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Keywords = inhomogeneous acoustic distribution

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25 pages, 2486 KiB  
Article
Influence of Intense Internal Waves Traveling Along an Acoustic Path on Source Holographic Reconstruction in Shallow Water
by Sergey Pereselkov, Venedikt Kuz’kin, Matthias Ehrhardt, Sergey Tkachenko, Alexey Pereselkov and Nikolay Ladykin
J. Mar. Sci. Eng. 2025, 13(8), 1409; https://doi.org/10.3390/jmse13081409 - 24 Jul 2025
Viewed by 316
Abstract
This paper studies how intense internal waves (IIWs) affect the holographic reconstruction of the sound field generated by a moving source in a shallow-water environment. It is assumed that the IIWs propagate along the acoustic path between the source and the receiver. The [...] Read more.
This paper studies how intense internal waves (IIWs) affect the holographic reconstruction of the sound field generated by a moving source in a shallow-water environment. It is assumed that the IIWs propagate along the acoustic path between the source and the receiver. The presence of IIWs introduces inhomogeneities into the waveguide and causes significant mode coupling, which perturbs the received sound field. This paper proposes the use of holographic signal processing (HSP) to eliminate perturbations in the received signal caused by mode coupling due to IIWs. Within the HSP framework, we examine the interferogram (the received sound intensity distribution in the frequency–time domain) and the hologram (the two-dimensional Fourier transform of the interferogram) of a moving source in the presence of space–time inhomogeneities caused by IIWs. A key finding is that under the influence of IIWs, the hologram is divided into two regions that correspond to the unperturbed and perturbed components of the sound field. This hologram structure enables the extraction and reconstruction of the interferogram corresponding to the unperturbed field as it would appear in a shallow-water waveguide without IIWs. Numerical simulations of HSP application under the realistic conditions of the SWARM’95 experiment were carried out for stationary and moving sources. The results demonstrate the high efficiency of holographic reconstruction of the unperturbed sound field. Unlike matched field processing (MFP), HSP does not require prior knowledge of the propagation environment. These research results advance signal processing methods in underwater acoustics by introducing efficient HSP methods for environments with spatiotemporal inhomogeneities. Full article
(This article belongs to the Section Physical Oceanography)
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23 pages, 1890 KiB  
Article
Physics-Informed Neural Networks for Modal Wave Field Predictions in 3D Room Acoustics
by Stefan Schoder
Appl. Sci. 2025, 15(2), 939; https://doi.org/10.3390/app15020939 - 18 Jan 2025
Cited by 1 | Viewed by 2114
Abstract
The generalization of Physics-Informed Neural Networks (PINNs) used to solve the inhomogeneous Helmholtz equation in a simplified three-dimensional room is investigated. PINNs are appealing since they can efficiently integrate a partial differential equation and experimental data by minimizing a loss function. However, a [...] Read more.
The generalization of Physics-Informed Neural Networks (PINNs) used to solve the inhomogeneous Helmholtz equation in a simplified three-dimensional room is investigated. PINNs are appealing since they can efficiently integrate a partial differential equation and experimental data by minimizing a loss function. However, a previous study experienced limitations in acoustics regarding the source term. A challenging but realistic excitation case is a confined (e.g., single-point) excitation area, yielding a smooth spatial wave field periodically with the wavelength. Compared to studies using smooth (unrealistic) sound excitation, the network’s generalization capabilities regarding a realistic sound excitation are addressed. Different methods like hyperparameter optimization, adaptive refinement, Fourier feature engineering, and locally adaptive activation functions with slope recovery are tested to tailor the PINN’s accuracy to an experimentally validated finite element analysis reference solution computed with openCFS. The hyperparameter study and optimization are conducted regarding the network depth and width, the learning rate, the used activation functions, and the deep learning backends (PyTorch 2.5.1, TensorFlow 2.18.0 1, TensorFlow 2.18.0 2, JAX 0.4.39). A modified (feature-engineered) PINN architecture was designed using input feature engineering to include the dispersion relation of the wave in the neural network. For smoothly (unrealistic) distributed sources, it was shown that the standard PINNs and the feature-engineered PINN converge to the analytic solution, with a relative error of 0.28% and 2×104%, respectively. The locally adaptive activation functions with the slope lead to a relative error of 0.086% with a source sharpness of s=1 m. Similar relative errors were obtained for the case s=0.2 m using adaptive refinement. The feature-engineered PINN significantly outperformed the results of previous studies regarding accuracy. Furthermore, the trainable parameters were reduced to a fraction by Bayesian hyperparameter optimization (around 5%), and likewise, the training time (around 3%) was reduced compared to the standard PINN formulation. By narrowing this excitation towards a single point, the convergence rate and minimum errors obtained of all presented network architectures increased. The feature-engineered architecture yielded a one order of magnitude lower accuracy of 0.20% compared to 0.019% of the standard PINN formulation with a source sharpness of s=1 m. It outperformed the finite element analysis and the standard PINN in terms time needed to obtain the solution, needing 15 min and 30 s on an AMD Ryzen 7 Pro 8840HS CPU (AMD, Santa Clara, CA, USA) for the FEM, compared to about 20 min (standard PINN) and just under a minute of the feature-engineered PINN, both trained on a Tesla T4 GPU (NVIDIA, Santa Clara, CA, USA). Full article
(This article belongs to the Special Issue Artificial Intelligence in Acoustic Simulation and Design)
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18 pages, 13069 KiB  
Article
Horizontal-Transverse Coherence of Bottom-Received Acoustic Field in Deep Water with an Incomplete Sound Channel
by Qianyu Wang, Zhaohui Peng, Bo Zhang, Feilong Zhu, Wenyu Luo, Tongchen Wang, Lingshan Zhang and Junjie Mao
J. Mar. Sci. Eng. 2024, 12(12), 2354; https://doi.org/10.3390/jmse12122354 - 21 Dec 2024
Viewed by 833
Abstract
The horizontal-transverse coherence of low-frequency (300 Hz) and long-range (10–40 km) acoustic fields near the bottom in deep water is investigated based on experimental data obtained from the South China Sea. The results indicate that the horizontal-transverse coherence length exhibits a strong dependence [...] Read more.
The horizontal-transverse coherence of low-frequency (300 Hz) and long-range (10–40 km) acoustic fields near the bottom in deep water is investigated based on experimental data obtained from the South China Sea. The results indicate that the horizontal-transverse coherence length exhibits a strong dependence on the source-receiver distance, with fluctuations consistent with sound intensity trends. In high-intensity regions, the horizontal-transverse coherence is relatively high, with a coherence length exceeding 600 λ, where λ is the acoustic wavelength, whereas in low-intensity regions, the horizontal-transverse coherence decreases significantly, with the coherence length shortening to 10–30 λ. The physical mechanisms underlying the horizontal-transverse coherence are analyzed using the ray theory. In high-intensity regions, the energy of the dominant ray (the ray with the highest energy) accounts for over 70% of the total energy of the rays, exerting a decisive influence on the coherence coefficient and leading to stable horizontal-transverse coherence in the received acoustic field. In contrast, in low-intensity regions, the energy distribution is dispersed, and when amplitude and phase disturbances due to spatial inhomogeneity are introduced, the horizontal coherence deteriorates significantly. The numerical simulations are also performed, and the results are consistent with the experimental observations. Full article
(This article belongs to the Section Ocean Engineering)
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19 pages, 4721 KiB  
Article
Study and Analysis of the Thunder Source Location Error Based on Acoustic Ray-Tracing
by Jinyuan Guo, Caixia Wang, Jia Xu, Song Jia, Hui Yang, Zhuling Sun and Xiaobao Wang
Remote Sens. 2024, 16(21), 4000; https://doi.org/10.3390/rs16214000 - 28 Oct 2024
Viewed by 854
Abstract
Error analysis and estimation of thunder source location results is a prerequisite for obtaining accurate location results of thunder sources, which is of great significance for a deeper understanding of the physical process of lightning channel discharges. Most of the thunder source location [...] Read more.
Error analysis and estimation of thunder source location results is a prerequisite for obtaining accurate location results of thunder sources, which is of great significance for a deeper understanding of the physical process of lightning channel discharges. Most of the thunder source location algorithms are based on the simplified model of the straight-line propagation of acoustic waves to determine the location of the thunder source; however, the acoustic wave is affected by the inhomogeneity of the atmosphere medium in the propagation process and its acoustic ray will be bent. Temperature and humidity are the main factors affecting the vertical distribution of the velocity of sound in the atmosphere, therefore, it is necessary to study the changes in location errors under the models of uniform vertical distribution of temperature only and uniform vertical distribution of humidity only. This paper focuses on the theory of acoustic ray-tracing in neglecting the presence of the wind and the acoustic attenuation and the theoretical derivation of the location error of thunder source inversion for the three models is carried out by using MATLAB R2019b programming. Then, simulation analysis and comparative study on the variation law of thunder source location error with the height of the source, ground temperature, ground humidity, and array position under the three models are carried out. The results of the study show that the maximum location error can be obtained from the straight-line propagation model, the location error obtained from the model of uniform vertical distribution of temperature only is the second, and the location error obtained from the model of uniform vertical distribution of humidity only is the least and can be negligible compared to the first two models. In the trend of error variation, the variation of location error with temperature and humidity is relatively flat in the first two models; however, the variation of location error with the height of the thunder source is more drastic, which can be more than 80%. The location error obtained from the array inversion closer to the thunder source increases linearly with the height of the thunder source, the location error obtained from the more distant array inversion shows a fast-decreasing trend at the height of the thunder source from 500 to 3500 m, and a flat trend above 3500 m. The location error varies relatively smoothly with the height of the thunder source, the ground temperature, and the ground humidity in the model of uniform vertical distribution of humidity only. In addition, the position of the array also has an important effect on lightning location. The further the horizontal distance from the source, the greater the location error will be obtained in the first two models, and when the thunder source is at a low height and detected at a long distance, the location error will be very large, so relevant data should be modified in actual observation. Full article
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13 pages, 4933 KiB  
Article
Spatial-Dependent Spectral Response of Acousto-Optic Tunable Filters with Inhomogeneous Acoustic Distribution
by Shujing Sun, Huijie Zhao, Qi Guo and Yijie Wang
Materials 2024, 17(18), 4537; https://doi.org/10.3390/ma17184537 - 15 Sep 2024
Cited by 2 | Viewed by 1148
Abstract
The spectral response of an acousto-optic tunable filter (AOTF) is crucial for an AOTF based spectral imaging system. The acousto-optic (AO) interaction within the spatial-distributed area of the acoustic field determines the spectral response of the light incidence. Assuming an ideally uniform acoustic [...] Read more.
The spectral response of an acousto-optic tunable filter (AOTF) is crucial for an AOTF based spectral imaging system. The acousto-optic (AO) interaction within the spatial-distributed area of the acoustic field determines the spectral response of the light incidence. Assuming an ideally uniform acoustic field distribution, phase-matching geometries can be applied to calculate the anisotropic Bragg diffraction in AO interactions, determining the wavelength and direction of the diffracted light. In this ideal scenario, the wavelength of the diffracted light depends solely on the direction of the incident light. However, due to the non-ideal nature of the acoustic field, the wavelength of the diffracted light exhibits slight variations with incident position. In this paper, an analytical model is proposed to calculate the spatial-dependent spectral response of the diffracted light under non-uniform acoustic field distribution. The study computes the variation pattern of the diffracted light amplitude caused by the inhomogeneous acoustic distribution. The theoretical considerations and computational model are confirmed by AOTF frequency scanning experiments. The study demonstrates that the distribution of the acoustic field leads to non-uniform spatial-spectral response in the AOTF, and the spatial AO interaction computational model can provide data support for calibrating AOTF systems in imaging applications. Full article
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18 pages, 21647 KiB  
Article
Distributed Acoustic Sensing Based on Microtremor Survey Method for Near-Surface Active Faults Exploration: A Case Study in Datong Basin, China
by Ao Song, Junjie Ren, Aichun Liu, Guangwei Zhang, Xiaoqiong Lei and Hao Zhang
Int. J. Environ. Res. Public Health 2023, 20(4), 2915; https://doi.org/10.3390/ijerph20042915 - 7 Feb 2023
Cited by 4 | Viewed by 2360
Abstract
Active fault detection has an important significance for seismic disaster prevention and mitigation in urban areas. The high-density station arrays have the potential to provide a microtremor survey solution for shallow seismic investigations. However, the resolution limitation of the nodal seismometer and small-scale [...] Read more.
Active fault detection has an important significance for seismic disaster prevention and mitigation in urban areas. The high-density station arrays have the potential to provide a microtremor survey solution for shallow seismic investigations. However, the resolution limitation of the nodal seismometer and small-scale lateral velocity being inhomogeneous hinder their application in near-surface active fault exploration. Distributed acoustic sensing (DAS) has been developed rapidly in the past few years; it takes an optical fiber as the sensing medium and signal transmission medium, which can continuously detect vibration over long distances with high spatial resolution and low cost. This paper tried to address the issue of near-surface active fault exploration by using DAS. We selected a normal fault in the southern Datong basin, a graben basin in the Shanxi rift system in north China, to carry out the research. Microtremor surveys across the possible range of the active fault were conducted using DAS and nodal seismometers, so as to obtain a shallow shear wave velocity model. Meanwhile, we applied a Brillouin optical time domain reflectometer (BOTDR) and distributed temperature sensing (DTS) to monitor the real-time fluctuation of ground temperature and strain. Our results show that the resolution of the deep structures of the fault via the microtremor survey based on DAS is lower than that via the seismic reflection; whereas, their fault location is consistent, and the near-surface structure of the fault can be traced in the DAS results. In addition, both the BOTDR and DTS results indicate an apparent consistent change in ground temperature and strain across the fault determined by the DAS result, and the combination of surface monitoring and underground exploration will help to accurately avoid active faults and seismic potential assessment in urban areas. Full article
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15 pages, 58751 KiB  
Article
Revealing the Microstructural Aspects of the Corrosion Dynamics in Rapidly Solidified Mg-Zn-Y Alloys Using the Acoustic Emission Technique
by Daria Drozdenko, Michiaki Yamasaki, Kristián Máthis, Patrik Dobroň, Shin-ichi Inoue and Yoshihito Kawamura
Materials 2021, 14(24), 7828; https://doi.org/10.3390/ma14247828 - 17 Dec 2021
Cited by 3 | Viewed by 2442
Abstract
This work was focused on revealing the relation between the microstructure and corrosion dynamics in dilute Mg97.94Zn0.56Y1.5 (at.%) alloys prepared by the consolidation of rapidly solidified (RS) ribbons. The dynamics of the corrosion were followed by common electrochemical [...] Read more.
This work was focused on revealing the relation between the microstructure and corrosion dynamics in dilute Mg97.94Zn0.56Y1.5 (at.%) alloys prepared by the consolidation of rapidly solidified (RS) ribbons. The dynamics of the corrosion were followed by common electrochemical methods and the acoustic emission (AE) technique. AE monitoring offers instantaneous feedback on changes in the dynamics and mode of the corrosion. In contrast, the electrochemical measurements were performed on the specimens, which had already been immersed in the solution for a pre-defined time. Thus, some short-term corrosion processes could remain undiscovered. Obtained results were completed by scanning electron microscopy, including analysis of a cross-section of the corrosion layer. It was shown that the internal strain distribution, the grain morphology, and the distribution of the secondary phases play a significant role in the corrosion. The alloys are characterized by a complex microstructure with elongated worked and dynamically recrystallized α-Mg grains with an average grain size of 900 nm. Moreover, the Zn- and Y-rich stacking faults (SFs) were dispersed in the grain interior. In the alloy consolidated at a lower extrusion speed, the homogeneous internal strain distribution led to uniform corrosion with a rate of 2 mm/year and a low hydrogen release. The consolidation at a higher extrusion speed resulted in the formation of uneven distribution of internal strains with remaining high strain levels in non-recrystallized grains, leading to inhomogeneous growth and breakdown of the corrosion layers. Therefore, homogeneity of the internal strain distribution is of key importance for the uniform formation of a protective layer. Full article
(This article belongs to the Special Issue Microstructure, Texture, Properties of Mg Alloy and Its Application)
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28 pages, 9019 KiB  
Article
Quantification of Wide-Area Norwegian Spring-Spawning Herring Population Density with Ocean Acoustic Waveguide Remote Sensing (OAWRS)
by Daniel Duane, Olav Rune Godø and Nicholas C. Makris
Remote Sens. 2021, 13(22), 4546; https://doi.org/10.3390/rs13224546 - 12 Nov 2021
Cited by 6 | Viewed by 2458
Abstract
Norwegian spring-spawning herring are a critical economic resource for multiple nations in the North Atlantic and a keystone species of the Nordic Seas ecosystem. Given the wide areas that the herring occupy, it is difficult to accurately measure the population size and spatial [...] Read more.
Norwegian spring-spawning herring are a critical economic resource for multiple nations in the North Atlantic and a keystone species of the Nordic Seas ecosystem. Given the wide areas that the herring occupy, it is difficult to accurately measure the population size and spatial distribution. Ocean Acoustic Waveguide Remote Sensing (OAWRS) was used to instantaneously measure the areal population density of Norwegian herring over more than one thousand square kilometers in spawning grounds near Ålesund, Norway. In the vicinity of the Ålesund trench near peak spawning, significant attenuation in signal-to-noise ratio and mean sensing range was observed after nautical sunset that had not been observed in previous OAWRS surveys in the Nordic Seas or in other regions. We show that this range-dependent decay along a given propagation path was caused by attenuation through dense herring shoals forming at sunset and persisting through the evening for transmissions near the swimbladder resonance peak. OAWRS transmissions are corrected for attenuation in a manner consistent with waveguide scattering theory and simultaneous downward directed local line-transect measurements in the region in order to produce instantaneous wide-area population density maps. Corresponding measured reductions in the median sensing range over the azimuth before ambient noise limitation are shown to be theoretically predictable from waveguide scattering theory and observed population densities. Spatial-temporal inhomogeneities in wide-area herring distributions seen synoptically in OAWRS imagery show that standard sparsely spaced line-transect surveys through this region during spawning can lead to large errors in the estimated population due to spatial and temporal undersampling. Full article
(This article belongs to the Section Ocean Remote Sensing)
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14 pages, 2159 KiB  
Article
Determination of Prestress in Circular Inhomogeneous Solid and Annular Plates in the Framework of the Timoshenko Hypotheses
by Ivan V. Bogachev
Appl. Sci. 2021, 11(21), 9819; https://doi.org/10.3390/app11219819 - 20 Oct 2021
Cited by 4 | Viewed by 1759
Abstract
Determination of prestress fields in structures is of the utmost importance, since they have a significant impact on operational characteristics, and their level and distribution must be strictly controlled. In this paper, we present modeling of bending vibrations of solid and annular round [...] Read more.
Determination of prestress fields in structures is of the utmost importance, since they have a significant impact on operational characteristics, and their level and distribution must be strictly controlled. In this paper, we present modeling of bending vibrations of solid and annular round inhomogeneous prestressed plates within the framework of the Timoshenko hypotheses. New inverse problems of prestress identification in plates are studied on the basis of the acoustic response subjected to some probing load. To solve direct problems on calculating oscillations and amplitude-frequency characteristics, a computational Galerkin-method-based scheme has been developed. In order to treat the inverse problems, we use a special projection approach based on the constructed weak problems statements, which makes it possible to determine the desired characteristics in the given classes of functions. The developed techniques for solving direct problems are implemented in the form of software packages realized via Maple. For both solid and annular plates, we estimate the sensitivity of the amplitude-frequency characteristics the values of which are used as the additional data in the inverse problems to a change in the prestress level; we conclude that the most favorable frequency range should be selected in the resonance vicinity. We have conducted a series of computational tests on reconstructing the plate’s prestresses of various levels and distribution patterns (decreasing, increasing, sign-changing laws). The results of computational tests revealed that the technique developed allows for the determination of the prestresses with a low error for two cases: when the cause of prestress formation and its type are known and when arbitrary prestress changing laws are considered. Full article
(This article belongs to the Special Issue Physics and Mechanics of New Materials and Their Applications 2021)
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14 pages, 5445 KiB  
Article
Identification for Abutment Stress by Drilling Cuttings
by Jian Tan, Yunliang Tan, Zihui Wang and Yubao Zhang
Appl. Sci. 2021, 11(20), 9467; https://doi.org/10.3390/app11209467 - 12 Oct 2021
Cited by 4 | Viewed by 1725
Abstract
The concentration of abutment pressure acting on coal seams induced by mining is a key factor to trigger rock burst. Understanding of abutment pressure or stress concentration is fundamental in preventing and controlling rock burst. The influence on abutment pressure fluctuation caused by [...] Read more.
The concentration of abutment pressure acting on coal seams induced by mining is a key factor to trigger rock burst. Understanding of abutment pressure or stress concentration is fundamental in preventing and controlling rock burst. The influence on abutment pressure fluctuation caused by the inhomogeneity of coal seams needs to be considered, but it is difficult to obtain by the present usual ways such as acoustic transmission, electromagnetic wave transmission, etc. In this article, the relationship between the amount of cuttings drilled in a coal seam and stress level was analyzed by considering the effect of drilling cutting expansion, and the drilling cutting test was carried out in Xinglongzhuang Coal Mine, Shandong Energy Ltd. It is found that the amount of cuttings drilled is positively related to the degree of stress concentration in both the plastic fracture zone and elastic zone. The amount of drilling cuttings is closely related to the roof weighting. In addition, the irregular fluctuation of drilling cuttings is an approximate map of distribution of stress concentration because of the non-uniformity of cracks and other defects in the coal seam. In order to meet the need of rock burst prevention by accurate pressure relief in high-stress zones, enough boreholes are needed. Full article
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19 pages, 2403 KiB  
Article
Numerical Characterization of Acoustic Cavitation Bubbles with Respect to the Bubble Size Distribution at Equilibrium
by Kaouther Kerboua, Oualid Hamdaoui and Abdulaziz Alghyamah
Processes 2021, 9(9), 1546; https://doi.org/10.3390/pr9091546 - 30 Aug 2021
Cited by 11 | Viewed by 2817
Abstract
In addition to bubble number density, bubble size distribution is an important population parameter governing the activity of acoustic cavitation bubbles. In the present paper, an iterative numerical method for equilibrium size distribution is proposed and combined to a model for bubble counting, [...] Read more.
In addition to bubble number density, bubble size distribution is an important population parameter governing the activity of acoustic cavitation bubbles. In the present paper, an iterative numerical method for equilibrium size distribution is proposed and combined to a model for bubble counting, in order to approach the number density within a population of acoustic cavitation bubbles of inhomogeneous sizing, hence the sonochemical activity of the inhomogeneous population based on discretization into homogenous groups. The composition of the inhomogeneous population is analyzed based on cavitation dynamics and shape stability at 300 kHz and 0.761 W/cm2 within the ambient radii interval ranging from 1 to 5 µm. Unstable oscillation is observed starting from a radius of 2.5 µm. Results are presented in terms of number probability, number density, and volume probability within the population of acoustic cavitation bubbles. The most probable group having an equilibrium radius of 3 µm demonstrated a probability in terms of number density of 27%. In terms of contribution to the void, the sub-population of 4 µm plays a major role with a fraction of 24%. Comparisons are also performed with the homogenous population case both in terms of number density of bubbles and sonochemical production of HO,HO2, and H under an oxygen atmosphere. Full article
(This article belongs to the Special Issue Redesign Processes in the Age of the Fourth Industrial Revolution)
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14 pages, 4065 KiB  
Article
Formation of Thermal Lesions in Tissue and Its Optimal Control during HIFU Scanning Therapy
by Xiao Zou, Shengyou Qian, Qiaolai Tan and Hu Dong
Symmetry 2020, 12(9), 1386; https://doi.org/10.3390/sym12091386 - 19 Aug 2020
Cited by 6 | Viewed by 3490
Abstract
A high intensity focused ultrasound (HIFU) scanning approach is needed to obtain multiple treatment spots for the ablation of large volume tumors, but it will bring some problems such as longer treatment times, the inhomogeneity of temperature and thermal lesions in tissues. Although [...] Read more.
A high intensity focused ultrasound (HIFU) scanning approach is needed to obtain multiple treatment spots for the ablation of large volume tumors, but it will bring some problems such as longer treatment times, the inhomogeneity of temperature and thermal lesions in tissues. Although some optimal control methods have been proposed, it is difficult to take into account the uniformity, efficiency and entirety of thermal lesions. In this study, based on the Helmholtz equation and Pennes’ bio-heat transfer equation, a coupled acoustic-thermal field model is proposed to investigate the relationship between temperature elevation, thermal lesions and neighboring treatment spots, and to analyze the effects of the heating time and acoustic intensity on thermal lesions by the finite element method (FEM). Consequently, optimal control schemes for the heating time and acoustic intensity based on the contribution from neighboring treatment spots to thermal lesions are put forward to reduce treatment times and improve the uniformity of temperature and thermal lesions. The simulation results show that the peak historical temperature elevation on one treatment spot is related to the number, distance and time interval of its neighboring treated spots, and the thermal diffusion from the neighboring untreated spots can slow down the drop of temperature elevation after irradiation, thus both of them affect the final shape of the thermal lesions. In addition, increasing the heating time or acoustic intensity of each treatment spot can expand the overall area of thermal lesions, but it would aggravate the elevation and nonuniformity of the temperature of the treatment region. Through optimizing the heating time, the total treatment time can be reduced from 249 s by 17.4%, and the mean and variance of the peak historical temperature elevation can decrease from 44.64 °C by 13.3% and decrease from 24.6317 by 45%, respectively. While optimizing the acoustic intensity, the total treatment time remains unchanged, and the mean of the peak historical temperature elevation is reduced by 4.3 °C. Under the condition of the same thermal lesions, the optimized schemes can reduce the treatment time, lower the peak of the temperature on treatment spots, and homogenize the temperature distributions. This work is of practical significance for the optimization of a HIFU scanning therapy regimen and the evaluation of its treatment effect. Full article
(This article belongs to the Special Issue Thermodynamics and Energy Conservation)
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16 pages, 2344 KiB  
Article
Gaussian Process Regression for Data Fulfilling Linear Differential Equations with Localized Sources
by Christopher G. Albert and Katharina Rath
Entropy 2020, 22(2), 152; https://doi.org/10.3390/e22020152 - 27 Jan 2020
Cited by 13 | Viewed by 5432
Abstract
Specialized Gaussian process regression is presented for data that are known to fulfill a given linear differential equation with vanishing or localized sources. The method allows estimation of system parameters as well as strength and location of point sources. It is applicable to [...] Read more.
Specialized Gaussian process regression is presented for data that are known to fulfill a given linear differential equation with vanishing or localized sources. The method allows estimation of system parameters as well as strength and location of point sources. It is applicable to a wide range of data from measurement and simulation. The underlying principle is the well-known invariance of the Gaussian probability distribution under linear operators, in particular differentiation. In contrast to approaches with a generic covariance function/kernel, we restrict the Gaussian process to generate only solutions of the homogeneous part of the differential equation. This requires specialized kernels with a direct correspondence of certain kernel hyperparameters to parameters in the underlying equation and leads to more reliable regression results with less training data. Inhomogeneous contributions from linear superposition of point sources are treated via a linear model over fundamental solutions. Maximum likelihood estimates for hyperparameters and source positions are obtained by nonlinear optimization. For differential equations representing laws of physics the present approach generates only physically possible solutions, and estimated hyperparameters represent physical properties. After a general derivation, modeling of source-free data and parameter estimation is demonstrated for Laplace’s equation and the heat/diffusion equation. Finally, the Helmholtz equation with point sources is treated, representing scalar wave data such as acoustic pressure in the frequency domain. Full article
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15 pages, 5648 KiB  
Article
Ultrasonic Measurement of Stress in SLM 316L Stainless Steel Forming Parts Manufactured Using Different Scanning Strategies
by Xiaoling Yan, Jincheng Pang and Yanlong Jing
Materials 2019, 12(17), 2719; https://doi.org/10.3390/ma12172719 - 25 Aug 2019
Cited by 25 | Viewed by 4223
Abstract
Selective Laser Melting (SLM) technology is a new kind of additive manufacturing technology developed in in the last decade. Measurement and control of stress in metal forming layer is the basic problem of SLM forming parts. Critical Refraction Longitudinal (LCR) wave method was [...] Read more.
Selective Laser Melting (SLM) technology is a new kind of additive manufacturing technology developed in in the last decade. Measurement and control of stress in metal forming layer is the basic problem of SLM forming parts. Critical Refraction Longitudinal (LCR) wave method was used to measure stress. The acoustic-elastic formulas for measuring stresses in SLM 316L stainless steel forming parts manufactured using meander, stripe, and chess board scanning strategies, respectively, were established based on static load tensile test. The experimental results show that the acoustic time difference of LCR wave in SLM specimen manufactured with 316L stainless steel increases linearly with the increase of stress when the tensile stress is less than critical stress (372 MPa, 465 MPa, and 494 MPa). Due to the inhomogeneous deformation of the anisotropic SLM forming layer and the dimple-micropore aggregation fracture mechanism, the acousto-elastic curve fluctuates up and down along the irregular curve when the tensile stress is larger than critical stress. The results of corroboration experiments show that nondestructive measurement of stress in SLM forming specimen can be realized by using LCR wave method. The scanning strategy can significantly affect the tensile strength and yield strength of SLM forming specimen. The stresses were all in tension stress state at the edge of the specimens, whatever scanning strategy was used. Sub-area scanning and scanning sequence of alternate and intersect were adopted, which can effectively reduce the stress in the SLM forming specimen. The overall stress values of SLM forming specimen manufactured using chess board scanning strategy were smaller than that using meander and stripe strategies. The distribution of stress were more uniform. Full article
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