Piezoelectric Lead Zirconate Titanate Patches Research Articles

Experimental Study on the Detection of the Existence and Location of Mimicked and Unexpected Interface Debonding Defects in an Existing Rectangular CFST Column with PZT Materials.

Interface bonding conditions between concrete and steel materials play key roles in ensuring the composite effect and load-carrying capacity of concrete-steel composite structures such as concrete-filled steel tube (CFST) members in practice. A method using both surface wave and electromechanical impedance (EMI) measurement for detecting the existence and the location of inaccessible interface debonding defects between the concrete core and steel tube in CFST members using piezoelectric lead zirconate titanate (PZT) patches as actuators and sensors is proposed. A rectangular CFST specimen with two artificially mimicked interface debonding defects was experimentally verified using PZT patches as the actuator and sensor. By comparing the surface wave measurement of PZT sensors at different surface wave travelling paths under both a continuous sinusoidal signal and a 10-period sinusoidal windowed signal, three potential interface debonding defects are quickly identified. Furthermore, the accurate locations of the three detected potential interface debonding defects are determined with the help of EMI measurements from a number of additional PZT sensors around the three potential interface debonding defects. Finally, the accuracy of the proposed interface debonding detection method is verified with a destructive observation by removing the local steel tube at the three detected interface debonding locations. The observation results show that the three detected interface debonding defects are two mimicked interface debonding defects, and an unexpected debonding defect occurred spontaneously due to concrete shrinkage in the past one and a half years before conducting the test. Results in this study indicate that the proposed method can be an efficient and accurate approach for the detection of unknown interface debonding defects in existing CFST members.

Solar cell micro crack detection technique using electromechanical impedance and finite element analysis

Electromechanical impedance (EMI) is one of the modern techniques employed in the field of structural health monitoring (SHM) and has witnessed a great expansion in many domains due to its ability to ensure continuous monitoring and high reliability with a lower cost. Hence, the purpose of this study is to investigate the effectiveness of EMI in monitoring and detecting pre-existing cracks in the silicon layer of the photovoltaic (PV) solar cells. Indeed, a detailed finite element analysis (FEA) on the effect of piezoelectric lead zirconate titanate (PZT) patch shape on the EMI of crystalline-silicon (c-Si) layer of the PV solar cells were performed. The typical structure (c-Si + PZT) of different scenarios were stimulated by giving a lower voltage and high frequency as input data to extract the EMI signature as an explainable output result. Different models were investigated based on PZT patch types and crack position in the silicon layer. The results indicate that the EMI technique is effective in detecting crack, even in its incipient stage. The analysis suggests using a higher frequency range (350–650 kHz) for characterizing damage with an invisible depth due to the higher sensitivity of the EMI technique in this specific frequency.

Adhesive curing effect of bonded piezoelectric transducer on electromechanical impedance-based concrete structural damage detection

Complete understanding of the adhesive curing effect of a bonded piezoelectric lead zirconate titanate (PZT) sensor on the electromechanical admittance (EMA, inverse of impedance) facilitates the accurate diagnosis of structural damages when employing the impedance technique for structural health monitoring. This article analytically and experimentally investigated the curing effect of adhesive layer on the EMA-based concrete structural damage detection. Curing effect was theoretically incorporated into shearing mechanism of adhesive layer to formulate a new one-dimensional PZT-structural impedance model. Analytical analysis of the curing effect on the EMA signature as well as the EMA-based damage diagnosis was calculably interpreted through the model. Proof-of-concept experiment was performed on testing a four-point bending reinforced concrete (RC) beam bonded with multiple PZT patches under adhesive curing. Experimental results demonstrated that singular shift in the EMA spectra under adhesive curing could be turned into three typical shifts when structural damage occurred, which cogently validated the analytical results. Quantifiable signal index further provided useful information for the identification of crack occurrence, progression, and reinforcement yielding of the RC beam. Results of this study potentially promoted the real-life engineering applications of impedance technique inclusive of deficient adhesive condition.

Corrosion assessment in rebars of high-strength concrete using electromechanical impedance technique

The corrosion of steel rebar in reinforced concrete structures is one of the main reasons for early deterioration and premature failure of concrete structures, leading to enormous restoration costs worldwide infrastructure restoration. In the past, many sensors and techniques have been developed to monitor corrosion in steel rebar. However, the Electromechanical Impedance (EMI) technique using the piezoelectric Lead Zirconate Titanate (PZT) patches has been immersed as a promising technique to detect damages at an incipient level. This paper presents the corrosion assessment in embedded rebar in high-strength concrete using surface-bonded PZT patches through the EMI technique. The High Yield Strength Deformed (HYSD) rebars of Fe415 grade embedded in high-strength M60 grade concrete cylindrical specimens were used for the experimental work. The artificial corrosion in the embedded rebar was simulated through the accelerated corrosion test for 180 days. The conductance signatures were acquired through a surface-bonded PZT patch on embedded rebar. First, qualitative and quantitative corrosion assessment was carried out based on the conductance signature and the Root Mean Square Deviation (RMSD). Second, the effectiveness of extracted equivalent parameters was demonstrated for capturing the degradation of stiffness and mass due to corrosion. Finally, the corrosion rate is evaluated through equivalent parameters, and a comparison was made with the actual mass loss. The experimental study demonstrated that the EMI technique could be used very effectively through the statical index RMSD and equivalent parameters to identify corrosion phases and resulting losses in stiffness and mass of the structure.

Mesoscale numerical analysis and test on the effect of debonding defect of rectangular CFSTs on wave propagation with a homogenization method

In this paper, in order to distinguish the influence of both interface debonding defect and the mesoscale structure of concrete core on the stress wave field and the response of an embedded Piezoelectric-lead-zirconate-titanate (PZT) sensor in rectangular concrete filled steel tube (RCFST) members efficiently, a two dimensional (2D) mesoscale numerical concrete homogenization approach for concrete core considering the random distribution of circular, elliptical and irregular polygonal aggregates is proposed firstly. Then, mesoscale simulation on stress wave fields within the cross-section of RCFST members with and without interface debonding defects using both mesoscale models and their homogenization models are carried out, respectively. The effect of both mesoscale structure of concrete core and the interface debonding defects on the stress wave field of each member is discussed and the efficiency of the homogenization approach is illustrated. Therefore, the time-domain response of an PZT sensor embedded in the concrete core of RCFST members coupled with PZT patches under sweep frequency excitation signal is determined with multi-physics field simulation and compared when both mesoscale models and their homogenization models are used. Then, the sensitivity of the wavelet packet energy of the embedded PZT sensor response on the variation of both mesoscale structure of concrete core and the dimension of interface debonding defects is investigated in details. Finally, in order to illustrate the difference in the significance of the effect of interface debonding defect and the mesoscale structure of concrete core on stress wave propagation, comparative test with a set of RCFST members without and with interface debonding defects is carried out. Test results also show that the influence of interface debonding defects on embedded PZT sensor response and the stress wave fields is dominant. The detectability of interface debonding detection approach using stress wave measurement is illustrated efficiently with the proposed equivalent homogenization mesoscale modelling approach even the mesoscale structure of the concrete core is considered.

Effect of external vibrations on Electro-Mechanical impedance signatures in damage detection

Piezoelectric Lead Zirconate Titanate (PZT) transducers have gained their application in Structural Health Monitoring (SHM). The surface bonded PZT patches are actuated by an external voltage under a specified frequency range and the Electro Mechanical Impedance (EMI) Signatures are captured which can be utilized to assess and monitor structural health. Generally, with the assumption of the structure is excited only by the PZT actuator the health of the structure is assessed and monitored. However, the changes in the EMI signatures due to external vibrations are not taken into account and interpretation will lead to wrong assessments. The current paper focuses on the study of external vibration with different excitation frequencies and amplitudes on EMI signatures of healthy and damaged beams. Finite element analysis is conducted on a cantilever aluminium flat and the conductance signatures are extracted and the influence of external vibrations on EMI signatures is analyzed and presented.

Numerical assessment of induced damages of RC frames using PZT patch in embedded configurations with and without bond layer

Abstract In the present times, health monitoring is playing a key role in assessing the damages occurred in the civil structures. The current study deals with estimating damages induced to a reinforced concrete (RC) frame using ceramic piezoelectric Lead zirconate titanate (PZT) patches in embedded forms. Coupled field analysis on finite element models have been performed for acquiring the electro-mechanical impedance (EMI) response of structure in transducer excitation frequency range of 100–200 kHz. Two-fold study have been carried out to numerically analyze the performance of damage monitoring system with increasing crack depths that are induced at critical locations in the presence and absence of adhesive bond layer between PZT patch and surrounding concrete. Regression models based on root mean square deviation of EMI signatures have been proposed to estimate the severity of damages in RC frames.

Delamination area quantification in composite structures using Gaussian process regression and auto-regressive models

After detecting initial delamination damage in a hotspot region of a composite structure monitored through a data-driven approach, the user needs to decide if there is an imminent structural failure or if the system can be kept in operation under monitoring to track the damage progression and its impact on the structural safety condition. Therefore, this study proposes delamination area quantification by stochastically interpolating global damage indices based on Gaussian process regression and taking into account uncertainty. Auto-regressive models are applied to extract damage-sensitive features from Lamb wave signals, and the Mahalanobis squared distance is used to compute damage indices. Two sets of laboratory tests are used to demonstrate the effectiveness of this methodology—one in carbon–epoxy laminate with simulated damage under temperature changes to show the general steps of the procedure, and a second test involving a set of carbon fiber–reinforced polymer coupons with actual delamination caused by repeated fatigue loads. Various levels of progression damage, measured by the covered area of delamination, are monitored using piezoelectric lead zirconate titanate patches bonded to the structural surfaces of these setups. The Gaussian process regression proved to be capable of accommodating the uncertainties to relate the damage indices versus the damaged area. The results exhibit a smooth and adequate prediction of the damaged area for both simulated damage and actual delamination.

Local wave propagation analysis in concrete-filled steel tubes with spectral element method using absorbing layers – Part II: Application in coupling system

In this paper, a two-dimensional (2D) time domain spectral element method (SEM) is developed for concrete-filled steel tube (CFST) and piezoelectric lead zirconate titanate (PZT) patches coupling system, where the piezoelectric and inverse piezoelectric effect of PZT actuator and sensor and their coupling effect with CFST are considered. The local wave field and the response of the embedded PZT sensor was numerically studied in a substructure of the CFST coupled with PZT patches and surrounded by absorbing layers with increasing damping (ALID) and the performance of the ALID in attenuating wave reflection at boundaries of the coupling substructure model is further investigated. Then, numerical simulation on the effect of interface debonding defect on local wave propagation within the coupling substructure model surrounded by the designed ALID was carried out. By comparing the displacement-based wave fields and the response of the embedded PZT sensor within the substructure, the effect of interface debonding defect on the wave propagation along the steel tube and in the concrete core, and the time history of the response voltage of the embedded PZT sensor is investigated in detail. Numerical results show that interface debonding defects in the substructure leads to changes in the wave propagation path, the local wave field, the time duration of wave travelling to the embedded PZT sensor from the PZT actuator mounted on the surface of the steel tube of CFST, as well as response voltage of the embedded PZT sensor. In addition, PZT sensor measurement is sensitive to the length of interface debonding defects but insensitive to their depth. SEM for the coupling substructure model with ALID instead of the model of whole cross section of CFST provides an efficient way to simulate the local elastic wave propagation for understanding the mechanism of the interface debonding defects detection approach based on wave measurement.

Embedded electrical impedance-based PZT sensor for monitoring hydrating concrete: development and evaluation

The development of an embeddable sensor, which can be placed inside concrete for continuous monitoring of changes in the material brought about by hydration is presented. The embedded sensor relies on monitoring changes in the electrical impedance (EI) measured from a piezoelectric lead zirconate titanate (PZT) patch placed inside hydrating concrete. The EI measurements over a range of frequencies is associated with the dynamic response of the PZT patch with distinct resonant frequencies. The EI of the PZT sensor is reflective of the mechanical impedance to its motion from the surrounding concrete medium. Changes in the EI measurements from an embedded PZT sensor with time relate with the kinetics of cement hydration. The increase in the resonant frequency in the EI spectrum is produced by the increase in the Young’s modulus of the concrete medium. The changes in the resonant conductance amplitude are sensitive to changes in the stiffness of medium associated with a change in the state and the setting behavior of concrete. The role of the epoxy coating provided as protection to the PZT element is to restrict the motion in the early stages of hydration and to allow relative motion of the PZT element when the concrete gains in stiffness. An idealized representation of the embedded PZT sensor is developed for representing the dynamic impedance to its motion from the epoxy and the surrounding concrete medium. The changes in the EI resonant amplitude of an embedded PZT provides a sensitive measure of the setting behavior and early stiffening of the concrete post-setting. The changes in the resonant frequency of the embedded PZT sensor provide a continuous measure of the evolution of stiffness of the concrete throughout the setting and hardening process.

Debonding detection for rectangular CFST using surface wave measurement: Test and multi-physical fields numerical simulation

Abstract The interfacial debonding detection approach for concrete-filled steel tubular (CFST) members using surface-mounted piezoelectric-lead-zirconate-titanate (PZT) actuators and sensors is experimentally and numerically investigated. In this study, an interfacial debonding detection approach using surface wave measurement with PZT patches is propoed firstly and experimental investigation on the feasibility of the proposed approach with two CFST specimens with different levels of interface debonding defects is carried out. For comparison, a PZT sensor is also embedded in concrete core to measure the stress wave traveling from the surface-mounted PZT actuator. Experiment results indicate that the voltage amplitude of the embedded PZT sensor representing the wave propagation from the steel plate into the concrete core decreases due to the existence of interfacial debonding defect, but the output signal of the surface-mounted PZT sensor increases accordingly when interface debonding occurs. Moreover, the increment of surface-mounted PZT sensor measurement is related to the dimension of the interface debonding defects. The experimental finding implies that the interface debonding is detectable using surface wave measurement. In order to investigate the mechanism of the proposed approach, numerical study on the wave propagation process in CFSTs is further discussed by using three-dimensional (3D) solid element models and two-dimensional (2D) plane strain models, respectively. Finally, in order to consider the effect of nonhomogeneous meso-scale structure of concrete on the wave propagation, a random aggregate method (RAM) is employed to model the concrete core and multi-physical fields coupling numerical analysis on stress wave propagation of the CFST member with different interface debonding defects is performed. The numerical findings meet well with the experimental observations and the results indicate that the interface debonding of CFST can be detected efficiently using surface wave measurement.

Multi-Scale Stress Wave Simulation for Aggregates Segregation Detection of Concrete Core in Circular CFST Coupled with PZT Patches.

In this study, the numerical investigation of the detectability of concrete aggregate segregation in circular concrete-filled steel tubulars (CCFST) based on piezoelectric lead zirconate titanate (PZT) measurement is performed. The stress wave propagation in the concrete core of circular CCFST excited with a surface-mounted PZT actuator is studied with multi-scale and multi-physical field coupling analysis. The piezoelectric effect of PZT patches and its coupling effect with CFSTs are considered. Numerical concrete modeling technology is employed to construct the concrete core composed of randomly distributed aggregates with and without aggregate segregation at different levels, mortar, and an interfacial transition zone (ITZ). The effects of the random distribution of elliptical aggregates, aggregate segregation, and the existence of ITZ in the concrete core on the wave fields in the cross-section and the corresponding voltage response of the embedded PZT sensor are discussed. An evaluation index based on wavelet packet analysis on the output voltage response is defined, and its sensitivity to concrete aggregate segregation is systematically investigated. The multi-scale and multi-physics coupling simulation results indicate that concrete aggregate segregation in the concrete core of CFST members can be efficiently detected based on the stress wave measurement with a PZT sensor.

Mechanical characterization of 3D printed anisotropic cementitious material by the electromechanical transducer

3D concrete printing is an innovative and promising construction method that is rapidly gaining ground in recent years. This technique extrudes premixed concrete materials through a nozzle to build structural components layer upon layer without formworks. The build-up process of depositing filaments or layers intrinsically produce laminated structures and create weak joints between adjacent layers. It is of great significance to clearly elaborate the mechanical characteristics of 3D printed components response to various applied loads and the different performance from the mould-cast ones. In this study, a self-developed 3D printing system was invented and applied to fabricate concrete samples. Three points bending test and direct double shear test were carried out to investigate the mechanical properties of 3D printed prisms. The anisotropic behaviors were probed by loading in different directions. Meanwhile, piezoelectric lead zirconate titanate (PZT) transducers were implemented to monitor the damage evolution of the printed samples in the loading process based on the electromechanical impedance method. Test results demonstrate that the tensile stresses perpendicular to the weaken interfaces formed between filaments were prone to induce cracks than those parallel to the interfaces. The damages of concrete materials resulted in the decrease in the frequency and a change in the amplitude in the conductance spectrum acquired by mounted PZT patches. The admittance signatures showed a clear gradation of the examined damage levels of printed prisms exposed to applied loadings.

2-D Statistical Damage Detection of Concrete Structures Combining Smart Piezoelectric Materials and Scanning Laser Doppler Vibrometry

In the present study a new structural health monitoring (SHM) technique is proposed as well as a new damage index based on 2-D error statistics. The proposed technique combines the electromechanical impedance technique (EMI) which is based on the use of piezoelectric Lead Zirconate Titanate (PZT) patches and Scanning Laser Doppler Vibrometry (SLDV) for damage detection purposes of concrete structures and early age monitoring. Typically the EMI technique utilizes the direct and inverse piezoelectric effect of a PZT patch attached to a host structure via an impedance analyzer that is used for both the actuation and sensing the response of the PZT-Host structure system. In the proposed technique the attached PZTs are actuated via a function generator and the PZT-Host structure response is obtained by a Scanning Laser Doppler Vibrometer. Spectrums of oscillation velocity of the surface of the attached PZTs vertical to the laser beam versus frequency are obtained and are evaluated for SHM purposes. This damage detection approach also includes the use of a damage index denoted as ECAR (Ellipse to Circle Area Ratio) based on 2-D error statistics and is compared to the Root Mean Square Deviation (RMSD) damage index commonly used in SHM applications. Experimental results include ascending uniaxial compressive load of concrete cubic specimens, ascending three point bending of reinforced concrete beam specimens and early age monitoring of concrete. Results illustrate the efficiency of the proposed technique in damage detection as well as early age monitoring as, in the first case, both severity and location of damage can be determined by examining the values of damage indices for each damaged state and in the early age monitoring case damage indices follow the strength gain curve.

Multi-physical field guided wave simulation for circular concrete-filled steel tubes coupled with piezoelectric patches considering debonding defects

The active interface debonding detection for concrete-filled steel tubes (CFSTs) using Piezoelectric Lead Zirconate Titanate (PZT) patches has been proposed and experimentally studied in recent years. In order to further investigate the guided wave propagation and the response of embedded PZT sensor, transient dynamic analysis on multi-physical field coupling models composed of surface-mounted PZT actuator, embedded PZT sensor and a circular CFST specimen considering the coupling effect between the PZT patches and CFST member and the influence of interface debonding defects is carried out numerically. The guided wave propagation within the CFST-PZT coupling system without and with interfacial debonding defects under single period impulse signal is simulated and compared. The voltage response time history of the embedded PZT sensor in coupling models under both sinusoidal and sweep frequency sinusoidal excitations are simulated as an alternative solver. Numerical results demonstrate that interface debonding leads to changes in guided wave propagation path, traveling time and the PZT sensor response. The sensitivity of a quantitative evaluation index called as the normalized wavelet packet energy of the output voltage of embedded PZT sensor to the initiation of interface debonding defect and its length and depth is illustrated.

Diagnosis of carbonation induced corrosion initiation and progression in reinforced concrete structures using piezo-impedance transducers

In addition to chloride induced corrosion, the other commonly occurring type of rebar corrosion in reinforced concrete structures is that induced by the ingress of atmospheric carbon dioxide into concrete, commonly referred to as ‘carbonation induced corrosion’. This paper presents a new approach for detecting the onset and quantifying the level of carbonation induced rebar corrosion. The approach is based on the changes in the mechanical impedance parameters acquired using the electro-mechanical coupling of a piezoelectric lead zirconate titanate (PZT) ceramic patch bonded to the surface of the rebar. The approach is non-destructive and is demonstrated though accelerated tests on reinforced concrete specimens subjected to controlled carbon dioxide exposure for a period spanning over 230days. The equivalent stiffness parameter, extracted from the frequency response of the admittance signatures of the PZT patch, is found to increase with penetration of carbon dioxide inside the surface and the consequent carbonation, an observation that is correlated with phenolphthalein staining. After the onset of rebar corrosion, the equivalent stiffness parameter exhibited a reduction in magnitude over time, providing a clear indication of the occurrence of corrosion and the results are correlated with scanning electron microscope images and Raman spectroscopy measurements. The average rate of corrosion is determined using the equivalent mass parameter. The use of PZT ceramic transducers, therefore, provides an alternate and effective technique for diagnosis of carbonation induced rebar corrosion initiation and progression in reinforced concrete structures non-destructively.

Active Debonding Detection for Large Rectangular CFSTs Based on Wavelet Packet Energy Spectrum with Piezoceramics

AbstractThe debonding between the steel tube and the confined concrete core of concrete-filled steel tubes (CFSTs) can weaken the confinement effect of the steel tube on the concrete core and may induce a decrease in the load-carrying capacity and in the ductility. The debonding detection technique for CFSTs is still a challenging problem resulting from the inaccessibility and invisibility of the interface. In this paper, by embedding piezoelectric lead zirconate titanate (PZT) based functional smart aggregates (SAs) in concrete core as actuators and pasting PZT patches on the predetermined locations of the outer surfaces of the specimen as sensors, a novel active interface condition monitoring approach for rectangular CFST members is proposed and is experimentally validated with a scale rectangular CFST specimen with artificial debonding defects. Analysis of the wavelet packet energy spectrum (WPES) of the measurements of PZT patches is carried out, and a damage index, called the weighted variation of WP...

Monitoring of the strength gain of concrete using embedded PZT impedance transducer

Piezoelectric lead zirconate titanate (PZT) impedance transducer in the electro-mechanical impedance (EMI) technique has emerged as a potential sensing tool for structural health monitoring. In the EMI technique, PZT acts as both sensor and actuator simultaneously due to its direct and inverse piezoelectric effects. The PZT impedance transducer provides a new alternative for monitoring the compressive strength gain of concrete since the conventional nondestructive detection techniques have many limitations. This paper briefly presents a waterproof process for PZT patches using asphalt lacquer material in order to use PZT patches as embedded transducers into concrete, and also presents a new monitoring technique of concrete strength based on embedded PZT impedance transducers. In the technique, a PZT patch covered with asphalt lacquers are embedded into one of concrete cubes. By monitoring the PZT admittance (inversion of impedance) signals and measuring the compressive strength of concrete cubes in different ages, and by combining with the indexes of the root mean-square deviation (RMSD) and the mean absolute percentage deviation (MAPD), the correlations between concrete strength gain and RMSD as well as its correlation with MAPD are founded. The feasibility of the new EMI method based on embedded PZT transducers for monitoring the concrete strength development in early ages is verified.

Piezoelectric sensor based nondestructive active monitoring of strength gain inconcrete

The recent advent of smart materials, such as piezoelectric materials, shape-memory alloys,and optical fibers, has added a new dimension to present structural health monitoringtechniques. In particular, the electro-mechanical impedance (EMI) sensing techniqueutilizing piezoelectric materials has emerged as a potential tool for the implementation of abuilt-in monitoring system for damage detection of civil structures. However, there is littleeffort to apply this technique for concrete monitoring. In this study, an effort to extend theapplicability of the EMI sensing technique is made for strength gain monitoringof early age concrete. PZT (piezoelectric lead zirconate titanate) patches areemployed to sense the EMI signature of curing concrete. A series of experiments wasconducted on concrete specimens to verify the applicability of the EMI sensingtechnique. The results show the excellent potential of the EMI sensing techniqueas a practical and reliable nondestructive method for strength gain monitoring.

Quantitative structural damage detection using high‐frequency piezoelectric signatures via the reverberation matrix method

AbstractHigh‐frequency structural analysis so far has been a major issue in dynamic analysis, for which many conventional methods such as finite element method and transfer matrix method are unable to perform well. Since the electromechanical impedance technique for structural health monitoring (SHM) operates at very high frequencies, the reverberation matrix method (RMM), which was just developed a few years ago, is employed to study dynamics of the monitored structures, which are bonded with piezoelectric lead zirconate titanate (PZT) patches. A piecewisely homogeneous Euler–Bernoulli beam model is introduced to approximate the non‐homogeneous beam and only one‐dimensional axial vibration of PZT wafers is considered. The imperfect interfacial bonding between PZT patches and the host beam is investigated based on a shear lag model. Using a hybrid technique combining electromechanical impedance method and RMM, an analytical expression of impedance (or admittance) related to the response of the coupled model of PZT patch‐bonding layer‐host beam system is derived for SHM. The proposed method is examined by comparing with other theoretical methods as well as by means of a test on an intelligent system using a steel beam with two symmetrically installed PZT wafers. It could be further applied to predicting the dynamics of monitored Timoshenko beams, continuous beams, and framed structures as well. Copyright © 2006 John Wiley & Sons, Ltd.