The purpose of this paper is to propose a new model of asymmetry for square contingency tables with ordered categories. The new model may be appropriate for a square contingency table if it is reasonable to assume an ...The purpose of this paper is to propose a new model of asymmetry for square contingency tables with ordered categories. The new model may be appropriate for a square contingency table if it is reasonable to assume an underlying bivariate t-distribution with different marginal variances having any degrees of freedom. As the degrees of freedom becomes larger, the proposed model approaches the extended linear diagonals-parameter symmetry model, which may be appropriate for a square table if it is reasonable to assume an underlying bivariate normal distribution. The simulation study based on bivariate t-distribution is given. An example is given.展开更多
The honey badger algorithm(HBA),as a new swarm intelligence(SI)optimization algorithm,has shown certain effectiveness in its applications.Aiming at the problems of unsatisfactory initial population distribution of HBA...The honey badger algorithm(HBA),as a new swarm intelligence(SI)optimization algorithm,has shown certain effectiveness in its applications.Aiming at the problems of unsatisfactory initial population distribution of HBA,poor ability to avoid local optimum,and slow convergence speed,this paper proposes a multi-strategy improved HBA based on periodical mutation and t-distribution perturbation,called MHBA.Firstly,a good point set population initialization is introduced to get a uniform initial population.Secondly,periodic mutation and t-distribution perturbation are successively used to improve the algorithm’s ability to avoid local optimum.Finally,the density factor is improved for balancing exploration and exploitation.By comparing MHBA with HBA and 7 other SIs on 6 benchmark functions,it is evident that the performance of MHBA is far superior to HBA.In addition,by applying MHBA to robot path planning,MHBA can identify the shortest path more quickly and consistently compared with competitors.展开更多
It is evident that complex optimization problems are becoming increasingly prominent,metaheuristic algorithms have demonstrated unique advantages in solving high-dimensional,nonlinear problems.However,the traditional ...It is evident that complex optimization problems are becoming increasingly prominent,metaheuristic algorithms have demonstrated unique advantages in solving high-dimensional,nonlinear problems.However,the traditional Sparrow Search Algorithm(SSA)suffers from limited global search capability,insufficient population diversity,and slow convergence,which often leads to premature stagnation in local optima.Despite the proposal of various enhanced versions,the effective balancing of exploration and exploitation remains an unsolved challenge.To address the previously mentioned problems,this study proposes a multi-strategy collaborative improved SSA,which systematically integrates four complementary strategies:(1)the Northern Goshawk Optimization(NGO)mechanism enhances global exploration through guided prey-attacking dynamics;(2)an adaptive t-distribution mutation strategy balances the transition between exploration and exploitation via dynamic adjustment of the degrees of freedom;(3)a dual chaotic initialization method(Bernoulli and Sinusoidal maps)increases population diversity and distribution uniformity;and(4)an elite retention strategy maintains solution quality and prevents degradation during iterations.These strategies cooperate synergistically,forming a tightly coupled optimization framework that significantly improves search efficiency and robustness.Therefore,this paper names it NTSSA:A Novel Multi-Strategy Enhanced Sparrow Search Algorithm with Northern Goshawk Optimization and Adaptive t-Distribution for Global Optimization.Extensive experiments on the CEC2005 benchmark set demonstrate that NTSSA achieves theoretical optimal accuracy on unimodal functions and significantly enhances global optimum discovery for multimodal functions by 2–5 orders of magnitude.Compared with SSA,GWO,ISSA,and CSSOA,NTSSA improves solution accuracy by up to 14.3%(F8)and 99.8%(F12),while accelerating convergence by approximately 1.5–2×.The Wilcoxon rank-sum test(p<0.05)indicates that NTSSA demonstrates a statistically substantial performance advantage.Theoretical analysis demonstrates that the collaborative synergy among adaptive mutation,chaos-based diversification,and elite preservation ensures both high convergence accuracy and global stability.This work bridges a key research gap in SSA by realizing a coordinated optimization mechanism between exploration and exploitation,offering a robust and efficient solution framework for complex high-dimensional problems in intelligent computation and engineering design.展开更多
Accurate forecasting of wind power is crucial for ensuring the reliable operation of the electrical grid.Due to the impact of various factors,wind power forecasting presents a significant challenge.This paper presents...Accurate forecasting of wind power is crucial for ensuring the reliable operation of the electrical grid.Due to the impact of various factors,wind power forecasting presents a significant challenge.This paper presents the model that integrates Osprey and adaptive T-distribution dung beetle algorithm for optimizing a convolutional neural network.The CNN-BiLSTM-Attention model combines bidirectional long short-term memory neural networks with an attention mechanism,thereby improving the accuracy of wind power generation predictions.The original data is subjected to Variational Mode Decomposition(VMD)for analysis,taking into account the fluctuations in wind power across different periods.The BiLSTM network with short-term memory processes time-series wind power data,yielding an optimal predictive performance.The integration of the osprey algorithm and adaptive T-distribution within the Dung Beetle Optimization Algorithm was utilized to optimize the hyperparameters of the CNN-BiLSTM-Attention model,thereby enhancing its predictive performance.To assess the efficacy of the CNN-BiLSTM-Attention algorithm,enhanced by Ospreys and adaptive T-distributed dung beetle algorithm,we conducted experiments using the CEC2021 benchmark function.The integrated Osprey and adaptive T-distribution Dung Beetle algorithm has excellent global optimization performance when dealing with complex optimization problems.The fusion of Osprey and the adaptive T-distribution Dung beetle algorithm optimized the CNN-BiLSTM-Attention algorithm as well as other optimization algorithms for ablation experiments.The results show that the improved algorithm performs well in predicting wind power.The experimental findings suggest that the model’s predictive efficiency has enhanced by a minimum of 17.74%.展开更多
A joint statistical model of wind speed and wind shear is critical for height-dependent wind resource characteristic analysis.However,given the different atmospheric conditions that may be involved,the statistical dis...A joint statistical model of wind speed and wind shear is critical for height-dependent wind resource characteristic analysis.However,given the different atmospheric conditions that may be involved,the statistical distribution of the two variables may show multimodal characteristics.In this work,a finite mixture bivariate statistical model was designed to describe the statistical properties,which is composed of several components,each with a Weibull distribution and a normal distribution for wind speed and wind shear,respectively,with a Gaussian copula to describe the dependency structure between the two variables.To confirm the developed model,reanalysis data from six positions in the coastal sea areas of China were used.Our results disclosed that the developed joint statistical model can accurately capture the different multimodal structures presented in all the bivariate samples under mixed atmospheric conditions,giving acceptable predictions of the joint probability distributions.Proper consideration of wind shear coefficient variation is crucial in estimating height-dependent wind resource characteristics.Importantly,unlike traditional methods that are limited to specific hub heights,the model developed here can estimate wind energy potential across different hub heights,enhancing the economic viability assessment of wind power projects.展开更多
In this study, a novel approach of the landslide numerical risk factor(LNRF) bivariate model was used in ensemble with linear multivariate regression(LMR) and boosted regression tree(BRT) models, coupled with radar re...In this study, a novel approach of the landslide numerical risk factor(LNRF) bivariate model was used in ensemble with linear multivariate regression(LMR) and boosted regression tree(BRT) models, coupled with radar remote sensing data and geographic information system(GIS), for landslide susceptibility mapping(LSM) in the Gorganroud watershed, Iran. Fifteen topographic, hydrological, geological and environmental conditioning factors and a landslide inventory(70%, or 298 landslides) were used in mapping. Phased array-type L-band synthetic aperture radar data were used to extract topographic parameters. Coefficients of tolerance and variance inflation factor were used to determine the coherence among conditioning factors. Data for the landslide inventory map were obtained from various resources, such as Iranian Landslide Working Party(ILWP), Forestry, Rangeland and Watershed Organisation(FRWO), extensive field surveys, interpretation of aerial photos and satellite images, and radar data. Of the total data, 30% were used to validate LSMs, using area under the curve(AUC), frequency ratio(FR) and seed cell area index(SCAI).Normalised difference vegetation index, land use/land cover and slope degree in BRT model elevation, rainfall and distance from stream were found to be important factors and were given the highest weightage in modelling. Validation results using AUC showed that the ensemble LNRF-BRT and LNRFLMR models(AUC = 0.912(91.2%) and 0.907(90.7%), respectively) had high predictive accuracy than the LNRF model alone(AUC = 0.855(85.5%)). The FR and SCAI analyses showed that all models divided the parameter classes with high precision. Overall, our novel approach of combining multivariate and machine learning methods with bivariate models, radar remote sensing data and GIS proved to be a powerful tool for landslide susceptibility mapping.展开更多
Both the Newton interpolating polynomials and the Thiele-type interpolating continued fractions based on inverse differences are used to construct a kind of bivariate blending rational interpolants and an error estima...Both the Newton interpolating polynomials and the Thiele-type interpolating continued fractions based on inverse differences are used to construct a kind of bivariate blending rational interpolants and an error estimation is given.展开更多
Inference are considered for the dependence competing risks model by using the Marshal-Olkin bivariate exponential distribution. Under generalized progressively hybrid censoring with partially observed failure causes,...Inference are considered for the dependence competing risks model by using the Marshal-Olkin bivariate exponential distribution. Under generalized progressively hybrid censoring with partially observed failure causes, the maximum likelihood estimators are established, and the approximate confidence intervals are also constructed via the observed Fisher information matrix.Moreover, Bayes estimates and highest probability density credible intervals are presented and the importance sampling technique is used to compute corresponding results. Finally, the numerical analysis is proposed for illustration.展开更多
An adaptive method of residual life estimation for deteriorated products with two performance characteristics (PCs) was proposed, which was sharply different from existing work that only utilized one-dimensional degra...An adaptive method of residual life estimation for deteriorated products with two performance characteristics (PCs) was proposed, which was sharply different from existing work that only utilized one-dimensional degradation data. Once new degradation information was available, the residual life of the product being monitored could be estimated in an adaptive manner. Here, it was assumed that the degradation of each PC over time was governed by a Wiener degradation process and the dependency between them was characterized by the Frank copula function. A bivariate Wiener process model with measurement errors was used to model the degradation measurements. A two-stage method and the Markov chain Monte Carlo (MCMC) method were combined to estimate the unknown parameters in sequence. Results from a numerical example about fatigue cracks show that the proposed method is valid as the relative error is small.展开更多
Copula-based bivariate frequency analysis can be used to investigate the changes in flood characteristics in the Huai River Basin that could be caused by climate change. The univariate distributions of historical floo...Copula-based bivariate frequency analysis can be used to investigate the changes in flood characteristics in the Huai River Basin that could be caused by climate change. The univariate distributions of historical flood peak, maximum 3-day and 7-day volumes in 1961-2000 and future values in 2061-2100 projected from two GCMs（CSIRO-MK3.5 and CCCma-CGCM3.1） under A2, A1 B and B1 emission scenarios are analyzed and compared. Then, bivariate distributions of peaks and volumes are constructed based on the copula method and possible changes in joint return periods are characterized. Results indicate that the Clayton copula is more appropriate for historical and CCCma-CGCM3.1 simulating flood variables, while that of Frank and Gumbel are better fitted to CSIRO-MK3.5 simulations. The variations of univariate and bivariate return periods reveal that flood characteristics may be more sensitive to different GCMs than different emission scenarios. Between the two GCMs, CSIRO-MK3.5 evidently predicts much more severe flood conditions in future, especially under B1 scenario, whereas CCCma-CGCM3.1 generally suggests contrary changing signals. This study corroborates that copulas can serve as a viable and flexible tool to connect univariate marginal distributions of flood variables and quantify the associated risks, which may provide useful information for risk-based flood control.展开更多
In the paper, firstly, based on new non-tensor-product-typed partially inverse divided differences algorithms in a recursive form, scattered data interpolating schemes are constructed via bivariate continued fractions...In the paper, firstly, based on new non-tensor-product-typed partially inverse divided differences algorithms in a recursive form, scattered data interpolating schemes are constructed via bivariate continued fractions with odd and even nodes, respectively. And equivalent identities are also obtained between interpolated functions and bivariate continued fractions. Secondly, by means of three-term recurrence relations for continued fractions, the characterization theorem is presented to study on the degrees of the numerators and denominators of the interpolating continued fractions. Thirdly, some numerical examples show it feasible for the novel recursive schemes. Meanwhile, compared with the degrees of the numera- tors and denominators of bivariate Thiele-typed interpolating continued fractions, those of the new bivariate interpolating continued fractions are much low, respectively, due to the reduc- tion of redundant interpolating nodes. Finally, the operation count for the rational function interpolation is smaller than that for radial basis function interpolation.展开更多
A new method for the construction of bivariate matrix valued rational interpolants (BGIRI) on a rectangular grid is presented in [6]. The rational interpolants are of Thiele-type continued fraction form with scalar de...A new method for the construction of bivariate matrix valued rational interpolants (BGIRI) on a rectangular grid is presented in [6]. The rational interpolants are of Thiele-type continued fraction form with scalar denominator. The generalized inverse introduced by [3]is gen-eralized to rectangular matrix case in this paper. An exact error formula for interpolation is ob-tained, which is an extension in matrix form of bivariate scalar and vector valued rational interpola-tion discussed by Siemaszko[l2] and by Gu Chuangqing [7] respectively. By defining row and col-umn-transformation in the sense of the partial inverted differences for matrices, two type matrix algorithms are established to construct corresponding two different BGIRI, which hold for the vec-tor case and the scalar case.展开更多
Reliability and remaining useful life(RUL)estimation for a satellite rechargeable lithium battery(RLB)are significant for prognostic and health management(PHM).A novel Bayesian framework is proposed to do reliability ...Reliability and remaining useful life(RUL)estimation for a satellite rechargeable lithium battery(RLB)are significant for prognostic and health management(PHM).A novel Bayesian framework is proposed to do reliability analysis by synthesizing multisource data,including bivariate degradation data and lifetime data.Bivariate degradation means that there are two degraded performance characteristics leading to the failure of the system.First,linear Wiener process and Frank Copula function are used to model the dependent degradation processes of the RLB's temperature and discharge voltage.Next,the Bayesian method,in combination with Markov Chain Monte Carlo(MCMC)simulations,is provided to integrate limited bivariate degradation data with other congeneric RLBs'lifetime data.Then reliability evaluation and RUL prediction are carried out for PHM.A simulation study demonstrates that due to the data fusion,parameter estimations and predicted RUL obtained from our model are more precise than models only using degradation data or ignoring the dependency of different degradation processes.Finally,a practical case study of a satellite RLB verifies the usability of the model.展开更多
By virtue of the operator-Hermite-polynomial method, we derive some new generating function formulas of the product of two bivariate Hermite polynomials. Their applications in studying quantum optical states are prese...By virtue of the operator-Hermite-polynomial method, we derive some new generating function formulas of the product of two bivariate Hermite polynomials. Their applications in studying quantum optical states are presented.展开更多
In this paper, the dimension of the spaces of bivariate spline with degree less that 2r and smoothness order r on the Morgan-Scott triangulation is considered. The concept of the instability degree in the dimension of...In this paper, the dimension of the spaces of bivariate spline with degree less that 2r and smoothness order r on the Morgan-Scott triangulation is considered. The concept of the instability degree in the dimension of spaces of bivariate spline is presented. The results in the paper make us conjecture the instability degree in the dimension of spaces of bivariate spline is infinity.展开更多
We propose a procedure to obtain accurate confidence intervals for the stress-strength reliability R = P (X > Y) when (X, Y) is a bivariate normal distribution with unknown means and covariance matrix. Our method i...We propose a procedure to obtain accurate confidence intervals for the stress-strength reliability R = P (X > Y) when (X, Y) is a bivariate normal distribution with unknown means and covariance matrix. Our method is more accurate than standard methods as it possesses a third-order distributional accuracy. Simulations studies are provided to show the performance of the proposed method relative to existing ones in terms of coverage probability and average length. An empirical example is given to illustrate its usefulness in practice.展开更多
文摘The purpose of this paper is to propose a new model of asymmetry for square contingency tables with ordered categories. The new model may be appropriate for a square contingency table if it is reasonable to assume an underlying bivariate t-distribution with different marginal variances having any degrees of freedom. As the degrees of freedom becomes larger, the proposed model approaches the extended linear diagonals-parameter symmetry model, which may be appropriate for a square table if it is reasonable to assume an underlying bivariate normal distribution. The simulation study based on bivariate t-distribution is given. An example is given.
基金Supported by the National Key Research and Development Program of China(No.2022ZD0119001)。
文摘The honey badger algorithm(HBA),as a new swarm intelligence(SI)optimization algorithm,has shown certain effectiveness in its applications.Aiming at the problems of unsatisfactory initial population distribution of HBA,poor ability to avoid local optimum,and slow convergence speed,this paper proposes a multi-strategy improved HBA based on periodical mutation and t-distribution perturbation,called MHBA.Firstly,a good point set population initialization is introduced to get a uniform initial population.Secondly,periodic mutation and t-distribution perturbation are successively used to improve the algorithm’s ability to avoid local optimum.Finally,the density factor is improved for balancing exploration and exploitation.By comparing MHBA with HBA and 7 other SIs on 6 benchmark functions,it is evident that the performance of MHBA is far superior to HBA.In addition,by applying MHBA to robot path planning,MHBA can identify the shortest path more quickly and consistently compared with competitors.
文摘It is evident that complex optimization problems are becoming increasingly prominent,metaheuristic algorithms have demonstrated unique advantages in solving high-dimensional,nonlinear problems.However,the traditional Sparrow Search Algorithm(SSA)suffers from limited global search capability,insufficient population diversity,and slow convergence,which often leads to premature stagnation in local optima.Despite the proposal of various enhanced versions,the effective balancing of exploration and exploitation remains an unsolved challenge.To address the previously mentioned problems,this study proposes a multi-strategy collaborative improved SSA,which systematically integrates four complementary strategies:(1)the Northern Goshawk Optimization(NGO)mechanism enhances global exploration through guided prey-attacking dynamics;(2)an adaptive t-distribution mutation strategy balances the transition between exploration and exploitation via dynamic adjustment of the degrees of freedom;(3)a dual chaotic initialization method(Bernoulli and Sinusoidal maps)increases population diversity and distribution uniformity;and(4)an elite retention strategy maintains solution quality and prevents degradation during iterations.These strategies cooperate synergistically,forming a tightly coupled optimization framework that significantly improves search efficiency and robustness.Therefore,this paper names it NTSSA:A Novel Multi-Strategy Enhanced Sparrow Search Algorithm with Northern Goshawk Optimization and Adaptive t-Distribution for Global Optimization.Extensive experiments on the CEC2005 benchmark set demonstrate that NTSSA achieves theoretical optimal accuracy on unimodal functions and significantly enhances global optimum discovery for multimodal functions by 2–5 orders of magnitude.Compared with SSA,GWO,ISSA,and CSSOA,NTSSA improves solution accuracy by up to 14.3%(F8)and 99.8%(F12),while accelerating convergence by approximately 1.5–2×.The Wilcoxon rank-sum test(p<0.05)indicates that NTSSA demonstrates a statistically substantial performance advantage.Theoretical analysis demonstrates that the collaborative synergy among adaptive mutation,chaos-based diversification,and elite preservation ensures both high convergence accuracy and global stability.This work bridges a key research gap in SSA by realizing a coordinated optimization mechanism between exploration and exploitation,offering a robust and efficient solution framework for complex high-dimensional problems in intelligent computation and engineering design.
基金supported by the National Natural Science Foundation of China[Grant No.12371378]the Fujian Natural Science Foundation[Grant No.2022J01378,Grant No.2023J011127].
文摘Accurate forecasting of wind power is crucial for ensuring the reliable operation of the electrical grid.Due to the impact of various factors,wind power forecasting presents a significant challenge.This paper presents the model that integrates Osprey and adaptive T-distribution dung beetle algorithm for optimizing a convolutional neural network.The CNN-BiLSTM-Attention model combines bidirectional long short-term memory neural networks with an attention mechanism,thereby improving the accuracy of wind power generation predictions.The original data is subjected to Variational Mode Decomposition(VMD)for analysis,taking into account the fluctuations in wind power across different periods.The BiLSTM network with short-term memory processes time-series wind power data,yielding an optimal predictive performance.The integration of the osprey algorithm and adaptive T-distribution within the Dung Beetle Optimization Algorithm was utilized to optimize the hyperparameters of the CNN-BiLSTM-Attention model,thereby enhancing its predictive performance.To assess the efficacy of the CNN-BiLSTM-Attention algorithm,enhanced by Ospreys and adaptive T-distributed dung beetle algorithm,we conducted experiments using the CEC2021 benchmark function.The integrated Osprey and adaptive T-distribution Dung Beetle algorithm has excellent global optimization performance when dealing with complex optimization problems.The fusion of Osprey and the adaptive T-distribution Dung beetle algorithm optimized the CNN-BiLSTM-Attention algorithm as well as other optimization algorithms for ablation experiments.The results show that the improved algorithm performs well in predicting wind power.The experimental findings suggest that the model’s predictive efficiency has enhanced by a minimum of 17.74%.
基金supported by the Key R&D Program of Shandong Province,China(No.2021ZLGX04)the National Natural Science Foundation of China(No.52171284)。
文摘A joint statistical model of wind speed and wind shear is critical for height-dependent wind resource characteristic analysis.However,given the different atmospheric conditions that may be involved,the statistical distribution of the two variables may show multimodal characteristics.In this work,a finite mixture bivariate statistical model was designed to describe the statistical properties,which is composed of several components,each with a Weibull distribution and a normal distribution for wind speed and wind shear,respectively,with a Gaussian copula to describe the dependency structure between the two variables.To confirm the developed model,reanalysis data from six positions in the coastal sea areas of China were used.Our results disclosed that the developed joint statistical model can accurately capture the different multimodal structures presented in all the bivariate samples under mixed atmospheric conditions,giving acceptable predictions of the joint probability distributions.Proper consideration of wind shear coefficient variation is crucial in estimating height-dependent wind resource characteristics.Importantly,unlike traditional methods that are limited to specific hub heights,the model developed here can estimate wind energy potential across different hub heights,enhancing the economic viability assessment of wind power projects.
基金supported by the Centre for Advanced Modelling and Geospatial Information Systems(CAMGIS),UTS under grant numbers 321740.2232335,323930,and 321740.2232357
文摘In this study, a novel approach of the landslide numerical risk factor(LNRF) bivariate model was used in ensemble with linear multivariate regression(LMR) and boosted regression tree(BRT) models, coupled with radar remote sensing data and geographic information system(GIS), for landslide susceptibility mapping(LSM) in the Gorganroud watershed, Iran. Fifteen topographic, hydrological, geological and environmental conditioning factors and a landslide inventory(70%, or 298 landslides) were used in mapping. Phased array-type L-band synthetic aperture radar data were used to extract topographic parameters. Coefficients of tolerance and variance inflation factor were used to determine the coherence among conditioning factors. Data for the landslide inventory map were obtained from various resources, such as Iranian Landslide Working Party(ILWP), Forestry, Rangeland and Watershed Organisation(FRWO), extensive field surveys, interpretation of aerial photos and satellite images, and radar data. Of the total data, 30% were used to validate LSMs, using area under the curve(AUC), frequency ratio(FR) and seed cell area index(SCAI).Normalised difference vegetation index, land use/land cover and slope degree in BRT model elevation, rainfall and distance from stream were found to be important factors and were given the highest weightage in modelling. Validation results using AUC showed that the ensemble LNRF-BRT and LNRFLMR models(AUC = 0.912(91.2%) and 0.907(90.7%), respectively) had high predictive accuracy than the LNRF model alone(AUC = 0.855(85.5%)). The FR and SCAI analyses showed that all models divided the parameter classes with high precision. Overall, our novel approach of combining multivariate and machine learning methods with bivariate models, radar remote sensing data and GIS proved to be a powerful tool for landslide susceptibility mapping.
文摘Both the Newton interpolating polynomials and the Thiele-type interpolating continued fractions based on inverse differences are used to construct a kind of bivariate blending rational interpolants and an error estimation is given.
基金supported by the National Natural Science Foundation of China(11501433)the Fundamental Research Funds for the Central Universities(JB180711)
文摘Inference are considered for the dependence competing risks model by using the Marshal-Olkin bivariate exponential distribution. Under generalized progressively hybrid censoring with partially observed failure causes, the maximum likelihood estimators are established, and the approximate confidence intervals are also constructed via the observed Fisher information matrix.Moreover, Bayes estimates and highest probability density credible intervals are presented and the importance sampling technique is used to compute corresponding results. Finally, the numerical analysis is proposed for illustration.
基金Project(60904002)supported by the National Natural Science Foundation of China
文摘An adaptive method of residual life estimation for deteriorated products with two performance characteristics (PCs) was proposed, which was sharply different from existing work that only utilized one-dimensional degradation data. Once new degradation information was available, the residual life of the product being monitored could be estimated in an adaptive manner. Here, it was assumed that the degradation of each PC over time was governed by a Wiener degradation process and the dependency between them was characterized by the Frank copula function. A bivariate Wiener process model with measurement errors was used to model the degradation measurements. A two-stage method and the Markov chain Monte Carlo (MCMC) method were combined to estimate the unknown parameters in sequence. Results from a numerical example about fatigue cracks show that the proposed method is valid as the relative error is small.
基金jointly supported by the General Program of National Natural Science Foundation of China (No. 51479140)the Major Program of National Natural Science Foundation of China (No. 51239004)+1 种基金the Meteorological Research Open Foundation of Huai River Basin (No. HRM201403)the National Natural Science Foundation of China (No. 41401612)
文摘Copula-based bivariate frequency analysis can be used to investigate the changes in flood characteristics in the Huai River Basin that could be caused by climate change. The univariate distributions of historical flood peak, maximum 3-day and 7-day volumes in 1961-2000 and future values in 2061-2100 projected from two GCMs（CSIRO-MK3.5 and CCCma-CGCM3.1） under A2, A1 B and B1 emission scenarios are analyzed and compared. Then, bivariate distributions of peaks and volumes are constructed based on the copula method and possible changes in joint return periods are characterized. Results indicate that the Clayton copula is more appropriate for historical and CCCma-CGCM3.1 simulating flood variables, while that of Frank and Gumbel are better fitted to CSIRO-MK3.5 simulations. The variations of univariate and bivariate return periods reveal that flood characteristics may be more sensitive to different GCMs than different emission scenarios. Between the two GCMs, CSIRO-MK3.5 evidently predicts much more severe flood conditions in future, especially under B1 scenario, whereas CCCma-CGCM3.1 generally suggests contrary changing signals. This study corroborates that copulas can serve as a viable and flexible tool to connect univariate marginal distributions of flood variables and quantify the associated risks, which may provide useful information for risk-based flood control.
基金Supported by the Special Funds Tianyuan for the National Natural Science Foundation of China(Grant No.11426086)the Fundamental Research Funds for the Central Universities(Grant No.2016B08714)the Natural Science Foundation of Jiangsu Province for the Youth(Grant No.BK20160853)
文摘In the paper, firstly, based on new non-tensor-product-typed partially inverse divided differences algorithms in a recursive form, scattered data interpolating schemes are constructed via bivariate continued fractions with odd and even nodes, respectively. And equivalent identities are also obtained between interpolated functions and bivariate continued fractions. Secondly, by means of three-term recurrence relations for continued fractions, the characterization theorem is presented to study on the degrees of the numerators and denominators of the interpolating continued fractions. Thirdly, some numerical examples show it feasible for the novel recursive schemes. Meanwhile, compared with the degrees of the numera- tors and denominators of bivariate Thiele-typed interpolating continued fractions, those of the new bivariate interpolating continued fractions are much low, respectively, due to the reduc- tion of redundant interpolating nodes. Finally, the operation count for the rational function interpolation is smaller than that for radial basis function interpolation.
文摘A new method for the construction of bivariate matrix valued rational interpolants (BGIRI) on a rectangular grid is presented in [6]. The rational interpolants are of Thiele-type continued fraction form with scalar denominator. The generalized inverse introduced by [3]is gen-eralized to rectangular matrix case in this paper. An exact error formula for interpolation is ob-tained, which is an extension in matrix form of bivariate scalar and vector valued rational interpola-tion discussed by Siemaszko[l2] and by Gu Chuangqing [7] respectively. By defining row and col-umn-transformation in the sense of the partial inverted differences for matrices, two type matrix algorithms are established to construct corresponding two different BGIRI, which hold for the vec-tor case and the scalar case.
基金Project(71371182) supported by the National Natural Science Foundation of China
文摘Reliability and remaining useful life(RUL)estimation for a satellite rechargeable lithium battery(RLB)are significant for prognostic and health management(PHM).A novel Bayesian framework is proposed to do reliability analysis by synthesizing multisource data,including bivariate degradation data and lifetime data.Bivariate degradation means that there are two degraded performance characteristics leading to the failure of the system.First,linear Wiener process and Frank Copula function are used to model the dependent degradation processes of the RLB's temperature and discharge voltage.Next,the Bayesian method,in combination with Markov Chain Monte Carlo(MCMC)simulations,is provided to integrate limited bivariate degradation data with other congeneric RLBs'lifetime data.Then reliability evaluation and RUL prediction are carried out for PHM.A simulation study demonstrates that due to the data fusion,parameter estimations and predicted RUL obtained from our model are more precise than models only using degradation data or ignoring the dependency of different degradation processes.Finally,a practical case study of a satellite RLB verifies the usability of the model.
基金supported by the National Natural Science Foundation of China(Grant No.11175113)the Fundamental Research Funds for the Central Universities of China(Grant No.WK2060140013)the Natural Science Foundation of Jiangsu Higher Education Institution of China(Grant No.14KJD140001)
文摘By virtue of the operator-Hermite-polynomial method, we derive some new generating function formulas of the product of two bivariate Hermite polynomials. Their applications in studying quantum optical states are presented.
基金Project Supported by the national Natural Science Foundation of China(No.19871010,No.69973010).
文摘In this paper, the dimension of the spaces of bivariate spline with degree less that 2r and smoothness order r on the Morgan-Scott triangulation is considered. The concept of the instability degree in the dimension of spaces of bivariate spline is presented. The results in the paper make us conjecture the instability degree in the dimension of spaces of bivariate spline is infinity.
文摘We propose a procedure to obtain accurate confidence intervals for the stress-strength reliability R = P (X > Y) when (X, Y) is a bivariate normal distribution with unknown means and covariance matrix. Our method is more accurate than standard methods as it possesses a third-order distributional accuracy. Simulations studies are provided to show the performance of the proposed method relative to existing ones in terms of coverage probability and average length. An empirical example is given to illustrate its usefulness in practice.
