequency domain is most commonly used for damage detection. To detect the existence of structural damage, the impedance response of the damaged structure is compared with that measured from the undamaged structure (baseline). The statistical damage index, for example, the root mean square deviation (RMSD) (Giurgiutiu and Rogers, 1998), was proposed to distinguish the baseline and damaged responses. In addition, other statistical techniques were also developed, such as mean absolute percentage deviation (MAPD), covariance (COV) and correlation coefficient (CC) (Tseng and Naidu, 2002). Owning to the computational efficiency and performance, such non-parametric damage indicators have been widely applied in the practical SHM applications (Bhalla et al., 2002; Bhalla and Soh, 2004a; Chen and Xu, 2012; Hu et al., 2014; Liang et al., 2016; Ong et al., 2002; Park et al., 2006, 2011). However, the above-mentioned studies based on the quantified difference between baseline and current impedance signatures are not able to provide detailed information of structural damage, such as the location and severity, since scenarios with minor damage closer to the measured location and severe damage far away from the measured location may have identical or similar damage indicator values (Fan et al., 2016). Considerable efforts have been made to study and improve the EMI technique to overcome such limitation. On one hand, combinations of using statistical damage indicators of impedance responses and other pattern recognition algorithms, such as Artificial Neural Networks (ANNs) (He et al., 2014; Lopes et al., 2000; Selva et al., 2013), Probabilistic Neural Network (PNN) (Na and Lee, 2013), clustering analysis (Langone et al., 2017; Palomino et al., 2012), etc., have been investigated to improve the performance of EMI based damage identification methods. On the other hand, studies on using EMI based damage detection methods and model updating have been carried out to overcome the limitation of classifying phenomenological characterizations with statistical indicators (Cao et al., 2018; Fan et al., 2018b; Shuai et al., 2017; Wang and Tang, 2009), since the aforementioned neural network based EMI methods still cannot relate the changes of impedance responses to changes in structural physical properties, such as stiffness, mass or damping [27].

Details about hardware, software and applications of EMI technique have been comprehensively reviewed by previous studies (Annamdas and Soh, 2010; Huang et al., 2010; Park et al., 2000a, 2003). For this reason, this article mainly focuses on summarizing and reporting the recent developments and investigations of data-driven based and physics-based EMI methods, to provide readers a comprehensive understanding about these two directions of applying EMI techniques for SHM of engineering structures. The advantages and the limitations of both categories of these techniques are also discussed.

Data-driven based EMI techniques

For the current state-of-the-art data-driven based EMI methods, quantification of the difference between the baseline and measured impedance signatures is the key to decide whether the damage occurs in the engineering structures. The typical data-driven based EMI methods for SHM are briefly reviewed and discussed in this section.

Statistical properties based methods

Statistical damage indicators

To determine the occurrence of structural damages using EMI based methods, the measured impedance responses of the monitored structure under the current and healthy states are compared. Consequently, it is necessary to quantitatively evaluate such difference to detect the existence of damage and imply the severity of structural damage. Giurgiutiu and Rogers (1998) proposed one of the most widely used statistical indicator for EMI applications, namely, root mean square deviation (RMSD), which can be expressed as

RMSD (%) = \sqrt{\frac{\sum_{i = 1}^{N} {(y_{i} - x_{i})}^{2}}{\sum_{i = 1}^{N} {(x_{i})}^{2}}}

(1)

where

y_{i}

is the measured impedance signature from the current state and

x_{i}

is the impedance response from the structure under the healthy state. Other statistical indicators, as mentioned in introduction, such as MAPD, COV and CC, have been developed and shown as

MAPD (%) = \frac{100}{N} \sum_{i = 1}^{N} | \frac{y_{i} - x_{i}}{x_{i}} |

(2)

Cov = \frac{1}{N} \sum_{i = 1}^{N} (x_{i} - \bar{x}) (y_{i} - \bar{y})

(3)

C C = \frac{Cov (x, y)}{σ_{X} σ_{Y}}

(4)

Investigations and comparisons have demonstrated the difference among these indicators for damage detection, and reported that RMSD has been found as the most sensitive one for the detection of new occurrence of damage, while CC and COV are more suitable for the detection of the increasing damage extent (Tseng and Naidu, 2002; Zagrai and Giurgiutiu, 2001).

Time-frequency analysis for EMI signature

To improve the performance of using these statistical evaluation methods for structural damage detection based on impedance signatures, time-frequency analysis methods have been developed to enhance the frequency domain based methods. Fan et al. (2016) introduced a time-frequency autoregressive moving average (TFARMA) model based analysis method to process the time domain frequency swept responses directly. Damage indicator was derived from the relevant time-frequency analysis spectrum by utilizing Singular Value Decomposition algorithm. The performance of the proposed method was validated by experimental studies on the gusset plate of a truss model. From the experimental results, it was found that the proposed time-frequency analysis based damage indicator has a better sensitivity than RMSD and CC that are based on frequency domain analysis.

Remarks

Applications of EMI techniques by setting thresholds for statistical damage indicators to identify the occurrence of structural damage are conducted. Owning to the high computational efficiency and performance, such non-parametric damage indicators have been applied for damage detection on different types of civil engineering structures and components (de Souza Rabelo et al., 2017; Giurgiutiu and Zagrai, 2005; Liu et al., 2017; Mascarenas et al., 2005; Tashakori et al., 2016; Yang et al., 2005). The shortcomings of such statistical based EMI methods have been discussed in previous studies (Cherrier et al., 2013; Lopes et al., 2000; Na and Baek, 2018; Naidu and Soh, 2004; Wang and Tang, 2009). First of all, more information is needed to be extracted from impedance response data to indicate the difference between a closer damage to the PZT sensor and a structural damage with a high severity (Fan et al., 2016). Furthermore, the above-mentioned methods based on the difference in the phenomenological characterizations of piezoelectric impedance response are not able to relate the signatures to detailed changes in structural physical properties. It is difficult to distinguish the changes in impedance patterns caused by real damages and other environmental variations (Fan et al., 2018b; Wang and Tang, 2009). Therefore, the identification of the exact location and severity of structural damage remains to be a challenging research topic, without the support of numerical model or pre-calibrated experimental data.

Machine learning algorithms based methods

Lopes et al. (2000) pointed out that using statistical indicators to evaluate the changes in piezoelectric impedance responses cannot correlate the impedance changes to the nature of structural damage and estimate damage severity. Furthermore, only summarizing the impedance signature with a single damage indicator value may not provide sufficient information for further damage localization (Selva et al., 2013). Therefore, numerous pattern recognition tools and data processing methods have been adopted to enhance the capability of these data-driven based EMI techniques. These studies are briefly reviewed in this section and summarized in Table 1.

Table 1.

Summary of data-driven based EMI methods for damage identification.

Authors	Application	Data processing method	Key contribution
Lopes et al. (2000)	Laboratorial bridge section and space-bay structure	Artificial neural network (ANN)	Quantitatively identify structural damage
Fekrmandi et al. (2016)	Aluminium beam	Artificial neural network (ANN)	Locate the applied load at 6 pre-set location on aluminium beam with 2 PZT sensors
Na and Lee (2013)	20 cm × 20 cm composite plate	Artificial neural network (PNN)	Identify damage location in 6 pre-set areas with 3 PZT sensors
Selva et al. (2013)	29 cm × 20 cm composite plate with clamped edges	Probabilistic neural network (PNN)	Damage localization with 3 PZT sensors
De Oliveira and Inman (2017)	Composite plate with bolted edges	Simplified Fuzzy Adaptive Resonance Theory Predictive Mapping (ARTMAP) Network	Classify the severity of bolt loosening at 6 locations
Park et al. (2008)	A bolt-jointed aluminium beam	Principal component analysis (PCA) and k-means clustering algorithm	Identify loosening of 4 bolts joint
Sevillano (2016)	Reinforced concrete beam externally strengthened with an FRP strip	Hierarchical clustering algorithm	Identify the severity of interfacial damage in several regions on FRP-strengthened concrete beam
Palomino et al. (2012)	Beam structure with small hole and loosen bolt	Fuzzy cluster analysis	Damage classification
Zuo et al. (2017)	Pipeline	Multi sensor data fusion technology	Crack identification with 8 PZT sensors
Singh et al. (2021)	Aluminium plate	Self-organizing maps	Identify different holes with the information of 8 PZT sensors
De Oliveira et al. (2018)	Aluminium plate with drilled holes	Convolutional neural network	Identify multiple damages with relatively small database
Zhou et al. (2021)	Aluminium plate with bolt connections	Graph convolutional networks	Locate and quantify the loosening of three bolts

Artificial Neural Network

As one of the most mature machine leaning techniques, ANN has been employed for EMI based damage identification by many researchers. Lopes et al. (2000) used ANN to improve the electrical impedance responses based statistical methods. In the proposed scheme, RMSD damage index is first used to determine the occurrence of damage, and then the pre-trained ANN was used to estimate the exact severity. Specific damages were adopted to generate the training data for ANN to recognize the different patterns of the intact and damaged structure. To quantify the pattern of an electrical impedance curve, following values estimated from both the real and imaginary parts of the impedance have been developed: the area of the impedance curves, root mean square (RMS) of each curve, the difference between RMS of intact and damaged structures and the CC between the intact and damaged impedance curves. The performance of the developed damage identification scheme has been verified by the experimental studies on a 1/4 scaled truss bridge model and a space truss model. Structural connection failure were defined as the specific damage type for the tests. Fekrmandi et al. (2016) presented the ANN based EMI technique using the Square of Differences (SSD) indicator between impedance responses for network training.

Probabilistic Neural Network and ARTMAP Network

Na and Lee (2013) developed EMI technique with the PNN for damage identification on composite structures. The host structure was split into several regions as shown in Figure 1. The training date consists of the matrix of the RMSD indictor values of these regions estimated from the PZT transducers bonded at different locations. For damage prediction, RMSD values from the PZT transducers are used as input to the trained network for determining the most possible damaged area. The research with a similar approach was conducted by Selva et al. (2013), using generated data from numerical simulations and various damage indicators for the training of PNN. De Oliveira and Inman (2017) explored the application of the Simplified Fuzzy ARTMAP Network for analysing the impedance responses for the identification of loosening bolts at different stages. The performance of the developed method has been compared to the PNN based method which was trained using the same input based on the Euclidean distance of the impedance responses. It was found that the proposed network can provide an accurate identification result and significantly reduce the training time.

Figure 1.

Configuration of composite plate with three PZT patches and results for the damage location prediction using PNN (Na and Lee, 2013).

Clustering techniques

Except machine learning based methods, other clustering algorithms have been investigated for EMI based damage identification technique in the last decade. Park et al. (2008) proposed the EMI technique with the principal component analysis (PCA)-based data compression for preprocessing. The pattern recognition using k-means clustering algorithm is carried out based on RMSD damage indicators of each order of principal components. Experimental studies showed that the proposed method successfully identified bolt loosening in a bolt-jointed aluminium structure. Sevillano (2016) implemented the hierarchical clustering algorithm to recognize the pattern of impedance responses with statistical index of each sub-frequency interval. The experimental studies showed that the approach is able to identify systematical debonding in FRP-strengthened RC beams. Palomino et al. (2012) applied the fuzzy cluster analysis for EMI technique based damage identification and classification. Loosen rivet and a small hole with 1 mm diameter were introduced to the beam structure as the incipient damages. The damage types were successfully distinguished by the proposed method; however, damage severity quantification is not conducted.

Data fusion strategy

For more precise structural damage detection, investigations on combining the data fusion strategy and multiple PZT sensors system have been carried out in recent years. An EMI based crack detection system for pipelines with PZT sensor networks has been developed by Zuo et al. (2017). The average observed effective impedance by a Monte Carlo simulation was considered as the baseline data. The mean value and standard deviation of RMSD indices of 8 PZT sensors were used to quantify the crack with statistical control limits. In 2021, Singh et al. (2021) developed a novel sensor network optimized data fusion method for the EMI based structural damage detection. PCA was used to evaluate the effective RMSD. An ANN based algorithm called Self-organizing Maps (SOMs) was developed for structural state classification. The impedance features extracted by both techniques were combined by a data fusion framework for damage identification on an aluminium plate.

Deep learning

More recently, the deep learning based methods have been explored in engineering applications as the most powerful and popular tools for pattern identification and classification. To improve the damage detection accuracy of the EMI based methods in complex structures, Convolutional Neural Network (CNN) was employed by De Oliveira et al. (2018). The Euclidian distances array between the baseline and measured impedance signatures was calculated as the training samples. Four different structural conditions containing three different damage types were successfully classified by the trained network. For multiple sensors system, Zhou et al. (2021) implemented the graph convolutional network (GCN) for bolts loosening locating and quantification. It is worthy to notice that 1080 groups of impedance signatures were collected in Ref. (De Oliveira et al., 2018). Deep learning networks based EMI methods have good performance but require a large set of diverse training samples to ensure the accuracy of damage prediction.

Remarks

Most of the existing studies on the data-driven based EMI methods are based on the idea of pattern recognition and clustering. These developments extended utilization of impedance signatures from one single statistical index to higher dimensional cases. In terms of superiorities, extracting the main components and features of the impedance response characteristics will also significantly reduce the amount of data for network training. It should be noted that the accuracy and generalization capacity of these pattern recognition techniques, for example, neural networks, are strongly dependent on the selected indicators for classifying patterns, since the raw data of impedance responses have no specific information of structural damages (Lopes et al., 2000). On the other hand, both the conventional machine leaning methods and the novel deep leaning methods are purely driven by data. The performance of such ‘black-box’ classification method highly depends on the quality and diversity of training data, for example, to include as many as different damage scenarios and the corresponding features. However, collecting such sufficient data in the real applications is difficult owning to the limitation of sensor number, environmental noise and incompleteness of measured state variables, and the realistic conditions with many different damage cases. For this reason, the pattern recognition method based EMI technique normally requires multiple sensors. It may limit the application of such techniques to relatively small size structures. The possible solution to overcome these limitations needs to be addressed and further studied.

Physics-based emi techniques

Similar as other vibration based SHM methods, physics-based EMI techniques treat damage identification as an inverse model updating problem based on optimization theory. Changes in the impedance response are directly related to one or several mechanical properties of the host structure. Therefore, accurate numerical model for the baseline structure is essential. In this section, representative numerical models for EMI system and physics-based EMI techniques for SHM will be reviewed and discussed.

Theoretical model for EMI system

Liang et al. (1994) first proposed an analytical model to establish a clear understanding of the electromechanical interaction for the theory behind the EMI technique. Further theoretical developments and applications have been subsequently studied by researchers (Bhalla, 2001; Bhalla et al., 2002, 2003; Bhalla and Soh, 2004b; Chaudhry et al., 1995; Giurgiutiu et al., 1999, 2002; Giurgiutiu and Zagrai, 2000; Liang et al., 1997; Park et al., 2000b; Sun et al., 1995; Zhou et al., 1995). The basic principle of EMI technique is using the PZT transducer to actuate structure vibration and receive the impedance response to detect the changes in physical parameters of the host structure in a nearby area based on the EMI response of the transducer. Therefore, the surface-bonded PZT transducer plays the role of both actuator and sensor simultaneously. Furthermore, the working frequency is generally higher than 10 kHz, which is much higher than the conventional vibration based SHM methods (Annamdas and Soh, 2010). In such a high frequency range, the wavelength is small enough to make the EMI technique sensitive to minor changes in structural physical properties. On the other hand, the localized detection area induces the EMI to be less dependent on the boundary conditions. Park et al. (2003) reported that multiple frequency ranges containing 20 to 30 peaks are normally selected for damage evaluation, owning to the fact that a higher density of modes implies a larger dynamic interaction.

A one-dimensional (1-D) EMI model, as shown in Figure 2, which quantitatively indicates the interaction between electrical response of PZT transducer and the mechanical properties of the host structure, was first presented by Liang et al. (1994) as

Y (ω) = \frac{I}{V} = i ω a (ε_{33}^{- T} - \frac{Z_{s} (ω)}{Z_{s} (ω) - Z_{a} (ω)} d_{3 x}^{2} {\hat{Y}}_{x x}^{E})

(5)

where Y denotes the electrical admittance (inverse of impedance) of the PZT transducer;

Z_{s}

and

Z_{a}

denote the mechanical impedances of the host structure and the PZT transducer, respectively;

{\hat{Y}}_{x x}^{E}

ε_{33}^{- T}

and

d_{3 x}^{2}

are the complex Young’s modulus, the complex electric permittivity and the piezoelectric strain coefficient, respectively;

ω

denotes the angular frequency of the driving voltage.

Figure 2.

Liang’s one-dimensional (1-D) electromechanical impedance model (Bhalla et al., 2009).

To extend the 1-D analytical model of PZT-structure system, numerous studies pioneered the theoretical development on the PZT-structure interaction. Zhou et al. (1997) extended Liang’s electromechanical model to a two-dimensional (2-D) structure model. Direct mechanical impedance and cross-impedance for the host structure between the x and y directions are involved in this model. The relationship between forces along x and y directions and the corresponding planar velocities, as shown in Figure 3, can be derived as

{\begin{matrix} F_{x} \\ F_{y} \end{matrix}} = - {\begin{matrix} Z_{x x} & Z_{x y} \\ Z_{y x} & Z_{y y} \end{matrix}} {\begin{matrix} {\dot{u}}_{x} \\ {\dot{u}}_{y} \end{matrix}}

(6)

Figure 3.

Two-dimensional (2-D) analytical model (Zhou et al., 1997).

Giurgiutiu and Zagrai (2000) investigated the PZT transducer and impedance responses under different boundary conditions based on the 2-D analytical model. Bhalla and Soh (2004b) used a new concept of ‘effective impedance’ instead of the mechanical impedance, which was directly restrained at the end points of the PZT patch. Experimental studies (Bhalla and Soh, 2004a) on concrete structures verified the accuracy of the proposed modelling method. Annamdas and Soh (2007) extended the 2-D model to three-dimensional (3-D). The impedance of the host structure is estimated by summing up the directional impedances acted on PZT as

- Z_{S} = Z_{S 1} + Z_{S 2} - Z_{S 3} + 2 Z_{12} - 2 Z_{23} - 2 Z_{31}

(7)

where the individual normal impedances

Z_{S 1}

Z_{S 2}

and

Z_{S 3}

, the cross-impedances

Z_{12}

Z_{23}

and

Z_{31}

are shown in Figure 4.

Figure 4.

Schematic 3-D model for impedance calculation (Annamdas and Soh, 2007).

Numerical model for PZT-structure interaction

To improve the accuracy of the numerical model to calculate the EMI, the finite element method is used to analyse the PZT-structure interaction. Lerch (1990) applied the finite element method to perform the vibration analysis of piezoelectric sensors and actuators with arbitrary structures. The objective was to use the simulation results to optimize the device with piezoelectric transducers. This research revealed deeper insights into the physical mechanisms of the acoustic property of piezoelectric media. Fairweather and Craig (1998) developed a semi-analytical model to predict the impedance output of a PZT transducer. The model was embedded with the finite element method to express the physical properties of the host structure and to simplify the PZT patch as a force or moment. The model used the advantage of finite element analysis in the modelling of anisotropic material and non-uniform boundary conditions.

Since commercially available finite element modelling software packages have become convenient tools for researchers, a number of studies have been carried out based on these commercial packages, that is, ANSYS, ABAQUS and COMSOL Multiphysics. Annamdas and Soh (2007) developed a 3-D finite element model in ANSYS for calculating the EMI responses. The model only considered one quadrant of the specimen due to symmetry in the X and Y directions. The host structure, PZT patch and bonding layer were all involved in their study. 3-D solid elements were used to mesh the model.

Yang et al. (2008) presented numerical simulations of a free PZT patch and PZT-structure interaction. Various finite element simulations were investigated in their study considering the effects of the bonding layer and variation in temperature. The commercial finite element analysis package ANSYS was used to accurately simulate the electrical impedances for a freely suspended PZT transducer, an aluminium beam and an L-shaped aluminium beam with surface-bonded PZT transducers. Zhang et al. (2011) presented the quantitative simulation of the impedance response of a Timoshenko beam with a crack. The shear lag model was adopted to express the load transfer between the PZT transducer and the host structure. Based on an accurate numerical simulation using ANSYS, a parametric study of the effect of the crack and the inertial force on impedance was conducted. The results showed that the accuracy of damage identification was influenced by the frequency range of the impedance signature. In 2014, a damping model for EMI simulation was discussed by Lim and Soh (2014). It is noted that using a hysteretic damping model to replace the conventional Rayleigh damping model can significantly improve the accuracy of impedance response predictions. Compared with Rayleigh damping, the hysteretic damping model is more suitable for the analysis of a large frequency range. The advantages of the finite element modelling method include the achievement of more accurate simulation results for structures with complex geometry and material properties, the involvement of the entire PZT transducer in the numerical simulation instead of simplifying the patch as a force or moment acting on points or boundaries and the ability to physically simulate the bonding layer. The parametric study for the single PZT patch under free vibrations was also carried out by Lim et al. (2015). The effects of mechanical and electrical parameters on the impedance signatures were presented in both 1-D and 2-D analytical models. The study recommended that the resonant peaks in impedance signatures are only dependent on the mechanical parameters but not electrical properties.

Based on the development of finite element models for the EMI technique, efforts have been made to analyse the effect of structural damage using finite element methods. Annamdas (2012) successfully predicted the impedance responses using a finite element model of a damaged beam before the propagation of a crack was obtained. Using the analytical approach, it is hard to achieve an accurate simulation of impedance for complex geometries, such as hollow structures or those containing a slot. Hamzeloo et al. (2012) developed a finite element model for a hollow structure using ABAQUS. In their research, crack damages were implemented on the host structure. The simulation results showed a promisingly high accuracy compared with those from the experimental study.

It is well known that the finite element model requires a fine mesh size which is smaller than the wavelength involved. With the high frequency range of the EMI techniques, to achieve the precise prediction of impedance responses, the finite element model needs a large number of elements, requiring high computation costs for the numerical simulation. For other piezoelectric wafer active sensor based techniques, such as guided wave methods, more convenient numerical simulation methods, such as the boundary element method (Ge and Chen, 2008), finite difference method (Xu et al., 2003), local interaction simulation approach (Shen and Cesnik, 2016, 2019) and Mass-Spring Lattice Model (Baek and Yim, 2011; Yim and Sohn, 2000), have been developed for the modelling of wave scattering with a reduced computational demand. To improve the computational efficiency, investigations on modelling EMI by making use of the spectral element method (SEM) were carried out. Since Doyle (1997) presented an analysis of the wave propagation problem using the SEM with an infinite number of wave trains at different frequencies, efforts have been made to apply the SEM method for wave propagation-based damage detection in pipes and other structures (Wang et al., 2009, 2011, 2012). Wang et al. (2009) conducted the damage detection of RC structures based on numerical simulations of wave propagation techniques using SEM method. Wang et al. [89, 90] presented methods based on SEM for modelling wave propagation in steel bars with boundary reflections and cracks, and further used for damage identification based on model updating with clonal selection algorithom. Recently, studies on solving the high frequency impedance problem based on the SEM have attracted a large amount of research interest. Esteban (1996) developed the spectral element model incorporated with the existing 1-D analytical model (Liang et al., 1994) to evaluate the sensing region of the EMI of a PZT transducer. Ritdumrongkul et al. (2003) simulated bolt joint connections using a modified SEM model based on the study of Lee and Kim (2001) about the active constrained layer SEM model.

Figure 5 shows an individual element in a SEM model, frequency-dependant shape functions are used in the SEM. The transversal displacement $\hat{v} (x)$ and rotation $\hat{θ} (x)$ about the median plane can be derived by the following equations, respectively

\hat{v} (x) = R_{1} A e^{- i k_{1} x} + R_{2} B e^{- i k_{2} x} - R_{1} C e^{- i k_{1} (L - x)} - R_{2} D e^{- i k_{2} (L - x)}

(8)

\hat{θ} (x) = A e^{- i k_{1} x} + B e^{- i k_{2} x} + C e^{- i k_{1} (L - x)} + D e^{- i k_{2} (L - x)}

(9)

where

A

B

C

and

D

are the unknowns.

L

denotes the length of the spectral element.

k_{1}

and

k_{2}

are the parameters dependent on spectral element’s mass density, Young’s modulus, cross-sectional area, the second moment of inertia and Timoshenko shear coefficient.

R_{j}

can be expressed as

R_{j} = \frac{i k_{j} {\bar{G}}_{b} A_{b} K_{1}}{{\bar{G}}_{b} A_{b} K_{1} k_{j}^{2} - ρ_{b} A_{b} ω^{2}}

(10)

where

{\bar{G}}_{b}

and

K_{1}

denote the shear modulus and the Timoshenko shear coefficient of the beam, respectively. In addition, Timoshenko beam theory is used in the model. The transversal force

\hat{V} (x)

and moment

\hat{M} (x)

can be derived as

\hat{V} (x) = {\bar{G}}_{b} A_{b} K_{1} (\frac{\partial \hat{v}}{\partial x} - \hat{θ})

(11)

\hat{M} (x) = {\bar{E}}_{b} I_{b} \frac{\partial \hat{θ}}{\partial x}

(12)

where

{\bar{G}}_{b}

and

{\bar{E}}_{b}

are the shear modulus and Young’s modulus of the beam element, respectively.

K_{1}

is the Timoshenko shear coefficient.

I_{b}

is the second moment of inertia of the beam. Then, the elemental stiffness matrix can be expressed as

{\begin{matrix} {\hat{V}}_{1} \\ {\hat{M}}_{1} \\ {\hat{V}}_{2} \\ {\hat{M}}_{2} \end{matrix}} = S_{e} (ω) {\begin{matrix} {\hat{v}}_{1} \\ {\hat{θ}}_{1} \\ {\hat{v}}_{2} \\ {\hat{θ}}_{2} \end{matrix}}

(13)

Figure 5.

Schematic illustration of a spectral element (Wang and Tang, 2009).

The system dynamic stiffness matrix $S (ω)$ can be obtained by assembling the elemental dynamic matrix. The piezoelectric impedance $\hat{Z}$ of the PZT-structure coupled system is expressed as

\hat{Z} = \frac{R_{S}}{{\bar{C}}_{C} ({\bar{C}}_{A} {\bar{C}}_{B} Q S {(ω)}^{- 1} Q^{T} + 1)} - R_{S}

(14)

where

R_{S}

is the resistance of the reference resistor in the low-cost impedance measurement method.

S (ω)

is the dynamic stiffness matrix of the beam structure. Vector

Q

is used to indicate the location of piezoelectric transducer.

{\bar{C}}_{A}

denotes the factor between the input voltage and the moment generated by the piezoelectric transducer.

{\bar{C}}_{B}

denotes the factor between the displacement vector and the voltage output of the piezoelectric transducer.

{\bar{C}}_{C}

is the ratio between the measured voltage on the reference resistor and the total voltage on the piezoelectric transducer. Compared with the finite element model, the homogeneous solutions of governing equations in the frequency domain are used instead of the Lagrange or Hermite interpolation polynomials, and the spatial discretization is not necessary. For this reason, SEM can represent geometry with less numbers of elements. Consequently, the method provides a higher computational efficiency. On the other hand, SEM is accurate for simplified structures, for example, beams, but may not provide accurate prediction for the structures with complex geometry and boundary conditions.

Physics-based damage identification using EMI technique

Taking advantage of accurate numerical modelling for PZT-structure interaction in the aforementioned studies, a number of physics-based EMI damage identification methods have been investigated in the last decade. Structural damage is normally simulated by stiffness reduction (Xia et al., 2002). Differences between the simulated and measured impedance signatures are used to estimate the magnitude and location of stiffness change in the host structure.

Naidu et al. (Naidu et al., 2006; Naidu and Soh, 2004) examined using the impedance method based on the nature frequency shifts and indicators of mode shape vectors for damage identification of a 2-D finite element model. The patterns of frequency shifts for damages at different locations are first extracted from the numerical simulation of the intact structure. Then the mode shape corresponding to the damaged structure is identified by searching for the similar frequency shifts pattern of the measured impedance signatures with Bayesian network model.

Based on Yang’s 2-D generic model for simulating the PZT-structure interaction (Yang et al., 2005), Xu (2005) proposed the impedance based damage identification approach for the small aluminium beam and plate. Damage is simulated as the reduction in Young’s modulus of the material. The optimization algorithm, that is, evolutionary programming, was adopted to identify the location and severity of structural damage. When the parameters of structural damage are identified with high fidelity, the peak frequencies of simulated impedance responses would be well matched with the measured impedance data.

Although the calculated impedance with analytical models has the ability to identify detailed information of structural damage (location and severity) by establishing the physical relationship between the phenomenological variations in impedance signatures and the changes in specific structural parameters of the host system, the identification accuracy is still limited by the precision of the modelling method, especially for the modelling of complex boundary conditions.

Albakri and Tarazaga (2017) presented the SEM based EMI technique for structural damage characterization. The SEM for an aluminium beam was developed with the length-varying spectral elements to minimize the element number for a low computational cost. Crack location, crack width and stiffness reduction, were determined by minimizing the relevant objective functions by sine-fit localization method integrated with the gradient descend method.

Shuai et al. (2017) developed the finite element model based EMI damage detection method for the beam structures by ranking the relative similarity and using a Bayesian inference approach. The relationship between the damage indices and impedance changes can be obtained as

D * Δ P = Δ Z

(15)

where

Δ P

and

D

are the change in the damage index vector and sensitivity matrix, respectively.

Δ Z

is the change vector between analytical and measured impedance responses. The similarity

S I

between the measured impedance changes

Δ Z

and a specific column vector of the sensitivity matrix

D

was derived as

S I = \arcsin (\frac{D_{k}^{T} Δ Z}{| D_{k} | * | Δ Z |} - 1)

(16)

where

D_{k}

is the

k

th column of the sensitivity matrix,

Δ Z

denotes the measured impedance change vector. When the measured impedance response is exactly the same as the predicted impedance response,

S I

equals to zero. To reduce the influence of noise and uncertainty effect, the relative similarity

I D

is defined as

I D = \frac{e^{- | S I |}}{\sum_{j = 1}^{m} e^{- | S I |}}

(17)

By comparing all the combinations of damage locations and severities, a larger relative similarity value indicates a higher likelihood of fault occurrence, as shown in Figure 6. In the meantime, to reduce the sample size of the fault location vector, a pre-screening method was conducted by calculating the fault severity index with the sensitivity vector of each segment. The segment with a severity index which is larger than 1 or less than 0 can be eliminated from the potential fault candidate.

Figure 6.

Experiment studies on an aluminium beam (Cao et al., 2018).

Ezzat et al. (2020) extended the model based EMI technique with a pre-screening method by using statistical calibration and surrogate model. The proposed method estimated the preliminary damage severity for each segment, which guided the selection of the Bayesian prior for the calibration. The statistical calibration scheme was then applied based on a Gaussian process surrogate model, which was used to represent the relationship between the specific structural property and the impedance changes. A number of pairs of damages with different severities and locations are then used to produce the best agreement between the final calibrated model and the observed physical measurements.

On the other hand, by taking advantage of the sensitivity-based identification strategy for inverse problems, EMI based damage detection methods using numerical model updating were developed. The basic principle behind such methods has been investigated by many studies for vibration based SHM methods (Bicanic and Chen, 1997; Cawley and Adams, 1979; Chen and Bicanic, 2000; Lu and Law, 2007). When using EMI techniques for structural damage identification, indicators that represent the changes between the baseline and measured impedance data are used to update the physical parameter vector of the host structure. When the impedance signatures from numerical simulation are matched well with the measured data, the location and severity of structural damage can be identified as the stiffness reductions in segments or elements.

Wang and Tang (2009) used the SEM to simulate a beam structure with a surface-bonded PZT transducer, and employed sensitivity-based method to detect structural damages. Damage location and severity, which are simulated as stiffness reduction, were identified. The advantage of using SEM is emphasized in improving computational efficiency, by comparing the simulation accuracy and computational time of using SEM and finite element model for the beam structure. The dynamic stiffness matrix of the host structure was expanded by Taylor series to extract the damage indices. Structural damage can be located and quantified by solving Equation (17). It should be noted that the magnitude changes at 121 frequency points around the pecks in the impedance curve were selected for identification. The results show a good agreement with the real location and severity of the introduced damage, with a few false identifications in the undamaged elements for a multiple damage scenario.

One major limitation of physics-based EMI techniques is that the insufficient number of measured data would make the sensitivity-based inverse identification problem seriously ill-posed, which significantly reduces the accuracy of identification results. Kim and Wang (2014) developed the adaptive piezoelectric circuitry based on the studies by Wang and Tang (2009) to improve the accuracy of damage identification by enriching the measured data, as shown in Figure 7. It is mentioned that the condition of the ill-posed inverse problem can be significantly improved by the increased number of measurement data. Tikhonov regularization is adopted to solve the inverse problem. The solution for Equation (15) can be obtained by optimizing the following objective function J

J = min ({‖ D * Δ P - Δ Z ‖}_{2} + λ {‖ Δ P ‖}_{2})

(18)

where

λ

is the regularization parameter, which is obtained from the L-curve method.

{‖ ‖}_{2}

denotes the second norm. To evaluate the performance of this method, random noise from 62 dB to 36 dB was applied. Comparing to the results with the conventional method, the identification accuracy was improved by the enriched data when the model includes estimation errors. However, these studies by using SEM only developed the 1-D beam model to simulate the monitored structure, under stationary conditions, because of the limitation of using SEM in modelling structures with complex geometry and boundary conditions. In contract, finite element modelling shows a stronger capacity in modelling a 2-D or 3-D structure.

Figure 7.

The configuration of the low-cost impedance measurement system (Kim and Wang, 2014).

Compressive sensing (CS) based technique has been applied to SHM. Comparing to the conventional Tikhonov regularization method, the solution of the ill-conditioned problem from CS technique based sparse regularization method is usually distributed to a few elements, which is closer to the realistic situation. The objective function for sparse regularization can be rewritten as

J = min ({‖ D * Δ P - Δ Z ‖}_{2} + λ {‖ Δ P ‖}_{p})

(19)

where

{‖ ‖}_{p}

denotes the l_p norm. As shown in Figure 8, optimization using the second norm tends to return a solution with more non-zero values. When

p = 1

, it is more likely for the obtained solution to converge to be sparse.

Figure 8.

Approximate solutions of undetermined identification equation by using $l_{1}$ and $l_{2}$ norm regularization techniques.

Fan et al. (2018b) presented the sparse regularization based EMI technique with sensitivity-based model updating for structural damage identification. The investigations utilized the developed numerical finite element model and frequency independent damping model by Lim and Soh (2014), to obtain the baseline impedance data of PZT from the undamaged structure. Resonance frequency shifts between the baseline and measured impedance data are used to update the stiffness matrix of the host structure which is split into a number of segments. $l_{1}$ regularization based method is implemented for model updating. The comparison between the results from using $l_{1}$ and $l_{2}$ regularization shows that the sparse regularization based method can significantly reduce the errors in damage identification of those undamaged segments, as shown in Figure 9. The study also presented the good robustness of the proposed sparse regularization based method under random noise. Sensitivity range of the proposed method was investigated by a parametric study.

Figure 9.

(a) Numerical model (b) Comparison of the identification results for the single damage scenarios by $l_{1}$ regularization method and Tikhonov regularization method (Fan et al., 2018a).

Cao et al. (2018) proposed physics-based EMI damage detection method incorporated with the $l_{0}$ norm regularization method. The research treated the difference between model prediction and the measurement, and the sparsity condition with separated objective functions to be minimized. For the multi-objective optimization problem, the multi-objective Dividing RECTangles (DIRECT) algorithm was implemented in this study. In experimental validations, an aluminium beam with a small added mass simulated as the minor structural damage is used. The electromechanical admittance data from 200 frequency points around two resonance peaks were used to update the numerical model. The results showed that using the single composite objective function is likely to yield incorrect solution for the multiple damage scenario.

Very recently, the concept of surrogated model has been introduced by Ezzat et al. (2020) to increase the computational efficiency of physics-based EMI models. A Gaussian process (GP) model was developed to replace the numerical modelling in each calibration loop of the above-mentioned physics-based damage identification framework. High computational efficiency of such statistical model can solve the time consuming problem and reduce computational demand of finite element modelling of the PZT-structure interaction, especially for complex structures.

Remarks

Physics-based EMI methods can provide a good understanding of the mechanism between the impedance response changes and structural damages. Repeatability of the monitoring results can be achieved. However, such physics-based methods are limited by the drawbacks of different modelling methods. Some finite element modelling techniques for PZT-structure interaction systems have been developed. SEM has been provided to be more efficient in modelling in the high frequency range; however, it is difficult to apply this modelling technique for structures with a complex geometry. The only successful application is for the beam structure. In recent years, 3-D numerical finite element modelling technique has been applied to simulate the PZT-structure interaction and calculate impedance responses of relatively large scale and complex civil engineering structures. The main limitation is that the accurate simulation using finite element modelling is always accompanied with the relatively low computational efficiency, since the accuracy of results and scales of the predictable damage are highly dependent on the mesh size. Especially for the sensitivity-based EMI technique using model updating, the identification process normally consists of several iterations to update the physical parameters of the numerical model. A large number of unknowns are also introduced with numerous elements and included for the identification. Using sparse regularization can significantly reduce the computational demand and improve the identification accuracy. This makes the damage identification of structures by using the impedance responses more feasible for large scale structures. The concept of surrogated or meta-model can be a potential solution for overcoming this limitation. Detailed discussions and comparisons between different meta-modelling approaches, such as machine learning networks, are still necessary. Besides, all existing basic ideas of physics-based EMI approaches are predicated on solving the sensitivity-based inverse identification problem. The derivation of sensitivity matrix of complex structures is a topic worthy of investigations. Future work on physics-based EMI methods may focus on the simplified and efficient but accurate numerical modelling method for complex 3-D structures or the efficient algorithm for solving highly undetermined ill-posed inverse identification problem.

Practical issues

Even though various data-driven based and physics-based techniques have been developed to improve the performance of EMI based SHM methods, the previous investigations are basically conducted in the laboratory environment with small scale specimens and simplified boundary conditions. Environmental uncertainties, such as temperature variation, humidity, bonding condition, etc., remain the enormous challenge to the real world application of EMI techniques to civil engineering structures. The summary of the possible environmental factors have been provided by researchers (Bhalla et al., 2002; Guo et al., 2016), which focused on the previous studies for the most common and significant factors to EMI based methods, for example, the temperature effect. On the other hand, the limitations of the above-mentioned algorithms and methods provide some challenges to structural damage identification by using EMI technique. This section summarises the relevant studies and discusses the remaining issues for both physics-based and data-driven based approaches.

The temperature effects on impedance signatures have been reported. Park et al. (1999) discovered that the temperature variation leads both horizontal and vertical shifts on impedance response signatures. In addition to the effects on the properties of piezoelectric material itself, the softening on the bonding layer caused by the increasing ambient temperature was also observed (Sun et al., 1995; Tawie and Lee, 2010). Bhalla (2004) recommended that the bonding thickness only affects the impedance signature when thickness exceeds the one-third of the PZT patch’s thickness. Yang et al. (2008) comprehensively investigated the effects of the bonding layer thickness and temperature variations on the impedance signatures based on experimental and numerical studies. Based on the comparison between groups of PZT patches (10 mm × 10 mm × 0.3 mm) with different thicknesses, the results showed that the bonding layers with different thicknesses basically possess identical interaction in PZT-structure system. Slight variation was only appeared in the high frequency range around 1000 kHz. On the other hand, a severe deviation was observed from the PZT patch with thicker bonding layer than the thinner specimen under temperature variation. Baptista et al. (2014) investigated temperature variation effect on the impedance signatures in different frequency ranges. It is found that the frequency shifts caused by temperature change are not constant over all frequency bands, but increase with the frequency.

To overcome the environmental effect on the above-mentioned impedance response calculation and structural identification results, compensation methods have been developed to recover the distorted impedance data. Koo et al. (2009) estimated the effective frequency shifts to compensate the temperature impact by obtaining the maximum cross-correlation between the measured and reference impedance signatures. It should be noted that the working frequency range in the experimental study is from 30.5 kHz to 31.5 kHz, approximately with 1 kHz bandwidth. Sepehry et al. (2011) trained the ANN by using impedance responses from the intact structure under different temperatures to reduce the temperature effect on statistical based damage identification. Baptista et al. (2011) developed the real time data acquisition system from multiple sensors and used the frequency compensation method based on the estimated maximum correlation coefficient. Nevertheless, researchers investigated the thermal-insensitive damage indicators for EMI based methods. Lim et al. (2011) presented the impedance based damage detection method incorporated with a data normalization technique using Kernel principal component analysis (KPCA) to improve the robustness under environmental variations. Training data for the intact structure under various environmental conditions were collected and used to develop the baseline data group in a higher dimensional feature space using KPCA method. Damage can be identified by statistical analysis of the measured data. This study showed that the EMI features obtained by KPCA method are more sensitive to structural damage than temperature variation.

Although the performance of the above-mentioned techniques has been validated by experimental studies, the applications of these methods to large scale structures still have limitations. First of all, the measured impedance signature may not be completely matched well with the reference data in such a high working frequency range for EMI technique, due to varying environmental conditions and testing uncertainties. Consequently, setting up the applicable tolerance of different damage indicators with the compensation methods based on minimizing the difference of impedance responses, becomes very hard (Baptista et al., 2011). Moreover, the frequency shift in the measured impedance signature might be introduced by structural damage and temperature variation simultaneously. Repairing the shifted impedance signature of the structure under the unknown state based on the baseline data could cause the information loss for damage identification. Besides, the peaks at different frequencies may shift in either positive or negative direction. It is extremely difficult to compensate this effect completely (Na and Lee, 2016).

To solve the complex coupling issue between the effects of temperature variation and real structural damage in impedance response signatures, Li et al. (2021) presented an innovative CNN based EMI approach which is trained by the impedance signature samples of damaged structure incorporated with the samples under temperature variations. The network model successfully identifies the severity level of the concrete crack under different temperatures.

To quantify the temperature effect, Grisso and Inman (2010) carried out the temperature dependent model to quantify the impedance changes with respect to temperature variation, considering the thermal dependency of PZT material properties. However, to the best of authors’ knowledge, no specific compensation method for temperature variation in physics-based EMI methods has been reported. Yang et al. (2008) presented an interesting observation that the temperature variation induced frequency shift in the high frequency range from 200 to 1000 kHz was negligible in the impedance signature with structural damages. With more experimental studies, structural damage and environmental uncertainties may be separated by using the impedance characteristics from different frequency ranges and different patterns. This remains as a further research question for experimental and numerical studies.

Conclusions

In this article, a comprehensive review of recent developments and applications of the EMI based SHM methods is provided. This review classifies the EMI based damage identification approaches into two categories: data-driven based and physics-based methods. The theoretical background and practical applications of these two categories of EMI based SHM methods are considered. Both merits and shortcomings of these methods are discussed.

While using EMI techniques for SHM has been developed for over two decades, the widely applied damage evaluation approaches based on estimating the impedance signatures by one statistical indicator still have limitations in damage quantification and localization. Conventional machine leaning approaches, new deep leaning approaches and other pattern recognition algorithms are incorporated with EMI technique to extend the capacity of these methods and the utilization of impedance signatures. Even though such combinations provide successful identification and characterization of structural damages, the data-driven based EMI techniques only provide phenomenological characterizations of impedance changes without formulating the relationship between the impedance responses and changes in mechanical parameters of the host structure. Achieving a high accuracy and repeatability of damage identification with limited impedance data remains as a big challenge. With accurate numerical models, physics-based EMI approaches have great potentials in detailed damage quantification and localization. However, finite element modelling with high fidelity may require a significant computational effort and the SEM may have the limitation of simulating complex structures, future studies of physics-based methods need to focus on the more efficient numerical modelling, and accurate optimization algorithms for inverse identification problem. Nevertheless, investigations on the reliable compensation method for environmental uncertainties are conducted, since temperature effect is crucial to both categories of EMI based damage identification approaches. With new technologies in numerical simulation and mathematical optimization, EMI technique is becoming a promising SHM technique with more capabilities.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Jun Li

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