Correction to: Contextual Application of Pulse-Compression and Multi-frequency Distance-Gain Size Analysis in Ultrasonic Inspection of Forging

The article “Contextual Application of Pulse-Compression and Multi-frequency Distance-Gain Size Analysis”.


Introduction
Ultrasonic NDT is the only technique that allows the inspection of the entire volume of large forgings. Pulse-echo (PuE) is a widespread method for which all the Standards and evaluation procedures have been developed. Among these, the analysis based on the DGS diagrams, is the standard method allowing the sizing of defects in large structures where the use of Distance Amplitude Curve (DAC) is not feasible [1][2][3]. Various probes at different incidence angles and with different central frequencies are used to guarantee the inspection of the whole sample's volume with an adequate sensitivity for each possible type of embedded defect.
Despite DGS analysis with PuE is effective in most of the situations, two main critical points emerge: 1) the need to automatize the inspection as much as possible makes the use of many different probes inconvenient; 2) in the presence of high attenuation and-or large dimensions of the forgings, PuE could not guarantee an adequate SNR and sensitivity. To face the former point, phased-array probes have been introduced making the automatic inspection easier: a single phased-array probe can replace several standard probes and moreover, being possible to vary the focusing of the ultrasonic beam, the sensitivity can be increased where needed to address also the latter issue. However, this is not enough in some critical applications requiring a high sensitivity even with very weak signals or high noise level.
Some of the present authors proposed to exploit pulse-compression (PuC) technique in combination with the use of two separate transducers, one transmitter -Tx-and one receiver -Rx-, and chirp signals to increase the SNR of the measurement and then to increase the defect detection sensitivity [4,5].
In the present work, the method is improved by developing a numerical simulation tool for calculating DGS curves for an arbitrary Tx-Rx configuration working with both single-element and phased-array probes. The resulting DGS diagrams are used to evaluate the size of known flat bottom hole defects realized on a steel forging. Two different DGS analysis procedures are implemented and compared: one makes use of a narrowband excitation chirp signal and of a single-frequency DGS analysis, so replicating the conditions of a standard single-frequency DGS analysis made in PuE with a single narrowband probe, the other makes use of a broadband chirp signal and a simultaneous multifrequency DGS analysis.
The paper is organized as follows: the basic theory of PuC is summarized in Section 2; in Section 3, the multi-frequency DGS analysis is introduced; in Section 4, experimental results and a comparison between single-frequency and multi-frequency DGS analysis are reported. In Section 5. some conclusions and perspectives are drawn.

Pulse compression basic theory
Flaw detection through ultrasonic inspection consists of measuring the impulse response ℎ( ) of the sample under test (SUT) with respect to a mechanical wave excitation. In standard PuE method, the impulse response ℎ( ) of the system under inspection is estimated by exciting the sample with a short pulse ̃( ) and then recording the system response h( ) =̃( ) * ℎ( ), where * is the convolution operator. If ̃( ) is short enough to cover uniformly the whole bandwidth of the transducers, the approximation can be considered very close to the true expected signals.
On the contrary, in a PuC measurement scheme an estimate ĥ( ) of ℎ( ) is retrieved by: (I) exciting the system with a coded signal ( ); (II) measuring the output of the coded excitation ( ) = ( ) * ℎ( ); (III) applying the so-called matched filter ( ) to the output [6]. At the end of the procedure we have: where the "pulse compression condition" ( ) * ( ) =̂( ) ≈ ( ) has been exploited. As in most of the applications, in the present paper the matched filter is defined as the time-reversed replica of ( ), ( ) = (− ), so that ̂( ) turns out to be the autocorrelation function of ( ).
The PuC condition can be therefore assured by every waveform having a -like autocorrelation function; a huge literature is available on this topic (see for example [4,[7][8][9]). In NDT applications, and in particular in the case of ultrasonic inspection, the most used waveform is the Linear Chirp (LC) that is the signal employed also for the present application. LC is described by the expression [10]: where T is the duration of the chirp signal, f1 is the start frequency, f2 is the stop frequency, = ( 1 + 2 )/2 is the centre frequency and % = ( 2 − 1 )/ is the percentage bandwidth of the chirp. Note that T and are not constrained by each other, so that the duration of the LC can be increased arbitrarily. In case of a rectangular window, i.e. ( ) = for ∈ [0, ], LC has a constant envelope and an almost flat power spectrum in the spanned frequency range ∈ [ 1 , 2 ]. However, a non-constant, usual symmetric, ( ) it is used to reduce sidelobes of ̂( ) and in the present work the Tukey-Elliptical window it is used [11].
Experimentally, while PuE requires only one transducer that acts both as Tx and Rx, PuC based schemes usually employ two separated Tx and Rx transducers in pitch-catch configuration to allow the excitation signal duration to be extended arbitrary. The increased complexity of the resultant procedure is justified by the benefits provided in terms of resolution and SNR enhancement. Indeed, by using two distinct transducers, the excitation signal can be long as the typical inspection time (few milliseconds for steel forgings) and therefore thousands of times longer than typical pulses used in PuE, which duration is inversely proportional to the transducer bandwidth. This allows more energy to be delivered to the system, increasing the SNR. Moreover, it was found that PuC is optimal to reduce noise, both environmental and due to the quantization step introduced by the Analog-to-Digital Converter [12,13]. Figure 1 summarizes the present PuC procedure adopted while Figure 2 reports an example of the PuC procedure applied to a benchmark forging on which a flat bottom hole was realized and hence filled with soldering to simulate a small void close to the backwall surface.

Multifrequency DGS analysis
As previously mentioned, the standard procedure for forgings inspection relies on two pillars: the PuE method and the DGS diagrams analysis. In the previous Section, a measurement procedure based on PuC, an alternative to PuE has been introduced to increase the SNR of the measurement and hence the sensitivity of the inspection. In this section, the procedure for applying DGS analysis in combination with PuC is shown, together with a thorough explanation on how to implement a multifrequency DGS analysis that can be beneficial when: (1) the optimal inspection frequency is not known; (2) the effect of the inspection frequency on the defect sizing must be considered and (3) an accuracy analysis of the defect sizing capability is of interest.
To accomplish these aims, first of all it is worth to note that after the application of the PuC procedure, the signals ĥ( ) are very similar to those provided by PuE, i.e. h( ), so the standard DGS analysis can be applied o ĥ( ) provided that: (i) the DGS diagrams for the Tx-Rx configuration are known; (ii) the overall measuring system composed of a linear chirp excitation signal and the Tx-Rx probes exhibits a narrowband nature, centred around the frequency of the DGS diagrams one want to use and with relative bandwidth %~4 0.
Regarding the point (i), a numerical tool has been implemented that calculate the DGS diagrams by exploiting the Rayleigh-Sommerfeld Integral Model. The two probes have been modelled both as piston transducers and full interference in the path Tx-defect-Rx has been taken into account [14][15][16]. Regarding the point (ii), usually the narrowband characteristic of the measurement system is guaranteed utilizing narrowband transducers. This is because the control over the excitation power spectrum is less when using single pulse or short burst excitation. Note that 40% is the typical % value of narrowband probes used for DGS analysis in PuE, e.g. GE Krautkamer B2S. Indeed, even if DGS are calculated by considering a single frequency value, in practical applications % < 40 implies a low range resolution that could hamper defect detection.
Conversely, by employing a l LC as input signal, the excited bandwidth can be shaped with great accuracy and almost arbitrarily, provided that the so-called time-bandwidth product of the chirp • is large enough, and this is the usual case for forgings inspection. So, the transducers can also be broadband, % > 100, but the ultrasonic generated spectrum is determined by the chirp.
DGS diagrams have been developed so far for PuE inspections, i.e. for single probe UT measurement setups. Hence, they cannot be applied to the PuC UT inspections, due to unique geometry of the dual probe measurement setup. In the subsequent sections, the results of numerical tools for DGS calculations are compared to the standard DGS diagrams and the process of multifrequency DGS analysis is described.

Field simulation and DGS calculation
A numerical tool was developed to compute the DGS diagrams for an arbitrary shape and positions of both the transducers and the defects, thus allowing the DGS method to be applied in PuC procedures employing pitch-catch configuration. The numerical tool solves the Rayleigh Summerfield integral model of wave propagation by considering the "full-interference" case and piston transducers [14]. Tx, Rx and defect are discretized, and the amplitude of the echo due to a defect is calculated by coherently summing up the contributions of all possible paths Tx-defect-Rx, i.e. considering amplitude and phase of each contribution. The defect is assumed to behave as a perfect reflector and the surfaces of the transducers are considered perfectly rigid.
In Figure 3, the DGS diagrams produced by using the numerical tool for a GE Krautkrämer's B2S probe in PuE configuration are compared with those reported in the probe data sheet. The diagram obtained for the infinite reflector and the DGS diagrams for various disk reflectors in the far field matched perfectly with the vendor DGS curves. Instead, in the near field, the numerical DGS curves exhibits a series of local minima and maxima while the standard DGS diagrams are more regular.
This phenomenon is well known, and it was first discussed by Krautkrämer brothers [1,16]: in numerical curves calculated at a single frequency, constructive and destructive interference is considered, and interference has a high impact especially for small defects in near field. In practical applications, although sometimes visible, interference phenomena are less relevant due to the finite but non-null bandwidth of the transducers, which implies different interference locations for each frequency value leading to a resultant averaging effect, and moreover it must be considered that real defects are not perfect reflectors as well as the propagating medium is not perfectly homogeneous. Increasingly, as a matter of fact, the equivalent defect size evaluation is made by considering not a single measurement point but a finite area of inspection. So, to remove the interference effects in probes' datasheet, the DGS diagrams in the near field are usually established by experiment or by performing frequency and spatial averaging on theoretical single-frequency calculated curves. Figure 4 report an example of this last approach and the relative effect on destructive and constructive interference: the averaged diagrams are very close to the experimental calculated one in the near field.
Once verified the tool for the calculation of DGS diagrams in PuE configuration, the DGS diagrams for two probes in pitch-catch used in the PuC procedures were evaluated. Figure 5 compares the single probe DGS diagrams of B2S probes with the DGS curves obtained for a pair of two B2S probes placed side-by-side. Note that here the probes' case dimensions (45mm of diameter) have been considered. In the near field, the DGS diagrams for pitch-catch configuration exhibit a lower sensitivity in PuC configuration than in PuE, that is the backwall echo or a defect echo give a signal of less amplitude in the PuC case. However, as far as the distance of backwall or defects increases, the PuC and PuE sensitivity values become close and close to almost coincide in the far field.
In the case considered here, the sensitivity difference in the near field is very large. This is because the case of the probes is approximately twice the element. Thus, the ultrasonic beam of the Tx and those of the Rx superimpose significantly only at a certain distance, and the Tx and Rx beam superposition is strictly related to the DGS diagrams values. Only beam sidelobes can superimpose at a very small distances for a pair of probes which elements are separated by some gap. This is depicted by the two-dimensional images reported in Figure 6 that visualize the sensitivity for both PuE and PuC cases for XZ and YZ planes, wherein the sensitivity map is formed by visualizing pixelwise the amplitude of the echo signal due to a defect of 1mm placed at the pixel position. For PuE, the Tx and Rx fields coincide, thus the sensitivity is proportional to the beam energy. In addition, for circular probes as the B2S here considered, the sensitivity on the XZ and YZ planes is the same.
On the other hand, in pitch-catch configuration, the Tx and Rx field superposition pattern is not symmetrical and so is the sensitivity. By using fingertips type probes, the centre-centre distance for the Tx-Rx pair can be minimized, implying the minimum lack of sensitivity in the near field. The experimental results reported later were obtained indeed by using finger-type probes.

Multi-frequency DGS analysis procedure
In this Section the multi-frequency DGS analysis procedure is introduced and quantitatively compared with the standard single frequency one. Please note that the single-frequency DGS analysis must be more properly defined as narrowband analysis and indeed when the standard singlefrequency analysis is considered, it is referred to the use of a narrowband signals, % = 40 or 60 exciting broadband transducers (VIDEOSCAN Tx-Rx-pairs from Olympus).
Which are the main reasons to introduce multi-frequency DGS analysis? One is the possibility to implement DGS defect sizing at different frequencies simultaneously, so as to increase reliability and accuracy; the second one is related to the fact that broadband signals exhibit a higher spatial/range resolution than narrowband one, and this help defect detection by reducing grain noise and possible pile-up of different echoes. In addition, the use of broadband signals is dual beneficial in PuC, since  the largest is the bandwidth, the higher is the SNR increment, and moreover the higher is the bandwidth, the smaller are sidelobes of ̂( ) [18].
At the same time, the use of broadband signals conflicts with direct application of the standard DGS procedure, even it has been proposed recently [17]. We therefore investigated if the DGS analysis could be extended to the use of broadband signals and transducers. In this paper we propose and test the following procedure: 1. A broadband LC signal and a broadband Tx-Rx transducers pair are used; 2. The PuC output ĥ( ) undergoes to a bank of digital filters that produce the set of narrowband signals {ĥ ( )}, centred at with %~4 0; 3. For each frequency , the standard DGS analysis is applied (the physical attenuation is calculated and counterbalanced numerically, the echo envelope is compared with the DGS diagrams). The process of standard single frequency and multifrequency DGS analysis is further explained in the flow chart in Figure 7. Moreover, an example of the procedure is depicted in Figure 8 while in the following Section some results obtained with both narrowband and broadband LC are reported.
In perspective, this method could be further developed to consider only a unique broadband DGS diagram. This can be done by considering the spectrum of the input signal and the frequencydependent attenuation within the sample, thus providing the estimation of the defects size as well as the defect detection sensitivity by exploiting the SNR values and the range resolution of broadband data. It is worth to note that a similar approach has been already considered in calculating standard narrowband DGS to deal with the real bandwidth of the transducers [17].

Experimental results
To test and compare the single-and the multi-frequency DGS analysis, experimental data were collected on two samples containing reference defects, see Figure 9. The first sample, (a), was a cylindrical forging of diameter 600 mm and length  1450mm with a flat bottom bore defect (FBB) of diameter D=3mm, length L=20mm and depth 1430mm realized on the back flat surface. The second sample, (b), was a section of a disk sample with outer radius 873 mm and the inner radius 147, in which there was a FBB defect of D=1mm and L=20mm drilled on one of the cross-section radial flat surfaces so that the normal incidence condition on its flat surface is attained by using an beam oriented at 45° with respect the normal of curved outer surface.  Sample (a) was inspected with a pair of Olympus fingertips V109 VIDEOSCAN probes (active element diameter =0.5 in, central frequency = 5MHz, with centre-centre distance in pitch catch of 17mm), and with a pair of Olympus, V108 VIDEOSCAN probes (active element diameter = 0.75 in, central frequency = 5 MHz, with centre-centre distance in pitch catch of 35mm). Both pairs were used without any wedge so that longitudinal waves were generated within the sample and the beam axis had a 0° angle with respect the normal of the inspection surface. Sample (b) was inspected with a pair of Olympus fingertips V109 VIDEOSCAN probes (active element diameter =0.5 in, central frequency = 5MHz, with centre-centre distance in pitch catch of 17mm) and with a pair of Olympus C106 CENTERSCAN probes (active element diameter = 0.5 in, central frequency = 2.25 MHz, with centre-centre distance in pitch catch of 17mm). To assure an orientation of the UT beam axis of 45° with respect the curved inspection surface normal, a 30° wedge was used. This allowed generation of solely share waves into the sample.
For both cases, and for all Tx-Rx pairs, the DGS diagrams were calculated for various central frequencies by means of the numerical simulation tool discussed above. Figures 10-17 report the results of the DGS analyses implemented.
On sample (a), both single-frequency and multi-frequency DGS analysis was done. Figures 10  and 12 depict the results obtained using a narrow-band linear chirp, % = , making several measurements at different central frequencies. For multi-frequency case instead, Figures 11 and 13, the analysis was carried out by acquiring a single broadband signal and then applying the procedure illustrated in Figure 7-bottom. The results obtained by using multi-frequency DGS are almost identical to those achieved by standard narrowband DGS and even more precise. This is illustrated by Figure 14 which summarizes the values of the equivalent defect diameter estimated at various frequency values by using both narrowband and wideband excitation signals.
In subplot (a), the values estimated for the 3mm defect by using a broadband excitation in combination with the multi-frequency DGS analysis are compared with the values retrieved by using narrowband chirp signals with % = , respectively. It clearly emerges that the results of multifrequency analysis applied to a broadband signal at different central frequencies are more precise and accurate than those attained by using a narrowband signal for each frequency.
In subplot (b) are compared the values estimated for the 3mm defect at various frequencies by using % = broadband chirps with different ′ : the results are almost identical in the three cases demonstrating that the procedure is robust and quite independent by the effective bandwidth of the excitation, provided that frequency range of the multiple DGS analysis is covered.
The two aspects evidenced by Figure 14 show that the proposed provides precise results at different frequencies and a reduction of the inspection time.
In addition, a better spatial resolution was also obtained employing the broadband excitation signal with respect to the narrowband one: Figure 15 reports the zoom of the defect signal echo envelope and of the backwall echo, which were ad 20mm of distance. The spatial width of the measured defect echoes is smaller by using broadband excitation and moreover, broadband signals allow reducing the sidelobes of the backwall echo, which can hide eventual defects placed at a very short distance from the backwall.
For sample (b), only results attained by using broadband excitation are reported. Figure 16 illustrates the results attained with the pair of V109 probes placed on a 30° wedge; Figure 17 illustrates the results attained with the pair of C106 probes placed on a 30° wedge.
The defect is clearly detected, and its diameter is quite good estimated except for the smaller frequency of analysis corresponding to 1.5 MHz.

Conclusions
An application of the pulse-compression technique to the ultrasonic inspection of forgings is presented. By using broadband probes and broadband excitation, the standard DGS analysis of echograms was extended to perform multi-frequency DGS analysis on a single measurement. The procedure was compared with the use of narrowband signals even in combination of pulse compression. Results showed that the defect sizing capability is not altered by using broadband signals and then applying filters before DGS analysis, but rather can increase the precision and accuracy of the defect dimensions estimate and the spatial resolution while lowering the inspection time. In addition, such procedure allows to define the optimal inspection frequency for a given measurement point. The results open space for further developments in terms of inspection frequency optimization and for the development of a broadband DGS defect estimation procedure that should take the maximum advantage from PuC in terms of SNR gain and spatial resolution. Moreover, the use of such procedure in combination with 3D imaging protocols (see for instance [19]) could further improve the defect characterization while providing its location within the sample, which is also relevant in the evaluation of defect impact [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].