PAPER REF: 17220
EXPERIMENTAL AND NUMERICAL STUDY OF RMSD - A DAMAGE INDEX OF ELECTRO-MECHANICAL IMPEDANCE-BASED
STRUCTURAL HEALTH MONITORING
Mojtaba Khayatazad1,4(*), Jonathan Deschodt1, Mia Loccufier2, Hans De Backer3, Wim De Waele1
1SOETE LAB., Dep. Electromech. Sys. and Metal Eng., Faculty of Eng. and Arch., Ghent Univ., Gent, Belgium
2DSC, Dep. Electromech., Sys. and Metal Eng., Faculty of Eng. and Arch., Ghent Univ., Gent, Belgium
3CEBR, Dep. Civil Engineering, Faculty of Eng. and Arch., Ghent Univ., Gent, Belgium
4VLAIO, Safelife Project (project number 179P04718W)
(*)Email: [email protected]
ABSTRACT
Structural health monitoring of civil infrastructures is of great importance to timely inform operators with respect to continued economic and safe exploitation. A promising technique for damage detection of components is to use piezoelectric sensors and the electromechanical impedance method. Despite a great amount of research that has already been published, there is an undeniable need for improved signal post-processing and defining a reliable damage index.
A damage index reported by many researchers is the so-called root mean square deviation (RMSD). RMSD is a statistical metric used to calculate the amount of deviation of the impedance signal of a structure in an unknown, probably damaged, condition with respect to a baseline signal which represents the undamaged condition. Based on a limited number of experiments, some researchers conclude that there exists a quantitative trend between RMSD and damage level while a sound scientific reason has not been presented. In this paper, we investigate the feasibility of this damage index by dedicated numerical simulations and experiments. The investigated component is a rectangular thick steel plate, hosting a rectangular piezoelectric patch and with different levels of crack-like damage introduced. This study reveals that although the commonly used damage index can be efficiently used to detect the presence of a crack, there is no meaningful trend between the extent of damage and the RMSD value. A scientific-based approach for monitoring (the change in) the damage level is under investigation by the authors.
Keywords: piezoelectric, RMSD, damage, Electro-mechanical impedance, SHM.
INTRODUCTION
Since the integrity, safety and durability of engineered structures such as bridges, aircrafts etc.
are of great importance, a huge amount of research studies on condition monitoring have been performed. There are plenty of review articles in the relevant literature, e.g. vibration based condition monitoring (Boscato, Fragonara, Cecchi, Reccia and Baraldi, 2019) and smart sensing technology (Sony, Laventure and Sadhu, 2019).
Among all health monitoring techniques, the electro-mechanical impedance-based method, hereafter EMI/SHM method, is a very promising technique because it uses low-cost, small and lightweight piezoelectric transducers, being minimally invasive and allowing its application in real-time and in-situ SHM systems (Fabricio Guimarães Baptista & Filho, 2009). The working principle of the EMI/SHM method is based on the piezoelectric property of specific materials
e.g. lead zirconate titanate (PZT). When deformation is applied on a piezoelectric material it generates an electrical charge, the direct effect, and it deforms by applying electric potential over it, the inverse effect, Figure 1a,b. This property sparked off the idea to make a device, a piezoelectric transducer, for sensing and actuating a host structure at the same time. (Liang, Sun and Rogers, 1994) showed that the mechanical impedance of the host structure is coupled to the electrical impedance of the attached piezoelectric transducer, Figure 1c. Based on the definition, electrical impedance is the ratio of the electric potential to the electrical current passing through a circuit. It is worthy to mention that the electrical impedance is measured in a frequency range of the applied alternating electric potential. The mechanical impedance means the resistance against movement and it can be calculated by dividing the applied harmonic force at a given point to the velocity of that point. Mechanical impedance is also calculated in a frequency domain.
(a) (b) (c)
Fig. 1 - Direct (a) and inverse effects (b) of piezoelectric materials open a new horizon to make sensing- actuating devices based on the coupling between electrical and mechanical impedance (c). Images are
taken from (Huynh, Dang, Kim, 2017)
In essence, to do condition monitoring by the EMI/SHM method, after installing the piezoelectric transducer on the host structure, the electrical impedance of the piezoelectric sensor is measured as a baseline. Any structure can be considered as a dynamic system with certain stiffness, mass and damping properties. Once some damage emerges in the structure, the structural parameters stiffness and damping will be affected which leads to a change in mechanical impedance and consequently a different electrical impedance measured by the piezoelectric transducer. This difference to the baseline impedance can be considered as an indication of structural damage. This paper focuses on the traditional way of comparing such impedance signals. In fact, various statistical indices can be found in the literature, including root mean square deviation (RMSD), mean absolute percentage deviation (MPAD), covariance (Cov) and correlation coefficient (CC). Equations of these damage metrics can be found in basic literature on the EMI/SHM method, e.g. (Na and Baek, 2018). Among all, RMSD is the most widely used damage metric for comparing different impedance signals. Many papers report RMSD as a metric to find and quantify damage in steel (Ai, Zhu, Luo and Yang, 2014), aluminium (Hamzeloo, Shamshirsaz and Rezaei, 2012a), concrete (Soh and Bhalla, 2005), and composite structures (Rebillat, Guskov, Balmes and Mechbal, 2016).
RMSD is more sensitive to the variations in the amplitude of the electrical impedance than the other damage metrics, (Sun, Chaudhry, Liang and Rogers, 1995), and can be calculated as follows:
…† ‡ ˆ‰ G…sGŠŒ‹N ‹JM1 …sGŠ‹J J/
‰ G…sGŠŒ‹N ‹J J/ (1)
Here, Re(Zk)i represents the real part of the baseline impedance of the intact structure, Re(Zk)j is the real part of the impedance corresponding to the unknown health state and N is the number
of frequencies under investigation. This index has been implemented as a damage indicator by several researchers, eg. (Huynh and Kim, 2017), (Koo, Park, Lee and Yun, 2009) and (Fabricio G. Baptista, Budoya, de Almeida and Ulson, 2014) state that by increasing the damage size, RMSD also increases. This claim has not been supported by any sound scientific reason and has been established based on a limited number of experiments. It is interesting to mention that, in some reports of this claim, one can see that by increasing the damage severity, RMSD values not continuously increase but also decrease, (Zhu, Wang and Qing, 2019).
In this paper, we investigate the feasibility of this damage index by dedicated numerical simulations and experiments. For this purpose, several tests on a steel plate with different damage scenarios are conducted and explained in section 2. In section 3, the procedure for numerical simulation of EMI/SHM is explained in detail and a numerical model with different damage scenarios is defined. Results of experimental tests and numerical simulations including EMI signatures for pristine and damaged models are gathered in section 4. The corresponding RMSD values are also calculated and presented in this section. Finally, this paper will arrive at a conclusion in section 5.
EXPERIMENTAL TEST
To study the effectiveness of RMSD for quantifying damage, a steel plate carrying 2 PZT transducers is tested. The dimensions of the steel plate and PZT transducers are 305×200×6 mm3 and 50×30×0.5 mm3 respectively. The PZT transducers are DuraAct P-876.A12. For installing the PZT transducers to the steel plate, a procedure for strain gauge installation was followed. This combination of steel plate and two PZT transducers constitute the pristine specimen.
Two damage configurations are investigated, defined as symmetric damage and asymmetric damage. Damage is introduced as through-thickness saw cuts that are executed in three steps, each time extended with an increment of 10 mm. Figure 2a shows the specimen and the damage locations. For measuring the EMI signatures, an NI data acquisition device (USB6356) accompanied by an auxiliary circuit is used, Figure 2b. The resistance of the auxiliary circuit is approximately 200 Ohms; the resistor value was chosen based on the DAQ data sheet, which states a maximal working current of 5 mA. Using this equipment, the EMI signature can be measured in a frequency range from 20 kHz to 160 kHz. To provide the free-free boundary condition, the specimen is hanged in a frame using some pieces of rubber. Figure 2c shows the final test setup.
(a) (b) (c)
Fig. 2 - (a) The schematic 2D drawing of the experimental setup (all dimensions in mm), (b) the auxiliary circuit for measuring the EMI signatures, (c) the final test setup
NUMERICAL SIMULATION
The numerical simulation of the interaction between a PZT buzzer and a host structure has been done by several authors using ANSYS (Lim and Soh, 2014), Abaqus (Hamzeloo et al., 2012a) and home-made software packages (Xu, Xu, Xu and Luo, 2016). In this paper, Abaqus CAE version 6.19.1 has been selected for this purpose. The development of the numerical simulation is explained hereafter by referring to the different modules of the simulation software.
Part module. Replicating the physical specimen mentioned in the previous section would result in a model with more than 1 million solid elements and extreme computational cost. This is because, for successful analysis, the element size should be small enough to represent the displacement of mechanical waves at very high frequencies. To solve this problem, a smaller but similar geometry, by keeping the aspect ratios constant, is used. The dimensions of the virtual steel plate and PZT transducer are 15×10×0.45 mm3 and 2.5×1.5×0.01 mm3 respectively.
Property module. The used material properties for the steel plate and the PZT transducers are presented in Table 1. The index notation in Table 1 is based on Abaqus’ conventions and the 3rd principal direction is considered as the polarization direction of the PZT transducer which is normal to the largest plane of the PZT transducer part. It should be mentioned that based on the recommendation of (Lim and Soh, 2014) for modeling the damping behavior of materials, the structural damping has been used.
Table 1 - Material data of PZT and steel PZT
Piezoelectric charge coefficients, 10-10[C/N] Permittivity, [F/m] 10-8 Damping
d1 13 d2 12 d3 11 d3 22 d3 33 D11 D22 D33 structural
5.500 5.500 -1.800 -1.800 4.000 1.461 1.461 1.549 6.25E-3
Stiffness, [N/m2] 1010 Density, [kg/m3]
D1111 D1122 D2222 D1133 D2233 D3333 D1212 D1313 D2323 !
10.200 5.480 10.200 5.310 5.310 8.420 2.000 2.000 2.000 7800
Steel
Stiffness, [N/m2] 1010 Poisson ratio Damping Density, [kg/m3]
E " structural !
21 0.3 1.00E-3 7800
Assembly module. The PZT transducer has been attached to the top surface of the steel plate.
There is no bonding layer in between for the sake of simplicity. Figure 3a shows the location of the PZT transducer on the steel plate.
Step module. To calculate the electrical impedance of a PZT transducer at a specific frequency, one should consider the steady-state dynamic response of the structure. A linear perturbation procedure using steady-state dynamic, direct analysis provided the frequency responses of the model between 50 kHz to 170 kHz at a frequency step of 10 Hz.
Interaction module. The backside of the PZT transducer is rigidly connected to the front side of the steel plate using tie constraint.
As will be explained in load module, constant electric potential should be applied to the back and front surface nodes of the PZT transducer. This necessitates the use of an equation constraint defined between a node, representative_node, and another group of nodes, node_group, Equation (2):
3 Y u • Ž /3 Žz ƒY ] (2)
where C1 and C2 are user-defined coefficients. For this paper, by defining C1=1 and C2=-1, the aforementioned condition for having constant electric potential will be obtained.
Seam in Abaqus is a 2-dimensional crack with a user-defined length and depth but its width is zero. In this paper, seam has been used for introducing a through-thickness edge crack at three different locations, Figure 3b-d. To study the damage progress at each location, three different crack lengths (0.25, 0.50, 0.75 mm) were simulated.
Load module. The model has a free-free boundary condition. For the back surface of the PZT transducer, a constant voltage of 0 volts is applied in initial and steady-state dynamic, direct analysis steps to simulate ground. A voltage of 1 volt is also applied at the front surface. It is worthy to mention that the polarization direction is normal to the front and back surfaces.
(a) (b) (c) (d) (e)
Fig. 3 - (a) The assembly of the steel plate and the PZT transducer, (b-d) different locations of the introduced damages, (e) the assigned mesh to the numerical model
Mesh module. Like any other FE analysis, mesh size determines the accuracy of the impedance spectrum. Mesh size should be several times smaller than the wavelength of the mechanical waves traveling in the steel and PZT material. (Wojcik, Vaughan, Abboud and Mould J, 1993) suggested a minimum of 15 elements per wavelength to limit wave dispersion errors to less than 1%. Based on this recommendation, (Hamzeloo, Shamshirsaz and Rezaei, 2012b) calculated the appropriate mesh size for steel and PZT material equal to 3.5 mm and 1.75 mm respectively for an FE electro-mechanical analysis up to 40 kHz. In this study, the maximum frequency for such an analysis has been considered to be 170 kHz. Therefore in this study, the used mesh sizes for the steel and the PZT parts are 0.8 mm and 0.4 mm respectively;
approximately 25% of those of Hamzeloo et al.. Fig. 3e shows the assigned mesh to the steel plate and the PZT transducer; the elements used are C3D8R and C3D8E respectively.
Post-processing. . From an experimental and numerical point of view, calculation of admittance (the inverse of impedance) is easier because in its denominator there is a real number, V( ). In this paper for both numerical simulation and experimental test, V( ) is equal 1. One can calculate the electrical admittance of the PZT transducer using Equation (3):
•G‚J •G‚J
G‚J •3 ‚3 … ‘#G‚J
G‚J (3)
where i is the imaginary unity, is the applied frequency of the potential voltage. RCHG is the complex nodal electric charge, for that representative node on which the non-zero voltage has been applied, obtained by applying a sweep frequency on the model.
RESULTS
In this section, the experimental and numerical results of the EMI/SHM study are presented.
Concerning the experiments, the reported results are limited to the signatures of PZT A, see Figure 2a. Figure 4 presents the real (conductance) and the imaginary (susceptance) parts of the electrical admittance when the specimen is in pristine condition. Introducing damage to the pristine specimen changes the EMI signatures; Figure 5 shows the conductance for different damage scenarios, three crack-like damages introduced at two different locations. To address these damages, a name format Damage-Loc-Len is used. For example, Damage-2-20 means damage at location 2 with a length of 20 mm. RMSD values for these damage scenarios are calculated using Equation (1) and are presented in this section after the numerical simulation results.
Fig. 4 - EMI signatures of the pristine specimen from the experimental test, (a) conductance, (b) susceptance. Conductance and susceptance are measured in siemens unit, S
.
Fig. 5 - EMI signatures of the pristine and damaged specimen from the experimental test, (a) Damage 1, (b) Damage 2
The results of the numerical simulation for the pristine model in the frequency range from 50 kHz to 170 kHz are presented in Figure 6. It is worth mentioning that one should not compare these results with the experimental results because the dimensions of the numerical and physical models are different. Figure 7 shows the effect of damage on the pristine EMI signatures between 120 kHz to 125 kHz. Similar to Figure 5, Figure 7 shows a small portion of the whole frequency range to deliver visually comparable images. As can be seen, the effects of damage on the signatures are very complex. As mentionedbefore, despite this complexity and without any sound scientific reason, some researchers try to find a relation between RMSD value and damage severity. So to investigate this claim, RMSD values are calculated and presented for the different damage scenarios and both numerical and experimental results. For calculating the RMSD values of experimental and numerical signatures, the frequency range of 20 kHz to 160 kHz and 50 kHz to 170 kHz have been used, respectively.
Fig. 6 - EMI signatures of the pristine specimen from the numerical simulation, (a) conductance, (b) susceptance
Fig. 7 - EMI signatures of the pristine and damaged specimen from the numerical simulation, (a) Damage 1, (b) Damage 2, (c) Damage 3
As shown in Figure 8a which is for the experimental test, the RMSD value for the small size damage at location 1 is less than the RMSD value for the small size damage at location 2, but this damage at location 2 is at a further distance from the PZT transducer. This subtlety is valuable because some other authors also suggest that the closer damage to a PZT transducer,
the more RMSD. But this claim does not hold here. By increasing the damage size from small to medium in Figure 8a, the RMSD values show different behaviors for damages at locations 1 and 2. And finally, going from the medium to the large damage size, the RMSD values of the experimental results change their trend for both damages at locations 1 and 2. So based on the experimental results, there is no uniform trend between RMSD and damage size. RMSD serves as a qualitative warning that damage has occurred, but it does not allow to quantify or locate damage. Figure 8b, showing the RMSD values obtained from the numerical results, does not show a meaningful trend as well. Interestingly, although for the small damage sizes, the damage at location 1 is closer to the PZT transducer, damage at location 2 has the most RMSD value.
For the medium size damages, the RMSD value of the damage at location 3 which is the farthest one is more than the others.
(a) (b)
Fig. 8 - RMSD calculated for (a) physical and (b) numerical models is a useful qualitative tool for damage detection but thus not allow to quantify the level of damage. For damage
locations, refer to Figures 2 and 3
CONCLUSION
This paper reports on an experimental and a numerical study to evaluate the effectiveness of RMSD as damage metric in EMI based structural health monitoring. The admittance signatures of PZT sensors installed on steel plates with different types of damage have been experimentally recorded and numerically simulated. Both numerical simulations and experiments reveal that RMSD is a useful metric to distinguish a damaged structure from an undamaged one, but that it does not show a unique relationship with the level of damage. The authors also evaluated RMSD values for different sub frequency ranges of the higher defined ranges; the conclusion is however similar. Damage has a complex effect on the high frequency mechanical behaviour of the structure and the electromechanical impedance that cannot be grasped in one unique parameter. The authors are currently investigating the feasibility of quantifying the amount of damage using an alternative approach based on evaluation of frequency shifts.
ACKNOWLEDGMENT
The authors acknowledge the financial support of Vlaio through the SafeLife project (project number 179P04718W) and also the support by SIM (Strategic Initiative Materials in Flanders) and the IBN Offshore Energy.
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