Accurate detection of pipeline leakage is essential to maintain the safety of pipeline transportation.Recently,deep learning(DL)has emerged as a promising tool for pipeline leakage detection(PLD).However,most existing...Accurate detection of pipeline leakage is essential to maintain the safety of pipeline transportation.Recently,deep learning(DL)has emerged as a promising tool for pipeline leakage detection(PLD).However,most existing DL methods have difficulty in achieving good performance in identifying leakage types due to the complex time dynamics of pipeline data.On the other hand,the initial parameter selection in the detection model is generally random,which may lead to unstable recognition performance.For this reason,a hybrid DL framework referred to as parameter-optimized recurrent attention network(PRAN)is presented in this paper to improve the accuracy of PLD.First,a parameter-optimized long short-term memory(LSTM)network is introduced to extract effective and robust features,which exploits a particle swarm optimization(PSO)algorithm with cross-entropy fitness function to search for globally optimal parameters.With this framework,the learning representation capability of the model is improved and the convergence rate is accelerated.Moreover,an anomaly-attention mechanism(AM)is proposed to discover class discriminative information by weighting the hidden states,which contributes to amplifying the normalabnormal distinguishable discrepancy,further improving the accuracy of PLD.After that,the proposed PRAN not only implements the adaptive optimization of network parameters,but also enlarges the contribution of normal-abnormal discrepancy,thereby overcoming the drawbacks of instability and poor generalization.Finally,the experimental results demonstrate the effectiveness and superiority of the proposed PRAN for PLD.展开更多
Buried pipelines are an essential component of the urban infrastructure of modern cities.Traditional buried pipes are mainly made of metal materials.With the development of material science and technology in recent ye...Buried pipelines are an essential component of the urban infrastructure of modern cities.Traditional buried pipes are mainly made of metal materials.With the development of material science and technology in recent years,non-metallic pipes,such as plastic pipes,ceramic pipes,and concrete pipes,are increasingly taking the place of pipes made from metal in various pipeline networks such as water supply,drainage,heat,industry,oil,and gas.The location technologies for the location of the buried metal pipeline have become mature,but detection and location technologies for the non-metallic pipelines are still developing.In this paper,current trends and future perspectives of detection and location of buried non-metallic pipelines are summarized.Initially,this paper reviews and analyzes electromagnetic induction technologies,electromagnetic wave technologies,and other physics-based technologies.It then focuses on acoustic detection and location technologies,and finally introduces emerging technologies.Then the technical characteristics of each detection and location method have been compared,with their strengths and weaknesses identified.The current trends and future perspectives of each buried non-metallic pipeline detection and location technology have also been defined.Finally,some suggestions for the future development of buried non-metallic pipeline detection and location technologies are provided.展开更多
A great number of pipelines in China are in unsatisfactory condition and faced with problems of corrosion and cracking,but there are very few approaches for underwater pipeline detection.Pipeline detection autonomous ...A great number of pipelines in China are in unsatisfactory condition and faced with problems of corrosion and cracking,but there are very few approaches for underwater pipeline detection.Pipeline detection autonomous underwater vehicle(PDAUV) is hereby designed to solve these problems when working with advanced optical,acoustical and electrical sensors for underwater pipeline detection.PDAUV is a test bed that not only examines the logical rationality of the program,effectiveness of the hardware architecture,accuracy of the software interface protocol as well as the reliability and stability of the control system but also verifies the effectiveness of the control system in tank experiments and sea trials.The motion control system of PDAUV,including both the hardware and software architectures,is introduced in this work.The software module and information flow of the motion control system of PDAUV and a novel neural network-based control(NNC) are also covered.Besides,a real-time identification method based on neural network is used to realize system identification.The tank experiments and sea trials are carried out to verify the feasibility and capability of PDAUV control system to complete underwater pipeline detection task.展开更多
Detecting a pipeline's abnormal status,which is typically a blockage and leakage accident,is important for the continuity and safety of mine backfill.The pipeline system for gravity-transport high-density backfill...Detecting a pipeline's abnormal status,which is typically a blockage and leakage accident,is important for the continuity and safety of mine backfill.The pipeline system for gravity-transport high-density backfill(GHB)is complex.Specifically designed,efficient,and accurate abnormal pipeline detection methods for GHB are rare.This work presents a long short-term memory-based deep learning(LSTM-DL)model for GHB pipeline blockage and leakage diagnosis.First,an industrial pipeline monitoring system was introduced using pressure and flow sensors.Second,blockage and leakage field experiments were designed to solve the problem of negative sample deficiency.The pipeline's statistical characteristics with different working statuses were analyzed to show their complexity.Third,the architecture of the LSTM-DL model was elaborated on and evaluated.Finally,the LSTM-DL model was compared with state-of-the-art(SOTA)learning algorithms.The results show that the backfilling cycle comprises multiple working phases and is intermittent.Although pressure and flow signals fluctuate stably in a normal cycle,their values are diverse in different cycles.Plugging causes a sudden change in interval signal features;leakage results in long variation duration and a wide fluctuation range.Among the SOTA models,the LSTM-DL model has the highest detection accuracy of98.31%for all states and the lowest misjudgment or false positive rate of 3.21%for blockage and leakage states.The proposed model can accurately recognize various pipeline statuses of complex GHB systems.展开更多
This paper describes a new framework for detection and tracking of underwater pipeline, which includes software system and hardware system. It is designed for vision system of AUV based on monocular CCD camera. First,...This paper describes a new framework for detection and tracking of underwater pipeline, which includes software system and hardware system. It is designed for vision system of AUV based on monocular CCD camera. First, the real-time data flow from image capture card is pre-processed and pipeline features are extracted for navigation. The region saturation degree is advanced to remove false edge point group after Sobel operation. An appropriate way is proposed to clear the disturbance around the peak point in the process of Hough transform. Second, the continuity of pipeline layout is taken into account to improve the efficiency of line extraction. Once the line information has lbeen obtained, the reference zone is predicted by Kalman filter. It denotes the possible appearance position of the pipeiine in the image. Kalman filter is used to estimate this position in next frame so that the information of pipeline of each frame can be known in advance. Results obtained on real optic vision data in tank experiment are displayed and discussed. They show that the proposed system can detect and track the underwater pipeline online, and is effective and feasible.展开更多
A fully distributed optical fiber sensor (DOFS) for monitoring long-distance oil pipeline health is proposed based on optical time domain reflectometry (OTDR). A smart and sensitive optical fiber cable is installe...A fully distributed optical fiber sensor (DOFS) for monitoring long-distance oil pipeline health is proposed based on optical time domain reflectometry (OTDR). A smart and sensitive optical fiber cable is installed along the pipeline acting as a sensor, The experiments show that the cable swells when exposed to oil and induced additional bending losses inside the fiber, and the optical attenuation of the fiber coated by a thin skin with periodical hardness is sensitive to deformation and vibration caused by oil leakage, tampering, or mechanical impact. The region where the additional attenuation occurred is detected and located by DOFS based on OTDR, the types of pipeline accidents are identified according to the characteristics of transmitted optical power received by an optical power meter, Another prototype of DOFS based on a forward traveling frequency-modulated continuous-wave (FMCW) is also proposed to monitor pipeline. The advantages and disadvantages of DOFSs based on OTDR and FMCW are discussed. The experiments show that DOFSs are capable of detecting and locating distant oil pipeline leakages and damages in real time with an estimated precision of ten meters over tens of kilometers.展开更多
In the traditional pipeline magnetic flux leakage(MFL)detection technology,circumferential or axial excitation is mainly used to excite the magnetic field of defects.However,the domestic and foreign pipeline detection...In the traditional pipeline magnetic flux leakage(MFL)detection technology,circumferential or axial excitation is mainly used to excite the magnetic field of defects.However,the domestic and foreign pipeline detection devices currently in operation are mainly axial excitation MFL detection tools,in which circumferential cracks can be clearly identified,but the detection sensitivity of axial cracks is not high,thus forming a detection blind zone.Therefore,a composite excitation multi-extension direction defect MFL detection method is proposed,which can realize the simultaneous detection of axial and circumferential defects.On the basis of the electromagnetic theory Maxwell equation and Biot Savart law,a mathematical model of circumferential and axial magnetization is firstly established.Then finite element simulation software is used to establish a model of a new type of magnetic flux leakage detection device,and a simulation analysis of crack detection in multiple extension directions is carried out.Finally,under the conditions of the relationship model between the change rate of leakage magnetic field and external excitation intensity under unsaturated magnetization and the multi-stage coil magnetization model,the sample vehicle towing experiment is carried out.The paper aims to analyze the feasibility and effectiveness of the new magnetic flux leakage detection device for detecting defects in different extension directions.Based on the final experimental results,the new composite excitation multi extension direction leakage magnetic field detector has a good detection effect for defects in the axial and circumferential extension directions.展开更多
As an important part of lifeline engineering in the development and utilization of marine resources, the submarine fluid-filled pipeline is a complex coupling system which is subjected to both internal and external fl...As an important part of lifeline engineering in the development and utilization of marine resources, the submarine fluid-filled pipeline is a complex coupling system which is subjected to both internal and external flow fields. By utilizing Kennard's shell equations and combining with Helmholtz equations of flow field, the coupling equations of submarine fluid-filled pipeline for n=0 axisymmetrical wave motion are set up. Analytical expressions of wave speed are obtained for both s=1 and s=2 waves, which correspond to a fluid-dominated wave and an axial shell wave, respectively. The numerical results for wave speed and wave attenuation are obtained and discussed subsequently. It shows that the frequency depends on phase velocity, and the attenuation of this mode depends strongly on material parameters of the pipe and the internal and the external fluid fields. The characteristics of PVC pipe are studied for a comparison. The effects of shell thickness/radius ratio and density of the contained fluid on the model are also discussed. The study provides a theoretical basis and helps to accurately predict the situation of submarine pipelines, which also has practical application prospect in the field of pipeline leakage detection.展开更多
In the field of pipeline inner wall inspection,the snake robot demonstrates significant advantages over other inspection methods.While a simple traveling wave or meandering motion will suffice for inspecting the inner...In the field of pipeline inner wall inspection,the snake robot demonstrates significant advantages over other inspection methods.While a simple traveling wave or meandering motion will suffice for inspecting the inner wall of small-diameter pipes,comprehensively and meticulously inspecting the inner wall of large-diameter pipes requires the snake robot to adopt a helical gait that closely adheres to the inner wall.Our review of existing literature indicates that most research and development on the helical gait of snake robots has focused on the outer surface of cylinders,with very few studies dedicated to developing a helical gait specifically for the inspection of the inner wall of pipes.Therefore,in this study,we propose a helical gait that is suitable for the inner wall of pipes and meets the requirements of gas pipeline engineering.The helical gait is designed using the backbone curve method.First,we create a mathematical model for a circular helix curve with constant curvature and torsion,ensuring it is applicable to a snake robot prototype in a laboratory environment.Subsequently.we calculate the joint angles required for two conical spiral curves with variable curvature and torsion,establish a new model,and define the physical significance of the specific parameters.To ensure the feasibility of the proposed gait,we conduct experiments involving meandering and traveling wave motions to verify the communication and control between the host computer and the snake robot.Building upon this foundation,we further validate the mathematical model of the complex helical motion gait through simulation experiments.Our findings provide a theoretical basis for realizing helical movement with a real snake robot.展开更多
To aid the magnetic anomaly detection(MAD)of underground ferromagnetic pipelines,this paper proposes a geometric modeling method based on the magnetic dipole reconstruction method(MDRM).First,the numerical modeling of...To aid the magnetic anomaly detection(MAD)of underground ferromagnetic pipelines,this paper proposes a geometric modeling method based on the magnetic dipole reconstruction method(MDRM).First,the numerical modeling of basic pipe components such as straight sections,bends and elbows,and tee joints are discussed and the relevant mathematical formulations for these components are derived.Next,after analyzing the function of MDRM and various element division strategies,the sectional division and blocked division methods are introduced and applied to the appropriate pipeline components to determine the volume and center coordinates of each element,establishing the general models for the three typical pipeline components considered.The resulting volume and center coordinates of each component are the fundamental parameters for determining the MAD forwarding of underground ferromagnetic pipelines using the MDRM.Finally,based on the combination and transformation of the basic pipeline components considered,the visualized geometric models of typical pipeline layouts including parallel pipelines,pipelines with elbows,and a pipeline with a tee joint are constructed.The results demonstrate the feasibility of the proposed method of geometric modeling for the MDRM,which can be further applied to the finite element modeling of these and other components when analyzing MAD data.Furthermore,the models with output parameters proposed in this paper establish a foundation for the inversion of MAD.展开更多
基金This work was supported in part by the National Natural Science Foundation of China(U21A2019,61873058),Hainan Province Science and Technology Special Fund of China(ZDYF2022SHFZ105)the Alexander von Humboldt Foundation of Germany.
文摘Accurate detection of pipeline leakage is essential to maintain the safety of pipeline transportation.Recently,deep learning(DL)has emerged as a promising tool for pipeline leakage detection(PLD).However,most existing DL methods have difficulty in achieving good performance in identifying leakage types due to the complex time dynamics of pipeline data.On the other hand,the initial parameter selection in the detection model is generally random,which may lead to unstable recognition performance.For this reason,a hybrid DL framework referred to as parameter-optimized recurrent attention network(PRAN)is presented in this paper to improve the accuracy of PLD.First,a parameter-optimized long short-term memory(LSTM)network is introduced to extract effective and robust features,which exploits a particle swarm optimization(PSO)algorithm with cross-entropy fitness function to search for globally optimal parameters.With this framework,the learning representation capability of the model is improved and the convergence rate is accelerated.Moreover,an anomaly-attention mechanism(AM)is proposed to discover class discriminative information by weighting the hidden states,which contributes to amplifying the normalabnormal distinguishable discrepancy,further improving the accuracy of PLD.After that,the proposed PRAN not only implements the adaptive optimization of network parameters,but also enlarges the contribution of normal-abnormal discrepancy,thereby overcoming the drawbacks of instability and poor generalization.Finally,the experimental results demonstrate the effectiveness and superiority of the proposed PRAN for PLD.
基金Supported by Downhole Intelligent Measurement and Control Science and Technology Innovation Team of Southwest Petroleum University(Grant No.2018CXTD04)National Natural Science Foundation of China(Grant Nos.61701085,51974273)+1 种基金Chengdu Municipal international science and technology cooperation project of China(Grant Nos.2020-GH02-00016-HZ)2020 National Mountain Highway Engineering Technology Research Center Open Fund Project(Grant No.GSGZJ-2020-01).
文摘Buried pipelines are an essential component of the urban infrastructure of modern cities.Traditional buried pipes are mainly made of metal materials.With the development of material science and technology in recent years,non-metallic pipes,such as plastic pipes,ceramic pipes,and concrete pipes,are increasingly taking the place of pipes made from metal in various pipeline networks such as water supply,drainage,heat,industry,oil,and gas.The location technologies for the location of the buried metal pipeline have become mature,but detection and location technologies for the non-metallic pipelines are still developing.In this paper,current trends and future perspectives of detection and location of buried non-metallic pipelines are summarized.Initially,this paper reviews and analyzes electromagnetic induction technologies,electromagnetic wave technologies,and other physics-based technologies.It then focuses on acoustic detection and location technologies,and finally introduces emerging technologies.Then the technical characteristics of each detection and location method have been compared,with their strengths and weaknesses identified.The current trends and future perspectives of each buried non-metallic pipeline detection and location technology have also been defined.Finally,some suggestions for the future development of buried non-metallic pipeline detection and location technologies are provided.
基金Project(2011AA09A106)supported by the Hi-tech Research and Development Program of ChinaProject(51179035)supported by the National Natural Science Foundation of ChinaProject(2015ZX01041101)supported by Major National Science and Technology of China
文摘A great number of pipelines in China are in unsatisfactory condition and faced with problems of corrosion and cracking,but there are very few approaches for underwater pipeline detection.Pipeline detection autonomous underwater vehicle(PDAUV) is hereby designed to solve these problems when working with advanced optical,acoustical and electrical sensors for underwater pipeline detection.PDAUV is a test bed that not only examines the logical rationality of the program,effectiveness of the hardware architecture,accuracy of the software interface protocol as well as the reliability and stability of the control system but also verifies the effectiveness of the control system in tank experiments and sea trials.The motion control system of PDAUV,including both the hardware and software architectures,is introduced in this work.The software module and information flow of the motion control system of PDAUV and a novel neural network-based control(NNC) are also covered.Besides,a real-time identification method based on neural network is used to realize system identification.The tank experiments and sea trials are carried out to verify the feasibility and capability of PDAUV control system to complete underwater pipeline detection task.
基金financially supported by the China Postdoctoral Science Foundation (No.2021M690362)the National Natural Science Foundation of China (Nos.51974014 and U2034206)。
文摘Detecting a pipeline's abnormal status,which is typically a blockage and leakage accident,is important for the continuity and safety of mine backfill.The pipeline system for gravity-transport high-density backfill(GHB)is complex.Specifically designed,efficient,and accurate abnormal pipeline detection methods for GHB are rare.This work presents a long short-term memory-based deep learning(LSTM-DL)model for GHB pipeline blockage and leakage diagnosis.First,an industrial pipeline monitoring system was introduced using pressure and flow sensors.Second,blockage and leakage field experiments were designed to solve the problem of negative sample deficiency.The pipeline's statistical characteristics with different working statuses were analyzed to show their complexity.Third,the architecture of the LSTM-DL model was elaborated on and evaluated.Finally,the LSTM-DL model was compared with state-of-the-art(SOTA)learning algorithms.The results show that the backfilling cycle comprises multiple working phases and is intermittent.Although pressure and flow signals fluctuate stably in a normal cycle,their values are diverse in different cycles.Plugging causes a sudden change in interval signal features;leakage results in long variation duration and a wide fluctuation range.Among the SOTA models,the LSTM-DL model has the highest detection accuracy of98.31%for all states and the lowest misjudgment or false positive rate of 3.21%for blockage and leakage states.The proposed model can accurately recognize various pipeline statuses of complex GHB systems.
基金supported by the National Natural Science Foundation of China (Grant No. 51009040)the National High Technology Research and Development Program of China (863 Program,Grant No. 2011AA09A106)+1 种基金the China Postdoctoral Science Foundation (Grant No. 2012M510928)Heilongjiang Postdoctoral Fund
文摘This paper describes a new framework for detection and tracking of underwater pipeline, which includes software system and hardware system. It is designed for vision system of AUV based on monocular CCD camera. First, the real-time data flow from image capture card is pre-processed and pipeline features are extracted for navigation. The region saturation degree is advanced to remove false edge point group after Sobel operation. An appropriate way is proposed to clear the disturbance around the peak point in the process of Hough transform. Second, the continuity of pipeline layout is taken into account to improve the efficiency of line extraction. Once the line information has lbeen obtained, the reference zone is predicted by Kalman filter. It denotes the possible appearance position of the pipeiine in the image. Kalman filter is used to estimate this position in next frame so that the information of pipeline of each frame can be known in advance. Results obtained on real optic vision data in tank experiment are displayed and discussed. They show that the proposed system can detect and track the underwater pipeline online, and is effective and feasible.
基金This project is supported by R&D Foundation of National Petroleum Corporation (CNPC) of China(No.2001411-4).
文摘A fully distributed optical fiber sensor (DOFS) for monitoring long-distance oil pipeline health is proposed based on optical time domain reflectometry (OTDR). A smart and sensitive optical fiber cable is installed along the pipeline acting as a sensor, The experiments show that the cable swells when exposed to oil and induced additional bending losses inside the fiber, and the optical attenuation of the fiber coated by a thin skin with periodical hardness is sensitive to deformation and vibration caused by oil leakage, tampering, or mechanical impact. The region where the additional attenuation occurred is detected and located by DOFS based on OTDR, the types of pipeline accidents are identified according to the characteristics of transmitted optical power received by an optical power meter, Another prototype of DOFS based on a forward traveling frequency-modulated continuous-wave (FMCW) is also proposed to monitor pipeline. The advantages and disadvantages of DOFSs based on OTDR and FMCW are discussed. The experiments show that DOFSs are capable of detecting and locating distant oil pipeline leakages and damages in real time with an estimated precision of ten meters over tens of kilometers.
基金National Natural Science Foundation of China(No.51804267)State Key Laboratory of Petroleum Resources and Prospecting,China University of Petroleum,Beijing(No.PRP/open-1610)。
文摘In the traditional pipeline magnetic flux leakage(MFL)detection technology,circumferential or axial excitation is mainly used to excite the magnetic field of defects.However,the domestic and foreign pipeline detection devices currently in operation are mainly axial excitation MFL detection tools,in which circumferential cracks can be clearly identified,but the detection sensitivity of axial cracks is not high,thus forming a detection blind zone.Therefore,a composite excitation multi-extension direction defect MFL detection method is proposed,which can realize the simultaneous detection of axial and circumferential defects.On the basis of the electromagnetic theory Maxwell equation and Biot Savart law,a mathematical model of circumferential and axial magnetization is firstly established.Then finite element simulation software is used to establish a model of a new type of magnetic flux leakage detection device,and a simulation analysis of crack detection in multiple extension directions is carried out.Finally,under the conditions of the relationship model between the change rate of leakage magnetic field and external excitation intensity under unsaturated magnetization and the multi-stage coil magnetization model,the sample vehicle towing experiment is carried out.The paper aims to analyze the feasibility and effectiveness of the new magnetic flux leakage detection device for detecting defects in different extension directions.Based on the final experimental results,the new composite excitation multi extension direction leakage magnetic field detector has a good detection effect for defects in the axial and circumferential extension directions.
基金financially supported by the National Natural Science Foundation of China(Grant No.50905036)
文摘As an important part of lifeline engineering in the development and utilization of marine resources, the submarine fluid-filled pipeline is a complex coupling system which is subjected to both internal and external flow fields. By utilizing Kennard's shell equations and combining with Helmholtz equations of flow field, the coupling equations of submarine fluid-filled pipeline for n=0 axisymmetrical wave motion are set up. Analytical expressions of wave speed are obtained for both s=1 and s=2 waves, which correspond to a fluid-dominated wave and an axial shell wave, respectively. The numerical results for wave speed and wave attenuation are obtained and discussed subsequently. It shows that the frequency depends on phase velocity, and the attenuation of this mode depends strongly on material parameters of the pipe and the internal and the external fluid fields. The characteristics of PVC pipe are studied for a comparison. The effects of shell thickness/radius ratio and density of the contained fluid on the model are also discussed. The study provides a theoretical basis and helps to accurately predict the situation of submarine pipelines, which also has practical application prospect in the field of pipeline leakage detection.
基金supported by the BUCEA Post Graduate Innovation Project,China(PG2023096).
文摘In the field of pipeline inner wall inspection,the snake robot demonstrates significant advantages over other inspection methods.While a simple traveling wave or meandering motion will suffice for inspecting the inner wall of small-diameter pipes,comprehensively and meticulously inspecting the inner wall of large-diameter pipes requires the snake robot to adopt a helical gait that closely adheres to the inner wall.Our review of existing literature indicates that most research and development on the helical gait of snake robots has focused on the outer surface of cylinders,with very few studies dedicated to developing a helical gait specifically for the inspection of the inner wall of pipes.Therefore,in this study,we propose a helical gait that is suitable for the inner wall of pipes and meets the requirements of gas pipeline engineering.The helical gait is designed using the backbone curve method.First,we create a mathematical model for a circular helix curve with constant curvature and torsion,ensuring it is applicable to a snake robot prototype in a laboratory environment.Subsequently.we calculate the joint angles required for two conical spiral curves with variable curvature and torsion,establish a new model,and define the physical significance of the specific parameters.To ensure the feasibility of the proposed gait,we conduct experiments involving meandering and traveling wave motions to verify the communication and control between the host computer and the snake robot.Building upon this foundation,we further validate the mathematical model of the complex helical motion gait through simulation experiments.Our findings provide a theoretical basis for realizing helical movement with a real snake robot.
基金This work is supported by the National Natural Science Foundation of China[No.41374151]the Sichuan Province Applied Basic Research Project of China[No.2017JY0162]the Young Scholars Development Fund of SWPU[No.201599010079].
文摘To aid the magnetic anomaly detection(MAD)of underground ferromagnetic pipelines,this paper proposes a geometric modeling method based on the magnetic dipole reconstruction method(MDRM).First,the numerical modeling of basic pipe components such as straight sections,bends and elbows,and tee joints are discussed and the relevant mathematical formulations for these components are derived.Next,after analyzing the function of MDRM and various element division strategies,the sectional division and blocked division methods are introduced and applied to the appropriate pipeline components to determine the volume and center coordinates of each element,establishing the general models for the three typical pipeline components considered.The resulting volume and center coordinates of each component are the fundamental parameters for determining the MAD forwarding of underground ferromagnetic pipelines using the MDRM.Finally,based on the combination and transformation of the basic pipeline components considered,the visualized geometric models of typical pipeline layouts including parallel pipelines,pipelines with elbows,and a pipeline with a tee joint are constructed.The results demonstrate the feasibility of the proposed method of geometric modeling for the MDRM,which can be further applied to the finite element modeling of these and other components when analyzing MAD data.Furthermore,the models with output parameters proposed in this paper establish a foundation for the inversion of MAD.