Transactions of Nanjing University of Aeronautics & Astronautics
Volume 37,Issue 6,2020 Table of Contents
2020, 37(6):831-838.
DOI: 10.16356/j.1005-1120.2020.06.001
Abstract:
It is urgent to effectively improve the production efficiency in the running process of manufacturing systems through a new generation of information technology. According to the current growing trend of the internet of things （IOT） in the manufacturing industry， aiming at the capacitor manufacturing plant， a multi-level architecture oriented to IOT-based manufacturing environment is established for a flexible flow-shop scheduling system. Next， according to multi-source manufacturing information driven in the manufacturing execution process， a scheduling optimization model based on the lot-streaming strategy is proposed under the framework. An improved distribution estimation algorithm is developed to obtain the optimal solution of the problem by balancing local search and global search. Finally， experiments are carried out and the results verify the feasibility and effectiveness of the proposed approach.
It is urgent to effectively improve the production efficiency in the running process of manufacturing systems through a new generation of information technology. According to the current growing trend of the internet of things （IOT） in the manufacturing industry， aiming at the capacitor manufacturing plant， a multi-level architecture oriented to IOT-based manufacturing environment is established for a flexible flow-shop scheduling system. Next， according to multi-source manufacturing information driven in the manufacturing execution process， a scheduling optimization model based on the lot-streaming strategy is proposed under the framework. An improved distribution estimation algorithm is developed to obtain the optimal solution of the problem by balancing local search and global search. Finally， experiments are carried out and the results verify the feasibility and effectiveness of the proposed approach.
2020, 37(6):839-847.
DOI: 10.16356/j.1005-1120.2020.06.002
Abstract:
Orthogonal turn-milling is a high-efficiency and precision machining method. Its cutting layer directly affects chip formation， cutting forces， and chatter， and further affects tool life， machining quality， etc. We studied The cutting layer geometry （CLG） in orthogonal turn-milling with zero eccentricity （OTMZE） is studied to explore orthogonal turn-milling cutting layer formation process. OTMZE principles of motion and formation processes are analyzed statically without considering kinetic influences. Mathematical models of the entrance and exit angles， cutting thickness， and cutting depth are established. In addition， these models are validated experimentally and some influences of cutting parameters on the tool cutting layer are analyzed. The results show that OTMZE cutting layer formation can be divided into two stages， chip shapes are nearly consistent with the simulated CLGs， and the most influencial parameter in affecting the cutting layer is found to be the tool feed per revolation of workpiece fa， followed by the ratio of the tool and workpiece speeds λ and the cutting depth ap. These models and results can provide theoretical guidance to clarify formation processes and quantitatively analyze changes in cutting layer geometry during OTMZE. In addition， they offer theoretical guidelines for cutting forces and chatter.
Orthogonal turn-milling is a high-efficiency and precision machining method. Its cutting layer directly affects chip formation， cutting forces， and chatter， and further affects tool life， machining quality， etc. We studied The cutting layer geometry （CLG） in orthogonal turn-milling with zero eccentricity （OTMZE） is studied to explore orthogonal turn-milling cutting layer formation process. OTMZE principles of motion and formation processes are analyzed statically without considering kinetic influences. Mathematical models of the entrance and exit angles， cutting thickness， and cutting depth are established. In addition， these models are validated experimentally and some influences of cutting parameters on the tool cutting layer are analyzed. The results show that OTMZE cutting layer formation can be divided into two stages， chip shapes are nearly consistent with the simulated CLGs， and the most influencial parameter in affecting the cutting layer is found to be the tool feed per revolation of workpiece fa， followed by the ratio of the tool and workpiece speeds λ and the cutting depth ap. These models and results can provide theoretical guidance to clarify formation processes and quantitatively analyze changes in cutting layer geometry during OTMZE. In addition， they offer theoretical guidelines for cutting forces and chatter.
2020, 37(6):848-857.
DOI: 10.16356/j.1005-1120.2020.06.003
Abstract:
Although the five-degree-of-freedom magnetic levitation system composed of two conical bearingless switched reluctance motors （CBSRMs） owns the simplest structure， the torque and levitation forces are coupled greatly. Therefore， it is difficult to make the rotor rotate and be fully levitated simultaneously. To solve this problem， two different role division control strategies are proposed in this paper， i.e. individual role division and mutual role division control strategies. The difference between them is the selection of motor which controls the torque or the axial force. In order to understand the characteristics of control variables， the principle and mathematical model of CBSRM are introduced. After that， two control strategies are explained in detail. To verify the demonstrated performance， the simulations are completed with MATLAB/Simulink.
Although the five-degree-of-freedom magnetic levitation system composed of two conical bearingless switched reluctance motors （CBSRMs） owns the simplest structure， the torque and levitation forces are coupled greatly. Therefore， it is difficult to make the rotor rotate and be fully levitated simultaneously. To solve this problem， two different role division control strategies are proposed in this paper， i.e. individual role division and mutual role division control strategies. The difference between them is the selection of motor which controls the torque or the axial force. In order to understand the characteristics of control variables， the principle and mathematical model of CBSRM are introduced. After that， two control strategies are explained in detail. To verify the demonstrated performance， the simulations are completed with MATLAB/Simulink.
2020, 37(6):858-871.
DOI: 10.16356/j.1005-1120.2020.06.004
Abstract:
The existing kinematic parameter calibration method cannot further improve the absolute positioning accuracy of the robot due to the uncertainty of positioning error caused by robot joint backlash. In view of this problem， a closed-loop feedback accuracy compensation method for robot joints was proposed. Firstly， a Chebyshev polynomial error estimation model was established which took geometric error and non-geometric error into account. In addition， the absolute linear grating scale was installed at each joint of the robot and the positioning error of the robot end was mapped to the joint angle. And the joint angle corrected value was obtained. Furthermore， the closed-loop feedback of robot joints was established to realize the online correction of the positioning error. Finally， an experiment on the KUKA KR210 industrial robot was conducted to demonstrate the effectiveness of the method. The result shows that the maximum absolute positioning error of the robot is reduced by 75% from 0.76 mm to 0.19 mm. This method can compensate the robot joint backlash effectively and further improve the absolute positioning accuracy of the robot.
The existing kinematic parameter calibration method cannot further improve the absolute positioning accuracy of the robot due to the uncertainty of positioning error caused by robot joint backlash. In view of this problem， a closed-loop feedback accuracy compensation method for robot joints was proposed. Firstly， a Chebyshev polynomial error estimation model was established which took geometric error and non-geometric error into account. In addition， the absolute linear grating scale was installed at each joint of the robot and the positioning error of the robot end was mapped to the joint angle. And the joint angle corrected value was obtained. Furthermore， the closed-loop feedback of robot joints was established to realize the online correction of the positioning error. Finally， an experiment on the KUKA KR210 industrial robot was conducted to demonstrate the effectiveness of the method. The result shows that the maximum absolute positioning error of the robot is reduced by 75% from 0.76 mm to 0.19 mm. This method can compensate the robot joint backlash effectively and further improve the absolute positioning accuracy of the robot.
2020, 37(6):872-883.
DOI: 10.16356/j.1005-1120.2020.06.005
Abstract:
A process parameter optimization method for mold wear during die forging process is proposed and a mold life prediction method based on polynomial fitting is presented， by combining the variance analysis method in the orthogonal test with the finite element simulation test in the forging process. The process parameters with the greatest influence on the mold wear during the die forging process and the optimal solution of the process parameters to minimize the wear depth of the mold are derived. The hot die forging process is taken as an example， and a mold wear correction model for hot forging processes is derived based on the Archard wear model. Finite element simulation analysis of die wear process in hot die forging based on deform software is performed to study the relationship between the wear depth of the mold working surface and the die forging process parameters during hot forging process. The optimized process parameters suitable for hot forging are derived by orthogonal experimental design and analysis of variance. The average wear amount of the mold during the die forging process is derived by calculating the wear depth of a plurality of key nodes on the mold surface. Mold life for the entire production process is predicted based on average mold wear depth and polynomial fitting.
A process parameter optimization method for mold wear during die forging process is proposed and a mold life prediction method based on polynomial fitting is presented， by combining the variance analysis method in the orthogonal test with the finite element simulation test in the forging process. The process parameters with the greatest influence on the mold wear during the die forging process and the optimal solution of the process parameters to minimize the wear depth of the mold are derived. The hot die forging process is taken as an example， and a mold wear correction model for hot forging processes is derived based on the Archard wear model. Finite element simulation analysis of die wear process in hot die forging based on deform software is performed to study the relationship between the wear depth of the mold working surface and the die forging process parameters during hot forging process. The optimized process parameters suitable for hot forging are derived by orthogonal experimental design and analysis of variance. The average wear amount of the mold during the die forging process is derived by calculating the wear depth of a plurality of key nodes on the mold surface. Mold life for the entire production process is predicted based on average mold wear depth and polynomial fitting.
2020, 37(6):884-897.
DOI: 10.16356/j.1005-1120.2020.06.006
Abstract:
Nonlinear dynamic analysis was performed on a planetary gear transmission system with meshing beyond the pitch point. The parameters of the planetary gear system were optimized， and a two-dimensional nonlinear dynamic model was established using the lumped-mass method. Time-varying meshing stiffness was calculated by the energy method. The model consumes the backlash， bearing clearance， time-varying meshing stiffness， time-varying bearing stiffness， and time-varying friction coefficient. The time-varying bearing stiffness was calculated according to the Hertz contact theory. The load distribution among the gears was computed， and the time-varying friction coefficient was calculated according to elastohydrodynamic lubrication （EHL） theory. The dynamical equations were solved via numerical integration. The global bifurcation characteristics caused by the input speed， backlash， bearing clearance， and damping were analyzed. The system was in a chaotic state at natural frequencies or frequency multiplication. The system transitioned from a single-period state to a chaotic state with the increase of the backlash. The bearing clearance of the sun gear had little influence on the bifurcation characteristics. The amplitude was restrained in the chaotic state as the damping ratio increased.
Nonlinear dynamic analysis was performed on a planetary gear transmission system with meshing beyond the pitch point. The parameters of the planetary gear system were optimized， and a two-dimensional nonlinear dynamic model was established using the lumped-mass method. Time-varying meshing stiffness was calculated by the energy method. The model consumes the backlash， bearing clearance， time-varying meshing stiffness， time-varying bearing stiffness， and time-varying friction coefficient. The time-varying bearing stiffness was calculated according to the Hertz contact theory. The load distribution among the gears was computed， and the time-varying friction coefficient was calculated according to elastohydrodynamic lubrication （EHL） theory. The dynamical equations were solved via numerical integration. The global bifurcation characteristics caused by the input speed， backlash， bearing clearance， and damping were analyzed. The system was in a chaotic state at natural frequencies or frequency multiplication. The system transitioned from a single-period state to a chaotic state with the increase of the backlash. The bearing clearance of the sun gear had little influence on the bifurcation characteristics. The amplitude was restrained in the chaotic state as the damping ratio increased.
2020, 37(6):898-902.
DOI: 10.16356/j.1005-1120.2020.06.007
Abstract:
There are amounts of issues to be resolved in the process of designing the fiber placement trajectory of the cylindrical component， such as the interference between the machine and the component and the over-travel of the axis of rotation on the fiber placement head. When the pressure on the cylinder surface inclines in a certain direction or at an angle within the normal plane， the motion characteristics of the rotation axis will be different. This paper analyzes the pressure angle effect of the concave cylinder surface on the motion features of a fiber placement machine. The placement area is enlarged by tilting pressure with the same lifting stroke， which is significant in preventing interference and selecting post-processing algorithm.
There are amounts of issues to be resolved in the process of designing the fiber placement trajectory of the cylindrical component， such as the interference between the machine and the component and the over-travel of the axis of rotation on the fiber placement head. When the pressure on the cylinder surface inclines in a certain direction or at an angle within the normal plane， the motion characteristics of the rotation axis will be different. This paper analyzes the pressure angle effect of the concave cylinder surface on the motion features of a fiber placement machine. The placement area is enlarged by tilting pressure with the same lifting stroke， which is significant in preventing interference and selecting post-processing algorithm.
8 Analysis of Effective Working Hours of Automatic Assembly Equipment for Aircraft Assembly Stations
2020, 37(6):903-913.
DOI: 10.16356/j.1005-1120.2020.06.008
Abstract:
To improve the accuracy of capacity analysis and prediction for the aircraft assembly stations， an approach for calculating the effective working hour （EWH） of automatic assembly equipment is introduced by using the dynamic mixed Weibull distribution （DMWD） model. Firstly， according to the features of aircraft assembling， a DMWD model considering the dynamic reliability of multiple subsystems and their synthetic effects on the whole equipment is established. A typical automatic drilling & riveting machine is selected as the research object， and the dynamic weights of reliability of three subsystems are modeled and solved. Subsequently the unknown parameters of the DMWD model are estimated based on maximum likelihood estimation （MLE） and Newton-Raphson method. Finally， the EWH of an automatic station is defined and modeled by using the solved dynamic reliability function. Based on the experimental study on a real automatic drilling & riveting machine from a wing panel assembly station， it is shown that the proposed DMWD and EWH models could effectively calculate the equipment reliability with full consideration of its multiple subsystems. The DMWD model is more suitable for improving the solution precision of EWH than the traditional three-parameter Weibull distribution.
To improve the accuracy of capacity analysis and prediction for the aircraft assembly stations， an approach for calculating the effective working hour （EWH） of automatic assembly equipment is introduced by using the dynamic mixed Weibull distribution （DMWD） model. Firstly， according to the features of aircraft assembling， a DMWD model considering the dynamic reliability of multiple subsystems and their synthetic effects on the whole equipment is established. A typical automatic drilling & riveting machine is selected as the research object， and the dynamic weights of reliability of three subsystems are modeled and solved. Subsequently the unknown parameters of the DMWD model are estimated based on maximum likelihood estimation （MLE） and Newton-Raphson method. Finally， the EWH of an automatic station is defined and modeled by using the solved dynamic reliability function. Based on the experimental study on a real automatic drilling & riveting machine from a wing panel assembly station， it is shown that the proposed DMWD and EWH models could effectively calculate the equipment reliability with full consideration of its multiple subsystems. The DMWD model is more suitable for improving the solution precision of EWH than the traditional three-parameter Weibull distribution.
2020, 37(6):914-927.
DOI: 10.16356/j.1005-1120.2020.06.009
Abstract:
The top relief surfaces of an hourglass worm gear hob are ground manually in the traditional manufacturing process， which cannot ensure the width of the land surfaces of the hob. Moreover， each geometric feature of the hob has been produced through different manufacturing techniques and machine tools， which results in low efficiency. To solve this problem， we propose a semi-automatic computer aided design （CAD） method for hobs. The point clouds of each feature surface of a hob are calculated by combing mathematical equations of the top relief surfaces built by the proposed method with other existing equations of hob surfaces. According to the point clouds， the method can achieve the automatic modeling for the hob in three-dimensional （3D） software by classifying and extracting the parameter information of the feature-hierarchical knowledge of the hob. Based on the generated 3D model， the entire surfaces of the hob can be manufactured on a four-axis computer numerical control （CNC） milling machine through only twice clamping. Verification of the width of the land surface of the hob manufactured by semi-automatic CAD method on a measuring projector proved the precision of the designed width can be ensured. The edge of the contact area on the worm wheel in a meshing experiment is clear and distinct， which means the worm gear drive is meshed well and the hob manufactured by the proposed method has improved machinability. The method simplifies the processing technique， and improves the design efficiency and production accuracy.
The top relief surfaces of an hourglass worm gear hob are ground manually in the traditional manufacturing process， which cannot ensure the width of the land surfaces of the hob. Moreover， each geometric feature of the hob has been produced through different manufacturing techniques and machine tools， which results in low efficiency. To solve this problem， we propose a semi-automatic computer aided design （CAD） method for hobs. The point clouds of each feature surface of a hob are calculated by combing mathematical equations of the top relief surfaces built by the proposed method with other existing equations of hob surfaces. According to the point clouds， the method can achieve the automatic modeling for the hob in three-dimensional （3D） software by classifying and extracting the parameter information of the feature-hierarchical knowledge of the hob. Based on the generated 3D model， the entire surfaces of the hob can be manufactured on a four-axis computer numerical control （CNC） milling machine through only twice clamping. Verification of the width of the land surface of the hob manufactured by semi-automatic CAD method on a measuring projector proved the precision of the designed width can be ensured. The edge of the contact area on the worm wheel in a meshing experiment is clear and distinct， which means the worm gear drive is meshed well and the hob manufactured by the proposed method has improved machinability. The method simplifies the processing technique， and improves the design efficiency and production accuracy.
2020, 37(6):928-936.
DOI: 10.16356/j.1005-1120.2020.06.010
Abstract:
The coordinated and integrated development of regional airport group system has been identified as an important research topic in the field of air traffic management in China. However， due to the clear limitation on airspace resources and severe traffic congestion， it is necessary to further study the problem of flight schedule coordination optimization for airport clusters. We take the Beijing-Tianjin-Hebei airport Group as an example and construct an optimization model of flight schedule with the minimum adjustment and delay. The design of the implementation algorithm is proposed. As demonstrated by the simulation results， the flight delay in the Beijing-Tianjin-Hebei multi-airport system is noticeably reduced by applying both the optimization model and the algorithm proposed in this paper.
The coordinated and integrated development of regional airport group system has been identified as an important research topic in the field of air traffic management in China. However， due to the clear limitation on airspace resources and severe traffic congestion， it is necessary to further study the problem of flight schedule coordination optimization for airport clusters. We take the Beijing-Tianjin-Hebei airport Group as an example and construct an optimization model of flight schedule with the minimum adjustment and delay. The design of the implementation algorithm is proposed. As demonstrated by the simulation results， the flight delay in the Beijing-Tianjin-Hebei multi-airport system is noticeably reduced by applying both the optimization model and the algorithm proposed in this paper.
11 Handling Label Noise in Air Traffic Complexity Evaluation Based on Confident Learning and XGBoost
2020, 37(6):936-946.
DOI: 10.16356/j.1005-1120.2020.06.011
Abstract:
Air traffic complexity is a critical indicator for air traffic operation， and plays an important role in air traffic management （ATM）， such as airspace reconfiguration， air traffic flow management and allocation of air traffic controllers （ATCos）. Recently， many machine learning techniques have been used to evaluate air traffic complexity by constructing a mapping from complexity related factors to air traffic complexity labels. However， the low quality of complexity labels， which is named as label noise， has often been neglected and caused unsatisfactory performance in air traffic complexity evaluation. This paper aims at label noise in air traffic complexity samples， and proposes a confident learning and XGBoost-based approach to evaluate air traffic complexity under label noise. The confident learning process is applied to filter out noisy samples with various label probability distributions， and XGBoost is used to train a robust and high-performance air traffic complexity evaluation model on the different label noise filtered ratio datasets. Experiments are carried out on a real dataset from the Guangzhou airspace sector in China， and the results prove that the appropriate label noise removal strategy and XGBoost algorithm can effectively mitigate the label noise problem and achieve better performance in air traffic complexity evaluation.
Air traffic complexity is a critical indicator for air traffic operation， and plays an important role in air traffic management （ATM）， such as airspace reconfiguration， air traffic flow management and allocation of air traffic controllers （ATCos）. Recently， many machine learning techniques have been used to evaluate air traffic complexity by constructing a mapping from complexity related factors to air traffic complexity labels. However， the low quality of complexity labels， which is named as label noise， has often been neglected and caused unsatisfactory performance in air traffic complexity evaluation. This paper aims at label noise in air traffic complexity samples， and proposes a confident learning and XGBoost-based approach to evaluate air traffic complexity under label noise. The confident learning process is applied to filter out noisy samples with various label probability distributions， and XGBoost is used to train a robust and high-performance air traffic complexity evaluation model on the different label noise filtered ratio datasets. Experiments are carried out on a real dataset from the Guangzhou airspace sector in China， and the results prove that the appropriate label noise removal strategy and XGBoost algorithm can effectively mitigate the label noise problem and achieve better performance in air traffic complexity evaluation.
2020, 37(6):947-954.
DOI: 10.16356/j.1005-1120.2020.06.012
Abstract:
A filtering method of aero-engine load spectrum based on the rain flow counting is proposed in this paper. Firstly， the original load spectrum is counted through the rain flow method to get the peak and valley values. Then， some data points in the original load spectrum are added between the peak and valley values. Finally， the filtering spectrum is obtained. The proposed method can reflect the path information of the original load spectrum. In addition， it can also eliminate the noise in the signal and improve the efficiency of signal processing， which is of practical significance for the research of aero-engine.
A filtering method of aero-engine load spectrum based on the rain flow counting is proposed in this paper. Firstly， the original load spectrum is counted through the rain flow method to get the peak and valley values. Then， some data points in the original load spectrum are added between the peak and valley values. Finally， the filtering spectrum is obtained. The proposed method can reflect the path information of the original load spectrum. In addition， it can also eliminate the noise in the signal and improve the efficiency of signal processing， which is of practical significance for the research of aero-engine.
2020, 37(6):955-961.
DOI: 10.16356/j.1005-1120.2020.06.013
Abstract:
To improve the crashworthiness and energy absorption performance， a novel crash box negative Poisson’s ratio （NPR） structure is proposed according to the characteristics of low speed collision of bumper system. Taking the peak collision force and the average collision force as two subsystems， a multidisciplinary collaborative optimization design is carried out， and its optimization results are compared with the ones optimized by NSGA-II algorithm. Simulation results show that the crashworthiness and energy absorption performance of the novel crash box is improved effectively based on the multidisciplinary optimization method.
To improve the crashworthiness and energy absorption performance， a novel crash box negative Poisson’s ratio （NPR） structure is proposed according to the characteristics of low speed collision of bumper system. Taking the peak collision force and the average collision force as two subsystems， a multidisciplinary collaborative optimization design is carried out， and its optimization results are compared with the ones optimized by NSGA-II algorithm. Simulation results show that the crashworthiness and energy absorption performance of the novel crash box is improved effectively based on the multidisciplinary optimization method.
2020, 37(6):962-969.
DOI: 10.16356/j.1005-1120.2020.06.014
Abstract:
Piezoelectric ceramic is hard to be integrated with the normal spring structure. To address the above problem， this paper proposed a new geometry of a clip-like spring which is very similar to binder clip in our daily life. The equivalent stiffness of the designed piezoelectric clip-like spring is thoroughly researched and discussed through the theoretical model， the finite element simulation and the experimental measurement. The results confirm the possibility of designing a compact piezoelectric clip-like spring， and the equivalent stiffness can be tuned through the several key geometric parameters. Finally， theoretical predictions confirmed by experimental results show that the equivalent stiffness of the spring structure is as function of the instantaneous angle of the clip， this stiffness variation caused by the geometric nonlinearity can be ignored in some practical engineering applications， which means it is possible to linearize the clip-like spring and simplify the following dynamic model of the corresponding piezoelectric oscillators.
Piezoelectric ceramic is hard to be integrated with the normal spring structure. To address the above problem， this paper proposed a new geometry of a clip-like spring which is very similar to binder clip in our daily life. The equivalent stiffness of the designed piezoelectric clip-like spring is thoroughly researched and discussed through the theoretical model， the finite element simulation and the experimental measurement. The results confirm the possibility of designing a compact piezoelectric clip-like spring， and the equivalent stiffness can be tuned through the several key geometric parameters. Finally， theoretical predictions confirmed by experimental results show that the equivalent stiffness of the spring structure is as function of the instantaneous angle of the clip， this stiffness variation caused by the geometric nonlinearity can be ignored in some practical engineering applications， which means it is possible to linearize the clip-like spring and simplify the following dynamic model of the corresponding piezoelectric oscillators.
2020, 37(6):970-978.
DOI: 10.16356/j.1005-1120.2020.06.015
Abstract:
The fatigue test between 105—109 cycles of GH4169 nickel-based superalloy commonly used in aircraft engines is carried out by ultrasonic fatigue machine at 650 ℃. The S-N curve is obtained and the fatigue fracture morphology is observed. The fatigue S-N curve presents a“step-like”shape， with the first inflection point near 1×107 cycles and the second inflection point near 1×108 cycles. There is no engineering fatigue limit， and it still shows a downward trend after 107 or even 109 cycles. The crack initiation location is related to its life. Cracks are generated on the surface below 107 cycles， while it is inside above 107 cycles. The crack initiation source in the ultra-high cycle fatigue at 650 ℃ is mainly the local intergranular fracture and casting defect of the matrix. In the phase of crack propagation， the mixed propagation of intergranular and cleavage is the main form.
The fatigue test between 105—109 cycles of GH4169 nickel-based superalloy commonly used in aircraft engines is carried out by ultrasonic fatigue machine at 650 ℃. The S-N curve is obtained and the fatigue fracture morphology is observed. The fatigue S-N curve presents a“step-like”shape， with the first inflection point near 1×107 cycles and the second inflection point near 1×108 cycles. There is no engineering fatigue limit， and it still shows a downward trend after 107 or even 109 cycles. The crack initiation location is related to its life. Cracks are generated on the surface below 107 cycles， while it is inside above 107 cycles. The crack initiation source in the ultra-high cycle fatigue at 650 ℃ is mainly the local intergranular fracture and casting defect of the matrix. In the phase of crack propagation， the mixed propagation of intergranular and cleavage is the main form.
2020, 37(6):979-994.
DOI: 10.16356/j.1005-1120.2020.06.016
Abstract:
Recently， inverse problems have attracted more and more attention in computational mathematics and become increasingly important in engineering applications. After the discretization， many of inverse problems are reduced to linear systems. Due to the typical ill-posedness of inverse problems， the reduced linear systems are often ill-posed， especially when their scales are large. This brings great computational difficulty. Particularly， a small perturbation in the right side of an ill-posed linear system may cause a dramatical change in the solution. Therefore， regularization methods should be adopted for stable solutions. In this paper， a new class of accelerated iterative regularization methods is applied to solve this kind of large-scale ill-posed linear systems. An iterative scheme becomes a regularization method only when the iteration is early terminated. And a Morozov’s discrepancy principle is applied for the stop criterion. Compared with the conventional Landweber iteration， the new methods have acceleration effect， and can be compared to the well-known acceleratedν ![]()
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Recently， inverse problems have attracted more and more attention in computational mathematics and become increasingly important in engineering applications. After the discretization， many of inverse problems are reduced to linear systems. Due to the typical ill-posedness of inverse problems， the reduced linear systems are often ill-posed， especially when their scales are large. This brings great computational difficulty. Particularly， a small perturbation in the right side of an ill-posed linear system may cause a dramatical change in the solution. Therefore， regularization methods should be adopted for stable solutions. In this paper， a new class of accelerated iterative regularization methods is applied to solve this kind of large-scale ill-posed linear systems. An iterative scheme becomes a regularization method only when the iteration is early terminated. And a Morozov’s discrepancy principle is applied for the stop criterion. Compared with the conventional Landweber iteration， the new methods have acceleration effect， and can be compared to the well-known accelerated
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