PSI - Issue 80

Available online at www.sciencedirect.com Available online at www.sciencedirect.com Available online at www.sciencedirect.com

ScienceDirect

Procedia Structural Integrity 80 (2026) 43–52 Structural Integrity Procedia 00 (2023) 000–000 Structural Integrity Procedia 00 (2023) 000–000

www.elsevier.com / locate / procedia www.elsevier.com / locate / procedia

© 2025 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Ferri Aliabadi Abstract Fatigue crack initiation and propagation pose critical challenges to structural integrity assessment, particularly in safety-critical applications where reliable in-service monitoring is essential. Previous studies have demonstrated the feasibility of baseline-free crack detection using higher-order harmonic parameters, specifically the second harmonic parameter ( β ′ ) and the third harmonic parameter ( γ ′ ). While these parameters showed the potential for online in-service crack detection, their fluctuations and the dependence of the first stage on sensor bonding conditions, thereby limiting ro bustness and interpretability. To address these limitations, the present study introduces an alternative feature based on the root mean square (RMS) value of time-domain signals for baseline-free in-service crack monitoring. owing to its direct reflection of the signal content, the RMS features demonstrates greater stability and reliability compared with harmonic based parameters. The Dynamic Piecewise Linear (DPL) method was employed to analyze RMS data obtained from fatigue experiments conducted on multiple specimens. Results reveal that the RMS change can be clearly divided into two stages, with the critical transition point closely coinciding with the experimentally observed crack initiation. Further more, the proposed approach successfully identified cracks smaller than 2 mm, yielding consistent detection outcomes across di ff erent specimens and sensor configurations. Most importantly, the RMS-based method exhibited insensitivity to sensor bonding conditions, thereby addressing one of the primary shortcomings of harmonic-based approaches. This study confirms the feasibility of using RMS as a robust and interpretable feature for baseline-free online crack detec tion. The observed two-stage evolution and the consistency of detection across varying test conditions provide a solid foundation for the practical implementation of structural health monitoring (SHM) systems in engineering applications. © 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of Professor Ferri Aliabadi. Keywords: Baseline free; In-service crack detection; Harmonic parameter; Root mean square (RMS); Dynamic Piecewise Linear (DPL); Structural health monitoring (SHM) Abstract Fatigue crack initiation and propagation pose critical challenges to structural integrity assessment, particularly in safety-critical applications where reliable in-service monitoring is essential. Previous studies have demonstrated the feasibility of baseline-free crack detection using higher-order harmonic parameters, specifically the second harmonic parameter ( β ′ ) and the third harmonic parameter ( γ ′ ). While these parameters showed the potential for online in-service crack detection, their fluctuations and the dependence of the first stage on sensor bonding conditions, thereby limiting ro bustness and interpretability. To address these limitations, the present study introduces an alternative feature based on the root mean square (RMS) value of time-domain signals for baseline-free in-service crack monitoring. owing to its direct reflection of the signal content, the RMS features demonstrates greater stability and reliability compared with harmonic based parameters. The Dynamic Piecewise Linear (DPL) method was employed to analyze RMS data obtained from fatigue experiments conducted on multiple specimens. Results reveal that the RMS change can be clearly divided into two stages, with the critical transition point closely coinciding with the experimentally observed crack initiation. Further more, the proposed approach successfully identified cracks smaller than 2 mm, yielding consistent detection outcomes across di ff erent specimens and sensor configurations. Most importantly, the RMS-based method exhibited insensitivity to sensor bonding conditions, thereby addressing one of the primary shortcomings of harmonic-based approaches. This study confirms the feasibility of using RMS as a robust and interpretable feature for baseline-free online crack detec tion. The observed two-stage evolution and the consistency of detection across varying test conditions provide a solid foundation for the practical implementation of structural health monitoring (SHM) systems in engineering applications. 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of Professor Ferri Aliabadi. Keywords: Baseline free; In-service crack detection; Harmonic parameter; Root mean square (RMS); Dynamic Piecewise Linear (DPL); Structural health monitoring (SHM) Fracture, Damage and Structural Health Monitoring A baseline-free method for in-service crack detection under complex loading conditions YuhangPan a, ∗ , Zahra Sharif Khodaei 1 , Ferri M.H. Aliabadi a a Department of Aeronautics, Imperial College London, South Kensington Campus, City and Guilds Building, Exhibition Road, SW7 2AZ, London, UK Fracture, Damage and Structural Health Monitoring a, ∗ , Zahra Sharif Khodaei 1 , Ferri M.H. Aliabadi a a Department of Aeronautics, Imperial College London, South Kensington Campus, City and Guilds Building, Exhibition Road, SW7 2AZ, London, UK

∗ Corresponding author. Tel.: + 44 (0) 771-392-0325. E-mail address: y.pan21@imperial.ac.uk ∗ Corresponding author. Tel.: + 44 (0) 771-392-0325. E-mail address: y.pan21@imperial.ac.uk

2452-3216 © 2025 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Ferri Aliabadi 10.1016/j.prostr.2026.02.005 2210-7843 © 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of Professor Ferri Aliabadi. 2210-7843 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of Professor Ferri Aliabadi.

Yuhang Pan et al. / Procedia Structural Integrity 80 (2026) 43–52

44

2

YuhangPan / Structural Integrity Procedia 00 (2023) 000–000

1. Introduction

Fatigue crack initiation and propagation remain critical challenges in structural engineering due to their potential to cause unexpected failures with severe safety and economic consequences (Zhou et al. (2025); Xu et al. (2024)). Their progressive nature, often invisible in the early stages, makes conventional inspection based approaches insu ffi cient for ensuring structural integrity (Zhou et al. (2022, 2025)). Traditional non destructive testing (NDT) techniques, such as ultrasonic testing or radiography (Golodov and Maltseva (2022)), are typically conducted periodically, which leaves structures vulnerable to undetected crack growth between inspections. These limitations have motivated the advancement of structural health monitoring (SHM) systems that enable continuous and real-time assessment, thereby reducing the risk of catastrophic failure while improving maintenance e ffi ciency and lowering operational costs (Marques et al. (2021); Chen et al. (2019)). SHM methods can generally be categorized by sensor type and underlying physical principle (Pan et al. (2024)). Acoustic emission (AE)-based techniques capture transient elastic waves produced during crack initiation and propagation, with features such as event counts, energy, and frequency content serving as in dicators of fatigue crack growth (FCG) (Karimian et al. (2020); Chai et al. (2022)). Despite their passive nature and high sensitivity, AE methods are often limited by signal stochasticity and susceptibility to envi ronmental noise. Another widely used approach is based on Lamb wave, where surface-bonded piezoelectric transducers (PZTs) are used to both excite and receive ultrasonic waves. Due to their capability for long range propagation and high sensitivity to small-scale defects, Lamb wave techniques have been extensively applied in aerospace structures. Linear Lamb wave methods typically extract features such as time-of-arrival, attenuation, and reflection characteristics (Wu et al. (2009); Ostachowicz et al. (2009)). In contrast, nonlinear methods exploit harmonic generation or subharmonic responses induced by crack-tip nonlinearity, thereby o ff ering enhanced sensitivity to early-stage damage and, in many cases, enabling baseline-free detection (Sampath and Sohn (2022)). Despite these advantages, several critical challenges remain unresolved. A sig nificant limitation of many SHM methods still requires interruptions to normal operation to acquire data, which limits their applicability for true monitoring in service (Zhao et al. (2023)). AE-based methods are attractive for passive monitoring but are limited by variability and noise contamination. Linear Lamb wave approaches are heavily baseline-dependent, making them vulnerable to environmental and operational vari ability, particularly temperature fluctuations (Pan et al. (2024)). Nonlinear methods alleviate the reliance on baseline data but typically demand stringent excitation conditions, which restrict their practicality in field applications (Pan et al. (2025)). To address these limitations, this study proposes an in-service, baseline-free method for fatigue crack detection by analyzing structural responses under operational loading, aiming to achieve reliable monitoring without the constraints of conventional approaches. The remainder of this paper is structured as follows: Section 2 presents the experimental setup, including the fatigue testing procedure and data acquisition system. Section 3 details the proposed baseline-free monitoring methodology. Section 4 presents the results together with an analysis of the associated uncertainties. Section 5 summarises the main conclusions and outlines future research directions.

Yuhang Pan et al. / Procedia Structural Integrity 80 (2026) 43–52

45

YuhangPan / Structural Integrity Procedia 00 (2023) 000–000

3

Nomenclature NDT

Non-destructive testing SHM Structural health monitoring FCG Fatigue crack growth AE Acoustic emission PZTs Piezoelectric transducer f Loading frequency ∆ σ t Stress range FFT Fast Fourier Transform RMS Root mean square β ′ Second harmonic parameter γ ′ Third harmonic parameter DPL Dynamic Piecewise Linear

2. The fatigue testing procedure

A 250 kN Instron hydraulic fatigue testing machine (Fig. 1a) was employed to apply cyclic loading to the specimens. For specimens T1–T3, the maximum and minimum applied stresses were 90 MPa (corre sponding to 62% of the material yield strength) and 9 MPa, respectively, yielding a stress ratio ( R ) of 0.1. Owing to stress concentration around the central hole, fatigue cracks initiated and propagated symmetrically from both sides. The initiation of the crack and subsequent propagation were continuously performed using a Canon EOS 5D Mark II camera equipped with a 21-megapixel full-frame CMOS sensor. Crack lengths were measured using a measurement tape attached directly to the specimen surface, as shown in Fig.1d, and Fig. 1e highlights three representative stages of fatigue damage progression: (I) no visible crack, (II) a crack length of 5.8 mm, and (III) final fracture. Two P-876 DuraAct PZT sensors were mounted on each specimen using thermoplastic adhesive film (Yue et al. (2021)). Their exact positions and geometries, referenced to the lower-left corner of the specimen as the origin, are showed in Fig.1b. Sensors P1 and P2 were placed symmetrically with respect to the central hole and vertically aligned, thus targeting the region most suscep tible to initiation and propogation of fatigue cracks. Following the findings of Pittarresi et al.(Pitarresi et al. (2019)), which demonstrated that loading frequencies above 5 Hz result in a quasi-steady material response, a loading frequency ( f ) of 6 Hz was adopted in this study. The dynamic responses under fatigue loading were acquired using a TiePie Handyscope HS5 oscilloscope and subsequently stored with Multi-Channel Oscilloscope software, as shown in Fig.1c. The proposed method for crack monitoring is summarized in Fig. 2. As illustrated in Fig. 2, the proposed crack monitoring approach integrates experimental loading, signal acquisition, and feature extraction. First, cyclic loading is applied to the specimen using a servo-hydraulic fatigue testing machine, while responses are continuously acquired by surface-bonded PZT sensors. Subsequently, the frequency domain is obtained using FFT, enabling the identification of the fundamental, second, and third harmonic frequency components. Three features are calculated: the RMS of the signal in the time domain, the second harmonic parameter β ′ , and the third harmonic parameter γ ′ , which are used to monitor the crack. Finally, these parameters are tracked over the entire fatigue process and correlated with periodic visual crack length measurements. 3. Method

4. Results and discussion

This section presents the feature extraction process, the crack growth and detection results obtained using the di ff erent features and specimens.

Yuhang Pan et al. / Procedia Structural Integrity 80 (2026) 43–52

46

4

YuhangPan / Structural Integrity Procedia 00 (2023) 000–000

Fig. 1: The experimental platform for online fatigue crack monitoring: (a) experimental fatigue setup; (b) specimen geometry and sensor layout; (c) data acquisition hardware; (d) photograph captured with a Canon 5D camera; (e) di ff erent stages of the fatigue test—Stage I: no crack; Stage II: 5.8 mm crack; Stage III: failure.

Fig. 2: The framework of the proposed method in this work.

4.1. Feature extraction

The signal obtained from fatigue loading is analyzed in both the time domain and the frequency domain. A comparative study was performed on pristine and fatigue-cracked specimens to investigate the changes in the time and frequency domains of the responses before and after cracking. The results are summarized in Fig. 3. Fig. 3 presents the variations in the time-domain and frequency-domain responses before and after fatigue crack initiation. As shown in Fig. 3(a), the 1 s time-domain signals reveal an overall reduction in response amplitude following crack initiation. Consistent with the feature selection strategy illustrated in Fig. 2, the RMS value was employed to quantify changes in the time-domain response. The RMS decreased from 7.29 (without crack) to 6.75 (with crack), corresponding to a reduction of approximately 7.4%. In the frequency domain (Fig. 3(b)), the amplitude of the fundamental frequency exhibited a reduction of 7.41% after crack initiation, while the second harmonic amplitude decreased by 26.9%. In contrast, the third harmonic am plitude increased by 8.34%. These observations indicate that fatigue crack not only attenuates the primary response but also induces distinct nonlinear spectral changes, particularly a pronounced reduction in the second harmonic component and an increase in the third harmonic component.

Yuhang Pan et al. / Procedia Structural Integrity 80 (2026) 43–52

47

YuhangPan / Structural Integrity Procedia 00 (2023) 000–000

5

(a) (b) Fig. 3: Response of time and frequency domain obtained from the intact specimen (1000 cycles, blue solid line) and specimen with a 11.8 mm fatigue crack (134,000 cycles, red dash line): (a) time-domain signals and (b) frequency-domain spectra

4.2. Crack growth result

Fig.4 illustrates the crack growth behavior of specimens T1–T3, where cracks initiated from the edges of the central hole and were monitored using the camera system. The first detectable crack in specimen T1 was observed at approximately 90,000 cycles with a crack length of 0.5 mm, whereas in specimen T2, a detectable crack appeared at around 86,000 cycles with a crack length of 0.7 mm (Fig.4a). Specimen T3 exhibited the latest crack initiation, with detection occurring at approximately 110,000 cycles and a corresponding crack length of 0.4 mm. The variability observed across specimens is attributed primarily to di ff erences in the machining quality of the central hole. As shown in Fig.4b, although all specimens were manufactured from the same aluminum sheet, minor variations in geometric dimensions, thickness, and mass, together with subtle di ff erences in edge finishing, contributed to discrepancies in crack initiation and propagation behaviour.

(a)

(b)

Fig. 4: (a) Crack growth result on coupons T1-T3 and (b) The variability of length, width, thickness and mass of coupons T1-T3

4.3. Crack detection result

Our previous studies Pan et al. (2024, 2025) have systematically demonstrated the e ff ectiveness of higher order harmonic features for fatigue crack monitoring. In particular, the second harmonic parameter ( β ′ ) and the third harmonic parameter ( γ ′ ) were shown to enable online, baseline-free crack detection and crack

Yuhang Pan et al. / Procedia Structural Integrity 80 (2026) 43–52 YuhangPan / Structural Integrity Procedia 00 (2023) 000–000

48

6

length prediction. Among them, γ ′ exhibits distinct advantages over β ′ : in addition to achieving baseline free monitoring, it facilitates fully automated in-service crack detection, thereby enhancing the robustness and practical applicability of the method in real-world engineering contexts. Building upon these findings, the present work applies the Dynamic Piecewise Linear (DPL) method, originally introduced in Pan et al. (2025), to the experimental data obtained in this paper. The DPL method dynamically performs piecewise linear fitting of harmonic parameters, enabling e ff ective segmentation and feature extraction across di ff erent stages of crack growth. Importantly, this analysis is conducted without reliance on prior baseline information. The results obtained from the DPL method on specimen T1 are presented in Fig. 5.

Fig. 5: Results of crack detection based on γ ′ : (a) The change of the γ ′ with respect to the fatigue loading cycles on T1, (b) The running details of dynamic fitted lines between second and third stage, (c) The di ff erent fatigue stages divided by the DPL method, and the crack size detected by the method. Fig. 5 presents the results obtained using the proposed DPL method. As shown in Fig. 5(a), the change of γ ′ during the fatigue process can be divided into three distinct stages. In the initial stage, γ ′ exhibits a sharp increase as the number of fatigue cycles increases. This is followed by a decreasing trend, reaching its minimum around 12,000 cycles. In the subsequent stage, γ ′ gradually rises again and stabilizes within the range of approximately 1 . 6 × 10 − 3 to 1 . 7 × 10 − 3 . Once γ ′ exceeds 1.7, its value starts to increase rapidly, marking the onset of the final stage. Notably, this rapid growth phase is well aligned with the trend of mea surable crack propagation, as shown by the crack length curve. This correlation suggests that the transition point between the second and third stages represents a critical indicator for crack detection. To further quan tify this behaviour, the DPL method was applied to fit the data, as illustrated in Fig. 5(b). During the early stage of fatigue loading, the slope of the fitted segments obtained from di ff erent moving windows remains relatively high. As the loading progresses, the slope gradually decreases, and distinct ”spikes” appear at the transition points due to the reduced degree of overlap between fittings. The final classification results derived from the DPL method are presented in Fig. 5(c). Three fatigue stages are clearly identified, and the method

Yuhang Pan et al. / Procedia Structural Integrity 80 (2026) 43–52 YuhangPan / Structural Integrity Procedia 00 (2023) 000–000

49

7

successfully detects the occurrence of a 0.7 mm crack at approximately 92,000 cycles. This demonstrates that the proposed DPL-based approach not only enables accurate stage segmentation but also provides a reliable way for early crack detection. Such results further validate the e ff ectiveness and robustness of the method in identifying critical transitions in the fatigue process, which are essential for structural integrity monitoring. Although our previous studies have demonstrated that the third harmonic parameter γ ′ can achieve in service baseline-free crack detection, some limitations remain to be addressed. In particular, the critical point between the second and third stages is located very close to the actual crack initiation point, which pro vides valuable reference for identifying crack onset and for early prognosis. However, the transition between the first and second stages exhibits more uncertainty. For example, in specimen T1 this transition occurred around the 12,000 cycles, the underlying mechanism of which is not yet fully understood. Based on exten sive experimental observations, this critical point appears to correspond not to crack initiation, but rather to the transition of the bonding condition—from the initial adjustment at the start of the fatigue test to a more stable state during cyclic loading. This interpretation is also supported by previous studies that reported similar observations in related fatigue experiments (Wang et al. (2023); Yue et al. (2018)). In addition, the inherent fluctuations of γ ′ may a ff ect the stability and robustness of the monitoring process, especially in practical applications where signal variability is inevitable. Therefore, it is necessary to further investigate alternative or complementary features that exhibit improved stability in order to achieve more reliable and robust crack monitoring under varying operational and environmental conditions. To address these limita tions, the RMS value of the time-domain signals was extracted as an alternative feature. The RMS parameter, which inherently reflects the energy content of the measured signal, is expected to provide a more stable and robust indicator of structural changes compared with the higher-order harmonic parameters. To evaluate its e ff ectiveness, the same DPL method was applied to the RMS data, and the results are summarised in Fig. 6. Fig. 6(a) illustrates the change of the RMS values throughout the fatigue experiment for specimen T1. Compared with the third harmonic parameter γ ′ , the RMS demonstrates a markedly more stable trend. While γ ′ typically exhibits three stages, the RMS response can be broadly divided into two stages: an initial plateau at approximately 6, followed by a sharp decrease after about 90,000 cycles. Notably, this transition point closely coincides with the experimentally observed onset of crack initiation. The application of the DPL method to the RMS data is presented in Fig.6(b). In the vicinity of the stage transition, the fitting procedure produces multiple “spikes,” indicating the sensitivity of the method to abrupt changes in the signal. These spikes form the basis for defining a threshold, as shown in Fig.6(c), which enables automated identification of the critical transition point. The resulting two-stage segmentation obtained from the threshold-based DPL analysis is summarized in Fig. 6(d). The critical point was identified at approximately 92,000 cycles, corre sponding to a detectable crack length of 0.7 mm.This result is in full agreement with the detection outcome obtained using γ ′ , thereby validating the feasibility of RMS as an alternative feature for online crack de tection. Furthermore, the clear two-stage behavior of RMS o ff ers a more straightforward and interpretable characterization of fatigue crack initiation and propagation. The results obtained from another two specimens, T2 and T3 are summarized in Fig. 7. Fig. 7(a) presents the crack monitoring results for specimen T2. Similar to specimen T1, the fatigue process of T2 can be clearly divided into two stages based on the RMS evolution. By applying the proposed DPL method, the critical point was identified at approximately 95,000 cycles, corresponding to a detectable crack length of 1.4 mm. For specimen T3, as shown in Fig. 7(b), a comparable two-stage behavior is observed. The transition point was detected at around 115,000 cycles, corresponding to a crack length of 1.0 mm. This result further demonstrates the robustness of the RMS-based DPL approach, as it consistently identifies crack initiation points across di ff erent specimens with varying fatigue lives. Moreover, the close agreement between the detected crack sizes with physically measurable crack lengths provides strong evidence of the method’s feasibility for practical online crack detection applications.

4.4. The e ff ect of the sensor position

As illustrated in Fig.2(b), two PZT sensors were employed in the present experimental setup. The results presented in the previous sections were primarily obtained from Sensor 1, which consistently exhibited reli able crack detection performance and strong agreement with the observed crack growth. To further evaluate the potential influence of sensor location on the proposed approach, additional analysis was performed using

Yuhang Pan et al. / Procedia Structural Integrity 80 (2026) 43–52

50

8

YuhangPan / Structural Integrity Procedia 00 (2023) 000–000

Fig. 6: Crack detection results for specimen T6 under a stress range of 9-90 MPa and a loading frequency of 6 Hz: (a) Variation of the RMS values with respect to the number of fatigue loading cycles; (b) Running details of the DPL method; (c) Slope values calculated using the DPL method, with the threshold set to 1 . 0 × 10 − 3 ; (d) The di ff erent fatigue stages divided by the DPL method, and the crack length detected by the method. The detectable crack length is 0.7 mm, and the corresponding number of cycles is 92 k.

Fig. 7: Crack detection results for (a) specimen T2 and (b) specimen T3 under a stress range of 1.8-18KN and a loading frequency of 6 Hz.

the data acquired from Sensor 2. The results obtained by applying the DPL method to Sensor 2 are presented inFig. 8.

Yuhang Pan et al. / Procedia Structural Integrity 80 (2026) 43–52

51

YuhangPan / Structural Integrity Procedia 00 (2023) 000–000

9

Fig. 8: The framework of the proposed method in this work.

As shown in Fig.8, the results obtained from Sensor 2 for specimen T1 display slight di ff erences in ampli tude compared with those from Sensor 1. However, the overall trend of the RMS change remains consistent between the two sensors. More importantly, application of the proposed DPL method to the Sensor 2 data identified the same critical point, corresponding to a crack length of 0.7 mm at approximately 92,000 cycles. This result is in agreement with the detection obtained from Sensor 1, thereby confirming the consistency of the proposed approach across di ff erent sensor locations and further demonstrating its robustness for practical applications. This study systematically investigated baseline-free online crack detection, extending our previous work on the second and third harmonic parameters. Although both parameters demonstrated the capability for baseline-free crack detection, their e ff ectiveness was constrained by the strong dependence of the initial stage on sensor bonding conditions, which undermines the overall stability of the method. To overcome these limitations, this work introduced the root mean square (RMS) value of time-domain signals as a more stable and interpretable feature for online fatigue crack monitoring. Experimental results showed that the proposed RMS-based approach not only enables baseline-free detection of cracks smaller than 2 mm, but also maintains excellent stability throughout the entire fatigue process. In contrast to higher-order harmonic parameters, the RMS feature exhibits minimal sensitivity to bonding conditions, thereby ensuring more consistent and reliable detection performance. These findings establish a solid foundation for the development of a robust and practically applicable methodology for fatigue crack monitoring. Future work will focus on enhancing the generality and applicability of the proposed method by incorpo rating additional influencing factors. Specifically, the performance of the approach will be investigated under variable loading conditions, including changes in loading amplitude and loading ratio, and its sensitivity to di ff erent sensor placements beyond the centerline configuration will be evaluated. Furthermore, the e ff ect of environmental conditions, particularly temperature variations, will be systematically evaluated. Finally, vali dation on more complex structural configurations will be undertaken to explore the scalability of the method and its potential for real-world engineering applications. Conclusion

5. Acknowledgments

This work was supported by UKRI under the UK Government’s Horizon Europe Guarantee (grant agree ment No 101096073, AVATAR project.

Yuhang Pan et al. / Procedia Structural Integrity 80 (2026) 43–52 YuhangPan / Structural Integrity Procedia 00 (2023) 000–000

52

10

References

Yue, N., Khodaei, Z.S., Aliabadi, M.H., 2021. Damage detection in large composite sti ff ened panels based on a novel SHM building block philosophy. Smart Mater. Struct. 30, 045004. Pitarresi, G., Ricotta, M., Meneghetti, G., 2019. Investigation of the crack tip stress field in a stainless steel SENT specimen by means of thermoelastic stress analysis. Procedia Struct. Integr. 18, 330–346. Xu, J., Zhou, X., Giglio, M., Sbarufatti, C., Dong, L., 2024. Variational neural network embedded with digital twins for probabilistic structural damage quantification. AIAA J. 0, 1–13. Vanniamparambil, P.A., Bartoli, I., Hazeli, K., Cuadra, J., Schwartz, E., Saralaya, R., Kontsos, A., 2012. An integrated structural health monitoring approach for crack growth monitoring. J. Intell. Mater. Syst. Struct. 23, 1563–1573. Pan, H., Azimi, M., Yan, F., Lin, Z., 2018. Time-frequency-based data-driven structural diagnosis and damage detection for cable-stayed bridges. Int. J. Bridge Eng. 23, 04018033. Golodov, V.A., Maltseva, A.A., 2022. Approach to weld segmentation and defect classification in radiographic images of pipe welds. NDT & E Int. 127, 102597. Marques, D.E.T., Vandepitte, D., Tita, V., 2021. Damage detection and fatigue life estimation under random loads: A new structural health monitoring methodology in the frequency domain. Fatigue Fract. Eng. Mater. Struct. 44, 1622–1636. Chen, J., Yuan, S., Jin, X., 2019. On-line prognosis of fatigue cracking via a regularized particle filter and guided wave monitoring. Mech. Syst. Signal Process. 131, 1–17. Karimian, S.F., Modarres, M., Bruck, H.A., 2020. A new method for detecting fatigue crack initiation in aluminum alloy using acoustic emission waveform information entropy. Eng. Fract. Mech. 223, 106771. Chai, M., Hou, X., Zhang, Z., Duan, Q., 2022. Identification and prediction of fatigue crack growth under di ff erent stress ratios using acoustic emission data. Int. J. Fatigue 160, 106860. Wu, Z., Qing, X.P., Chang, F.K., 2009. Damage detection for composite laminate plates with a distributed hybrid PZT / FBG sensor network. J. Intell. Mater. Syst. Struct. 20, 1069–1077. Ostachowicz, W., Kudela, P., Malinowski, P., Wandowski, T., 2009. Damage localisation in plate-like structures based on PZT sensors. Mech. Syst. Signal Process. 23, 1805–1829. Sampath, S., Sohn, H., 2022. Detection and localization of fatigue crack using nonlinear ultrasonic three-wave mixing technique. Int. J. Fatigue 155, 106582. Zhao, F., Zhou, X., Wang, C., Dong, L., Atluri, S.N., 2023. Setting adaptive inspection intervals in helicopter components, based on a digital twin. AIAA J. 61, 2675–2688. Pan, Y., Khodaei, Z.S., Aliabadi, M.H.F., 2024. A robust hybrid method for damage detection under varying environmental conditions. Struct. Health Monit. 1–16. Pan, Y., Khodaei, Z.S., Aliabadi, M.H.F., 2025. In-service fatigue crack monitoring through baseline-free automated detection and physics-informed neural network quantification. NDT & E Int. 153, 103360. Paris, P.C., Erdogan, F., 1963. A critical analysis of crack propagation laws. J. Basic Eng. 85, 528–533. Chen, J., Yuan, S., Sbarufatti, C., Jin, X., 2021. Dual crack growth prognosis by using a mixture proposal particle filter and on-line crack monitoring. Reliab. Eng. Syst. Saf. 215, 107758. Wang, S., Tang, S., He, C., Wang, Q., 2023. Cyclic deformation and fatigue failure mechanisms of thermoplastic polyurethane in high cycle fatigue. Polymers 15, 899. https: // doi.org / 10.3390 / polym15040899. Yue, N., Khodaei, Z.S., Aliabadi, M.H., 2018. An innovative secondary bonding of sensors to composite structures for SHM application. Key Eng. Mater. 774, 516–522. https: // doi.org / 10.4028 / www.scientific.net / KEM.774.516. Zhou, X., Dong, L., Dziendzikowski, M., Dragan, K., Giglio, M., Sbarufatti, C., 2025. Real-time in-service load tracking toward airframe digital twins. AIAA J. 1–14. https: // doi.org / 10.2514 / 1.J0XXXXX Xu, J., Zhou, X., Giglio, M., Sbarufatti, C., Dong, L., 2024. Variational neural network embedded with digital twins for probabilistic structural damage quantification. AIAA J. 0, 1–13. https: // doi.org / 10.2514 / 1.J064808 Zhao, F., Zhou, X., Wang, C., Dong, L., Atluri, S.N., 2023. Setting adaptive inspection intervals in helicopter components, based on a digital twin. AIAA J. 61, 2675–2688. https: // doi.org / 10.2514 / 1.J062222 Zhou, X., He, S., Dong, L., Atluri, S.N., 2022. Real-time prediction of probabilistic crack growth with a helicopter component digital twin. AIAA J. 60, 2555–2567. https: // doi.org / 10.2514 / 1.J060890

Available online at www.sciencedirect.com Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2022) 000–000 Available online at www.sciencedirect.com Structural Integrity Procedia 00 (2022) 000–000

www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia

ScienceDirect

Procedia Structural Integrity 80 (2026) 136–145

Fracture, Damage and Structural Health Monitoring A digital twin to optimize monitoring and maintenance of pressure vessels

M. Bennebach a , I. Khaled a , JL. Iwaniack a, * a Centre technique des Industries Mécaniques, Senlis 60304, France a a a, a Centre technique des Industries Mécaniques, Senlis 60304, France

© 2025 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Ferri Aliabadi When used online, the developed digital twin can estimate the progressive fatigue damage of the equipment. It can regularly monitor the evolution of loading in real-time and update itself with data from the physical model in service. Additionally, it can monitor hardly accessible critical areas, facilitating decisions making about future inspections. If used offline, it allows simulating different loading scenarios and evaluating their impact on the equipment’s life. © 2023 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Professor Ferri Aliabadi Keywords: Digital twin, pressure vessel, fatigue, monitoring, predictive maintenance Abstract A digital twin is a virtual clone of a physical system or a process. It systematically implies the existence of a "digital model" coupled with the object it copies. Depending on the system concerned and the desired usage, it can be a geometric, multiphysical, functional, behavioral, and decision-making model. It can be used to improve the control, security and optimize production, ensuring digital continuity. Applied to pressure vessels, the digital twin appears as a reliable way to monitor operation, evaluate resistance and safety in real service conditions, and finally to capitalize on data to optimize the design of new products. This paper presents an application of the digital twin concept to optimize predictive maintenance of an industrial polymerization reactor. The steps involved in this work are: - Design, manufacturing of the physical twin and optimized deployment of sensors for a smart, connected device, - Fatigue testing under representative loads, - Modeling of the reactor behavior and construction of the digital twin by hybridization of physical / data models. When used online, the developed digital twin can estimate the progressive fatigue damage of the equipment. It can regularly monitor the evolution of loading in real-time and update itself with data from the physical model in service. Additionally, it can monitor hardly accessible critical areas, facilitating decisions making about future inspections. If used offline, it allows simulating different loading scenarios and evaluating their impact on the equipment’s life. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Professor Ferri Aliabadi Keywords: Digital twin, pressure vessel, fatigue, monitoring, predictive maintenance Abstract A digital twin is a virtual clone of a physical system or a process. It systematically implies the existence of a "digital model" coupled with the object it copies. Depending on the system concerned and the desired usage, it can be a geometric, multiphysical, functional, behavioral, and decision-making model. It can be used to improve the control, security and optimize production, ensuring digital continuity. Applied to pressure vessels, the digital twin appears as a reliable way to monitor operation, evaluate resistance and safety in real service conditions, and finally to capitalize on data to optimize the design of new products. This paper presents an application of the digital twin concept to optimize predictive maintenance of an industrial polymerization reactor. The steps involved in this work are: - Design, manufacturing of the physical twin and optimized deployment of sensors for a smart, connected device, - Fatigue testing under representative loads, - Modeling of the reactor behavior and construction of the digital twin by hybridization of physical / data models.

* Corresponding author. Tel.: +33 637454934. E-mail address: mohamed.bennebach@cetim.fr * Corresponding author. Tel.: +33 637454934. E-mail address: mohamed.bennebach@cetim.fr

2452-3216 © 2023 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Professor Ferri Aliabadi 2452-3216 © 2023 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Professor Ferri Aliabadi

2452-3216 © 2025 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Ferri Aliabadi 10.1016/j.prostr.2026.02.013

M. Bennebach et al. / Procedia Structural Integrity 80 (2026) 136–145 Author name / Structural Integrity Procedia 00 (2019) 000–000

137

2

1. Introduction Pressure vessels are used in many industrial sectors such as petrochemical, power generation, chemical and pharmaceutical industries. These types of equipment are subjected to harsh operating conditions, which can lead to progressive degradation of their structural integrity, resulting in risks to the safety of people, property and environment. Design, manufacture and operation of pressure vessels are strictly regulated by laws and building codes, making it difficult to replace traditional maintenance strategies with innovative ones. Developing real-time monitoring techniques of industrial equipment is increasingly necessary to avoid unplanned production downtime and reduce maintenance costs. In this context, digital twins are emerging as an effective solution, however, despite their potential, their implementation remains a challenge and requires consideration of several factors such as service loads, material properties, equipment geometry and environmental conditions, which makes modelling complex. In this paper, we present a digital twin-based methodology for real-time residual life and damage monitoring, combining models based on physics and data science. During the last few years, the use of digital twins has grown rapidly due to evolutions in IOT (Internet of Things), HPC (High Performance Computing) and modelling techniques such as ROMs (Reduced Order Models). Several studies have been conducted for pressure vessels, which have shown the potential benefits of digital twins for equipment monitoring and maintenance, however, these approaches suffer from limitations, such as lack of accuracy in damage prediction, and inefficient use of sensors in terms of cost and resources. In addition, the fatigue criteria and approaches used in construction codes like ASME, IIW or CODAP are not directly adapted to in-service equipment monitoring, which can cause difficulties. The proposed approach, schematized in Figure 1, aims to overcome some of these limitations. It proposes an innovative approach using hybridization of finite element and data science techniques, to predict the damage rate and residual life of the equipment in real time, based on minimal information from strain gauges. To improve monitoring efficiency, use of principal component analysis is combined with sensor placement optimization. This approach maximizes the coverage of the strain field with a minimal number of sensors, which reduces the cost and time required for sensor installation and maintenance. Figure describes the global approach.

Fig. 1. Global approach description.

2. Construction of the virtual clone The objective of this phase is to develop a high-fidelity numerical model of the equipment, which allows identification of the critical zones in terms of stress levels, potential defects occurrence and estimate the fatigue damage. The model has been calibrated from experimental test data to ensure that simulation results agree with experimental measurements. By identifying critical areas before instrumentation, the modelling will also allow for sensor placement optimization.

M. Bennebach et al. / Procedia Structural Integrity 80 (2026) 136–145 Author name / Structural Integrity Procedia 00 (2019) 000–000

138

3

A physical demonstrator has been designed and manufactured, in a reduced scale, representative of a chemical polymerization reactor. The demonstrator shown in Figure 2 is 1.7 m high and 1.1 m in diameter. It is made of P265GH steel whose mechanical properties are detailed in EN10028 (2009). A synthesis of main characteristics is given table 1.

Table 1: main mechanical characteristics of P265GH Material

P265GH

Young’s modulus Yield strength

201000 MPa

265 MPa 460 MPa

Ultimate tensile strength

Fig. 2. (a) CAD model of the equipment, (b) nomenclature of the pressure vessel parts

A finite element model of the equipment, subjected to different service loadings was done in commercial software Abaqus. Special attention was dedicated to welded zones between the lower coil and the shell, representing critical areas as pointed out by the FE model and from service experience. The pressure vessel is modelled using shell elements (S4R type) and the welds are modelled according to the IIW recommendations for the hot spot stress approach. In general, to limit modelling and computational efforts, simple models and relatively coarse meshes are preconized. Models with either thin plate or shell elements or with solid elements may be used. When using plate or shell elements, these are arranged in the midplane of the plates. In simplified models, the welds may be omitted except for cases where the results are affected by local bending, due for example to plate offsets or to interaction between welds close to each other. In such cases, the welds may be modelled by vertical or inclined plate elements having appropriate stiffness or by introducing constraint equations or rigid links to couple node displacements. For complex cases, solid elements may be used, allowing the weld to be modelled with prismatic elements. If isoparametric 20 nodes elements are used, one element is sufficient in thickness direction due to the quadratic displacement function and linear stress distribution. By reduced integration, the linear part of the stresses can be directly evaluated at the surface and extrapolated to the weld toe. It should be noted that when the weld is not modelled, extrapolation must be done to the intersection point. Figure 3 illustrates typical finite element models and extrapolation paths.

M. Bennebach et al. / Procedia Structural Integrity 80 (2026) 136–145 Author name / Structural Integrity Procedia 00 (2019) 000–000

139

4

Fig. 3. Example modelling according to IIW recommendations

The IIW gives also recommendations on mesh size and extrapolations points for the hot spot stress, as illustrated in figure 4.

Fig. 4. Recommendations on meshing and extrapolation according to IIW

Following these recommendations, an FE model of 795955 shell elements is constructed.

M. Bennebach et al. / Procedia Structural Integrity 80 (2026) 136–145 Author name / Structural Integrity Procedia 00 (2019) 000–000

140

5

The applied loading, corresponding to the laboratory pressure cycling test is 5.3 bar in the shell and 3.8 bar in the coil. Figure 5 illustrates the resultant stress distribution and critical location.

Fig. 5. Stress field distribution from FE calculations

This finite element model will be the main source of further numerical data generation for fatigue life evaluation and intelligent sensor placement. To comply with a digital twin strategy, data from experimental campaign and in service conditions is continuously used to update the models.

3. Experimental campaign This part concerns the physical twin. The objective of the experimental phase is to target the gauges placement zones, confirm the reliability of the numerical model developed for the fatigue analysis and provide data exchange with the digital twin. Thanks to previous FE simulations, return on in service experience and pressure vessels experts feedback, an instrumentation and inspection strategy was developed. This guides us towards monitoring critical areas, with highest probability of failure, corresponding to welded zones in the bottom part of the equipment. To inspect critical areas, the multi-encoded ultrasonic inspection method according to NF EN ISO 9712 (2022), NF EN ISO 13588 (2019), and NF EN ISO 19285 (207) is involved. This method is based on the use of incidence angles of the ultrasonic waves emitted from a 5L16 type probe, to cover different inspection areas. It allows the detection of defects such as cracks, porosities, and inclusions in the welded areas. Five critical welds were selected for monitoring: the longitudinal weld of the shell, the circumferential weld that joins the shell and the half-sphere, the two corner welds that join the two coils to the vessel, and the weld that joins the half sphere to the nozzle (see Figure 6). The inspection of the welds with ultrasound revelated several defects (red circles in Figure 6). These defects were used as reference points for instrumentation. A total of eight strategic locations were identified, each located near a defect detected during the inspection of the five welds. In addition, two other locations were chosen outside of these welds for model calibration purposes.

M. Bennebach et al. / Procedia Structural Integrity 80 (2026) 136–145 Author name / Structural Integrity Procedia 00 (2019) 000–000

141

6

Fig. 6. Identification and results of inspection areas

Several sets of strain gauges were placed in the selected locations, in accordance with the IIW recommendations with respect to hot spot stress derivation from measurements. Figure 7 shows examples of such strain gauges placement.

Fig. 7. Strain gauges placement

The instrumented equipment is then tested under cyclic pressure and monitored all along the tests. Figure 8 illustrates

M. Bennebach et al. / Procedia Structural Integrity 80 (2026) 136–145 Author name / Structural Integrity Procedia 00 (2019) 000–000

142

7

a portion of the pressure cycles applied.

Fig. 8. Sample pressure cycles applied.

4. Fatigue life calculations For fatigue life calculations, several approaches either derived from design standards or from state-of-the-art methods were investigated. The first methodology is based on CODAP, which provides specific fatigue criteria and is widely used in the French pressure vessels industry. This standard gives detailed guidelines for the design and verification of pressure equipment, considering the cyclic loading in service and appropriate safety factors. Application of this approach involves the use of analytical methods to estimate fatigue life; with results that are often highly conservative. The second methodology is based on several state-of-the-art criteria using advanced modeling and simulation techniques to predict fatigue life. This allows for more accurate analysis, considering the local stress/strain state and major influencing factors on durability. It also gives us the ability to run real time analysis from measured strain gauges data, facilitating then the hybridization between physics-based models and data driven ones. As critical areas are welded zones, the equivalent stress used in fatigue calculations is the hot spot stress derived from a quadratic extrapolation. The hot spot stress approach was initially used for welded tubular joints in the offshore sector and pressure vessels analysis since the 1960’s; then extended to the case of plated welded structures. In the IIW recommendations, the hot spot stress corresponds to the maximum principal stress in the base metal at the weld toe, considering the effects of stress concentration due to the overall geometry of the considered detail, but excluding the local stress concentration effects due to weld local geometry and discontinuities. It is applicable to fatigue failure at weld toes. Traditional approach to derive this stress is based on linear or quadratic extrapolation of strains or stresses from two or three reference points at certain distances from the weld toe. The non-linear notch stress effect, not included in the structural hot spot stress definition, is considered to vanish within a distance 0.3 to 0.4 times the plate thickness from the weld toe. That’s why IIW recommends making extrapolation from points which distance from the weld toe is over 0.4 times the plate thickness. The extrapolation procedure and hot spot calculation either from measurements or FE calculations are illustrated in figures 9 and 10.