For multivariate failure time with auxiliary covariate information,an estimated pseudo-partial-likelihood estimator under the marginal hazard model with distinguishable baseline hazard has been proposed.However,the as...For multivariate failure time with auxiliary covariate information,an estimated pseudo-partial-likelihood estimator under the marginal hazard model with distinguishable baseline hazard has been proposed.However,the asymptotic properties of the corresponding estimated cumulative hazard function have not been studied.In this paper,based on counting process martingale,we use the continuous mapping theorem and Lenglart inequality and prove the consistency of the estimated cumulative hazard function in estimated pseudo-partial-likelihood approach.展开更多
The log-normal distribution function(LNDF)and Weibull cumulative density function(WCDF)represent two prevalent approaches for characterizing sediment grain size distributions.This study analyzes annual average suspend...The log-normal distribution function(LNDF)and Weibull cumulative density function(WCDF)represent two prevalent approaches for characterizing sediment grain size distributions.This study analyzes annual average suspended load grain size data(standardized to equivalent settling diameters)from seven hydrological stations in the lower Yellow River(LYR)spanning 1962–2020,employing various distribution functions for grain size fitting.Results demonstrate that the Weibull probability density function(WPDF)offers significant advantages over both LNDF and WCDF in terms of fitting accuracy,parameter stability,simplicity,and practical applicability for characterizing suspended load grain size distributions in the LYR.Based on these findings,universal formulas were developed for the suspended load grain size distribution across the seven stations and the entire lower reaches,yielding determination coefficients(R2)exceeding 0.9.These formulas can be applied to estimate suspended load grain size in data-scarce cross-sections.The existence of such universal formulas suggests that interannual fluctuations in suspended load grain size in the LYR are constrained within a limited range,suggesting that sediment grain size may represent an inherent property of the river channel.This limited variability may be attributed to the fact that sediments in the LYR are primarily derived from a relatively fixed source region—the Loess Plateau.The observed stability over an extended period also offers valuable insights into the fundamental properties of river systems and their long-term behavior.展开更多
A new explicit quadratic radical function is found by numerical experiments,which is simpler and has only 70.778%of the maximal distance error compared with the Fisher z transformation.Furthermore,a piecewise function...A new explicit quadratic radical function is found by numerical experiments,which is simpler and has only 70.778%of the maximal distance error compared with the Fisher z transformation.Furthermore,a piecewise function is constructed for the standard normal distribution:if the independent variable falls in the interval(-1.519,1.519),the proposed function is employed;otherwise,the Fisher z transformation is used.Compared with the Fisher z transformation,this piecewise function has only 38.206%of the total error.The new function is more exact to estimate the confidence intervals of Pearson product moment correlation coefficient and Dickinson best weights for the linear combination of forecasts.展开更多
In this paper, based on random left truncated and right censored data, the authors derive strong representations of the cumulative hazard function estimator and the product-limit estimator of the survival function. wh...In this paper, based on random left truncated and right censored data, the authors derive strong representations of the cumulative hazard function estimator and the product-limit estimator of the survival function. which are valid up to a given order statistic of the observations. A precise bound for the errors is obtained which only depends on the index of the last order statistic to be included.展开更多
Diameter distribution models play an important role in forest inventories,growth prediction,and management.The Weibull probability density function is widely used in forestry.Although a number of methods have been pro...Diameter distribution models play an important role in forest inventories,growth prediction,and management.The Weibull probability density function is widely used in forestry.Although a number of methods have been proposed to predict or recover the Weibull distribution,their applicability and predictive performance for the major tree species of China remain to be determined.Trees in sample plots of three even-aged coniferous species(Larix olgensis,Pinus sylvestris and Pinus koraiensis)were measured both in un-thinned and thinned stands to develop parameter prediction models for the Weibull probability density function.Ordinary least squares(OLS)and maximum likelihood regression(MLER),as well as cumulative distribution function regression(CDFR)were used,and their performance compared.The results show that MLER and CDFR were better than OLS in predicting diameter distributions of tree plantations.CDFR produced the best results in terms of fitting statistics.Based on the error statistics calculated for different age groups,CDFR was considered the most suitable method for developing prediction models for Weibull parameters in coniferous plantations.展开更多
The United States,Russia and China are militarily and economically among the most powerful countries in the post-Cold War period,and the interactions between the three powers heavily influence the international system...The United States,Russia and China are militarily and economically among the most powerful countries in the post-Cold War period,and the interactions between the three powers heavily influence the international system.However,different conclusions about this question are generally made by researchers through qualitative analysis,and it is necessary to objectively and quantitatively investigate their interactions.Monthly-aggregated event data from the Global Data on Events,Location and Tone(GDELT)to measure cooperative and conflictual interactions between the three powers,and the complementary cumulative distribution function(CCDF)and the vector autoregression(VAR)method are utilized to investigate their interactions in two periods:January,1991 to September,2001,and October,2001 to December,2016.The results of frequencies and strengths analysis showed that:the frequencies and strengths of USA-China interactions slightly exceeded those of USA-Russia interactions and became the dominant interactions in the second period.Although that cooperation prevailed in the three dyads in two periods,the conflictual interactions between the USA and Russia tended to be more intense in the second period,mainly related to the strategic contradiction between the USA and Russia,especially in Georgia,Ukraine and Syria.The results of CCDF indicated that similar probabilities in the cooperative behaviors between the three dyads,but the differences in the probabilities of conflictual behaviors in the USA-Russia dyad showed complicated characteristic,and those between Russia and China indicated that Russia had been consistently giving China a hard time in both periods when dealing with conflict.The USA was always an essential factor in affecting the interactions between Russia and China in both periods,but China’s behavior only played a limited role in influencing the interactions between the USA-Russia dyad.Our study provides quantitative insight into the direct cooperative and conflictual interactions between the three dyads since the end of the Cold War and helps to understand their interactions better.展开更多
Traditional Global Sensitivity Analysis（GSA） focuses on ranking inputs according to their contributions to the output uncertainty.However,information about how the specific regions inside an input affect the output ...Traditional Global Sensitivity Analysis（GSA） focuses on ranking inputs according to their contributions to the output uncertainty.However,information about how the specific regions inside an input affect the output is beyond the traditional GSA techniques.To fully address this issue,in this work,two regional moment-independent importance measures,Regional Importance Measure based on Probability Density Function（RIMPDF） and Regional Importance Measure based on Cumulative Distribution Function（RIMCDF）,are introduced to find out the contributions of specific regions of an input to the whole output distribution.The two regional importance measures prove to be reasonable supplements of the traditional GSA techniques.The ideas of RIMPDF and RIMCDF are applied in two engineering examples to demonstrate that the regional moment-independent importance analysis can add more information concerning the contributions of model inputs.展开更多
The application of the saddlepoint approximation to reliability analysis of dynamic systems is investigated. The failure event in reliability problems is formulated as the exceedance of a single performance variable o...The application of the saddlepoint approximation to reliability analysis of dynamic systems is investigated. The failure event in reliability problems is formulated as the exceedance of a single performance variable over a prescribed threshold level. The saddlepoint approximation technique provides a choice to estimate the cumulative distribution function （CDF） of the performance variable. The failure probability is obtained as the value of the complement CDF at a specified threshold. The method requires computing the saddlepoint from a simple algebraic equation that depends on the cumulant generating function （CGF） of the performance variable. A method for calculating the saddlepoint using random samples of the performance variable is presented. The applicable region of the saddlepoint approximation is discussed in detail. A 10-story shear building model with white noise excitation illustrates the accuracy and efficiency of the proposed methodology.展开更多
This work is about analyzing surface mounted permanent magnet machines regarding their sensitiveness related to erroneous magnet positioning.A finite element analysis based approach is presented and different topologi...This work is about analyzing surface mounted permanent magnet machines regarding their sensitiveness related to erroneous magnet positioning.A finite element analysis based approach is presented and different topologies in terms of slot and pole count are compared.The study further includes the analysis of multiple magnet widths and stator teeth widths.By contrast to most of previous studies,the work is based on evaluating the cumulative distribution function of the cogging torque in case of non-idealities.A Monte Carlo importance sampling based strategy is focused.This approach facilitates studying arbitrary tolerance distributions.Results reveal that topologies with particularly promising rated cogging torque behaviour exhibit the most significant performance degradation in presence of tolerances.A linear relationship is identified for cogging torque performance as function of the accuracy in magnet positioning.Results emphasize the necessity of tolerance analyses for electric machine design to not overrate their performance in the presence of manufacturing uncertainties.展开更多
Since the early 2000s, many satellite passive microwave brightness temperature （BT） archives, such as the Advanced Microwave Scanning Radiometer for the Earth Observing System （AMSR-E） BTs, have become the useful ...Since the early 2000s, many satellite passive microwave brightness temperature （BT） archives, such as the Advanced Microwave Scanning Radiometer for the Earth Observing System （AMSR-E） BTs, have become the useful resources for assessing the changes in the surface and deep soil moistures over both arid and semi-arid regions. In this study, we used a new soil effective temperature （T scheme and the archived AMSR-E BTs to estimate surface soil moisture （SM） over the Nagqu region in the central Tibetan Plateau, China. The surface and deep soil temperatures required for the calculation of regional-scale T were obtained from outputs of the Community Land Model version 4.5 （CLM4.5）. In situ SM measurements at the CEOP-CAMP/Tibet （Coordinated Enhanced Observing Period Asia-Australia Monsoon Project on the Tibetan Plateau） experimental sites were used to validate the AMSR-E-based SM estimations at regional and single-site scales. Furthermore, the spatial distribution of monthly mean surface SM over the Nagqu region was obtained from 16 daytime AMSR-E BT observations in July 2004 over the Nagqu region. Results revealed that the AMSR-E-based surface SM estimations agreed well with the in situ-based surface SM measurements, with the root mean square error （RMSE） ranging from 0.042 to 0.066 m3/m3 and the coefficient of determination （R2） ranging from 0.71 to 0.92 during the nighttime and daytime. The regional surface soil water state map showed a clear spatial pattern related to the terrain. It indicated that the lower surface SM values occurred in the mountainous areas of the northern, mid-western and southeastern parts of Nagqu region, while the higher surface SM values appeared in the low elevation areas such as the Tongtian River Basin, Namco Lake and bog meadows in the central part of Nagqu region. Our analysis also showed that the new T^scheme does not require special fitting parameters or additional assumptions, which simplifies the data requirements for regional-scale applications. This scheme combined with the archived satellite passive microwave BT observations can be used to estimate the historical surface SM for hydrological process studies over the Tibetan Plateau regions.展开更多
The load balance is a critical issue of distributed Hash table （DHT）, and the previous work shows that there exists O（logn） imbalance of load in Chord. The load distribution of Chord, Pastry, and the virtual serve...The load balance is a critical issue of distributed Hash table （DHT）, and the previous work shows that there exists O（logn） imbalance of load in Chord. The load distribution of Chord, Pastry, and the virtual servers （VS） balancing scheme and deduces the closed form expressions of the probability density function （PDF） and cumulative distribution function （CDF） of the load in these DHTs is analyzes. The analysis and simulation show that the load of all these DHTs obeys the gamma distribution with similar formed parameters.展开更多
he logical tree methods are used for evaluate quantitatively relationship between frequency and magnitude, and deduce uncertainties of annual occurrence rate of earthquakes in the periods of lower magnitude earthquake...he logical tree methods are used for evaluate quantitatively relationship between frequency and magnitude, and deduce uncertainties of annual occurrence rate of earthquakes in the periods of lower magnitude earthquake. The uncertainties include deviations from the self-similarity of frequency-magnitude relations, different fitting methods, different methods obtained the annual occurrence rate, magnitude step used in fitting, start magnitude, error of magnitude and so on. Taking Xianshuihe River source zone as an example, we analyze uncertainties of occurrence rate of earthquakes M4, which is needed in risk evaluation extrapolating from frequency-magnitude relations of stronger earthquakes. The annual occurrence rate of M4 is usually required for seismic hazard assessment.The sensitivity analysis and examinations indicate that, in the same frequencymagnitude relations fitting method, the most sensitive factor is annual occurrence rate, the second is magnitude step and the following is start magnitude. Effect of magnitude error is rather small.Procedure of estimating the uncertainties is as follows:①Establishing a logical tree described uncertainties in frequencymagnitude relations by available data and knowledge about studied region.② Calculating frequencymagnitude relations for each end branches. ③ Examining sensitivities of each uncertainty factors, amending structure of logical tree and adjusting original weights. ④ Recalculating frequencymagnitude relations of end branches and complementary cumulative distribution function (CCDF) in each magnitude intervals.⑤ Obtaining an annual occurrence rate of M4 earthquakes under given fractiles.Taking fractiles as 20% and 80%, annual occurrence rate of M 4 events in Xianshuihe seismic zone is 0.643 0. The annual occurrence rate is 0.631 8 under fractiles of 50%, which is very close to that under fractiles 20% and 80%.展开更多
In probability theory, the mixture distribution M has a density function for the collection of random variables and weighted by w<sub>i</sub> ≥ 0 and . These mixed distributions are used in various discip...In probability theory, the mixture distribution M has a density function for the collection of random variables and weighted by w<sub>i</sub> ≥ 0 and . These mixed distributions are used in various disciplines and aim to enrich the collection distribution to more parameters. A more general mixture is derived by Kadri and Halat, by proving the existence of such mixture by w<sub>i</sub> ∈ R, and maintaining . Kadri and Halat provided many examples and applications for such new mixed distributions. In this paper, we introduce a new mixed distribution of the Generalized Erlang distribution, which is derived from the Hypoexponential distribution. We characterize this new distribution by deriving simply closed expressions for the related functions of the probability density function, cumulative distribution function, moment generating function, reliability function, hazard function, and moments.展开更多
Single-value prediction such as the End of Life and Remaining Useful Life is a common method of estimating the lifetime of Li-ion batteries.Information from such prediction is limited when the entire degradation patte...Single-value prediction such as the End of Life and Remaining Useful Life is a common method of estimating the lifetime of Li-ion batteries.Information from such prediction is limited when the entire degradation pattern is needed for practical applications such as dynamic adjustment of battery warranty,improved maintenance scheduling,and battery stock management.In this research,a predictive,semi-parametric survival model called the Cox Proportional Hazards is proposed for the prediction of cell degradation in the form of survival probability(battery reliability)and cumulative hazard(battery risk)functions.Once this model is trained,the two functions can be obtained directly for a new cell without having to predict several cogent points.The model is trained on the first 50 cycles of only the voltage profile from either the charge or discharge data regime,implying that our methodology is data region agnostic.The signature method with both desirable mathematical and machine learning properties was adopted as a feature extraction technique.展开更多
Based on the idea of local polynomial double-smoother, we propose an estimator of a conditional cumulative distribution function with dependent and left-truncated data. It is assumed that the observations form a stati...Based on the idea of local polynomial double-smoother, we propose an estimator of a conditional cumulative distribution function with dependent and left-truncated data. It is assumed that the observations form a stationary a-mixing sequence. Asymptotic normality of the estimator is established. The finite sample behavior of the estimator is investigated via simulations.展开更多
Unmanned aerial vehicle(UAV)path planning plays an important role in power systems.In order to address the challenge in UAV path planning,an improved crested porcupine optimizer(ICPO)combining the Cauchy inverse cumul...Unmanned aerial vehicle(UAV)path planning plays an important role in power systems.In order to address the challenge in UAV path planning,an improved crested porcupine optimizer(ICPO)combining the Cauchy inverse cumulative distribution function and JAYA algorithm is proposed in this paper.First,the traditional random initialization is replaced by sine chaotic mapping,making the initial population more evenly distributed in the search space and improving the quality of the initial solution.Since the global search ability of the crested porcupine optimizer(CPO)is limited,the Cauchy inverse cumulative distribution strategy is introduced.In addition,as CPO is prone to fall into local optima in later stages,a weighted JAYA-CPO attack strategy is proposed to balance the global exploration and local exploitation,thereby improving the algorithm’s ability to escape from local optima.Finally,ICPO is compared with another 10 algorithms on the cec2017 and cec2020 test sets.The experimental results show that ICPO has excellent competitiveness and optimization performance.The ICPO algorithm is applied to the path planning problem of power inspection UAV and is compared with four algorithms.The results show that the algorithm can generate more feasible path trajectories across two terrains with varying complexity,demonstrating the effectiveness and significance of the ICPO algorithm for UAV power inspection path planning.展开更多
The saddlepoint approximation(SA)can directly estimate the probability distribution of linear performance function in non-normal variables space.Based on the property of SA,three SA based methods are developed for the...The saddlepoint approximation(SA)can directly estimate the probability distribution of linear performance function in non-normal variables space.Based on the property of SA,three SA based methods are developed for the structural system reliability analysis.The first method is SA based reliability bounds theory(RBT),in which SA is employed to estimate failure probability and equivalent normal reliability index for each failure mode firstly,and then RBT is employed to obtain the upper and the lower bounds of system failure probability.The second method is SA based Nataf approximation,in which SA is used to estimate the probability density function(PDF)and cumulative distribution function(CDF)for the approximately linearized performance function of each failure mode.After the PDF of each failure mode and the correlation coefficients among approximately linearized performance functions are estimated,Nataf distribution is employed to approximate the joint PDF of multiple structural system performance functions,and then the system failure probability can be estimated directly by numerical simulation using the joint PDF.The third method is SA based line sampling(LS).The standardization transformation is needed to eliminate the dimensions of variables firstly in this case.Then LS method can express the system failure probability as an arithmetic average of a set of failure probabilities of the linear performance functions,and the probabilities of the linear performance functions can be estimated by the SA in the non-normal variables space.By comparing basic concepts,implementations and results of illustrations,the following conclusions can be drawn:(1)The first method can only obtain the bounds of system failure probability and it is only acceptable for the linear limit state function;(2)the second method can give the estimation of system failure probability,and its error mostly results from the approximation of Nataf distribution for the joint PDF of the structural system performance functions and the linearization of the performance functions;(3)the SA based LS method can obtain the estimator of system failure probability,which converges to the actual value along with the increase of sample size.The SA based LS method considers the influence of nonlinearity of limit state function on the failure probability,and it is acceptable for the structural system both with a single failure mode and with multiple failure modes,therefore it has the widest applicability.展开更多
For the stochastic structure with stochastic excitation, an advanced stratified line sampling (SLS) method is presented to obtain the cumulative distribution function (CDF) of the structural response and its sensitivi...For the stochastic structure with stochastic excitation, an advanced stratified line sampling (SLS) method is presented to obtain the cumulative distribution function (CDF) of the structural response and its sensitivity. The advanced stratified line sampling method introduces a set of middle failure subsets firstly. And for each subset, the conventional line sampling can be used to obtain the corresponding value of the response's CDF. At the same time, the sensitivity estimations of each failure subset can also be computed by modifying the important direction and corresponding reliability coefficients. The properties of CDF sensitivity are proved while the performance function is linear with normal random variables. After two simple examples are used to demonstrate the properties of CDF sensitivity and the feasibility of the presented method, the method employed to analyze the CDF and corresponding sensitivity of root bending moment (RBM) responses for the stochastic BAH is wing with gust excitation to a square-edged gust and to a Dryden gust. The results show that the parameters of the second and the fifth order modals exert more influence on the CDF of response than the other ones, and the presented SLS method can more significantly reduce the computational cost compared with Monte Carlo simulation (MCS).展开更多
基金Supported by the National Natural Science Foundation of China(10771163)
文摘For multivariate failure time with auxiliary covariate information,an estimated pseudo-partial-likelihood estimator under the marginal hazard model with distinguishable baseline hazard has been proposed.However,the asymptotic properties of the corresponding estimated cumulative hazard function have not been studied.In this paper,based on counting process martingale,we use the continuous mapping theorem and Lenglart inequality and prove the consistency of the estimated cumulative hazard function in estimated pseudo-partial-likelihood approach.
基金National Natural Science Foundation of China,Grant/Award Number:U2243218。
文摘The log-normal distribution function(LNDF)and Weibull cumulative density function(WCDF)represent two prevalent approaches for characterizing sediment grain size distributions.This study analyzes annual average suspended load grain size data(standardized to equivalent settling diameters)from seven hydrological stations in the lower Yellow River(LYR)spanning 1962–2020,employing various distribution functions for grain size fitting.Results demonstrate that the Weibull probability density function(WPDF)offers significant advantages over both LNDF and WCDF in terms of fitting accuracy,parameter stability,simplicity,and practical applicability for characterizing suspended load grain size distributions in the LYR.Based on these findings,universal formulas were developed for the suspended load grain size distribution across the seven stations and the entire lower reaches,yielding determination coefficients(R2)exceeding 0.9.These formulas can be applied to estimate suspended load grain size in data-scarce cross-sections.The existence of such universal formulas suggests that interannual fluctuations in suspended load grain size in the LYR are constrained within a limited range,suggesting that sediment grain size may represent an inherent property of the river channel.This limited variability may be attributed to the fact that sediments in the LYR are primarily derived from a relatively fixed source region—the Loess Plateau.The observed stability over an extended period also offers valuable insights into the fundamental properties of river systems and their long-term behavior.
基金Supported by Natural Science Foundation of Tianjin(No.09JCYBJC07700)
文摘A new explicit quadratic radical function is found by numerical experiments,which is simpler and has only 70.778%of the maximal distance error compared with the Fisher z transformation.Furthermore,a piecewise function is constructed for the standard normal distribution:if the independent variable falls in the interval(-1.519,1.519),the proposed function is employed;otherwise,the Fisher z transformation is used.Compared with the Fisher z transformation,this piecewise function has only 38.206%of the total error.The new function is more exact to estimate the confidence intervals of Pearson product moment correlation coefficient and Dickinson best weights for the linear combination of forecasts.
文摘In this paper, based on random left truncated and right censored data, the authors derive strong representations of the cumulative hazard function estimator and the product-limit estimator of the survival function. which are valid up to a given order statistic of the observations. A precise bound for the errors is obtained which only depends on the index of the last order statistic to be included.
基金supported by the Natural Science Foundation of China(32071758 and U21A20244)the Fundamental Research Funds for the Central Universities of China(No.2572020BA01)。
文摘Diameter distribution models play an important role in forest inventories,growth prediction,and management.The Weibull probability density function is widely used in forestry.Although a number of methods have been proposed to predict or recover the Weibull distribution,their applicability and predictive performance for the major tree species of China remain to be determined.Trees in sample plots of three even-aged coniferous species(Larix olgensis,Pinus sylvestris and Pinus koraiensis)were measured both in un-thinned and thinned stands to develop parameter prediction models for the Weibull probability density function.Ordinary least squares(OLS)and maximum likelihood regression(MLER),as well as cumulative distribution function regression(CDFR)were used,and their performance compared.The results show that MLER and CDFR were better than OLS in predicting diameter distributions of tree plantations.CDFR produced the best results in terms of fitting statistics.Based on the error statistics calculated for different age groups,CDFR was considered the most suitable method for developing prediction models for Weibull parameters in coniferous plantations.
基金The Second Tibetan Plateau Scientific Expedition and Research(STEP)program,No.2019QZKK0608Talent Start Project of Beijing Normal University。
文摘The United States,Russia and China are militarily and economically among the most powerful countries in the post-Cold War period,and the interactions between the three powers heavily influence the international system.However,different conclusions about this question are generally made by researchers through qualitative analysis,and it is necessary to objectively and quantitatively investigate their interactions.Monthly-aggregated event data from the Global Data on Events,Location and Tone(GDELT)to measure cooperative and conflictual interactions between the three powers,and the complementary cumulative distribution function(CCDF)and the vector autoregression(VAR)method are utilized to investigate their interactions in two periods:January,1991 to September,2001,and October,2001 to December,2016.The results of frequencies and strengths analysis showed that:the frequencies and strengths of USA-China interactions slightly exceeded those of USA-Russia interactions and became the dominant interactions in the second period.Although that cooperation prevailed in the three dyads in two periods,the conflictual interactions between the USA and Russia tended to be more intense in the second period,mainly related to the strategic contradiction between the USA and Russia,especially in Georgia,Ukraine and Syria.The results of CCDF indicated that similar probabilities in the cooperative behaviors between the three dyads,but the differences in the probabilities of conflictual behaviors in the USA-Russia dyad showed complicated characteristic,and those between Russia and China indicated that Russia had been consistently giving China a hard time in both periods when dealing with conflict.The USA was always an essential factor in affecting the interactions between Russia and China in both periods,but China’s behavior only played a limited role in influencing the interactions between the USA-Russia dyad.Our study provides quantitative insight into the direct cooperative and conflictual interactions between the three dyads since the end of the Cold War and helps to understand their interactions better.
基金supported by the National Natural Science Foundation of China(No.NSFC51608446)the Fundamental Research Fund for Central Universities of China(No.3102016ZY015)
文摘Traditional Global Sensitivity Analysis（GSA） focuses on ranking inputs according to their contributions to the output uncertainty.However,information about how the specific regions inside an input affect the output is beyond the traditional GSA techniques.To fully address this issue,in this work,two regional moment-independent importance measures,Regional Importance Measure based on Probability Density Function（RIMPDF） and Regional Importance Measure based on Cumulative Distribution Function（RIMCDF）,are introduced to find out the contributions of specific regions of an input to the whole output distribution.The two regional importance measures prove to be reasonable supplements of the traditional GSA techniques.The ideas of RIMPDF and RIMCDF are applied in two engineering examples to demonstrate that the regional moment-independent importance analysis can add more information concerning the contributions of model inputs.
基金Research Committee of University of Macao Under Grant No. G074/05-06S/YKV/FST UMAC.
文摘The application of the saddlepoint approximation to reliability analysis of dynamic systems is investigated. The failure event in reliability problems is formulated as the exceedance of a single performance variable over a prescribed threshold level. The saddlepoint approximation technique provides a choice to estimate the cumulative distribution function （CDF） of the performance variable. The failure probability is obtained as the value of the complement CDF at a specified threshold. The method requires computing the saddlepoint from a simple algebraic equation that depends on the cumulant generating function （CGF） of the performance variable. A method for calculating the saddlepoint using random samples of the performance variable is presented. The applicable region of the saddlepoint approximation is discussed in detail. A 10-story shear building model with white noise excitation illustrates the accuracy and efficiency of the proposed methodology.
基金supported by the COMET-K2“Center for Symbiotic Mechatronics”of the Linz Center of Mechatronics(LCM)funded by the Austrian federal government and the federal state of Upper Austria.
文摘This work is about analyzing surface mounted permanent magnet machines regarding their sensitiveness related to erroneous magnet positioning.A finite element analysis based approach is presented and different topologies in terms of slot and pole count are compared.The study further includes the analysis of multiple magnet widths and stator teeth widths.By contrast to most of previous studies,the work is based on evaluating the cumulative distribution function of the cogging torque in case of non-idealities.A Monte Carlo importance sampling based strategy is focused.This approach facilitates studying arbitrary tolerance distributions.Results reveal that topologies with particularly promising rated cogging torque behaviour exhibit the most significant performance degradation in presence of tolerances.A linear relationship is identified for cogging torque performance as function of the accuracy in magnet positioning.Results emphasize the necessity of tolerance analyses for electric machine design to not overrate their performance in the presence of manufacturing uncertainties.
基金supported by the National Natural Science Foundation of China (41575013)the National Supercomputer Center in Guangzhou, China
文摘Since the early 2000s, many satellite passive microwave brightness temperature （BT） archives, such as the Advanced Microwave Scanning Radiometer for the Earth Observing System （AMSR-E） BTs, have become the useful resources for assessing the changes in the surface and deep soil moistures over both arid and semi-arid regions. In this study, we used a new soil effective temperature （T scheme and the archived AMSR-E BTs to estimate surface soil moisture （SM） over the Nagqu region in the central Tibetan Plateau, China. The surface and deep soil temperatures required for the calculation of regional-scale T were obtained from outputs of the Community Land Model version 4.5 （CLM4.5）. In situ SM measurements at the CEOP-CAMP/Tibet （Coordinated Enhanced Observing Period Asia-Australia Monsoon Project on the Tibetan Plateau） experimental sites were used to validate the AMSR-E-based SM estimations at regional and single-site scales. Furthermore, the spatial distribution of monthly mean surface SM over the Nagqu region was obtained from 16 daytime AMSR-E BT observations in July 2004 over the Nagqu region. Results revealed that the AMSR-E-based surface SM estimations agreed well with the in situ-based surface SM measurements, with the root mean square error （RMSE） ranging from 0.042 to 0.066 m3/m3 and the coefficient of determination （R2） ranging from 0.71 to 0.92 during the nighttime and daytime. The regional surface soil water state map showed a clear spatial pattern related to the terrain. It indicated that the lower surface SM values occurred in the mountainous areas of the northern, mid-western and southeastern parts of Nagqu region, while the higher surface SM values appeared in the low elevation areas such as the Tongtian River Basin, Namco Lake and bog meadows in the central part of Nagqu region. Our analysis also showed that the new T^scheme does not require special fitting parameters or additional assumptions, which simplifies the data requirements for regional-scale applications. This scheme combined with the archived satellite passive microwave BT observations can be used to estimate the historical surface SM for hydrological process studies over the Tibetan Plateau regions.
基金supported by the National Development and Reform Commission of China (CNGI-04-12-1D).
文摘The load balance is a critical issue of distributed Hash table （DHT）, and the previous work shows that there exists O（logn） imbalance of load in Chord. The load distribution of Chord, Pastry, and the virtual servers （VS） balancing scheme and deduces the closed form expressions of the probability density function （PDF） and cumulative distribution function （CDF） of the load in these DHTs is analyzes. The analysis and simulation show that the load of all these DHTs obeys the gamma distribution with similar formed parameters.
文摘he logical tree methods are used for evaluate quantitatively relationship between frequency and magnitude, and deduce uncertainties of annual occurrence rate of earthquakes in the periods of lower magnitude earthquake. The uncertainties include deviations from the self-similarity of frequency-magnitude relations, different fitting methods, different methods obtained the annual occurrence rate, magnitude step used in fitting, start magnitude, error of magnitude and so on. Taking Xianshuihe River source zone as an example, we analyze uncertainties of occurrence rate of earthquakes M4, which is needed in risk evaluation extrapolating from frequency-magnitude relations of stronger earthquakes. The annual occurrence rate of M4 is usually required for seismic hazard assessment.The sensitivity analysis and examinations indicate that, in the same frequencymagnitude relations fitting method, the most sensitive factor is annual occurrence rate, the second is magnitude step and the following is start magnitude. Effect of magnitude error is rather small.Procedure of estimating the uncertainties is as follows:①Establishing a logical tree described uncertainties in frequencymagnitude relations by available data and knowledge about studied region.② Calculating frequencymagnitude relations for each end branches. ③ Examining sensitivities of each uncertainty factors, amending structure of logical tree and adjusting original weights. ④ Recalculating frequencymagnitude relations of end branches and complementary cumulative distribution function (CCDF) in each magnitude intervals.⑤ Obtaining an annual occurrence rate of M4 earthquakes under given fractiles.Taking fractiles as 20% and 80%, annual occurrence rate of M 4 events in Xianshuihe seismic zone is 0.643 0. The annual occurrence rate is 0.631 8 under fractiles of 50%, which is very close to that under fractiles 20% and 80%.
文摘In probability theory, the mixture distribution M has a density function for the collection of random variables and weighted by w<sub>i</sub> ≥ 0 and . These mixed distributions are used in various disciplines and aim to enrich the collection distribution to more parameters. A more general mixture is derived by Kadri and Halat, by proving the existence of such mixture by w<sub>i</sub> ∈ R, and maintaining . Kadri and Halat provided many examples and applications for such new mixed distributions. In this paper, we introduce a new mixed distribution of the Generalized Erlang distribution, which is derived from the Hypoexponential distribution. We characterize this new distribution by deriving simply closed expressions for the related functions of the probability density function, cumulative distribution function, moment generating function, reliability function, hazard function, and moments.
基金funded by an industry-academia collaborative grant EPSRC EP/R511687/1 awarded by EPSRC&University of Edinburgh,United Kingdom program Impact Acceleration Account(IAA)R.Ibraheem is a Ph.D.student in EPSRC’s MAC-MIGS Centre for Doctoral Training.MAC-MIGS is supported by the UK’s Engineering and Physical Science Research Council(grant number EP/S023291/1)+2 种基金G.dos Reis acknowledges partial support from the FCT-Fundação para a Ciência e a Tecnologia,PortugalI.P.,under the scope of the projects UIDB/00297/2020(https://doi.org/10.54499/UIDB/00297/2020)and UIDP/00297/2020(https://doi.org/10.54499/UIDP/00297/2020)(Center for Mathematics and Applications,NOVA Math)G.dos Reis acknowledges support from the Faraday Institution,United dom King-(grant number FIRG049).
文摘Single-value prediction such as the End of Life and Remaining Useful Life is a common method of estimating the lifetime of Li-ion batteries.Information from such prediction is limited when the entire degradation pattern is needed for practical applications such as dynamic adjustment of battery warranty,improved maintenance scheduling,and battery stock management.In this research,a predictive,semi-parametric survival model called the Cox Proportional Hazards is proposed for the prediction of cell degradation in the form of survival probability(battery reliability)and cumulative hazard(battery risk)functions.Once this model is trained,the two functions can be obtained directly for a new cell without having to predict several cogent points.The model is trained on the first 50 cycles of only the voltage profile from either the charge or discharge data regime,implying that our methodology is data region agnostic.The signature method with both desirable mathematical and machine learning properties was adopted as a feature extraction technique.
基金supported by National Natural Science Foundation of China(No.11301084)Natural Science Foundation of Fujian Province(No.2014J01010)
文摘Based on the idea of local polynomial double-smoother, we propose an estimator of a conditional cumulative distribution function with dependent and left-truncated data. It is assumed that the observations form a stationary a-mixing sequence. Asymptotic normality of the estimator is established. The finite sample behavior of the estimator is investigated via simulations.
基金supported by the National Natural Sci-ence Foundation of China(No.62102373,No.62273243,and No.62473341)Henan Province Key R&D Project(No.241111210400)Joint Fund Key Project of science and Technology R&D Plan of Henan Province(No.235200810022).
文摘Unmanned aerial vehicle(UAV)path planning plays an important role in power systems.In order to address the challenge in UAV path planning,an improved crested porcupine optimizer(ICPO)combining the Cauchy inverse cumulative distribution function and JAYA algorithm is proposed in this paper.First,the traditional random initialization is replaced by sine chaotic mapping,making the initial population more evenly distributed in the search space and improving the quality of the initial solution.Since the global search ability of the crested porcupine optimizer(CPO)is limited,the Cauchy inverse cumulative distribution strategy is introduced.In addition,as CPO is prone to fall into local optima in later stages,a weighted JAYA-CPO attack strategy is proposed to balance the global exploration and local exploitation,thereby improving the algorithm’s ability to escape from local optima.Finally,ICPO is compared with another 10 algorithms on the cec2017 and cec2020 test sets.The experimental results show that ICPO has excellent competitiveness and optimization performance.The ICPO algorithm is applied to the path planning problem of power inspection UAV and is compared with four algorithms.The results show that the algorithm can generate more feasible path trajectories across two terrains with varying complexity,demonstrating the effectiveness and significance of the ICPO algorithm for UAV power inspection path planning.
基金supported by the National Natural Science Foundation of China(Grant Nos.10572117,50875213)the Program for New Century Excellent Talents in University(Grant No.NCET-05-0868)+2 种基金Aviation Science Foundation(Grant No.2007ZA53012)the National Hi-Tech Research and Development Program of China("863"Project)(Grant No.2007AA04Z401)the Doctorate Foundation of Northwestern Poly-technical University(Grant No.CX200801)
文摘The saddlepoint approximation(SA)can directly estimate the probability distribution of linear performance function in non-normal variables space.Based on the property of SA,three SA based methods are developed for the structural system reliability analysis.The first method is SA based reliability bounds theory(RBT),in which SA is employed to estimate failure probability and equivalent normal reliability index for each failure mode firstly,and then RBT is employed to obtain the upper and the lower bounds of system failure probability.The second method is SA based Nataf approximation,in which SA is used to estimate the probability density function(PDF)and cumulative distribution function(CDF)for the approximately linearized performance function of each failure mode.After the PDF of each failure mode and the correlation coefficients among approximately linearized performance functions are estimated,Nataf distribution is employed to approximate the joint PDF of multiple structural system performance functions,and then the system failure probability can be estimated directly by numerical simulation using the joint PDF.The third method is SA based line sampling(LS).The standardization transformation is needed to eliminate the dimensions of variables firstly in this case.Then LS method can express the system failure probability as an arithmetic average of a set of failure probabilities of the linear performance functions,and the probabilities of the linear performance functions can be estimated by the SA in the non-normal variables space.By comparing basic concepts,implementations and results of illustrations,the following conclusions can be drawn:(1)The first method can only obtain the bounds of system failure probability and it is only acceptable for the linear limit state function;(2)the second method can give the estimation of system failure probability,and its error mostly results from the approximation of Nataf distribution for the joint PDF of the structural system performance functions and the linearization of the performance functions;(3)the SA based LS method can obtain the estimator of system failure probability,which converges to the actual value along with the increase of sample size.The SA based LS method considers the influence of nonlinearity of limit state function on the failure probability,and it is acceptable for the structural system both with a single failure mode and with multiple failure modes,therefore it has the widest applicability.
基金the National Nature Science Foundation of China (Grant No. 51175425)the Aviation Science Foundation (Grant No. 2011ZA53015)+1 种基金the Aerospace Science and Technology Innovative Foundation (Grant No. 2011200093)the Nature Science Basic Research Fund of Shaanxi Province (Grant No. 2012JQ1015)
文摘For the stochastic structure with stochastic excitation, an advanced stratified line sampling (SLS) method is presented to obtain the cumulative distribution function (CDF) of the structural response and its sensitivity. The advanced stratified line sampling method introduces a set of middle failure subsets firstly. And for each subset, the conventional line sampling can be used to obtain the corresponding value of the response's CDF. At the same time, the sensitivity estimations of each failure subset can also be computed by modifying the important direction and corresponding reliability coefficients. The properties of CDF sensitivity are proved while the performance function is linear with normal random variables. After two simple examples are used to demonstrate the properties of CDF sensitivity and the feasibility of the presented method, the method employed to analyze the CDF and corresponding sensitivity of root bending moment (RBM) responses for the stochastic BAH is wing with gust excitation to a square-edged gust and to a Dryden gust. The results show that the parameters of the second and the fifth order modals exert more influence on the CDF of response than the other ones, and the presented SLS method can more significantly reduce the computational cost compared with Monte Carlo simulation (MCS).
