Failures due to high-cycle fatigue have led to a high cost in aerospace engineering over the past few decades.In this paper,the experimental results of the fatigue behavior of compressor blade specimen subjected to re...Failures due to high-cycle fatigue have led to a high cost in aerospace engineering over the past few decades.In this paper,the experimental results of the fatigue behavior of compressor blade specimen subjected to resonance and the effects of a damping hard coating on relieving the fatigue progress are presented.The crack initiation and propagation processes were observed under resonance of the first bending mode by using the resonant frequencies as the indicator.Significant nonlinear features were observed in the spectrum of the blade with a fatigue crack.The finite element model considering the breathing crack was established with nonlinear contact based on the crack localization and size,which was obtained by ultrasonic phased array technology.The simulation results of the vibration behavior of the cracked blade were obtained and consistent with the experimental results.A NiCrAlY coating was deposited on the blade,and increases in the fatigue life were observed under the same condition.The results of this paper can help to better understand the fatigue of a compressor blade subjected to resonance and provide a preference for the application of a damping hard coating on compressor blades.展开更多
In order to effectively improve meshing performance of spiral bevel and hypoid gears generated by the duplex helical method, the effects of straight lined and circular cutting edges profile on meshing and contact of s...In order to effectively improve meshing performance of spiral bevel and hypoid gears generated by the duplex helical method, the effects of straight lined and circular cutting edges profile on meshing and contact of spiral bevel and hypoid gears were investigated analytically. Firstly, a mathematical model of spiral bevel and hypoid gears with circular blade profile was established according to the cutting characteristics of the duplex helical method. Based on a hypoid gear drive, the tooth bearings and the functions of transmission errors of four design cases were analyzed respectively by the use of the tooth contact analysis(TCA), and the contact stresses of the four design cases were analyzed and compared using simulation software. Finally, the curvature radius of the circular profile blade was optimized. The results show that the contact stresses are availably reduced, and the areas of edge contact and severe contact stresses can be avoided by selecting appropriate circular blade profile. In addition, the convex and concave sides are separately modified by the use of different curvature radii of inside and outside blades, which can increase the flexibility of the duplex helical method.展开更多
The parameter sensitivities affecting the flutter speed of the NREL （National Renewable Energy Laboratory） 5-MW baseline HAWT （horizontal axis wind turbine） blades are analyzed. An aeroelastic model, which compris...The parameter sensitivities affecting the flutter speed of the NREL （National Renewable Energy Laboratory） 5-MW baseline HAWT （horizontal axis wind turbine） blades are analyzed. An aeroelastic model, which comprises an aerodynamic part to calculate the aerodynamic loads and a structural part to determine the structural dynamic responses, is established to describe the classical flutter of the blades. For the aerodynamic part, Theodorsen unsteady aerodynamics model is used. For the structural part, Lagrange’s equation is employed. The flutter speed is determined by introducing “V–g” method to the aeroelastic model, which converts the issue of classical flutter speed determination into an eigenvalue problem. Furthermore, the time domain aeroelastic response of the wind turbine blade section is obtained with employing Runge-Kutta method. The results show that four cases （i.e., reducing the blade torsional stiffness, moving the center of gravity or the elastic axis towards the trailing edge of the section, and placing the turbine in high air density area） will decrease the flutter speed. Therefore, the judicious selection of the four parameters （the torsional stiffness, the chordwise position of the center of gravity, the elastic axis position and air density） can increase the relative inflow speed at the blade section associated with the onset of flutter.展开更多
Cavitation will reduce the turbine performance and even damage the turbine components.To verify the effects of splitter blades on improving the cavitation performance,the cavitation flow inside a Francis turbine runne...Cavitation will reduce the turbine performance and even damage the turbine components.To verify the effects of splitter blades on improving the cavitation performance,the cavitation flow inside a Francis turbine runner with splitter blades was numerically simulated by using the Singhal cavitation model and the standard k-ε turbulence model.The distributions of static pressure and gas volume fractions on the surface of the runner blades were predicated under different conditions,and the cavitation in the flow field of the runner was analyzed.The results show that the static pressure and gas volume fractions are more uniformly distributed on the short blades than those on the long blades in Francis turbines with splitter blades,and there is almost no cavitation on the short blades;their distributions are more uniform under small flow conditions than those under large flow conditions;and large gas volume fractions are concentrated at the outlet tip near the band on the suction side of the long blade.The installation of splitter blades can improve the cavitation performance of conventional Francis turbines.展开更多
This paper proposes a parity recognition of blade number and manoeuvre intention classification algorithm of rotor target based on the convolutional neural network(CNN) using micro Doppler features. Firstly, the time-...This paper proposes a parity recognition of blade number and manoeuvre intention classification algorithm of rotor target based on the convolutional neural network(CNN) using micro Doppler features. Firstly, the time-frequency spectrograms are acquired from the radar echo by the short-time Fourier transform.Secondly, based on the obtained spectrograms, a seven-layer CNN architecture is built to recognize the blade-number parity and classify the manoeuvre intention of the rotor target. The constructed architecture contains a leaky rectified linear unit and a dropout layer to accelerate the convergence of the architecture and avoid over-fitting. Finally, the spectrograms of the datasets are divided into three different ratios, i.e., 20%, 33% and 50%,and the cross validation is used to verify the effectiveness of the constructed CNN architecture. Simulation results show that, on the one hand, as the ratio of training data increases, the recognition accuracy of parity and manoeuvre intention is improved at the same signal-to-noise ratio(SNR);on the other hand, the proposed algorithm also has a strong robustness: the accuracy can still reach 90.72% with an SNR of – 6 dB.展开更多
In order to describe and control the stress distribution and total deformation of bladed disk assemblies used in the aeroengine, a highly efficient and precise method of probabilistic analysis which is called extremum...In order to describe and control the stress distribution and total deformation of bladed disk assemblies used in the aeroengine, a highly efficient and precise method of probabilistic analysis which is called extremum response surface method(ERSM) is produced based on the previous deterministic analysis results with the finite element model(FEM). In this work, many key nonlinear factors, such as the dynamic feature of the temperature load, the centrifugal force and the boundary conditions, are taken into consideration for the model. The changing patterns with time of bladed disk assemblies about stress distribution and total deformation are obtained during the deterministic analysis, and at the same time, the largest deformation and stress nodes of bladed disk assemblies are found and taken as input target of probabilistic analysis in a scientific and reasonable way. Not only their reliability, historical sample, extreme response surface(ERS) and the cumulative probability distribution function but also their sensitivity and effect probability are obtained. Main factors affecting stress distribution and total deformation of bladed disk assemblies are investigated through the sensitivity analysis of the model. Finally, compared with the response surface method(RSM) and the Monte Carlo simulation(MCS), the results show that this new approach is effective.展开更多
In order to investigate the feasibility of monitoring the fatigue cracks in turbine blades using acoustic emission (AE) technique, the AE characteristics of fatigue crack growth were studied in the laboratory. And the...In order to investigate the feasibility of monitoring the fatigue cracks in turbine blades using acoustic emission (AE) technique, the AE characteristics of fatigue crack growth were studied in the laboratory. And the characteristics were compared with those of background noise received from a real hydraulic turbine unit. It is found that the AE parameters such as the energy and duration can qualitatively describe the fatigue state of the blades. The correlations of crack propagation rates and acoustic emission count rates vs stress intensity factor (SIF) range are also obtained. At the same time, for the specimens of 20SiMn under the given testing conditions, it is noted that the rise time and duration of events emitted from the fatigue process are lower than those from the background noise; amplitude range is 49-74 dB, which is lower than that of the noise (90-99 dB); frequency range of main energy of crack signals is higher than 60 kHz while that in the noise is lower than 55 kHz. Thus, it is possible to extract the useful crack signals from the noise through appropriate signal processing methods and to represent the crack status of blade materials by AE parameters. As a result, it is feasible to monitor the safety of runners using AE technique.展开更多
Due to the variation of the blade cross-section, the deformation stress and strain of the workpiece keep changing during the rolling process and the conventional rolling theory is no longer valid. The complexity and d...Due to the variation of the blade cross-section, the deformation stress and strain of the workpiece keep changing during the rolling process and the conventional rolling theory is no longer valid. The complexity and diversity of the blade cross-section determine it impossible to establish an universal theoretical model for the rolling process. Finite element analysis(FEA) provides a perspective solution to the prediction. The FEA software DEFORM was applied to discovering the deformation, stress, strain and velocity field of the variable cross-section workpiece, and the effects of friction coefficient and rolling speed during the rolling process. which indicates that the average rolling force at friction coefficient of 0.4 is 6.5% higher than that at 0.12, and the rolling velocity has less effect on the equivalent stress and strain distribution, which would confer instructive significance on the theoretical study as well as the engineering practice.展开更多
Aimed at the difficulty in revealing the vibration localization mechanism of mistuned bladed disks by using simple non-linear model,a mechanical model of the bladed disk with random mistuning of hysteretic dry frictio...Aimed at the difficulty in revealing the vibration localization mechanism of mistuned bladed disks by using simple non-linear model,a mechanical model of the bladed disk with random mistuning of hysteretic dry friction damping was established.Then,the incremental harmonic balance method was used to analyze the effects of the parameters of bladed disks,such as the mistuning strength of dry friction force,coupled strength,viscous damping ratio and friction strength,on the forced response of the bladed disks.The results show that the vibrational energy localization phenomenon turns up in the tuned bladed disks if the nonlinear friction damping exists,and the random mistuning of the dry friction force intensifies this kind of vibration localization.展开更多
A finite element analysis method was used to simulate the stamping process of the blade of a large concrete-mixer truck. The updated Lagrange method and the elasto-plastic constitutive equation were adopted to solve t...A finite element analysis method was used to simulate the stamping process of the blade of a large concrete-mixer truck. The updated Lagrange method and the elasto-plastic constitutive equation were adopted to solve the large strain and displacement deformation of the blade. A modified Coulomb friction model was used to solve the sliding contact between the blade and the dies. The von Mises stress distribution in the blade, the spatial displacement variation and the spring-back of the typical node were investigated in the simulation. The von Mises stress in the blade where the spring-back occurs is lowered from 463.0MPa to 150.0MPa before and after the spring-back. A typical node in the blade has a 3.33mm spring-back in Z direction. The results of the (experiments) agree well with the simulation. The analysis results are valuable for designing optimal tool dies.展开更多
The effects of ply orientation angle of composite flexures on stability of hingeless rotor blade system are studied.The composite hingeless rotor blade system is simplified as a hub,a flap flexure and a lag flexure.pi...The effects of ply orientation angle of composite flexures on stability of hingeless rotor blade system are studied.The composite hingeless rotor blade system is simplified as a hub,a flap flexure and a lag flexure.pitch bearing and main blade.The kinematics formulations are inferred by employing the moderate deflection beam theory.The shear deformation and warping related to torsion are considered.The quasi-steady strip theory with dynamic inflow effects is applied to obtain the aerodynamic loads acting on the blade.Based on these.the set of finite element formulations of a hingeless rotor blade system is worked out.The numerical results show that the ply angle of the composite flexures has great effects on the aeroelastic stability of rotor blade.展开更多
In this study,wind tunnel experiment was carried out to investigate the self-staring capability for straight-bladed vertical axis wind turbine.The flow visualization also was been performed at the rest of the rotor.Th...In this study,wind tunnel experiment was carried out to investigate the self-staring capability for straight-bladed vertical axis wind turbine.The flow visualization also was been performed at the rest of the rotor.The effect of the azimuthal angle of blade position relative to wind direction on the self-starting capability was discussed based on the results of flow visualization.The torque and centripetal force of the rotor when the self-starting behavior starts were roughly calculated with the flow visualization results of the rotor.It is suggested that there exists the condition of wind speed and configuration of the blade position of the rotor at the rest of rotor to the reach to situational rotation number.展开更多
To ameliorate reliability analysis efficiency for aeroengine components, such as compressor blade, support vector machine response surface method(SRSM) is proposed. SRSM integrates the advantages of support vector mac...To ameliorate reliability analysis efficiency for aeroengine components, such as compressor blade, support vector machine response surface method(SRSM) is proposed. SRSM integrates the advantages of support vector machine(SVM) and traditional response surface method(RSM), and utilizes experimental samples to construct a suitable response surface function(RSF) to replace the complicated and abstract finite element model. Moreover, the randomness of material parameters, structural dimension and operating condition are considered during extracting data so that the response surface function is more agreeable to the practical model. The results indicate that based on the same experimental data, SRSM has come closer than RSM reliability to approximating Monte Carlo method(MCM); while SRSM(17.296 s) needs far less running time than MCM(10958 s) and RSM(9840 s). Therefore,under the same simulation conditions, SRSM has the largest analysis efficiency, and can be considered a feasible and valid method to analyze structural reliability.展开更多
基金Project(DUT20RC(3)014)supported by the Fundamental Research Funds for the Central Universities,China,Project(VCAME201801)supported by Key Laboratory of Vibration and Control of Aero-Propulsion System(Ministry of Education),ChinaProject(11472068)supported by the National Natural Science Foundation of China。
文摘Failures due to high-cycle fatigue have led to a high cost in aerospace engineering over the past few decades.In this paper,the experimental results of the fatigue behavior of compressor blade specimen subjected to resonance and the effects of a damping hard coating on relieving the fatigue progress are presented.The crack initiation and propagation processes were observed under resonance of the first bending mode by using the resonant frequencies as the indicator.Significant nonlinear features were observed in the spectrum of the blade with a fatigue crack.The finite element model considering the breathing crack was established with nonlinear contact based on the crack localization and size,which was obtained by ultrasonic phased array technology.The simulation results of the vibration behavior of the cracked blade were obtained and consistent with the experimental results.A NiCrAlY coating was deposited on the blade,and increases in the fatigue life were observed under the same condition.The results of this paper can help to better understand the fatigue of a compressor blade subjected to resonance and provide a preference for the application of a damping hard coating on compressor blades.
基金Project(2011CB706800-G)supported by the National Basic Research Program of ChinaProject(51375159)supported by the National Natural Science Foundation of China+1 种基金Project(20120162110004)supported by the Postdoctoral Science Foundation of ChinaProject(2015JJ5020)supported by the Science Foundation of Hunan Province,China
文摘In order to effectively improve meshing performance of spiral bevel and hypoid gears generated by the duplex helical method, the effects of straight lined and circular cutting edges profile on meshing and contact of spiral bevel and hypoid gears were investigated analytically. Firstly, a mathematical model of spiral bevel and hypoid gears with circular blade profile was established according to the cutting characteristics of the duplex helical method. Based on a hypoid gear drive, the tooth bearings and the functions of transmission errors of four design cases were analyzed respectively by the use of the tooth contact analysis(TCA), and the contact stresses of the four design cases were analyzed and compared using simulation software. Finally, the curvature radius of the circular profile blade was optimized. The results show that the contact stresses are availably reduced, and the areas of edge contact and severe contact stresses can be avoided by selecting appropriate circular blade profile. In addition, the convex and concave sides are separately modified by the use of different curvature radii of inside and outside blades, which can increase the flexibility of the duplex helical method.
基金Project(2015B37714)supported by the Fundamental Research Funds for the Central Universities of ChinaProject(51605005)supported by the National Natural Science Foundation of China+1 种基金Project(ZK16-03-03)supported by the Open Foundation of Jiangsu Wind Technology Center,ChinaProject([2013]56)supported by the First Group of 2011 Plan of Jiangsu Province,China
文摘The parameter sensitivities affecting the flutter speed of the NREL （National Renewable Energy Laboratory） 5-MW baseline HAWT （horizontal axis wind turbine） blades are analyzed. An aeroelastic model, which comprises an aerodynamic part to calculate the aerodynamic loads and a structural part to determine the structural dynamic responses, is established to describe the classical flutter of the blades. For the aerodynamic part, Theodorsen unsteady aerodynamics model is used. For the structural part, Lagrange’s equation is employed. The flutter speed is determined by introducing “V–g” method to the aeroelastic model, which converts the issue of classical flutter speed determination into an eigenvalue problem. Furthermore, the time domain aeroelastic response of the wind turbine blade section is obtained with employing Runge-Kutta method. The results show that four cases （i.e., reducing the blade torsional stiffness, moving the center of gravity or the elastic axis towards the trailing edge of the section, and placing the turbine in high air density area） will decrease the flutter speed. Therefore, the judicious selection of the four parameters （the torsional stiffness, the chordwise position of the center of gravity, the elastic axis position and air density） can increase the relative inflow speed at the blade section associated with the onset of flutter.
基金Comprehensive Health Management Promotion Center of Xihua University(kgl2018-019)Scientific Research Project of the Education Department of Sichuan,China(18ZB0560)National Natural Science Foundation of China(51279172)
文摘Cavitation will reduce the turbine performance and even damage the turbine components.To verify the effects of splitter blades on improving the cavitation performance,the cavitation flow inside a Francis turbine runner with splitter blades was numerically simulated by using the Singhal cavitation model and the standard k-ε turbulence model.The distributions of static pressure and gas volume fractions on the surface of the runner blades were predicated under different conditions,and the cavitation in the flow field of the runner was analyzed.The results show that the static pressure and gas volume fractions are more uniformly distributed on the short blades than those on the long blades in Francis turbines with splitter blades,and there is almost no cavitation on the short blades;their distributions are more uniform under small flow conditions than those under large flow conditions;and large gas volume fractions are concentrated at the outlet tip near the band on the suction side of the long blade.The installation of splitter blades can improve the cavitation performance of conventional Francis turbines.
基金supported by the National Natural Science Foundation of China (61901514)the Young Talent Program of Air Force Early Warning Academy (TJRC425311G11)。
文摘This paper proposes a parity recognition of blade number and manoeuvre intention classification algorithm of rotor target based on the convolutional neural network(CNN) using micro Doppler features. Firstly, the time-frequency spectrograms are acquired from the radar echo by the short-time Fourier transform.Secondly, based on the obtained spectrograms, a seven-layer CNN architecture is built to recognize the blade-number parity and classify the manoeuvre intention of the rotor target. The constructed architecture contains a leaky rectified linear unit and a dropout layer to accelerate the convergence of the architecture and avoid over-fitting. Finally, the spectrograms of the datasets are divided into three different ratios, i.e., 20%, 33% and 50%,and the cross validation is used to verify the effectiveness of the constructed CNN architecture. Simulation results show that, on the one hand, as the ratio of training data increases, the recognition accuracy of parity and manoeuvre intention is improved at the same signal-to-noise ratio(SNR);on the other hand, the proposed algorithm also has a strong robustness: the accuracy can still reach 90.72% with an SNR of – 6 dB.
基金Projects(51375032,51175017,51245027)supported by the National Natural Science Foundation of China
文摘In order to describe and control the stress distribution and total deformation of bladed disk assemblies used in the aeroengine, a highly efficient and precise method of probabilistic analysis which is called extremum response surface method(ERSM) is produced based on the previous deterministic analysis results with the finite element model(FEM). In this work, many key nonlinear factors, such as the dynamic feature of the temperature load, the centrifugal force and the boundary conditions, are taken into consideration for the model. The changing patterns with time of bladed disk assemblies about stress distribution and total deformation are obtained during the deterministic analysis, and at the same time, the largest deformation and stress nodes of bladed disk assemblies are found and taken as input target of probabilistic analysis in a scientific and reasonable way. Not only their reliability, historical sample, extreme response surface(ERS) and the cumulative probability distribution function but also their sensitivity and effect probability are obtained. Main factors affecting stress distribution and total deformation of bladed disk assemblies are investigated through the sensitivity analysis of the model. Finally, compared with the response surface method(RSM) and the Monte Carlo simulation(MCS), the results show that this new approach is effective.
基金Project(50465002) supported by the National Natural Science Foundation of China
文摘In order to investigate the feasibility of monitoring the fatigue cracks in turbine blades using acoustic emission (AE) technique, the AE characteristics of fatigue crack growth were studied in the laboratory. And the characteristics were compared with those of background noise received from a real hydraulic turbine unit. It is found that the AE parameters such as the energy and duration can qualitatively describe the fatigue state of the blades. The correlations of crack propagation rates and acoustic emission count rates vs stress intensity factor (SIF) range are also obtained. At the same time, for the specimens of 20SiMn under the given testing conditions, it is noted that the rise time and duration of events emitted from the fatigue process are lower than those from the background noise; amplitude range is 49-74 dB, which is lower than that of the noise (90-99 dB); frequency range of main energy of crack signals is higher than 60 kHz while that in the noise is lower than 55 kHz. Thus, it is possible to extract the useful crack signals from the noise through appropriate signal processing methods and to represent the crack status of blade materials by AE parameters. As a result, it is feasible to monitor the safety of runners using AE technique.
基金Project(F12-256-1-00)supported by the Key Laboratory Program of Shenyang City,ChinaProject(N090403006)supported by the Seed Cultivation Fund,ChinaProject supported by the Research Innovation Fund for Young Teachers,China
文摘Due to the variation of the blade cross-section, the deformation stress and strain of the workpiece keep changing during the rolling process and the conventional rolling theory is no longer valid. The complexity and diversity of the blade cross-section determine it impossible to establish an universal theoretical model for the rolling process. Finite element analysis(FEA) provides a perspective solution to the prediction. The FEA software DEFORM was applied to discovering the deformation, stress, strain and velocity field of the variable cross-section workpiece, and the effects of friction coefficient and rolling speed during the rolling process. which indicates that the average rolling force at friction coefficient of 0.4 is 6.5% higher than that at 0.12, and the rolling velocity has less effect on the equivalent stress and strain distribution, which would confer instructive significance on the theoretical study as well as the engineering practice.
基金Project(2007CB707706) supported by the National Basic Research Program of China
文摘Aimed at the difficulty in revealing the vibration localization mechanism of mistuned bladed disks by using simple non-linear model,a mechanical model of the bladed disk with random mistuning of hysteretic dry friction damping was established.Then,the incremental harmonic balance method was used to analyze the effects of the parameters of bladed disks,such as the mistuning strength of dry friction force,coupled strength,viscous damping ratio and friction strength,on the forced response of the bladed disks.The results show that the vibrational energy localization phenomenon turns up in the tuned bladed disks if the nonlinear friction damping exists,and the random mistuning of the dry friction force intensifies this kind of vibration localization.
基金Project(2002A1040703) supported by the Science and Technology Fund of Guangdong Province
文摘A finite element analysis method was used to simulate the stamping process of the blade of a large concrete-mixer truck. The updated Lagrange method and the elasto-plastic constitutive equation were adopted to solve the large strain and displacement deformation of the blade. A modified Coulomb friction model was used to solve the sliding contact between the blade and the dies. The von Mises stress distribution in the blade, the spatial displacement variation and the spring-back of the typical node were investigated in the simulation. The von Mises stress in the blade where the spring-back occurs is lowered from 463.0MPa to 150.0MPa before and after the spring-back. A typical node in the blade has a 3.33mm spring-back in Z direction. The results of the (experiments) agree well with the simulation. The analysis results are valuable for designing optimal tool dies.
文摘The effects of ply orientation angle of composite flexures on stability of hingeless rotor blade system are studied.The composite hingeless rotor blade system is simplified as a hub,a flap flexure and a lag flexure.pitch bearing and main blade.The kinematics formulations are inferred by employing the moderate deflection beam theory.The shear deformation and warping related to torsion are considered.The quasi-steady strip theory with dynamic inflow effects is applied to obtain the aerodynamic loads acting on the blade.Based on these.the set of finite element formulations of a hingeless rotor blade system is worked out.The numerical results show that the ply angle of the composite flexures has great effects on the aeroelastic stability of rotor blade.
基金supported in part by International Platform for Dryland Research and Education (IPDRE),Tottori University
文摘In this study,wind tunnel experiment was carried out to investigate the self-staring capability for straight-bladed vertical axis wind turbine.The flow visualization also was been performed at the rest of the rotor.The effect of the azimuthal angle of blade position relative to wind direction on the self-starting capability was discussed based on the results of flow visualization.The torque and centripetal force of the rotor when the self-starting behavior starts were roughly calculated with the flow visualization results of the rotor.It is suggested that there exists the condition of wind speed and configuration of the blade position of the rotor at the rest of rotor to the reach to situational rotation number.
基金Project(51335003)supported by the National Natural Science Foundation of ChinaProject(20111102110011)supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China
文摘To ameliorate reliability analysis efficiency for aeroengine components, such as compressor blade, support vector machine response surface method(SRSM) is proposed. SRSM integrates the advantages of support vector machine(SVM) and traditional response surface method(RSM), and utilizes experimental samples to construct a suitable response surface function(RSF) to replace the complicated and abstract finite element model. Moreover, the randomness of material parameters, structural dimension and operating condition are considered during extracting data so that the response surface function is more agreeable to the practical model. The results indicate that based on the same experimental data, SRSM has come closer than RSM reliability to approximating Monte Carlo method(MCM); while SRSM(17.296 s) needs far less running time than MCM(10958 s) and RSM(9840 s). Therefore,under the same simulation conditions, SRSM has the largest analysis efficiency, and can be considered a feasible and valid method to analyze structural reliability.
