Implementation of KENDA at ARPA-SIMC and first experiences with an OSSE
Damage Analysis in a Composite Plate Using ......SIMC 2018 - Proceedings of the VI Symposium of...
3
SIMC 2018 - Proceedings of the VI Symposium of Intelligent Materials and Control Ilha Solteira, SP, Brazil, April 18-19, 2018 Damage Analysis in a Composite Plate Using Autoregressive mod- els Jess ´ e A. Paix˜ ao 1 , Luis G. G. Villani 2 and Samuel da Silva 3 1,2,3 Universidade Estadual Paulista - UNESP, Faculdade de Engenharia de Ilha Solteira, Departamento de En- genharia Mec ˆ anica, Av. Brasil, 56, Ilha Solteira — SP, Brasil — 15385-000. [email protected] 1 , [email protected] 2 , [email protected] 3 . Abstract: Composite structures are widely employed in many industrial sectors due to their high strenght properties. However, the damage scenario complexity of these materials complicates the use of SHM techniques based on physic models. In this context, it is proposed the identification of autorregressive models, considering a stiffened compos- ite plate, to study the relationship between the models coefficients variation and presence of damage, under different temperatures. The results had shown that autorregressive coefficients are sensible to the presence of damage. Keywords: composite plate, damage detection, Lamb waves,autoregressive model. INTRODUCTION Composite materials have been increasingly used in various industrial sectors, in particular, the aeronautic industry that requires a high structural reliability. Unfortunately, like all materials, they have inherent defects caused by imper- fections and manufacturing flaws that due to aging and degradations processes can generate damage, compromising the structure operation and causing an immense monetary loss and even loss of life (Worden, 2007). Driven by this problem, recent advances and technical breakthroughs, the process of applying damage detection methods called Structural Health Monitoring has been widely studied in composite materials, in particular Lamb-wave-based damage identification method in recent years (Su and Ye, 2009). Lamb waves - elastic waves in thin plate/shell structures have high sensitivity to abnormalities near the wave propa- gation path. This characteristic is very helpful to damage identification, because analyzing the wave propagation signal from an actuator to a sensor in two different states (healthy and damaged) it is possible to predict the structure state and the severity. Another characteristic that makes Lamb wave attractive to SHM on composite material is the propagation over a relatively long distance even in materials with high attenuation ratios, allowing a broad area to be covered with only a few transducers. So, the damage detection problem in composite materials considering Lamb waves propagation, it is mature in academic scenery (Su and Ye, 2009). One of the greatest current challenges is to evaluate the damage progression without the need of intricate physics based models in the presence of measurement variability (Cano, 2015). In this work it is proposed to use the coefficients of autoregressive models (AR), identified in healthy and damaged conditions, in the SHM problem applied in a composite plate with the goal of study the relationship between the models coefficients variation and presence of damage, under different temperatures, as initial step aiming the solution of the damage progression problem. DAMAGE ANALYSIS USING AR-COEFFICIENTS VARIATION Considering a discrete-time linear system, time-invariant, the output y(k) can be expressed using a simple AR-model (Ljung, 1998) y(k)= -a 1 y(k - 1) - ... - a n a y(k - n a )+ ξ (k) (1) where a 1 ,..., a n a are the model coefficients and ξ (k) is a Gaussian noise and n a is the order of the AR model. So, in this situation, the output in instant k can be estimated by the sum of the system output in the previously instants weighted by the model coefficients. The model error ξ (k) is assumed to be a white noise without any dynamics behavior. So, to study the influence of the presence of damage and temperature variation to the value of the coefficients estimated, a model is identified in each different structural condition, and compared through the relation Δ(a n )= |a unk n - a re f n | |a re f n | × 100 (2) where Δ represents the percentage variation of the coefficient, n is the number of the AR-coefficient, a re f n is the coefficient estimated in reference condition, a unk n is the coefficient estimated in unknown condition and | ... | is the absolute operator. With the calculation of this index it is possible to study the variation of the AR-coefficients with changes in temperature and structural conditions (presence of damage).
Transcript of Damage Analysis in a Composite Plate Using ......SIMC 2018 - Proceedings of the VI Symposium of...
SIMC 2018 - Proceedings of the VI Symposium of Intelligent Materials and ControlIlha Solteira, SP, Brazil, April 18-19, 2018
Damage Analysis in a Composite Plate Using Autoregressive mod-elsJesse A. Paixao1, Luis G. G. Villani2 and Samuel da Silva3
1,2,3 Universidade Estadual Paulista - UNESP, Faculdade de Engenharia de Ilha Solteira, Departamento de En-genharia Mecanica, Av. Brasil, 56, Ilha Solteira — SP, Brasil — 15385-000. [email protected],[email protected], [email protected].
Abstract: Composite structures are widely employed in many industrial sectors due to their high strenght properties.However, the damage scenario complexity of these materials complicates the use of SHM techniques based on physicmodels. In this context, it is proposed the identification of autorregressive models, considering a stiffened compos-ite plate, to study the relationship between the models coefficients variation and presence of damage, under differenttemperatures. The results had shown that autorregressive coefficients are sensible to the presence of damage.
Keywords: composite plate, damage detection, Lamb waves,autoregressive model.
INTRODUCTION
Composite materials have been increasingly used in various industrial sectors, in particular, the aeronautic industrythat requires a high structural reliability. Unfortunately, like all materials, they have inherent defects caused by imper-fections and manufacturing flaws that due to aging and degradations processes can generate damage, compromising thestructure operation and causing an immense monetary loss and even loss of life (Worden, 2007). Driven by this problem,recent advances and technical breakthroughs, the process of applying damage detection methods called Structural HealthMonitoring has been widely studied in composite materials, in particular Lamb-wave-based damage identification methodin recent years (Su and Ye, 2009).
Lamb waves - elastic waves in thin plate/shell structures have high sensitivity to abnormalities near the wave propa-gation path. This characteristic is very helpful to damage identification, because analyzing the wave propagation signalfrom an actuator to a sensor in two different states (healthy and damaged) it is possible to predict the structure state andthe severity. Another characteristic that makes Lamb wave attractive to SHM on composite material is the propagationover a relatively long distance even in materials with high attenuation ratios, allowing a broad area to be covered withonly a few transducers. So, the damage detection problem in composite materials considering Lamb waves propagation,it is mature in academic scenery (Su and Ye, 2009). One of the greatest current challenges is to evaluate the damageprogression without the need of intricate physics based models in the presence of measurement variability (Cano, 2015).
In this work it is proposed to use the coefficients of autoregressive models (AR), identified in healthy and damagedconditions, in the SHM problem applied in a composite plate with the goal of study the relationship between the modelscoefficients variation and presence of damage, under different temperatures, as initial step aiming the solution of thedamage progression problem.
DAMAGE ANALYSIS USING AR-COEFFICIENTS VARIATION
Considering a discrete-time linear system, time-invariant, the output y(k) can be expressed using a simple AR-model(Ljung, 1998)
y(k) =−a1y(k−1)− ...−anay(k−na)+ξ (k) (1)
where a1, . . . ,ana are the model coefficients and ξ (k) is a Gaussian noise and na is the order of the AR model. So, in thissituation, the output in instant k can be estimated by the sum of the system output in the previously instants weighted bythe model coefficients. The model error ξ (k) is assumed to be a white noise without any dynamics behavior.
So, to study the influence of the presence of damage and temperature variation to the value of the coefficients estimated,a model is identified in each different structural condition, and compared through the relation
∆(an) =|aunk
n −are fn |
|are fn |
×100 (2)
where ∆ represents the percentage variation of the coefficient, n is the number of the AR-coefficient, are fn is the coefficient
estimated in reference condition, aunkn is the coefficient estimated in unknown condition and | . . . | is the absolute operator.
With the calculation of this index it is possible to study the variation of the AR-coefficients with changes in temperatureand structural conditions (presence of damage).
Damage Analysis in a Composite Plate Using Autoregressive models
APPLICATION IN A COMPOSITE PLATE
The system considered in this study is a 400 × 300 [mm2] composite stiffened plate made of monolithic carbonepoxy (Fig. 1) (Mechbal and Rebillat, 2017). It is a multi-layered structure consisting of 4-plies oriented along [0◦/ 45◦/-45◦/ 0◦]. There are 6 numbered piezoelectric elements (PZTs) positioned at specific points on the plate’s surface to beused as actuators and sensors (Fig. 1). The PZTs have a diameter of 20 [mm], a thickness of 0.1 [mm] and have beenmanufactured by Noliac. The measurements are repeat considering 6 different controlled temperatures (0,15,30,45,60and 75◦C) and a real debonding on the center of the bottom part of the stiffener is considered as damage condition. Thesystem is monitored through the use of Lamb waves. The excitation signal is a 5 cycles ”burst” with a central frequencyof 200 [kHz] and with an amplitude of 10 [V]. In all experiments conduced, one PZT is set as actuator and all of them assensors. The signals are sampled considering sampling ratio of 1 [MHz] and 500 samples.
(a) Photo. (b) Scheme.
Figure 1 – Experimental setup.
Damage evaluation
The main results were obtained considering the PZT 2 as actuator, because this PZT is closer to the damage. In allstructural conditions emulated, considering different environmental temperatures, the AR-models were estimated, andthen, the index presented in Eq. 2 was calculated. The reference state considered was the healthy condition and 0◦ C oftemperature. It is important to observe that the model order is different depending of the number of the PZT consideredas sensor, because waves propagation it is very sensible of the path chosen. Figure 2 shows one example of the predictionobtained through model estimated. The order chosen in this situation was na = 20 and this path of propagation shows thebetter results to damage evaluation. It is observed that the model is able to describe the wave behavior.
0 100 200 300 400 500Time [µs]
-0.1
-0.05
0
0.05
0.1
Amplitude[V
]
(a) Comparison. (b) Resid.
Figure 2 – Model evaluation, considering PZT 2 as actuator, PZT 4 as sensor, healthy condition and 0◦ C oftemperature. −− represents the experimental response and −− the model response.
Figure 3 shows the variation of the AR coefficients, considering different temperatures and structural conditions. It isclear that, the greater variation caused by the presence of damage it is observed in PZTs 4, 5 and 6 in comparison withthe variation caused by temperature changes. This occurs because, in these situations, the wave is crossing the stiffener,where the damage is located. Additionally, Tab. 1 shows the mean variation obtained to the AR coefficients when PZT 2is choose as actuator. The greatest variation caused by the damage it is observed when the PTZ 4 is chose as sensor, butPZTs 5 and 6 also shows great variation. The dependence of the path chosen in the index performance it is interestingin the context of damage localization that can be explored in future works. The relationship between the AR coefficientsvariation and the damage propagation, even in the presence of temperature variation, has showed satisfactory results asdamage indicator, and can be, probably, used in the context of damage progression evaluation in future works.
L.G.G. Villani, S. da Silva, A. Cunha Jr
0 5 10 15 20AR coefficients
0
5
10
15V
aria
tion
[%]
(a) PZT 1 (na = 16).
0 5 10 15 20AR coefficients
0
2
4
6
8
10
12
Var
iatio
n [%
]
(b) PZT 2 (na = 20).
0 5 10 15 20AR coefficients
0
2
4
6
8
10
Var
iatio
n [%
]
(c) PZT 3 (na = 16).
0 5 10 15 20AR coefficients
0
20
40
60
80
100
120
Var
iatio
n [%
]
(d) PZT 4 (na = 20).
0 5 10 15 20AR coefficients
0
50
100
150
200
Var
iatio
n [%
]
(e) PZT 5 (na = 19).
0 5 10 15 20AR coefficients
0
20
40
60
80
100
Var
iatio
n [%
]
(f) PZT 6 (na = 20).
Figure 3 – Percentage variation of the AR coefficients, considering PZT 2 as actuator. represents 30◦ C andreference condition, represents 75◦ C and reference condition and represents 0◦ C and damaged condition.
Table 1 – Mean percentage variation of the AR coefficients, considering PZT 2 as actuator.
Sensor (PZT) Damaged condition Healthy condition Healthy conditionTemperature = 0◦C Temperature = 75◦C Temperature = 30◦ C
1 10 3 32 3 3 33 6 3 14 54 8 55 39 11 146 48 9 18
ACKNOWLEDGMENTS
The authors are thankful for the financial support provided from FAPESP, grant number 2012/09135-3, 2014/02971-6and 2015/25676-2, CNPq grant number 307520/2016-1, and Prof. Nazih Mechbal and Prof. Marc Rebillat from Arts etMetiers - Paristech for the data provided used in this work.
REFERENCESCano, W. F. R. (2015). Aplicao da anlise de sries temporais para deteco e prognstico de danos em estruturas inteligentes.
PhD thesis, Universidade Estadual Paulista. Faculdade de Engenharia de Ilha Solteira.
Ljung, L. (1998). System Identification, pages 163–173. Birkhauser Boston, Boston, MA.
Mechbal, N. and Rebillat, M. (2017). Damage indexes comparison for the structural health monitoring of a stiffenedcomposite plate. In VIII ECCOMAS Thematic Conference on Smart Structures and Materials.
Su, Z. and Ye, L. (2009). Identification of Damage Using Lamb Waves: From Fundamentals to Applications. LectureNotes in Applied and Computational Mechanics. Springer London.
Worden, K. (2007). The fundamental axioms of structural health monitoring. In Proceedings of the Royal Society A:Mathematical, Physical and Engineering Science, The Royal Society.
RESPONSIBILITY NOTICE
The author(s) is (are) the only responsible for the printed material included in this paper.
