Load monitoring and compensation strategies for guided-waves based structural health monitoring using piezoelectric transducers

Journal of Sound and Vibration 351 (2015) 206–220

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Load monitoring and compensation strategies for guided-waves based structural health monitoring using piezoelectric transducers Surajit Roy a,n, Purim Ladpli b, Fu-Kuo Chang b a b

Pacific Northwest National Laboratory, Richland, WA 99354, USA Stanford University, Department of Aeronautics and Astronautics, Stanford, CA 94305, USA

a r t i c l e in f o

abstract

Article history: Received 21 October 2014 Received in revised form 23 March 2015 Accepted 20 April 2015 Handling Editor: G. Degrande Available online 11 May 2015

Accurate interpretation of in-situ piezoelectric sensor signals is a challenging task. This paper presents the development of a numerical compensation model based on physical insight to address the influence of structural loads on piezo-sensor signals. The model requires knowledge of in-situ strain and temperature distribution in a structure while acquiring piezoelectric sensor signals. The parameters of the numerical model are obtained using experiments on flat aluminum plate under uniaxial tensile loading. It is shown that the model parameters obtained experimentally can be used for different structures, and sensor layout. Furthermore, the combined effects of load and temperature on the piezo-sensor response are also investigated and it is observed that both of these factors have a coupled effect on the sensor signals. It is proposed to obtain compensation model parameters under a range of operating temperatures to address this coupling effect. An important outcome of this study is a new load monitoring concept using in-situ piezoelectric sensor signals to track changes in the load paths in a structure. Published by Elsevier Ltd.

1. Introduction Ultrasonic guided-waves based structural health monitoring (SHM) using in-situ piezoelectric sensor measurements has received considerable attention in the recent decades. These high frequency mechanical disturbances can propagate to remote and inaccessible locations in a structure, carrying the potential to enable automated, on-demand health inspection, thus paving the way for real-time integrity assessment of the structure in service. However, certain challenges still exist that need to be addressed especially in the area of compensation of environmental and operational influence on the guidedwaves based sensing. The guided-waves apart from being sensitive to structural changes are also influenced by variations in ambient temperature and loading conditions which, if not addressed, will make it difficult to interpret and monitor the health of a structure from in-situ sensor data, leading to false diagnostics and prognostics. Several strategies in literature for compensating the influence of change in ambient temperature on ultrasonic guide-waves do exist [1–5] that primarily require a set of baseline sensor measurements under different temperature environments. However, very little research has

n

Corresponding author. E-mail addresses: [email protected] (S. Roy), [email protected] (P. Ladpli), [email protected] (F.-K. Chang).

http://dx.doi.org/10.1016/j.jsv.2015.04.019 0022-460X/Published by Elsevier Ltd.

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been carried out to develop load compensation models for ultrasonic guided waves based SHM using piezoelectric transducers. Dependency of wave propagation velocity in stressed solids is referred to as acoustoelasticity. Hughes et al. [6] first derived expressions for velocities of elastic waves in stressed solids. It was shown that for isotropic materials, apart from Lame's constants λ, and μ, three additional constants l, m, and n are required to describe the material. These additional constants were later referred to as Murnaghan constants in the literature. The paper also reported values of these additional materials constants based on experimental observation of variations in longitudinal and transverse wave velocities under applied stress. Later Toupin et al. [7] extended the results from [6], for the case of materials with arbitrary symmetry. The equations derived in the paper formed the basis for analysis of plane waves of small amplitudes, propagating in an initially deformed and stressed elastic material. Gandhi et al. [8] derived disperse relations for Lamb wave propagation in an initially stressed elastic material. The study found linear variation of wave propagation velocity with applied uniaxial stress, and an angular variation due to directional dependency of wave propagation. Based on these observations, Michaels et al. [9] proposed an expression for change in phase velocity of Lamb waves that depends on the magnitude of applied stress and wave propagation direction. Lee et al. [10] presented comparison of changes in applied loads, and homogeneous temperatures on guided-wave propagation in an aluminum plate. It was observed that both of these factors affect the wave propagation velocity by same order of magnitude. It should be noted here that for guided-waves based SHM using piezoelectric transducers, apart from changes in phase shifts under varying ambient temperatures and loads, amplitudes of the piezoelectric sensor measurements also get affected. Very few studies in the literature are available to account for the changes in signal amplitude of piezo-transducers under the influence of applied loads. This paper attempts to develop a load compensation model for ultrasonic guided waves based SHM using piezoelectric transducers accounting for the changes in both the phase-shifts and signal amplitude. 2. Problem statement Real-time SHM based on ultrasonic guided-waves has to address the influence of varying environments and operating conditions on the sensor signals. Existing data-driven temperature compensation models (no such models for loads as yet) require a set of baseline sensor measurements. Acquiring baseline sensor data for model training under the combined influence of different ambient temperatures and operating loads will be practically challenging with implications on time and cost involved in the process. Hence, given piezoelectric sensor layout and structural configuration, it is desired to develop an efficient physics-based compensation model that can address the combined influence of varying loads and ambient temperatures on in-situ piezoelectric sensor measurements. 3. Method of approach Fig. 1 shows the schematic of the method of approach as proposed in this study for developing load compensation model for guided-wave based SHM using piezo-sensor signals. The influence of variation in applied loads on piezo-sensor response, especially on signal amplitudes, is experimentally investigated on thin metallic plates. A numerical compensation model is developed based on theoretical framework and insight from the experimental observations. The developed compensation model takes strain and temperature distribution on the structure as an input and reconstructs piezo-sensor signal under the specified environments for a given structure and sensor layout. Reconstructed sensor signals thus obtained may be used to filter out the influence of varying ambient temperature and load conditions from in-situ sensor measurements however, the scope of this study is restricted to obtain accurate compensated waveforms under different environments. In this paper, investigation of load influence on sensor signals is primarily carried out on the first wave packets corresponding to the direct wave propagation path between an actuator and sensor. This is due to the fact that later parts of the received sensor signal are affected by contributions from primary wave sources, as well as by reflections from structural edges and boundaries (secondary sources) making the task of signal processing and interpretation, difficult.

Fig. 1. Proposed method of approach for developing load compensation model.

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Fig. 2. Data acquisition setup and typical effect of uniaxial loads on piezo-transducers response; (a) uniaxial testing machine with environmental chamber, (b) schematic of instrumented flat plate, (c) typical piezoelectric sensor signal using S6–S2 transducer pair, (d) relative change in signal amplitude under different uniaxial tensile loads.

4. Experimental stuides: load influence Fig. 2a shows uniaxial testing machine which is also equipped with an environmental chamber to collect sensor signals under varying ambient temperatures. Fig. 2b shows the schematic of a test coupon, a thin aluminum plate, instrumented with piezo-transducers spatially distributed in order to capture the angular variation of signal amplitude and time-of-arrival (ToA) data under applied mechanical loads. The sensor data are obtained using toneburst actuation waveform (5-cycle Gaussian with Hanning-window) at center excitation frequency of 250 kHz using ScanGenies, a 64-channel data acquisition system provided by Acellent Technologies Inc. The excitation frequency is selected so as to obtain clear wave packets in the sensor response. Signals were collected at incremental uniaxial tensile loads in pitch-catch mode wherein one transducer acts as an actuator while the others act as sensors. Fig. 2c shows a typical actuation and sensor response for a specific piezotransducer pair. As mentioned earlier, first wave packets in the sensor signals are identified and focused upon to study the influence of applied loads. Fig. 2d shows the effect of uniaxial tensile load on first wave packet of piezo-sensor response. It can be observed that signal amplitude (maximum peak of the envelope) for an actuator–sensor pair varies linearly with load. And the slope of this linear relationship seems to be influenced by the wave propagation direction and the loading direction. This behavior, effect of change in signal amplitude under applied loads, as observed experimentally is quite similar to the angular dependency of change in wave propagation velocity with applied uniaxial tensile loads as reported in the literature [8,9] wherein a uniaxial tensile load is supposed to have two primary direct effects on guided wave propagation between two attached sensors. The first relates to changes in dimensions, which affect both the plate thickness and the transducer

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Fig. 3. Ultrasonic guided wave propagation in plate like structures.

separation distance. The second is the change in wave speeds with applied loads. A numerical expression for capturing the change in wave propagation velocity due to applied load in the material was proposed in Michaels et al. [9]. h

i

δcp ¼ cp K 1 cos 2 θ þ K 2 sin 2 θ σ 11

(1)

where cp is the wave propagation velocity, σ 11 is the uniaxial stress, θ is the direction of wave propagation, K 1 , and K 2 are the acoustoelastic constants for the particular excitation frequency and applied stress direction. However, no such relationship exists to account for the changes in piezo-sensor signal amplitude under the influence of applied loads. The following section presents a theoretical framework to address changes in signal amplitude under varying environments and operating conditions, by associating it with the affected material properties related to guided-wave based sensing system.

5. Analytical framework Fig. 3 shows the stage-wise description of generation, transmission and recording of ultrasonic guided waves from a pair of piezoelectric transducers attached to the surface of a flat plate-like structure. Typically, ultrasonic guided-waves are induced using piezoelectric transducers attached to a structure. A piezo-transducer is excited with a voltage waveform, inducing ultrasonic disturbances in the form of radially propagating waves in a structure. These mechanical disturbances propagate to the other transducer locations in a structure wherein due to piezoelectric effect; electric charge distribution is set up owing to the induced mechanical strains in the transducer. An output voltage waveform can thus be measured resulting from this electric charge distribution. As shown in Roy et al. [11], for piezoelectric transducers surface-bonded on a flat isotropic plate, voltage output V out ðt Þ measured from a piezo-sensor can be related to the excitation voltage V in ðt Þ applied to a piezo-actuator as: V out ðt Þ ¼ d31

ðact Þ

C actuator ðΓÞC sensor ðΓÞ



d31 Y E ε33 ð1  νÞ

ðsenÞ

V in ðt Þ

(2)

ðact Þ

where d31 is the piezoelectric actuation coefficient in the in-plane (1-) direction due to applied electric field in the poling (3-) or thickness direction of the piezo-transducer. ½d31 Y E =ε33 ð1  νÞðsenÞ is the sensing coefficient of the piezoelectric transducer. C actuator ðΓ Þ and C sensor ðΓ Þ are functions of shear lag parameter Γ at the actuator and sensor side respectively as shown in Roy et al. [11]. Let T denotes steady-state ambient temperature, and ϵ denotes in-plane strain on the surface of a structure resulting from applied mechanical loads. Piezo-sensor output voltage under small changes in the in-plane surface strain ϵ under constant temperature can be expressed as: V out ðT; ϵ; t Þ ¼ DðT; ϵÞ V in ðt Þ

(3)

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where D ¼ d31

ðact Þ

 ðsenÞ d31 Y E C actuator ðΓ ÞC sensor ðΓ Þ ε33 ð1  νÞ

  V out T; ϵ þ Δϵ; t ¼ DðT; ϵ þ ΔϵÞ V in ðt Þ Subtracting Eq. (3) from Eq. (5)     V out T; ϵ þ Δϵ; t  V out ðT; ϵ; t Þ ¼ D T; ϵ þ Δϵ V in ðt Þ  DðT; ϵÞ V in ðt Þ

(4) (5)

(6)

Dependency of physical properties on applied mechanical loads can be used to account for changes in signal amplitude at a specific constant temperature. As shown in Eq. (1), change in phase velocity is observed to have a linear variation with the applied stress. If the phase shift in the sensor response can be independently accounted for, change in signal amplitude due to applied mechanical loads can be expressed as:     V out T; ϵ þ Δϵ; t  V out ðT; ϵ; t Þ D T; ϵ þ Δϵ; t  DðT; ϵ; t Þ ¼ (7) V out ðT; ϵ; t Þ DðT; ϵ; t Þ Let composite function D is expressed as:    ðsenÞ h i G d31 ðact Þ  g adh  h D p f d31 YE ε33

(8)

where f , g, and h are hypothetical independent functions of different material properties. Gadh is the adhesive shear moduli, Y E is the Young's modulus of the piezo-transducer, and ε33 is the dielectric permittivity of the piezo-transducer. Eq. (7) can be expressed as:

ΔV out ðϵÞ V out

¼

ΔDðϵÞ D

p

Δf ðϵÞ ΔgðϵÞ ΔhðϵÞ f

þ

g

þ

h

(9)

Where relative change in signal amplitude is expressed as a linear combination of relative changes in material properties due to applied mechanical strains. Piezo-transducer signals are influenced by varying mechanical loads as a part of the normal operating conditions of a structure. Dependency of physical properties of piezo-ceramics on applied mechanical loads is explained in Lynch [12]. An unpolarized piezoceramic material usually has dipole moments in random orientations. However after undergoing polarization, the dipole moments try to align themselves, constrained by the domain walls, along the applied electric field direction. Under the influence of applied mechanical loads, displacement of domain wall from its original configuration results in change in dipole moment and the net polarization. This change is more pronounced if the applied load is along the poling direction. The change in polarization of piezoceramic material due to applied mechanical strains will affect the piezoelectric actuation, and sensing coefficients which will lead to changes in piezo-sensor voltage output (refer Eq. 2). Assuming mechanical stiffness of the adhesive interface to vary negligibly under applied loads (Δg ðϵÞ =g  0), the development of load compensation model in the linear elastic regime, and under strain fields is described next. 6. Load compensation model Eq. (9) presents a framework to relate the change in signal amplitude to the change in material properties affected by applied loads. However it should be noted here that experimental characterization of piezo-transducer properties under the influence of applied mechanical loads is a challenging task. Crawley et al. [13] proposed a numerical relationship between the applied mechanical strains and the piezoelectric coefficients. Following a similar line of reasoning, let ϵpath be the inplane surface strain component along the wave propagation path in the base substrate. Let the variation of piezoelectric actuation ðd31 Þ and sensing coefficients ðg 31 Þ be expressed in terms of in-plane surface strain components along the wave propagation path as: d31 ¼ d31;base þ kd F act ϵpath ðactÞ

(10)

g 31 ¼ g 31;base þkg F sen ϵpath ðsenÞ

(11)

where d31;base , and g 31;base are the piezo-coupling coefficients corresponding to the substrate without any applied mechanical loads. kd , and kg are proportionality constants. F act , and F sen are parameters related to shear lag effect of the soft adhesive interface relating to the reduction of strain transfer from the base substrate to the piezo-transducer. The shear lag parameters are assumed not to vary under applied loads. ϵpath ðactÞ , and ϵpath ðsenÞ are the in-plane strain components along wave propagation direction on the surface of base substrate underneath piezo-transducers. The relative change in piezosensor output due to mechanical loads at constant temperature can be expressed using Eqs. (9), (10), and (11) as:

ΔV out ðϵÞ V out

ffi

Δf ðϵÞ ΔhðϵÞ f

þ

h

(12)

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As f and h are linear functions

ΔV out ðϵÞ V out

ffi

Δd31 ðϵÞ Δg31 ðϵÞ þ

d31

g 31

(13)

Using Eqs. (10) and (11),

ΔV out ðϵÞ V out

ffi

k F kd F act ϵ ðactÞ þ g sen ϵpath ðsenÞ d31;base path g 31;base

ΔV out ðϵÞ V out

ffi Aϵpath ðactÞ þ Bϵpath ðsenÞ

(14)

(15)

where A¼

kd F act ; d31;base

B¼

kg F sen g 31;base

Eq. (15) represents a characteristic surface that relates the change in piezo-sensor output with known strain field distribution in the base substrate. The unknown model constants, A and B, can be obtained using experimental sensor signals collected under varying loading conditions and constant ambient temperatures. It should be noted here that the unknown model constants may vary with ambient temperatures. Temperature dependency of model constants may arise due to the contribution of physical properties that will undergo change under the influence of varying ambient temperature environments. This can induce a load–temperature coupling effect to the piezo-sensor output with a probable change in orientation of the characteristic surface (Eq. 15) at different temperatures. Apart from influencing piezoelectric actuation, and sensing coefficients, mechanical loads also cause deformation of the wave propagation path as well as affect wave propagation velocity thus causing change in time of arrival of the signal. As discussed in [14] the change in time of arrival can be expressed as:

ΔToA ¼

Δd v



Δv v2

d

(16)

where d is the distance between a piezoelectric actuator–sensor pair, and v is the velocity of wave propagation. Let

Δd ¼ dϵpath ;

Δv ¼ K ϵpath

(17)

Eq. (17) expressed change in d, and v as proportional to the strain along the wave propagation path ϵpath . The change in time of arrival can now be expressed in terms of ϵpath as:   1 K  2 dϵpath ΔToA ¼ (18) v v K in Eq. (17) is a proportionality constant related to acoustoelasticity. In order to address the non-uniform distribution of strains along the wave propagation path, let d be discretized into small segments, as shown in Fig. 4, each having uniform length di (i¼1, 2… N) and averaged strain ϵpath ðiÞ   1 K  2 di ϵpath ðiÞ ΔToAðiÞ ¼ (19) v v

ΔToA ¼

N X

ΔToAðiÞ ¼

i¼1

Let K phase be defined as:

  N 1 K X ðiÞ  2 dϵ v v i ¼ 1 i path

 K phase ¼

1 K  v v2

(20)



Fig. 4. Discretization of the wave propagation path to address phase-shift due to non-uniform strain distribution.

(21)

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Fig. 5. Flowchart for reconstructing piezoelectric sensor signal based on load compensation model.

ΔToA ¼ K phase

N X

di ϵpath ðiÞ

(22)

i¼1

Eq. (19) represents change in ΔToAðiÞ for the ith segment along the wave propagation path, which can be summed up to provide the net change in ToA for a given actuator–sensor pair as shown in Eq. (22). The unknown constant K phase can be numerically estimated using experimental sensor measurements, and strain distribution along the wave propagation path. 7. Compensation methodology A MATLAB code LCMODEL is developed to reconstruct piezoelectric sensor signals under known strain field distribution at specified temperature based on the aforementioned compensation model represented by Eqs. (15) and (22). Fig. 5 shows the model implementation to filter out influence of applied loads from piezo-sensor response. The methodology is divided into two parts; (i) model parameters estimation for load compensation, and (ii) signal reconstruction under combined influence of load and temperature. The methodology for estimating model parameters is described as follows: 1) Given structural geometry, sensor layout, and material properties; generate piezo-sensor signals under different load conditions at a constant ambient temperature. The sensor lay out should be designed to serve two purposes. First objective is to obtain clear wavepackets in the sensor signals corresponding to the direct path between a pair of actuator and sensor. And the second purpose is to distribute the sensors in order to ensure data measurements for the following cases (a) actuator location has dominating (or relatively higher magnitude) path strains than the sensor location, (b) sensor location has dominating path strains, and (c) both actuator and sensor locations have path strains that are in same order of magnitude. These conditions are required to ensure robust estimation of model parameters A, and B from the sensor data. 2) Calculate path strains ϵpath ðactÞ , and ϵpath ðsenÞ on the substrate, at the actuator and sensor location respectively, owing to the applied mechanical loads. In this study, surface strain distribution on the substrate is obtained using numerical finite element (FE) simulations which requires loads and boundary conditions to be known beforehand. Alternatively, path

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strains can also be obtained by direct measurements of surface strains at the actuator and sensor locations using strain gages at the time instants wherein piezo-sensor signals are being recorded. 3) Once the path strains are obtained, isolate first wave packets from the sensor measurements and estimate change in signal amplitude ΔV out , and change in signal phase ΔToA at different loads. 4) Numerically estimate model parameters A, B, and K phase using Eqs. (15) and (22) in the least square setting with more number of measurements than the number of unknowns. 5) Repeat the above steps at different ambient temperatures to obtain load compensation model parameters at different temperatures. Once the model parameters are known as function of ambient temperatures, first wave packets of the piezo-sensor signals can be reconstructed using known strain distribution in the structure. However sensor signals under no load conditions and at specific temperature need to be determined. Recently, the authors [11] proposed a temperature compensation methodology using matching pursuit (MP) based signal analysis and reconstruction scheme that uses limited set of in-situ sensor measurements under unloaded condition. MP algorithm is an iterative signal decomposition algorithm that used Gabor dictionary of basis functions. The sensor signal vector is projected along these basis functions with ak , and bk , (k ¼1, 2…Nmax) as the projection coefficients. Nmax is the total number of MP iterations that is required to reconstruct the signal accurately. As shown in (11), change in signal projection coefficients are related to the change in temperature dependent material properties of piezo-transducer and adhesive interface as: 8 9 ( ) " #> Δd31 =d31;base > < = α α α Δ a 1k 2k 3k 1 k Δg31 =g31;base ¼ þε (23) β β β > > Δ b ‖Sbase ‖ k 1k 2k 3k : T1C Δkp;shear =kp;shear;base ; T 1C

where Δak and Δbk are the changes in signal projection coefficients for the ith MP iteration. Δd31 =d31;base and Δg 31 =g 31;base are the relative changes in the actuation, and sensing coefficients of the piezoelectric transducer respectively. Δkp;shear =kp;shear;base defines the relative change in shear-lag coefficient of the adhesive interface. Sbase is the sensor measurement recorded at base or reference temperature. αjk and βjk (j ¼1, 2, 3) are the unknown model constants that are to be determined using experimental sensor signals collected under different ambient temperatures. The unknown model constants are determined by minimizing the L-2 norm of the model error ε. Details of the temperature compensation model are explained in [11]. As shown in Fig. 5, the signal reconstruction under combined influence of varying loads and ambient temperature environments can be achieved as follows: 1) The first step here is to reconstruct piezo-sensor signals at desired temperatures. Collect a set of piezoelectric sensor signals, S¼ {Sbase ; S1; S2 ; ::; SM }, at Mþ1 different temperatures, (M Z3) evenly spaced in the operating range of a typical structural component under no load conditions. 2) Perform free MP decomposition of Sbase to determine signal projection coefficients ak;base , bk;base , and Gabor functions. ðpÞ 3) Perform constrained MP decomposition of the sensor responses at M different temperatures to determine ak ðpÞ and bk (p ¼1, 2… M). Following constraints on Gabor parameters are imposed (i) to ensure basis functions remain intact, and (ii) the phase-shift effect is compensated automatically. sk;T

1C

¼ sk;base ; vk;T

uk;T

1C

1C

¼ vk;base ;

¼ uk;base þ κΔT

(24) (25)

where κ is the slope of linear relationship between ToA and temperature data. 4) Estimate Δak , and Δbk at a specified temperature using Eq. (23). 5) Calculate ΔV out ðϵÞ , and ΔToA using load compensation model parameters at specified temperature and introduce corresponding changes on the signal projection coefficients Δak , and Δbk as obtained from temperature compensation model in the previous step. The knowledge of signal projection coefficients ak , and bk along with Gabor parameters at a specified temperature will allow complete reconstruction of the sensor signal SðtÞ [11].

8. Validation The unknown load compensation model parameters A, B in Eq. (15), and K phase in Eq. (22) are obtained using experimental sensor signals and strain field distributions on a flat aluminum plate under applied mechanical loads (refer Fig. 2b). Fig. 6a shows the longitudinal strain field distribution in the flat plate obtained using finite element (FE) simulations in ABAQUS, a commercial FE software package. Linear 8-noded brick elements (C3D8) were used in the FE analysis. The loading and boundary conditions in the FE simulations were matched closely to the experimental setup.

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Fig. 6. (a) Longitudinal strain field distribution obtained from FEM simulation using ABAQUS, (b) 3D representation of change in signal amplitude due to mechanical strains induced by uniaxial tensile loading, (c) rotated view of the 3D representation along a plane, (d) rotated view of the 3D plane at different temperatures.

In-plane strains on the surface of the plate, at the transducer locations, and along the direct wave propagation path between an actuator and sensor is obtained using strain-transformation equations. Fig. 6b shows the relative change in signal amplitude with respect to in-plane strains at the actuator and sensor location, along the wave propagation path. The figure also shows a fitted surface, represented by Eq. (15), and obtained by estimating model parameters using sensor data. Fig. 6c shows the rotated view of the same fitted surface with sensor data lying along it. The model parameters estimated using sensor data at 30 1C are: A¼141.46, B¼ 132.64, and K phase ¼0.0108 s/mm. As stated in Section 6, load compensation model parameters are hypothesized to be function of ambient temperatures. Fig. 6d shows the orientation of the characteristic surface obtained from the sensor data collected under combination of different ambient temperatures and loading environments. The figure also plots the sensor data recorded at 50 1C from two different measurement instances using the same experimental set up, and loading conditions. The values of estimated model parameters at different temperatures are shown in Table 1. It can be seen from Fig. 6d, and the values listed in Table 1 that there is no clear trend of the model parameter values with temperature. One of the possible reasons is the data fitting procedure with large scatter in the sensor measurements that induces uncertainty in the estimation of model parameters at different temperatures. Furthermore, the inherent assumption of small strain fields may not be appropriate at elevated temperatures due to thermal softening of the adhesive interface. It also needs to be mentioned here that the values of model parameters shown in Table 1 are obtained from single measurement instance only. Thus, even though both load and

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Table 1 Load compensation model parameters at different ambient temperatures. Temperature

Load compensation model parameters

T 1C

A

B

K phase

30 50 (Measurement set 1) 50 (Measurement set 2) 70

141.46 145.94 158.46 153.83

132.64 148.69 158.15 159.05

0.0108 0.0137 0.0124 0.0143

temperature influences piezo-sensor response, establishing and understanding the existence of coupling between the two effects is still inconclusive and needs further investigation beyond the scope of the present study. Fig. 7a shows the experimental setup of different plate geometries with different piezoelectric sensor layouts. Sensor signals were obtained under varying uniaxial tensile loads. Fig. 7b and d shows the representation of sensor data along the same characteristic surface as obtained earlier using six piezo-transducers plate configuration (refer Fig. 6). The surface plots are shown for two different load cases; Case A: uniaxial tensile load applied along the center line of the plate, and Case B: uniaxial tensile load applied away from the center line of the plate. It can be observed that the sensor measurements lie along the same characteristic surface for both the cases under known path strains at the actuator and sensor locations. Thus, it can be inferred that the load compensation model parameters are dependent only on material properties and are not influenced by change in specimen geometry, and piezo-sensor lay outs. The in-plane strain distribution at the piezo-actuator and sensor locations along the wave propagation path, referred to as actuation strain ðϵpath ðactÞ Þ, and sensing strainðϵpath ðsenÞ Þ in the figure respectively, are obtained using FE simulations. The concept of characteristic surface is important from the perspective that given surface strain distribution and fitted model parameters A, B, and K phase for a given material system, the relative change in signal amplitude and phase shift can be obtained easily. Fig. 7e shows comparison between model-based reconstructed first wavepacket of the sensor signal, and actual measurements recorded from a piezoelectric actuator and sensor pair for Case A load condition. Change in signal amplitude and ToA is obtained using Eqs. (15), and (22) with the model parameters estimated earlier using six piezotransducers plate configuration (shown in Fig. 6). Comparison between experimental and model based reconstructed sensor signals is quantified by a signal scatter metric defined as:  ! SðtÞ  current  SðtÞbaseline   ScatterRatiomax ¼ max 20 log (26) SðtÞ  baseline where baseline refers to the experimentally measured sensor response, and current refers to the model based reconstructed signal. Table 2 shows the ScatterRatiomax values for different piezo-transducer pairs along with sensitivity study due to assumed uncertainties in the strain field distribution along the wave propagation path. Low values of ScatterRatiomax for both the load cases, Case A, and Case B, indicate good degree of match between experimental and model-based reconstructed sensor signals. One important outcome of this study is development of an environmental compensation model that can be used to numerically generate piezoelectric sensor signals for a pristine (healthy) structure, under varying environments and operating conditions. These model-based, numerically generated baseline signals can be used to train data-driven SHM algorithms for robust structural damage detection, quantification, and characterization [15]. 9. Load monitoring As mentioned in [16], load monitoring and measurements are essential tasks for design certification of structural component. The certification tasks are costly and have to cater to uncertainties in the actual loads a structure is subjected to during its intended operation, which may be widely different from the calculated design loads. This necessitates the need for continuous load monitoring in a structure that will not only enable condition-based maintenance but also will increase the overall safety and reliability of the structure. Currently load monitoring task is typically carried out using strain gages, accelerometers, micro-electro-mechanical systems (MEMS) or combinations of these. Recently Martinez et al. [16] proposed the use of MEMS based sensors for load monitoring on aerospace structures. They demonstrated accurate estimation of strains and shear forces on simple structure; however for complex structure an accurate FE model is required. Again for an accurate FE model, in-situ material properties, established and pre-defined load paths and boundary conditions will be required which makes the monitoring process difficult and challenging. Further, the paper mentions challenges in load monitoring using strain gages such as, complex wiring and data acquisition system, vulnerability to electro-magnetic interference, issues of bonding, electrical contacts, and fatigue damage that paves the requirement and need for developing load monitoring systems based on different sensor types. Another outcome of the proposed load compensation model in this paper is a framework to monitor applied loads in a structure. Fig. 8 shows the amplitude variation of piezo-sensor signals under the influence of applied loads for specific actuator–sensor pairs. It can be observed from Fig. 8b, and d that the sensor signals vary linearly with applied loads characterized by strain distribution in the structure. Furthermore, for a given load path the slope of this linear relationship is

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Fig. 7. Experimental setup and longitudinal strain field distribution obtained using ABAQUS under uniaxial tensile load (a) along the center line of the plate (Case A), and (c) away from the center line of the plate (Case B); 3D representation of change in signal amplitude due to applied mechanical strains for (b) Case A, and (d) Case B; (e) Comparison between reconstructed sensor response and actual measurements from S5–S1 transducer pair under 4 kips tensile loading corresponding to Case A.

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Table 2 Signal scatter metric for different piezo-transducer pairs due to error in the strain field estimation along wave propagation path. Sensor signals are reconstructed under uniaxial tensile load of 4 kips. Target ScatterRatiomax ¼  25 dB based on detecting flaw size of 5 mm crack in an aluminum plate [11]. Strain estimation

Scatter metric (in dB) for different actuator–sensor pairs

Error (%)

Case A

0 5 10 20

Case B

S5 –S1

S5 –S2

S5 –S3

S5 –S4

S1 –S2

S1 –S3

S1 –S4

S1 –S5

26.6647 26.1762 25.7137 24.8567

31.8557 31.8802 31.9016 31.9258

30.3614 31.2795 32.3062 33.2273

26.5585 26.4053 26.2548 25.9614

21.5742 21.5557 21.5372 21.4994

26.7798 26.5685 26.3614 25.9617

21.3119 21.2371 21.1478 20.9265

27.0228 26.1146 25.2905 23.8449

Case A: uniaxial load applied along the center line of the plate. Case B: uniaxial load applied away from the center line of the plate.

Fig. 8. Schematic of instrumented flat plate coupon under uniaxial load, and sensor data variation under applied loads for different actuator sensor pairs; (a), and (b) Case A: uniaxial load applied along the center line of the plate, (b), and (d) Case B: uniaxial load applied away from center line of the plate.

S. Roy et al. / Journal of Sound and Vibration 351 (2015) 206–220

ΔV41/ V41 (%)

218

Actuator S4 Sensor S1

Load (kips)

ΔV42/ V42 (%)

ΔV42/ V42 (%)

Actuator S4 – Sensors S1, and S2 Actuator S5 – Sensors S1, and S2 Actuator S5 – Sensors S1, and S4

Actuator S4 Sensors S1 & S2

Actuator S4 Sensor S2 Load (kips)

ΔV52/ V52 (%)

ΔV54/ V54 (%)

ΔV41/ V41 (%)

Actuator S5 Sensors S1 & S2 ΔV51/ V51 (%)

Actuator S5 Sensors S1 & S4 ΔV51/ V51 (%)

Fig. 9. Load monitoring using signal amplitudes of actuator–sensor pairs having different geometric orientations; (a) schematic of the plate with different actuator–sensor pairs under consideration; relative change in signal amplitude of (b) S4–S1, and (c) S4–S2 transducer pairs with applied loads; plot of relative change in signal amplitude of different transducer pairs (d) S4–S2 vs. S4–S1, (e) S5–S2 vs. S5–S1, (f) S5–S4 vs. S5–S1.

observed to remain constant. This can also be seen from Fig. 9b and c that plots the variation of signal amplitude under uniaxial tensile loads for two different load paths, corresponding to Case A and Case B, and for two different actuator–sensor pairs. The dashed lines shown in the figures are linear fits to the data, with coefficient of correlation close to unity. As the load paths change, strain distribution in the structure gets affected which in turn influence the slope of the sensor data

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points. This inference may be used to develop a load monitoring framework as demonstrated in Fig. 9d–f wherein ratio of relative amplitude changes of different transducer pairs are shown to be constant for a given load path. Also, the amount of change in the sensor signal amplitude can be related to strains, and eventually to the load magnitudes for a given load path. In Fig. 9c, signal amplitude is observed to remain almost stationary (relative change E0) for the case when loads are applied along the center line of the plate. This can be explained from the strain field distribution of Case A (refer Fig. 7a), wherein the actuator, S4, and sensor, S2, are placed away from the main load path resulting in low strain values along the wave propagation direction. A similar situation arises for actuator S5, and sensor, S2, corresponding to Case B (refer Fig. 7c), which explains the discrepancy observed in Fig. 9e regarding the ratio of relative amplitude changes not remaining constant as load varies (correlation coefficient of the linear fit o1). Fig. 9f depicts another interesting case wherein changes in load paths cannot be determined from the plots of relative change in signal amplitudes. This is primarily due to the fact that the strains at the actuator and sensor location along the wave propagation direction do not see any appreciable change for both Case A, and Case B. Thus, the geometric orientation of the actuator–sensor pairs with respect to the loading direction is critical and needs consideration not only for the load compensation strategies but also for load monitoring capabilities. Furthermore, Eq. (22) shows that ΔToA for an actuator–sensor pair can be used to provide an estimate of average strain distribution along the wave propagation direction. This may be useful to monitor strains along the wave propagation paths in a structure, away from the regions of stress gradients such as geometric corners, edges, holes etc. Qualitatively, under known ambient temperature and in the absence of structural damage, different piezoelectric actuator–sensor pairs will act like uniaxial strain gages aligned along the guided wave propagation direction. 10. Discussions The idea being pursued in this study is to explicitly determine the material property dependency of piezoelectric transducers on applied strains at different temperatures and relate them to the changes in piezo-sensor response. Piezoelectric properties are assumed to vary in proportion to applied mechanical strains in the base substrate under small strainfield assumptions whereas, mechanical stiffness of the adhesive interface is assumed to remain invariant. Relative change in sensor signal amplitudes as well as change in time of arrival of the guided-waves is expressed in terms of existing strainfield in a structure, which needs to be determined beforehand either through numerical finite element simulations under known loads and boundary conditions, or through direct in-situ measurements. The role of characteristic surface is highlighted in the proposed load compensation methodology to account for change in signal amplitudes under specified strain field distribution along the wave propagation path. The current limitations of the proposed compensation model that are worth discussions and, also define the scope of future research are: 1) Clear wave packets need to be identified in the sensor response for relating with the path strains in the base substrate. Ambiguity in knowing the wave propagation direction may result in erroneous estimation of change in signal amplitudes and phase shift. This is especially important for complex structural geometries where it is difficult to clearly identify and isolate the first wave packets. 2) A single characteristics surface is fitted to the sensor data wherein implicitly it is assumed that both the tensile and compressive strains would affect the piezo-transducer properties in a similar fashion. This assumption needs to be looked into for different types of piezo-transducers. 3) The proposed compensation model is shown to work well for plates under in-plane loadings. The effects of more general loading types, resulting in through-thickness variation of strains, and non-homogenous temperature distributions, on ultrasonic sensing signals need further investigation. 4) Also as discussed earlier, efforts to establish coupling between load, and ambient temperature effects on the piezo-sensor response are still inconclusive and need more in-depth analysis.

11. Conclusions A load compensation model is developed to reconstruct piezo-sensor signals under known strain distribution in a structure. Using the knowledge of structural strain distribution at the piezoelectric actuator and sensor locations, changes in sensor signal amplitude are shown to lie along a characteristic surface, which is observed to be a function of material properties only. The orientation of this characteristic surface for a given material system, and ambient temperature, remains same irrespective of the sensor layout and different load paths in a structure. This is vital from the perspective of using same model parameters for different structural geometries and load paths. Numerically reconstructed first wave packets in the sensor signals showed excellent agreement with the experimental measurements. Another important outcome of the proposed load compensation methodology is the ability to monitor the load paths in a structure. It is observed that change in load paths in a structure can be monitored by tracking the changes in signal amplitude of at least two piezoelectric actuator and sensor pairs attached to a structure, at different orientations with respect to the to the applied mechanical loads. A detailed study is however required to corroborate this finding and understand this behavior with respect to the changes in direction, nature, and magnitude of applied mechanical loads.

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The advantage of using physics based environmental compensation model is that one need not collect a large set of baseline sensor measurements from the structure under different loads and ambient conditions. Instead, baseline sensor signals for structural change detection can be numerically generated at any specified ambient temperature and loads, using the proposed model with limited set of in-situ training data. This concept states the practical efficacy and usefulness of the proposed compensation model and necessitates further development for field implementation under real environments. Acknowledgments This research was supported by Multidisciplinary University Research Initiative (MURI) (Grant no: FA9550-09-1-0677), and Air Force Office of Scientific Research (AFOSR) (Grant No: FA9550-08-1-0391). The authors would like to thank Acellent Technologies Inc. for providing necessary hardware support for the experiments conducted in this research. References [1] T. Clarke, F. Simonetti, P. Cawley, Guided wave health monitoring of complex structures by sparse array systems: influence of temperature changes on performance, Journal of Sound and Vibration 329 (2010) 2306–2322. [2] A. Croxford, J. Moll, P. Wilcox, J. Michaels, Efficient temperature compensation strategies for guided wave structural health monitoring, Ultrasonics 50 (2010) 517–528. [3] Y. Lu, J. Michaels, Numerical implementation of matching pursuit for the analysis of complex ultrasonic signals, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 55 (2008) 173–182. [4] Z. Lu, S.-J. Lee, T. Michaels, J. Michaels, On the optimization of temperature compensation for guided wave structural health monitoring, Review of Quantitative Nondestructive Evaluation 29 (2010) 1860–1867. [5] J. Harley, J.M. Moura, Scale transform signal processing for optimal ultrasonic temperature compensation, IEEE Transactions on Ultrasonics, Ferroelectric, and Frequency Control 59 (2012) 2226–2236. [6] D. Hughes, J. Kelly, Second-order elastic deformation of solids, Physical Review 92 (1953) 1145–1149. [7] R. Toupin, B. Bernstein, Sound waves in deformed perfectly elastic materials. Acoustoelastic effect, The Journal of the Acoustical Society of America 33 (1961) 216–225. [8] N. Gandhi, S.J. Lee, and J. Michaels, Acoustoeleastic lamb wave propagation in a homogeneous, isotropic aluminum plate, Review of Progress in Quantitative Nondestructive Evaluation, AIP Conference Proceedings 1335, vol. 30, 2011, pp. 161–168. [9] J. Michaels, S.J. Lee, and T. Michaels, Impact of applied loads on guided wave structural health monitoring, Review of Progress in Quantitative Nondestructive Evaluation, AIP Conference Proceedings 1335, vol. 30, 2011, pp. 1515–1522. [10] S.J. Lee, N. Gandhi, J. Michaels, and T. Michaels, Comparison of the effects of applied loads and temperature variations on guided wave propagation, Review of Progress in Quantitative Nondestructive Evaluation, American Institute of Physics, vol. 30, 2011, pp. 175–182. [11] S. Roy, K. Lonkar, V. Janapati, F.-K. Chang, A novel physics-based temperature compensation model for structural health monitoring using ultrasonic guided waves, Structural Health Monitoring 13 (2014) 321–342. [12] C. Lynch, The effect of uniaxial stress on the electro-mechanical response 0f 8/65/35 pzt, Acta Materialia 44 (1996) 4137–4148. [13] E. Crawley, K. Lazarus, Induced strain actuation of isotropic and anisotropic plates, AIAA Journal 29 (1991) 944–951. [14] M. Bao, J. Michaels, T. Michaels, An ultrasonic method for dynamic monitoring of fatigue crack initiation and growth, Acoustical Society of America 119 (2006) 74–85. [15] C.R. Farrar, K. Worden, Structural Health Monitoring: A Machine Learning Perspective, 1st ed. John Wiley and Sons, Wiley-Blackwell, New Jersey, 2012. [16] M. Martinez, M. Li, G. Shi, A. Beltempo, R. Rutledge, M. Yanishevsky, Load monitoring of aerospace structures utilizing micro-electro-mechanical systems for static and quasi-static loading conditions, Smart Materials and Structures 21 (2012) 621–630.