Structural Health Monitoring Based on AR Models and PZT Sensors

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detection in Structural Health Monitoring (SHM) systems, which is based on ... The AR models are obtained in both healthy and damaged conditions and used.
Structural Health Monitoring Based on AR Models and PZT Sensors Mario Anderson de Oliveira

Jozue Vieira Filho

Department of Electric and Electronic Federal Institute of Education, Science and Technology of Mato Grosso (IFMT) Cuiabá/MT, Brazil [email protected]

Department of Electrical Engineering Universidade Estadual Paulista (UNESP) Ilha Solteira/SP, Brazil [email protected]

Abstract—This paper presents a new approach for damage detection in Structural Health Monitoring (SHM) systems, which is based on the Electromechanical Impedance (EMI) principle and Autoregressive (AR) models. Typical applications of EMI in SHM are based on computing the Frequency Response Function (FRF). In this work the procedure is based on the EMI principle but the results are determined through the coefficients of AR models, which are computed from the time response of PZT transducers bonded to the monitored structure, and acting as actuator and sensors at the same time. The procedure is based on exciting the PZT transducers using a wide band chirp signal and getting its time response. The AR models are obtained in both healthy and damaged conditions and used to compute statistics indexes. Practical tests were carried out in an aluminum plate and the results have demonstrated the effectiveness of the proposed method.

time series analysis to detect, locate and estimate the extent of structural changes. The authors used Auto-Regressive models with eXogenous input (ARX) to create clusters for different set of sensors. In [5], it was proposed an AR model to characterize nonlinear damages and the exogenous coefficients were used to characterize linear damage states. In [6], a damage indicator was proposed as being the distance between ARMA models. In [7] the authors proposed to use ARX model in the frequency domain along with Extreme Value Statistics (EVS) for non–linear damage detection in vibration problems. In [8-9] the authors used the AR models for linear prediction model combined with ARX models. It was employed to compute input parameters for the subsequent analysis. Another application of damage detection and localization for structure using time series analysis can be found in [10].

I. INTRODUCTION Researches in Structural Health Monitoring (SHM) and damage detection have been developed in several academics and industries laboratories. The monitoring of structural integrity through Nondestructive Evaluation (NDE) methods has been grown in the last years because its capacity of detecting a variety of structural damages. The goal is to offer a better degree of security and reduce costs of maintenance. There is a variety of NDE methods for SHM applications, but special attentions has been given to those based on Electromechanical Impedance (EMI) [1], which are anchored in small and lightweight piezoelectric wafer active sensor bonded to the monitored structure.

This work proposes a new approach for damage detection which is based on Electromechanical Impedance (EMI) principle. Differently of traditional EMI applications in which Frequency Response Function (FRF) is a basic parameter, the proposed method uses the time response of the PZTs bonded to the structure to directly estimate AR models. Afterward, the AR model coefficients are used to compute the Root Mean Square Deviation (RMSD) indexes. The RMSD index is widely used in damage detection applications and it is computed considering a reference signal called baseline and obtained from the structure in healthy condition. The results were compared to the ones obtained using a traditional EMI method [13] and show that the proposed method is efficient in detecting damage.

Different type of numeric analysis, signal processing, statistic indexes, time series and other mathematics techniques have been used for detecting and localizing structural damages. Currently, autoregressive models (AR) have widely been used by several researchers. In [2], the authors proposed a time analyses of EMI using AR models. Nevertheless, the ARX was used to estimate a frequency response function (FRF). In [3], autoregressive move average (ARMA) model was used along with principal components analysis (PCA) in a vibration problem. In [4] the authors used

II. AR METHOD BASED ON THE EMI PRINCIPLE The technique based on the Electromechanical Impedance (EMI) applied to SHM was originally proposed by [11]. In this technique is necessary to excite the structure in an appropriated frequency range through the PZT attached to the monitored structure and get its response using the same PZT. In other words, the PZT is acting as actuator and sensor at the same time. In general, the results from these measurements

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are used to determine the FRF and later the Electromechanical Impedance (EMI) [12]. In a following step, statistical indexes are calculated and analyzed to verify the structure condition. The more common statistics indexes used for the purpose of SHM are Root Mean Square Deviation (RMSD) and Correlation Coefficient Deviation Metric (CCDM), which are computed using signals obtained from the set PZT/structure in both healthy and unknown conditions. The analysis in time-domain based on the EMI principle is very recent and it was proposed by [13]. In that work, the authors proposed to detect damage using multilevel wavelet decomposition through the response from a piezoelectric wafer in an impedance-based SHM system. The authors compared the traditional EMI based on FRF with wavelet based method through the RMSD and CCDM indexes. In [14], the authors proposed a new method in which the time response of PZT provides information on the electromechanical impedance variation when a monitored structure was damaged. The results using the FRF and time response were compared through the RMSD index as well. The time-domain analysis can be analyzed using the circuit presented in Fig. 1. This circuit is used to excite the PZT and gets its response [15].

At =

1

At-1 +

2

At-2 + …+

n

At-n +

t

(2)

In (2), t represents a process with zero of mean and variance 2 . Defining an AR operator of order n by (3), (D) = 1-

1

D-

2

D 2 - …-

n

Dn

(3)

the AR model can be rewritten briefly as follows: (D) At = t.

(4)

The coefficients 1, 2, …, n can be determinate through several methods such as: Burg method, method of moments (through Yule Walker equations), least square method and other. In this work, the coefficients are estimated by using the least square method. The signals used in this work were acquired through the system presented in Fig 2 [15], which is based on a multifunctional Data Acquisition (DAQ) device (model USB6259). A microcomputer running LabVIEW® controls the DAQ device and provides the discrete signals x[n] and y[n] which represent the excitation and response signals, respectively. For the correct application of this methodology, the D/A (digital to analog) and A/D (analog to digital) converters, which are integrated to the DAQ device, must be synchronized. Therefore, each sample n is synchronously generated and sampled in the excitation and response signals.

Figure 1. Excitation circuit of PZT and get its signal response.

From Fig. 1 the transfer function is given by: Y/X= Z/(Z + Rs)

(1)

In (1), Z represents the impedance of the couple PZTstructure, Rs is a precision resistor used to limit current through the PZT, and Y and X represent the phasors voltage of Vy(t) and Vx(t), respectively. The time response Vy(t) can be obtained through an inverse Fourier or Laplace transform considering the excitation signal Vx(t). In fact, when Z and Vx(t) change, the response Vy(t) changes as well. Considering Vx(t) as a fixed signal, any change in the response signal Vy(t) is caused only by variation of the impedance Z. In this work, the AR coefficients are estimated directly from the time response signal and used to calculate the RMSD indexes. Thus, the inverse transform is not necessary and the damage detection process becomes quick and objective. AR models are considered stochastic models and can be useful used to represent time series. Thus, an AR process of order n can be represented by a linear combination of previous values and a white noise t as follows [16 - 17]:

Figure 2. Measurement system.

III. EXPERIMENTAL SETUP AND RESULTS The proposed method is based on the electromechanical impedance principle. For this, a chirp signal from DC to 250 kHz was used to excite the set PZT/structure (Fig.1). Using the systems presented in the Fig 2, four response signals (sensors 1, 2, 3 and 4) were acquired considering the structure in healthy condition to storage the reference signals called baseline. After that, the damage A was simulated and new signals were obtained from the PZT. This procedure was similarly repeated for other two simulated damages (B and C). As a result, twenty datasets were obtained considering the healthy and damaged structural conditions. The resistance Rs was fixed at 10 and each sampled signal contains 262,144 data points sampled at 1.25 Msample/s. The AR models were estimated according to equation (4) and using Matlab®. A total of twenty AR model was obtained.

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A. Results and analysis for proposed method To verify the proposed method, tests were carried out using an aluminum plate of size 500 x 300 x 2 mm. Four piezoceramic wafers PSI-5H4E sized of 20 x 20 x 0.267 mm from Piezo Systems were bonded to the plate using “super glue”. Three removable damages (A, B and C) were simulated bonding a steel nut of 4 x 2 mm and about 1 g to the structure at different distances from the actuators and the sensors. This procedure is illustrated in the Fig. 3.

Figure 5. RMSD indexes for sensor 2.

Figure 3. Experimental configuration (dimensions in millimeters).

Using the procedure described previously, the dataset were acquired and analyzed. The orders of the AR models were chosen through Akaike information criterion (AIC). As an example, Fig. 4 shows the AIC for baseline and damage B considering only the sensor 4. For other cases the results are very similar. Analyzing the Fig. 4, it can be seen that an AR model of 10th order is good enough to represent the signals.

Figure 4. Akaike information criterion.

Figure 6. RMSD indexes for sensor 4.

B. Results and comparison between FRF and AR method In order to compare the proposed method (AR coefficients) with the traditional EMI based on the FRF, the FRF was computed according to the system proposed in [19]. The frequency range chose for this approach was 30 to 40 kHz which provides more sensitivity for damage detection. Also, only the real part of impedance was used to compute the damage indexes [12]. The RMSD indexes were calculated considering the healthy condition (baseline) as a reference. Fig 7 shows the results for both EMI and AR model techniques. Because the 8th coefficient is the best one, the comparison was carried out using only that coefficient. Then, it is possible to detect the presence/absence of structural damage in both techniques. As one can see, both methods indicate that it is possible to distinguish healthy and damaged conditions.

Considering only models of order ten, it was estimated one model for each test situation, summarizing 20 models. From the estimated AR models coefficients, the RMSD indexes were calculated using always the baseline as a reference. Although the variations among the AR coefficients are very subtle, a good prognostic on damage can be obtained using the RMSD indexes. Accordingly, the RMSD indexes were computed for each sensor (1, 2, 3 and 4) and each simulated damage (A, B and C). The results for sensor 2 an sensor 4 are presented in Fig. 5 and Fig. 6, respectively. It can be observed that the 8th coefficients are more propitious for damage detection. The results are similar for the other sensors. Figure 7. Comparison between AR and EMI (without normalization).

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As a way to improve the results analysis, the RMSD indexes for both techniques (EMI and AR coefficients) were normalized considering the healthy condition as a reference for each sensor. These results, considering only the 8th AR coefficients, are presented in the Fig. 8.

REFERENCES [1]

[2]

[3]

[4]

[5]

[6]

[7] Figure 8. General comparison between AR and EMI (normalizated).

Although both methods have presented excellent results for damage detection, it can be seen that the sensitivity for the proposed method, using time-domain with AR coefficients, is more significant than traditional method using FRF/EMI.

[8]

[9]

IV. CONCLUSION This work presented a novel method for damage detection applied to SHM using AR models. This method is based on EMI principle but the AR coefficients are estimated directly from the signals response in time-domain. As a consequence, it is not necessary to compute both FRF and electromechanical impedance. The RMSD indexes were calculated from the AR coefficients and used to detect damage. The 8th coefficients of the AR model showed more sensitivity to detect damage than the other ones. Furthermore, the experimental results show that the proposed method is more sensitive than FRF based methods. Perhaps, methods based only on time-domain and AR models can be used for damage detection applications in which the traditional EMI present low sensitivity.

ACKNOWLEDGMENT The authors would like to thank the Capes Foundation, Ministry of Education of Brazil, by support through the process DINTER 23038.034330/2008-32, and CNPq and FAPEMIG for partially funding the present research work through the INCT-EIE.

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

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K. Worden and J. M. Dulieu-Barton, “Overview of Intelligent Fault Detection in System and Structures,” Structural Health Monitoring, vol. 03, pp. 85–98, March 2004. S. Silva, M. Dias Junior and V. Lopes Junior, “Structural Health Monitoring in Smart Structures Through Time Series Analysis,” Structural Health Monitoring, vol. 7(3), pp. 231–244, September 2008. S. Silva, M. Dias junior, V. Lopes Junior and M. J. Brennan, “Structural Health Monitoring in Smart Structures Through Time Series Analysis,” Mechanical System and Signal Processing, vol. 22(7), pp. 1636–1649, October 2008. M. Gul and F. N. Catbas, “Structural Health Monitoring and Damage Assessment Using a Novel Time Series Analysis Methodology with Sensor Clustering,” Journal of Sound and Vibration, vol. 330, pp. 1196–1210, March 2011. D. E. Adams and C. R. Farrar, “Classifying Linear and Nonlinear Structural Damage Using Frequency Domain ARX Models,” Structural Health Monitoring, vol. 1(2), pp. 185–201, October 2002. D. E. Adams and C. R. Farrar, “Damage Indicator Dened as the Distance between ARMA Models for Structural Health Monitoring,” Structural Control and Health Monitoring, vol. 15, pp. 992–1005, November 2008. T. R. Fasel, H. Sohn, G. Park and C. R. Farrar, “Active Sensing Using Impedance-Based ARX Models and Extreme Value Statistics for Damage Detection,” Earthquake Engineering and Structural Dynamics, vol. 34, pp. 763–785, January 2005. H. Sohn, D. W. Allen, K. Worden and C. R. Farrar, “Structural Damage Classification Using Extreme Value Statistics,” Journal of Dynamic Systems, Measurement and Control, vol. 127, pp. 125–132, March 2005. H. Sohn and C. R. Farrar, “Damage Diagnosis Using Time Series Analysis of Vibration Signals,” Smart Material and Structures, vol. 10, pp. 446–451, September 2000. Z. Xing and A. Mita, “A Substructure Approach to Local Damage Detection of Shear Structure,” Structural Control and Health Monitoring, vol. 19(2), pp. 309–318, March 2012. C. Liang, F. P. Sun and C. A. Rogers, “Coupled Electromechanical Analysis of Adaptive Material Systems – Determination of the Actuator Power Consumption and System Energy Transfer,” Journal of Intelligent Material Systems and Structures, vol. 5, pp. 12 – 20, January 1994. G. Park, H. Sohn, C. R. Farrar and D. J. Inman, “Overview of Piezoelectric Impedance-Based Health Monitoring and Path Forward,” Shock and Vibration Digest, vol. 35, pp. 451–463, November 2003. J. Vieira Filho, F. G. Baptista and D. J. Inman, “Time-Domain Analysis of Piezoelectric Impedance-Based Structural Health Monitoring Using Multilevel Wavelet Decomposition,” Mechanical Systems and Signal Processing, vol. 25, pp. 1550–1558, July 2011. J. Vieira Filho, F. G. Baptista, J. Farmer and D. J. Inman, “TimeDomain Electromechanical Impedance for Structural Health Monitoring,” In: 8th International Conference on Structural Dynamics (Eurodyn 2011), pp. 2043–2046, July 2011. F. G. Baptista and J. Vieira Filho, “A New Impedance Measurement System for PZT-Based Structural Health Monitoring,” IEEE Transactions on Instrumentation and Measurement, vol. 58(10), pp. 3602–3608, October 2009. D. S. G. Pollock, R. Green and T. Nguyen, A Handbook of Time-Series Analysis, Signal Processing and Dynamics, 1rd ed., vol. 1. Academic Press, 1999. G. E. P. Box, G. M. Jenkins and G. C. Reinsel, Times Series Analysis Forecasting and Control, 4rd ed., Wiley, 2008.