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Symplectic multi-level method for solving nonlinear optimal control problem
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作者 彭海军 高强 +1 位作者 吴志刚 钟万勰 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第10期1251-1260,共10页
By converting an optimal control problem for nonlinear systems to a Hamiltonian system,a symplecitc-preserving method is proposed.The state and costate variables are approximated by the Lagrange polynomial.The state v... By converting an optimal control problem for nonlinear systems to a Hamiltonian system,a symplecitc-preserving method is proposed.The state and costate variables are approximated by the Lagrange polynomial.The state variables at two ends of the time interval are taken as independent variables.Based on the dual variable principle,nonlinear optimal control problems are replaced with nonlinear equations.Furthermore,in the implementation of the symplectic algorithm,based on the 2N algorithm,a multilevel method is proposed.When the time grid is refined from low level to high level,the initial state and costate variables of the nonlinear equations can be obtained from the Lagrange interpolation at the low level grid to improve efficiency.Numerical simulations show the precision and the efficiency of the proposed algorithm in this paper. 展开更多
关键词 nonlinear optimal control dual variable variational principle multi-level iteration symplectic algorithm
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Research on Multi-Level Automatic Filling Optimization Design Method for Layered Cross-Sectional Layout of Umbilical 被引量:1
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作者 YIN Xu FAN Zhi-rui +4 位作者 CAO Dong-hui LIU Yu-jie LI Meng-shu YAN Jun YANG Zhi-xun 《China Ocean Engineering》 2025年第5期891-903,共13页
The umbilical,a key component in offshore energy extraction,plays a vital role in ensuring the stable operation of the entire production system.The extensive variety of cross-sectional components creates highly comple... The umbilical,a key component in offshore energy extraction,plays a vital role in ensuring the stable operation of the entire production system.The extensive variety of cross-sectional components creates highly complex layout combinations.Furthermore,due to constraints in component quantity and geometry within the cross-sectional layout,filler bodies must be incorporated to maintain cross-section performance.Conventional design approaches based on manual experience suffer from inefficiency,high variability,and difficulties in quantification.This paper presents a multi-level automatic filling optimization design method for umbilical cross-sectional layouts to address these limitations.Initially,the research establishes a multi-objective optimization model that considers compactness,balance,and wear resistance of the cross-section,employing an enhanced genetic algorithm to achieve a near-optimal layout.Subsequently,the study implements an image processing-based vacancy detection technique to accurately identify cross-sectional gaps.To manage the variability and diversity of these vacant regions,the research introduces a multi-level filling method that strategically selects and places filler bodies of varying dimensions,overcoming the constraints of uniform-size fillers.Additionally,the method incorporates a hierarchical strategy that subdivides the complex cross-section into multiple layers,enabling layer-by-layer optimization and filling.This approach reduces manufac-turing equipment requirements while ensuring practical production process feasibility.The methodology is validated through a specific umbilical case study.The results demonstrate improvements in compactness,balance,and wear resistance compared with the initial cross-section,offering novel insights and valuable references for filler design in umbilical cross-sections. 展开更多
关键词 UMBILICAL cross-sectional layout multi-level filling layered layout optimization design
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A robust method for large-scale route optimization on lunar surface utilizing a multi-level map model
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作者 Yutong JIA Shengnan ZHANG +5 位作者 Bin LIU Kaichang DI Bin XIE Jing NAN Chenxu ZHAO Gang WAN 《Chinese Journal of Aeronautics》 2025年第3期134-150,共17页
As we look ahead to future lunar exploration missions, such as crewed lunar exploration and establishing lunar scientific research stations, the lunar rovers will need to cover vast distances. These distances could ra... As we look ahead to future lunar exploration missions, such as crewed lunar exploration and establishing lunar scientific research stations, the lunar rovers will need to cover vast distances. These distances could range from kilometers to tens of kilometers, and even hundreds and thousands of kilometers. Therefore, it is crucial to develop effective long-range path planning for lunar rovers to meet the demands of lunar patrol exploration. This paper presents a hierarchical map model path planning method that utilizes the existing high-resolution images, digital elevation models and mineral abundance maps. The objective is to address the issue of the construction of lunar rover travel costs in the absence of large-scale, high-resolution digital elevation models. This method models the reference and semantic layers using the middle- and low-resolution remote sensing data. The multi-scale obstacles on the lunar surface are extracted by combining the deep learning algorithm on the high-resolution image, and the obstacle avoidance layer is modeled. A two-stage exploratory path planning decision is employed for long-distance driving path planning on a global–local scale. The proposed method analyzes the long-distance accessibility of various areas of scientific significance, such as Rima Bode. A high-precision digital elevation model is created using stereo images to validate the method. Based on the findings, it can be observed that the entire route spans a distance of 930.32 km. The route demonstrates an impressive ability to avoid meter-level impact craters and linear structures while maintaining an average slope of less than 8°. This paper explores scientific research by traversing at least seven basalt units, uncovering the secrets of lunar volcanic activities, and establishing ‘golden spike’ reference points for lunar stratigraphy. The final result of path planning can serve as a valuable reference for the design, mission demonstration, and subsequent project implementation of the new manned lunar rover. 展开更多
关键词 Crewed lunar exploration Long-range path planningi multi-level map Deep learning Volcanic activities
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A New Rational-based Optimal Design Strategy of Ship Structure Based on Multi-level Analysis and Super-element Modeling Method 被引量:6
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作者 Li Sun Deyu Wang 《Journal of Marine Science and Application》 2011年第3期272-280,共9页
A new multi-level analysis method of introducing the super-element modeling method, derived from the multi-level analysis method first proposed by O. F. Hughes, has been proposed in this paper to solve the problem of ... A new multi-level analysis method of introducing the super-element modeling method, derived from the multi-level analysis method first proposed by O. F. Hughes, has been proposed in this paper to solve the problem of high time cost in adopting a rational-based optimal design method for ship structural design. Furthermore,the method was verified by its effective application in optimization of the mid-ship section of a container ship. A full 3-D FEM model of a ship,suffering static and quasi-static loads, was used as the analyzing object for evaluating the structural performance of the mid-ship module, including static strength and buckling performance. Research results reveal that this new method could substantially reduce the computational cost of the rational-based optimization problem without decreasing its accuracy, which increases the feasibility and economic efficiency of using a rational-based optimal design method in ship structural design. 展开更多
关键词 rational-based optimal design method (RBODM) multi-level analysis SUPER-ELEMENT ship module genetic algorithm
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An Operational Test Method for VSC-HVDC Valves Based on Modular Multi-level Converters 被引量:12
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作者 WU Yanan LU Tianguang +2 位作者 TANG Guangfu ZHA Kunpeng GAO Chong 《中国电机工程学报》 EI CSCD 北大核心 2012年第30期I0002-I0002,4,共1页
为给基于模块化多电平换流器(modular multi-levelconverter,MMC)的电压源换流器高压直流输电(voltagesourced converter HVDC,VSC-HVDC)换流阀提供有效的检验手段,以验证其设计的正确性及其运行可靠性,对换流阀的运行特性和关键应... 为给基于模块化多电平换流器(modular multi-levelconverter,MMC)的电压源换流器高压直流输电(voltagesourced converter HVDC,VSC-HVDC)换流阀提供有效的检验手段,以验证其设计的正确性及其运行可靠性,对换流阀的运行特性和关键应力进行分析,提出基于原理等效的MMC阀运行试验方法,设计试验电路并阐明其运行机理。搭建的PSCAD电磁暂态仿真模型和实际的试验验证证明了试验方法的正确性和有效性。 展开更多
关键词 运行测试 多电平变换器 模块化 阀门 试验方法 高压直流输电 电平转换器 AC-DC
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A new tracking error detection method using amplitude difference detection for signal waveform modulation multi-level discs 被引量:1
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作者 严明铭 裴京 潘龙法 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第10期319-323,共5页
The sub-land/sub-pit affects the characteristic of the tracking error signal which is generated by the conventional differential phase detection (DPD) method in the signal waveform modulation multi-level (SWML) re... The sub-land/sub-pit affects the characteristic of the tracking error signal which is generated by the conventional differential phase detection (DPD) method in the signal waveform modulation multi-level (SWML) read-only disc. To solve this problem, this paper proposes a new tracking error detection method using amplitude difference. Based on the diffraction theory, the amplitude difference is proportional to the tracking error and is feasible to be used for obtaining the off-track information. The experimental system of the amplitude difference detection method is developed. The experimental results show that the tracking error signal derived from the new method has better performance in uniformity and signal-to-noise ratio than that derived from the conventional DPD method in the SWML read-only disc. 展开更多
关键词 signal waveform modulation multi-level technology tracking error amplitude difference
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A Multi-Level Threshold Method for Edge Detection and Segmentation Based on Entropy 被引量:1
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作者 Mohamed A.El-Sayed Abdelmgeid A.Ali +1 位作者 Mohamed E.Hussien Hameda A.Sennary 《Computers, Materials & Continua》 SCIE EI 2020年第4期1-16,共16页
The essential tool in image processing,computer vision and machine vision is edge detection,especially in the fields of feature extraction and feature detection.Entropy is a basic area in information theory.The entrop... The essential tool in image processing,computer vision and machine vision is edge detection,especially in the fields of feature extraction and feature detection.Entropy is a basic area in information theory.The entropy,in image processing field has a role associated with image settings.As an initial step in image processing,the entropy is always used the image’s segmentation to determine the regions of image which is used to separate the background and objects in image.Image segmentation known as the process which divides the image into multiple regions or sets of pixels.Many applications have been development to enhance the image processing.This paper utilizes the Shannon entropy to achieve edge detection process and segmentation of the image.It introduces a new method of edge detection for 2-D histogram and Shannon entropy based on multilevel threshold.The method utilizes the gray value and the average gray value of the pixels to achieve the two dimensional histogram.The current method has apriority in comparison to some upper classical methods.The experimental results exhibited that the proposed method could capture a moderate quality and execution time better than other comparative methods,particularly in the largest images size.The proposed method offers good results when applied with images of different sizes from the civilization of ancient Egyptians. 展开更多
关键词 multi-level threshold edge detection 2D histogram ENTROPY
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Effect of heterogeneity on mechanical and micro-seismic behaviors of sandstone subjected to multi-level cyclic loading: A discrete element method investigation 被引量:2
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作者 Zhengyang Song Zhen Yang +3 位作者 Min Zhang Fei Wang Martin Herbst Heinz Konietzky 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2023年第10期2556-2581,共26页
In numerical simulation of the mechanical responses and acoustic emission(AE)characteristics of rocks under cyclic loading,the impacts of compositional heterogeneities of mineral grains have barely been considered.Thi... In numerical simulation of the mechanical responses and acoustic emission(AE)characteristics of rocks under cyclic loading,the impacts of compositional heterogeneities of mineral grains have barely been considered.This will lead to a poor reproduction of rock’s behaviors in terms of stress-strain relationship and micro-seismic characteristics in numerical simulation.This work aims to analyze and reveal the impact of parameter heterogeneity on the rock’s fatigue and micro-seismic properties based on PFC3D.Two distribution patterns(uniform and Weibull distributions),are implemented to assign four critical parameters(i.e.tensile strength,cohesion,parallel bond stiffness and linear stiffness)for 32 sets of numerical schemes.The results show that the models with high heterogeneity of tensile strength and cohesion can better reproduce the stress-strain relationship as well as the patterns of cumulative AE counts and energy magnitude.The evolution of the proportion of three-level AE events in the laboratory test is consistent with the numerical results when the highly heterogeneous tensile strength and cohesion are distributed.The numerical results can provide practical guidance to the PFC-based modeling of rock heterogeneity when exposed to multi-level cyclic loading and AE monitoring. 展开更多
关键词 Discrete element method(DEM) HETEROGENEITY Weibull distribution PFC3D Cyclic loading Acoustic emission(AE)
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Method of multi-level recursive and application to nonlinear dynamic deformation forecasting
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作者 LIU Guo-lin~(1, 2), ZHANG Lian-peng~2, OU Ji-kun~1 (1. Institute of Geodesy and Geophysics, Chinese Academy of Science, Wuhan, 430077,China 2. Shandong University of Science and Technology, Tai’an 271019, China) 《中国有色金属学会会刊:英文版》 CSCD 2005年第S1期172-175,共4页
The time-dependence bilinear mixed-regression deformation model and time-dependence bilinear dynamic system deformation model are established for deformation observation series. According to the multi- level recursive... The time-dependence bilinear mixed-regression deformation model and time-dependence bilinear dynamic system deformation model are established for deformation observation series. According to the multi- level recursive method, the time-dependence parameters are first traced and predicted, and then the dynamic system states. Due to the method considering time-dependence of deformation and having stronger adaptability to time-dependence system, it can improve forecast’s precision. It is very effective for data processing of nonlinear dynamic deformation monitoring to make multi-step forecasting. 展开更多
关键词 multi-level RECURSIVE DYNAMIC MONITORING timedependence PARAMETERS
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A Multi-level Topological Environment Modeling Method for Multiple Mobile Robots
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作者 战强 《High Technology Letters》 EI CAS 1999年第1期69-74,共6页
After comparisons and analyses of different environment modeling methods, a concludsion that using topological rather than geometrical method can greatly decrease the computation complexity of the motion planning of m... After comparisons and analyses of different environment modeling methods, a concludsion that using topological rather than geometrical method can greatly decrease the computation complexity of the motion planning of multiple mobile robots is given. This paper introduces the construction of topological maps of three types of environments, and presents a new multi level topological environment modeling method for the modeling of large environment, which has less storing space and less computation complexity than geometrical method. 展开更多
关键词 Motion planning ENVIRONMENT models TOPOLOGICAL method GEOMETRICAL method
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Equal Switching Distribution Method for Multi-Level Cascaded Inverters
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作者 Saad Tapuchi Raul Rabinovici +2 位作者 Dmitry Baimel Nina Baimel Svetlana Bronstein 《Energy and Power Engineering》 2013年第9期560-569,共10页
The paper proposes a new method of equal switching distribution that can be applied to cascaded multi-level inverters. This method is based on the fact that in the cascaded multilevel inverters, the output phase volta... The paper proposes a new method of equal switching distribution that can be applied to cascaded multi-level inverters. This method is based on the fact that in the cascaded multilevel inverters, the output phase voltage is the sum of voltage waveforms produced by all cascaded cells. By periodically exchanging cells’ voltage waveforms, the proposed method ensures equal average switchings distribution between all cascaded cells. This method is applied to the 13-level inverter, which consists of three cascaded 5-level H-bridge cells per phase. However, the proposed method can be extended to any desired number of voltage levels and applied to any type of cascaded multi-level inverter. Extensive simulation results of the tested 13-level inverter with the equal switching distribution are presented. Moreover, the proposed method is compared to the standard control approaches and its advantages are shown. 展开更多
关键词 Switchings Cascaded INVERTER multi-level PWM
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Improved partial response maximum likelihood method combining modulation code for signal waveform modulation multi-level disc
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作者 王鹤群 裴京 潘龙法 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第10期213-219,共7页
In this paper, we describe an improved adaptive partial response maximum likelihood (PRML) method combining modulation code tbr signal waveform modulation multi-level disc. This improved adaptive PRML method employs... In this paper, we describe an improved adaptive partial response maximum likelihood (PRML) method combining modulation code tbr signal waveform modulation multi-level disc. This improved adaptive PRML method employs partial response equalizer and adaptive viterbi detector combining modulation code. Compared with the traditional adaptive PRML detector, the improved PRML detector additionally employs illogical sequence detector and corrector. Illogical sequence detector and corrector can aw)id the appearance of illogical sequences effectively, which do not follow the law of modulation code for signal waveform modulation multi-level disc, and obtain the correct sequences. We implement the improved PRML detector using a DSP and an FPGA chip. The experimental results show good performance. The higher efficient and lower complexity can be obtained by using the improved PRML method than by using the previous PRML method. Meanwhile, resource utilization of the improved PRML detector is not changed, but the bit error rate (BER) is reduced by more than 20%. 展开更多
关键词 multi-level disc signal waveform modulation viterbi detector partial response maximum likeli-hood
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Study on Multi-level Treatment Method of Waste Gas from Sewage Treatment Plant
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作者 WANG Na 《外文科技期刊数据库(文摘版)工程技术》 2021年第4期166-171,共6页
With the continuous development of economy and society and the speeding up development of industrial industry, people's living standards are gradually improving, which leads to the increasing discharge of domestic... With the continuous development of economy and society and the speeding up development of industrial industry, people's living standards are gradually improving, which leads to the increasing discharge of domestic waste and industrial waste, so the working pressure of sewage treatment plants invisibly increases. Sewage treatment plant is the concentration of waste treatment and it will produce a large number of wastes generated by the accumulation of odor, that is, waste gas, with the characteristics of strong diffusion. Therefore, if the wastewater treatment plant can not properly treat these waste gases in time, it is easy to cause large-scale air pollution. If people live in this odor environment for a long time, it will seriously harm their health. Starting from waste gas treatment methods, do multi-level deodorization and purification of waste gas, which is the key measure to effectively help improve people's quality of life. 展开更多
关键词 sewage treatment plant waste gas multi-level treatment method
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Study of the Transport Behavior of Multispherical Proppant in Intersecting Fracture Based on Discrete Element Method 被引量:1
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作者 Chengyong Peng JianshuWu +2 位作者 Mao Jiang Biao Yin Yishan Lou 《Energy Engineering》 EI 2025年第1期185-201,共17页
To analyze the differences in the transport and distribution of different types of proppants and to address issues such as the short effective support of proppant and poor placement in hydraulically intersecting fract... To analyze the differences in the transport and distribution of different types of proppants and to address issues such as the short effective support of proppant and poor placement in hydraulically intersecting fractures,this study considered the combined impact of geological-engineering factors on conductivity.Using reservoir production parameters and the discrete elementmethod,multispherical proppants were constructed.Additionally,a 3D fracture model,based on the specified conditions of the L block,employed coupled(Computational Fluid Dynamics)CFD-DEM(Discrete ElementMethod)for joint simulations to quantitatively analyze the transport and placement patterns of multispherical proppants in intersecting fractures.Results indicate that turbulent kinetic energy is an intrinsic factor affecting proppant transport.Moreover,the efficiency of placement and migration distance of low-sphericity quartz sand constructed by the DEM in the main fracture are significantly reduced compared to spherical ceramic proppants,with a 27.7%decrease in the volume fraction of the fracture surface,subsequently affecting the placement concentration and damaging fracture conductivity.Compared to small-angle fractures,controlling artificial and natural fractures to expand at angles of 45°to 60°increases the effective support length by approximately 20.6%.During hydraulic fracturing of gas wells,ensuring the fracture support area and post-closure conductivity can be achieved by controlling the sphericity of proppants and adjusting the perforation direction to control the direction of artificial fractures. 展开更多
关键词 Hydraulic fracturing discrete element method PROPPANT SPHERICITY CFD-DEM
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Structural Modal Parameter Recognition and Related Damage Identification Methods under Environmental Excitations:A Review 被引量:3
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作者 Chao Zhang Shang-Xi Lai Hua-Ping Wang 《Structural Durability & Health Monitoring》 EI 2025年第1期25-54,共30页
Modal parameters can accurately characterize the structural dynamic properties and assess the physical state of the structure.Therefore,it is particularly significant to identify the structural modal parameters accordi... Modal parameters can accurately characterize the structural dynamic properties and assess the physical state of the structure.Therefore,it is particularly significant to identify the structural modal parameters according to the monitoring data information in the structural health monitoring(SHM)system,so as to provide a scientific basis for structural damage identification and dynamic model modification.In view of this,this paper reviews methods for identifying structural modal parameters under environmental excitation and briefly describes how to identify structural damages based on the derived modal parameters.The paper primarily introduces data-driven modal parameter recognition methods(e.g.,time-domain,frequency-domain,and time-frequency-domain methods,etc.),briefly describes damage identification methods based on the variations of modal parameters(e.g.,natural frequency,modal shapes,and curvature modal shapes,etc.)and modal validation methods(e.g.,Stability Diagram and Modal Assurance Criterion,etc.).The current status of the application of artificial intelligence(AI)methods in the direction of modal parameter recognition and damage identification is further discussed.Based on the pre-vious analysis,the main development trends of structural modal parameter recognition and damage identification methods are given to provide scientific references for the optimized design and functional upgrading of SHM systems. 展开更多
关键词 Structural health monitoring data information modal parameters damage identification AI method
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A Multi-Level Semantic Constraint Approach for Highway Tunnel Scene Twin Modeling 被引量:1
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作者 LI Yufei XIE Yakun +3 位作者 CHEN Mingzhen ZHAO Yaoji TU Jiaxing HU Ya 《Journal of Geodesy and Geoinformation Science》 2025年第2期37-56,共20页
As a key node of modern transportation network,the informationization management of road tunnels is crucial to ensure the operation safety and traffic efficiency.However,the existing tunnel vehicle modeling methods ge... As a key node of modern transportation network,the informationization management of road tunnels is crucial to ensure the operation safety and traffic efficiency.However,the existing tunnel vehicle modeling methods generally have problems such as insufficient 3D scene description capability and low dynamic update efficiency,which are difficult to meet the demand of real-time accurate management.For this reason,this paper proposes a vehicle twin modeling method for road tunnels.This approach starts from the actual management needs,and supports multi-level dynamic modeling from vehicle type,size to color by constructing a vehicle model library that can be flexibly invoked;at the same time,semantic constraint rules with geometric layout,behavioral attributes,and spatial relationships are designed to ensure that the virtual model matches with the real model with a high degree of similarity;ultimately,the prototype system is constructed and the case region is selected for the case study,and the dynamic vehicle status in the tunnel is realized by integrating real-time monitoring data with semantic constraints for precise virtual-real mapping.Finally,the prototype system is constructed and case experiments are conducted in selected case areas,which are combined with real-time monitoring data to realize dynamic updating and three-dimensional visualization of vehicle states in tunnels.The experiments show that the proposed method can run smoothly with an average rendering efficiency of 17.70 ms while guaranteeing the modeling accuracy(composite similarity of 0.867),which significantly improves the real-time and intuitive tunnel management.The research results provide reliable technical support for intelligent operation and emergency response of road tunnels,and offer new ideas for digital twin modeling of complex scenes. 展开更多
关键词 highway tunnel twin modeling multi-level semantic constraints tunnel vehicles multidimensional modeling
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Combing the Entropy Weight Method with Fuzzy Mathematics for Assessing the Quality and Post-Ripening Mechanism of High-Temperature Daqu during Storage 被引量:1
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作者 YANG Junlin YANG Shaojuan +8 位作者 WU Cheng YIN Yanshun YOU Xiaolong ZHAO Wenyu ZHU Anran WANG Jia HU Feng HU Jianfeng WANG Diqiang 《食品科学》 北大核心 2025年第9期48-62,共15页
This study investigated the physicochemical properties,enzyme activities,volatile flavor components,microbial communities,and sensory evaluation of high-temperature Daqu(HTD)during the maturation process,and a standar... This study investigated the physicochemical properties,enzyme activities,volatile flavor components,microbial communities,and sensory evaluation of high-temperature Daqu(HTD)during the maturation process,and a standard system was established for comprehensive quality evaluation of HTD.There were obvious changes in the physicochemical properties,enzyme activities,and volatile flavor components at different storage periods,which affected the sensory evaluation of HTD to a certain extent.The results of high-throughput sequencing revealed significant microbial diversity,and showed that the bacterial community changed significantly more than did the fungal community.During the storage process,the dominant bacterial genera were Kroppenstedtia and Thermoascus.The correlation between dominant microorganisms and quality indicators highlighted their role in HTD quality.Lactococcus,Candida,Pichia,Paecilomyces,and protease activity played a crucial role in the formation of isovaleraldehyde.Acidic protease activity had the greatest impact on the microbial community.Moisture promoted isobutyric acid generation.Furthermore,the comprehensive quality evaluation standard system was established by the entropy weight method combined with multi-factor fuzzy mathematics.Consequently,this study provides innovative insights for comprehensive quality evaluation of HTD during storage and establishes a groundwork for scientific and rational storage of HTD and quality control of sauce-flavor Baijiu. 展开更多
关键词 microbial community high-temperature Daqu comprehensive quality evaluation entropy weight method maturation process
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In situ stress inversion using nonlinear stress boundaries achieved by the bubbling method 被引量:1
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作者 Xige Liu Chenchun Huang +3 位作者 Wancheng Zhu Joung Oh Chengguo Zhang Guangyao Si 《Journal of Rock Mechanics and Geotechnical Engineering》 2025年第3期1510-1527,共18页
Due to the heterogeneity of rock masses and the variability of in situ stress,the traditional linear inversion method is insufficiently accurate to achieve high accuracy of the in situ stress field.To address this cha... Due to the heterogeneity of rock masses and the variability of in situ stress,the traditional linear inversion method is insufficiently accurate to achieve high accuracy of the in situ stress field.To address this challenge,nonlinear stress boundaries for a numerical model are determined through regression analysis of a series of nonlinear coefficient matrices,which are derived from the bubbling method.Considering the randomness and flexibility of the bubbling method,a parametric study is conducted to determine recommended ranges for these parameters,including the standard deviation(σb)of bubble radii,the non-uniform coefficient matrix number(λ)for nonlinear stress boundaries,and the number(m)and positions of in situ stress measurement points.A model case study provides a reference for the selection of these parameters.Additionally,when the nonlinear in situ stress inversion method is employed,stress distortion inevitably occurs near model boundaries,aligning with the Saint Venant's principle.Two strategies are proposed accordingly:employing a systematic reduction of nonlinear coefficients to achieve high inversion accuracy while minimizing significant stress distortion,and excluding regions with severe stress distortion near the model edges while utilizing the central part of the model for subsequent simulations.These two strategies have been successfully implemented in the nonlinear in situ stress inversion of the Xincheng Gold Mine and have achieved higher inversion accuracy than the linear method.Specifically,the linear and nonlinear inversion methods yield root mean square errors(RMSE)of 4.15 and 3.2,and inversion relative errors(δAve)of 22.08%and 17.55%,respectively.Therefore,the nonlinear inversion method outperforms the traditional multiple linear regression method,even in the presence of a systematic reduction in the nonlinear stress boundaries. 展开更多
关键词 In situ stress field Inversion method The bubbling method Nonlinear stress boundary Multiple linear regression method
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Transfer matrix method for free and forced vibrations of multi-level functionally graded material stepped beams with different boundary conditions
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作者 Xiaoyang SU Tong HU +3 位作者 Wei ZHANG Houjun KANG Yunyue CONG Quan YUAN 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2024年第6期983-1000,共18页
Functionally graded materials(FGMs)are a novel class of composite materials that have attracted significant attention in the field of engineering due to their unique mechanical properties.This study aims to explore th... Functionally graded materials(FGMs)are a novel class of composite materials that have attracted significant attention in the field of engineering due to their unique mechanical properties.This study aims to explore the dynamic behaviors of an FGM stepped beam with different boundary conditions based on an efficient solving method.Under the assumptions of the Euler-Bernoulli beam theory,the governing differential equations of an individual FGM beam are derived with Hamilton’s principle and decoupled via the separation-of-variable approach.Then,the free and forced vibrations of the FGM stepped beam are solved with the transfer matrix method(TMM).Two models,i.e.,a three-level FGM stepped beam and a five-level FGM stepped beam,are considered,and their natural frequencies and mode shapes are presented.To demonstrate the validity of the method in this paper,the simulation results by ABAQUS are also given.On this basis,the detailed parametric analyses on the frequencies and dynamic responses of the three-level FGM stepped beam are carried out.The results show the accuracy and efficiency of the TMM. 展开更多
关键词 transfer matrix method(TMM) free vibration forced vibration functionally graded material(FGM) stepped beam
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Insight Into the Separation-of-Variable Methods for the Closed-Form Solutions of Free Vibration of Rectangular Thin Plates
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作者 Yufeng Xing Ye Yuan Gen Li 《Computer Modeling in Engineering & Sciences》 SCIE EI 2025年第1期329-355,共27页
The separation-of-variable(SOV)methods,such as the improved SOV method,the variational SOV method,and the extended SOV method,have been proposed by the present authors and coworkers to obtain the closed-form analytica... The separation-of-variable(SOV)methods,such as the improved SOV method,the variational SOV method,and the extended SOV method,have been proposed by the present authors and coworkers to obtain the closed-form analytical solutions for free vibration and eigenbuckling of rectangular plates and circular cylindrical shells.By taking the free vibration of rectangular thin plates as an example,this work presents the theoretical framework of the SOV methods in an instructive way,and the bisection–based solution procedures for a group of nonlinear eigenvalue equations.Besides,the explicit equations of nodal lines of the SOV methods are presented,and the relations of nodal line patterns and frequency orders are investigated.It is concluded that the highly accurate SOV methods have the same accuracy for all frequencies,the mode shapes about repeated frequencies can also be precisely captured,and the SOV methods do not have the problem of missing roots as well. 展开更多
关键词 Separation-of-variable method Rayleigh quotient nodal line eigenvalue equation bisection method
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