This paper investigates the reliability of internal marine combustion engines using an integrated approach that combines Fault Tree Analysis(FTA)and Bayesian Networks(BN).FTA provides a structured,top-down method for ...This paper investigates the reliability of internal marine combustion engines using an integrated approach that combines Fault Tree Analysis(FTA)and Bayesian Networks(BN).FTA provides a structured,top-down method for identifying critical failure modes and their root causes,while BN introduces flexibility in probabilistic reasoning,enabling dynamic updates based on new evidence.This dual methodology overcomes the limitations of static FTA models,offering a comprehensive framework for system reliability analysis.Critical failures,including External Leakage(ELU),Failure to Start(FTS),and Overheating(OHE),were identified as key risks.By incorporating redundancy into high-risk components such as pumps and batteries,the likelihood of these failures was significantly reduced.For instance,redundant pumps reduced the probability of ELU by 31.88%,while additional batteries decreased the occurrence of FTS by 36.45%.The results underscore the practical benefits of combining FTA and BN for enhancing system reliability,particularly in maritime applications where operational safety and efficiency are critical.This research provides valuable insights for maintenance planning and highlights the importance of redundancy in critical systems,especially as the industry transitions toward more autonomous vessels.展开更多
Disaster mitigation necessitates scientifi c and accurate aftershock forecasting during the critical 2 h after an earthquake. However, this action faces immense challenges due to the lack of early postearthquake data ...Disaster mitigation necessitates scientifi c and accurate aftershock forecasting during the critical 2 h after an earthquake. However, this action faces immense challenges due to the lack of early postearthquake data and the unreliability of forecasts. To obtain foundational data for sequence parameters of the land-sea adjacent zone and establish a reliable and operational aftershock forecasting framework, we combined the initial sequence parameters extracted from envelope functions and incorporated small-earthquake information into our model to construct a Bayesian algorithm for the early postearthquake stage. We performed parameter fitting and early postearthquake aftershock occurrence rate forecasting and effectiveness evaluation for 36 earthquake sequences with M ≥ 4.0 in the Bohai Rim region since 2010. According to the results, during the early stage after the mainshock, earthquake sequence parameters exhibited relatively drastic fl uctuations with signifi cant errors. The integration of prior information can mitigate the intensity of these changes and reduce errors. The initial and stable sequence parameters generally display advantageous distribution characteristics, with each parameter’s distribution being relatively concentrated and showing good symmetry and remarkable consistency. The sequence parameter p-values were relatively small, which indicates the comparatively slow attenuation of signifi cant earthquake events in the Bohai Rim region. A certain positive correlation was observed between earthquake sequence parameters b and p. However, sequence parameters are unrelated to the mainshock magnitude, which implies that their statistical characteristics and trends are universal. The Bayesian algorithm revealed a good forecasting capability for aftershocks in the early postearthquake period (2 h) in the Bohai Rim region, with an overall forecasting effi cacy rate of 76.39%. The proportion of “too low” failures exceeded that of “too high” failures, and the number of forecasting failures for the next three days was greater than that for the next day.展开更多
To study the uncertainty quantification of resonant states in open quantum systems,we developed a Bayesian framework by integrating a reduced basis method(RBM)emulator with the Gamow coupled-channel(GCC)approach.The R...To study the uncertainty quantification of resonant states in open quantum systems,we developed a Bayesian framework by integrating a reduced basis method(RBM)emulator with the Gamow coupled-channel(GCC)approach.The RBM,constructed via eigenvector continuation and trained on both bound and resonant configurations,enables the fast and accurate emulation of resonance properties across the parameter space.To identify the physical resonant states from the emulator’s output,we introduce an overlap-based selection technique that effectively isolates true solutions from background artifacts.By applying this framework to unbound nucleus ^(6)Be,we quantified the model uncertainty in the predicted complex energies.The results demonstrate relative errors of 17.48%in the real part and 8.24%in the imaginary part,while achieving a speedup of four orders of magnitude compared with the full GCC calculations.To further investigate the asymptotic behavior of the resonant-state wavefunctions within the RBM framework,we employed a Lippmann–Schwinger(L–S)-based correction scheme.This approach not only improves the consistency between eigenvalues and wavefunctions but also enables a seamless extension from real-space training data to the complex energy plane.By bridging the gap between bound-state and continuum regimes,the L–S correction significantly enhances the emulator’s capability to accurately capture continuum structures in open quantum systems.展开更多
Emergency medical services (EMS) are a vital element of the public healthcare system in China,^([1])providing an opportunity to respond to critical medical conditions and save people’s lives.^([2])The accessibility o...Emergency medical services (EMS) are a vital element of the public healthcare system in China,^([1])providing an opportunity to respond to critical medical conditions and save people’s lives.^([2])The accessibility of EMS has received considerable attention in health and transport geography studies.^([3])One of the optimal gauges for evaluating the accessibility of EMS is the response time,which is defined as the time from receiving an emergency call to the arrival of an ambulance.^([4])Beijing has already reduced the response time to approximately12 min,and the next goal is to ensure that the response time across Beijing does not exceed 12 min (the information comes from the Beijing Emergency Medical Center).展开更多
In order to improve crash occurrence models to account for the influence of various contributing factors, a conditional autoregressive negative binomial （CAR-NB） model is employed to allow for overdispersion （tackl...In order to improve crash occurrence models to account for the influence of various contributing factors, a conditional autoregressive negative binomial （CAR-NB） model is employed to allow for overdispersion （tackled by the NB component）, unobserved heterogeneity and spatial autocorrelation （captured by the CAR process）, using Markov chain Monte Carlo methods and the Gibbs sampler. Statistical tests suggest that the CAR-NB model is preferred over the CAR-Poisson, NB, zero-inflated Poisson, zero-inflated NB models, due to its lower prediction errors and more robust parameter inference. The study results show that crash frequency and fatalities are positively associated with the number of lanes, curve length, annual average daily traffic （AADT） per lane, as well as rainfall. Speed limit and the distances to the nearest hospitals have negative associations with segment-based crash counts but positive associations with fatality counts, presumably as a result of worsened collision impacts at higher speed and time loss during transporting crash victims.展开更多
To improve the accuracy and speed in cycle-accurate power estimation, this paper uses multiple dimensional coefficients to build a Bayesian inference dynamic power model. By analyzing the power distribution and intern...To improve the accuracy and speed in cycle-accurate power estimation, this paper uses multiple dimensional coefficients to build a Bayesian inference dynamic power model. By analyzing the power distribution and internal node state, we find the deficiency of only using port information. Then, we define the gate level number computing method and the concept of slice, and propose using slice analysis to distill switching density as coefficients in a special circuit stage and participate in Bayesian inference with port information. Experiments show that this method can reduce the power-per-cycle estimation error by 21.9% and the root mean square error by 25.0% compared with the original model, and maintain a 700 ＋ speedup compared with the existing gate-level power analysis technique.展开更多
The nonlinear mixed-effects model with stochastic differential equations （SDEs） is used to model the population pharmacokinetic （PPK） data that are extended from ordinary differential equations （ODEs） by adding ...The nonlinear mixed-effects model with stochastic differential equations （SDEs） is used to model the population pharmacokinetic （PPK） data that are extended from ordinary differential equations （ODEs） by adding a stochastic term to the state equation. Compared with the ODEs, the SDEs can model correlated residuals which are ubiquitous in actual pharmacokinetic problems. The Bayesian estimation is provided for nonlinear mixed-effects models based on stochastic differential equations. Combining the Gibbs and the Metropolis-Hastings algorithms, the population and individual parameter values are given through the parameter posterior predictive distributions. The analysis and simulation results show that the performance of the Bayesian estimation for mixed-effects SDEs model and analysis of population pharmacokinetic data is reliable. The results suggest that the proposed method is feasible for population pharmacokinetic data.展开更多
A Bayesian approach is proposed for the inference of the geotechnical parameters used in slope design.The methodology involves the construction of posterior probability distributions that combine prior information on ...A Bayesian approach is proposed for the inference of the geotechnical parameters used in slope design.The methodology involves the construction of posterior probability distributions that combine prior information on the parameter values with typical data from laboratory tests and site investigations used in design.The posterior distributions are often complex,multidimensional functions whose analysis requires the use of Markov chain Monte Carlo(MCMC)methods.These procedures are used to draw representative samples of the parameters investigated,providing information on their best estimate values,variability and correlations.The paper describes the methodology to define the posterior distributions of the input parameters for slope design and the use of these results for evaluation of the reliability of a slope with the first order reliability method(FORM).The reliability analysis corresponds to a forward stability analysis of the slope where the factor of safety(FS)is calculated with a surrogate model from the more likely values of the input parameters.The Bayesian model is also used to update the estimation of the input parameters based on the back analysis of slope failure.In this case,the condition FS?1 is treated as a data point that is compared with the model prediction of FS.The analysis requires a sufficient number of observations of failure to outbalance the effect of the initial input parameters.The parameters are updated according to their uncertainty,which is determined by the amount of data supporting them.The methodology is illustrated with an example of a rock slope characterised with a Hoek-Brown rock mass strength.The example is used to highlight the advantages of using Bayesian methods for the slope reliability analysis and to show the effects of data support on the results of the updating process from back analysis of failure.展开更多
One of the main difficulties in the geotechnical design process lies in dealing with uncertainty. Uncertainty is associated with natural variation of properties, and the imprecision and unpredictability caused by insu...One of the main difficulties in the geotechnical design process lies in dealing with uncertainty. Uncertainty is associated with natural variation of properties, and the imprecision and unpredictability caused by insufficient information on parameters or models. Probabilistic methods are normally used to quantify uncertainty. However, the frequentist approach commonly used for this purpose has some drawbacks.First, it lacks a formal framework for incorporating knowledge not represented by data. Second, it has limitations in providing a proper measure of the confidence of parameters inferred from data. The Bayesian approach offers a better framework for treating uncertainty in geotechnical design. The advantages of the Bayesian approach for uncertainty quantification are highlighted in this paper with the Bayesian regression analysis of laboratory test data to infer the intact rock strength parameters σand mused in the Hoek-Brown strength criterion. Two case examples are used to illustrate different aspects of the Bayesian methodology and to contrast the approach with a frequentist approach represented by the nonlinear least squares(NLLS) method. The paper discusses the use of a Student’s t-distribution versus a normal distribution to handle outliers, the consideration of absolute versus relative residuals, and the comparison of quality of fitting results based on standard errors and Bayes factors. Uncertainty quantification with confidence and prediction intervals of the frequentist approach is compared with that based on scatter plots and bands of fitted envelopes of the Bayesian approach. Finally, the Bayesian method is extended to consider two improvements of the fitting analysis. The first is the case in which the Hoek-Brown parameter, a, is treated as a variable to improve the fitting in the triaxial region. The second is the incorporation of the uncertainty in the estimation of the direct tensile strength from Brazilian test results within the overall evaluation of the intact rock strength.展开更多
This paper presents a new approach for offshore risk analysis that is capable of dealing with linguistic probabilities in Bayesian networks （ BNs）. In this paper, linguistic probabilities are used to describe occurr...This paper presents a new approach for offshore risk analysis that is capable of dealing with linguistic probabilities in Bayesian networks （ BNs）. In this paper, linguistic probabilities are used to describe occurrence likelihood of hazardous events that may cause possible accidents in offshore operations. In order to use fuzzy information, an f-weighted valuation function is proposed to transform linguistic judgements into crisp probability distributions which can be easily put into a BN to model causal relationships among risk factors. The use of linguistic variables makes it easier for human experts to express their knowledge, and the transformation of linguistic judgements into crisp probabilities can significantly save the cost of computation, modifying and maintaining a BN model. The flexibility of the method allows for multiple forms of information to be used to quantify model relationships, including formally assessed expert opinion when quantitative data are lacking, or when only qualitative or vague statements can be made. The model is a modular representation of uncertain knowledge caused due to randomness, vagueness and ignorance. This makes the risk analysis of offshore engineering systems more functional and easier in many assessment contexts. Specifically, the proposed f-weighted valuation function takes into account not only the dominating values, but also the a-level values that are ignored by conventional valuation methods. A case study of the collision risk between a Floating Production, Storage and Off-loading （FPSO） unit and the anthorised vessels due to human elements during operation is used to illustrate the application of the proposed model.展开更多
The bearings of a certain type have their lives following a Weibull distribution. In a life test with 20 sets of bearings, only one set failed within the specified time, and none of the remainder failed even after th...The bearings of a certain type have their lives following a Weibull distribution. In a life test with 20 sets of bearings, only one set failed within the specified time, and none of the remainder failed even after the time of test has been extended. With a set of testing data like that in Table 1, it is required to estimate the reliability at the mission time. In this paper, we first use hierarchical Bayesian method to determine the prior distribution and the Bayesian estimates of various probabilities of failures, p i 's, then use the method of least squares to estimate the parameters of the Weibull distribution and the reliability. Actual computation shows that the estimates so obtained are rather robust. And the results have been adopted for practical use.展开更多
Based on the principle of Bayesian discriminant analysis, we established a model of Bayesian discriminant analysis for predicting coal and gas outbursts. We selected five major indices which affect outbursts, i.e., in...Based on the principle of Bayesian discriminant analysis, we established a model of Bayesian discriminant analysis for predicting coal and gas outbursts. We selected five major indices which affect outbursts, i.e., initial speed of methane diffusion, a consistent coal coefficient, gas pressure, destructive style of coal and mining depth, as discriminating factors of the model. In our model, we divided the type of coal and gas outbursts into four grades regarded as four normal populations. We then obtained the corresponding discriminant functions through training a set of data from engineering examples as learning samples and evaluated their criteria by a back substitution method to verify the optimal properties of the model. Finally, we applied the model to the prediction of coal and gas outbursts in the Yunnan Enhong Mine. Our results coincided completely with the actual situation. These results show that a model of Bayesian discriminant analysis has excellent recognition performance, high prediction accuracy and a low error rate and is an effective method to predict coal and gas outbursts.展开更多
In this paper, variational inference is studied on manifolds with certain metrics. To solve the problem, the analysis is first proposed for the variational Bayesian on Lie group, and then extended to the manifold that...In this paper, variational inference is studied on manifolds with certain metrics. To solve the problem, the analysis is first proposed for the variational Bayesian on Lie group, and then extended to the manifold that is approximated by Lie groups. Then the convergence of the proposed algorithm with respect to the manifold metric is proved in two iterative processes： variational Bayesian expectation （VB-F） step and variational Bayesian maximum （VB-M） step. Moreover, the effective of different metrics for Bayesian analysis is discussed.展开更多
Buried natural gas pipelines are vulnerable to external corrosion because they are encased in a soil environment for a long time.Identifying the causes of external corrosion and taking specific maintenance measures is...Buried natural gas pipelines are vulnerable to external corrosion because they are encased in a soil environment for a long time.Identifying the causes of external corrosion and taking specific maintenance measures is essential.In this work,a risk analysis and maintenance decision-making model for natural gas pipelines with external corrosion is proposed based on a Bayesian network.A fault tree model is first employed to identify the causes of external corrosion.The Bayesian network for risk analysis is determined accordingly.The maintenance strategies are then inserted into the Bayesian network to show a reduction of the risk.The costs of maintenance strategies and the reduced risk after maintenance are combined in an optimization function to build a decision-making model.Because of the limitations of historical data,some of the parameters in the Bayesian network are obtained from a probabilistic estimation model,which combines expert experience and fuzzy set theory.Finally,a case study is carried out to verify the feasibility of the maintenance decision model.This indicates that the method proposed in this work can be used to provide effective maintenance schemes for different pipeline external corrosion scenarios and to reduce the possible losses caused by external corrosion.展开更多
Geomechanical parameters are complex and uncertain.In order to take this complexity and uncertainty into account,a probabilistic back-analysis method combining the Bayesian probability with the least squares support v...Geomechanical parameters are complex and uncertain.In order to take this complexity and uncertainty into account,a probabilistic back-analysis method combining the Bayesian probability with the least squares support vector machine(LS-SVM) technique was proposed.The Bayesian probability was used to deal with the uncertainties in the geomechanical parameters,and an LS-SVM was utilized to establish the relationship between the displacement and the geomechanical parameters.The proposed approach was applied to the geomechanical parameter identification in a slope stability case study which was related to the permanent ship lock within the Three Gorges project in China.The results indicate that the proposed method presents the uncertainties in the geomechanical parameters reasonably well,and also improves the understanding that the monitored information is important in real projects.展开更多
Sea-crossing bridges have attracted considerable attention in recent years as an increasing number of projects have been constructed worldwide.Situated in the coastal area,sea-crossing bridges are subjected to a harsh...Sea-crossing bridges have attracted considerable attention in recent years as an increasing number of projects have been constructed worldwide.Situated in the coastal area,sea-crossing bridges are subjected to a harsh environment(e.g.strong winds,possible ship collisions,and tidal waves)and their performance can deteriorate quickly and severely.To enhance safety and serviceability,it is a routine process to conduct vibration tests to identify modal properties(e.g.natural frequencies,damping ratios,and mode shapes)and to monitor their long-term variation for the purpose of early-damage alert.Operational modal analysis(OMA)provides a feasible way to investigate the modal properties even when the cross-sea bridges are in their operation condition.In this study,we focus on the OMA of cable-stayed bridges,because they are usually long-span and flexible to have extremely low natural frequencies.It challenges experimental capability(e.g.instrumentation and budgeting)and modal identification techniques(e.g.low frequency and closely spaced modes).This paper presents a modal survey of a cable-stayed sea-crossing bridge spanning 218 m+620 m+218 m.The bridge is located in the typhoon-prone area of the northwestern Pacific Ocean.Ambient vibration data was collected for 24 h.A Bayesian fast Fourier transform modal identification method incorporating an expectation-maximization algorithm is applied for modal analysis,in which the modal parameters and associated identification uncertainties are both addressed.Nineteen modes,including 15 translational modes and four torsional modes,are identified within the frequency range of[0,2.5 Hz].展开更多
How to obtain proper prior distribution is one of the most critical problems in Bayesian analysis. In many practical cases, the prior information often comes from different sources, and the prior distribution form cou...How to obtain proper prior distribution is one of the most critical problems in Bayesian analysis. In many practical cases, the prior information often comes from different sources, and the prior distribution form could be easily known in some certain way while the parameters are hard to determine. In this paper, based on the evidence theory, a new method is presented to fuse the information of multiple sources and determine the parameters of the prior distribution when the form is known. By taking the prior distributions which result from the information of multiple sources and converting them into corresponding mass functions which can be combined by Dempster-Shafer (D-S) method, we get the combined mass function and the representative points of the prior distribution. These points are used to fit with the given distribution form to determine the parameters of the prior distribution. And then the fused prior distribution is obtained and Bayesian analysis can be performed. How to convert the prior distributions into mass functions properly and get the representative points of the fused prior distribution is the central question we address in this paper. The simulation example shows that the proposed method is effective.展开更多
The load and corrosion caused by the harsh marine environment lead to the severe degradation of offshore equipment and to their compromised security and reliability. In the quantitative risk analysis, the failure mode...The load and corrosion caused by the harsh marine environment lead to the severe degradation of offshore equipment and to their compromised security and reliability. In the quantitative risk analysis, the failure models are difficult to establish through traditional statistical methods. Hence, the calculation of the occurrence probability of small sample events is often met with great uncertainty. In this study, the Bayesian statistical method is implemented to analyze the oil and gas leakages of FPSO internal turret, which is a typical small sample risk but could lead to severe losses.According to the corresponding failure mechanism, two Bayesian statistical models using the Weibull distribution and logarithmic normal distribution as the population distribution are established, and the posterior distribution of the corresponding parameters is calculated. The optimal Bayesian statistical model is determined according to the Bayesian information criterion and Akaike criterion. On the basis of the determined optimal model, the corresponding reliability index is solved to provide basic data for the subsequent risk assessments of FPSO systems.展开更多
Owing to the fact that the conventional deterministic back analysis of the permeability coefficient cannot reflect the uncertainties of parameters, including the hydraulic head at the boundary, the permeability coeffi...Owing to the fact that the conventional deterministic back analysis of the permeability coefficient cannot reflect the uncertainties of parameters, including the hydraulic head at the boundary, the permeability coefficient and measured hydraulic head, a stochastic back analysis taking consideration of uncertainties of parameters was performed using the generalized Bayesian method. Based on the stochastic finite element method （SFEM） for a seepage field, the variable metric algorithm and the generalized Bayesian method, formulas for stochastic back analysis of the permeability coefficient were derived. A case study of seepage analysis of a sluice foundation was performed to illustrate the proposed method. The results indicate that, with the generalized Bayesian method that considers the uncertainties of measured hydraulic head, the permeability coefficient and the hydraulic head at the boundary, both the mean and standard deviation of the permeability coefficient can be obtained and the standard deviation is less than that obtained by the conventional Bayesian method. Therefore, the present method is valid and applicable.展开更多
This study developed a hierarchical Bayesian(HB)model for local and regional flood frequency analysis in the Dongting Lake Basin,in China.The annual maximum daily flows from 15 streamflow-gauged sites in the study are...This study developed a hierarchical Bayesian(HB)model for local and regional flood frequency analysis in the Dongting Lake Basin,in China.The annual maximum daily flows from 15 streamflow-gauged sites in the study area were analyzed with the HB model.The generalized extreme value(GEV)distribution was selected as the extreme flood distribution,and the GEV distribution location and scale parameters were spatially modeled through a regression approach with the drainage area as a covariate.The Markov chain Monte Carlo(MCMC)method with Gibbs sampling was employed to calculate the posterior distribution in the HB model.The results showed that the proposed HB model provided satisfactory Bayesian credible intervals for flood quantiles,while the traditional delta method could not provide reliable uncertainty estimations for large flood quantiles,due to the fact that the lower confidence bounds tended to decrease as the return periods increased.Furthermore,the HB model for regional analysis allowed for a reduction in the value of some restrictive assumptions in the traditional index flood method,such as the homogeneity region assumption and the scale invariance assumption.The HB model can also provide an uncertainty band of flood quantile prediction at a poorly gauged or ungauged site,but the index flood method with L-moments does not demonstrate this uncertainty directly.Therefore,the HB model is an effective method of implementing the flexible local and regional frequency analysis scheme,and of quantifying the associated predictive uncertainty.展开更多
基金supported by Istanbul Technical University(Project No.45698)supported through the“Young Researchers’Career Development Project-training of doctoral students”of the Croatian Science Foundation.
文摘This paper investigates the reliability of internal marine combustion engines using an integrated approach that combines Fault Tree Analysis(FTA)and Bayesian Networks(BN).FTA provides a structured,top-down method for identifying critical failure modes and their root causes,while BN introduces flexibility in probabilistic reasoning,enabling dynamic updates based on new evidence.This dual methodology overcomes the limitations of static FTA models,offering a comprehensive framework for system reliability analysis.Critical failures,including External Leakage(ELU),Failure to Start(FTS),and Overheating(OHE),were identified as key risks.By incorporating redundancy into high-risk components such as pumps and batteries,the likelihood of these failures was significantly reduced.For instance,redundant pumps reduced the probability of ELU by 31.88%,while additional batteries decreased the occurrence of FTS by 36.45%.The results underscore the practical benefits of combining FTA and BN for enhancing system reliability,particularly in maritime applications where operational safety and efficiency are critical.This research provides valuable insights for maintenance planning and highlights the importance of redundancy in critical systems,especially as the industry transitions toward more autonomous vessels.
基金supported by the Natural Science Foundation of Tianjin (No. 22JCQNJC01070)the National Natural Science Foundation of China (No. 42404079)the Key Project of Tianjin Earthquake Agency (No. Zd202402)。
文摘Disaster mitigation necessitates scientifi c and accurate aftershock forecasting during the critical 2 h after an earthquake. However, this action faces immense challenges due to the lack of early postearthquake data and the unreliability of forecasts. To obtain foundational data for sequence parameters of the land-sea adjacent zone and establish a reliable and operational aftershock forecasting framework, we combined the initial sequence parameters extracted from envelope functions and incorporated small-earthquake information into our model to construct a Bayesian algorithm for the early postearthquake stage. We performed parameter fitting and early postearthquake aftershock occurrence rate forecasting and effectiveness evaluation for 36 earthquake sequences with M ≥ 4.0 in the Bohai Rim region since 2010. According to the results, during the early stage after the mainshock, earthquake sequence parameters exhibited relatively drastic fl uctuations with signifi cant errors. The integration of prior information can mitigate the intensity of these changes and reduce errors. The initial and stable sequence parameters generally display advantageous distribution characteristics, with each parameter’s distribution being relatively concentrated and showing good symmetry and remarkable consistency. The sequence parameter p-values were relatively small, which indicates the comparatively slow attenuation of signifi cant earthquake events in the Bohai Rim region. A certain positive correlation was observed between earthquake sequence parameters b and p. However, sequence parameters are unrelated to the mainshock magnitude, which implies that their statistical characteristics and trends are universal. The Bayesian algorithm revealed a good forecasting capability for aftershocks in the early postearthquake period (2 h) in the Bohai Rim region, with an overall forecasting effi cacy rate of 76.39%. The proportion of “too low” failures exceeded that of “too high” failures, and the number of forecasting failures for the next three days was greater than that for the next day.
基金supported by the National Key Research and Development Program(MOST 2023YFA1606404 and MOST 2022YFA1602303)the National Natural Science Foundation of China(Nos.12347106,12147101,and 12447122)the China Postdoctoral Science Foundation(No.2024M760489).
文摘To study the uncertainty quantification of resonant states in open quantum systems,we developed a Bayesian framework by integrating a reduced basis method(RBM)emulator with the Gamow coupled-channel(GCC)approach.The RBM,constructed via eigenvector continuation and trained on both bound and resonant configurations,enables the fast and accurate emulation of resonance properties across the parameter space.To identify the physical resonant states from the emulator’s output,we introduce an overlap-based selection technique that effectively isolates true solutions from background artifacts.By applying this framework to unbound nucleus ^(6)Be,we quantified the model uncertainty in the predicted complex energies.The results demonstrate relative errors of 17.48%in the real part and 8.24%in the imaginary part,while achieving a speedup of four orders of magnitude compared with the full GCC calculations.To further investigate the asymptotic behavior of the resonant-state wavefunctions within the RBM framework,we employed a Lippmann–Schwinger(L–S)-based correction scheme.This approach not only improves the consistency between eigenvalues and wavefunctions but also enables a seamless extension from real-space training data to the complex energy plane.By bridging the gap between bound-state and continuum regimes,the L–S correction significantly enhances the emulator’s capability to accurately capture continuum structures in open quantum systems.
基金supported by National Key Research & Development Program of China (2022YFC3006201)。
文摘Emergency medical services (EMS) are a vital element of the public healthcare system in China,^([1])providing an opportunity to respond to critical medical conditions and save people’s lives.^([2])The accessibility of EMS has received considerable attention in health and transport geography studies.^([3])One of the optimal gauges for evaluating the accessibility of EMS is the response time,which is defined as the time from receiving an emergency call to the arrival of an ambulance.^([4])Beijing has already reduced the response time to approximately12 min,and the next goal is to ensure that the response time across Beijing does not exceed 12 min (the information comes from the Beijing Emergency Medical Center).
基金The National Science Foundation by Changjiang Scholarship of Ministry of Education of China(No.BCS-0527508)the Joint Research Fund for Overseas Natural Science of China(No.51250110075)+1 种基金the Natural Science Foundation of Jiangsu Province(No.SBK200910046)the Postdoctoral Science Foundation of Jiangsu Province(No.0901005C)
文摘In order to improve crash occurrence models to account for the influence of various contributing factors, a conditional autoregressive negative binomial （CAR-NB） model is employed to allow for overdispersion （tackled by the NB component）, unobserved heterogeneity and spatial autocorrelation （captured by the CAR process）, using Markov chain Monte Carlo methods and the Gibbs sampler. Statistical tests suggest that the CAR-NB model is preferred over the CAR-Poisson, NB, zero-inflated Poisson, zero-inflated NB models, due to its lower prediction errors and more robust parameter inference. The study results show that crash frequency and fatalities are positively associated with the number of lanes, curve length, annual average daily traffic （AADT） per lane, as well as rainfall. Speed limit and the distances to the nearest hospitals have negative associations with segment-based crash counts but positive associations with fatality counts, presumably as a result of worsened collision impacts at higher speed and time loss during transporting crash victims.
文摘To improve the accuracy and speed in cycle-accurate power estimation, this paper uses multiple dimensional coefficients to build a Bayesian inference dynamic power model. By analyzing the power distribution and internal node state, we find the deficiency of only using port information. Then, we define the gate level number computing method and the concept of slice, and propose using slice analysis to distill switching density as coefficients in a special circuit stage and participate in Bayesian inference with port information. Experiments show that this method can reduce the power-per-cycle estimation error by 21.9% and the root mean square error by 25.0% compared with the original model, and maintain a 700 ＋ speedup compared with the existing gate-level power analysis technique.
基金The National Natural Science Foundation of China(No.11171065,81130068)the Natural Science Foundation of Jiangsu Province(No.BK2011058)the Fundamental Research Funds for the Central Universities(No.JKPZ2013015)
文摘The nonlinear mixed-effects model with stochastic differential equations （SDEs） is used to model the population pharmacokinetic （PPK） data that are extended from ordinary differential equations （ODEs） by adding a stochastic term to the state equation. Compared with the ODEs, the SDEs can model correlated residuals which are ubiquitous in actual pharmacokinetic problems. The Bayesian estimation is provided for nonlinear mixed-effects models based on stochastic differential equations. Combining the Gibbs and the Metropolis-Hastings algorithms, the population and individual parameter values are given through the parameter posterior predictive distributions. The analysis and simulation results show that the performance of the Bayesian estimation for mixed-effects SDEs model and analysis of population pharmacokinetic data is reliable. The results suggest that the proposed method is feasible for population pharmacokinetic data.
基金supported by the Large Open Pit Ⅱ project through contract No.019799 with the Geotechnical Research Centre of The University of Queensland,Australia and by SRK Consulting South Africa
文摘A Bayesian approach is proposed for the inference of the geotechnical parameters used in slope design.The methodology involves the construction of posterior probability distributions that combine prior information on the parameter values with typical data from laboratory tests and site investigations used in design.The posterior distributions are often complex,multidimensional functions whose analysis requires the use of Markov chain Monte Carlo(MCMC)methods.These procedures are used to draw representative samples of the parameters investigated,providing information on their best estimate values,variability and correlations.The paper describes the methodology to define the posterior distributions of the input parameters for slope design and the use of these results for evaluation of the reliability of a slope with the first order reliability method(FORM).The reliability analysis corresponds to a forward stability analysis of the slope where the factor of safety(FS)is calculated with a surrogate model from the more likely values of the input parameters.The Bayesian model is also used to update the estimation of the input parameters based on the back analysis of slope failure.In this case,the condition FS?1 is treated as a data point that is compared with the model prediction of FS.The analysis requires a sufficient number of observations of failure to outbalance the effect of the initial input parameters.The parameters are updated according to their uncertainty,which is determined by the amount of data supporting them.The methodology is illustrated with an example of a rock slope characterised with a Hoek-Brown rock mass strength.The example is used to highlight the advantages of using Bayesian methods for the slope reliability analysis and to show the effects of data support on the results of the updating process from back analysis of failure.
基金supported by the Large Open PitⅡProject through contract No.019799 with the Geotechnical Research Centre of The University of Queensland and by SRK Consulting South Africa
文摘One of the main difficulties in the geotechnical design process lies in dealing with uncertainty. Uncertainty is associated with natural variation of properties, and the imprecision and unpredictability caused by insufficient information on parameters or models. Probabilistic methods are normally used to quantify uncertainty. However, the frequentist approach commonly used for this purpose has some drawbacks.First, it lacks a formal framework for incorporating knowledge not represented by data. Second, it has limitations in providing a proper measure of the confidence of parameters inferred from data. The Bayesian approach offers a better framework for treating uncertainty in geotechnical design. The advantages of the Bayesian approach for uncertainty quantification are highlighted in this paper with the Bayesian regression analysis of laboratory test data to infer the intact rock strength parameters σand mused in the Hoek-Brown strength criterion. Two case examples are used to illustrate different aspects of the Bayesian methodology and to contrast the approach with a frequentist approach represented by the nonlinear least squares(NLLS) method. The paper discusses the use of a Student’s t-distribution versus a normal distribution to handle outliers, the consideration of absolute versus relative residuals, and the comparison of quality of fitting results based on standard errors and Bayes factors. Uncertainty quantification with confidence and prediction intervals of the frequentist approach is compared with that based on scatter plots and bands of fitted envelopes of the Bayesian approach. Finally, the Bayesian method is extended to consider two improvements of the fitting analysis. The first is the case in which the Hoek-Brown parameter, a, is treated as a variable to improve the fitting in the triaxial region. The second is the incorporation of the uncertainty in the estimation of the direct tensile strength from Brazilian test results within the overall evaluation of the intact rock strength.
基金This project is funded bythe UK Engineering and Physical Sciences Research Council (EPSRC) under Grant Refer-ences:GR/S85504 and GR/S85498
文摘This paper presents a new approach for offshore risk analysis that is capable of dealing with linguistic probabilities in Bayesian networks （ BNs）. In this paper, linguistic probabilities are used to describe occurrence likelihood of hazardous events that may cause possible accidents in offshore operations. In order to use fuzzy information, an f-weighted valuation function is proposed to transform linguistic judgements into crisp probability distributions which can be easily put into a BN to model causal relationships among risk factors. The use of linguistic variables makes it easier for human experts to express their knowledge, and the transformation of linguistic judgements into crisp probabilities can significantly save the cost of computation, modifying and maintaining a BN model. The flexibility of the method allows for multiple forms of information to be used to quantify model relationships, including formally assessed expert opinion when quantitative data are lacking, or when only qualitative or vague statements can be made. The model is a modular representation of uncertain knowledge caused due to randomness, vagueness and ignorance. This makes the risk analysis of offshore engineering systems more functional and easier in many assessment contexts. Specifically, the proposed f-weighted valuation function takes into account not only the dominating values, but also the a-level values that are ignored by conventional valuation methods. A case study of the collision risk between a Floating Production, Storage and Off-loading （FPSO） unit and the anthorised vessels due to human elements during operation is used to illustrate the application of the proposed model.
文摘The bearings of a certain type have their lives following a Weibull distribution. In a life test with 20 sets of bearings, only one set failed within the specified time, and none of the remainder failed even after the time of test has been extended. With a set of testing data like that in Table 1, it is required to estimate the reliability at the mission time. In this paper, we first use hierarchical Bayesian method to determine the prior distribution and the Bayesian estimates of various probabilities of failures, p i 's, then use the method of least squares to estimate the parameters of the Weibull distribution and the reliability. Actual computation shows that the estimates so obtained are rather robust. And the results have been adopted for practical use.
基金supported by the National Hi-tech Research and Development Program of China (No.2006BAK03B02-04) the New Century Excellent Talent Support Plan of Ministry of Education of China (No.NCET-06-0477)
文摘Based on the principle of Bayesian discriminant analysis, we established a model of Bayesian discriminant analysis for predicting coal and gas outbursts. We selected five major indices which affect outbursts, i.e., initial speed of methane diffusion, a consistent coal coefficient, gas pressure, destructive style of coal and mining depth, as discriminating factors of the model. In our model, we divided the type of coal and gas outbursts into four grades regarded as four normal populations. We then obtained the corresponding discriminant functions through training a set of data from engineering examples as learning samples and evaluated their criteria by a back substitution method to verify the optimal properties of the model. Finally, we applied the model to the prediction of coal and gas outbursts in the Yunnan Enhong Mine. Our results coincided completely with the actual situation. These results show that a model of Bayesian discriminant analysis has excellent recognition performance, high prediction accuracy and a low error rate and is an effective method to predict coal and gas outbursts.
基金This work was supported by the National Key Research and Development Program of China （No. 2016YF-B0901900） and the National Natural Science Foundation of China （Nos. 61733018, 61333001, 61573344）.
文摘In this paper, variational inference is studied on manifolds with certain metrics. To solve the problem, the analysis is first proposed for the variational Bayesian on Lie group, and then extended to the manifold that is approximated by Lie groups. Then the convergence of the proposed algorithm with respect to the manifold metric is proved in two iterative processes： variational Bayesian expectation （VB-F） step and variational Bayesian maximum （VB-M） step. Moreover, the effective of different metrics for Bayesian analysis is discussed.
基金supported by the National Key R&D Program of China(Grant No.2018YFC0809300)the National Natural Science Foundation of China(Grant No.51806247)+2 种基金the Key Technology Project of Petro China Co Ltd.(Grant No.ZLZX2020-05)the Foundation of Sinopec(Grant No.320034)the Science Foundation of China University of Petroleum,Beijing(Grant No.2462020YXZZ052)
文摘Buried natural gas pipelines are vulnerable to external corrosion because they are encased in a soil environment for a long time.Identifying the causes of external corrosion and taking specific maintenance measures is essential.In this work,a risk analysis and maintenance decision-making model for natural gas pipelines with external corrosion is proposed based on a Bayesian network.A fault tree model is first employed to identify the causes of external corrosion.The Bayesian network for risk analysis is determined accordingly.The maintenance strategies are then inserted into the Bayesian network to show a reduction of the risk.The costs of maintenance strategies and the reduced risk after maintenance are combined in an optimization function to build a decision-making model.Because of the limitations of historical data,some of the parameters in the Bayesian network are obtained from a probabilistic estimation model,which combines expert experience and fuzzy set theory.Finally,a case study is carried out to verify the feasibility of the maintenance decision model.This indicates that the method proposed in this work can be used to provide effective maintenance schemes for different pipeline external corrosion scenarios and to reduce the possible losses caused by external corrosion.
基金Projects(2013BAB02B01,2013BAB02B03)supported by the National Key Technologies R&D Program of ChinaProjects(41072224,41272347)supported by the National Natural Science Foundation of China
文摘Geomechanical parameters are complex and uncertain.In order to take this complexity and uncertainty into account,a probabilistic back-analysis method combining the Bayesian probability with the least squares support vector machine(LS-SVM) technique was proposed.The Bayesian probability was used to deal with the uncertainties in the geomechanical parameters,and an LS-SVM was utilized to establish the relationship between the displacement and the geomechanical parameters.The proposed approach was applied to the geomechanical parameter identification in a slope stability case study which was related to the permanent ship lock within the Three Gorges project in China.The results indicate that the proposed method presents the uncertainties in the geomechanical parameters reasonably well,and also improves the understanding that the monitored information is important in real projects.
基金supported by the Start-up Fund from Zhejiang University(No.130000-171207704/018)the National Natural Science Foundation of China(Nos.U1709207,51578506 and 51908494)。
文摘Sea-crossing bridges have attracted considerable attention in recent years as an increasing number of projects have been constructed worldwide.Situated in the coastal area,sea-crossing bridges are subjected to a harsh environment(e.g.strong winds,possible ship collisions,and tidal waves)and their performance can deteriorate quickly and severely.To enhance safety and serviceability,it is a routine process to conduct vibration tests to identify modal properties(e.g.natural frequencies,damping ratios,and mode shapes)and to monitor their long-term variation for the purpose of early-damage alert.Operational modal analysis(OMA)provides a feasible way to investigate the modal properties even when the cross-sea bridges are in their operation condition.In this study,we focus on the OMA of cable-stayed bridges,because they are usually long-span and flexible to have extremely low natural frequencies.It challenges experimental capability(e.g.instrumentation and budgeting)and modal identification techniques(e.g.low frequency and closely spaced modes).This paper presents a modal survey of a cable-stayed sea-crossing bridge spanning 218 m+620 m+218 m.The bridge is located in the typhoon-prone area of the northwestern Pacific Ocean.Ambient vibration data was collected for 24 h.A Bayesian fast Fourier transform modal identification method incorporating an expectation-maximization algorithm is applied for modal analysis,in which the modal parameters and associated identification uncertainties are both addressed.Nineteen modes,including 15 translational modes and four torsional modes,are identified within the frequency range of[0,2.5 Hz].
文摘How to obtain proper prior distribution is one of the most critical problems in Bayesian analysis. In many practical cases, the prior information often comes from different sources, and the prior distribution form could be easily known in some certain way while the parameters are hard to determine. In this paper, based on the evidence theory, a new method is presented to fuse the information of multiple sources and determine the parameters of the prior distribution when the form is known. By taking the prior distributions which result from the information of multiple sources and converting them into corresponding mass functions which can be combined by Dempster-Shafer (D-S) method, we get the combined mass function and the representative points of the prior distribution. These points are used to fit with the given distribution form to determine the parameters of the prior distribution. And then the fused prior distribution is obtained and Bayesian analysis can be performed. How to convert the prior distributions into mass functions properly and get the representative points of the fused prior distribution is the central question we address in this paper. The simulation example shows that the proposed method is effective.
基金financially supported by the National International Science and Technology Cooperation Specific Projectthe Development of Risk Assessment Software for Floating Offshore Wind Turbine(Grant No.2013DFE73060)the Development of Failure Database and Risk Assessment System for FPSO(Grant No.G014614002)
文摘The load and corrosion caused by the harsh marine environment lead to the severe degradation of offshore equipment and to their compromised security and reliability. In the quantitative risk analysis, the failure models are difficult to establish through traditional statistical methods. Hence, the calculation of the occurrence probability of small sample events is often met with great uncertainty. In this study, the Bayesian statistical method is implemented to analyze the oil and gas leakages of FPSO internal turret, which is a typical small sample risk but could lead to severe losses.According to the corresponding failure mechanism, two Bayesian statistical models using the Weibull distribution and logarithmic normal distribution as the population distribution are established, and the posterior distribution of the corresponding parameters is calculated. The optimal Bayesian statistical model is determined according to the Bayesian information criterion and Akaike criterion. On the basis of the determined optimal model, the corresponding reliability index is solved to provide basic data for the subsequent risk assessments of FPSO systems.
基金supported by the National Natural Science Foundation of China (Grant No. 50579090)the National Basic Research Program of China (973 Program, Grant No. 2007CB714102)National Science and Technology Support Program of China (Program for the Eleventh Five-Year Plan, Grant No. 2006BAB04A06)
文摘Owing to the fact that the conventional deterministic back analysis of the permeability coefficient cannot reflect the uncertainties of parameters, including the hydraulic head at the boundary, the permeability coefficient and measured hydraulic head, a stochastic back analysis taking consideration of uncertainties of parameters was performed using the generalized Bayesian method. Based on the stochastic finite element method （SFEM） for a seepage field, the variable metric algorithm and the generalized Bayesian method, formulas for stochastic back analysis of the permeability coefficient were derived. A case study of seepage analysis of a sluice foundation was performed to illustrate the proposed method. The results indicate that, with the generalized Bayesian method that considers the uncertainties of measured hydraulic head, the permeability coefficient and the hydraulic head at the boundary, both the mean and standard deviation of the permeability coefficient can be obtained and the standard deviation is less than that obtained by the conventional Bayesian method. Therefore, the present method is valid and applicable.
基金supported by the National Natural Science Foundation of China(Grants No.51779074 and 41371052)the Special Fund for the Public Welfare Industry of the Ministry of Water Resources of China(Grant No.201501059)+3 种基金the National Key Research and Development Program of China(Grant No.2017YFC0404304)the Jiangsu Water Conservancy Science and Technology Project(Grant No.2017027)the Program for Outstanding Young Talents in Colleges and Universities of Anhui Province(Grant No.gxyq2018143)the Natural Science Foundation of Wanjiang University of Technology(Grant No.WG18030)
文摘This study developed a hierarchical Bayesian(HB)model for local and regional flood frequency analysis in the Dongting Lake Basin,in China.The annual maximum daily flows from 15 streamflow-gauged sites in the study area were analyzed with the HB model.The generalized extreme value(GEV)distribution was selected as the extreme flood distribution,and the GEV distribution location and scale parameters were spatially modeled through a regression approach with the drainage area as a covariate.The Markov chain Monte Carlo(MCMC)method with Gibbs sampling was employed to calculate the posterior distribution in the HB model.The results showed that the proposed HB model provided satisfactory Bayesian credible intervals for flood quantiles,while the traditional delta method could not provide reliable uncertainty estimations for large flood quantiles,due to the fact that the lower confidence bounds tended to decrease as the return periods increased.Furthermore,the HB model for regional analysis allowed for a reduction in the value of some restrictive assumptions in the traditional index flood method,such as the homogeneity region assumption and the scale invariance assumption.The HB model can also provide an uncertainty band of flood quantile prediction at a poorly gauged or ungauged site,but the index flood method with L-moments does not demonstrate this uncertainty directly.Therefore,the HB model is an effective method of implementing the flexible local and regional frequency analysis scheme,and of quantifying the associated predictive uncertainty.
