In the actual engineering of the structure, mechanical notch is inevitable, which will significantly reduce the fatigue life of the structure. In order to ensure the application of notch structures in engineering, the...In the actual engineering of the structure, mechanical notch is inevitable, which will significantly reduce the fatigue life of the structure. In order to ensure the application of notch structures in engineering, the accurate evaluation of the impact of notch on fatigue life has become the basis of fatigue reliability design of structures. To investigate the influence of the concave structure on the overall fatigue life in practical engineering, three different sizes of V-notch parts and concave structure simulation parts were designed, and the life prediction was carried out by using the critical distance method. The results show that the stress gradient of the concave structure with the same stress concentration coefficient is much greater than that of the V-notch structure. Considering the notch effect, the S-T model in the critical distance method is modified by the stress concentration coefficient and stress gradient, and it is found that the life prediction accuracy reaches the ideal.展开更多
The spudcan foundation has been widely used in offshore engineering for jack-up rigs. However, “punch through' failure often occurs where a stronger soil layer overlays a softer soil layer. In this study, spudcan...The spudcan foundation has been widely used in offshore engineering for jack-up rigs. However, “punch through' failure often occurs where a stronger soil layer overlays a softer soil layer. In this study, spudcan penetration into double layered soils is investigated numerically. The soil profile is set up as a stronger soil layer overlaying a softer soil layer, with the soil strength ratio (bottom soil strength / top soil strength) varied from 0.1 to 1.0 (1 means uniform soil). The bearing behaviour is discussed and the bearing capacity factors are given for various cases involving different layer thicknesses and different strength ratios of the two clay layers. The development of the plastic zones and the effect of soil self-weight on the bearing capacity are also discussed. From this study, it is found that, when a spudcan is distant from the soil layer boundary, the spudcan can be analysed with single soil layer data. However, when a spudcan becomes closer to the soil boundary layer, the influence of the lower soft soil layer is significant, and the bearing capacity of the spudcan decreases. The critical distance is an indication of the occurrence of “punch through' failure. The critical distance between the spudcan and the layer boundary is larger for a rough spudcan than the one for a smooth one, and the critical distance decreases with increasing soil strength ratio. The depth of cavity formed during initial spudcan penetration depends on the top layer soil strength, soil strength ratio and unit soil self-weight, and the cavity affects the spudcan bearing behaviour as well.展开更多
The primary objective of this work is to explore how drivers react to flashing green at signalized intersections. Through video taping and data procession based on photogrammetry, the operating speeds of vehicles befo...The primary objective of this work is to explore how drivers react to flashing green at signalized intersections. Through video taping and data procession based on photogrammetry, the operating speeds of vehicles before and after the moment when flashing green started was compared using paired-samples T-test. The critical distances between go and stop decisions was defined through cumulative percentage curve. The boundary of dilemma zone was determined by comparing stop distance and travel distance.Amber-running violation was analyzed on the basis of the travel time to the stop line. And finally, a logistic model for stop and go decisions was constructed. The results shows that the stopping ratios of the first vehicles of west-bound and east-bound approaches are 41.3% and 39.8%, respectively; the amber-light running violation ratios of two approaches are 31.6% and 25.4%, respectively;the operating speed growth ratios of first vehicles selecting to cross intersection after the moment when flashing green started are26.7% and 17.7%, respectively; and the critical distances are 48 m and 46 m, respectively, which are close to 44 m, the boundary of dilemma zone. The developed decision models demonstrate that the probability of go decision is higher when the distance from the stop line is shorter or operating speed is higher. This indicates that flashing green is an effective way to enhance intersection safety,but it should work together with a strict enforcement. In addition, traffic signs near critical distance and reasonable speed limitation are also beneficial to the safety of intersections.展开更多
On March 13,2007,two earthquakes with M4.7 and M4.6 occurred in Zhengfang Village,Shunchang,Fujian.The M4.7 earthquake is the most intensive one in the Fujian region since the establishment of the Fujian digital seism...On March 13,2007,two earthquakes with M4.7 and M4.6 occurred in Zhengfang Village,Shunchang,Fujian.The M4.7 earthquake is the most intensive one in the Fujian region since the establishment of the Fujian digital seismic networks.These two earthquakes provide us with valuable first-hand observation data for seismological research.This paper analyzes their wave-forms and concludes that(1)the crustal thickness in the seismic region is estimated to be about 40km according to the observed head-wave critical distance;(2)there is a salient difference between the ratios of S-wave's maximum amplitudes of these two earthquakes;(3)the focal depth of the M4.7 earthquake is estimated to be 8.4km according to the clear depth phrase sPn in waveforms,which is the same with the result of other determination methods.展开更多
According to the representation theorem of seismic energy radiation, we know that, at any point on the fault, the instantaneous seismic radiation energy, Es, the seismic moment M0, and the apparent stress σa=μEs /M0...According to the representation theorem of seismic energy radiation, we know that, at any point on the fault, the instantaneous seismic radiation energy, Es, the seismic moment M0, and the apparent stress σa=μEs /M0 (μ is the shear modulus on the fault plane) should be positive values at any time during an earthquake faulting. However, we have noticed that, in recent source parameter inversion scheme for deriving the critical slip-weakening distance, the apparent stress used as a constraint condition on the fault plane could be less than zero or negative value, and the negative part was considered as dissipation energy and incorporated to the fracture energy. Although the mathematical formula in such case has no influence to the final resolution, however, the earthquake dynamic source process violates obviously the basic physical law, which could results in the overestimating of radiated seismic energy. In this study, we have proposed an alternative way to take account of the apparent stress expression based on the earthquake energy partition principle, and at the same time, we have also suggested that an additional constraint regarding to the radiation energy conservation on the fault could be added into the source parameter inversion in order to estimate the critical slip-weakening distance Dc.展开更多
In this study,we attempted to perform an earthquake source dynamic inversion to obtain dynamic parameters on fault system with complex geometry.The forward modeling of the spontaneous rupture process is carried out us...In this study,we attempted to perform an earthquake source dynamic inversion to obtain dynamic parameters on fault system with complex geometry.The forward modeling of the spontaneous rupture process is carried out using a boundary integral equation method(BIEM)based on unstructured meshing,and the inversion method is implemented by a genetic algorithm based on a parallel acceleration of the GPU.The source model in this study is a branched fault,which is described by two physical parameters,the initial stress T0 and the critical slip-weakening distance Dc.We investigated the effect of the inherited parameters on the accuracy and convergence of the inversion simulation.Numerical results showed that if a set of parameters are assigned properly,the inversion of rupture parameters is accurate and converges fast.It is easy to converge to a local optimal solution during the inversion process if inappropriate inherited parameters are selected.Compared with T0,D。has better convergence and accuracy in.the inversion process.展开更多
In this paper,we derived the relationships between the travel time difference of sPn and Pn and the local earthquake focal depth.In these equations,the travel time difference of sPn and Pn is not related to the epicen...In this paper,we derived the relationships between the travel time difference of sPn and Pn and the local earthquake focal depth.In these equations,the travel time difference of sPn and Pn is not related to the epicentral distance,but depends only on the regional crustal mode and the focal depth.According to the equations,we provided a simple and accurate method to determine local earthquake focal depth by using the travel time difference between phase sPn and Pn.This method has been used to determine the focal depths of two earthquake of MS6.1 and MS5.6 which occurred at the junction of Panzhihua and Huili,Sichuan on August 30 and 31,2008.The results were compared to those from other sources such as the China Earthquake Networks Center,and the comparison shows that the results are accurate and reliable.展开更多
Based on the density functional theory(DFT),we investigate the friction properties of inevitable oxidized black phosphorus(o-BP).o-BP with the weaker interlayer adhesion exhibits their great potential as a solid lubri...Based on the density functional theory(DFT),we investigate the friction properties of inevitable oxidized black phosphorus(o-BP).o-BP with the weaker interlayer adhesion exhibits their great potential as a solid lubricant.At the zero load,the friction property of o-BP is adjusted by its oxidation degree.Expressly,ultra-low friction of P4O2(50%oxidation,O:P=2:4=50%)is obtained,which is attributed to the upper O atoms with lower sliding resistance in the O channel formed by lower layer O atoms.More attractive,we observe superlubricity behavior of o-BP at the critical load/distance due to the flattening potential energy surface(PES).The flattening PES is controlled by the electrostatic role for the high-load(P4O3,O:P=3:4=75%),and by the electrostatic and dispersion roles for the low-load(P4O2).Distinctly,the transform from ultra-low friction to superlubricity state of black phosphorus(BP)can be achieved by critical oxidation and load,which shows an important significance in engineering application.In addition,negative friction behavior of o-BP is a general phenomenon(Z>Z_(min),Z_(min)is the interlayer distances between the outermost P atoms of minimum load.),while its surface-surface model is different from the fold mechanism of the tip-surface model(Z_(0)<Z<Z_(min),Z_(0)is the interlayer distances between the outermost P atoms of equilibrium state.).Thus,this phenomenon cannot be captured due to the jump effect with instability of the atomic force microscopy(AFM)(Z>Z_(min)).In summary,o-BP improves the friction performance and reduces the application limitation,comparing to graphene(Gr),MoS2,and their oxides.展开更多
In engineering applications,the notch effect and size effect significantly influence the evaluation of fatigue performance in components,necessitating special attention in life prediction.This study proposes a new pro...In engineering applications,the notch effect and size effect significantly influence the evaluation of fatigue performance in components,necessitating special attention in life prediction.This study proposes a new probabilistic model,based on the theory of critical distance(TCD),to predict fatigue life,with the aim of quantitatively assessing the impact of notch effect and size effect.The stress distribution on the critical plane is first characterized using a sixth-order multinomial function,and the relative stress gradient function is utilized to calculate the value of the critical distance.Furthermore,the effect of the ratio of shear strain to normal strain on fatigue life under multiaxial loading is considered.Additionally,the integration of the Weibull distribution into the TCD is employed for conducting probabilistic modeling of fatigue life.Finally,fatigue experiments are conducted on notched specimens of Q355D steel,demonstrating that the life prediction results under 50%survival probability are superior to the traditional TCD method.展开更多
The critical slip distance in rate and state model for fault friction in the study of potential earthquakes can vary wildly from micrometers to few me-ters depending on the length scale of the critically stressed faul...The critical slip distance in rate and state model for fault friction in the study of potential earthquakes can vary wildly from micrometers to few me-ters depending on the length scale of the critically stressed fault.This makes it incredibly important to construct an inversion framework that provides good estimates of the critical slip distance purely based on the observed ac-celeration at the seismogram.To eventually construct a framework that takes noisy seismogram acceleration data as input and spits out robust estimates of critical slip distance as the output,we first present the performance of the framework for synthetic data.The framework is based on Bayesian inference and Markov chain Monte Carlo methods.The synthetic data is generated by adding noise to the acceleration output of spring-slider-damper idealization of the rate and state model as the forward model.展开更多
The adsorption of nano-particles on bubble surface is discussed for saturated boiling on thin wire of nano-particle suspensions. Owing to the decrease of surface tension for suspensions, the nano-particles tend to ads...The adsorption of nano-particles on bubble surface is discussed for saturated boiling on thin wire of nano-particle suspensions. Owing to the decrease of surface tension for suspensions, the nano-particles tend to adsorb on the bubble surface to decrease the Gibbs free energy for stability, and meanwhile the velocity of nano-particles would be smaller than that of bubble growth. The long-range van der Waals force existing between “water particles” and nano-particles is considered the attractive force between the nano-particles and the bubble surface. Thus, the nano-particles would attach on the bubble surface if the particle-surface distance is smaller than its critical value. The distribution of nano-particles on the bubble surface and in the adjacent region is also investigated.展开更多
Fatigue fracture is one of the most common failure modes of engineering compo-nents,and the combined action of geometrie discontinuity and multiaxial loading is more likely to cause severe fatigue damage of components...Fatigue fracture is one of the most common failure modes of engineering compo-nents,and the combined action of geometrie discontinuity and multiaxial loading is more likely to cause severe fatigue damage of components.This work focuses on the fatigue behavior of U-notched Q345 steel specimens with differen t notch sizes under proportional cyclic tension-torsion.Firstly,based on the concept of strain energy,the calculation method of critical plane is given and the equivalent stress of the specified path on the critical plane is extracted to char-acterize the equivalent stress distribution state and the stress gradient effect.Then,based on the high stress volume method and theory of critical distance,a simple method for determining the critical distance is given considering the contribution of stress at the dangerous point and the critical point.In addition,based on the idea of stress-distance normalization,a new stress gradient impact factor is defined and a new method for predicting the multiaxial fatigue life of notched specimens is given.The prediction results of the proposed model,the local stress-strain method and the point method of theory of critical distance are compared with the experimental results.The comparisons show that the prediction results of the proposed model are closer to experimentai life,and the calculation accuracy is higher.展开更多
文摘In the actual engineering of the structure, mechanical notch is inevitable, which will significantly reduce the fatigue life of the structure. In order to ensure the application of notch structures in engineering, the accurate evaluation of the impact of notch on fatigue life has become the basis of fatigue reliability design of structures. To investigate the influence of the concave structure on the overall fatigue life in practical engineering, three different sizes of V-notch parts and concave structure simulation parts were designed, and the life prediction was carried out by using the critical distance method. The results show that the stress gradient of the concave structure with the same stress concentration coefficient is much greater than that of the V-notch structure. Considering the notch effect, the S-T model in the critical distance method is modified by the stress concentration coefficient and stress gradient, and it is found that the life prediction accuracy reaches the ideal.
文摘The spudcan foundation has been widely used in offshore engineering for jack-up rigs. However, “punch through' failure often occurs where a stronger soil layer overlays a softer soil layer. In this study, spudcan penetration into double layered soils is investigated numerically. The soil profile is set up as a stronger soil layer overlaying a softer soil layer, with the soil strength ratio (bottom soil strength / top soil strength) varied from 0.1 to 1.0 (1 means uniform soil). The bearing behaviour is discussed and the bearing capacity factors are given for various cases involving different layer thicknesses and different strength ratios of the two clay layers. The development of the plastic zones and the effect of soil self-weight on the bearing capacity are also discussed. From this study, it is found that, when a spudcan is distant from the soil layer boundary, the spudcan can be analysed with single soil layer data. However, when a spudcan becomes closer to the soil boundary layer, the influence of the lower soft soil layer is significant, and the bearing capacity of the spudcan decreases. The critical distance is an indication of the occurrence of “punch through' failure. The critical distance between the spudcan and the layer boundary is larger for a rough spudcan than the one for a smooth one, and the critical distance decreases with increasing soil strength ratio. The depth of cavity formed during initial spudcan penetration depends on the top layer soil strength, soil strength ratio and unit soil self-weight, and the cavity affects the spudcan bearing behaviour as well.
基金Project(51208451)supported by the National Natural Science Foundation of ChinaProject(10KJB580004)supported by the Natural Science Foundation for Colleges and Universities of Jiangsu Province,ChinaProject supported by the New Century Talents Project of Yangzhou University,China
文摘The primary objective of this work is to explore how drivers react to flashing green at signalized intersections. Through video taping and data procession based on photogrammetry, the operating speeds of vehicles before and after the moment when flashing green started was compared using paired-samples T-test. The critical distances between go and stop decisions was defined through cumulative percentage curve. The boundary of dilemma zone was determined by comparing stop distance and travel distance.Amber-running violation was analyzed on the basis of the travel time to the stop line. And finally, a logistic model for stop and go decisions was constructed. The results shows that the stopping ratios of the first vehicles of west-bound and east-bound approaches are 41.3% and 39.8%, respectively; the amber-light running violation ratios of two approaches are 31.6% and 25.4%, respectively;the operating speed growth ratios of first vehicles selecting to cross intersection after the moment when flashing green started are26.7% and 17.7%, respectively; and the critical distances are 48 m and 46 m, respectively, which are close to 44 m, the boundary of dilemma zone. The developed decision models demonstrate that the probability of go decision is higher when the distance from the stop line is shorter or operating speed is higher. This indicates that flashing green is an effective way to enhance intersection safety,but it should work together with a strict enforcement. In addition, traffic signs near critical distance and reasonable speed limitation are also beneficial to the safety of intersections.
基金sponsored by the Joint Earthquake Science Foundation of China (106094)
文摘On March 13,2007,two earthquakes with M4.7 and M4.6 occurred in Zhengfang Village,Shunchang,Fujian.The M4.7 earthquake is the most intensive one in the Fujian region since the establishment of the Fujian digital seismic networks.These two earthquakes provide us with valuable first-hand observation data for seismological research.This paper analyzes their wave-forms and concludes that(1)the crustal thickness in the seismic region is estimated to be about 40km according to the observed head-wave critical distance;(2)there is a salient difference between the ratios of S-wave's maximum amplitudes of these two earthquakes;(3)the focal depth of the M4.7 earthquake is estimated to be 8.4km according to the clear depth phrase sPn in waveforms,which is the same with the result of other determination methods.
基金supported by Foundation for Seismological Researches of the Institute of Crustal Dynamics,China Earthquake Administration,(ZDJ2007-1)One Hundred Individual Program of Chinese Academy of Sciences and National Natural Science Foundation of China (40574022)
文摘According to the representation theorem of seismic energy radiation, we know that, at any point on the fault, the instantaneous seismic radiation energy, Es, the seismic moment M0, and the apparent stress σa=μEs /M0 (μ is the shear modulus on the fault plane) should be positive values at any time during an earthquake faulting. However, we have noticed that, in recent source parameter inversion scheme for deriving the critical slip-weakening distance, the apparent stress used as a constraint condition on the fault plane could be less than zero or negative value, and the negative part was considered as dissipation energy and incorporated to the fracture energy. Although the mathematical formula in such case has no influence to the final resolution, however, the earthquake dynamic source process violates obviously the basic physical law, which could results in the overestimating of radiated seismic energy. In this study, we have proposed an alternative way to take account of the apparent stress expression based on the earthquake energy partition principle, and at the same time, we have also suggested that an additional constraint regarding to the radiation energy conservation on the fault could be added into the source parameter inversion in order to estimate the critical slip-weakening distance Dc.
基金the National Natural Science Foundation of China(No.41874047)the High-performance Computing Platform of Peking University.
文摘In this study,we attempted to perform an earthquake source dynamic inversion to obtain dynamic parameters on fault system with complex geometry.The forward modeling of the spontaneous rupture process is carried out using a boundary integral equation method(BIEM)based on unstructured meshing,and the inversion method is implemented by a genetic algorithm based on a parallel acceleration of the GPU.The source model in this study is a branched fault,which is described by two physical parameters,the initial stress T0 and the critical slip-weakening distance Dc.We investigated the effect of the inherited parameters on the accuracy and convergence of the inversion simulation.Numerical results showed that if a set of parameters are assigned properly,the inversion of rupture parameters is accurate and converges fast.It is easy to converge to a local optimal solution during the inversion process if inappropriate inherited parameters are selected.Compared with T0,D。has better convergence and accuracy in.the inversion process.
基金funded by the special support projectentitled "Sorting out and processing of seismic data " of central public-interest basic scientific and technological research of Institute of Crustal DynamicsChina Earthquake Administration (ZDJ2007-4)
文摘In this paper,we derived the relationships between the travel time difference of sPn and Pn and the local earthquake focal depth.In these equations,the travel time difference of sPn and Pn is not related to the epicentral distance,but depends only on the regional crustal mode and the focal depth.According to the equations,we provided a simple and accurate method to determine local earthquake focal depth by using the travel time difference between phase sPn and Pn.This method has been used to determine the focal depths of two earthquake of MS6.1 and MS5.6 which occurred at the junction of Panzhihua and Huili,Sichuan on August 30 and 31,2008.The results were compared to those from other sources such as the China Earthquake Networks Center,and the comparison shows that the results are accurate and reliable.
基金The authors were grateful to the financial support from the National Natural Science Foundation of China(52175168)the Natural Science Foundation of Guangdong Province(2021A1515012266),ChinaGuangdong Basic and Applied Basic Research Foundation(2022A1515010513),China.
文摘Based on the density functional theory(DFT),we investigate the friction properties of inevitable oxidized black phosphorus(o-BP).o-BP with the weaker interlayer adhesion exhibits their great potential as a solid lubricant.At the zero load,the friction property of o-BP is adjusted by its oxidation degree.Expressly,ultra-low friction of P4O2(50%oxidation,O:P=2:4=50%)is obtained,which is attributed to the upper O atoms with lower sliding resistance in the O channel formed by lower layer O atoms.More attractive,we observe superlubricity behavior of o-BP at the critical load/distance due to the flattening potential energy surface(PES).The flattening PES is controlled by the electrostatic role for the high-load(P4O3,O:P=3:4=75%),and by the electrostatic and dispersion roles for the low-load(P4O2).Distinctly,the transform from ultra-low friction to superlubricity state of black phosphorus(BP)can be achieved by critical oxidation and load,which shows an important significance in engineering application.In addition,negative friction behavior of o-BP is a general phenomenon(Z>Z_(min),Z_(min)is the interlayer distances between the outermost P atoms of minimum load.),while its surface-surface model is different from the fold mechanism of the tip-surface model(Z_(0)<Z<Z_(min),Z_(0)is the interlayer distances between the outermost P atoms of equilibrium state.).Thus,this phenomenon cannot be captured due to the jump effect with instability of the atomic force microscopy(AFM)(Z>Z_(min)).In summary,o-BP improves the friction performance and reduces the application limitation,comparing to graphene(Gr),MoS2,and their oxides.
基金supported by the National Natural Science Foundation of China(Grant Number 52365016)Gansu Province Young Doctor Fund Project(Grant Number 2023QB-030)Lanzhou University of Technology Graduate Research Exploration Project.
文摘In engineering applications,the notch effect and size effect significantly influence the evaluation of fatigue performance in components,necessitating special attention in life prediction.This study proposes a new probabilistic model,based on the theory of critical distance(TCD),to predict fatigue life,with the aim of quantitatively assessing the impact of notch effect and size effect.The stress distribution on the critical plane is first characterized using a sixth-order multinomial function,and the relative stress gradient function is utilized to calculate the value of the critical distance.Furthermore,the effect of the ratio of shear strain to normal strain on fatigue life under multiaxial loading is considered.Additionally,the integration of the Weibull distribution into the TCD is employed for conducting probabilistic modeling of fatigue life.Finally,fatigue experiments are conducted on notched specimens of Q355D steel,demonstrating that the life prediction results under 50%survival probability are superior to the traditional TCD method.
文摘The critical slip distance in rate and state model for fault friction in the study of potential earthquakes can vary wildly from micrometers to few me-ters depending on the length scale of the critically stressed fault.This makes it incredibly important to construct an inversion framework that provides good estimates of the critical slip distance purely based on the observed ac-celeration at the seismogram.To eventually construct a framework that takes noisy seismogram acceleration data as input and spits out robust estimates of critical slip distance as the output,we first present the performance of the framework for synthetic data.The framework is based on Bayesian inference and Markov chain Monte Carlo methods.The synthetic data is generated by adding noise to the acceleration output of spring-slider-damper idealization of the rate and state model as the forward model.
基金This project is supported by the National Natural Science Foundation of China(Grant No.59995553).
文摘The adsorption of nano-particles on bubble surface is discussed for saturated boiling on thin wire of nano-particle suspensions. Owing to the decrease of surface tension for suspensions, the nano-particles tend to adsorb on the bubble surface to decrease the Gibbs free energy for stability, and meanwhile the velocity of nano-particles would be smaller than that of bubble growth. The long-range van der Waals force existing between “water particles” and nano-particles is considered the attractive force between the nano-particles and the bubble surface. Thus, the nano-particles would attach on the bubble surface if the particle-surface distance is smaller than its critical value. The distribution of nano-particles on the bubble surface and in the adjacent region is also investigated.
基金This research was supported by the National Natural Science Foundation of China(Grant No.51605212)the Natural Science Foundation of Gansu Province(Grant No.20JR10RA161)the Project of Hongliu Excellent Youth Program of Lanzhou University of Technology(Grant No.2020062001).
文摘Fatigue fracture is one of the most common failure modes of engineering compo-nents,and the combined action of geometrie discontinuity and multiaxial loading is more likely to cause severe fatigue damage of components.This work focuses on the fatigue behavior of U-notched Q345 steel specimens with differen t notch sizes under proportional cyclic tension-torsion.Firstly,based on the concept of strain energy,the calculation method of critical plane is given and the equivalent stress of the specified path on the critical plane is extracted to char-acterize the equivalent stress distribution state and the stress gradient effect.Then,based on the high stress volume method and theory of critical distance,a simple method for determining the critical distance is given considering the contribution of stress at the dangerous point and the critical point.In addition,based on the idea of stress-distance normalization,a new stress gradient impact factor is defined and a new method for predicting the multiaxial fatigue life of notched specimens is given.The prediction results of the proposed model,the local stress-strain method and the point method of theory of critical distance are compared with the experimental results.The comparisons show that the prediction results of the proposed model are closer to experimentai life,and the calculation accuracy is higher.