Progress Towards a Forward Model of the ... - Michael I Friswell

Advanced Materials Research Vols. 13-14 (2006) pp. 69-75 online at http://www.scientific.net © (2006) Trans Tech Publications, Switzerland

Progress Towards a Forward Model of the Complete Acoustic Emission Process 1

Wilcox, P. D., 1Lee, C. K., 2Scholey, J. J., 2Friswell, M. I., 2Wisnom M. R. and 1Drinkwater, B. W. 1

Department of Mechanical Engineering, University of Bristol, BS8 1TR, UK Department of Aerospace Engineering, University of Bristol, BS8 1TR, UK [email protected]

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Keywords: modeling, guided waves, probability of detection

Abstract. Acoustic emission (AE) techniques have obvious attractions for structural health monitoring (SHM) due to their extreme sensitivity and low sensor density requirement. A factor preventing the adoption of AE monitoring techniques in certain industrial sectors is the lack of a quantitative deterministic model of the AE process. In this paper, the development of a modular AE model is described that can be used to predict the received time-domain waveform at a sensor as a result of an AE event elsewhere in the structure. The model is based around guided waves since this is how AE signals propagate in many structures of interest. Separate modules within the model describe (a) the radiation pattern of guided wave modes at the source, (b) the propagation and attenuation of guided waves through the structure, (c) the interaction of guided waves with structural features and (d) the detection of guided waves with a transducer of finite spatial aperture and frequency response. The model is implemented in the frequency domain with each element formulated as a transfer function. Analytic solutions are used where possible; however, by virtue of its modular architecture it is straightforward to include numerical data obtained either experimentally or through finite element analysis (FEA) at any stage in the model. The paper will also show how the model can used, for example, to produce probability of detection (POD) data for an AE testing configuration. Introduction Acoustic emission (AE) is well known as a highly sensitive technique to detect various types of damage, such as fatigue crack growth, corrosion, impacts, delaminations and so forth (Scruby and Buttle, 1991; Ono, 1991; Fregonese et al., 2001). This sensitivity coupled with the small number of sensors required potentially makes AE very attractive for structural health monitoring (SHM) applications. Although ambient acoustic noise may be high during in-service monitoring, the fact that monitoring can be performed over extended periods of time means that AE based SHM can exploit the repetitive nature of events that may occur in each loading cycle (Rogers, 2001; O’Brien, 2002). AE testing methodology tends to fall into one of two categories (Scruby and Buttle, 1991): deterministic and probabilistic. In the deterministic methodology, suitable models of the AE process are used to analyze AE data, whereas, in the probabilistic methodology, a variety of techniques are employed to identify empirical trends in experimental data. While the probabilistic approach is well suited to repetitive testing of similar components, it is the belief of the authors that this approach is much less suitable for monitoring limited numbers of complex, high value, safety-critical structures of the type likely to be encountered in SHM. The authors believe that for AE to be used as the basis for an SHM system with quantifiable performance it is necessary to have a deterministic model of the complete AE process from source to received waveform. In this paper, progress on the development of a modular framework (referred to as QAE-Forward) for quantitative forward modeling of the complete AE process in real structures is presented. The purpose of QAE-Forward is to predict the actual AE waveforms received from sensors when an AE event occurs anywhere in a structure. QAE-Forward is comprised of a growing All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of the publisher: Trans Tech Publications Ltd, Switzerland, www.ttp.net. (ID: 213.105.224.17-22/09/06,00:09:01)

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Acoustic Emission Testing

number of separate functions that model different aspects of the AE process, such as wave generation at AE sources, wave propagation and transduction. The modular framework enables a high degree of complexity to be introduced gradually into the overall model. It should be stressed that the underlying mathematical modeling of QAE-Forward is not new but drawn together from a number of existing guided wave modeling techniques (Ceranoglu and Pao, 1981; Gorman, 1991; Gorman and Prosser, 1996; Maji et al., 1997; Prosser et al., 1999). At present QAE-Forward can predict the waveforms obtained in isotropic or anisotropic planar structures from in-plane or out-ofplane point forces and includes the effects of dispersion, multi-modal propagation, reflections from simple boundaries and signal reception by transducers with finite spatial aperture and frequency response. These elements of the model have been implemented using analytic solutions available from the literature. However for AE sources such as fatigue crack growth, analytic models do not exist and here the intention is to use data from either numerical modeling or experimental measurements in QAE-Forward. Similarly the propagation of AE signals past structural features such as bends, welds and joints will be implemented in QAE-Forward using externally generated data. The final part of the paper suggests a definition of probability of detection (POD) that may be used for AE testing and shows how QAE-Forward can be used to calculate POD for a given test configuration. The Forward model of the Acoustic Emission Process Motivation and Methodology. QAE-Forward is a forward model of the AE process from source to detection. The goal is to be able to simulate the time-domain signal that is received from a transducer when an AE even occurs anywhere in a structure. Such a model has great importance for the development of AE SHM systems since it can be used to, for example: 1. Optimize sensor placement and spacing to achieve a desired level of sensitivity, 2. Perform probability of detection (POD) and false call ratio (FCR) simulations, and 3. Support safety cases based on the use of AE in a complex structure. QAE-Forward is based on a modular linear systems architecture using frequency-domain transfer functions and is implemented within Matlab (The MathWorks, Inc., Natick, MA). A fundamental aspect of QAE-Forward is that the modular architecture enables the source, propagation and detection of AE signals to be separated. The overall architecture of QAE-Forward is illustrated schematically in Fig. 1. Where possible, the building blocks of QAE-Forward are developed from existing analytic models, in particular those related to guided wave excitation and propagation. This is based on the observation that a wide range of structures are made up of plate-like elements, through which AE signals will propagate as guided waves. However, it is recognized that there are no analytic solutions to some aspects of the AE process, such as wave propagation through complex geometries, and here the plan is to link QAE-Forward to transfer functions obtained either experimentally or through numerical finite element (FE) models. Source

Propagation

Detection

Source characteristics Frequency content Stress tensor (orientation, amplitude etc)

Wave propagation model Phase and group velocity Attenuation Interaction with features

Transducer characteristics Frequency response In-plane/out-of-plane response Spatial aperture

Excitability model Modal amplitudes Radiation pattern

Received waveform

Noise Discrete acoustic sources Acoustic signal reflections Random acoustic noise Random electrical noise

Fig. 1. Block diagram showing the main components of QAE-Forward. The overall model for the frequency spectrum, H(ω), of a received time-domain signal, excluding noise terms, can be expressed as a single equation:

Advanced Materials Research Vols. 13-14

H (ω ) =

⎡ ⎤ ⎢ E (ω )P (ω )BA(ω )RX (ω ) ∏ RC (ω ) ∏ TC (ω )⎥ All rays ⎣ All reflections All transmissions ⎦ and modes

∑

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(1)

where E(ω) is the modal excitability at the source, P(ω) is the delay due to propagation, A(ω) is attenuation, B is beam spreading, RX(ω) is the sensitivity of the receiver, RC(ω) is the reflection coefficients of all features at which the ray is reflected and TC(ω) are the transmission coefficients of all features that the ray has traversed. The final received time-domain signal is the inverse Fourier transform of H(ω). The outer summation is performed over all possible ray paths of all possible wave modes from source to receiver. The following subsections describe the nature of the terms in Eq. 1 in more detail. Source. QAE-Forward begins at the AE source which is characterized by a frequency dependent radiation pattern of guided wave energy partitioned between various modes, the so-called source function, E(ω). In the past, the mechanism of AE signal generation by a variety of sources has been well studied in the case of sources buried in an infinite medium (Scruby and Buttle, 1991). What has received much less attention due to its inherent complexity is the case of sources in finite media, such as plates, which has much greater applicability to practical testing. The types of source functions that can currently be obtained analytically for plate-like structure are those for transient point loads either on the surface or embedded within the structure. Such sources including Hsu-Neilson lead breaks, used by many workers to simulate AE events, which can be modeled as an out-of-plane force applied to the surface of the plate. In the case of an isotropic plate subjected to an out-of-plane surface force, the source function can be easily calculated to show that only the fundamental Lamb wave modes A0 and S0 are excited and that there is no angular dependence. However in the case of anisotropic plates, such as those made from fibre-epoxy composites, the modal amplitude becomes dependent on angle. For AE sources that involve a discontinuity in the structure such as fatigue crack growth, analytic solutions are not available. However, it is possible to obtain numerical results for the source function using finite element techniques (Lee et al., 2006) which may then by input into QAE-Forward. Propagation, attenuation and beam spreading. Once the amplitude of a mode in a particular direction is known it is straightforward to simulate its propagation as a guided wave through uninterrupted structure by applying an appropriate phase delay: (2) P (ω ) = exp[− ik (ω )d ] where i is √-1, k(ω) is the wavenumber of the wave mode and d is the propagation distance. Note that if k is not proportional to ω then the mode is dispersive. The energy spreading in time due to dispersion is implicitly accounted for in this equation. In a plate-like structure, the guided wave rays from a point source such as an AE event diverge in two dimensions. For conservation of energy, this requires that the amplitude of guided waves decays with the square root of propagation distance. This is the basis of the beam spreading term: 1 (3) B= d Material attenuation and energy leakage into surrounding media appear as exponential decays in signal amplitude with distance that can be represented by one exponential function: (4) A = exp[− α (ω )d ] -1 where α is the attenuation in Nepers m , which is, in general, a function of both mode and frequency. The data required to implement the propagation and attenuation functions are the wavenumber and attenuation characteristics of possible guided wave modes in the structure in the propagation direction of interest. Both of these quantities are, in general, functions of frequency. For most single and multi-layered planar structures, the phase velocity dispersion relationships can be computed

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using established techniques from the material stiffness and density. For structures where the material properties are unknown there are experimental techniques available to measure the phase velocity dispersion data experimentally. More importantly, experimental data is essential for accurately determining the attenuation, which is much more difficult to calculate due to uncertainties in the governing material properties (Scholey et al., 2006). Detection. Practical detection of AE signals is almost invariably performed using some sort of surface mounted piezoelectric transducer, although in the laboratory other methods such as laser interferometry are available. As a first approximation, it can be assumed that a surface mounted piezoelectric transducer is primarily sensitive to out-of-plane surface displacement. However, the output from the transducer will not be an exact replica of the out-of-plane displacement at a point on the surface of the plate for a number of reasons. Firstly, the transducer has its own frequency response function which can be readily included in the transfer function model if it can be measured. For accurate transducer simulation, the amplitude and phase of the frequency response is required. This is particularly important in the case of transducers with high sensitivity over a wide bandwidth, where the sensitivity is achieved by a transducer design with multiple lightly damped resonances that overlap over a range of frequencies. Such transducers are high-sensitivity but are not high-fidelity in terms of replicating the surface displacement of the structure on which they are mounted. In addition to having frequency response, a transducer of finite size also has a wavelength response to incident guided waves, due to averaging over the transducer aperture. This is a significant effect as the diameter of a typical AE transducer is around 10 mm, which is of similar order to the wavelength of guided waves in the frequency range of interest. Currently in QAE-Forward, the frequency and wavelength responses are assumed to be uncoupled and the wavelength response of a transducer is estimated by integrating out-of-plane surface displacement over its aperture. In the case of circular transducers, this gives rise to a wavelength response, RX(λ), in the following form: ⎛ πD ⎞⎤ πD 2 ⎡ ⎛ πD ⎞ ⎟⎟ + J 2 ⎜⎜ ⎟⎟⎥ RX(λ ) (ω ) = (5) ⎢ J o ⎜⎜ 4 ⎣ ⎝ λ (ω ) ⎠ ⎝ λ (ω ) ⎠⎦ where D is the diameter of the transducer, λ is wavelength, and J0 and J2 are zeroth and second order Bessel functions of the first kind respectively. For Lamb wave modes in a 3 mm thick aluminum plate at 250 kHz a 10 mm diameter transducer is around 2.5 times more sensitive to the S0 mode than the A0 mode. This illustrates the importance of this effect.

Interaction with Features. The interaction of guided waves with simple straight features, such as edges, can be readily modeled using a simple ray-tracing approach, and requires the length of all possible ray paths that pass through a sensor location over a given time period to be calculated. In QAE-Forward currently only reflections from perfect straight edges are included. Mode conversions are ignored (correct for A0 Lamb waves but no for S0 ones where obliquely incident waves will partially mode convert to SH waves) and reflection coefficients for all modes are assumed to be unity for all incident angles. In the future, the possibility of including mode conversions and reflection coefficients that are functions of frequency and incident angle can be added, subject to the availability of data.


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Example Results The simplest AE source that has been considered is the standard Hsu-Neilson source that is widely used to simulate AE signals. This consists of a pencil lead being broken on the surface of the structure and can therefore be regarded as a step force applied to the surface in the out-of-plane direction. The excitability function, E(ω), for guided waves excited by such a force can be obtained analytically as noted previously and the time-domain signals recorded by a remote transducer can therefore be predicted. Fig. 2 shows a comparison between the simulated and experimental timedomain signals and it can be seen that good agreement is achieved. The discrepancies between the two signals, in particular the slight tails on each signal that are observed experimentally, have been attributed to inaccurate modeling of the frequency response function of the transducer. The apparent extra signal at around 130 ms in the experimental time-trace is thought to be due to a S0 to SH0 to S0 double mode conversion occurring at a corner reflection, which is not included in the model. (a)

(b)

0

100 Time (μs)

200

300

0

100 Time (μs)

200

300

Fig. 2. (a) Experimental recorded time-trace and (b) time-trace simulated using QAE-Forward for Hsu-Neilson source 300 mm away from transducer on 3 mm thick aluminum plate. Quantifying the Performance of AE Testing In the NDE community, techniques are characterized by certain metrics. Given a population of samples that may or may not contain defects the terms probability of detection (POD) and false call ratio (FCR) are defined for a particular method of inspection. POD is the probability that the technique can detect a defect and is therefore the number of true-positives divided by the number of samples containing defects. FCR is the probability of false-positives and is the number of falsepositives divided by the number of defect free samples. The terms POD and FCR are exactly equivalent to the terms sensitivity and selectivity used to quantify the performance of medical diagnosis techniques. It is unfortunately almost invariably the case that altering the test to improve one parameter has a detrimental effect on the other, hence the choice of test is a balance between achieving an acceptably high POD or an acceptably low FCR. It is suggested that a method of characterizing AE systems in a similar way should be developed and in this section a possible definition of POD for AE is suggested. The practical use of these metrics is in the development of testing strategy. Typically the values of POD and FCR are plotted against one another as some parameter of the test is varied to yield a receiver operator characteristic (ROC) curve. In the case of AE the test parameter could be, for example, threshold level or mean sensor spacing. Probability of Detection (POD). The proposed definition of POD for AE testing is as follows: Given a particular structure and type of AE event the POD of a system is defined as the probability that an event of the given type can be detected anywhere in the monitored area or volume of the structure. The random variable is therefore the location and possibly orientation of the AE event within the structure. As a simple example the case of Hsu-Neilson sources in a 3 mm thick aluminium plate structure are considered. Three sensors are considered arranged at the vertices of an equilateral triangle with 1 m long sides and the monitored area of the structure is the area within the triangle. For the purposes of illustration, two different detection strategies for an event are modelled: (1) the

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event produces a signal that exceeds the threshold at one or more sensors and (2) the event produces a signal that exceeds the threshold at all three sensors. QAE-Forward is used to simulate HsuNeilson events at locations throughout the monitored area and the fraction of events detected for various threshold settings is computed. Fig. 3(a) shows examples of the locations of successfully detected events for the two detection strategies, with the threshold setting for chosen to give a POD of 50 % in each case. It can be seen that the location of successful detections is fundamentally different in the two cases. Fig. 3(b) shows the PODs as a function of threshold level for both detection strategies. The latter graph enables the relative effect of the different detection strategies to be quantified but does not, on its own, enable the optimum threshold level to be deduced, since there is no information about false-positives. Sensor Detected by all Detected by any Events

(b)

100 90

Probability of detection (%)

(a)

80 70

Detection by all

60 50 40 30

Detection by any

20 10 0

0

10

20

30

40

50

60

70

80

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Threshold level (arb. units)

Fig. 3.Two different two detection: (a) map of events detected by the strategies with thresholds set to produce PODs of 50 % in both cases and (b) variation of POD with threshold level. False Call Ratio (FCR). FCR is a more challenging proposition to model given the multitude of possible sources of spurious signals, and has not been studied in detail at the time of writing. Significantly, the calculation of FCR also requires consideration of time since the number of random events likely to occur increases with time. The number of false-positives over a given period of time can be modeled but there is no direct equivalent of the number of defect free samples by which to divide this number in order to calculate FCR in the manner in which it would be calculated for an NDT technique. Instead it is proposed that the number of false calls is divided by the time period and it can therefore be interpreted as number of false-positives per second. For consistency with the definition of POD, a false-positive should only be recognized if the same criteria that a genuine event must satisfy are met. The implication of this is that the more sensitive to genuine events a system is, then the more sensitive it must be to false calls. Conclusion An overview of a systematic modeling framework, QAE-Forward, for simulating the AE process in real structures has been presented. Good simulations of experimentally received waveforms have been achieved using analytical functions to represent AE sources, wave propagation in finite plate structures and reception by finite sized transducers. A definition of probability of detection for AE testing systems has been proposed and it has been shown how QAE-Forward can be used to investigate the POD performance of an AE system.


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Acknowledgement This work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) through the UK Research Centre in NDE and by Airbus, Rolls-Royce and Nexia Solutions. Jonathan Scholey is funded through an Industrial CASE studentship with Airbus. References Ceranoglu, A.N. and Pao, Y.H. (1981) “Propagation of Elastic Pulses and Acoustic-Emission in a Plate: Parts 1 to 3”, J. Appl. Mech., Vol. 48, No. 1, pp. 125-132. Fregonese, M., Idrissi, H., Mazille, H., Renaud, L. and Cetre, Y. (2001) “Initiation and Propagation Steps in Pitting Corrosion of Austenitic Stainless Steel: Monitoring by Acoustic Emission”, Corros. Sci., Vol. 43, pp. 627-641. Gorman, M.R. (1991) “Plate Wave Acoustic Emission”, J. Acoust. Soc. Am., Vol. 90, No. 1, pp. 358-364. Gorman, M.R. and Prosser, W.H. (1996) “Application of normal mode expansion to acoustic emission waves in finite plates”, J. Appl. Mech., Vol. 63, No. 2, pp. 555-557. Lee, C.K., Scholey, J.J., Wilcox, P.D., Wisnom, M.R., Friswell, M.I. and Drinkwater, B.W. (2006) “Guided Wave Acoustic Emission from Fatigue Crack Growth in Aluminium Plate”, in these proceedings. Maji, A.K., Satpathi, D. and Kratochvil, T. (1997) “Acoustic Emission Source Location Using Lamb Wave Modes”. J. Eng. Mech., Vol. 123, No. 2, pp. 154-161. O'Brien, E.W. (2002) “An Experimental Mechanics Approach to Structural Health Monitoring for Civil Aircraft” in Gdoutos, E.E. (Ed.), Recent Advances in Experimental Mechanics, Kluwer Academic Publishers, pp. 727-736. Ono, K. (1991) “Acoustic Emission”, in Marsh, K.J., Smith, R.A. and Ritchie, R.O. (Eds.), Fatigue Crack Measurement: Techniques and Applications, Engineering Materials Advisory Service Ltd., pp. 173-205. Prosser, W.H., Hamstad, M.A., Gary, J. and O’Gallagher, A. (1999) “Reflections of AE Waves in Finite Plates: Finite Element Modeling and Experimental Measurements”, J. Acoust. Emiss., Vol. 17, Nos. 1-2, pp. 37-47. Rogers, L.M. (2001) “Structural and Engineering Monitoring by Acoustic Emission Methods Fundamentals and Applications”, Lloyd’s Register Technical Investigation Department. Scholey, J.J., Lee, C.K., Wilcox, P.D., Wisnom, M.R. and Friswell, M.I. (2006) “Acoustic Emission in Large Scale Composite Specimens” in these proceedings. Scruby, C.B. and Buttle, D.J. (1991) “Quantitative Fatigue Crack Measurement by Acoustic Emission” in Marsh, K.J., Smith, R.A. and Ritchie, R.O. (Eds.), Fatigue Crack Measurement: Techniques and Applications, Engineering Materials Advisory Service Ltd., pp. 207-287.