Thickness Error Research Articles

Research on microstructure evolution and deformation mechanisms of fine-grained Mg alloys minitube during manufacturing process

In this work, high-performance Mg alloys minitubes were successfully produced through multi-pass cold drawing and intermediate annealing, and the microstructural evolution and deformation mechanisms during the manufacturing process were systematically investigated. The length of finished minitube was more than 1000 mm and the wall thickness error was less than 7.7 %. The finished minitube exhibited a yield strength (YS) of 230 ± 8 MPa, an ultimate tensile strength (UTS) of 290 ± 8 MPa, and an elongation of 23.8 ± 0.5 %. The deformation mechanisms of fine-grained Mg alloys minitubes were certainly influenced by the intricate tapestry of different cross-section reduction rates (CRRs) during cold drawing. When the CRR was about 9.38 %, the fine-grained minitubes occurred deformation through grain boundary sliding (GBS) and a small amount of dislocation slips. When CRRs were about 21.1 % and 19.6 %, the minitubes occurred deformation by activating pyramidal slips and 〈11−20〉 tension twins. The texture evolution of cold-drawn minitubes with different CRRs shown a similar pattern, wherein the texture of deformed grains constituted primary texture components of whole texture, and DRXed grains further weaken and random whole texture. The grain of annealed minitubes with 〈−12−10〉 orientation exhibited a larger average grain size than those with other orientations, which may be related to preferential grain growth. This study also demonstrated that fine grains and second phase particles (SPPs), as well as elements segregation contributed to GBS.

Research on Multi-Parameter Error Model of Backcalculated Modulus Using Abaqus Finite Element Batch Modeling Based on Python Language

The error in modulus backcalculation is a crucial component in validating the rationality and reliability of results for engineering applications. The objective of this study is to identify the theoretical limitations associated with backcalculated modulus errors under typical parameter uncertainties and to determine the primary factors contributing to these errors. Firstly, using the actual measurements or data from the Long-Term Pavement Performance (LTPP) project, the statistical distributions of errors for typical parameters in the modulus backcalculation model were determined. Subsequently, a factor level table for orthogonal experimental design was developed, leading to the construction of 81 orthogonal design experimental schemes and their corresponding theoretical pavement structure models based on the actual error distributions. The deflection responses of 81 theoretical pavement structure models were then computed using an ABAQUS finite element batch analysis method devised in Python. Furthermore, a multi-parameter error model for modulus was established using multiple linear regression and variance analysis. Finally, the theoretical limitations of modulus errors under actual errors were analyzed. The results show that the errors of thickness, load amplitude and load frequency follow a normal distribution, while the distribution of backcalculated modulus errors follows an approximate mixed Gaussian distribution. When the errors of multiple parameters are combined randomly, the modulus errors range from −100% to 595%, and the probability of the modulus errors being less than 15% is highest in the asphalt surface layer, followed by the subgrade, and then the base and subbase layers. Within the same error range, the modulus error is random. However, with different error ranges, the overall level of modulus error increases in proportion to the size of those ranges. Compared to factors such as thickness, load amplitude, and load frequency, the errors in deflections have a highly contribution rate on the modulus errors exceeding 99%.

Investigation on droplet spreading and energy conversion process on solid surface with low impinging velocity

Accurately and quantitatively tracking the droplet impinging and spreading process in theory is of paramount importance for informing and advancing engineering application. However, the existing models have problems such as large energy calculation deviations and imprecise shape hypotheses, which lead to significant theoretical errors and require in-depth correction. In this paper, a numerical model based on the laminar flow equation coupled phase field method and the dynamic contact angle model involved in the droplet impinging and spreading process is first developed and validated. The morphology and parameters of droplet spreading at various conditions and the role and influence of gravitational potential energy are further investigated. Subsequently, a semi-empirical modified spoon-like model grounded in numerical outcomes and attempting to overcome traditional assumptions limitations is advanced, with its practical applicability rigorously discussed. Results show that the droplet spreading process basically undergoes “round sphere”, “round cap”, and “pancake-like /cylinder-like” to “shallow bottomed round tray”. Changes in Weber number (We) and equilibrium contact angle (θe) marginally alter the duration, spreading size, and droplet morphology characteristics in each process. The impact of gravitational potential energy is notably modulated by process parameters, exhibiting an increase with escalating droplet diameter and density, while decreasing in response to heightened initial droplet velocity and surface tension coefficients. Conversely, it remains largely invariant to changes in droplet viscosity and equilibrium contact angle. The consideration of shape factor and viscosity modification factor allows the surface energy and viscous dissipation energy to be accurately defined, making the proposed semi-empirical modified spoon-like model exhibit good performance, for all 65 studied cases the relative errors of droplet maximum spreading length factor (βmax) and center thickness (h) fall essentially within the 5% and 10% interval respectively.

Influence of input parameters on the measurement accuracy of external clamp-on ultrasonic flowmeters: An experimental study

Abstract This study comprehensively evaluated the performance of clamp-on ultrasonic gas flowmeters at a natural gas field. The research focused on the influence of key input parameters on flow measurement accuracy during practical application of the instrument and proposed specific measures to improve measurement results. It was found that errors in outer diameter and wall thickness not only lead to flow calculation inaccuracies but also directly impact the propagation path of ultrasonic waves. Therefore, accurate input parameters are crucial to ensure precise flow results. Additionally, the study revealed that changes in installation distance have minimal effects on flow measurement results and adjustments can be made as needed to obtain better signal parameters. Variations in input temperature and pressure mainly affect the conversion coefficient from operating conditions to standard conditions, with minor impacts on flow velocity and operating flow rate. Thus, the velocity ratio method can be considered during on-site calibration to mitigate the effects of temperature and pressure changes.

Research on icing model and calculation methods

Aircraft icing seriously threatens flight safety. This paper describes a modified shallow-water icing thermodynamic model that is applicable to unstructured grids and considers the effects of changes in water physical parameters and sublimation on icing. An icing calculation method enables the automatic determination of whether freezing occurs and the type of icing. An autonomous icing calculation program is developed to extract the geometric coordinates and mesh information of the icing surface and combine this information with the multiphase flow field of air-supercooled water droplets. The icing equations in the Godnov format are discretized to produce a large-scale sparse matrix that is solved iteratively using the biconjugate gradient stabilized method. The output includes parameter distributions for the ice thickness, water film thickness, and equilibrium temperature. Taking the National Advisory Committee for Aeronautic 0012 airfoil as the study object, the results of icing simulations are compared with experimental data from an ice wind tunnel and the ice shapes calculated by the FENSAP-ICE software. The results are found to be in good agreement with the experimental data, and the ice height errors at stagnation points are less than 15%. In the case of rime ice, single-horned ice shapes are simulated for both conventional and large supercooled droplets. For mixed ice and glaze ice, double-horned ice shapes are simulated for both droplet conditions. FENSAP-ICE fails to simulate the ice horns and produces large errors in ice thickness and ice range.

Modified Layer-based Ultrasound Imaging of Irregularly Cortical Bone

Abstract Cortical bone, known for its multilayered composition with a diverse sound velocity distribution and anisotropy dependent on anatomical position, poses a challenge in conventional medical ultrasound imaging. The limitations arise due to the inability of uniform velocity to appropriately capture the intricate properties of hard tissues, leading to inaccurate reconstruction of the inner cortical layers. To tackle this complexity, a modified layer-based method utilizing a 5-layer model and estimated sound velocity was introduced for irregularly cortical bone imaging. Validated through an ex-vivo study using goat tibia, this method showcased remarkable effectiveness. The experimental outcomes revealed an ultrasound-reconstructed cortical image that closely matched the μCT-measured ground truth model, demonstrating mean cortical thickness errors of 0.31 mm. This method stands as a validated and precise approach for accurately imaging cortical bone using a 5-layer model.

Transfer Learning-Based Approach for Thickness Estimation on Optical Coherence Tomography of Varicose Veins.

In-depth mechanical characterization of veins is required for promising innovations of venous substitutes and for better understanding of venous diseases. Two important physical parameters of veins are shape and thickness, which are quite challenging in soft tissues. Here, we propose the method TREE (TransfeR learning-based approach for thicknEss Estimation) to predict both the segmentation map and thickness value of the veins. This model incorporates one encoder and two decoders which are trained in a special manner to facilitate transfer learning. First, an encoder-decoder pair is trained to predict segmentation maps, then this pre-trained encoder with frozen weights is paired with a second decoder that is specifically trained to predict thickness maps. This leverages the global information gained from the segmentation model to facilitate the precise learning of the thickness model. Additionally, to improve the performance we introduce a sensitive pattern detector (SPD) module which further guides the network by extracting semantic details. The swept-source optical coherence tomography (SS-OCT) is the imaging modality for saphenous varicose vein extracted from the diseased patients. To demonstrate the performance of the model, we calculated the segmentation accuracy-0.993, mean square error in thickness (pixels) estimation-2.409 and both these metrics stand out when compared with the state-of-art methods.

A droplet-intermixing printing method for high-uniformity pixel ink volume control based on integer programming

Inkjet printing is a promising technology for new display mass production. However, a major challenge in inkjet printing applications is pixel ink volume nonuniformity caused by the volume error of droplets ejected from multiple nozzles. This nonuniformity can lead to nonuniform pixel film thickness and Mura defects in a display panel. To address this issue, an integer programming-based droplet-intermixing printing method for high-uniformity pixel ink volume control is proposed in this study. The printing method is used to homogenize the volume of ink deposited in each pixel by intermixing droplets from different nozzles to improve the whole-panel uniformity. To ensure that the droplet intermixing results meet the printing process requirements, a specific scheduling and printing planning model for the method is established. According to the droplet volume from each nozzle and the printing pattern, the most efficient printing path and nozzle ejection action are obtained by the established model while meeting the volume uniformity requirement of pixel ink. Experiments show that the proposed printing method can realize pixel film thickness error control under ±6 nm on a 400 cm2 display substrate, and the uniformity of different pixels is less than ±4.62 %. Compared with traditional method, the achieved uniformity is improved at 45.4 % under the same conditions. This method has been applied in printed display manufacturing equipment and achieved good results.

GMSA-Net: A Transmission Line Ice Thickness Identification Network Based on Global Micro Strip Awareness.

Ice-covered transmission lines seriously affect the normal operation of the power transmission system. Resonance deicing based on different ice thicknesses is an effective method to solve the issue of ice-covered transmission lines. In order to obtain accurate ice thickness of transmission lines, this paper designs an ice thickness of transmission line recognition model based on Global Micro Strip Awareness Net (GMSA-Net) and proposes a Mixed Strip Convolution Module (MSCM) and a global micro awareness module (GMAM). The MSCM adapts to the shape of ice-covered transmission lines by using strip convolutions with different receptive fields, improving the encoder's ability to extract ice-covered features; the GMAM perceives through both global and micro parts, mining the connections between semantic information. Finally, the ice thickness of the generated segmented image is calculated using the method of regional pixel statistics. Experiments are conducted on the dataset of ice-covered transmission lines. The mean Intersection over Union (mIoU) of image segmentation reaches 96.4%, the balanced F-Score (F1-Score) is 98.1%, and the identification error of ice thickness is within 3.8%. Experimental results prove that this method can accurately identify the ice thickness of transmission lines, providing a control basis for the application of resonant deicing engineering.

Numerical investigate on the heat transfer performance and mechanical analysis of a water sublimator

Water sublimators play a critical role in efficiently managing the high thermal load of spacecraft in a vacuum environment, ensuring their proper functioning. This article focuses on a novel cold plate water sublimator driven by a porous sublimation tube structure, which is still in the theoretical research stage. Numerical methods are employed to study the evaporation, freezing, and sublimation processes, with validation against experimental data. The average absolute error of the four operating conditions is 1.33 K, and the ice layer thickness error is 8.33 %. Additionally, a method to calculate the effective thermal conductivity of porous aluminum foam is proposed, with a model error of 9 %. The sublimator's heat transfer characteristics are significantly influenced by the porosity of the aluminum foam and sublimation tubes. The impacts on temperature behavior, ice thickness, feed water pressure, and stress are carefully examined. Results reveal aluminum foam porosity of 0.7 and sublimation tube porosity of 0.3. Moreover, the study explores how different heat loads affect the sublimator's operation mode. Heat loads above 2 W/cm2 cause evaporation and dryness within the sublimation tube, while excessively small heat loads lead to ice formation and increased stress on the aluminum foam structure. These findings provide valuable insights for water sublimator design.

Comparison of early visual outcomes after SMILE using VISUMAX 800 and VISUMAX 500 for myopia: a retrospective matched case–control study

VISUMAX 800 was introduced to improve the patient experience and clinical outcomes of small incision lenticule extraction (SMILE). This was a retrospective, matched, and case–control study (1:2) controlled for preoperative central corneal thickness and refractive error that compared early refractive and visual outcomes after SMILE using VISUMAX 800 and VISUMAX 500 to treat myopia. We included 50 eyes that underwent the VISUMAX 800 SMILE and 100 eyes that underwent the VISUMAX 500 SMILE. SMILE using VISUMAX 800 was performed using the CentraLign aid for vertex centration. Cyclotorsion was controlled by an OcuLign assistant in the VISUMAX 800 group after corneal marking. Corneal higher-order aberrations (HOAs) were evaluated using a Pentacam 1 month after surgery. No differences were observed in the pre- and post-operative refractive and visual outcomes at 1 day, 1 month, and 6 months after surgery. VISUMAX 800 induced less total HOAs than VISUMAX 500 (P = 0.036). No statistically significant differences were observed in the amounts of induced spherical aberrations or vertical and horizontal comas. No differences were observed in the 1 month and 6 months refractive and visual outcomes between two SMILE procedures, except for VISUMAX 800, which resulted in lower postoperative total HOAs than VISUMAX 500.

A numerical study of heterogeneous nucleation of ice crystals and frost layer growth on horizontal cold surfaces

In engineering applications, the formation and growth of frost layers can significantly affect the normal operation of equipment, leading to undesirable influences. Therefore, it is imperative to understand the frost formation mechanisms as a basis for developing effective anti-frosting and defrosting methodologies. This study proposes a model for the growth of horizontal cold surface frost layers using the classical nucleation theory and the Eulerian multiphase flow model. Compared to numerous models that investigate the frost formation issues using the computational fluid dynamics (CFD) method, our proposed model takes into account the crystal growth period (the heterogeneous nucleation process of ice). The predicted results of the proposed model were found to be in good agreement with the data collected from five related experimental studies. In this regard, the maximum frost layer thickness error was 23.9 % with a mean error of 5.1 %, and the maximum density error was 22.8 % with a mean error of 8.1 %. Compared to existing models in the literature, the proposed model can reduce the maximum thickness and density uncertainties by 17.4 % and 10.2 %, respectively. Additionally, the effects of the surface contact angle and environmental parameters on the nucleation process were analyzed using the established model. It was found that a larger contact angle, higher cold surface temperature, and lower air temperature, humidity, and velocity were unfavorable conditions for supporting the formation and growth of ice crystals. Moreover, the nucleation completion time was shortened with the increase in the moist air supersaturation degree, varying as an exponential function. The findings of this study provide an important theoretical basis for the development of optimizing strategies for anti-frosting and defrosting.

Quality control of NiCr-Cr3C2-hBN@Ni coating on thin-walled GH4169 alloy surface prepared by plasma spraying

As equipment lightweight trends progress, thin-walled structures have seen extensive application in critical aerospace components. Nevertheless, the aero-engine tail nozzle flaps are exposed to the harsh operating conditions of high-temperature friction, so there is an urgent requirement to prepare wear-resistant, self-lubricating coatings with a wide range of temperatures for their protection. Due to the poor rigidity and weak strength of thin-walled workpieces and complex forms of structural stresses, the processing is extremely difficult. In order to solve the thermal deformation problem of coating workpieces prepared by spraying on the surface of thin-walled workpieces, the effects of spraying path, cooling airflow, and spraying interval on the thermal force field of thin-walled workpieces to prepare NiCr-Cr3C2-hBN@Ni coating are investigated in this study using finite element simulation. As a result, the deformation and stress of thin-walled workpieces can be minimized by adding back-side cooling air during the spraying process and moving the cooling air with the gun in a set interval, with the maximum warpage and maximum stress being less than 2.366 mm and 0.177 GPa, respectively. During the spraying process by simulating the optimum spraying process, no significant warpage of the substrate occurred and the coating was sprayed with uniform thickness. Typically, the thickness error rate is 16.7 %, and the coating hardness reaches 15–20 GPa, with excellent tribological properties in a wear rate of 10−5 mm3·N−1·m−1 and 10−6 mm3·N−1·m−1, which protects the workpiece effectively.

Preparation and measurement of an x-ray Laue-type monochromator based on a WSi2/Si multilayer

The Laue-type multilayer monochromator (LMM) is a promising optical element with a small size and high efficiency in a synchrotron radiation facility. By the dynamical diffraction theory, using DC magnetron sputtering technology, an LMM with a total thickness of 47 µm and a periodic thickness of 4.7 nm WSi2/Si multilayer at 26 keV is designed and fabricated. During the preparation, the total number of layers is up to 20000, and every 300th layer of Si is replaced by WSi2 as the marker, so the multilayer is divided into 67 areas. The cross section of the multilayer is measured by a scanning electron microscope (SEM), and the marker region thickness error is 0.28% (RMS). The diffraction test experiment of the LMM is carried out at the Shanghai synchrotron radiation facility (SSRF). The 1st-order peak angle is 5.05 mrad, and the efficiency is 75.0%, which is close to the theoretical calculation result of 5.1 mrad and 79.1%. The Darwin width of the LMM is 0.17 mrad which is equal to the theoretical calculation. Based on the Bragg’s diffraction equation, the energy resolution (ΔE/E) is 3.3%.

Changes in peripapillary retinal nerve fibre layer and ocular parameters in acute anterior uveitis

ABSTRACT Clinical relevance Acute anterior uveitis (AAU) can lead to the thickening of the peripapillary retinal nerve fibre layer (pRNFL) and induce refractive changes during its active phase. Background AAU is a common form of uveitis characterised by inflammation in the anterior chamber. A notable prevalence of optical coherence tomography – defined pRNFL thickening was observed among patients with AAU. The alterations in pRNFL thickness and their associations with other relevant ocular parameters in patients with AAU were investigated. Methods A retrospective, consecutive case series was conducted at a specialised uveitis referral clinic in Taiwan. This study gathered data on various demographic characteristics and various ocular parameters, namely anterior chamber cell grading, refractive error, best-corrected visual acuity, intraocular pressure, and optical coherence tomography measurements. A comparative analysis of baseline and subsequent follow-up data was conducted. Additionally, this study examined the correlations between alterations in pRNFL thickness and various ocular parameters. Twenty-one patients with AAU (21 affected eyes/21 unaffected eyes) were examined. Results Initial measurements revealed pRNFL thickening in 20 patients. Treatment led to significant improvements in best-corrected visual acuity, intraocular pressure recovery, and pRNFL thickening (p < 0.01). The correlation between changes in pRNFL thickness and best-corrected visual acuity was weak (r = 0.20, p = 0.41). By contrast, a significant negative correlation was identified between changes in pRNFL thickness and refractive error alterations (r = −0.71, p = 0.01). Conclusion This study demonstrated that AAU is associated with pRNFL thickening, which in turn is inversely correlated with changes in refractive error alterations throughout the disease course. Monitoring changes in pRNFL thickness can be effective in assessing ocular inflammation status.

Surface reconstruction and thickness error calculation of optical components with a complex curved surface

The increasing demand for free-form irregular optical components in both military and civilian sectors has made the inspection of such unique shapes a central challenge that hinders their production and use. In particular, the shape and thickness errors of low- and medium-precision components thermally pressed from flat optical materials are greater than those of hard brittle optical components fabricated by subtractive manufacturing, and the resulting impact on human vision is more severe. Reasonable, convenient, efficient, and accurate 3D scanning and data processing for surface reconstruction that combines application scenarios and batch manufacturing needs are urgently needed. Based on the principles of optical ray tracing and triangulation processing, the sampling and calculation of optical path thickness proposed in this paper effectively establish a theoretical model for macroscopic distortion, providing a reasonable solution for distortion correction, batch manufacturing of free-form surface pressing formed components, and defect repair.

Fringe Projection Profilometry for Three-Dimensional Measurement of Aerospace Blades

The aero-engine serves as the “heart” of an aircraft and is a primary factor determining the aircraft’s performance. Among the crucial components in the core of aero-engines, aero-engine compressor blades stand out as extremely important. They are not only numerous but also characterized by a multitude of parameters, making them the most complex parts in an aero-engine. This paper aims to address the trade-off between accuracy and efficiency in the existing measurement methods for asymmetric blades. Non-contact measurements were conducted using a structured light system composed of a stereo camera and a DLC projector. The point cloud data of the blades are processed using methods such as the PCA (Principal Component Analysis) algorithm, binary search, and least squares fitting. This paper established a fringe-projection profilometry light sensor system for the multi-view measurement of the blades. High-precision rotary tables are utilized to rotate and extract complete spatial point cloud data of aviation blades. Finally, measurements and comparative experiments on the blade body are conducted. The obtained blade point cloud data undergo sorting and denoising processes, resulting in improved measurement accuracy. The measurement error of the blade chord length is 0.001%, the measurement error of blade maximum thickness is 0.895%, compared to CMM (Coordinate Measuring Machine), where the measurement error of chord is 0.06%.

Measurement of Nuchal Translucency Thickness in First Trimester Ultrasound Foetal Images Using Markov Random Field

Background The first-trimester ultrasound assessment of nuchal translucency (NT) thickness has lately been recommended as the most helpful sign in early screening for prenatal chromosomal disorders. Increased foetal NT thickness between 11 and 13+6 weeks of gestation is a frequent phenotypic manifestation of chromosomal abnormalities as well as a variety of foetal deformities and genetic disorders. Purpose At the moment, clinicians conduct the measurement manually. The measurement may take a long time to complete, requires highly competent operators, and is susceptible to mistakes. So, an automatic method is required for NT measurement. Materials and Methods This study proposes a Markov random Field-based approach for contextually segmenting the NT area from foetal pictures and offering a quick and inexpensive diagnostic even during the early stages of pregnancy. Results Proposed method gives maximum NT thickness error 0.03 and minimum NT thickness error 0.04. Conclusion The proposed research work developed a prototype for an automated NT thickness measuring system. This study proposes an MRF-based model for segmentation and detection of NT area from foetal pictures which gives error is less than other methods.

A low-cost and open-source approach for supraglacial debris thickness mapping using UAV-based infrared thermography

Abstract. Debris-covered glaciers exist in many mountain ranges and play an important role in the regional water cycle. However, modelling the surface mass balance, runoff contribution and future evolution of debris-covered glaciers is fraught with uncertainty as accurate observations on small-scale variations in debris thickness and sub-debris ice melt rates are only available for a few locations worldwide. Here we describe a customised low-cost unoccupied aerial vehicle (UAV) for high-resolution thermal imaging of mountain glaciers and present a complete open-source pipeline that facilitates the generation of accurate surface temperature and debris thickness maps from radiometric images. First, a radiometric orthophoto is computed from individual radiometric UAV images using structure-from-motion and multi-view-stereo techniques. User-specific calibration and correction procedures can then be applied to the radiometric orthophoto to account for atmospheric and environmental influences that affect the radiometric measurement. The thermal orthophoto reveals distinct spatial variations in surface temperature across the surveyed debris-covered area. Finally, a high-resolution debris thickness map is derived from the corrected thermal orthophoto using an empirical or inverse surface energy balance model that relates surface temperature to debris thickness and is calibrated against in situ measurements. Our results from a small-scale experiment on the Kanderfirn (also known as Kander Neve) in the Swiss Alps show that the surface temperature and thickness of a relatively thin debris layer (ca. 0–15 cm) can be mapped with high accuracy using an empirical or physical model. On snow and ice surfaces, the mean deviation of the mapped surface temperature from the melting point (∼ 0 ∘C) was 0.6 ± 2.0 ∘C. The root-mean-square error of the modelled debris thickness was 1.3 cm. Through the detailed mapping, typical small-scale debris features and debris thickness patterns become visible, which are not spatially resolved by the thermal infrared sensors of current-generation satellites. The presented approach paves the way for comprehensive high-resolution supraglacial debris thickness mapping and opens up new opportunities for more accurate monitoring and modelling of debris-covered glaciers.

Research on intelligent identification algorithm of coal and rock strata based on Hilbert transform and amplitude stacking

AbstractThe high precision identification of coal–rock layers is a significant challenge in intelligent mining. There is a large amount of electromagnetic noise and metal reflector signals in the full space detection environment of mining roadway, which makes it hard to distinguish the reflected waves at interface from a set of echo signals generated by the interface due to the similar amplitudes among them. So the method of identifying layers solely based on amplitude characteristics has poor stability and accuracy in coal mining environments. This paper proposes a method for identifying coal–rock layers based on Hilbert transform and tracking–scanning–stacking technology. There are two steps to achieve the recognition of air–coal–rock interfaces. First, by analysing the instantaneous amplitude spectrum obtained from the Hilbert transform, the first extreme point that is always the maximum value within a wavelength range is determined as the rough position of the air–coal interface. To solve the problem of recognition errors caused by noise and energy dispersion, the density difference method is used to remove discrete points. Second, the precise position of the air–coal interface is determined by tracking the extreme points within the 1.5 wavelength range around the rough position, and using the amplitude stacking method to quantitatively analyse and compare the degree of energy concentration. The data between zero time and the reflected waves at the air–coal interface is removed to avoid the impact of them on the recognition of the coal–rock interface. Results of physical model experiments and actual coal mine experiments show that this method yields better results and has high stability compared to conventional recognition method. Moreover, the average relative thickness errors are 4.5% for air layer and 4.2% for coal layer.