In dynamic scenarios,visual simultaneous localization and mapping(SLAM)algorithms often incorrectly incorporate dynamic points during camera pose computation,leading to reduced accuracy and robustness.This paper prese...In dynamic scenarios,visual simultaneous localization and mapping(SLAM)algorithms often incorrectly incorporate dynamic points during camera pose computation,leading to reduced accuracy and robustness.This paper presents a dynamic SLAM algorithm that leverages object detection and regional dynamic probability.Firstly,a parallel thread employs the YOLOX object detectionmodel to gather 2D semantic information and compensate for missed detections.Next,an improved K-means++clustering algorithm clusters bounding box regions,adaptively determining the threshold for extracting dynamic object contours as dynamic points change.This process divides the image into low dynamic,suspicious dynamic,and high dynamic regions.In the tracking thread,the dynamic point removal module assigns dynamic probability weights to the feature points in these regions.Combined with geometric methods,it detects and removes the dynamic points.The final evaluation on the public TUM RGB-D dataset shows that the proposed dynamic SLAM algorithm surpasses most existing SLAM algorithms,providing better pose estimation accuracy and robustness in dynamic environments.展开更多
We study the conditional entropy of topological dynamical systems using a family of metrics induced by probability bi-sequences.We present a Brin-Katok formula by replacing the mean metric by a family of metrics induc...We study the conditional entropy of topological dynamical systems using a family of metrics induced by probability bi-sequences.We present a Brin-Katok formula by replacing the mean metric by a family of metrics induced by a probability bi-sequence.We also establish the Katok’s entropy formula for conditional entropy for ergodic measures in the case of the new family of metrics.展开更多
The study aims to develop an empirical model to predict the rainfall intensity in Al-Diwaniyah City,Iraq,according to a statistical analysis based on probability and the specific rainfall return period.Rainfall data w...The study aims to develop an empirical model to predict the rainfall intensity in Al-Diwaniyah City,Iraq,according to a statistical analysis based on probability and the specific rainfall return period.Rainfall data were collected daily for 25 years starting in 2000.Daily rainfall data were converted to rainfall intensity for five duration periods ranging from one to five hours.The extreme values were checked,and data that deviated from the group trend were removed for each period,and then arranged in descending order using the Weibull formula to calculate the probability.Statistically,the model performance with a return period of two years is considered good when compared with observed results and other methods such as Talbot and Sherman with a coefficient of determination(R2)>0.97 and Nash-Sutcliffe efficiency(NSE)>0.80.The results showed that a mathematical equation was obtained that describes the relationship between rainfall intensity,probability,and rainfall duration,which can be used for a confined return period with a 50% probability.Therefore,decision-makers can rely on the model to improve the performance of the city’s current drainage system during flood periods in the future.展开更多
In order to solve the problems of high experimental cost of ammunition,lack of field test data,and the difficulty in applying the ammunition hit probability estimation method in classical statistics,this paper assumes...In order to solve the problems of high experimental cost of ammunition,lack of field test data,and the difficulty in applying the ammunition hit probability estimation method in classical statistics,this paper assumes that the projectile dispersion of ammunition is a two-dimensional joint normal distribution,and proposes a new Bayesian inference method of ammunition hit probability based on normal-inverse Wishart distribution.Firstly,the conjugate joint prior distribution of the projectile dispersion characteristic parameters is determined to be a normal inverse Wishart distribution,and the hyperparameters in the prior distribution are estimated by simulation experimental data and historical measured data.Secondly,the field test data is integrated with the Bayesian formula to obtain the joint posterior distribution of the projectile dispersion characteristic parameters,and then the hit probability of the ammunition is estimated.Finally,compared with the binomial distribution method,the method in this paper can consider the dispersion information of ammunition projectiles,and the hit probability information is more fully utilized.The hit probability results are closer to the field shooting test samples.This method has strong applicability and is conducive to obtaining more accurate hit probability estimation results.展开更多
On May 22,2021,an M_(S)7.4 earthquake occurred in Maduo County,Qinghai Province,on the western plateau of China.The level of seismic monitoring in this area was inadequate,and incomplete seismic waveforms were obtaine...On May 22,2021,an M_(S)7.4 earthquake occurred in Maduo County,Qinghai Province,on the western plateau of China.The level of seismic monitoring in this area was inadequate,and incomplete seismic waveforms were obtained from a few broadband seismometers located within 300 km of the epicentre.All waveforms showed“truncation”phenomena.The waveforms of earthquakes can guide ground motion inputs in near-fault areas.This paper uses the empirical Green's function method to consider the uncertainties in source parameters and source rupture processes by synthesizing high-probability,accurate waveforms in Maduo County(MAD station)near the epicentre.The acceleration waveform at the DAW strong-motion station,located 176 km from the epicentre,is first synthesized with the observed waveform of the mainshock.This critical step not only provides a more accurate source and rupture model of the Maduo earthquake but also establishes an essential reference standard.Secondly,the inferred models are rigorously applied to synthesize the acceleration waveform of the MAD station,ensuring that the results maintain a high accuracy and probability.The findings suggest that(1)the simulated acceleration waveform for the MAD station can better characterize the actual ground motion characteristics of the M_(S)7.4 earthquake in Maduo County,with high accuracy and probability in peak ground acceleration(Abbreviated as PGA)ranges of 140–240 and 350–390 cm/s^(2),respectively,and(2)the M_(S)7.4 earthquake did not undergo a complete supershear rupture process.The first asperity located on the east side of the epicentre is most likely to undergo supershear rupture.However,the Maduo earthquake may have been a complete subshear rupture.(3)The fault dislocation model of the three-asperity model better matches the actual source rupture process of the Maduo earthquake.This method can provide relatively accurate acceleration waveforms for regions with limited earthquake monitoring capabilities and assist in analysis of building seismic damage response,earthquake-induced geological disasters and sand liquefaction,and estimation of regional disaster losses.展开更多
Fatigue analysis of engine turbine blade is an essential issue.Due to various uncertainties during the manufacture and operation,the fatigue damage and life of turbine blade present randomness.In this study,the random...Fatigue analysis of engine turbine blade is an essential issue.Due to various uncertainties during the manufacture and operation,the fatigue damage and life of turbine blade present randomness.In this study,the randomness of structural parameters,working condition and vibration environment are considered for fatigue life predication and reliability assessment.First,the lowcycle fatigue problem is modelled as stochastic static system with random parameters,while the high-cycle fatigue problem is considered as stochastic dynamic system under random excitations.Then,to deal with the two failure modes,the novel Direct Probability Integral Method(DPIM)is proposed,which is efficient and accurate for solving stochastic static and dynamic systems.The probability density functions of accumulated damage and fatigue life of turbine blade for low-cycle and high-cycle fatigue problems are achieved,respectively.Furthermore,the time–frequency hybrid method is advanced to enhance the computational efficiency for governing equation of system.Finally,the results of typical examples demonstrate high accuracy and efficiency of the proposed method by comparison with Monte Carlo simulation and other methods.It is indicated that the DPIM is a unified method for predication of random fatigue life for low-cycle and highcycle fatigue problems.The rotational speed,density,fatigue strength coefficient,and fatigue plasticity index have a high sensitivity to fatigue reliability of engine turbine blade.展开更多
This paper focuses on the ideological and political construction of the course“Probability Theory and Mathematical Statistics.”Aiming at the current situation in teaching where emphasis is placed on knowledge impart...This paper focuses on the ideological and political construction of the course“Probability Theory and Mathematical Statistics.”Aiming at the current situation in teaching where emphasis is placed on knowledge imparting while value guidance is neglected,and combined with the requirements of ideological and political education policies in the new era,this paper explores the integration path between professional courses and ideological and political education.Through literature analysis,case comparison,and empirical research,the study proposes a systematic implementation plan covering the design of teaching objectives,the reconstruction of teaching content,and the optimization of the evaluation system.The purpose is to cultivate students’sense of social responsibility and innovative awareness by excavating the ideological and political elements in mathematics.The research results provide practical reference for colleges and universities to deepen the reform of ideological and political education in courses,and promote the implementation of the fundamental task of fostering virtue through education in STEM education.展开更多
Fires are one of the most destructive natural disasters and have serious long-term effects on the environment,economy,and human health.In Inner Mongolia Autonomous Region,China,frequent fire disturbance occurs due to ...Fires are one of the most destructive natural disasters and have serious long-term effects on the environment,economy,and human health.In Inner Mongolia Autonomous Region,China,frequent fire disturbance occurs due to the intensification of climate change and human activities.It is crucial to understand the fire regime and estimate the probability of regional fire occurrence and reducing fire losses.However,most studies have primarily focused on the dynamic changes,probability of occurrence,and driving mechanisms of wildfires in the grassland and forest land ecosystems in Inner Mongolia,while insufficient research has been conducted on the spatiotemporal variations in active fires and their impact on the wildfire risk in forest land and grassland.Therefore,in this study,we analyzed the active fire regime based on Moderate Resolution Imaging Spectroradiometer(MODIS)thermal anomalies and burned area products from 2000 to 2022.Combined with climate,topographic,landscape,anthropogenic,and vegetation datasets,logistic regression(LR),support vector machine(SVM),random forest(RF),and convolutional neural network(CNN)models were chosen to estimate the probability of active fire occurrence at the seasonal timescale.The results revealed that:(1)a total of 100,343 active fires occurred in Inner Mongolia and the burned area reached 6.59×104 km².The number of ignition point exhibited a significant increasing trend,while the burned area exhibited a nonsignificant decreasing trend;(2)four active fire belts were detected,namely,the Hetao-Tumochuan Plain fire belt,Xiliao River Plain fire belt,Songnen Plain fire belt,and Hailar River Eroded Plain fire belt.The centroid of the active fires has shifted 456.4 km toward the southwest;(3)RF model achieved the highest accuracy in estimating the probability of active fire occurrence,followed by CNN,and LR and SVM models had lower accuracies;and(4)the distribution of the high and extremely high fire risk areas largely aligned with the four fire belts.The probability of active fire occurrence was the highest in spring,followed by that in autumn,and it gradually decreased in summer and winter.Our results revealed active fires migrated to the southwest and ignition sources increased,despite reduction of the burned area was not significant.The RF model outperformed the other models in predicting the probability of active fire occurrence.These findings contribute to future fire prevention and prediction in Inner Mongolia.展开更多
This study presents an innovative approach to calculating the failure probability of slopes by incorporating fuzzylimit-state functions,a method that significantly enhances the accuracy and efficiency of slope stabili...This study presents an innovative approach to calculating the failure probability of slopes by incorporating fuzzylimit-state functions,a method that significantly enhances the accuracy and efficiency of slope stability analysis.Unlike traditional probabilistic techniques,this approach utilizes a least squares support vector machine(LSSVM)optimized with a grey wolf optimizer(GWO)and K-fold cross-validation(CV)to approximate the limit-statefunction,thus reducing computational complexity.The novelty of this work lies in its application to one-dimensional(1D),two-dimensional(2D),and three-dimensional(3D)slope models,demonstrating its versatility andhigh precision.The proposed method consistently achieves error margins within 3%of Monte Carlo simulation(MCS)results,while substantially reducing computation time,particularly for 2D and 3D models.This makes theapproach highly practical for real-world engineering applications.Furthermore,by applying fuzzy mathematics tohandle uncertainties in geotechnical properties,the method offers a more realistic and comprehensive understandingof slope stability.As water is the main factor influencing the stability of slopes,this aspect is investigatedby calculating the phreatic line after the change in water level.Relevant examples are used to show that the failureprobability of a slope under water wading condition can increase by more than 20%(increase rates in 1D,2D and3D conditions being 25%,27%and 31%,respectively)compared with the natural condition.The influence ofdiverse fuzzy membership functions—linear,normal,and Cauchy—on failure probability is also considered.Thisresearch not only provides a strategy for better calculation of the slope failure probability but also pioneers theintegration of computational intelligence,fuzzy logic and fluid-dynamics in geotechnical engineering,presentingan innovative and efficient tool for slope stability analysis.展开更多
The process of entrainment-mixing between cumulus clouds and the ambient air is important for the development of cumulus clouds.Accurately obtaining the entrainment rate(λ)is particularly important for its parameteri...The process of entrainment-mixing between cumulus clouds and the ambient air is important for the development of cumulus clouds.Accurately obtaining the entrainment rate(λ)is particularly important for its parameterization within the overall cumulus parameterization scheme.In this study,an improved bulk-plume method is proposed by solving the equations of two conserved variables simultaneously to calculateλof cumulus clouds in a large-eddy simulation.The results demonstrate that the improved bulk-plume method is more reliable than the traditional bulk-plume method,becauseλ,as calculated from the improved method,falls within the range ofλvalues obtained from the traditional method using different conserved variables.The probability density functions ofλfor all data,different times,and different heights can be well-fitted by a log-normal distribution,which supports the assumed stochastic entrainment process in previous studies.Further analysis demonstrate that the relationship betweenλand the vertical velocity is better than other thermodynamic/dynamical properties;thus,the vertical velocity is recommended as the primary influencing factor for the parameterization ofλin the future.The results of this study enhance the theoretical understanding ofλand its influencing factors and shed new light on the development ofλparameterization.展开更多
Historically,landslides have been the primary type of geological disaster worldwide.Generally,the stability of reservoir banks is primarily affected by rainfall and reservoir water level fluctuations.Moreover,the stab...Historically,landslides have been the primary type of geological disaster worldwide.Generally,the stability of reservoir banks is primarily affected by rainfall and reservoir water level fluctuations.Moreover,the stability of reservoir banks changes with the long-term dynamics of external disastercausing factors.Thus,assessing the time-varying reliability of reservoir landslides remains a challenge.In this paper,a machine learning(ML)based approach is proposed to analyze the long-term reliability of reservoir bank landslides in spatially variable soils through time series prediction.This study systematically investigated the prediction performances of three ML algorithms,i.e.multilayer perceptron(MLP),convolutional neural network(CNN),and long short-term memory(LSTM).Additionally,the effects of the data quantity and data ratio on the predictive power of deep learning models are considered.The results show that all three ML models can accurately depict the changes in the time-varying failure probability of reservoir landslides.The CNN model outperforms both the MLP and LSTM models in predicting the failure probability.Furthermore,selecting the right data ratio can improve the prediction accuracy of the failure probability obtained by ML models.展开更多
The exploration of Mars would heavily rely on Martian rocks mechanics and engineering technology.As the mechanical property of Martian rocks is uncertain,it is of utmost importance to predict the probability distribut...The exploration of Mars would heavily rely on Martian rocks mechanics and engineering technology.As the mechanical property of Martian rocks is uncertain,it is of utmost importance to predict the probability distribution of Martian rocks mechanical property for the success of Mars exploration.In this paper,a fast and accurate probability distribution method for predicting the macroscale elastic modulus of Martian rocks was proposed by integrating the microscale rock mechanical experiments(micro-RME),accurate grain-based modeling(AGBM)and upscaling methods based on reliability principles.Firstly,the microstructure of NWA12564 Martian sample and elastic modulus of each mineral were obtained by micro-RME with TESCAN integrated mineral analyzer(TIMA)and nanoindentation.The best probability distribution function of the minerals was determined by Kolmogorov-Smirnov(K-S)test.Secondly,based on best distribution function of each mineral,the Monte Carlo simulations(MCS)and upscaling methods were implemented to obtain the probability distribution of upscaled elastic modulus.Thirdly,the correlation between the upscaled elastic modulus and macroscale elastic modulus obtained by AGBM was established.The accurate probability distribution of the macroscale elastic modulus was obtained by this correlation relationship.The proposed method can predict the probability distribution of Martian rocks mechanical property with any size and shape samples.展开更多
This paper proposed an efficient research method for high-dimensional uncertainty quantification of projectile motion in the barrel of a truck-mounted howitzer.Firstly,the dynamic model of projectile motion is establi...This paper proposed an efficient research method for high-dimensional uncertainty quantification of projectile motion in the barrel of a truck-mounted howitzer.Firstly,the dynamic model of projectile motion is established considering the flexible deformation of the barrel and the interaction between the projectile and the barrel.Subsequently,the accuracy of the dynamic model is verified based on the external ballistic projectile attitude test platform.Furthermore,the probability density evolution method(PDEM)is developed to high-dimensional uncertainty quantification of projectile motion.The engineering example highlights the results of the proposed method are consistent with the results obtained by the Monte Carlo Simulation(MCS).Finally,the influence of parameter uncertainty on the projectile disturbance at muzzle under different working conditions is analyzed.The results show that the disturbance of the pitch angular,pitch angular velocity and pitch angular of velocity decreases with the increase of launching angle,and the random parameter ranges of both the projectile and coupling model have similar influence on the disturbance of projectile angular motion at muzzle.展开更多
The formation control of multiple unmanned aerial vehicles(multi-UAVs)has always been a research hotspot.Based on the straight line trajectory,a multi-UAVs target point assignment algorithm based on the assignment pro...The formation control of multiple unmanned aerial vehicles(multi-UAVs)has always been a research hotspot.Based on the straight line trajectory,a multi-UAVs target point assignment algorithm based on the assignment probability is proposed to achieve the shortest overall formation path of multi-UAVs with low complexity and reduce the energy consumption.In order to avoid the collision between UAVs in the formation process,the concept of safety ball is introduced,and the collision detection based on continuous motion of two time slots and the lane occupation detection after motion is proposed to avoid collision between UAVs.Based on the idea of game theory,a method of UAV motion form setting based on the maximization of interests is proposed,including the maximization of self-interest and the maximization of formation interest is proposed,so that multi-UAVs can complete the formation task quickly and reasonably with the linear trajectory assigned in advance.Finally,through simulation verification,the multi-UAVs target assignment algorithm based on the assignment probability proposed in this paper can effectively reduce the total path length,and the UAV motion selection method based on the maximization interests can effectively complete the task formation.展开更多
The generation and propagation mechanism of strong nonlinear waves in the South China Sea is an essential research area. In this study, the third-generation wave model WAVEWATCH Ⅲ is employed to simulate wave fields ...The generation and propagation mechanism of strong nonlinear waves in the South China Sea is an essential research area. In this study, the third-generation wave model WAVEWATCH Ⅲ is employed to simulate wave fields under extreme sea states. The model, integrating the ST6 source term, is validated against observed data, demonstrating its credibility. The spatial distribution of the occurrence probability of strong nonlinear waves during typhoons is shown, and the waves in the straits and the northeastern part of the South China Sea show strong nonlinear characteristics. The high-order spectral model HOS-ocean is employed to simulate the random wave surface series beneath five different platform areas. The waves during the typhoon exhibit strong nonlinear characteristics, and freak waves exist. The space-varying probability model is established to describe the short-term probability distribution of nonlinear wave series. The exceedance probability distributions of the wave surface beneath different platform areas are compared and analyzed. The results show that with an increase in the platform area, the probability of a strong nonlinear wave beneath the platform increases.展开更多
In this paper,the problem of online distributed optimization subject to a convex set is studied via a network of agents.Each agent only has access to a noisy gradient of its own objective function,and can communicate ...In this paper,the problem of online distributed optimization subject to a convex set is studied via a network of agents.Each agent only has access to a noisy gradient of its own objective function,and can communicate with its neighbors via a network.To handle this problem,an online distributed stochastic mirror descent algorithm is proposed.Existing works on online distributed algorithms involving stochastic gradients only provide the expectation bounds of the regrets.Different from them,we study the high probability bound of the regrets,i.e.,the sublinear bound of the regret is characterized by the natural logarithm of the failure probability's inverse.Under mild assumptions on the graph connectivity,we prove that the dynamic regret grows sublinearly with a high probability if the deviation in the minimizer sequence is sublinear with the square root of the time horizon.Finally,a simulation is provided to demonstrate the effectiveness of our theoretical results.展开更多
The paper investigates the escape probability for isotropic emitters near a Kerr black hole.We propose a new approach to obtain the escape probability in a general manner,going beyond previous case-by-case studies.Thi...The paper investigates the escape probability for isotropic emitters near a Kerr black hole.We propose a new approach to obtain the escape probability in a general manner,going beyond previous case-by-case studies.This approach is based on studies of the black hole shadow with astrometric observable and can be applied to emitters with an arbitrary 4-velocities and locations,even to the emitters outside of the equatorial plane.We also consider representative examples illustrating how escape probabilities vary with distance,velocity,and inclination angle.Overall,this new approach provides an effective method for studying escape probabilities near Kerr black holes.展开更多
Several densities or probability laws of continuous random variables derive from the Euler Gamma function. These laws form the basis of sampling theory, namely hypothesis testing and estimation. Namely the gamma, beta...Several densities or probability laws of continuous random variables derive from the Euler Gamma function. These laws form the basis of sampling theory, namely hypothesis testing and estimation. Namely the gamma, beta, and Student law, through the chi-square law and the normal law are all distributions resulting from applications of Euleur functions.展开更多
In time-variant reliability problems,there are a lot of uncertain variables from different sources.Therefore,it is important to consider these uncertainties in engineering.In addition,time-variant reliability problems...In time-variant reliability problems,there are a lot of uncertain variables from different sources.Therefore,it is important to consider these uncertainties in engineering.In addition,time-variant reliability problems typically involve a complexmultilevel nested optimization problem,which can result in an enormous amount of computation.To this end,this paper studies the time-variant reliability evaluation of structures with stochastic and bounded uncertainties using a mixed probability and convex set model.In this method,the stochastic process of a limit-state function with mixed uncertain parameters is first discretized and then converted into a timeindependent reliability problem.Further,to solve the double nested optimization problem in hybrid reliability calculation,an efficient iterative scheme is designed in standard uncertainty space to determine the most probable point(MPP).The limit state function is linearized at these points,and an innovative random variable is defined to solve the equivalent static reliability analysis model.The effectiveness of the proposed method is verified by two benchmark numerical examples and a practical engineering problem.展开更多
The secure and normal operation of distributed networks is crucial for accurate parameter estimation.However,distributed networks are frequently susceptible to Byzantine attacks.Considering real-life scenarios,this pa...The secure and normal operation of distributed networks is crucial for accurate parameter estimation.However,distributed networks are frequently susceptible to Byzantine attacks.Considering real-life scenarios,this paper investigates a probability Byzantine(PB)attack,utilizing a Bernoulli distribution to simulate the attack probability.Historically,additional detection mechanisms are used to mitigate such attacks,leading to increased energy consumption and burdens on distributed nodes,consequently diminishing operational efficiency.Differing from these approaches,an adaptive updating distributed estimation algorithm is proposed to mitigate the impact of PB attacks.In the proposed algorithm,a penalty strategy is initially incorporated during data updates to weaken the influence of the attack.Subsequently,an adaptive fusion weight is employed during data fusion to merge the estimations.Additionally,the reason why this penalty term weakens the attack has been analyzed,and the performance of the proposed algorithm is validated through simulation experiments.展开更多
基金the National Natural Science Foundation of China(No.62063006)to the Guangxi Natural Science Foundation under Grant(Nos.2023GXNSFAA026025,AA24010001)+3 种基金to the Innovation Fund of Chinese Universities Industry-University-Research(ID:2023RY018)to the Special Guangxi Industry and Information Technology Department,Textile and Pharmaceutical Division(ID:2021 No.231)to the Special Research Project of Hechi University(ID:2021GCC028)to the Key Laboratory of AI and Information Processing,Education Department of Guangxi Zhuang Autonomous Region(Hechi University),No.2024GXZDSY009。
文摘In dynamic scenarios,visual simultaneous localization and mapping(SLAM)algorithms often incorrectly incorporate dynamic points during camera pose computation,leading to reduced accuracy and robustness.This paper presents a dynamic SLAM algorithm that leverages object detection and regional dynamic probability.Firstly,a parallel thread employs the YOLOX object detectionmodel to gather 2D semantic information and compensate for missed detections.Next,an improved K-means++clustering algorithm clusters bounding box regions,adaptively determining the threshold for extracting dynamic object contours as dynamic points change.This process divides the image into low dynamic,suspicious dynamic,and high dynamic regions.In the tracking thread,the dynamic point removal module assigns dynamic probability weights to the feature points in these regions.Combined with geometric methods,it detects and removes the dynamic points.The final evaluation on the public TUM RGB-D dataset shows that the proposed dynamic SLAM algorithm surpasses most existing SLAM algorithms,providing better pose estimation accuracy and robustness in dynamic environments.
文摘We study the conditional entropy of topological dynamical systems using a family of metrics induced by probability bi-sequences.We present a Brin-Katok formula by replacing the mean metric by a family of metrics induced by a probability bi-sequence.We also establish the Katok’s entropy formula for conditional entropy for ergodic measures in the case of the new family of metrics.
文摘The study aims to develop an empirical model to predict the rainfall intensity in Al-Diwaniyah City,Iraq,according to a statistical analysis based on probability and the specific rainfall return period.Rainfall data were collected daily for 25 years starting in 2000.Daily rainfall data were converted to rainfall intensity for five duration periods ranging from one to five hours.The extreme values were checked,and data that deviated from the group trend were removed for each period,and then arranged in descending order using the Weibull formula to calculate the probability.Statistically,the model performance with a return period of two years is considered good when compared with observed results and other methods such as Talbot and Sherman with a coefficient of determination(R2)>0.97 and Nash-Sutcliffe efficiency(NSE)>0.80.The results showed that a mathematical equation was obtained that describes the relationship between rainfall intensity,probability,and rainfall duration,which can be used for a confined return period with a 50% probability.Therefore,decision-makers can rely on the model to improve the performance of the city’s current drainage system during flood periods in the future.
基金supported by the National Natural Science Foundation of China(No.71501183).
文摘In order to solve the problems of high experimental cost of ammunition,lack of field test data,and the difficulty in applying the ammunition hit probability estimation method in classical statistics,this paper assumes that the projectile dispersion of ammunition is a two-dimensional joint normal distribution,and proposes a new Bayesian inference method of ammunition hit probability based on normal-inverse Wishart distribution.Firstly,the conjugate joint prior distribution of the projectile dispersion characteristic parameters is determined to be a normal inverse Wishart distribution,and the hyperparameters in the prior distribution are estimated by simulation experimental data and historical measured data.Secondly,the field test data is integrated with the Bayesian formula to obtain the joint posterior distribution of the projectile dispersion characteristic parameters,and then the hit probability of the ammunition is estimated.Finally,compared with the binomial distribution method,the method in this paper can consider the dispersion information of ammunition projectiles,and the hit probability information is more fully utilized.The hit probability results are closer to the field shooting test samples.This method has strong applicability and is conducive to obtaining more accurate hit probability estimation results.
基金jointly supported by the Youth Fund of the National Natural Science Foundation(No.42104053)the Research Project Fund of the Institute of Geophysics,China Earthquake Administration(No.DQJB22R30)the independent project initiated by the institute of Geophysics,China Earthquake Administration(No.JY2022Z41)。
文摘On May 22,2021,an M_(S)7.4 earthquake occurred in Maduo County,Qinghai Province,on the western plateau of China.The level of seismic monitoring in this area was inadequate,and incomplete seismic waveforms were obtained from a few broadband seismometers located within 300 km of the epicentre.All waveforms showed“truncation”phenomena.The waveforms of earthquakes can guide ground motion inputs in near-fault areas.This paper uses the empirical Green's function method to consider the uncertainties in source parameters and source rupture processes by synthesizing high-probability,accurate waveforms in Maduo County(MAD station)near the epicentre.The acceleration waveform at the DAW strong-motion station,located 176 km from the epicentre,is first synthesized with the observed waveform of the mainshock.This critical step not only provides a more accurate source and rupture model of the Maduo earthquake but also establishes an essential reference standard.Secondly,the inferred models are rigorously applied to synthesize the acceleration waveform of the MAD station,ensuring that the results maintain a high accuracy and probability.The findings suggest that(1)the simulated acceleration waveform for the MAD station can better characterize the actual ground motion characteristics of the M_(S)7.4 earthquake in Maduo County,with high accuracy and probability in peak ground acceleration(Abbreviated as PGA)ranges of 140–240 and 350–390 cm/s^(2),respectively,and(2)the M_(S)7.4 earthquake did not undergo a complete supershear rupture process.The first asperity located on the east side of the epicentre is most likely to undergo supershear rupture.However,the Maduo earthquake may have been a complete subshear rupture.(3)The fault dislocation model of the three-asperity model better matches the actual source rupture process of the Maduo earthquake.This method can provide relatively accurate acceleration waveforms for regions with limited earthquake monitoring capabilities and assist in analysis of building seismic damage response,earthquake-induced geological disasters and sand liquefaction,and estimation of regional disaster losses.
基金supports of the National Natural Science Foundation of China(Nos.12032008,12102080)the Fundamental Research Funds for the Central Universities,China(No.DUT23RC(3)038)are much appreciated。
文摘Fatigue analysis of engine turbine blade is an essential issue.Due to various uncertainties during the manufacture and operation,the fatigue damage and life of turbine blade present randomness.In this study,the randomness of structural parameters,working condition and vibration environment are considered for fatigue life predication and reliability assessment.First,the lowcycle fatigue problem is modelled as stochastic static system with random parameters,while the high-cycle fatigue problem is considered as stochastic dynamic system under random excitations.Then,to deal with the two failure modes,the novel Direct Probability Integral Method(DPIM)is proposed,which is efficient and accurate for solving stochastic static and dynamic systems.The probability density functions of accumulated damage and fatigue life of turbine blade for low-cycle and high-cycle fatigue problems are achieved,respectively.Furthermore,the time–frequency hybrid method is advanced to enhance the computational efficiency for governing equation of system.Finally,the results of typical examples demonstrate high accuracy and efficiency of the proposed method by comparison with Monte Carlo simulation and other methods.It is indicated that the DPIM is a unified method for predication of random fatigue life for low-cycle and highcycle fatigue problems.The rotational speed,density,fatigue strength coefficient,and fatigue plasticity index have a high sensitivity to fatigue reliability of engine turbine blade.
基金Shaanxi Provincial 14th Five-Year Plan for Educational Science Research(SGH24Q481)。
文摘This paper focuses on the ideological and political construction of the course“Probability Theory and Mathematical Statistics.”Aiming at the current situation in teaching where emphasis is placed on knowledge imparting while value guidance is neglected,and combined with the requirements of ideological and political education policies in the new era,this paper explores the integration path between professional courses and ideological and political education.Through literature analysis,case comparison,and empirical research,the study proposes a systematic implementation plan covering the design of teaching objectives,the reconstruction of teaching content,and the optimization of the evaluation system.The purpose is to cultivate students’sense of social responsibility and innovative awareness by excavating the ideological and political elements in mathematics.The research results provide practical reference for colleges and universities to deepen the reform of ideological and political education in courses,and promote the implementation of the fundamental task of fostering virtue through education in STEM education.
基金funded by the First-Class Discipline Research Special Project of Inner Mongolia(YLXKZX-NSD-040)the Natural Science Foundation of Inner Mongolia(2022LHQN04003,2023QN04009)+1 种基金the Fundamental Research Funds for the Inner Mongolia University of Finance and Economics(NCXKY25019,NCYWZ22003)the National Social Science Fund of China(22BZS134).
文摘Fires are one of the most destructive natural disasters and have serious long-term effects on the environment,economy,and human health.In Inner Mongolia Autonomous Region,China,frequent fire disturbance occurs due to the intensification of climate change and human activities.It is crucial to understand the fire regime and estimate the probability of regional fire occurrence and reducing fire losses.However,most studies have primarily focused on the dynamic changes,probability of occurrence,and driving mechanisms of wildfires in the grassland and forest land ecosystems in Inner Mongolia,while insufficient research has been conducted on the spatiotemporal variations in active fires and their impact on the wildfire risk in forest land and grassland.Therefore,in this study,we analyzed the active fire regime based on Moderate Resolution Imaging Spectroradiometer(MODIS)thermal anomalies and burned area products from 2000 to 2022.Combined with climate,topographic,landscape,anthropogenic,and vegetation datasets,logistic regression(LR),support vector machine(SVM),random forest(RF),and convolutional neural network(CNN)models were chosen to estimate the probability of active fire occurrence at the seasonal timescale.The results revealed that:(1)a total of 100,343 active fires occurred in Inner Mongolia and the burned area reached 6.59×104 km².The number of ignition point exhibited a significant increasing trend,while the burned area exhibited a nonsignificant decreasing trend;(2)four active fire belts were detected,namely,the Hetao-Tumochuan Plain fire belt,Xiliao River Plain fire belt,Songnen Plain fire belt,and Hailar River Eroded Plain fire belt.The centroid of the active fires has shifted 456.4 km toward the southwest;(3)RF model achieved the highest accuracy in estimating the probability of active fire occurrence,followed by CNN,and LR and SVM models had lower accuracies;and(4)the distribution of the high and extremely high fire risk areas largely aligned with the four fire belts.The probability of active fire occurrence was the highest in spring,followed by that in autumn,and it gradually decreased in summer and winter.Our results revealed active fires migrated to the southwest and ignition sources increased,despite reduction of the burned area was not significant.The RF model outperformed the other models in predicting the probability of active fire occurrence.These findings contribute to future fire prevention and prediction in Inner Mongolia.
基金Ministry of Education,Center for Scientific Research and Development of Higher Education Institutions“Innovative Application of Virtual Simulation Technology in Vocational Education Teaching”Special Project,Project No.ZJXF2022110.
文摘This study presents an innovative approach to calculating the failure probability of slopes by incorporating fuzzylimit-state functions,a method that significantly enhances the accuracy and efficiency of slope stability analysis.Unlike traditional probabilistic techniques,this approach utilizes a least squares support vector machine(LSSVM)optimized with a grey wolf optimizer(GWO)and K-fold cross-validation(CV)to approximate the limit-statefunction,thus reducing computational complexity.The novelty of this work lies in its application to one-dimensional(1D),two-dimensional(2D),and three-dimensional(3D)slope models,demonstrating its versatility andhigh precision.The proposed method consistently achieves error margins within 3%of Monte Carlo simulation(MCS)results,while substantially reducing computation time,particularly for 2D and 3D models.This makes theapproach highly practical for real-world engineering applications.Furthermore,by applying fuzzy mathematics tohandle uncertainties in geotechnical properties,the method offers a more realistic and comprehensive understandingof slope stability.As water is the main factor influencing the stability of slopes,this aspect is investigatedby calculating the phreatic line after the change in water level.Relevant examples are used to show that the failureprobability of a slope under water wading condition can increase by more than 20%(increase rates in 1D,2D and3D conditions being 25%,27%and 31%,respectively)compared with the natural condition.The influence ofdiverse fuzzy membership functions—linear,normal,and Cauchy—on failure probability is also considered.Thisresearch not only provides a strategy for better calculation of the slope failure probability but also pioneers theintegration of computational intelligence,fuzzy logic and fluid-dynamics in geotechnical engineering,presentingan innovative and efficient tool for slope stability analysis.
基金supported by the National Natural Science Foundation of China(Grant Nos.42175099,42027804,42075073)the Innovative Project of Postgraduates in Jiangsu Province in 2023(Grant No.KYCX23_1319)+3 种基金supported by the National Natural Science Foundation of China(Grant No.42205080)the Natural Science Foundation of Sichuan(Grant No.2023YFS0442)the Research Fund of Civil Aviation Flight University of China(Grant No.J2022-037)supported by the National Key Scientific and Technological Infrastructure project“Earth System Science Numerical Simulator Facility”(Earth Lab)。
文摘The process of entrainment-mixing between cumulus clouds and the ambient air is important for the development of cumulus clouds.Accurately obtaining the entrainment rate(λ)is particularly important for its parameterization within the overall cumulus parameterization scheme.In this study,an improved bulk-plume method is proposed by solving the equations of two conserved variables simultaneously to calculateλof cumulus clouds in a large-eddy simulation.The results demonstrate that the improved bulk-plume method is more reliable than the traditional bulk-plume method,becauseλ,as calculated from the improved method,falls within the range ofλvalues obtained from the traditional method using different conserved variables.The probability density functions ofλfor all data,different times,and different heights can be well-fitted by a log-normal distribution,which supports the assumed stochastic entrainment process in previous studies.Further analysis demonstrate that the relationship betweenλand the vertical velocity is better than other thermodynamic/dynamical properties;thus,the vertical velocity is recommended as the primary influencing factor for the parameterization ofλin the future.The results of this study enhance the theoretical understanding ofλand its influencing factors and shed new light on the development ofλparameterization.
基金supported by the National Natural Science Foundation of China(Grant No.52308340)the Innovative Projects of Universities in Guangdong(Grant No.2022KTSCX208)Sichuan Transportation Science and Technology Project(Grant No.2018-ZL-01).
文摘Historically,landslides have been the primary type of geological disaster worldwide.Generally,the stability of reservoir banks is primarily affected by rainfall and reservoir water level fluctuations.Moreover,the stability of reservoir banks changes with the long-term dynamics of external disastercausing factors.Thus,assessing the time-varying reliability of reservoir landslides remains a challenge.In this paper,a machine learning(ML)based approach is proposed to analyze the long-term reliability of reservoir bank landslides in spatially variable soils through time series prediction.This study systematically investigated the prediction performances of three ML algorithms,i.e.multilayer perceptron(MLP),convolutional neural network(CNN),and long short-term memory(LSTM).Additionally,the effects of the data quantity and data ratio on the predictive power of deep learning models are considered.The results show that all three ML models can accurately depict the changes in the time-varying failure probability of reservoir landslides.The CNN model outperforms both the MLP and LSTM models in predicting the failure probability.Furthermore,selecting the right data ratio can improve the prediction accuracy of the failure probability obtained by ML models.
文摘The exploration of Mars would heavily rely on Martian rocks mechanics and engineering technology.As the mechanical property of Martian rocks is uncertain,it is of utmost importance to predict the probability distribution of Martian rocks mechanical property for the success of Mars exploration.In this paper,a fast and accurate probability distribution method for predicting the macroscale elastic modulus of Martian rocks was proposed by integrating the microscale rock mechanical experiments(micro-RME),accurate grain-based modeling(AGBM)and upscaling methods based on reliability principles.Firstly,the microstructure of NWA12564 Martian sample and elastic modulus of each mineral were obtained by micro-RME with TESCAN integrated mineral analyzer(TIMA)and nanoindentation.The best probability distribution function of the minerals was determined by Kolmogorov-Smirnov(K-S)test.Secondly,based on best distribution function of each mineral,the Monte Carlo simulations(MCS)and upscaling methods were implemented to obtain the probability distribution of upscaled elastic modulus.Thirdly,the correlation between the upscaled elastic modulus and macroscale elastic modulus obtained by AGBM was established.The accurate probability distribution of the macroscale elastic modulus was obtained by this correlation relationship.The proposed method can predict the probability distribution of Martian rocks mechanical property with any size and shape samples.
基金the National Natural Science Foundation of China(Grant No.11472137).
文摘This paper proposed an efficient research method for high-dimensional uncertainty quantification of projectile motion in the barrel of a truck-mounted howitzer.Firstly,the dynamic model of projectile motion is established considering the flexible deformation of the barrel and the interaction between the projectile and the barrel.Subsequently,the accuracy of the dynamic model is verified based on the external ballistic projectile attitude test platform.Furthermore,the probability density evolution method(PDEM)is developed to high-dimensional uncertainty quantification of projectile motion.The engineering example highlights the results of the proposed method are consistent with the results obtained by the Monte Carlo Simulation(MCS).Finally,the influence of parameter uncertainty on the projectile disturbance at muzzle under different working conditions is analyzed.The results show that the disturbance of the pitch angular,pitch angular velocity and pitch angular of velocity decreases with the increase of launching angle,and the random parameter ranges of both the projectile and coupling model have similar influence on the disturbance of projectile angular motion at muzzle.
基金supported by the Basic Scientific Research Business Expenses of Central Universities(3072022QBZ0806)。
文摘The formation control of multiple unmanned aerial vehicles(multi-UAVs)has always been a research hotspot.Based on the straight line trajectory,a multi-UAVs target point assignment algorithm based on the assignment probability is proposed to achieve the shortest overall formation path of multi-UAVs with low complexity and reduce the energy consumption.In order to avoid the collision between UAVs in the formation process,the concept of safety ball is introduced,and the collision detection based on continuous motion of two time slots and the lane occupation detection after motion is proposed to avoid collision between UAVs.Based on the idea of game theory,a method of UAV motion form setting based on the maximization of interests is proposed,including the maximization of self-interest and the maximization of formation interest is proposed,so that multi-UAVs can complete the formation task quickly and reasonably with the linear trajectory assigned in advance.Finally,through simulation verification,the multi-UAVs target assignment algorithm based on the assignment probability proposed in this paper can effectively reduce the total path length,and the UAV motion selection method based on the maximization interests can effectively complete the task formation.
基金financially supported by the National Key R&D Program of China(No.2022YFC3104205)the National Natural Science Foundation of China(No.42377457).
文摘The generation and propagation mechanism of strong nonlinear waves in the South China Sea is an essential research area. In this study, the third-generation wave model WAVEWATCH Ⅲ is employed to simulate wave fields under extreme sea states. The model, integrating the ST6 source term, is validated against observed data, demonstrating its credibility. The spatial distribution of the occurrence probability of strong nonlinear waves during typhoons is shown, and the waves in the straits and the northeastern part of the South China Sea show strong nonlinear characteristics. The high-order spectral model HOS-ocean is employed to simulate the random wave surface series beneath five different platform areas. The waves during the typhoon exhibit strong nonlinear characteristics, and freak waves exist. The space-varying probability model is established to describe the short-term probability distribution of nonlinear wave series. The exceedance probability distributions of the wave surface beneath different platform areas are compared and analyzed. The results show that with an increase in the platform area, the probability of a strong nonlinear wave beneath the platform increases.
文摘In this paper,the problem of online distributed optimization subject to a convex set is studied via a network of agents.Each agent only has access to a noisy gradient of its own objective function,and can communicate with its neighbors via a network.To handle this problem,an online distributed stochastic mirror descent algorithm is proposed.Existing works on online distributed algorithms involving stochastic gradients only provide the expectation bounds of the regrets.Different from them,we study the high probability bound of the regrets,i.e.,the sublinear bound of the regret is characterized by the natural logarithm of the failure probability's inverse.Under mild assumptions on the graph connectivity,we prove that the dynamic regret grows sublinearly with a high probability if the deviation in the minimizer sequence is sublinear with the square root of the time horizon.Finally,a simulation is provided to demonstrate the effectiveness of our theoretical results.
基金supported by the National Key Research and Development Program of China, Grant No. 2020YFC2201502by grants from the National Natural Science Foundation of China (Grant No. 11991052)the Key Research Program of Frontier Sciences, CAS, Grant No. ZDBS-LY-7009
文摘The paper investigates the escape probability for isotropic emitters near a Kerr black hole.We propose a new approach to obtain the escape probability in a general manner,going beyond previous case-by-case studies.This approach is based on studies of the black hole shadow with astrometric observable and can be applied to emitters with an arbitrary 4-velocities and locations,even to the emitters outside of the equatorial plane.We also consider representative examples illustrating how escape probabilities vary with distance,velocity,and inclination angle.Overall,this new approach provides an effective method for studying escape probabilities near Kerr black holes.
文摘Several densities or probability laws of continuous random variables derive from the Euler Gamma function. These laws form the basis of sampling theory, namely hypothesis testing and estimation. Namely the gamma, beta, and Student law, through the chi-square law and the normal law are all distributions resulting from applications of Euleur functions.
基金partially supported by the National Natural Science Foundation of China(52375238)Science and Technology Program of Guangzhou(202201020213,202201020193,202201010399)GZHU-HKUST Joint Research Fund(YH202109).
文摘In time-variant reliability problems,there are a lot of uncertain variables from different sources.Therefore,it is important to consider these uncertainties in engineering.In addition,time-variant reliability problems typically involve a complexmultilevel nested optimization problem,which can result in an enormous amount of computation.To this end,this paper studies the time-variant reliability evaluation of structures with stochastic and bounded uncertainties using a mixed probability and convex set model.In this method,the stochastic process of a limit-state function with mixed uncertain parameters is first discretized and then converted into a timeindependent reliability problem.Further,to solve the double nested optimization problem in hybrid reliability calculation,an efficient iterative scheme is designed in standard uncertainty space to determine the most probable point(MPP).The limit state function is linearized at these points,and an innovative random variable is defined to solve the equivalent static reliability analysis model.The effectiveness of the proposed method is verified by two benchmark numerical examples and a practical engineering problem.
文摘The secure and normal operation of distributed networks is crucial for accurate parameter estimation.However,distributed networks are frequently susceptible to Byzantine attacks.Considering real-life scenarios,this paper investigates a probability Byzantine(PB)attack,utilizing a Bernoulli distribution to simulate the attack probability.Historically,additional detection mechanisms are used to mitigate such attacks,leading to increased energy consumption and burdens on distributed nodes,consequently diminishing operational efficiency.Differing from these approaches,an adaptive updating distributed estimation algorithm is proposed to mitigate the impact of PB attacks.In the proposed algorithm,a penalty strategy is initially incorporated during data updates to weaken the influence of the attack.Subsequently,an adaptive fusion weight is employed during data fusion to merge the estimations.Additionally,the reason why this penalty term weakens the attack has been analyzed,and the performance of the proposed algorithm is validated through simulation experiments.
