5. Ultrasonic Methods

In general, guided wave inspection can be categorized into either active or passive. Passive techniques aim to record structural response induced by natural loads of the structure which happen during the flight of an aircraft. A comprehensive review of passive acoustic NDT techniques is presented in Chap. 7 of this book. One other good example of the passive technique is an embedded optical fibre Bragg grating sensor which has a series of parallel engraved lines (index points of refraction) that provide different reflection and transmission of light under varying strains in the structure. In case of fibre breakage, loss of transmitted light is observed, while the strain changes leads to altered refraction coefficient (Papantoniou et al. 2011). Optical fibre sensors have been extensively used to measure the temperature and strain of aircraft structures and even to detect the delamination type defects by analysing the wavelength shifts and reflection spectra of light (Ecke 2000; Takeda et al. 2002). Such inspection techniques are covered in Chap. 8. Active SHM utilizes both actuators and sensors to measure a response of the structure to a known input. Both bulk wave and guided wave techniques can be categorized as active, however in aerospace SHM applications the guided waves inspections are more commonly used. Guided wave excitation is usually determined by the design of the structural health monitoring system. It essentially depends on the type of defects which has to be detected and the structure under analysis. In the ideal case, the best guided wave mode for inspection should feature low dispersion and attenuation, high sensitivity to damage, easy excitability and detectability (Su and Ye 2006). The dispersion and attenuation depend on the excitation frequency and material properties, while the sensitivity to the defect is determined by the displacement profile of each mode.

High dispersion usually limits the sensitivity to the defect and the inspection length, as the wave-packet of the mode becomes distorted with the distance. To reduce the effect of dispersion, narrowband excitation is usually applied by increasing the number of cycles of the excitation signal. As a result, the bandwidth of the signal decreases, limiting the extent of dispersion (Wilcox et al. 2001b). On the other hand, it means that the signal itself becomes longer in duration which reduces the temporal resolution. Wilcox et al. introduced a concept of minimum resolvable distance (MRD), which shows the sweet spot on the dispersion curve, where the best compromise between propagation distance, number of excitation signal cycles, wavelength and resolution can be estimated (Wilcox et al. 2001a):where l and d are the wave propagation distance and the plate thickness; c_min, c_max are the minimum and maximum velocities through the distance l; c₀ is the velocity at the central frequency; T_in is the initial time duration of the wave-packet. Typically, fundamental modes of guided waves such as A₀ and S₀ possess low MRD values and therefore require less cycles for adequate resolution.

Different post-processing strategies exist that can be used to reduce the effect of dispersion after the signal arrives to the sensor. For example, Wilcox presented a technique that uses a priori knowledge of dispersive characteristics of guided wave mode to compress the signals by mapping the time to distance domains (Wilcox 2003). De Marchi et al. introduced the warped frequency transform method to reduce the effect of dispersion. The authors used chirped pulse excitation with the proposed dispersion compensation technique to improve arrival time estimation in the detection of simulated defects on aluminium plate (De Marchi et al. 2013). However, in most cases the reconstructed signals are either still deformed due to non-linearity of the transformation function or the compensation methods are usually efficient for the reconstruction of one targeted mode (Luo et al. 2016). Recently, the sparse decomposition methods, that use a dictionary of non-dispersive signals to decompose guided wave responses obtained from the structures were proposed (Xu et al. 2018). The dictionaries are built exploiting the dispersion curves of the signal, which requires precise knowledge of the material properties. Each atom in the dictionary represents a dispersive signal at a certain distance. By comparing each atom to the measured signal, the non-dispersive analogue can be found.

Attenuation is another limiting factor that can influence the design of the monitoring system. Considering that the reflection from damage is usually weak, the attenuation of guided waves has to be sufficiently low in order to capture such reflections at some distance. The main factors that determine the level of attenuation are dispersion, beam divergence, material damping and leakage of the acoustic energy into the surrounding media (Long et al. 2003; Mustapha and Ye 2014). The leakage depends on the difference between the phase velocity of guided waves in the structure and the velocity of bulk waves in the surrounding medium. Significant leakage is observed in those cases when the phase velocity of guided waves is above the bulk wave velocity in the embedded media. The leaky behaviour of guided waves are usually exploited while investigating flow and defects in gas or fluid loaded pipes (Djili et al. 2013; Zichuan et al. 2018; Mazzotti et al. 2014).

Ultrasonic guided waves can be excited using different strategies, depending on the application of the monitoring system. Direct contact methods can be either surface mounted or embedded into the structure. Surface-mounted sensors, like piezoelectric wafers are cheap, lightweight, can be arranged in different configurations and easily replaced if necessary (Giurgiutiu 2015). Simple instrumentation is required for such sensors as they operate on the direct and inverse piezoelectric effect. However, surface mounted solutions are not very attractive for in-situ applications as they change the aerodynamics of the structure. Thus for in-service aerospace monitoring systems, integrated sensors are preferred. These have high requirements for durability, as the monitoring system has to be reliable for the whole life-time of an aircraft. Different studies are available that analyse the durability of integrated sensors under varying environmental and cyclic conditions (Giurgiutiu et al. 2004; Melnykowycz et al. 2006; Tsoi and Rajic 2008). Different type of integrated sensors exists, while most commonly piezoelectric and fibre Bragg grating are used. Sensor integration can introduce additional resin-rich regions in the laminate or the sources of crack initiation around the corners of the piezoelectric sensor, therefore the shape and integration design has to be considered carefully taking into account overall strength of the host structure (Veidt and Liew 2012). Fibre Bragg grating sensors are lightweight and designed to be integrated into the composite structures. Such sensors do not require wiring, are cheap, durable and do not change the strength of the host structure (Veidt and Liew 2012; Majumder et al. 2008). Non-contact inspection methods like air-coupled or laser ultrasonics provide an ability to adjust to the complex surface of the structure. Such methods can be adjusted to excite different guided wave modes as the angle between the transducer and the sample can be easily adjusted (Panda et al. 2018; Römmeler et al. 2020). Laser and conventional air-coupled monitoring are usually combined, using conventional piezoelectric transducers for transmission and laser vibrometer for the reception (Jurek et al. 2018). Other researchers combined air-coupled ultrasonic testing with thermal imaging (Rheinfurth et al. 2011). Despite the advantages of air-coupled ultrasonic inspection, it requires some expensive equipment, such as scanners, laser heads etc. and also access to inspected parts; hence, it can be performed only during the maintenance break of an aircraft.

In real-world situations, using many abovementioned guided wave excitation methods multiple modes are being generated simultaneously, unless some specific excitation strategies are applied. Many studies are available that seek to excite specific mode of guided waves (Lee et al. 2008; Li et al. 2016). The simplest solution is to select specific operating points of guided wave dispersion curves, where only a desired modes exist. For example, at low frequency-thickness products, fundamental zone with zeroth order modes exist. Such modes possess relatively simple mode shapes, are less dispersive and may be easily generated. Limiting the excitation bandwith and operating at low frequencies can effectively control number of modes present in the structure and the amount of their dispersion. At very high frequency-thickness products (20 MHz · mm and above), higher order guided wave modes have similar group velocities, hence they form a non-dispersive cluster which is called Higher Order Mode Cluster (HOMC) (Jayaraman et al. 2009). Such cluster of modes possess reduced surface sensitivy, thus it’s a good choice for localised flaw detection, like pitting corrosion. In the medium frequency-thickness range, many modes exist which are usually dispersive and possess much more complex mode shapes. Inspection at such operating point provides better sensitivity to small defects and thickness variations which is achieved at a cost of mode purity. In order to supress unwanted modes, some of the following techniques could be mentioned. For instance, in case of air-coupled or laser beam excitation, the ultrasonic signal can be introduced at some incidence angle, which allows to excite specific modes and reduce coherent noise. Such incidence angle is frequency-dependent and may be calculated analytically. This selective mode excitation approach is usually valid for fundamental modes only, as the incident angles of different modes tend to overlap at higher frequencies.

In case of direct sensor placement on the surface of component, different selective mode excitation strategies must be applied. Giurgiutiu et al. used piezoelectric wafer active sensors to excite single guided wave mode (Giurgiutiu 2005; Xu and Giurgiutiu 2007). For a particular mode, the maximum of the strain and displacement functions is achieved when the width of the transducer is equal to odd multiple half wavelengths of the desired mode. In contrast, the minimum occurs in case the width of the sensor is equal to an even number of half wavelengths. In such a way, the size of the transducer introduces spatial filtering phenomena, which allow to enhance or suppress the vibrations of the particular guided wave mode (Giurgiutiu 2011; Samaitis and Mažeika 2017). Another approach for excitation of single guided wave mode is based on the use of interdigital or comb transducers, which consist of two-finger type electrodes that are interchanged and driven by an opposite phase electrical field (Monkhouse et al. 2000; Bellan et al. 2005). The type of mode which is introduced to the structure is determined by the pitch between finger electrodes which has to be equal to half the wavelength of the desired mode. Several design extensions of the classical interdigital transducers can be found, which were proposed by Salas et al. (Salas and Cesnik 2009) and Jin et al. (Jin et al. 2005). Glushkov et al. used a co-axial ring-type transducer for selective omnidirectional mode excitation (Glushkov et al. 2010). The major drawback of piezoelectric wafers and interdigital transducers is that the mode selectivity is related to the size of the transducer. It means that the set of sensors is required to excite different modes. At low frequencies, the physical dimensions of such transducers become large and not convenient for many applications.

Other approaches to generate a single mode are based on the positioning of two or more piezoelectric elements in a sequence on the surface of the sample at the inter-element distance equal to the wavelength of the desired mode (Grondel et al. 2002). Similarly, elements can be positioned on the opposite surfaces and in-phase or out-of-phase excitation is then used to drive the mode of interest (Seung and Hoon 2007). The use of the phased-arrays is another field that contributes to the selective guided wave excitation. Fromme used 32-element circular array and phase addition algorithm to excite A₀ mode on aluminium plate (Fromme et al. 2006). The abovementioned approaches are most suitable for excitation of fundamental guided wave modes such as A₀ or S₀. It has to be considered that all modes of the wavelength determined by the pitch of array elements will be excited, which is especially important working with higher-order guided wave modes, thus reducing the mode selectivity. To overcome such a problem, recently Veit et al. proposed an approach for selective guided wave excitation using conventional phased array probe having small pitch relative to wavelength of targeted mode. By controlling the input signal bandwidth and the angle of generated beam even higher order modes can be excited both on metallic and composite structures (Veit and Bélanger 2020).

Different researches show, that the mode purity is an important issue for selective guided wave excitation. Usually, the approaches described above can produce some dominant modes; however, other modes might exist with significantly lower displacements and contribute to an overall noise of the signal. Other transducers, especially phased arrays, possess low dynamic range, thus they are limited to detection of relatively large defects.

Both abovementioned methods are dedicated to detecting structural changes. Unfortunately, these are not suitable to localize and characterize damage. In general, two defect detection approaches based on sensor type and placement can be identified—sensor networks or sparsed arrays and phased arrays (Rocha et al. 2013; Michaels 2016). Sparse arrays use a distributed network of discrete omnidirectional transducers which are positioned at specific regions of interest. Meanwhile phased arrays use closely spaced elements and are based on steering of the wavefront at different directions by applying different lag to each array element. Despite different sensor architectures, all damage detection and localisation methods are based on the assumption that any present discontinuity will produce an unexpected echo, which can be received by sensor.

Defect localization methods are mostly based on time-of-flight (ToF) measurement of defect scattered guided wave signals. In the simplest 1D case damage can be localized as shown in Fig. 5.2a. In such arrangement, the distance l₀ and signal arrival time T₀ between sensors A and B are known. In case of the defect, an additional reflection will be received by sensor B at time instant T₁. The distance x to the defect can be calculated according to the equation (Dai and He 2014):

This works well in presence of single mode only, however the corrections are necessary in case of mode-conversion. In 2-D case (Fig. 5.2b), the spatial defect position can be estimated by calculating the ToF of the signal going from the transmitter through the flaw (Michaels and Michaels 2007):where subscripts t, r, and f denote the 2-D coordinates of the transmitter, receiver and flaw. To detect damage location with sparsed array, at least three sensors are required. By using triangulation method it’s possible to find an intersection of three regions produced by the sensors, where the possible damage is likely to occur. The shape of regions of the likely defect position will depend on transmission and reception approach. If the measurements are taken recording an echo received by each transducer and the wave propagates spherically, the region of the sensor will be in the shape of circle. On the other hand if each transducer acts as transmitter once, while all the transducers act as receivers, the region of the sensor will be in the shape of ellipse (Rocha et al. 2013). Such approach works well if wave velocity is the same in every direction. Otherwise the corrections have to be made and the actual location of the damage will be different. By using at least three sensors the image over the region of interest can be generated. In case of N sensors, the defect scattered signals will arrive at different time instances for each transmitter-receiver pair, depending on actual defect position leading to N(N−1)/2 different signals paths. To create an image, the evenly spaced grid points over the inspection area are defined. Then the pixel value at the reconstruction point (x,y) according to the delay and sum (DAS) algorithm can be estimated as (Michaels 2008):where ω_nxy—is reconstruction weight at specific point (x,y), t_nxy—is the time delay which can be calculated as d_nxy/c_g where d_nxy—distance from transmitter through point (x,y) to receiver, c_g is the group velocity. Then the 2-D defect map can be created, by repeating this procedure at spatially distributed reconstruction points. At the actual defect locations, such addition will lead to constructive interference of received signals. The major drawback of the DAS method is a large point spread function and artefacts which may be caused by wave reflections from the boundaries and mode-conversion (Michaels 2016).

Reconstruction algorithm for probabilistic inspection of defects (RAPID) method can be shown as another example of sparse array imaging (Zhao et al. 2007). RAPID method uses a circular arrangement of the sensors and assumes that most significant signal changes appear in the direct wave path. Hence, between each transmitter receiver pair a linearly decreasing elliptical spatial distribution of signal change effects due to defects is presumed. In case of N PZT elements, the defect probability at imaging position (x,y) can be expressed as (Zhao et al. 2007):where P_i,j(x,y) is defect distribution probability estimate for i^th transmitter and j^th receiver, A_i,j is signal difference coefficient of the same sensor pair, (β-R_i,j(x,y))/(β-1) is the lineary decreasing elliptical spatial distribution. Different indicators can be used for 2-D reconstruction of the defect position and definition of the pixel value in the reconstruction grid using sparse arrays. For example, Kudela et al. (Kudela et al. 2008) used a concept of damage influence map, which measures the match between the excitation signal and reflection from defect. The idea is based on the arbitrary positioning of the excitation signal on the response from the structure employing different time delays. The delay applied to the signal is then equal to the ToF from the transmitter to the likely damage position. The match between two signals at location (x,y) here is expressed by (Kudela et al. 2008):

where t₀ and Δt* are the start and the width of the time window; \( {\hat{s}}_{\mathrm{T}}(t)={S}_{\mathrm{T}}\left({t}_0,{t}_0+\varDelta t\ast \right) \) is the windowed excitation signal; \( {\hat{S}}_{\mathrm{R},k}(t)={S}_{\mathrm{R},k}\left({t}_0+\Delta t,{t}_0+\Delta t\ast \right) \) is the signal registered with the k^th receiver, F(t) is the window function (Gauss, Hann, etc.); G(x,y) = e^α(d0P+dPk) is the function dependent on the attenuation; α is the attenuation coefficient; d_0P and d_Pk represent the distances between the transmitter-imaging point and imaging point-receiver; Δt is the signal time shift, which depends on the x, y coordinates of the imaging point and the group velocities c_0P and c_Pk. The total match at location (x,y) for all transmitter-receiver pairs can be expressed as (Kudela et al. 2008):

Modifications of the proposed technique exist, which were introduced by Wandowski et al. (Wandowski et al. 2011; Wandowski et al. 2016). A slightly different approach was used by Michaels (Michaels and Michaels 2007), where authors used band pass filters with various central frequencies to obtain a set of bandlimited signals for each transmitter-receiver pair. Then the defect map is being created for each central frequency of the applied filter. Eventually, all individual images are combined taking minimum pixel value from all corresponding images, which minimizes phasing and other artefacts.

A modification of sparse array architecture was proposed by Giridhara et al. (Giridhara et al. 2010) who implemented the radial segmentation technique. It consists of a single transmitter and radially distributed receivers, which divide the object into circumferential segments. The signals from neighbouring transducers are compared to determine the location of the defect. If the flaw is somewhere along x axis (Fig. 5.3a), the sensor signals (S₂ and S₈; S₂ and S₁; S₁ and S₈) will indicate some changes in the structure. If two signals from sensors S₂ and S₈ match, then the damage is in the segment S₁ and S₂ or in the segment S₁ and S₈. The radial segment of the defect is determined by measuring the ToF of the reflection from the flaw with sensors S₂ and S₈. The exact defect angular, θ, and radial, r_d, position estimates are found by using triangulation as shown in Fig. 5.3b (Giridhara et al. 2010):where \( p={x}_i^2+{y}_i^2+{d}_i^2,q={x}_{i+1}^2+{y}_{i+1}^2+{d}_{i+1}^2, \) d_i and d_i+1 are the total travel path from the transmitter through the flaw to the sensors S_i and S_i+1 respectively (d_i = r_d + a, d_i+1 = r_d + b, r_d = x² + y²); a and b are the distances of the sensors S_i(x_i,y_i), S_i+1 (x_i+1,y_i+1) to the damage P (a² = (x–x_i)² + (y–y_i)², b² = (x–x_i+1)² + (y–y_i+1)²).

The sparse array approach interrogates the damage from multiple angles, hence the forward scattered and backscattered signals can be recorded if the damage is present within the area of array. Moreover, the reflection energy from the defect is more uniform within the region of sparse array in contrast to phased array inspections. On the other hand, as the phased array elements are located in close proximity to each other, it’s much easier to leverage the phase difference which is mainly caused by errors in phase velocity, transducer locations and variation of transducer characteristics (Michaels 2016). Using the phased array imaging, the array elements are delayed so that the azimuth of the wave φ is equal to the azimuth of target reflector φ₀. To obtain the target direction most of phased array methods sweep the beam at different directions and estimate the maximum of received signal energy. Once the target direction φ₀ is obtained, the distance to the reflector can be estimated using cross correlation or other time delay measurement method. An example of phased array imaging can be embedded ultrasonic structural radar (EUSR) method (Giurgiutiu and Bao 2004; Purekar et al. 2004). The use of phased arrays offers some advantages over single transmitter-receiver measurements, such as steering and focusing, hence large area of the sample can be examined and direction of reflector can be determined almost instantly. However, in practice due to multiple reflections and structural noise it becomes difficult both to distinquish reflector and to measure the time-of-flight precisely, which leads to defect positioning errors. Aircraft components made from composite materials introduce additional complexity for damage detection and localisation. The mechanical properties of composites are direction dependent, hence the circular or elliptical damage regions are no longer valid. Phased array beam steering becomes more complex, as radial velocity distributions must be known. As the velocity of guided waves varies with the propagation direction, wavelength and operating point on the dispersion curve (and dispersion itself) change as well. It means that the sensitivity to the defect and resolution are changing, especially if operating point is located on the dispersive region of the selected mode. This shows that each unique structure requires adaptation of the monitoring system—determination of radial velocity distributions, evaluation of boundary reflections (taking into the account velocity information), identification of present modes. Guided wave tomography is one of the most common imaging methods used to detect and localize structural changes. The tomography aims to reconstruct the spatial distribution of the material properties, which can be based on the projection of wave velocity, attenuation, frequency shift or other features (Belanger and Cawley 2009). To get the desired resolution, a large number of projections are required which can be collected either using transmission or reflection approach. Among the sensor arrangement topologies, the crosshole, double-crosshole and fan-beam are the most popular ones (Park et al. 2020). Several different tomographic reconstruction techniques exist, namely straight-ray, bent ray and diffraction tomography (Belanger and Cawley 2009; Willey et al. 2014; Belanger et al. 2010). The straight-ray methods neglect refraction and diffraction assuming that projection data corresponds to a line integral of given parameter. Bent ray methods take into account wave field of reflected from the defect, while diffraction tomography is based on Born’s approximation.

The damage detection and localisation principles described above exploit many assumptions that simplify the reconstruction. In realistic structures, the reponse of the defect is much more complex. For example, delamination is one of the most common defects found in multi-layered structures, which develop internally between neighbouring layers of the laminate. After the interaction with delamination, guided waves are scattered and convert to other modes (Feng et al. 2018). Various researches show that fundamental modes of guided waves propagate separately in two sub-laminates created by defect and then interact with each other after exiting the damaged area. A detailed guided wave interaction with delamination type defects was presented by Ramadas et al. who found that in case of delaminations positioned symmetrically across the thickness of the laminate, incident A₀ mode converts to S₀ within the defect and then back to A₀ after exiting. For asymmetrical defects, the mechanism is slightly different as an additional S₀ mode is present upon interaction with defect (Ramadas et al. 2009; Ramadas et al. 2010). It was also observed by various research groups that Lamb wave scattering at the beginning and tip of defect is determined by its position. Schaal et al. estimated frequency-dependent scattering coefficients for fundamental Lamb wave modes at both ends of the defect (Schaal et al. 2017). Based on this approach, Hu proposed a technique to locate delamination defects based on reflection and transmission coefficients of A₀ and S₀ modes (Hu et al. 2008). Shkerdin and Glorieux (Shkerdin and Glorieux 2004) related the transmission coefficients of Lamb waves with the depth and length of delamination, while Birt et al. (Birt 1998) analyzed the magnitude of reflected S₀ mode and its relation to the width of delamination. This shows that different indicators can be developed to detect defects and to assess their parameters. A complex guided wave scattering and mode conversion upon interaction with defects allows to develop various tools to identify and characterize the damage. In most simple cases, ToF measurements of reflected and transmitted guided wave modes can be used to detect the existence and location of the damage. Furthermore, by analysing the magnitude patterns and velocities of guided wave modes, other features like defect size and depth can be extracted.

POD is the probability of specified NDE inspection to detect defects in the structure at the time of inspection. MIL-HDBK-1823A provides all statistical tools and procedures to assess POD for reliability validation of NDE techniques. Usually, POD is a function of defect characteristics, i.e. length of the defect. Log Odds and Log Probit probabilistic models are commonly used for POD assessment (Gallina et al. 2013; Aldrin et al. 2016). POD can be assessed by Hit/Miss and signal response analysis. The objective of both configurations is to produce a POD curve vs characteristic parameter of the defect (usually size). Typical POD curve is presented in Fig. 5.4.

Small size of the defect is characterized by 0 POD (0%) meaning that the system could not detect defect of the specified size. The POD is 1 (100%) in the case of large defects meaning that the system detects defect of specified size reliabily. Transition zone where POD curve is increasing between 0 and 1 is under most interest. Additionally, the confidence interval is associated with POD and indicates the content of true value in the interval (Chapuis et al. 2018a; Chapuis et al. 2018b). Hence, confidence bounds characterize the ability of the system to detect particular characteristic parameter (defect size) with defined probability and confidence (Gallina et al. 2013). The usual requirement, especially for aerospace applications, is to determine the minimum size of defect which is detectable in 90% of the inspections at 95 % confidence level, a_90/95 (Gallina et al. 2013).

Hit/Miss approach is characterized by measurement of qualitative information and determines the presence or absence of the damage. The response of the inspection is binary value of 1 (defect is detected) and 0 (fail to detect the defect). The model of POD in Log-Odds functional is expressed (Chapuis et al. 2018b):where a is a characteristic parameter (defect size), g(a) = a or g(a) =  log (a), μ is a defect size detected with a probability of 50% and σ is the steepeness of the function.

Also, POD can be evaluated by signal response approach (â vs a) or quantitative measure of defect size. POD curve is based on methodology when there is a relationship between the defect size, a (physical dimension of a defect size), and sensor response â (measured response of the system to a target size). In the case of ultrasonic inspection the system provides a response from the defect whose amplitude is dependent on it’s size. Signal response approach is able to estimate and build POD curve using greatly smaller amount of data comparing to Hit/Miss analysis (Meeker et al. 2019; Chapuis et al. 2018b). Generally, this approach has a linear model and is expressed as following (Chapuis et al. 2018b):where β₀ and β₁ are the coefficients of linear function, g(a) = a or g(a) =  log (a), ε is a random error.

Since the noise exists in any inspection data the boundary which determines damage or no damage output has to be established. For this task the the detection threshold a_thres is fixed. Further, the POD curve can be expressed as a function of density of scattered data which is above the detection threshold y_thres (Gallina et al. 2013; Chapuis et al. 2018b):where Φ_norm(z) is the normal density function and \( \mu =\frac{y_{\mathrm{thres}}-{\beta}_0}{\beta_1} \), \( \sigma =\frac{\sigma_{\upvarepsilon}}{\beta_1} \). The parameters μ and σ are determined according to the methodology of maximum likelihood estimation (Chapuis et al. 2018b).

As it was mentioned in Sect. 5.4, the probability of false alarms or Relative Operating Characteristics (ROC) curve has a significant importance to estimate the performance of SHM and NDE systems (Gallina et al. 2013). Selection of adequate detection threshold is an essential part in PFA assessment. It is a high possibility to classify undamaged regions of the component as damaged due to high number of observations in SHM system. For instance, the detection threshold can be exceeded by the impact of strong background noise when no defect is present. However, the POD and PFA are spatially dependent. Therefore, in order to determine appropriate detection threshold it is useful to plot POD and PFA in the same diagram to establish the overlap between two metrics of system performance (Fig. 5.5) (Gallina et al. 2013; Chapuis et al. 2018b; Schoefs et al. 2012).

In the case of NDE inspections a_thres is determined from the measurement when no flaw in the structure is present and the value is set above the background noise level. Since the threshold is set quite high in NDT applications the PFA has usually a low value (Fisher and Michaels 2009). Consequently, the threshold value in NDE for signal response approach is the highest level of noise in the defect free region (Fisher and Michaels 2009). However, it is a challenging task to determine detection threshold for SHM application. In the case of SHM system, a number of measurements of not defective structure will be available before damage occurs. Since the sensors are fixed in SHM system, in-situ effects will affect the signal response—temperature, operational load or sensor degradation. As a result, detection threshold can be determined as a variance in signal response over time from the undamaged structure. Another complexity to define a_thres is a dependent measurement of SHM. Due to a large degree of variability the measurement response can be classified as damage even if there is none in accordance with prior measurements (Meeker et al. 2019; Fisher and Michaels 2009; Cobb et al. 2009).

Before POD assessment , NDE and SHM systems should be completely evaluated in terms of the limits of operational parameters and application in order to list factors that significantly affect the variability of the system (Department of Defense 2009). It is essential to capture all sources of variability. Otherwise, the results of system performance evaluation will be invalid due to missed significant variables. After analysis, variables which have negligible impact on the detection can be eliminated (Mandache et al. 2011). There is a risk to overestimate the POD of smaller size defects and underestimate the PFA in the case of missing important influential sources. Factors of SHM system which could affect the signal are as follows (Meeker et al. 2019; Mandache et al. 2011):

One of the advantages of SHM system is a reduction of human intervention as an important factor affecting the results due to automatization. However, there is still human involvement in the case of instrumentation installation and interpretation of the recorded data if required, but manual coordination is avoided (Mandache et al. 2011).

To ensure reliable work of SHM system backup power provision has to be implemented, since, power line is often at the risk to fail during emergency cases. Furthermore, SHM sensors durability depends on the power requirements. In the case of battery power supply, low weight and charging capabilities has to be feasible. More appropriate solution is to use self-powered sensors through energy harvesting. Additionally, to reduce the problem of sensors failure within years of exploitation they have to be self-diagnosed or redundant. Redundant SHM system involves sensors, which are not expensive and easy to install. The approach essence is to install multiple number of sensors with overlapping range to provide redundant sensing. Consequently, if one of the sensors fails, the others take over and perform the task. This redundant configuration can create more defect-tolerant and robust system (Mandache et al. 2011; Aldrin et al. 2013). However, redundant elements increase the weight of the system, which, especially in aerospace, should be kept as low as possible.

The sensors have to be optimally placed to assure the sensitivity to the damage as well as condition of structure surface. The guided waves have the ability to confine in thin-wall structures, so they are able to propagate over large distance of the structure with minimal loss of energy and attenuation. In addition, the guided waves are suitable for the inspection of various shapes and geometries of the long structures. Therefore, it is possible to monitor the condition of surface of the structure of different shape. Generally, the more sensors are placed on structure the more detailed information about structure health is received. The coverage of the sensors should be performed in specific way in order to provide adequate information from collected data. Performance requirement and sensor network robustness have to be fulfilled (Mandache et al. 2011; Yi and Li 2012; Abbas and Shafiee 2018).

In the case of monitoring high risk zones the sensors should be placed in close proximity in order to have higher sensitivity in the case of damage occurrence but not placed in potential risk of impact damage place since this can affect the sensor itself (Mandache et al. 2011).

A good quality of coupling between sensor and structure has to be provided. Usually, adhesive is used as a coupling medium. However, degradation of adhesive properties can also affect on the response of the sensor. In aerospace industry during aircraft exploitation, sensors which are placed on the surface of the structure are not applicable due to aerodynamic conditions. This method is possible on the measuring stands in laboratory conditions (Mandache et al. 2011).

Traditional wired SHM system consists of sensor system, data communication and storage system as well as the information analysis system to assess the integrity of the structure. The main disadvantages of wired system is a high cost of long cables, low productivity, time consumption, low flexibility, impact on the weight of the structure and heavy traffic of monitoring channels (Wang et al. 2020). Wired system is exposed to cable and wire breakage during the exploitation and leading to system malfunction. Wireless sensor networks have advantages of low cost, high efficiency, high flexibility. There are various protocols of communication technology widely described in (Alonso et al. 2018). Selection of the communication technology is dependent on the characteristics of infrastructure and monitoring requirements. However, if the data is transmitted and stored wirelessly there is still issues on the effect of SHM system interaction with other aircraft systems and avionics, electromagnetic and radio frequency interferences, what data has to be collected and at what frequency and etc. (Mandache et al. 2011).

In order to define methodology for verifying reliability of SHM it is necessary to understand how sensors and other factors respond to the damage. In the case of guided waves, environmental and operational conditions can change the phase and the amplitude of the signal. The challenge in SHM system is to identify signal changes due to the damage presence from the false calls caused by the environmental and operational parameters influence. Guided wave technique is a suitable tool for damage detection and characterization, however, it has a high sensitivity to these factors. According to the work performed in this field, the impact of these parameters is compensated by development of appropriate modelling process, variation of sensor technologies, processing of the acquired signals, extraction of features as well as statistical methods and machine learning (Mandache et al. 2011; Gorgin et al. 2020). Environmental and operational conditions are huge source of variability in aerospace industry, civil and mechanical engineering. In this section, temperature and mechanical loading are discussed more widely due to their significant influence on SHM systems.

Temperature is the important condition, variation of which is limiting the guided wave SHM systems. Temperature change is dominant influential property of environment condition that affects robustness of guided wave SHM (GWSHM) system (Fendzi et al. 2016). Temperature affects the component under monitoring and the sensing system. Propagation characteristics of Lamb waves significantly depends on temperature variation. Volume and density of the component changes with the temperature variation. This leads to a modification in the elastic properties, change of ultrasound velocity in the material that influence the response of the sensor at damage free place in the component (Mandache et al. 2011).

In order to mitigate this problem many investigations on the change in guided waves properties caused by temperature were conducted experimentally, numerically and analytically. Different configurations of the technique as well as temperature range was studied. Generally, by changing the temperature signal amplitude, time of flight and velocity can change. For instance, Abbas et al. (Abbas and Shafiee 2018) generated wave velocity function for guided wave group velocity evaluation considering frequency and temperature effect. It was found that the function can be used at the temperature which is not higher than 130 °C, since, further temperature increase influences on the bonding characteristics of the sensors. However, the relation between temperature and the output of GWSHM is not linear, since, many factors caused by temperature variation influence on the guided waves. Changed stiffness of the materials has the impact on group and phase velocity; change of elastic and shear moduli leads to longitudinal and transverse velocitites change resulting the decrease of phase velocity of the waves. As a result, in the case of temperature increase the propagating signals arrive later compared to temperature decrease. Expansion and contraction effect can lead to a change of distance between sensors and actuators, additionally, temperature variation has an impact on sensor properties and bonding layer properties (thickness and shear modulus) (Gorgin et al. 2020). Some numerical investigations presented a high impact of the temperature on the propagation of guided waves due to the change of physical properties.

If baseline subtraction technique described in previous section is used to detect structural changes, temperature compensation strategies is a must in order to minimise the residuals caused by environmental factors and to be able to detect smaller defects. Compensation techniques like optimal baseline subtraction (OBS), cointegration or baseline signal stretch (BSS) exist to reduce the influence of temperature to guided wave signals (Croxford et al. 2010; Gorgin et al. 2020; Konstantinidis et al. 2007). A comprehensive study on the influence of temperature to reflection, transmission and velocity of guided waves was recently presented by Abbas et al. (Abbas et al. 2020). In the case of OBS temperature compensation technique the baseline signals are measured over the temperature range whereupon the best matched baseline signal is selected according to subtract from any further reading from the structure. This technique requires large number of baseline signals each at different environmental condition and high temperature resolution. BSS temperature compensation technique is based on model building of the effects on wave signals due to temperature change. The shape change of the signals over the time is calculated (stretch factor) in order to perform time-stretch estimation (dilation or compression of the signal). This method works well for small temperature differences between baseline and current signal, however it’s performance deteriorates at sufficiently large temperature differences (Croxford et al. 2007). Clarke et al. proposed to use a combination of OBS and BSS methods to reduce amount of baseline signals describing different temperature regimes (Clarke et al. 2010). In most cases, it’s considered, that wave velocity is most important factor that changes with variation of temperature. However, recent studies show, that phase and amplitude of the signal are temperature sensitive as well. Changes in the temperature may cause variation of bonding stiffness between the sensor and the structure. This may alter the frequency response of transducer and lead to phase delay in the signal. Fendzi et al. proposed temperature compensation method that estimates linear dependencies of amplitude and phase delay versus temperature for each transducer pair mounted on the structure (Fendzi et al. 2016). Based on derived amplitude and phase factors, the regression model is then estimated and signal can be reconstructed at selected temperature. Recently Herdovics et al. proposed temperature compensation method which uses two sensors in close proximity only, hence the phase changes are compensated according to the incident wave, while the wave velocity changes are supressed from echoes. (Herdovics and Cegla 2019). The authors concluded that proposed compensation technique is able to reduce effect of environmental conditions from 7 dB to 20 dB in comparison to conventional single stretch BSS method at temperature difference of 41.5 °C between signals. Mariani et al. presented a method for temperature compensation that takes into the account both velocity and phase information (Mariani et al. 2020). The main difference is that the later method provides estimate solely based on baseline and subsequent signals. The method demonstrated 97% POD for 0.1% probability of false alarm when the temperature difference ranges were between 7 °C to 28 °C and 35 °C to 55 °C. Meanwhile at the same conditions, standard BSS yielded up to 23% POD only.

Propagation of guided waves, also, can be affected by operational conditions which include vibration, loads and sensor bonding. Vibration can lead to interpretation complexity of structural behavior. The load applied on the structure can change a isotropic medium into an anisotropic medium, effective elastic constants lose symmetry, cause time-shift and phase velocity changes. To compensate the effect of load, the changes of phase shift and signal amplitude have to be taken into account. Additionally, sensor degradation occurs due to mechanical loading leading to piezoceramic transducer deterioration. In order to identify degradation mode as transducer disbonding the electromechanical impedance spectrum is determined by the electrical and the mechanical properties of the transducer and host structure which includes the adhesive line (Rajic et al. 2011). In order to ensure reliable performance of SHM system the influence of mechanical loading on the sensors, which cause its degradation, has to be reduced. The compensation strategy implies the use of specific element as a structural augmentation which is placed between transducer and the structure. As a result, the stresses in transducers caused by loading are reduced (Rajic et al. 2011).

Comparing to NDE techniques which produce independent observation the data received from SHM system is dependent due to continuous data collection. Despite the fact that uncertainty factors of NDE and SHM differ, the same mathematical framework is applied for both systems (Gianneo et al. 2016). Guided waves provide fast and cost-effecive evaluation of different damage types compared to other approaches of SHM system. GWSHM has several indicators allowing to detect defects in the structure: changes in natural frequencies, in time of flight, in strain, in time domain signal and other characteristics. In order to evaluate POD of SHM system it is necessary to cover all sources of variability. As it was mentioned above, there are two configurations to assess POD—signal response and Hit/Miss. PFA has to be evaluated for SHM system due to high possibility of false calls (De Luca et al. 2020).

Mandache et al. (Mandache et al. 2011) described time-based POD assessment of SHM system. In comparison to NDE, SHM detects time evolution of the defect with respect to baseline signal. Therefore, POD can be defined not as a function of the defect size, but as a function of time it takes until the damage of certain size is firstly detected or a damage growth on pre-defined percentage. This approach was proposed by Pollock who investigated the probability of detection of growing crack using acoustic emission. The crack of 4mm was growing to 4.05 mm and detected with a probability of 90% within 6 weeks of monitoring. Shorter period of monitoring time gives lower probability in the case of same crack (Mandache et al. 2011). Another approach to estimate POD of SHM system is to transfer POD from NDT to SHM. Firstly, POD assessment for NDT technique is performed. Then using transfer function where all influencing parameters are taken into account the POD is converted to POD curve equivalent to SHM system. One more alternative is to analyse two parallel structures under similar conditions periodically with NDT and continuously with SHM. The relationship of signal responses to damage between two systems is transferred to the POD curves, assuming that POD of NDT is known (Mandache et al. 2011).

Gianneo et al. (Gianneo et al. 2016) investigated Multi Parameter POD approach for guided waves of SHM. This approach implies the combination of Finite Element numerical simulations and experimental data to receive required POD curve. The combination of numerical and experimental data establishes “Measured â vs. Modelled a” data diagram considering influencing factors and uncertain parameters. As a result, non-linear responses of the GWSHM system is being linearized by the diagram allowing the use of Berens’ statistical model. Then a POD curve is estimated as a function of modelling data. Multi-Dimensional POD implies the analysis of SHM system responses as a function of damage size with the influence of factors and isolate the recorded signals that are sensitive only to a single influencing factor, including damage. After POD curves of damage size for each independent influencing factor are found then POD fusion of these curves can be performed. Therefore, SHM reliability in the presence of combined influencing factors can be determined (Mandache et al. 2011).

Large scale of experiments are required in order to evaluate POD of the system. A number of repetitive tests has to be performed for the same crack size to take in consideration the uncertainty of influencing factors. This approach of POD evaluation is time-consuming and expensive. Thus, Model Assisted POD (MAPOD) was developed as a solution of the problem (Gallina et al. 2013).

Alfredo et al. states that the support of numerical simulations is required for POD assessment. Verification and validation method of the SHM system has to evaluate all aspects which can influence on detection capability, localization and characterization of the defect as well as an effect of environment and exploitation over time. Since sensors of SHM system are fixed at the same position the main difficulty is that the flaw may occur anywhere what will cause the change in response due to distance between sensors and defect. As a result, model for guided waves SHM system POD assessment is proposed and shown in Fig. 5.6 (Güemes et al. 2020).

Mainly, there are two MAPOD approaches of high interest: transfer function and full model assisted. Transfer function approach is physics based and used to transfer POD of specific inspection to another with different parameters of inspection. Full model assisted approach is based on the models of uncertainty propagation of specified inspection parameters. Numerical signal of the approach is combined with experimental noise. Nowadays, the use of computer models to evaluate the reliability of SHM system is the most suitable approach. MAPOD reduces experimental inspections of the samples by modelling responses of inspection of the defected material. In the case of effective MAPOD calculations enhance statistical models have to be created. These statistical models characterize system dependency on various influencing factors including defect. Additionally, the polynomial chaos methods reduce the number of samples required for assessment and speed up the MAPOD as well as parallel computing techniques greatly cut down the time of simulations (Gallina et al. 2013; Mandache et al. 2011).

Gallina et al. (Gallina et al. 2013) proposed the MAPOD approach to analyze the Lamb wave SHM system. Propagation signals received by the sensors were collected. Then the effect of dispersion was eliminated by the linear mapping algorithm. All signals were delayed and summed. Location and detection of the damage was performed using imagining technique. Numerical experiments were modelled and empirical white Gaussian noise was added to the recorded signals of sensors for consideration of in-situ factors. The data of simulated experiments was used in statistical analysis for POD curve and PFA evaluation.

Additional example of MAPOD evaluation of SHM systems is described. Cobb et al. (Cobb et al. 2009) proposes hit/miss configuration and model assisted approach for POD estimation of SHM system. Proposed model assisted approach comprises a creation of a series of models:

After, Hit/Miss analysis of resulting data was performed. Logistics regression was used for modelling binomial response data. POD curve was evaluated and indicates the percentage of all defects of specific size which will be detected (Cobb et al. 2009).