Current seismic damage assessments for high-speed railway(HSR)bridges primarily focus on the overall structural safety,lacking evaluations from multiple performance perspectives,which affects the post-earthquake traff...Current seismic damage assessments for high-speed railway(HSR)bridges primarily focus on the overall structural safety,lacking evaluations from multiple performance perspectives,which affects the post-earthquake traffic decision-making for the bridges.This study proposes a performance-based comprehensive functional damage probability assessment framework for high-speed railway simply supported bridges(HSRSSBs)under earthquakes.The framework categorizes the functions of HSR bridges into three levels:post-earthquake traffic function(PTF),structural bearing function(SBF),and collapse resistance function(CRF),corresponding to the operational,structural safety,and structural integrity requirements of HSRSSB,respectively.By analyzing the damage states of key bridge components during earthquakes,the functional damage probability assessment indicators and classification thresholds are established according to various performance requirements.Damage probability calculations are conducted using the probability density evolution method and vulnerability method.Finally,based on the relationship between damage probabilities at different functional levels,a comprehensive damage probability assessment framework considering the three-level performance requirements of HSRSSBs is developed,and the influence of varying pier heights on the functional damage probability relationship is examined.The results indicate that current HSRSSB designs meet all performance requirements under frequent earthquakes.Under design-level earthquake conditions,the SBF remains in a slight damage state,while the PTF exhibits varying degrees of damage,which worsens as pier height increases.The pier structure satisfies seismic demands even under rare earthquake conditions.展开更多
The upcoming Euro 7 vehicle emissions regulation sets new requirements for calibrating particle number portable emissions measurement systems(PN-PEMS).In current PN concentration calibration methods,arbitrary selectio...The upcoming Euro 7 vehicle emissions regulation sets new requirements for calibrating particle number portable emissions measurement systems(PN-PEMS).In current PN concentration calibration methods,arbitrary selection of aerosolmaterials and incorrect estimation ofmultiply-charged particles lead to calibration deviation.This study proposes a novel,accurate calibration method based on the calibration and correction of the actual charging probability of soot for calibrating PN-PEMS.The accurate calibration results of a PN-PEMS show a maximum reduction of 7.65%in the+1-charging probability deviation and of 3.15%in the counting efficiency deviation.The calibration of the actual charging probability of soot introduces a calibration uncertainty increment of 0.09%-2.71%,and the overall uncertainty is<4.76%,whichmakes the calibration results more credible.The interaction of calibration aerosols of different physicochemical properties with the condensation particle counter working fluid and catalytic stripper device is the main reason for the different PN-PEMS calibration results.The calibration of the actual charging probability of particles is the fundamental method to eliminate the calibration deviation caused by the estimation and correction of multiply-charged particles.展开更多
Predicting surface settlement of soft soil under the combined prefabricated vertical drain(PVD)-embankment system remains a critical challenge in geotechnical engineering due to the complex and time-dependent nature o...Predicting surface settlement of soft soil under the combined prefabricated vertical drain(PVD)-embankment system remains a critical challenge in geotechnical engineering due to the complex and time-dependent nature of soil behavior.This study leverages in situ data collected from various real-world projects to develop a hybrid machine learning model that incorporates prediction uncertainty(confidenceinterval).Twelve input variables are determined based on conventional theories of radial soil consolidation under embankment,encompassing soil properties,PVD parameters,and loading conditions.Different machine learning algorithms are extensively evaluated with the Categorical boosting(CATB),which emerges as the most reliable and accurate algorithm for predicting the settlement of PVD-treated soft soil.The CATB performance is further enhanced by the adaptive step random search(ASRS),proving its exceptional predictive accuracy and robustness.The developed model is applied to an independent case from the field-scaleembankment test at Australia's National Field Testing Facility(NFTF),yielding promising outcomes.Importance-based sensitivity analysis revealed the dominant influenceof key parameters,including time,pre-consolidation pressure,recompression index,and PVD characteristics,on settlement behavior,offering actionable insights for optimized design.The probabilistic parameters are incorporated into the data-driven model,facilitating the assessment of prediction confidence,advancing practical design of soft soil improvement,and bridging the gap between theoretical modeling and real-world geotechnical design needs.展开更多
The western Los Angeles(LA)wildfires of early January 2025 caused catastrophic social and environmental impacts,drawing widespread attention.This study investigates the characteristics of these wildfires and quantifie...The western Los Angeles(LA)wildfires of early January 2025 caused catastrophic social and environmental impacts,drawing widespread attention.This study investigates the characteristics of these wildfires and quantifies the influence of heat and drought on their likelihood using a copula-based Bayesian probability framework.The wildfires were characterized by burned area(BA)and intensity(fire radiative power,FRP).The criteria establishing the presence of“hot drought”conditions were identified using the 5-day Standardized Temperature Index(STI)and 75-day Standardized Precipitation Index(SPI),respectively.The wildfire outbreak began on 7 January 2025 and burned for more than six days,with the total burned area exceeding 245 km2 and the cumulative FRP exceeding 41060 MW.Based on satellite-derived active fire observations from 2001 to 2025,we estimate that such large and intense wildfires during LA’s rainy season represent a once-in-a-67-year event.The wildfires were largely driven by the combination of hot and dry conditions,which dried out soils and vegetation that had proliferated due to above-average precipitation in previous winter seasons,thereby providing abundant fuel.Our seasonal analysis reveals that extreme drought increased the probability of wildfires matching the 2025 intensity and BA by 54%and 75%,respectively.Hot drought further amplified these probabilities by 149%(intensity)and 210%(BA).These findings suggest an elevated risk of large wildfires under hot drought conditions,contributing to their expansion into the non-traditional fire season.展开更多
In this short article,we wish to initiate a probability theory to describe the(in)famous transition to turbulence phenomena.For normal systems,the instability threshold can be predicted because the transition probabil...In this short article,we wish to initiate a probability theory to describe the(in)famous transition to turbulence phenomena.For normal systems,the instability threshold can be predicted because the transition probability jumps from zero to P→1 when the control parameter exceeds the threshold.However,for non-normal systems,such a transition is probabilistic,which depends on the control parameter and initial energy.A low-dimensional reduction idea is proposed to give a detailed description of the transition probability of non-normal systems in the future.We also wish that such an idea could be transplanted for understanding such a transition in more complex flows,e.g.,atmospheric flows,mantle convection,and ocean circulation.展开更多
An analysis of Beijing urban rail transit emergency data from 2016 to 2018 is conducted to identify the factors influencing emergency severity.A severity probability distribution model is proposed,incorporating season...An analysis of Beijing urban rail transit emergency data from 2016 to 2018 is conducted to identify the factors influencing emergency severity.A severity probability distribution model is proposed,incorporating seasonal effects,multi-dimensional features(passenger,vehicle,line,environment),random parameters,interaction terms,and weather variables(temperature,humidity,wind speed)to capture severity probability changes driven by seasonally influenced factors.High performance is achieved by the model,with 92.10%accuracy,95.17%sensitivity,and 87.58%specificity.Five key factors—bad weather(correlation=-0.0611,p<0.001),track failure(correlation=-0.0503,p<0.001),signal failure(correlation=-0.0483,p<0.001),urban area(correlation=-0.0441,p<0.001),and vehicle failure(correlation=-0.0435,p<0.001)—are identified,with their interactions amplifying risks,particularly the coupling effect between bad weather and train system failures.Notable seasonal effects are observed:In summer,high temperature and humidity increase vehicle and equipment failures;in autumn,temperature fluctuations raise signaling anomaly risks;in winter,low temperatures elevate track and equipment failure risks;and in spring and winter,windy weather exacerbates risks for suburban elevated lines.This study highlights the need for refined risk identification and response mechanisms at the seasonal and regional levels,such as targeted inspections and weather-triggered controls,to enhance operational safety in urban rail transit under complex weather conditions.展开更多
The stack effect in super high-rise buildings is mainly influenced by the temperature difference between the indoor and outdoor environments,wind pressure,building height,and the airtightness of building components.Co...The stack effect in super high-rise buildings is mainly influenced by the temperature difference between the indoor and outdoor environments,wind pressure,building height,and the airtightness of building components.Consequently,the intensity and frequency of the stack effect are inherently impacted by regional and seasonal climate conditions.This study initially examines two critical meteorological elements-temperature and wind speed-that are closely related to the stack effect in high-rise buildings.Then the appropriate climate demarcation for evaluating the stack effect in high-rise buildings,which is based on the building climate demarcation in China is investigated,and the land area of China is divided into four climate regions for the purpose of stack effect assessment.Utilizing annual meteorological monitoring data from each region,the probability function models for temperature and wind speed are developed,and a joint probability distribution function for temperature and wind speed in each region is derived using a binary copula function.Finally,the probabilistic assessment of the stack effect under both pure and combined thermal pressures across different climatic zones is numerically investigated by employing a standardized high-rise building model.This research enables a refined assessment of the stack effect for high-rise building,and provides a useful reference to improve the design codes in future.展开更多
We investigate numerically the effects of long-range temporal and spatial correlations based on the rescaled distributions of the squared interface width W2(L,t)and the interface height h(x,t)in the(1+1)-dimensiona...We investigate numerically the effects of long-range temporal and spatial correlations based on the rescaled distributions of the squared interface width W2(L,t)and the interface height h(x,t)in the(1+1)-dimensional Kardar-Parisi-Zhang(KPZ)growth system within the early growth regime.Through extensive numerical simulations,we find that long-range temporally correlated noise does not significantly impact the distribution form of the interface width.Generally,W2(L,t)approximately obeys a lognormal distribution when the temporal correlation exponentθ≥0.On the other hand,the effects of long-range spatially correlated noise are evidently different from the temporally correlated case.Our results show that,when the spatial correlation exponentρ≤0.20,the distribution forms of W2(L,t)approach the lognormal distribution,and whenρ>0.20,the distribution becomes more asymmetric,steep,and fat-tailed,and tends to an unknown distribution form.As a comparison,probability distributions of the interface height are also provided in the temporally and spatially correlated KPZ system,exhibiting quite different characteristics from each other within the whole correlated strengths.For the temporal correlation,the height distributions follow Tracy-Widom Gaussian orthogonal ensemble(TW-GOE)whenθ→0,and with increasingθ,the height distributions crossover continuously to an unknown distribution.However,for the spatial correlation,the height distributions gradually transition from the TW-GOE distribution to the standard Gaussian form.展开更多
In this paper,the joint design of transmit and receive beamformers for transmit subaperturing multiple-input-multiple-output(TS-MIMO)radar is investigated,aiming to enhance its low probability of intercept(LPI)capabil...In this paper,the joint design of transmit and receive beamformers for transmit subaperturing multiple-input-multiple-output(TS-MIMO)radar is investigated,aiming to enhance its low probability of intercept(LPI)capability.The main objective is to simultaneously minimize the transmission power,suppress the transmit sidelobe levels,and minimize the probability of intercept,thus bolstering the LPI performance of the radar system while maintaining the desired target detection performance.An alternative optimization method is proposed to jointly optimize the transmit and receive beamformers,yielding an unified LPI optimization framework.Particularly,the proposed iterative algorithm based on the Lagrange duality theory for transmit beamforming is more efficient than the conventional convex optimization method.Numerical experiments highlight the effectiveness of the proposed approach in sidelobe suppression and computational efficiency.展开更多
Quantum linear equation solvers generate a solution vector that sits in a subspace of the quantum computer’s larger state space.Accessing the solution vector relies on applying measurement projectors that remove comp...Quantum linear equation solvers generate a solution vector that sits in a subspace of the quantum computer’s larger state space.Accessing the solution vector relies on applying measurement projectors that remove components in the orthogonal subspace.This study examines the probability that the projectors are successful and how the success probability is influenced by the properties of the linear system,e.g.,the matrix condition number,and approximations made in the quantum solver.The analysis is performed within a non-linear computational fluid dynamics code where,at each iteration,a linearised system is passed to an emulated quantum solver.The linear systems are solved using quantum singular value transformation,for which the accuracy of the matrix inversion polynomial can be controlled via user input.The results show that success probabilities vary between 10−6and 10−2for the cases considered.More accurate approximations have lower success probabilities and require longer circuits.Less accurate approximations are analysed and show that variations during the non-linear iterations are related to the eigen content of the right-hand side vector.The use of amplitude amplification is shown to be able to increase success probabilities from 10−6to 10−2,in accordance with theory,but at a cost of a 100 times increase in circuit depth.Whilst these results are specific to the fluid flow test cases,they are generalisable to other types of linear solvers.展开更多
Artificial intelligence(AI)aims to simulate the thinking process of human perception,learning,and decision-making,but uncertainty problems,such as data noise,information loss,and semantic ambiguity are commonly presen...Artificial intelligence(AI)aims to simulate the thinking process of human perception,learning,and decision-making,but uncertainty problems,such as data noise,information loss,and semantic ambiguity are commonly present in real environments.Traditional deterministic mathematics is difficult to complete modeling and inference in complex scenarios.Probability theory,as a mathematical branch that studies the statistical laws of random phenomena,can quantify the likelihood of events occurring and provide a theoretical basis for uncertainty reasoning,parameter optimization,and distribution modeling for AI.This paper focuses on core probability knowledge,such as conditional probability,Bayesian formula,and probability distribution.It systematically discusses the specific applications of probability theory in traditional machine learning,deep learning,generative AI,natural language processing,computer vision,and reinforcement learning.It summarizes the supporting role of probability theory in the development of AI and looks forward to the research direction of the integration of the two in combination with current technological trends.展开更多
In recent years,with the rapid development of artificial intelligence and big data technologies,knowledge graphs have gained widespread attention and application.As a fundamental course in mathematics and statistics,P...In recent years,with the rapid development of artificial intelligence and big data technologies,knowledge graphs have gained widespread attention and application.As a fundamental course in mathematics and statistics,Probability Theory and Mathematical Statistics contains complex and highly interconnected knowledge points,making traditional learning methods less effective for understanding its internal logic.Therefore,constructing a knowledge graph and developing a corresponding question-answering system for this subject is of great significance.This project uses the Probability Theory and Mathematical Statistics Tutorial(3rd Edition)as the data source to construct a knowledge graph based on Neo4j.Cypher language and APOC tools were used for data import and graph construction,while Neo4j Bloom was employed for visualization.In addition,a question-answering system was developed using natural language processing techniques and the Flask framework to provide intelligent query services.The system can help students better understand and learn probability theory and mathematical statistics while reducing dependence on traditional textbooks.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
Recently,machine learning has become a powerful tool for predicting nuclear charge radius RC,providing novel insights into complex physical phenomena.This study employs a continuous Bayesian probability(CBP)estimator ...Recently,machine learning has become a powerful tool for predicting nuclear charge radius RC,providing novel insights into complex physical phenomena.This study employs a continuous Bayesian probability(CBP)estimator and Bayesian model averaging(BMA)to optimize the predictions of RCfrom sophisticated theoretical models.The CBP estimator treats the residual between the theoretical and experimental values of RCas a continuous variable and derives its posterior probability density function(PDF)from Bayesian theory.The BMA method assigns weights to models based on their predictive performance for benchmark nuclei,thereby accounting for the unique strengths of each model.In global optimization,the CBP estimator improved the predictive accuracy of the three theoretical models by approximately 60%.The extrapolation analyses consistently achieved an improvement rate of approximately 45%,demonstrating the robustness of the CBP estimator.Furthermore,the combination of the CBP and BMA methods reduces the standard deviation to below 0.02 fm,effectively reproducing the pronounced shell effects on RCof the Ca and Sr isotope chains.The studies in this paper propose an efficient method to accurately describe RCof unknown nuclei,with potential applications in research on other nuclear properties.展开更多
To ensure the structural integrity of life-limiting component of aeroengines,Probabilistic Damage Tolerance(PDT)assessment is applied to evaluate the failure risk as required by airworthiness regulations and military ...To ensure the structural integrity of life-limiting component of aeroengines,Probabilistic Damage Tolerance(PDT)assessment is applied to evaluate the failure risk as required by airworthiness regulations and military standards.The PDT method holds the view that there exist defects such as machining scratches and service cracks in the tenon-groove structures of aeroengine disks.However,it is challenging to conduct PDT assessment due to the scarcity of effective Probability of Detection(POD)model and anomaly distribution model.Through a series of Nondestructive Testing(NDT)experiments,the POD model of real cracks in tenon-groove structures is constructed for the first time by employing the Transfer Function Method(TFM).A novel anomaly distribution model is derived through the utilization of the POD model,instead of using the infeasible field data accumulation method.Subsequently,a framework for calculating the Probability of Failure(POF)of the tenon-groove structures is established,and the aforementioned two models exert a significant influence on the results of POF.展开更多
To address prediction errors and limited information extraction in machine learning(ML)-based interval prediction,a hybrid model was proposed for interval estimation and failure assessment of step-like landslides unde...To address prediction errors and limited information extraction in machine learning(ML)-based interval prediction,a hybrid model was proposed for interval estimation and failure assessment of step-like landslides under uncertainty.The model decomposed displacements into trend and periodic components via Variational Mode Decomposition(VMD)and K-shape clustering.The Residual and Moving Block Bootstrap methods were used to generate pseudo datasets.Polynomial regressionwas adopted for trend forecasting,whereas the Dense Convolutional Network(DenseNet)and Long Short-Term Memory(LSTM)networks were employed for periodic displacement prediction.An Extreme Learning Machine(ELM)was used to estimate the noise variance,enabling the construction of Prediction Intervals(PIs)and quantificationof displacement uncertainty.Failure probabilities(Pf)were derived from PIs using an improved tangential angle criterion and reliability analysis.The model was validated on three step-like landslides in the Three Gorges Reservoir Area,achieving stability assessment accuracies of 99.88%(XD01),99.93%(ZG93),99.89%(ZG118),and 100%for ZG110 and ZG111 across the Baishuihe and Bazimen landslides.For the Shuping landslide,the predictions aligned with fieldobservations before and after the 2014–2015 remediation,with Pfremaining near zero post-2015 except for occasional peaks.The model outperformed conventional ML approaches by yielding narrower PIs.At XD01 with 90%PI nominal confidencelevel(PINC),the coverage width-based criterion(CWC)and PI average width(PIAW)were 3.38 mm.The mean values of the PIs exhibited high accuracy,with a Mean Absolute Error(MAE)of 0.28 mm and Root Mean Square Error(RMSE)of 0.39 mm.These results demonstrate the robustness of the proposed model in improving landslide risk assessment and decision-making under uncertainty.展开更多
On May 22,2021,an MS7.4 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 MS7.4 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 MS7.4 earthquake in Maduo County,with high accuracy and probability in peak ground acceleration(Abbreviated as PGA)ranges of 140–240 and 350–390 cm/s2,respectively,and(2)the MS7.4 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
Vaccination is critical for controlling infectious diseases,but negative vaccination information can lead to vaccine hesitancy.To study how the interplay between information diffusion and disease transmission impacts ...Vaccination is critical for controlling infectious diseases,but negative vaccination information can lead to vaccine hesitancy.To study how the interplay between information diffusion and disease transmission impacts vaccination and epidemic spread,we propose a novel two-layer multiplex network model that integrates an unaware-acceptant-negative-unaware(UANU)information diffusion model with a susceptible-vaccinated-exposed-infected-susceptible(SVEIS)epidemiological framework.This model includes individual exposure and vaccination statuses,time-varying forgetting probabilities,and information conversion thresholds.Through the microscopic Markov chain approach(MMCA),we derive dynamic transition equations and the epidemic threshold expression,validated by Monte Carlo simulations.Using MMCA equations,we predict vaccination densities and analyze parameter effects on vaccination,disease transmission,and the epidemic threshold.Our findings suggest that promoting positive information,curbing the spread of negative information,enhancing vaccine effectiveness,and promptly identifying asymptomatic carriers can significantly increase vaccination rates,reduce epidemic spread,and raise the epidemic threshold.展开更多
Estimating probability density functions(PDFs)is critical in data analysis,particularly for complex multimodal distributions.traditional kernel density estimator(KDE)methods often face challenges in accurately capturi...Estimating probability density functions(PDFs)is critical in data analysis,particularly for complex multimodal distributions.traditional kernel density estimator(KDE)methods often face challenges in accurately capturing multimodal structures due to their uniform weighting scheme,leading to mode loss and degraded estimation accuracy.This paper presents the flexible kernel density estimator(F-KDE),a novel nonparametric approach designed to address these limitations.F-KDE introduces the concept of kernel unit inequivalence,assigning adaptive weights to each kernel unit,which better models local density variations in multimodal data.The method optimises an objective function that integrates estimation error and log-likelihood,using a particle swarm optimisation(PSO)algorithm that automatically determines optimal weights and bandwidths.Through extensive experiments on synthetic and real-world datasets,we demonstrated that(1)the weights and bandwidths in F-KDE stabilise as the optimisation algorithm iterates,(2)F-KDE effectively captures the multimodal characteristics and(3)F-KDE outperforms state-of-the-art density estimation methods regarding accuracy and robustness.The results confirm that F-KDE provides a valuable solution for accurately estimating multimodal PDFs.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
基金supported by the National Natural Science Foundation of China(Grant No.5247084033)Natural Science Foundation of Hunan Province of China(Grant No.2022JJ30745)+2 种基金Frontier cross research project of Central South University(Grant No.2023QYJC006),ScienceTechnology Research and Development Program Project of China railway group limited(Major Special Project,No.2021-Special-04-2)China Scholarship Council(CSC).
摘要Current seismic damage assessments for high-speed railway(HSR)bridges primarily focus on the overall structural safety,lacking evaluations from multiple performance perspectives,which affects the post-earthquake traffic decision-making for the bridges.This study proposes a performance-based comprehensive functional damage probability assessment framework for high-speed railway simply supported bridges(HSRSSBs)under earthquakes.The framework categorizes the functions of HSR bridges into three levels:post-earthquake traffic function(PTF),structural bearing function(SBF),and collapse resistance function(CRF),corresponding to the operational,structural safety,and structural integrity requirements of HSRSSB,respectively.By analyzing the damage states of key bridge components during earthquakes,the functional damage probability assessment indicators and classification thresholds are established according to various performance requirements.Damage probability calculations are conducted using the probability density evolution method and vulnerability method.Finally,based on the relationship between damage probabilities at different functional levels,a comprehensive damage probability assessment framework considering the three-level performance requirements of HSRSSBs is developed,and the influence of varying pier heights on the functional damage probability relationship is examined.The results indicate that current HSRSSB designs meet all performance requirements under frequent earthquakes.Under design-level earthquake conditions,the SBF remains in a slight damage state,while the PTF exhibits varying degrees of damage,which worsens as pier height increases.The pier structure satisfies seismic demands even under rare earthquake conditions.
基金supported by the National Key Research and Development Program of China(No.2023YFC3705400)the Research Team Construction Project of Hefei Comprehensive Science Center Environmental Research Institute(No.HYKYTD2024006)+3 种基金the Open Fund of Key Laboratory of Vehicle Emission Control and Simulation,Ministry of Ecology and Environment(No.VECS2024S01)the National Natural Science Foundation of China(Nos.42005108 and U2133212)the Major Subject of Science and Technology of Anhui Province(No.202203a07020004)the National Engineering Laboratory for Mobile Source Emission Control Technology(No.NELMS2020A09).
摘要The upcoming Euro 7 vehicle emissions regulation sets new requirements for calibrating particle number portable emissions measurement systems(PN-PEMS).In current PN concentration calibration methods,arbitrary selection of aerosolmaterials and incorrect estimation ofmultiply-charged particles lead to calibration deviation.This study proposes a novel,accurate calibration method based on the calibration and correction of the actual charging probability of soot for calibrating PN-PEMS.The accurate calibration results of a PN-PEMS show a maximum reduction of 7.65%in the+1-charging probability deviation and of 3.15%in the counting efficiency deviation.The calibration of the actual charging probability of soot introduces a calibration uncertainty increment of 0.09%-2.71%,and the overall uncertainty is<4.76%,whichmakes the calibration results more credible.The interaction of calibration aerosols of different physicochemical properties with the condensation particle counter working fluid and catalytic stripper device is the main reason for the different PN-PEMS calibration results.The calibration of the actual charging probability of particles is the fundamental method to eliminate the calibration deviation caused by the estimation and correction of multiply-charged particles.
摘要Predicting surface settlement of soft soil under the combined prefabricated vertical drain(PVD)-embankment system remains a critical challenge in geotechnical engineering due to the complex and time-dependent nature of soil behavior.This study leverages in situ data collected from various real-world projects to develop a hybrid machine learning model that incorporates prediction uncertainty(confidenceinterval).Twelve input variables are determined based on conventional theories of radial soil consolidation under embankment,encompassing soil properties,PVD parameters,and loading conditions.Different machine learning algorithms are extensively evaluated with the Categorical boosting(CATB),which emerges as the most reliable and accurate algorithm for predicting the settlement of PVD-treated soft soil.The CATB performance is further enhanced by the adaptive step random search(ASRS),proving its exceptional predictive accuracy and robustness.The developed model is applied to an independent case from the field-scaleembankment test at Australia's National Field Testing Facility(NFTF),yielding promising outcomes.Importance-based sensitivity analysis revealed the dominant influenceof key parameters,including time,pre-consolidation pressure,recompression index,and PVD characteristics,on settlement behavior,offering actionable insights for optimized design.The probabilistic parameters are incorporated into the data-driven model,facilitating the assessment of prediction confidence,advancing practical design of soft soil improvement,and bridging the gap between theoretical modeling and real-world geotechnical design needs.
基金supported by the National Natural Science Foundation of China(Grant Nos.42471034,42330604)the Qing Lan Projectsupport from the National Key Scientific and Technological Infrastructure project“Earth System Numerical Simulation Facility”(EarthLab).
摘要The western Los Angeles(LA)wildfires of early January 2025 caused catastrophic social and environmental impacts,drawing widespread attention.This study investigates the characteristics of these wildfires and quantifies the influence of heat and drought on their likelihood using a copula-based Bayesian probability framework.The wildfires were characterized by burned area(BA)and intensity(fire radiative power,FRP).The criteria establishing the presence of“hot drought”conditions were identified using the 5-day Standardized Temperature Index(STI)and 75-day Standardized Precipitation Index(SPI),respectively.The wildfire outbreak began on 7 January 2025 and burned for more than six days,with the total burned area exceeding 245 km2 and the cumulative FRP exceeding 41060 MW.Based on satellite-derived active fire observations from 2001 to 2025,we estimate that such large and intense wildfires during LA’s rainy season represent a once-in-a-67-year event.The wildfires were largely driven by the combination of hot and dry conditions,which dried out soils and vegetation that had proliferated due to above-average precipitation in previous winter seasons,thereby providing abundant fuel.Our seasonal analysis reveals that extreme drought increased the probability of wildfires matching the 2025 intensity and BA by 54%and 75%,respectively.Hot drought further amplified these probabilities by 149%(intensity)and 210%(BA).These findings suggest an elevated risk of large wildfires under hot drought conditions,contributing to their expansion into the non-traditional fire season.
基金support of Investigation into Turbulence Transport in Spheres under Multiphysics Fields(Grant No.KJZ-YY-NLT0604)the National Natural Science Foundation of China(Grant No.52176065)。
摘要In this short article,we wish to initiate a probability theory to describe the(in)famous transition to turbulence phenomena.For normal systems,the instability threshold can be predicted because the transition probability jumps from zero to P→1 when the control parameter exceeds the threshold.However,for non-normal systems,such a transition is probabilistic,which depends on the control parameter and initial energy.A low-dimensional reduction idea is proposed to give a detailed description of the transition probability of non-normal systems in the future.We also wish that such an idea could be transplanted for understanding such a transition in more complex flows,e.g.,atmospheric flows,mantle convection,and ocean circulation.
基金supported by the Project of the Ministry of Public Security Science and Technology Program(2025JSYJC18)the Central Universities Basic Research Funds Program of China(2024JKF02ZK12).
摘要An analysis of Beijing urban rail transit emergency data from 2016 to 2018 is conducted to identify the factors influencing emergency severity.A severity probability distribution model is proposed,incorporating seasonal effects,multi-dimensional features(passenger,vehicle,line,environment),random parameters,interaction terms,and weather variables(temperature,humidity,wind speed)to capture severity probability changes driven by seasonally influenced factors.High performance is achieved by the model,with 92.10%accuracy,95.17%sensitivity,and 87.58%specificity.Five key factors—bad weather(correlation=-0.0611,p<0.001),track failure(correlation=-0.0503,p<0.001),signal failure(correlation=-0.0483,p<0.001),urban area(correlation=-0.0441,p<0.001),and vehicle failure(correlation=-0.0435,p<0.001)—are identified,with their interactions amplifying risks,particularly the coupling effect between bad weather and train system failures.Notable seasonal effects are observed:In summer,high temperature and humidity increase vehicle and equipment failures;in autumn,temperature fluctuations raise signaling anomaly risks;in winter,low temperatures elevate track and equipment failure risks;and in spring and winter,windy weather exacerbates risks for suburban elevated lines.This study highlights the need for refined risk identification and response mechanisms at the seasonal and regional levels,such as targeted inspections and weather-triggered controls,to enhance operational safety in urban rail transit under complex weather conditions.
基金the financial supports from the National Natural Science Foundation of China under Grant No.52178480 and the State Key Laboratory of Subtropical Building and Urban Science under Grant No.2024ZB10.
摘要The stack effect in super high-rise buildings is mainly influenced by the temperature difference between the indoor and outdoor environments,wind pressure,building height,and the airtightness of building components.Consequently,the intensity and frequency of the stack effect are inherently impacted by regional and seasonal climate conditions.This study initially examines two critical meteorological elements-temperature and wind speed-that are closely related to the stack effect in high-rise buildings.Then the appropriate climate demarcation for evaluating the stack effect in high-rise buildings,which is based on the building climate demarcation in China is investigated,and the land area of China is divided into four climate regions for the purpose of stack effect assessment.Utilizing annual meteorological monitoring data from each region,the probability function models for temperature and wind speed are developed,and a joint probability distribution function for temperature and wind speed in each region is derived using a binary copula function.Finally,the probabilistic assessment of the stack effect under both pure and combined thermal pressures across different climatic zones is numerically investigated by employing a standardized high-rise building model.This research enables a refined assessment of the stack effect for high-rise building,and provides a useful reference to improve the design codes in future.
摘要We investigate numerically the effects of long-range temporal and spatial correlations based on the rescaled distributions of the squared interface width W2(L,t)and the interface height h(x,t)in the(1+1)-dimensional Kardar-Parisi-Zhang(KPZ)growth system within the early growth regime.Through extensive numerical simulations,we find that long-range temporally correlated noise does not significantly impact the distribution form of the interface width.Generally,W2(L,t)approximately obeys a lognormal distribution when the temporal correlation exponentθ≥0.On the other hand,the effects of long-range spatially correlated noise are evidently different from the temporally correlated case.Our results show that,when the spatial correlation exponentρ≤0.20,the distribution forms of W2(L,t)approach the lognormal distribution,and whenρ>0.20,the distribution becomes more asymmetric,steep,and fat-tailed,and tends to an unknown distribution form.As a comparison,probability distributions of the interface height are also provided in the temporally and spatially correlated KPZ system,exhibiting quite different characteristics from each other within the whole correlated strengths.For the temporal correlation,the height distributions follow Tracy-Widom Gaussian orthogonal ensemble(TW-GOE)whenθ→0,and with increasingθ,the height distributions crossover continuously to an unknown distribution.However,for the spatial correlation,the height distributions gradually transition from the TW-GOE distribution to the standard Gaussian form.
基金supported by the National Natural Science Foundation of China(62271247)the Natural Science Foundation of Jiangsu Province(BK20240181)+4 种基金the Dreams Foundation of Jianghuai Advance Technology Center(2023-ZM01D001)the National Aerospace Science Foundation of China(20220055052001)the Qing Lan Project of Jiangsu Provincethe Fund of Prospective Layout of Scientific Research for Nanjing University of Aeronautics and Astronauticsthe Key Laboratory of Radar Imaging and Microwave Photonics(Nanjing University of Aeronautics and Astronautics),Ministry of Education。
摘要In this paper,the joint design of transmit and receive beamformers for transmit subaperturing multiple-input-multiple-output(TS-MIMO)radar is investigated,aiming to enhance its low probability of intercept(LPI)capability.The main objective is to simultaneously minimize the transmission power,suppress the transmit sidelobe levels,and minimize the probability of intercept,thus bolstering the LPI performance of the radar system while maintaining the desired target detection performance.An alternative optimization method is proposed to jointly optimize the transmit and receive beamformers,yielding an unified LPI optimization framework.Particularly,the proposed iterative algorithm based on the Lagrange duality theory for transmit beamforming is more efficient than the conventional convex optimization method.Numerical experiments highlight the effectiveness of the proposed approach in sidelobe suppression and computational efficiency.
基金completed under funding received from the UK’s Commercialising Quantum Technologies Programme(Grant No.10071684).
摘要Quantum linear equation solvers generate a solution vector that sits in a subspace of the quantum computer’s larger state space.Accessing the solution vector relies on applying measurement projectors that remove components in the orthogonal subspace.This study examines the probability that the projectors are successful and how the success probability is influenced by the properties of the linear system,e.g.,the matrix condition number,and approximations made in the quantum solver.The analysis is performed within a non-linear computational fluid dynamics code where,at each iteration,a linearised system is passed to an emulated quantum solver.The linear systems are solved using quantum singular value transformation,for which the accuracy of the matrix inversion polynomial can be controlled via user input.The results show that success probabilities vary between 10−6and 10−2for the cases considered.More accurate approximations have lower success probabilities and require longer circuits.Less accurate approximations are analysed and show that variations during the non-linear iterations are related to the eigen content of the right-hand side vector.The use of amplitude amplification is shown to be able to increase success probabilities from 10−6to 10−2,in accordance with theory,but at a cost of a 100 times increase in circuit depth.Whilst these results are specific to the fluid flow test cases,they are generalisable to other types of linear solvers.
摘要Artificial intelligence(AI)aims to simulate the thinking process of human perception,learning,and decision-making,but uncertainty problems,such as data noise,information loss,and semantic ambiguity are commonly present in real environments.Traditional deterministic mathematics is difficult to complete modeling and inference in complex scenarios.Probability theory,as a mathematical branch that studies the statistical laws of random phenomena,can quantify the likelihood of events occurring and provide a theoretical basis for uncertainty reasoning,parameter optimization,and distribution modeling for AI.This paper focuses on core probability knowledge,such as conditional probability,Bayesian formula,and probability distribution.It systematically discusses the specific applications of probability theory in traditional machine learning,deep learning,generative AI,natural language processing,computer vision,and reinforcement learning.It summarizes the supporting role of probability theory in the development of AI and looks forward to the research direction of the integration of the two in combination with current technological trends.
摘要In recent years,with the rapid development of artificial intelligence and big data technologies,knowledge graphs have gained widespread attention and application.As a fundamental course in mathematics and statistics,Probability Theory and Mathematical Statistics contains complex and highly interconnected knowledge points,making traditional learning methods less effective for understanding its internal logic.Therefore,constructing a knowledge graph and developing a corresponding question-answering system for this subject is of great significance.This project uses the Probability Theory and Mathematical Statistics Tutorial(3rd Edition)as the data source to construct a knowledge graph based on Neo4j.Cypher language and APOC tools were used for data import and graph construction,while Neo4j Bloom was employed for visualization.In addition,a question-answering system was developed using natural language processing techniques and the Flask framework to provide intelligent query services.The system can help students better understand and learn probability theory and mathematical statistics while reducing dependence on traditional textbooks.
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。
摘要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supported by the National Natural Science Foundation of China(Nos.12475135,12035011,and 12475119)the Shandong Provincial Natural Science Foundation,China(No.ZR2020MA096)the Fundamental Research Funds for the Central Universities(No.22CX03017A)。
摘要Recently,machine learning has become a powerful tool for predicting nuclear charge radius RC,providing novel insights into complex physical phenomena.This study employs a continuous Bayesian probability(CBP)estimator and Bayesian model averaging(BMA)to optimize the predictions of RCfrom sophisticated theoretical models.The CBP estimator treats the residual between the theoretical and experimental values of RCas a continuous variable and derives its posterior probability density function(PDF)from Bayesian theory.The BMA method assigns weights to models based on their predictive performance for benchmark nuclei,thereby accounting for the unique strengths of each model.In global optimization,the CBP estimator improved the predictive accuracy of the three theoretical models by approximately 60%.The extrapolation analyses consistently achieved an improvement rate of approximately 45%,demonstrating the robustness of the CBP estimator.Furthermore,the combination of the CBP and BMA methods reduces the standard deviation to below 0.02 fm,effectively reproducing the pronounced shell effects on RCof the Ca and Sr isotope chains.The studies in this paper propose an efficient method to accurately describe RCof unknown nuclei,with potential applications in research on other nuclear properties.
基金supported by the National Major Science and Technology Project,China(No.J2019-Ⅳ-0007-0075)the Fundamental Research Funds for the Central Universities,China(No.JKF-20240036)。
摘要To ensure the structural integrity of life-limiting component of aeroengines,Probabilistic Damage Tolerance(PDT)assessment is applied to evaluate the failure risk as required by airworthiness regulations and military standards.The PDT method holds the view that there exist defects such as machining scratches and service cracks in the tenon-groove structures of aeroengine disks.However,it is challenging to conduct PDT assessment due to the scarcity of effective Probability of Detection(POD)model and anomaly distribution model.Through a series of Nondestructive Testing(NDT)experiments,the POD model of real cracks in tenon-groove structures is constructed for the first time by employing the Transfer Function Method(TFM).A novel anomaly distribution model is derived through the utilization of the POD model,instead of using the infeasible field data accumulation method.Subsequently,a framework for calculating the Probability of Failure(POF)of the tenon-groove structures is established,and the aforementioned two models exert a significant influence on the results of POF.
基金funding support from the National Science Fund for Distinguished Young Scholars(Grant No.52125904)the National Key R&D Plan(Grant No.2022YFC3004403)the National Natural Science Foundation of China(Grant No.52039008).
摘要To address prediction errors and limited information extraction in machine learning(ML)-based interval prediction,a hybrid model was proposed for interval estimation and failure assessment of step-like landslides under uncertainty.The model decomposed displacements into trend and periodic components via Variational Mode Decomposition(VMD)and K-shape clustering.The Residual and Moving Block Bootstrap methods were used to generate pseudo datasets.Polynomial regressionwas adopted for trend forecasting,whereas the Dense Convolutional Network(DenseNet)and Long Short-Term Memory(LSTM)networks were employed for periodic displacement prediction.An Extreme Learning Machine(ELM)was used to estimate the noise variance,enabling the construction of Prediction Intervals(PIs)and quantificationof displacement uncertainty.Failure probabilities(Pf)were derived from PIs using an improved tangential angle criterion and reliability analysis.The model was validated on three step-like landslides in the Three Gorges Reservoir Area,achieving stability assessment accuracies of 99.88%(XD01),99.93%(ZG93),99.89%(ZG118),and 100%for ZG110 and ZG111 across the Baishuihe and Bazimen landslides.For the Shuping landslide,the predictions aligned with fieldobservations before and after the 2014–2015 remediation,with Pfremaining near zero post-2015 except for occasional peaks.The model outperformed conventional ML approaches by yielding narrower PIs.At XD01 with 90%PI nominal confidencelevel(PINC),the coverage width-based criterion(CWC)and PI average width(PIAW)were 3.38 mm.The mean values of the PIs exhibited high accuracy,with a Mean Absolute Error(MAE)of 0.28 mm and Root Mean Square Error(RMSE)of 0.39 mm.These results demonstrate the robustness of the proposed model in improving landslide risk assessment and decision-making under uncertainty.
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)。
摘要On May 22,2021,an MS7.4 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 MS7.4 earthquake in Maduo County,with high accuracy and probability in peak ground acceleration(Abbreviated as PGA)ranges of 140–240 and 350–390 cm/s2,respectively,and(2)the MS7.4 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supported by the National Social Science Foundation of China(Grant Nos.21BGL217 and 22CGL050)the Philosophy and Social Science Fund of Education Department of Jiangsu Province(Grant No.2020SJA2346).
摘要Vaccination is critical for controlling infectious diseases,but negative vaccination information can lead to vaccine hesitancy.To study how the interplay between information diffusion and disease transmission impacts vaccination and epidemic spread,we propose a novel two-layer multiplex network model that integrates an unaware-acceptant-negative-unaware(UANU)information diffusion model with a susceptible-vaccinated-exposed-infected-susceptible(SVEIS)epidemiological framework.This model includes individual exposure and vaccination statuses,time-varying forgetting probabilities,and information conversion thresholds.Through the microscopic Markov chain approach(MMCA),we derive dynamic transition equations and the epidemic threshold expression,validated by Monte Carlo simulations.Using MMCA equations,we predict vaccination densities and analyze parameter effects on vaccination,disease transmission,and the epidemic threshold.Our findings suggest that promoting positive information,curbing the spread of negative information,enhancing vaccine effectiveness,and promptly identifying asymptomatic carriers can significantly increase vaccination rates,reduce epidemic spread,and raise the epidemic threshold.
基金supported by the Natural Science Foundation of Guangdong Province(Grant 2023A1515011667)Science and Technology Major Project of Shenzhen(Grant KJZD20230923114809020)Key Basic Research Foundation of Shenzhen(Grant JCYJ20220818100205012).
摘要Estimating probability density functions(PDFs)is critical in data analysis,particularly for complex multimodal distributions.traditional kernel density estimator(KDE)methods often face challenges in accurately capturing multimodal structures due to their uniform weighting scheme,leading to mode loss and degraded estimation accuracy.This paper presents the flexible kernel density estimator(F-KDE),a novel nonparametric approach designed to address these limitations.F-KDE introduces the concept of kernel unit inequivalence,assigning adaptive weights to each kernel unit,which better models local density variations in multimodal data.The method optimises an objective function that integrates estimation error and log-likelihood,using a particle swarm optimisation(PSO)algorithm that automatically determines optimal weights and bandwidths.Through extensive experiments on synthetic and real-world datasets,we demonstrated that(1)the weights and bandwidths in F-KDE stabilise as the optimisation algorithm iterates,(2)F-KDE effectively captures the multimodal characteristics and(3)F-KDE outperforms state-of-the-art density estimation methods regarding accuracy and robustness.The results confirm that F-KDE provides a valuable solution for accurately estimating multimodal PDFs.
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).
摘要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.