The synthesized system is exposed to a set of structural, morphological, and optical investigations. The apparent crystallite size is less than 30 nm, reflecting the nanoscale of the structure, and thus validating the preparation route as evident on XRD pattern. SEM images show a fibrous structure where polyaniline dominates and covers most of the structure’s surface. The evident bands of the FTIR spectrum are designated to the component used in synthesis confirming the chemical structure of the fabricated system. The humidity sensing study of the synthesized structure is carried out through a wide range of relative humidity (RH) levels range of 11–97%. The response and recovery times of the fabricated structure are found to be around 120 and 220s, respectively.Humidity sensing has been offering a noticeable contribution in different industrial, medical, and agricultural activities. Here, graphene quantum dots doped with polyaniline (PANI) and MnO Optimizing the sensor performance concerning stability, detection range, sensitivity, rapid response, fast recovery elapsed durations, and cost-effectiveness is the major challenge facing the employment of humidity sensors and expanding their scope in these directions15. From this aspect, the selection of the materials and synthesis protocol involved in humidity sensors design is essential19. Numerous materials such as ceramics, metal oxide semiconductors, polymeric matrices, and carbonic substances were investigated for the use in humidity sensing devices22. The operation of nanocomposites as a humidity sensor is favorable due to their elevated surface-to-volume ratio and their capability to provide enhanced physicochemical specifications. Graphene quantum dots (GQDs), a member of the carbon nanomaterials family comprising graphene sheet layers with reduced lateral dimension have been incorporated in many composite materials. GQDs possess few desirable physicochemical properties such as noticeable bandgap  and quantum confinement, thus, supporting potential applications in energy, medical, and sensing fields25.The manipulation and monitoring of the environments surrounding humidity are demanded in various applications in recent years. Inherently, humidity sensors emerged and evolved in versatile areas such as the agricultural sector, food storage, medical devices, and others2 is a promising metal oxide owing to its chemical stability, specific capacitance, ease of acquisition, tailorable morphology, and reduced cost27. It was reported that the combination of MnO2 and graphene derivates hinders the stacking of the graphene layers due to the contribution of van der Waals forces. Moreover, MnO2 gains a better dispersion due to the presence of the graphene layers28.MnO30. PANI was previously reported as a promising candidate in sensing applications32, anti-corrosion coatings33 Photocatalysis35, optoelectronics37, and energy storage appliances42.Owing to its superior conductivity, thermal stability, and sensitivity to gases, polyaniline (PANI) became an ideal polymeric candidate43. Characteristically, the humidity sensing devices using metal oxide constrain a few undesirable specifications such as increased lag, lowered response, and prolonged recovery and response times45.A few disadvantages are limiting the wide-spread employment of PANI and opposing its functionality and application such as insolubility in some solvents and its limited mechanical stability48. The implementation of PANI and metal oxide promotes the adsorption locations accompanied by raised thermal stability and conductivity. Furthermore, the incorporation of PANI into graphene or graphene derivatives can enhance the overall conductivity, mechanical stability, functional groups, and more.Therefore, the combination of GQDs with other metal oxide materials to acquire a hybrid binary or ternary system facilitates novel tailored characteristics and expands the scope for enhanced functionality. Researchers devoted a desirable set of efforts and experimentation towards overcoming the aforementioned limitations of PANI through the implementation of organic–inorganic hybrid composites for the humidity sensing devices2 metal oxide to work as a humidity sensor was investigated in this work. To the authors’ best knowledge, this work is the first to report on this structure as a humidity sensor.Motivated by the aforementioned points, the ternary system composed of PANI as a polymeric matrix and GQDs with MnO49. In another report, authors synthesized silver nanoparticles doped with GQDs through the hydrothermal process. The report signifies the 1:1 ratio of Ag: GQDs to deliver an optimum response of 98% within a 25–95% humidity range at ambient temperature50. The following report revealed a humidity sensor formed by graphene quantum dots doped with chitosan and chemically synthesized was reported. The outcomes revealed a fast response and recovery times of 3 and 36 s, respectively, with a limited hysteresis of around 1.6%. The humidity sensing studies for PANI-containing composites was also reported51.Khouloud Jlassi et al., fabricated functionalized GQDs films from graphene waste using the spin coating method for humidity sensing applications. The synthesized films provided a low hysteresis (~ 2%) at a 30%RH level. Furthermore, the response and recovery times were found to be 15 s and 55 s, respectively1. Besides, PANI-titania nanotube-rGO was also investigated for humidity sensing within a wide humidity range of 7–97% RH. The system sensitivity of 3.28 MΩ/RH% and a rapid response of 13 s was observed18. Polyaniline-doped WO3 was prepared by in situ deposition technique as a single-step polymerization procedure. The results elucidated a linear behavior throughout a humidity range of 10 and 95% RH52. MnO2-CaO was also studied for humidity sensing and reporting an average sensitivity of ∼2.225 μW/% RH with a nominal response and recovery times of 47 and 59 s, respectively53.B. Chethan et al., synthesized a polyaniline-yttrium oxide composite prepared via the mechanical mixing method and studied the composite for humidity sensing applications. The structure delivered an optimum sensing response of 99% with a nominal response and recovery times of 3 and 4 s, respectively 2 composite was not studied. In this report, GQDs-PANI- MnO2 nanocomposite via a feasible two-pot process is successfully synthesized. The structural, optical, and morphological implication of the desired structure is explored. The humidity sensing performance is introduced through a wide span of humidity levels (11–97% RH). The proposed composite is promising for humidity sensing and related applications.Despite these efforts directed towards the humidity sensing area, and to the best of our knowledge, the introduction of a humidity sensor based on GQDs-PANI-MnO4), Ammonium persulfate ((NH4)2S2O8) (APS), Aniline (C6H5NH2), hydrochloric acid , Citric acid (99.5%), and sodium hydroxide (≥ 97%) were obtained from Fisher chemical. Toluene  was purchased from Thermo Scientific Chemicals. The above-mentioned chemicals and reagents were used as delivered without any added purification or treatments. The deionized Milli-Q water was used during this experiment.Potassium permanganate (KMnO54. Citric acid was used as a carbon source to create graphene quantum dots (GQDs). In brief, 5 g of citric acid was melted at 180 °C for 12 h, 1.5 M NaOH solution was added dropwise to the melted thick citric acid solution at ambient temperature, and then hydrothermal treated at 180°C for an additional 12 h. The resulting dark brown powder was removed from the liquor using dialysis filtration, washed, and dried overnight in a vacuum oven at 70 °C.GQDs were prepared as per the previous report2, 0.6 g of KMnO4 were added to 45 ml of DI water, next, 1.5 ml of sulphuric acid  was added under sustained magnetic stirring for an hour. To obtain the final powder, the solution was then transferred into an autoclave and kept at 120 ºC for 4 h. Afterward, the powder was purified and cleaned using water, and ethanol till acquiring the final dried MnO2.To acquire the desired MnO54.The ternary nanocomposite was prepared through two successive steps comprising the hydrothermal route and in-situ polymerization as represented in Fig. 12/GQDs nanocomposite was obtained via hydrothermal technique. 0.6 g of KMnO4 was dissolved in 45 ml of deionized Milli-Q water under continuous starring, subsequently, 1.5 ml of Conc. H2SO4 was added carefully to the dark purple solution. The solution was kept under constant stirring for an additional hour. The obtained precipitates from the solution, it was washed thoroughly and dried overnight. The PANI/MnO2/GQDs nanocomposite was executed through an in-situ polymerization reaction. Two separate solutions were prepared individually, then mixed. In the first beaker, 150 mg of MnO2/GQDs was dispersed in 45 ml of 1 M HCl aqueous solution using an ultrasonic bath for 30 min, then 1 ml of aniline was added into the suspension, it was cooled down to 5 °C and kept under constant stirring for additional 30 min. The second solution composed of 2.6 g of APS and 45 ml of 1 M HCl aqueous solution was dropped slowly to the first solution for 2 h, while the reaction temperature was kept at 5 °C. The resultant dark green precipitates were recovered, washed many times, and dried overnight. The obtained material was investigated by different characterization techniques.The MnO−6 Torr then Ar (99.99%) gas for backfilling till reaching a pressure of 6 × 10−3 Torr as a base pressure where Ar gas flow was 20 standards cubic centimeters per minute (sccm). DC head was used to sputter a thin Cr layer of 8 nm thickness at 250° C as a wetting layer, after that, RF head was used to deposit 90 nm of Au layer at room temperature. Interdigitated electrode (IDE) patterns were fabricated using XT-Laser 50 W near-Infrared 1064 nm Q-switched Ytterbium pulsed fiber laser (Raycus RFl-P50QB) coupled with high-speed galvo scan head of 8000 mm/s maximum speed. 10 pairs of fingers of 8 mm length and 500 µm width were engraved using 20% power, 250 mm scan speed, 50 kHz frequency, and pulse duration of 13ns. The collected sensing material was mixed with Polyvinylpyrrolidone PVP 2%) and a suitable amount of de-ionized water till forming a homogeneous paste. The paste was applied on the fabricated IDE using spin coating machine at 2000 rpm. Silver paste and copper cladding were used to prepare the sensor for measurement. Figure The proposed microscopic soda–lime glass substrates were cleaned using an acidic piranha solution of 98% sulfuric acid with 30% hydrogen peroxide 3:1 to remove organic contaminations, after rinsing with DI water several times, base piranha of 3:1 mixture of Ammonium hydroxide with 30% hydrogen peroxide was applied to enhance surface quality. The slides were rinsed in type 1 DI water several times. An ultrasonic bath was used for 15 min of ethanol and acetone, respectively. Finally, the substrates were submitted to Ar plasma surface treatment to promote surface characteristics and adhesion. DC/RF sputtering VTC-600-2HD system was used for metallic layer deposition. The chamber was evacuated to a base pressure of 3 × 10The fabricated sensor was allowed to dry to eliminate mixing water at 60°C for 24 h. The sensor was subjected to two different levels of humidity (7% and 97%) while applying 1 VAC for 12 h to enhance its stability. The response of the sensor was evaluated using saturated salt solution in a humidity range 11%-97%. The measured parameters included sensitivity, repeatability, and response and recovery times. the sensing mechanism was explained based on complex impedance measurements up to 5 M Hz. The schematic representation of sensor fabrication is dipected in Fig. -1 scanning range and 4 cm-1 scanning resolution. Besides, Raman analysis was acquired by the device .The X-ray diffraction (XRD) planes and the pattern were investigated using the XRD Device  within a scanning scale from 5° to 75 º, UV–Vis absorption spectra of the prepared samples were acquired using Agilent Varian Cary 5000 double-beam UV–Vis-NIR spectrophotometer in the wavelength range of 200–800 nm to study the optical properties of the prepared samples. The Fourier Transform Infrared (FTIR) was analyzed using the KBr disks method by  within a 400–4000 cm2, GQDs and MnO2/GQDs/PANI were caried out from 2θ = 5 to 75º with a scanning rate of 2º/min as demonstrated in Fig. 2 were observed. The tetragonal system of the MnO2 with a space group of I4/m was verified. The diffraction planes were observed at the angles of 12.8°, 18.07°, 28.7°, 37.55°, 41.96°, 49.9°, 56.3°, 60.2°, 65.4°, and 69.5°, corresponding to the planes of (110), (200), (310). (211), (301), (411), (600), (521), (002), and (541), respectively, with the most intense peak residing at a degree around 37 º. The results are in acceptable agreement with prior reported works56. For the composite, the three components' card numbers and peaks are included as 00–012-0720, 00–048-1206, 00–065-0826 for MnO2, Carbon component, and the PANI, respectively.XRD is an important technique that is considered as a primary tool for investigating the structure of various composite materials. The phase identification and composition of MnO57.27The corresponding card no. is PDF 01–072-1982. While implementing other constitutes of the structure, the material's sharpness and the intensity of the peaks get a bit broader and become distorted. This might be attributed to the occurring rearrangement of the structure for the atoms, resulting in a deformation of the composite structure. The nominal crystallite size of the structure is calculated based on the Scherrer equation as previously reportedArea (c), Area (A) are the crystalline and amorphous areas respectively.The dislocation density existing is determined from the inverse of the crystallite size as–4, 44 × 10–4 for MnO2 and MnO2-GQDs-PANI composite respectively.The values of crystallite size (D), crystallinity degree (XC), and dislocation density (δ) are 20, 15 nm and 75%, 36%, and 25 × 10The HRTEM of the GQDs is illustrated in Fig. 2/GQDs/PANI were examined by scanning electron microscope (SEM) at two different magnifications as shown in Fig. The surface morphological features of the MnO2 particles, thereby no evidence for the presence of these particles (MnO2). More importantly, the dimensions of GQDs are too small to be seen by this technique. the XRD can penetrate through the sample to some specific depth, hence the presence of MnO2 particles was confirmed through XRD measurements. By combining the results of both techniques (XRD and SEM), it was concluded that the MnO2 nanoparticles and GQDs are present and covered with the PANI fibers. The elemental mapping of the ternary composite is shown in Fig. The low magnification SEM image demonstrates a fibrous-like structure of PANI. The entire sample just reveals the presence of PANI without any evidence of the presence of other materials. By looking at the higher magnified SEM image, the fibers are clearly demonstrated with some other irregular ferments. The PANI could have covered the entire MnO2/GQDs/PANI prove the presence of oxygen carbon and nitrogen as a proof fro the presence of PANI and GQDs. The elemental mapping analysis proves the presence manganese as a constuent elemnt of the ternary nano composite. the distribution of the individual elements seems to homogeniuos without any agglomeration.The elemental mapping of the ternary composite MnO−1 to 400 cm−1 with a spectral resolution 4 cm-1. The FTIR spectra of MnO2, GQDs and nanocomposite (MnO2/GQDs/PANI) are depicted in Fig. −1, 1381 cm−1, 1611 cm−1, and 1738 cm−1 are ascribed to the C–O stretching vibrations, C–H bindings, C = C, and C = O, respectively. The FTIR spectrum of MnO2 reveals an absorption band at 710 cm−1 that arises from the stretching vibrations of the Mn–O. The nanocomposite (MnO2/GQDs/PANI) demonstrates the characteristics band of MnO2, GQDs and PANI. The benzene ring presents a stretching vibration at 1487 cm-1 due to the presence of C = C60.The chemical bonding and interaction between elements were verified through the FTIR measurements from 4000 cm\. The disordered band (D band at 1339 cm−1) is related to the defects that originate from the carbon atom vibrations with dangling bonds. G band at 1564 cm−1, the vibration of carbon atom in the hexagonal lattice due to the E2g phonon mode of sp2 is resulted in the graphitization band. More additional wide band at 3022cm−1 is devoted to G\ or overtone. One of the most valuable parameters that are generally used to judge the quality and the intercalation of the prepared materials is ID/IG ratio. The intercalation between GQDs and PANI can be verified by measuring the ID/IG ratio. This ratio was estimated and found to 0.96, thus indicating significant defects, that promote the sensitivity of the materials to humidity measurement61.The Raman spectrum of the composite nanostructure is presented in Fig. 2/GQDs/PANI is recorded from 200 cm−1 to 800 cm−1 as displayed in Fig. * transition due to the C = C bonds. The absorption band at about 281 nm is due to the electronic transition of the pure MnO2 nanoparticles. The electronic transition of π → polaron for PANI demonstrates a characteristic peak at about 485 nm. The most surprising phenomenon is the formation of radical cations in PANI that improves the delocalization of charges in PANI thereby enhancing the electrical conductivity of the PANI. the characteristic peak of PANI is in the range 400 -430 nm, however, the absence of this band, blue shift in the UV spectra, and the presence of a broad peak, confirm the incorporation of MnO2 and PANI conducting matrix during the in-situ polymerization process62.MnO2 adsorption–desorption isotherm of the ternary MnO2/GQDs/PANI is illustrated in Fig. 2 adsorption–desorption isotherm is belong to type III. In this case (type III isotherm), the interaction between the adsorbent-adsorbate are relatively weak, and the adsorbed molecules are accumulated all over the active sites on the surface of the studied material. The BET surface area of the ternary MnO2/GQDs/PANI was found to be 54.9 m2/g. Different parameters have been measured and calculated from N2 adsorption–desorption isotherm and tabulated in Table The NThe humidity sensing experiments were carried out using a saturated salt solution to generate a fixed relative humidity level. The saturated salt solutions were stored in a closed vessel to generate the required humidity level. The investigated sensor was inserted above the saturated salt solution in the closed vessel for a while, then the impedance/capacitance change was recorded using LCR meter at different frequencies . The sensor was evaluated in a humidity range of 11–97%, at different frequencies from 50 Hz up to 100 kHz. All experiments were conducted at room temperature. In these measurements, the impedance and capacitance variations were recorded as a function of humidity level to evaluate the humidity sensing performance of the studied structure.18. Based on the measured values for impedance and capacitance, the optimal testing frequency was found to be 200 Hz. The impedance decreases when the capacitance increases as the humidity increases. The measured curves can be divided into two regions, low humidity up to 43% and high humidity from 75% up to 97%. In the first region the impedance/capacitance variation is less than that of the second region. The impedance variation seems to be linear at high humidity level (greater than 75%). The capacitance variation is mostly having an expositional increment trend. The sensitivity can be defined as the change of measured signal per change in relative humidity level. the sensitivity can be estimated using the following Eqs. 65:The impedance/capacitance variation as a function of relative humidity is displayed in Fig. 6 Ω/RH and 5.02 × 10−11 F/RH for impedance and capacitance measurements respectively.The calculated sensitivities are 1.18 × 10The repeatability of the sensor describes the ability of the sensor to offer the same value of change when subject to two different humidity levels many times. The repeatability could be a good way to describe the stability of the sensor over a short period of time. The repeatability of the sensor was tested for three successive cycles between 11 and 43%. The repeatability of the sensors is described in Fig. To get a closer vision, response and recovery time were studied as depicted in Fig. The humidity sensing mechanism can be explained based on complex impedance spectroscopy (CIS) measurements.3O). The synthesized emeraldine base polyaniline has two forms of oxidized (−N =) and reduced (—NH—) groups. The presence of un-bonded electron pair on the nitrogen atom resulted in the protonation of above stated forms (–N = and —NH—). This can be described as follows:The sensing mechanism can be divided into two regimes. The first regime comprises low humidity up to 43%, whereas the relationship between real and imaginary parts of impedance is linear as depicted in Fig. 2+) to the protonated oxidized form (NH+). Since (NH2+) is incapable to leave an electron without earlier leaving a proton, thus the electron hopping occurs conditionally before the transformation of a proton. This type of conduction occurs in the presence of water molecules66.The conduction mechanism of the polyaniline is governed by the electron hopping from protonated reduced form (NHThe proposed sensing mechanism is provided schematically in Fig. The results of the obtained humidty sensor was comapered with thous obtained from similar structures as shown in Table 2. The validity of the preparation strategy is explored via versatile examination apparatus such as XRD, SEM, FTIR, UV–Vis, and Raman spectra. The dimensions of the crystallite size and other related structural parameters are emerged from the XRD, and SEM which verifies the nanoscale and crystallinity of the structure. The feasible and resulted implantation of the components is promoted through the bands arising in FTIR, and Raman as well as UV–Vis spectra. The structure is investigated for the humidity sensing throughout a wide scale of humidity levels up to 97 RH% which verifies the decent response and recovery times in both capacitance and impedance modes. The delivered structure might pursue a desirable set of specifications directed towards humidity sensing for the upcoming years in various areas.In the studied work, ternary composite of polymeric matrix as polyaniline combined with graphene quantum dots and MnO


Large language models (LLMs) have demonstrated significant potential in diverse domains, including medicine. Nonetheless, there is a scarcity of studies examining their performance in medical examinations, especially those conducted in languages other than English, and in direct comparison with medical students. Analyzing the performance of LLMs in state medical examinations can provide insights into their capabilities and limitations and evaluate their potential role in medical education and examination preparation. This study aimed to assess and compare the performance of 3 LLMs, GPT-4, Bing, and GPT-3.5-Turbo, in the German Medical State Examinations of 2022 and to evaluate their performance relative to that of medical students. t tests for pairwise comparisons. The relative strength of the LLMs in comparison with that of the students was also evaluated. The LLMs were assessed on a total of 630 questions from the spring and fall German Medical State Examinations of 2022. The performance was evaluated with and without media-related questions. Statistical analyses included 1-way ANOVA and independent samples GPT-4 achieved the highest overall performance, correctly answering 88.1% of questions, closely followed by Bing (86.0%) and GPT-3.5-Turbo (65.7%). The students had an average correct answer rate of 74.6%. Both GPT-4 and Bing significantly outperformed the students in both examinations. When media questions were excluded, Bing achieved the highest performance of 90.7%, closely followed by GPT-4 (90.4%), while GPT-3.5-Turbo lagged (68.2%). There was a significant decline in the performance of GPT-4 and Bing in the fall 2022 examination, which was attributed to a higher proportion of media-related questions and a potential increase in question difficulty. LLMs, particularly GPT-4 and Bing, demonstrate potential as valuable tools in medical education and for pretesting examination questions. Their high performance, even relative to that of medical students, indicates promising avenues for further development and integration into the educational and clinical landscape.  The minimum duration of study for the medical degree in Europe is 6 years. In Germany, state examinations take place after the second, fifth, and sixth years. The first and second examinations are multiple-choice tests . In the Today, promising applications of large language models (LLMs), particularly ChatGPT, are already being observed in education and research, with the potential to trigger a paradigm shift in health care . New, hiChatGPT is a web-based platform using advanced AI-driven LLMs such as GPT-3.5-Turbo and GPT-4 developed by OpenAI . HoweverCompared to GPT-3.5-Turbo, its successor GPT-4 can understand more nuanced instructions and questions and is expected to provide false information less frequently. Moreover, it is more likely to refuse queries that could result in harmful responses . GPT-3.5Bing is an AI chatbot developed by Microsoft and has been unveiled in 2023. In the development process, technology from GPT-4 was used to enhance its accuracy and performance capabilities ,13. In cOverall, ChatGPT and Bing represent a significant advancement in the field of AI and natural language processing. The ability to generate human-like responses and adapt to new information make them valuable tools for a wide range of applications, including content creation, customer service, and research.This study critically examines the capabilities of ChatGPT and Bing in medical education, by addressing how Bing, GPT-4, and GPT-3.5-Turbo perform in answering multiple-choice questions on the German Medical State Examination of 2022. Specifically, we assessed the number of correct answers of these LLMs in German, which is not their main training language, and compared it to the performance of medical students to evaluate their usefulness in the medical field.precise settings [We conducted a retrospective analysis of the spring and fall 2022 German Medical State Examinations. A total of 630 out of 640 multiple-choice questions in German (including questions containing media) were analyzed. Questions that were excluded post hoc for factual incorrectness were excluded from further analysis . The questions were taken from the learning platform Amboss . We usedsettings . No datasettings .We asked examination questions based on a German translation of the scheme used in previous studies evaluating OpenAI’s models : “The fot tests were carried out with python statistical library scipy (version 1.7.3) to assess statistical differences between means.We used a MacBook M1 pro 14-inch 2021 device with macOS Ventura (version 13.4), with Python (version 3.8.11) installed, and the data analysis libraries numpy (version 1.21.6) and pandas (version 1.4.3). For visualization, we used matplotlib (version 3.5.2) and seaborn (version 0.11.2). One-way ANOVA and independent samples For analysis without media content , 38 out of 311 (12.2%) questions were excluded for the spring examination and 22 out of 319 (6.9%) questions for the fall examination. The models’ strength was calculated as a relative proportion of the number of correct answers provided by students; a value above 100% means that the model was outperforming the average student, whereas a value under 100% shows below average student performance.When writing this paper, the authors used Grammarly  and GPT-4 to improve the language of the manuscript and correct grammatical errors. After using these tools, the authors reviewed and edited the content as needed and take full responsibility for the content of the publication.We compared the performance of 3 LLMs, GPT-4, GPT-3.5-Turbo, and Bing, in the German Medical State Examinations of 2022, both in spring and fall, and with and without questions containing media. The performance of the models was also compared to that of the students who participated in the examinations.GPT-4 had the highest overall performance with 555 correct answers out of 630 (88.1%) questions. Bing followed closely with 542 out of 630 (86.0%) correct answers. GPT-3.5-Turbo lagged with 414 out of 630 (65.7%) correct answers. The students performed in between .F2=64.1, P<.001). Independent samples t tests were conducted to make pairwise comparisons between the models. There was no significant difference in performance between Bing and GPT-4 . However, both Bing  and GPT-4  performed significantly better than GPT-3.5-Turbo.One-way ANOVA revealed significant differences among the 3 models . However, both GPT-4  and Bing  significantly outperformed the students. In the fall 2022 examination, GPT-3.5-Turbo’s performance was significantly lower than that of the students . In contrast, both GPT-4  and Bing  again significantly outperformed the students . Further investigation into these differences was conducted using independent samples t tests for pairwise comparisons between the models. There was no significant difference in performance between Bing and GPT-4 . However, both Bing  and GPT-4  significantly outperformed GPT-3.5-Turbo. Since there are no officially published data on students' performance on individual questions, we were unable to compare the models’ performance on nonmedia questions with that of the students.Next, the 40 questions containing media content were excluded, leaving a total of 590 questions for analysis. Bing achieved the highest performance with 517 correct answers out of 590 (90.7%). GPT-4 was slightly behind, with 515 out of 590 (90.4%) correct answers. GPT-3.5-Turbo, on the other hand, answered 389 out of 590 (68.2%) questions correctly. One-way ANOVA revealed that there were significant differences among the 3 models  questions correctly, Bing answered 254 out of 311 (81.7%) questions correctly, and GPT-3.5-Turbo answered 195 out of 311 (62.7%) questions correctly. When questions containing media were excluded, the performance of all models increased, with Bing having answered 239 out of 273 (87.5%) questions correctly, GPT-4 also having answered 239 out of 273 (87.5%) questions correctly, and GPT-3.5-Turbo having answered 181 out of 273 (66.3%) questions correctly. In comparison, the students answered a mean of 230.7 (SD 22.6) questions correctly out of 311 (74.2%).When evaluating the performance of the models relative to that of the students for the spring 2022 examination, GPT-4 displayed a relative strength of 116.6% when including questions with media and 118.0% when including questions without media, whereas Bing demonstrated strengths of 115.4% and 118.7%, respectively. Slightly worse performance, but still exceeding that of the students, was observed for the fall 2022 examination. The relative performance of GPT-3.5-Turbo for both examinations, compared to that of the students, with and without questions containing media, ranged between 88.5% for the fall 2022 examination including questions with media to 95.1% for the spring 2022 examination with questions without media.P=.007, t628=2.71). Furthermore, there were significant differences in Bing’s performance . When questions with media were excluded, the differences remained significant, with GPT-4 showing +37 (+5.4%) correct answers  between the spring and fall 2022 examinations. Bing had +39 (+6.1%) correct answers  between the spring and fall 2022 examinations  or excluded . The difference in the number of correct answers for GPT-3.5-Turbo was +24 (+6.0%) with and +27 (+5.7%) without questions containing media; however, these differences were not significant.In contrast, for GPT-3.5-Turbo, there was no significant difference in performance between the spring and fall 2022 examinations, irrespective of whether questions with media were included  questions, and Bing correctly answered 288 out of 319 (90.3%) questions, whereas on average, students correctly answered 239 out of 319 (74.9%) questions. Thus, both models showed outstanding results. A comparison with the highest scoring students revealed that only 0.5% of participants achieved a score between 291 and 300 . Even thIn comparison, both Bing and GPT-4 showed a significant decline in performance in the fall 2022 examination. However, both LLMs were still able to significantly outperform the students and ChatGPT-3.5-Turbo. The performance of GPT-3.5-Turbo and that of the students did not differ significantly between the 2 examinations. Overall, there was a significant difference in performance between Bing and the students in both the spring and fall 2022 examinations, as well as between GPT-4 and the students in both examinations. While GPT-3.5-Turbo was not significantly worse than the students in the spring 2022 examination, a significant difference was observed in the fall 2022 examination. Therefore, not every model appears to be equally suitable for correctly answering medical examination questions. However, a noticeable improvement has been noted with the further developed models. To what extent this can be further improved in the future should be investigated through further comparisons of different models.An explanation for the poorer performance is the higher proportion of media-related questions in the fall 2022 examination, as there is no image recognition in the current version of the LLMs. This feature is already announced for GPT-4 and needs to be considered in future analyses. The consistent performance of the students and GPT-3.5-Turbo also suggests that there may have been more questions with a higher degree of difficulty in the fall 2022 examination; this also aligns with a current negative trend in the results of the state examinations, with a large variation among individual examinations [Another prominent point in the fall 2022 examination compared to the spring 2022 examination is the relatively high proportion of questions that were subsequently excluded. In the spring 2022 examination, only 1 question was excluded post hoc, whereas 9 were in the fall 2022 examination. Since only those questions that are factually incorrect or whose answer options are contentious were excluded, a high proportion of such questions can lead to uncertainty among students regarding their own decision-making process. Given the outstanding performance of GPT-4 and Bing, it might be worth considering using these LLMs to pretest questions for future examinations to reduce the number of contentious questions. This could be a relevant aspect for further examinations. Bing seems to be a qualified medium, as it can also provide sources for the given answer. The issue remains that incorrect answers from these programs are difficult to detect, especially as the examiner is presented with a seemingly correct solution with explanations. This should be tested in further investigations.In addition to the actual testing of examinations using the LLMs, the aspect of preparation for these is a crucial point. Besides traditional textbooks, LLMs appear to provide a valuable supplement to conventional learning by elucidating medical issues, offering students the opportunity to obtain rapid solutions for specific medical questions. This also plays a significant role in preparation for examinations. LLMs could be used to quickly inquire about specific medical queries, hence simplifying learning. For instance, extensive research could be made easier by Bing's citation of sources. Future research should investigate how image recognition functions in a medical context to provide, for example, support in radiographic diagnostics or dermatologic findings. ChatGPT is already being increasingly used in the field of radiology, where it can aid in education and assist in making clinical decisions . EspeciaCertainly, programs using LLMs such as OpenAI’s ChatGPT , MicrosoIn this study, the evaluation was limited to OpenAI's models and focused on single prompts and answers from just 1 year’s German Medical State Examinations. The inability of the models to process media content and the lack of diversity in examination content and languages confines the scope of insights. Additionally, the rapid evolution of LLMs means that the results may quickly become outdated. Moreover, there are implications regarding the accuracy of the LLMs’ outputs and the level of trust that should be placed in them, particularly in the context of medical education. The study did not investigate the potential for misinformation or inaccuracy in the responses generated by the LLMs, which is critical given that medical students might rely on these tools for preparation for examinations. Lastly, potential biases or errors intrinsic to the models were not explored. These constraints warrant measured interpretation of the results and indicate the need for more extensive and varied studies, as well as a critical analysis of the reliability of the LLMs in a medical education setting. Being the fastest growing web platform ever , LLMs wi


The reports on bone mineral loss or major osteoporosis fracture (MOF) in sarcoidosis are scarce and have conflicting outcomes. This study aimed to evaluate the prevalence and risk factors of MOF in sarcoidosis patients.In a single-center cohort of 382 patients with sarcoidosis (55.8 ± 11.6 years) we evaluated bone mineral density at lumbar spine, at femoral neck and at total hip and the presence of MOF. Lung function measurements including diffusion capacity for carbon monoxide (DLCO) were assessed. Chest X-rays were performed and radiological staging was done by Scadding score.T-scores were lower in sarcoidosis with MOF with respect to those without MOF, but the difference was statistically significant only for BMD at femoral neck (p < 0.05). Moreover, BMD values at total hip was positively correlated with DLCO (%) (p < 0.001). Prevalence of MOF was higher in patients with sarcoidosis with lung parenchymal involvement  than in patients with sarcoidosis in chest X-ray stages 0 and 1 . Moreover, multiple regression analyses showed that X-ray Scadding score was positively associated with MOF.Ninety patients (23.6%) with sarcoidosis have history of a MOF. BMD This study shows that MOF represent a common and important complication in patients with moderate/severe sarcoidosis. The chest X-ray evaluation and the pulmonary function test could allow to define the risk of MOF in sarcoidosis patients. Osteoporosis is defined as a systemic skeletal disease characterized by low bone mass and microarchitectural deterioration of bone tissue, with a consequent increase in bone fragility and susceptibility to fracture .It is associated with an excess of mortality, a decrease in quality of life, and co morbidities; and has a high social and economic burden, representing a major public health problem. Osteoporosis affects mostly postmenopausal women and fewer men. It is mainly related to the normal aging process—primary osteoporosis. Nevertheless, it can also occur due to secondary causes such as bone-affecting treatments, clinical disorders, or lifestyle habits-secondary osteoporosis. Nine million osteoporotic fractures occur worldwide yearly . The lasSarcoidosis is a systemic inflammatory disorder characterized by the formation of granulomas, which are clusters of inflammatory cells, typically in the lungs, lymph nodes, and other organs .Several factors contribute to the increased risk of osteoporosis in sarcoidosis patients, including the chronic inflammation associated with the disease and the use of corticosteroids as a treatment. In fact, the chronic inflammation seen in sarcoidosis can disrupt the normal bone remodeling process. Inflammation leads to an imbalance between bone formation and resorption, resulting in increased bone loss and reduced bone quality –7. CytokAmong MOF in sarcoidosis patients vertebral fractures are the most serious. In fact, vertebral fractures can have various effects on lung diseases depending on the specific circumstances and the severity of the fracture. In particular, the vertebral fractures can cause pain and restrict the movement of the chest wall. This can lead to shallow breathing and decreased lung expansion, resulting in reduced lung function. Moreover, lung diseases such as chronic obstructive pulmonary disease (COPD) or pulmonary fibrosis such as sarcoidosis, can make individuals more susceptible to lung infections . FracturTo identify the prevalence of major osteoporotic fractures in patients with sarcoidosis.To assess risk factors for major osteoporotic fractures.The aim of this single-center cross-sectional study was twofold:We studied a cohort of 382 subjects (mean age 55.8 ± 11.6 years) affected by sarcoidosis, referred to the Regional Referral Center for Sarcoidosis and other Interstitial Lung Diseases at Siena University Hospital  from January 2018 to December 2022. Diagnosis of sarcoidosis was performed through a multidisciplinary evaluation according to the diagnostic criteria of the ATS/ERS/JRS/ALAT guidelines , 13. AllT value lower than − 2.5 was diagnosed as osteoporosis, and a T value between − 1.0 but higher than − 2.5 was diagnosed as low bone density. Sex-matched Italian reference data were used for the calculation of T-score [In all subjects we measured BMD at the lumbar spine [LS-BMD] and at femoral subregions  using a dual-energy X-ray absorptiometry device . Osteoporosis and osteopenia were diagnosed according to the World Health Organization (WHO) definition: a  T-score .The information on history of previous fracture was collected during osteoporosis visit. All surveys included details of fracture location, including spine, hip, wrist, clavicle, upper arm/shoulder, rib, pelvis, ankle, upper leg and lower leg. Besides, the occurrence of fractures was assessed by way chart review in the Carestream database, by reviewing progress notes, and by radiological evidence of vertebral fracture. Magnetic Resonance Imaging (MRI), CT with 18F-fluorodeoxyglucose (FDG PET-CT), chest high resolution computed tomography (HRCT) and Computed Tomography (CT) reports were also reviewed. In particular, all radiological images were examined for the presence of any vertebral fracture according to Genant’s method’s . Namely,In all subjects blood samples were collected in the morning under fasting conditions to evaluate serum levels of calcium (Ca), phosphate (P), creatinine (Cr), alkaline phosphatase (ALP), 25-hydroxyvitam D (25OHD), Serum1,25-hydroxyvitam2D  and intact parathyroid hormone (PTH). At the same time points 24-h urine samples were collected for the evaluation of calcium, phosphate and creatinine. Serum 25OHD was determined by a radioimmunometric method . In our Institution the intra- and inter-assay coefficients of variation for 25OHD were 6.8 and 9.2%, respectively. Serum1,25(OH)2D was assessed by chemiluminescence immunoassay . In our institution the intra- and inter-assay coefficients of variation were 4.1 and 5.3%, respectively. Serum PTH was assessed by an immunoradiometric assay . The results were expressed in picograms per millilitre, and the intra and inter-assay coefficients of variation were 3.6 and 4.9%, respectively. Urinary calcium, phosphate and creatinine were determined by a colorimetric method  in 24-h urine samples.All participants underwent pulmonary function tests performed according to the American Thoracic Society/European Respiratory Society (ATS/ERS) standards , 18, usiAll subjects with sarcoidosis performed a chest X-ray with radiological staging according to Scadding criteria . The radt-test. Categorical variables were compared by Chi-square test or Fisher’s exact test, as appropriate. The correlations between the groups were analyzed with the Pearson’s correlation test. Multiple linear regression models were used to assess the association of independent predictors such as sex, BMI, creatinine, vitamin D, FVC (%), FEV1 (%), DLCO (%), COS classification, Radiological stages, therapy for sarcoidosis, prednisone dosage to the presence of osteoporosis and MOF. All tests were two-sided, and p < 0.05 was considered statistically significant. All statistical tests were performed using SPSS 10.1 statistical software (SPSS 10.1).The Kolmogorov–Smirnov test was used to verify the normality of the distribution of the outcome variables. All the variables were normally distributed and were expressed as mean ± SD. The significance between the means was tested using Student’s p < 0.05). As expected patients with sarcoidosis and MOF were older than those without MOF.The clinical and biochemical characteristics of sarcoidosis patients with or without MOF are shown in Table N = 81), femur (N = 4), wrist (N = 7) and humerus (N = 5). Moreover, 52 patients had history of more than one MOF. The prevalence of vertebral fractures in patients with sarcoidosis, by spinal location, is shown in Fig. Ninety patients (23.6%) with sarcoidosis have presented a major osteoporosis fracture. In particular, the MOF reported involved vertebrae N = 8, femur  and BMD-TH (p < 0.01).Figure p < 0.001). Also BMD-LS and BMD-FN were significantly correlated with DLCO% (r = 0.20 p < 0.001 and r = 0.18 p < 0.001 respectively). Instead, no significant associations between BMD values with FVC (%) and FEV1 (%) were observed.Figure p < 0.05).Figure In multiple regression analysis, statistically significant associations were found for predictors of osteoporosis (model 1) and of MOF model 2). In particular, multiple regression analyses showed that BMI was positively associated with osteoporosis, while DLCO (%) was negatively associated  had a MOF. According to a classification based on the frequency with which they occur, MOF consider a grouping of the most common fractures which include hip, clinical vertebral, distal forearm and proximal humerus fractures , 24. MorAn important finding of this study is that approximately a quarter of sarcoidosis patients had a MOF and over a fifth of them had at least one vertebral fracture. Similarly, in the Maastricht study at baseline 20% of patients with sarcoidosis had vertebral fractures while non-vertebral fractures were rare . MoreoveThe severity of sarcoidosis has been suggested as a potential risk factor for the development of osteoporosis and major fragility fractures (MOF). In fact, we have found that patients with more severe sarcoidosis, as indicated by lung involvement, multiorgan involvement, or higher disease activity, may be at a higher risk of developing osteoporosis and experiencing MOF. However, it is important to note that the association between sarcoidosis severity and osteoporosis/MOF is not fully understood and requires further investigation. Other factors, such as age, gender, menopausal status (in women), vitamin D deficiency, and physical inactivity, can also contribute to the development of osteoporosis in sarcoidosis patients .Another important finding in this study is represented by the close correlation between the worsening of the respiratory decalages, expressed by the DLCO%, and the reduction of femoral BMD; moreover, the multiple linear regression model confirms that the DLCO% is able to predict the risk of osteoporosis. Multiple regression analysis also reported that BMI shows a protective effect against osteoporosis. This finding seems to be in agreement with a previous study by Nuti et al. witch reported that an association between the reduction in BMI and the risk of vertebral fracture in COPD patients . MoreoveMoreover, the extent of chest radiology involvement evaluated according by Scadding’s criteria is able to predict the risk of MOF in sarcoidosis patients independently of BMD. The better association of femoral BMD with disease severity and MOF with respect to lumbar BMD may be explained by the increased occurrence of spondyloarthritis in sarcoidosis patients .Our study has some limitations. Firstly, the cross-sectional nature of the study does not allow the establishing of any causality relationships between the parameters. Secondly, the lack of data about markers of inflammation. Nevertheless, this study presents several strengths: firstly, the large study sample of a rare condition such as sarcoidosis disease; secondly, it was a single-centre study and this may ensure its internal validity; thirdly, has confirmed that the severity of pulmonary involvement is related to the risk of osteoporosis and fragility vertebral fractures.Our data obtained from a large cohort of sarcoidosis patients confirm that MOF and particularly vertebral fracture represent a common and important complication in patients with moderate/severe sarcoidosis. In these patients, the radiological evaluation according to the Scadding’s criteria and the measurements of DLCO could allow to define the risk of MOF and to implement adequate therapeutics strategies.


Capacity distribution is a challenging issue for an airline under financial budget and resource consideration. It is a large-scale optimization problem covering both long-term planning and short-term operating arrangements. This study investigates on the airline capacity distribution problem with financial budget and resource consideration. It contains subproblems of financial budget arrangement, fleet introduction, and fleet assignment. Among them, financial budget is arranged in multiple decision periods, fleet introduction is decided under fixed time points, while fleet assignment is decided under all available time points. To tackle this problem, an integer programming model is formulated for descriptions. Then, an integrated algorithm of modified Variable Neighborhood Search (VNS) and Branch-and-bound (B&B) strategy is developed to find solutions. In detail, a greedy heuristic approach is utilized to generate an initial solution for fleet introduction, the modified B&B strategy is utilized to generate the optimal solution for fleet assignment and the modified VNS is applied to update current solution for a new one with better quality. In addition, budget limit checks are added for financial budget arrangements. Finally, the hybrid algorithm is tested on efficiency and stability. It is also compared to other algorithms which replace the modified VNS by basic VNS, differential evolution and genetic algorithm. Computational results show that performance of our approach is powerful in terms of objective value, convergence speed and stability. Airline capacity distribution problem (ACDP) is a combination of subproblems which contain financial budget distribution, fleet introduction, and fleet assignment. Airlines usually deal with this problem in batches  are applied. Rezgui et al.  apply VNAccording to studies above, VNS is an efficient framework to deal with multi-stage optimization problems which are similar to ACDP. In addition, to improve solution quality, exact method can be incorporated into VNS framework. As a result, in this study, ACDP under financial budget and resource consideration is presented and a hybrid algorithm of VNS and an exact method is proposed to maximize profits. The main contributions are as follows: (1) ACDP under financial budget and resource consideration is described mathematically as an integer programming model; (2) a greedy heuristic approach is designed to improve quality of initial solution; (3) VNS encoding process is utilized to integrate budget distribution and fleet introduction for dimension reduction; (4) a shaking strategy and special neighborhood structure are applied to generate efficient perturbation solutions; (5) an exact method is applied to improve solution quality; (6) the hybrid algorithm is tested on efficiency and stability and compared to other algorithms.The remaining chapters of this study are arranged below. Section In this study, ACDP under financial budget and resource consideration is studied. It is an integration problem involving three stages: budget distribution, fleet introduction, and fleet assignment. The notations used throughout this paper are given in Table During the first stage, a long planning term is divided as a set of Additionally, a proportion upper limitation mentclass2pt{minimFor example, an airline’s fleet prices, flying missions, flight demands and budget limits are defined in Tables 8. Total planning term is 10 years and divided into 5 periods with 2 years in the same period. Then, the budget can be distributed as 4 × 108, 2 × 108,0, 1 × 108 and 0 from H1–H5, not exceeding the proportion limit in each period of 50%, 30%, 20%, 20% and 20%. Then, the airline decides on fleet introduction. There are three decisions containing buying one 787 in H1, one 757 in H2 and leasing one 737 in H4. These decisions are shown in a square box, a circle and a triangle respectively in Table According to the example above, total financial budget is set as 8 × 10After fleet numbers are determined, an airline assigns available fleets to flying missions in all planning years. Results are shown in Table  How many budgets to be distributed in each planning period, Which time point is chosen to buy or lease an aircraft, Which type of aircraft is chosen, How many aircrafts is bought or leased, How to match flying missions with suitable available aircrafts.To summarize, for our ACDP study, a combination of subproblems containing budget distribution, fleet introduction, and fleet assignment, the following decisions should be made:Among the decisions, (1) belongs to budget distribution, (2–4) belong to fleet introduction and (5) belongs to fleet assignment. In the next sections, this problem is formulated as an integer programming model and then valuable solutions are searched by a designed hybrid algorithm.According to descriptions and assumptions above, an integer programming model for ACDP is constructed. As mentioned before, there are mainly three parts of ACDP containing financial budget distribution, fleet introduction, and fleet assignment. The fleet introduction part refers to formulation of Bazargan and Hartman . The fleEquation  illustraEquation  promisesThis section introduces the proposed hybrid algorithm of VNS and B&B in detail. Firstly, algorithm design motivations and framework are illustrated. Secondly, with regards to problem-specific characteristics, algorithm components, involving initial solution generation, encoding, decoding, modified B&B strategy and VND process, are presented respectively. Finally, the whole procedure of the hybrid algorithm for addressing ACDP is summarized.In ACDP, there exist mainly three subproblems containing budget distribution, fleet introduction, and fleet assignment. They are considered simultaneously. Since these subproblems are dependent, the whole problem has NP-hard property and its various variables cannot be dealt efficiently with exact methods in limited time. As a result, we adopt a VNS metaheuristic framework to solve this problem. In addition, as one of the subproblems, fleet assignment, can be handled with B&B  and (4);Buy-down-lease-up: combination of (2) and (3);Fleet-Change: change one fleet type to another randomly;Buy-Lease-Swap: swaps values of bought and leased fleets in one period;Yearly swap: choose two years randomly, swap all the fleet numbers.There are nine neighborhood structures to deal with encoding results involving: Add-Buy, Minus-Buy, Add-Lease, Minus-Lease, Add-Buy-Minus-Lease, Add-Lease-Minus-Buy, Fleet-Change, Buy-Lease-Swap, and Period-Swap. They are indexed in Fig. For these nine structures, (1–4) only change one value in the encoded results, (5–7) change two values, (8) changes six values, while (9) involves two periods and change 18 numbers totally. From a multi-layer view, (1–6) and (8) are concerned with buy-or-lease choices, (7) is related to fleet type decisions, while (9) represents time period choices.Once a neighborhood of fleet introduction is generated in Fig. Our budget limit checks are incorporated into neighborhood generation process in Sect. After comparison, if the fleet introduction cost of the new code exceeds relative period budgets or total budget, the code is invalid and should be deleted. The previous code is output for VND process.Algorithms of period and total budget checks are illustrated in Fig. This section intends to systematically evaluate our integer programming model and modified VNS-B&B hybrid algorithm. It is compared with three metaheuristics containing basic VNS, differential evolution (DE), and genetic algorithm (GA). They only replace the modified VNS part and incorporate with B&B. Three different sets of benchmarks are set and collected to compare their performance involving objective value, running speed and robustness. All experiments of the modified VNS-B&B hybrid algorithm and compared metaheuristics are coded in C++. They are run on a windows 10 system with a 1.10 GHz Intel Core i7-10710U CPU processor and a 16G RAM.To solve ACDP problem, we set four instances scaled with 3, 10, 20, and 50 routes, which covers airlines of small and medium sizes. For each instance, there are four sets of input data involving budget, fleet, route, and flying mission information shown in Fig. Data sources are open websites and reports. Because most of airlines keep data privacy, direct and complete company-specific data is difficult to obtain. As a result, open resources are referred for numerical settings. To be specific, total budget volume, period limit numbers, fleet capacity and fleet prices are estimated based on open reports on Statista Erick , b. OnlyTo test our modified VNS-B&B algorithm, the modified VNS part is tested and then replaced by other efficient metaheuristics involving DE, GA, and basic VNS. There are various parameters to be predefined before the experiments described in Table For all experiments, ACDP is planned in the future 10 years and they are divided into 5 periods with 2 years in each period. Assuming there are 365 days in each year, flying missions are repeated in each day, once a mission is assigned a fleet type, it would repeat in each day. Then, yearly operating profits can be calculated as daily profits multiplied by 365 days, which is a widely used simplification (Kenan et al. For our modified VNS, number of VND neighborhoods u et al. . To imprg et al. , populatm et al. , populatThis subsection intends to evaluate the performance of modified VNS-B&B algorithm and compare it with DE-B&B, GA-B&B and basic VNS-B&B algorithms. The first phases of the four hybrid algorithms deal with two subproblems of ACDP containing budget distribution and fleet introduction with metaheuristics. The second phases apply modified B&B strategy to solve fleet assignment, another subproblem of ACDP. The four algorithms are compared on running speeds, objective values and robustness. For robustness, an evaluator named Relative Percent Deviation (mentclasspt{minimaExperiments of the four instances in Sect. In terms of objective value, the modified VNS-B&B is dominant among all the four algorithms. Because the objective in Eq.  is to maIn terms of running speed, the modified VNS-B&B also has advantage over the other three algorithms. The running speed is measured as the running time in second, which starts from the beginning of our algorithms and ends after the final iteration is finished. A smaller value of seconds means a better running speed of an algorithm. In all cases, the modified VNS-B&B algorithm obtains the smallest values of running time with the numbers of 4.79 s, 18.60 s, 49.78 s and 265.82 s. To compare it with other algorithms, our modified VNS-B&B is approximately 1/3 faster than basic VNS-B&B and 1/2 faster than GA/DE-B&B. For example, in case 1, the modified VNS-B&B has a running time of 4.79 s while the basic VNS-B&B has a running time of 6.46 s, which means that the former is 25.81% faster than the latter. The proportion for case 2 is 33.62% and similar in other cases.Comprehensively, although there are adjacent objective values compared to those of modified VNS-B&B, their speeds are considerably slower than those of modified VNS-B&B. For example, the objective value of GA-B&B in case 1 with the number of 5.78E + 08 has the smallest deviation to that of the modified VNS-B&B, while the running time of the former with the number of 4.79 s is considerably slower than that of the latter with the number of 8.25 s. For the objective value of DE-B&B in case 4 with the number of 6.94E + 09, the situation is similar.In terms of robustness, as mentioned before, RPDs are utilized for evaluations. In Table In detail, in all cases and algorithms, iterative processes are tracked and recorded as convergence curves shown in Fig. Furtherly, to test out whether the robustness of modified VNS-B&B algorithm is sensitive to input disturbance, we make changes on input numbers of total budget and passenger demands, which are likely to fluctuate under volatile market conditions. To be specific, total budget and passenger demands are assumed to be 10% more or less than before while the other input numbers remain the same. Then, two more groups of experiments are conduced besides those shown in Table In Fig. To summarize, compared to DE-B&B, GA-B&B, and basic VNS-B&B hybrid algorithms, the modified VNS-B&B algorithm has advantages on objective value and running speed. In terms of robustness, the modified VNS-B&B algorithm performs good and only has slight deviations in limited conditions.This paper investigates on the ACDP problem with resource and budget consideration. It is an integration of subproblems containing budget distribution, fleet introduction, and fleet assignment. An integer programming model is formulated to describe the problem and a hybrid algorithm of modified VNS and B&B strategy is designed to find solutions. The hybrid algorithm consists of seven components containing initial solution generation, encoding, decoding, modified B&B, VND and shaking process processes. Moreover, budget limit checks are added once a new neighborhood is generated to avoid invalid solutions and improve search efficiency. The modified VNS-B&B algorithm is compared with the DE/GA/basic VNS-B&B algorithms on objective values, running speeds, and robustness. Experimental results show that the efficiency and stability of the modified VNS-B&B algorithm take advantage over the other compared algorithms.Our study contributes to reduce dimensions of the complex integrated ACDP problem and provide practical advice for airline planning decisions under budget and resource limits. In the future, relative research can focus on incorporate more limited considerations into ACDP problem and solve it with a more efficient method in larger cases.


The atomic-thick anticorrosion coating for copper (Cu) electrodes is essential for the miniaturisation in the semiconductor industry. Graphene has long been expected to be the ultimate anticorrosion material, however, its real anticorrosion performance is still under great controversy. Specifically, strong electronic couplings can limit the interfacial diffusion of corrosive molecules, whereas they can also promote the surficial galvanic corrosion. Here, we report the enhanced anticorrosion for Cu simply via a bilayer graphene coating, which provides protection for more than 5 years at room temperature and 1000 h at 200 °C. Such excellent anticorrosion is attributed to a nontrivial Janus-doping effect in bilayer graphene, where the heavily doped bottom layer forms a strong interaction with Cu to limit the interfacial diffusion, while the nearly charge neutral top layer behaves inertly to alleviate the galvanic corrosion. Our study will likely expand the application scenarios of Cu under various extreme operating conditions. Atomically thick anticorrosion coatings on Cu are desired for future applications, but still at its infancy. Here, the authors report a Janus-doping mechanism in bilayer graphene on Cu substrate that results in an enhanced anticorrosion performance. However, the susceptibility of Cu to oxidation greatly limits its advanced applications6. For example, Cu will lose more than 99.99999% of its electrical conductivity at 200 °C in air for only 30 min7. Conventional organic coating8 and sacrificial anode9 anticorrosion techniques have made significant success in traditional industries, unfortunately, these methods typically rely on a thick coating and fail to comply with the miniaturisation requirements of the integrated circuits industry2. Currently, the rise of two-dimensional (2D) materials has provided new opportunities for the development of anticorrosion technology12. Graphene, in particular, has emerged as a promising candidate for an ultimate anticorrosion coating due to its excellent characteristics at the atomic thickness, including absolute impermeability, high electrical and thermal conductivity, excellent chemical stability, and great optical transparency15. However, previous studies have shown that the anticorrosion performance of graphene is far from satisfactory under real working conditions, especially in complex and diverse environments29, which limits its application to an early stage.Cu is widely used in the modern semiconductor industry as electrical connectors due to its high conductivity23. Second, graphene is cathodic to most metals and will lead to local galvanic reaction24. As a result, corrosive molecules will interact with the free electrons on graphene surface and thus accelerate the electrochemical corrosion process28. Recently, efforts have been made to enhance the graphene-Cu couplings to prevent interfacial molecular diffusion, for example, by forming a commensurate graphene/Cu(111) system30 or producing an ultra-flat Cu surface13. However, these methods impose overly restrictive limitations on Cu or graphene and still cannot address the electrochemical corrosion issue. Therefore, there is an urgent need to develop a robust and effective anticorrosion strategy for graphene coating that can address all those three requirements.In principle, an ideal anticorrosion coating material should comply with three requirements: (i) intrinsically, being impermeable to corrosive agents and having low penetrating defect density; (ii) interfacially, being tightly coupled with metal to prevent further horizontal diffusion once corrosive agents reach the interface, and (iii) surficially, being electrically inert to prevent electrochemically facilitated corrosion reactions. A defect-free graphene film naturally fulfils the first requirement, but it generally fails to meet the interfacial and surficial ones. First, the easily formed wrinkles on graphene and intrinsic step bunches on Cu allow for the diffusion of corrosive molecules at the interface31. It is found that the bilayer coating strategy not only integrates the advantages of the monolayer , but also demonstrates excellent prospects far beyond expectation (with a Janus-doping effect for improved anticorrosion). Specifically, it can simultaneously satisfy the demands of both reinforcing the graphene-Cu interactions to limit interfacial molecular diffusion and maintaining the intrinsic charge neutrality of the top layer graphene to suppress surficial electrochemical reactions  arbitrary-twisted bilayer graphene coating on Cu by wet transfer method (see Methods for more details). After being oxidized at 250 °C for 6 hours, the monolayer graphene coated Cu quickly deteriorated and turned black , whereas the bilayer coated area maintained the initial Cu state with shining metallic lustre  images further confirmed that the Cueps Fig. . Previou34 (see Methods for more details), and deduced from the model that bilayer graphene could effectively protect Cu for more than 1000 h at 200 °C, while monolayer graphene only works for ~36 h  of bilayer graphene is confirmed to be orders of magnitude lower than that of monolayer graphene  were readily estimated from the Arrhenius equation36  to track the evolution of the penetrating defects on graphene film Fig. . After bFurthermore, the oxidation process under extreme working conditions was investigated by in situ environmental scanning electron microscopy (ESEM), which allowed for real-time observations with an oxygen pressure of 150 Pa, a hydrogen pressure of 80 Pa, and a temperature of 600 °C. Under such oxygen-rich and high-temperature conditions, monolayer graphene could not withstand even one second of exposure Fig. . In cont2O became increasingly prominent, proving the chemical state of Cu has risen from 0 to +1  was carried out to gain insight into the chemical state of Cu during oxidation. As the oxidation progressed at 150 °C, the satellite peak and Auger peak of Cu +1 Fig. . Notablyess Fig. , demonstene Fig. . These fene Fig. . By comb38. Based on these findings, we propose that the bilayer graphene/Cu system demonstrates a Janus-doped characteristic, where the bottom layer is heavily doped and forms an enhanced interaction with Cu which limits the interfacial diffusion and migration of corrosive molecules, while the top layer is nearly charge neutral, thus can cut off the electron pathway and block the catastrophic electrochemical reactions. By successfully manipulating the electronic structures of the two layers, both the interfacial diffusion and surficial electrochemical reaction pathways are suppressed, finally resulting in the ultraslow corrosion of Cu.We further utilized first-principles calculations to understand the ultrahigh anticorrosion performance in the bilayer graphene/Cu system  experiments were performed to investigate the detailed electronic structures. The calculation results demonstrate an energy shift between the Dirac point and the Fermi surface in the graphene/Cu system, and the shift of the bottom layer graphene is significantly larger than that of the monolayer , such an upshift of 12 cm-2 versus ~1.4 × 1012 cm-2). This evident doping effect leads to a strengthened interaction between bottom graphene and Cu, thus effectively blocking the interfacial diffusion pathway for corrosive agents at the graphene-Cu interface  measurements revealed that the surface potential of bilayer graphene on Cu was ~135 mV higher than that of monolayer graphene Fig. , indicatyer Fig. . Accordiace Fig. .In the case of substantial electron transfer for monolayer coating, graphene is more likely to provide electrons to corrosive agents, and its high electrical conductivity will provide a channel for electrons to migrate on the surface and participate in the cathodic reactions. Regarding the top layer of bilayer graphene, both our calculations and nano-ARPES results confirm that there are negligible electrons transferring onto the top layer Fig. . Such an5. As a further demonstration, we transferred bilayer graphene coatings onto Cu conductors on a printed circuit board (PCB). After annealing at 120 °C for 20 h, the bilayer graphene successfully protected the Cu conductors with no visible signs of oxidation -1 (NH4)2S2O8 solution in a water tank. After that the obtained free-standing PMMA/graphene film was smoothly placed onto another as-grown monolayer graphene/Cu without deliberately controlling the twisted angle. Finally, the obtained PMMA/bilayer graphene/Cu sample was baked at 80 °C for 10 min and then annealed in Ar and H2 atmosphere at 400 °C for 10 h. The second way is using the typical chemical vapour deposition (CVD) growth method, and these bilayer domains are of several tens of micrometres. In detail, a Cu foil was first placed on a quartz substrate and loaded into the CVD furnace. Then the system was heated to 1040 °C under a reducing atmosphere of 500 standard cubic centimetres per minute (sccm) Ar and 30 sccm H2. After holding at 1040 °C for 1 hour, 0.05 sccm/50 sccm of CH4/H2 was introduced into the system for 10–30 min to obtain bilayer graphene on Cu.Bilayer graphene coated Cu samples are prepared in two ways. The first one is using the typical wet transfer method, and the bilayer coating area can be on the decimetre scale. Specifically, 8% polymethyl methacrylate (PMMA) in anisole solution was spin-coated onto the surface of the as-grown monolayer graphene/Cu sample and then the sample was baked at 120 °C for 2 min. Then the Cu was etched by 0.2 mol LThe oxidation experiments were carried out by baking the samples in a CVD chamber in air at 120–275 °C for up to 15 days. The room temperature oxidation experiments were carried out in Beijing with the temperature controlled within 20–30 °C and the relative humidity controlled between 30 and 50%.+ cluster at 30 keV with an incidence angle of 45°. The dual sputtering beam uses Cs+ cluster at 500 V and 27 nA with an incidence angle of 45°. The ARPES measurements were performed at the nano ARPES beamline BL07U of the Shanghai Synchrotron Radiation Facility, with a beam spot size of ~500 nm and energy/momentum resolution of 50 meV per 0.2°. Graphene sample was measured in an ultrahigh vacuum with a base pressure of more than 5 × 10-11 mbar and photon energy of 91 eV, and the data were collected by DA30L analysers. NAP-XPS was performed on a system which is manufactured by SPECS Surface Nano Analysis GmbH. The facility is composed of three chambers, an analysis chamber, a preparation chamber, and a load-lock chamber. The X-ray source in the vacuum environment is separated from the high-pressure analysis chamber using a Si3N4 window. The analysis chamber is equipped with a PHOIBOS NAP hemispherical electron energy analyser, a microfocus monochromatized Al Kα X-ray source with beam size of 300 μm, a SPECS IQE-11A ion gun, and an infrared laser heater. The base pressure of the main chamber is kept below 1 × 10-9 mbar.Optical images were obtained using an Olympus BX51 microscope. Raman spectra were obtained with a Witec alpha 300 R system with a laser excitation wavelength of 514 nm. EBSD characterizations were carried out using PHI 710 Scanning Auger Nanoprobe. AFM images were acquired using a Bruker Dimensional ICON system under ambient conditions. KPFM measurements were performed using Asylum Research Cypher under ambient conditions. Depth resolution mass spectra were conducted on a ToF-SIMS 5–100 instrument (ION-ToF GmbH), which relates to a UHV preparation chamber. The primary ion source uses BiThe in situ experiments were conducted in a specially modified commercial ESEM (Thermo Fisher Quattro-s), using oil-free pre-vacuum pumps for the vacuum system, a homemade laser heating stage for temperature control, and a K-type thermocouple for temperature monitoring. A gas supply module facilitated by mass flow controllers (Bronkhorst) was employed, together with a mass spectrometer (Pfeiffer OmniStar) to analyse the atmosphere in the chamber. Prior to the experiments, the ESEM chamber was cleaned using plasma. The acceleration voltage was set between 3.0 and 7.5 kV, and images were captured using a large field detector. Throughout the experiments, no influence of the electron beam on the oxidation process was detected.We divide the oxidation of Cu into two processes, the first is the formation of graphene point defects, at a rate 40. The interaction between the valance electrons and ion core were described by the projector augmented wave (PAW) method42. The exchange-correlation potential was formulated by the generalised gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) scheme43. The kinetic energy cut-off of plane wave basis is set to 417 eV. First, the bulk Cu was relaxed until the force is less than 0.02 eV/Å, and the obtained primitive lattice constant is 2.5412 Å, which is about 3% mismatch of the graphene lattice constant (2.46 Å). This relaxed Cu lattice constant was employed in the following calculations. The Cu substrate was cleaved from the bulk phase with three Cu atom layers. The bottom two layers are fixed to simulate bulk Cu, while the topmost Cu layer and bilayer graphene are relaxed until the force less than 0.02 eV/Å. As determined from the ARPES results, the bilayer graphene has ~27.5° rotation, therefore, a superlattice matrix 45. The adsorption energy was calculated by The calculations were carried out using Vienna ab initio simulation package (VASP)Supplementary InformationPeer Review FileDescription of Additional Supplementary FilesSupplementary Movie 1


The fatigue crack growth rate (FCGR) of aluminium alloys under the combined influence of temperature and humidity remains a relatively unexplored area, receiving limited attention due to its intricate nature and challenges in predicting the combined impact of these factors. The challenge was to investigate and address the specific mechanisms and interactions between temperature and humidity, as in coastal environment conditions, on the FCGR of aluminium alloy. The present study conducts a comprehensive investigation into the combined influence of temperature and humidity on the FCGR of the Al6082 alloy. The fatigue pre-cracked compact tension specimens were corroded for 7 days and then subjected to various temperature and humidity conditions in a thermal chamber for 3 days to simulate coastal environments. The obtained data were analysed to determine the influence of temperature and humidity on the FCGR of the Al6082 alloy. An empirical model was also established to precisely predict fatigue life cycle values under these environmental conditions. The correlation between FCGR and fracture toughness models was also examined. The Al6082 alloy exhibits a 34% increase in the Paris constant C, indicating reduced FCGR resistance due to elevated temperature and humidity levels. At the same time, fatigue, corrosion, moisture-assisted crack propagation, and hydrogen embrittlement lead to a 27% decrease in threshold fracture toughness. The developed model exhibited accurate predictions for fatigue life cycles, and the correlation between fracture toughness and FCGR showed an error of less than 10%, indicating a strong relationship between these parameters. Aluminium alloys in the 6xxx series have gained significant popularity and are widely utilised in diverse structural applications such as marine applications , rotor bThe connection between FCGR and fracture toughness is essential in understanding the fatigue behaviour of aluminium alloys . VariousThe coastal environment, characterised by high humidity levels and fluctuating temperatures, poses unique challenges to materials due to the corrosive nature of the atmosphere . Middle Several factors, including corrosion, temperature, and humidity, influence the aluminium’s FCGR. Corrosion can lead to localized weakening of the material, accelerating crack growth. Temperature variations can affect the diffusion of atoms along the crack front, influencing crack growth rates. Additionally, higher humidity levels can promote crack propagation due to moisture and environmental factors.The correlation between FCGR and fracture toughness is critical in understanding the fatigue behaviour of the Al6082 alloy. Fracture toughness represents the material’s capability to resist crack propagation and absorb energy before failure. Higher fracture toughness values indicate better crack resistance. Meanwhile, FCGR measures the rate at which cracks extend under cyclic loading. The FCGR is influenced by factors such as stress levels and crack size.The Paris model, also known as the Paris Law or Paris–Erdogan Law, is a mathematical relationship used to predict the growth of fatigue cracks in materials over time. Three distinct regions are observed in a da/dN vs. ΔK plot. The threshold region, characterized by low ΔK values, shows minimal crack growth due to closure effects. The Paris region, with intermediate ΔK values, displays a linear connection between da/dN and ΔK, representing stable crack growth. At high ΔK values beyond the Paris region, the accelerated growth region significantly increases da/dN, leading to failure .In coastal conditions, environmental factors such as temperature and humidity impact the corrosion FCGR of aluminium alloys. Hassaan Bin Younis et al.  utilizedHowever, despite utilising various models ,22,23 toThis research aims to address this knowledge gap by studying the Al6082 alloy’s FCGR under controlled temperature and humidity conditions that simulate a coastal environment. This study focuses solely on investigating the stable crack growth regime in the da/dN vs. ΔK plot. The research is limited to examining crack growth behaviour within this region, where crack growth is predictable and stable. The influence of temperature and humidity variations on the crack propagation characteristics will be evaluated by subjecting the alloy to cyclic loading and monitoring crack growth. The novelty of this work lies in the thorough investigation of FCGR under combined temperature and humidity conditions in a coastal environment, the development of an empirical model for accurate fatigue life prediction, and the correlation between FCGR and fracture toughness models. These contributions significantly advance the understanding of the fatigue behaviour of the Al6082 alloy in coastal environments, leading to a comprehensive understanding of aluminium alloy for potential applications in coastal environments.3, elastic modulus of 70 GPa, yield strength of 320 MPa, tensile strength of 348 MPa, and elongation of 17.5%. Its fracture toughness is 28.63 MPa√m in non-corroded conditions and 23 MPa√m in high humidity conditions at room temperature [The Al6082 alloy is well-known for being strong and lightweight, making it popular in the aerospace, automotive, and marine industries . Table 1The preparation of the compact tension (CT) specimen from a 7 mm thick sheet of Al6082 alloy was undertaken following the specified geometry, as depicted in The fatigue pre-cracked CT specimens were placed in a 3.5% NaCl solution for 3 days at room temperature in order to conduct localised corrosion testing. Subsequently, the specimens were removed, air-dried, and subjected to harsh coastal environmental conditions using a thermal chamber. This chamber simulated temperatures of 20, 40, 60, and 80 °C along with humidity ranging from 40% to 90%, as shown in FCGR investigation on the Al6082 alloy is performed using a servo-hydraulic testing apparatus on a 7 mm thick specimen with a 3 mm initial fatigue pre-crack size. The servo-hydraulic testing machine can apply controlled cyclic loads to the specimen shown in In this experiment, the fatigue life cycles and related crack lengths of the Al6082 alloy were recorded under cyclic loading conditions. The change in crack size over the number of fatigue cycles provided valuable data by which to analyse the FCG behaviour. The FCGR values were also determined under different temperature and humidity conditions.I Alqathani et al.  has estaOne of the crack growth functions, the Paris–Erdogan model, is given in Equation (2) . The ParFurther understanding of the connection between FCGR (da/dN) and SIF range (ΔK) involved using the obtained data to plot da/dN against ΔK. The plot, often presented on a log–log scale, allows for a linear representation of the FCGR within a specific SIF range. By fitting the experimental data on the da/dN vs. ΔK plot, the FCG coefficients (C and m) can be determined. The da/dN vs. ΔK plot for the power law regime  was drawIt is evident from From The constant m values as humidity increases indicate that the material’s crack growth behaviour remains consistent, and that the da/dN vs. ΔK curves a–d remaiThe information presented in th), were calculated from the Paris constants C and m, as per the equation mentioned by Robertson and Ritchie [FCG was investigated by subjecting fatigue pre-cracked Al6082 alloy samples to a 3.5% NaCl solution for 168 h, followed by 72 h of temperature and humidity exposure. The presence of moisture can accelerate corrosion processes, further contributing to crack growth. Thus, the pre-crack fatigue becomes smaller as it gets deeper into the material. Small-crack fatigue thresholds, represented by the threshold SIF range (ΔK Ritchie  and Nest Ritchie .(3)∆Kth−6 mm/cycle. The threshold SIF values have been calculated and are listed in Using Equation (3), it is possible to predict the threshold SIF range for small cracks by extending the linear stable growth-rate curve downward to a level as low as 10From the data, it can be observed that an increment in the temperature leads to an increment in the threshold SIF. This means the material exhibits greater resistance to crack initiation and propagation at higher temperatures. The higher threshold SIF values indicate that the material can withstand higher SIF ranges before cracks propagate. On the other hand, as humidity increases, the threshold SIF decreases. Higher humidity levels make the material more susceptible to crack initiation and growth at lower SIF ranges. This suggests that moisture and increased corrosion potential under humid conditions can reduce the Al6082 alloy’s resistance to crack growth.th value of 0.61 MPa√m, indicates that the Al6082 alloy is susceptible to crack initiation under varying temperature and humidity conditions. The combination of fatigue, corrosion, moisture-assisted crack propagation, and hydrogen embrittlement due to high humidity contributes to the reduced threshold SIF. These factors act together, promoting crack initiation and propagation at relatively low stress levels.The observed range of threshold SIF values, with a low ΔKThe effect of temperature and humidity is discussed in two sections, focusing on the effects of temperature and humidity. This is considered an effective approach to present the findings clearly and in an organised fashion.In (a) Reduced Corrosion:As temperatures increase, the Al6082 alloy experiences a reduction in the corrosion rate, which can impact crack initiation and growth behaviour. As the temperature increases, the rate of oxide formation accelerates, resulting in a thicker and more protective oxide layer on the surface of the Al6082 alloy, as shown in 2O3) on the surface [This enhanced oxide layer acts as a barrier , effecti surface . This oxMoreover, the more stable oxide layer formed at higher temperatures adheres more firmly to the metal surface, enhancing its resistance to degradation. This increased stability and adhesion make it more difficult for aggressive agents to dislodge or degrade the oxide layer, further reducing the overall corrosion rate.The data also reveal that the activity of aggressive agents, represented by their respective values (0.46 to 0.26), decreases at higher temperatures, as shown in (b) Crack Closure:As temperatures increase, the Al6082 alloy undergoes the formation of an oxide layer, develops the presence of phase particles in dimples, and plastic deformation ahead of the crack tip, among other mechanisms . These fThe roughness around the crack tip leads to interlocking and meshing of the crack surfaces, causing crack closure and slowing down FCGR . Additio(c) Presence of Phase Particles:As the temperature rises from 20 °C to 80 °C, the Al6082 alloy’s percentage elongation also increases, resulting in improved ductility and enhanced resistance to FCGR. The samples subjected to testing at 60 °C and 80 °C exhibited noticeable phase particles, whereas their presence was considerably diminished at 20 °C and 40 °C a,b. This2Si intermetallic compound [Upon reaching a temperature of 70 °C and above and then cooling, elements such as Mg within the Al6082 alloy tend to aggregate, creating stable particles referred to as precipitates, specifically the Mgcompound . These fAt room temperature, dislocation motion is low. It increases rapidly from 30 °C to 60 °C but slows down after 60 °C. An increment in temperature from 60 °C to 80 °C minimally impacts resistance to FCG in the Al6082 alloy due to reduced dislocation motion. This reduction allows phase particles to act as effective barriers, regulating void formation, reducing crack nucleation at the crack tip, and slowing down the crack propagation, increasing resistance to fatigue crack growth.In (a) Corrosion/Corrosion Fatigue:Varying humidity levels can significantly influence the corrosion process in the Al6082 alloy and subsequently impact crack initiation and growth. The presence of chloride ions, which increase with higher humidity levels, is critical in initiating aggressive localized corrosion on the metal surface, such as pitting corrosion.At 60 °C and 40% humidity, the chloride content is relatively low (0.11%), which may result in minimal localized corrosion. As humidity increases to 60%, 70%, and 90%, the chloride content rises to 0.27%, 0.35%, and 0.53%, respectively, as shown in This increase in chloride content significantly enhances the potential for localized corrosion, particularly in pitting . The syn(b) Moisture-Assisted Crack Propagation:When a material is exposed to higher humidity levels, the absorption and diffusion of moisture into it promote the formation of a thin electrolyte layer (TEL) , this caAt low humidity conditions (40%), the reduced moisture on the material’s surface slows down the corrosion process, resulting in a less aggressive corrosion rate than in higher humidity conditions. Typical corrosion products that can form under such conditions include oxides and hydroxides . At high(c) Hydrogen Embrittlement:As humidity increases, aluminium becomes more susceptible to hydrogen embrittlement, reducing its ductility and toughness and promoting a transition from ductile to brittle fracture behaviour . The obsThese hydrogen embrittlement effects extend beyond the crack tip region, influencing the material’s mechanical behaviour. As humidity increases, the material’s crack growth behaviour becomes more influenced by hydrogen-induced embrittlement, leading to an accelerated crack growth rate. The presence of hydrogen in the material can lower the threshold for crack initiation and promote faster crack propagation, reducing the material’s fatigue life and overall resistance to crack growth. The combined impact of hydrogen embrittlement (HE) contributes to the observed reduction in aluminium’s resistance to fatigue crack growth at higher humidity levels.Hydrogen embrittlement (HE) is common in various aluminium alloy series when exposed to humid environments . HoweverDuring stage II of FCG, the distance separating fatigue striations is equal to the rate at which the fatigue crack expands within a single cycle ,58,59. AAs humidity increases from 40% to 90%, the environmental conditions become more conducive to corrosion and crack propagation. This can lead to an acceleration in the FCGR of the material. The faster crack growth rate means that the crack propagates over a larger distance during each fatigue cycle, resulting in wider spacing between individual striations on the fractured surface, as shown in Therefore, the experimental observation of increased striation spacing with increasing humidity is consistent with the higher FCGR and larger C values. The combination of these factors indicates that, as humidity increases, the material’s FCGR becomes more rapid, leading to wider spacing between the striations on the fractured surface.The study of crack propagation paths at different temperatures (ranging from 20 to 80 °C) under 80% humidity has revealed a consistent trend, i.e., that the fatigue cracks propagate along relatively straight paths , as showThis observation indicates that the fatigue cracks growth behaviour in the Al6082 alloy remains relatively stable across the tested temperature range and under specific humidity conditions. The material exhibits a consistent crack propagation pattern, indicating that the environmental conditions, including humidity and temperature, have a relatively uniform influence on the crack propagation mechanism. The consistent and relatively straight crack propagation paths imply that the material’s fatigue behaviour remains predictable and reliable under temperature and humidity conditions.The significance of this study lies in its comprehensive examination of FCGR in an Al6082 alloy under combined temperature and humidity conditions within a coastal environment. By subjecting the material to varying temperature and humidity levels, we have gained valuable insights into the material’s fatigue crack growth behaviour, crack initiation, and propagation mechanisms. This work aims to develop an empirical model to predict fatigue life cycles and the Paris constant C . BecauseThis study employs a novel curve fitting technique to develop an empirical model that predicts fatigue life cycles and the Paris constant C for the Al6082 alloy under various temperature and humidity variations within a coastal environment. The curve fitting process is applied to the experimental data points to identify the mathematical relationship that best represents the correlation between fatigue life cycles and crack growth rates with temperature and humidity.A 3D scatter plot, as shown in The equation indicates that the fatigue life cycles of the material are influenced by both temperature and humidity. A positive coefficient for T suggests that an increase in temperature is associated with an increase in the predicted fatigue life cycles. On the other hand, a negative coefficient for H implies that an increase in humidity leads to a decrease in the predicted fatigue life cycles.Similarly, a 3D scatter plot, as shown in The equation represents how temperature and humidity levels influence the Paris constant C. A negative coefficient for T suggests that an increment in temperature reduces the predicted Paris constant C. In contrast, a positive coefficient for H signifies that an increase in humidity is associated with an increase in the predicted Paris constant C. Therefore, as humidity increases, the C value increases, and the material’s resistance to FCGR decreases, and as temperature increases, the C value decreases and the resistance to FCGR increases.The novelty of this work lies in conducting a comprehensive investigation of the FCGR under combined temperature and humidity conditions in a coastal environment, developing an empirical model for accurate fatigue life prediction, and establishing a correlation between FCGR and fracture toughness models.The established empirical model of fracture toughness  is repreIn Ic) has been developed as Equation (6):The empirical model for fracture toughness ) was derived through fracture toughness testing . EmpiricLikewise, the comparison between experimental and empirical model results of fatigue life cycle values is documented in Similarly, the comparison between experimental and empirical model results of fracture toughness values is presented in The strong correlation observed between the experimental and developed models, with a maximum error of 10%, can be attributed to the alignment of the validation conditions  within the broader investigated range of temperature (20–80 °C) and humidity (40–90%). This strategic selection facilitated the verification of the consistency of the equations across diverse environmental scenarios.The combined influence of an increase in temperature and humidity levels, in line with coastal environmental conditions, decreases the FCGR resistance of the Al6082 alloy. The corrosion under higher humidity levels reduces the threshold fracture toughness, facilitating crack initiation and propagation at relatively low stress levels. This is evident from the notable decrease in threshold fracture toughness by 27% and the increase in the fatigue crack growth constant C by 34% as temperature and humidity increase.Higher temperature conditions enhance the alloy’s resistance to FCGR by introducing precipitated phase particles, facilitating the formation of an oxide layer, and inducing crack closure. In contrast, heightened humidity conditions diminish the resistance of the Al6082 alloy to FCGR due to escalated corrosion, moisture-assisted crack propagation, and hydrogen embrittlement.The precision of the developed empirical models is remarkable, showcasing an error of less than 10% in predicting Paris constant C, fatigue life cycles, and the relationship between fracture toughness and FCGR. This robust correspondence underscores the models’ reliability for both researchers and engineers. The alignment between experimental and developed models, confirmed through validation experiments, establishes a solid foundation for predicting FCGR in diverse environmental conditions.This research investigated the combined influence of temperature and humidity on fatigue crack growth rate in the Al6082 alloy within a coastal environment. The outcomes of this study hold considerable significance for the scientific community, shedding light on the complex relationship between temperature, humidity, and fatigue crack growth rate in the Al6082 alloy within coastal conditions. Through the comprehensive experimental study, the following significant conclusions were drawn: