Engineering tests can yield inaccurate data due to instrument errors,human factors,and environmental interference,introducing uncertainty in numerical model updating.This study employs the probability-box(p-box)method...Engineering tests can yield inaccurate data due to instrument errors,human factors,and environmental interference,introducing uncertainty in numerical model updating.This study employs the probability-box(p-box)method for representing observational uncertainty and develops a two-step approximate Bayesian computation(ABC)framework using time-series data.Within the ABC framework,Euclidean and Bhattacharyya distances are employed as uncertainty quantification metrics to delineate approximate likelihood functions in the initial and subsequent steps,respectively.A novel variational Bayesian Monte Carlo method is introduced to efficiently apply the ABC framework amidst observational uncertainty,resulting in rapid convergence and accurate parameter estimation with minimal iterations.The efficacy of the proposed updating strategy is validated by its application to a shear frame model excited by seismic wave and an aviation pump force sensor for thermal output analysis.The results affirm the efficiency,robustness,and practical applicability of the proposed method.展开更多
It is difficult to build accurate model for measurement noise covariance in complex backgrounds. For the scenarios of unknown sensor noise variances, an adaptive multi-target tracking algorithm based on labeled random...It is difficult to build accurate model for measurement noise covariance in complex backgrounds. For the scenarios of unknown sensor noise variances, an adaptive multi-target tracking algorithm based on labeled random finite set and variational Bayesian （VB） approximation is proposed. The variational approximation technique is introduced to the labeled multi-Bernoulli （LMB） filter to jointly estimate the states of targets and sensor noise variances. Simulation results show that the proposed method can give unbiased estimation of cardinality and has better performance than the VB probability hypothesis density （VB-PHD） filter and the VB cardinality balanced multi-target multi-Bernoulli （VB-CBMeMBer） filter in harsh situations. The simulations also confirm the robustness of the proposed method against the time-varying noise variances. The computational complexity of proposed method is higher than the VB-PHD and VB-CBMeMBer in extreme cases, while the mean execution times of the three methods are close when targets are well separated.展开更多
In this paper,the approximate Bayesian computation combines the particle swarm optimization and se-quential Monte Carlo methods,which identify the parameters of the Mathieu-van der Pol-Duffing chaotic energy harvester...In this paper,the approximate Bayesian computation combines the particle swarm optimization and se-quential Monte Carlo methods,which identify the parameters of the Mathieu-van der Pol-Duffing chaotic energy harvester system.Then the proposed method is applied to estimate the coefficients of the chaotic model and the response output paths of the identified coefficients compared with the observed,which verifies the effectiveness of the proposed method.Finally,a partial response sample of the regular and chaotic responses,determined by the maximum Lyapunov exponent,is applied to detect whether chaotic motion occurs in them by a 0-1 test.This paper can provide a reference for data-based parameter iden-tification and chaotic prediction of chaotic vibration energy harvester systems.展开更多
Bayesian structural equation model(BSEM)integrates the advantages of the Bayesian methods into the framework of structural equation modeling and ensures the identification by assigning priors with small variances.Prev...Bayesian structural equation model(BSEM)integrates the advantages of the Bayesian methods into the framework of structural equation modeling and ensures the identification by assigning priors with small variances.Previous studies have shown that prior specifications in BSEM influence model parameter estimation,but the impact on model fit indices is yet unknown and requires more research.As a result,two simulation studies were carried out.Normal distribution priors were specified for factor loadings,while inverse Wishart distribution priors and separation strategy priors were applied for the variance-covariance matrix of latent factors.Conditions included five sample sizes and 24 prior distribution settings.Simulation Study 1 examined the model-fitting performance of BCFI,BTLI,and BRMSEA proposed by Garnier-Villarreal and Jorgensen(Psychol Method 25(1):46-70,2020)and the PPp value.Simulation Study 2 compared the performance of BCFI,BTLI,BRMSEA,and DIC in model selection between three data generation models and three fitting models.The findings demonstrated that prior settings would affect Bayesian model fit indices in evaluating model fitting and selecting models,especially in small sample sizes.Even under a large sample size,the highly improper factor loading priors resulted in poor performance of the Bayesian model fit indices.BCFI and BTLI were less likely to reject the correct model than BRMSEA and PPp value under different prior specifications.For model selection,different prior settings would affect DIC on selecting the wrong model,and BRMSEA preferred the parsimonious model.Our results indicate that the Bayesian approximate fit indices perform better when evaluating model fitting and choosing models under the BSEM framework.展开更多
Many properties of natural fractures are uncertain,such as their spatial distribution,petrophysical properties,and fluid flow performance.Bayesian theorem provides a framework to quantify the uncertainty in geological...Many properties of natural fractures are uncertain,such as their spatial distribution,petrophysical properties,and fluid flow performance.Bayesian theorem provides a framework to quantify the uncertainty in geological modeling and flow simulation,and hence to support reservoir performance predictions.The application of Bayesian methods to fractured reservoirs has mostly been limited to synthetic cases.In field applications,however,one of the main problems is that the Bayesian prior is falsified,because it fails to predict past reservoir production data.In this paper,we show how a global sensitivity analysis(GSA)can be used to identify why the prior is falsified.We then employ an approximate Bayesian computation(ABC)method combined with a tree-based surrogate model to match the production history.We apply these two approaches to a complex fractured oil and gas reservoir where all uncertainties are jointly considered,including the petrophysical properties,rock physics properties,fluid properties,discrete fracture parameters,and dynamics of pressure and transmissibility.We successfully identify several reasons for the falsification.The results show that the methods we propose are effective in quantifying uncertainty in the modeling and flow simulation of a fractured reservoir.The uncertainties of key parameters,such as fracture aperture and fault conductivity,are reduced.展开更多
Due to the flexibility and feasibility of addressing ill-posed problems,the Bayesian method has been widely used in inverse heat conduction problems(IHCPs).However,in the real science and engineering IHCPs,the likelih...Due to the flexibility and feasibility of addressing ill-posed problems,the Bayesian method has been widely used in inverse heat conduction problems(IHCPs).However,in the real science and engineering IHCPs,the likelihood function of the Bayesian method is commonly computationally expensive or analytically unavailable.In this study,in order to circumvent this intractable likelihood function,the approximate Bayesian computation(ABC)is expanded to the IHCPs.In ABC,the high dimensional observations in the intractable likelihood function are equalized by their low dimensional summary statistics.Thus,the performance of the ABC depends on the selection of summary statistics.In this study,a machine learning-based ABC(ML-ABC)is proposed to address the complicated selections of the summary statistics.The Auto-Encoder(AE)is a powerful Machine Learning(ML)framework which can compress the observations into very low dimensional summary statistics with little information loss.In addition,in order to accelerate the calculation of the proposed framework,another neural network(NN)is utilized to construct the mapping between the unknowns and the summary statistics.With this mapping,given arbitrary unknowns,the summary statistics can be obtained efficiently without solving the time-consuming forward problem with numerical method.Furthermore,an adaptive nested sampling method(ANSM)is developed to further improve the efficiency of sampling.The performance of the proposed method is demonstrated with two IHCP cases.展开更多
Understanding speciation has long been a fundamental goal of evolutionary biology.It is widely accepted that speciation requires an interruption of gene flow to generate strong reproductive isolation between species.T...Understanding speciation has long been a fundamental goal of evolutionary biology.It is widely accepted that speciation requires an interruption of gene flow to generate strong reproductive isolation between species.The mechanism of how speciation in sexually dichromatic species operates in the face of gene flow remains an open question.Two species in the genus Chrysolophus,the Golden Pheasant(C.pictus)and Lady Amherst’s Pheasant(C.amherstiae),both of which exhibit significant plumage dichromatism,are currently parapatric in southwestern China with several hybrid recordings in field.In this study,we estimated the pattern of gene flow during the speciation of the two pheasants using the Approximate Bayesian Computation(ABC)method based on data from multiple genes.Using a newly assembled de novo genome of Lady Amherst’s Pheasant and resequencing of widely distributed individuals,we reconstructed the demographic history of the two pheasants by the PSMC(pairwise sequentially Markovian coalescent)method.The results provide clear evidence that the gene flow between the two pheasants was consistent with the predictions of the isolation with migration model during divergence,indicating that there was long-term gene flow after the initial divergence(ca.2.2 million years ago).The data further support the occurrence of secondary contact between the parapatric populations since around 30 kya with recurrent gene flow to the present,a pattern that may have been induced by the population expansion of the Golden Pheasant in the late Pleistocene.The results of the study support the scenario of speciation between the Golden Pheasant and Lady Amherst’s Pheasant with cycles of mixing-isolation-mixing,possibly due to the dynamics of geographical context in the late Pleistocene.The two species provide a good research system as an evolutionary model for testing reinforcement selection in speciation.展开更多
Approximate Bayesian Computation(ABC)is a popular approach for Bayesian modeling,when these models exhibit an intractable likelihood.However,during each proposal of ABC,a great number of simulators are required and ea...Approximate Bayesian Computation(ABC)is a popular approach for Bayesian modeling,when these models exhibit an intractable likelihood.However,during each proposal of ABC,a great number of simulators are required and each simulation is always time-consuming.The overall goal of this work is to avoid inefficient computational cost of ABC.A pre-judgment rule(PJR)is proposed,which mainly aims to judge the acceptance condition using a small fraction of simulators instead of the whole simulators,thus achieving less computational complexity.In addition,it provided a theoretical study of the error bounded caused by PJR Strategy.Finally,the methodology was illustrated with various examples.The empirical results show both the effectiveness and efficiency of PJR compared with the previous methods.展开更多
Constitutive modeling is crucial for engineering design and simulations to accurately describe material behavior.However,traditional phenomenological models often struggle to capture the complexities of real materials...Constitutive modeling is crucial for engineering design and simulations to accurately describe material behavior.However,traditional phenomenological models often struggle to capture the complexities of real materials under varying stress conditions due to their fixed forms and limited parameters.While recent advances in deep learning have addressed some limitations of classical models,purely data-driven methods tend to require large data sets,lack interpretability,and struggle to generalize beyond their training data.To tackle these issues,we introduce“Fusion-based Constitutive model(FuCe):Toward model-data augmentation in constitutive modeling.”This approach combines established phenomenological models with an Input Convex Neural Network architecture,designed to train on the limited and noisy force-displacement data typically available in practical applications.The hybrid model inherently adheres to necessary constitutive conditions.During inference,Monte Carlo dropout is employed to generate Bayesian predictions,providing mean values and confidence intervals that quantify uncertainty.We demonstrate the model's effectiveness by learning two isotropic constitutive models and one anisotropic model with a single fiber direction,across six different stress states.The framework's applicability is also showcased in finite element simulations across three geometries of varying complexities.Our results highlight the framework's superior extrapolation capabilities,even when trained on limited and noisy data,delivering accurate and physically meaningful predictions across all numerical examples.展开更多
We introduce a new Python package glabcmcmc,which implements an approximate Bayesiancomputation Markovchain Monte Carlo(ABCMCMC)algorithm that combines global and local proposal strategies to address the limitations o...We introduce a new Python package glabcmcmc,which implements an approximate Bayesiancomputation Markovchain Monte Carlo(ABCMCMC)algorithm that combines global and local proposal strategies to address the limitations of standard ABC-MCMC.The proposed package includes key innovations such as the determination of global proposal frequencies,the implementation of a hybrid ABC-MCMC algorithm integrating global and local proposals,and an adaptive version that utilizes normalizing flows and gradient-based computations for enhanced proposal mechanisms.The functionality of the software package is demonstrated through illustrative examples.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.U23B20105).
文摘Engineering tests can yield inaccurate data due to instrument errors,human factors,and environmental interference,introducing uncertainty in numerical model updating.This study employs the probability-box(p-box)method for representing observational uncertainty and develops a two-step approximate Bayesian computation(ABC)framework using time-series data.Within the ABC framework,Euclidean and Bhattacharyya distances are employed as uncertainty quantification metrics to delineate approximate likelihood functions in the initial and subsequent steps,respectively.A novel variational Bayesian Monte Carlo method is introduced to efficiently apply the ABC framework amidst observational uncertainty,resulting in rapid convergence and accurate parameter estimation with minimal iterations.The efficacy of the proposed updating strategy is validated by its application to a shear frame model excited by seismic wave and an aviation pump force sensor for thermal output analysis.The results affirm the efficiency,robustness,and practical applicability of the proposed method.
基金supported by the National High Technology Research and Development Program of China (No.2014AA7014061)the National Natural Science Foundation of China (No.61501484)
文摘It is difficult to build accurate model for measurement noise covariance in complex backgrounds. For the scenarios of unknown sensor noise variances, an adaptive multi-target tracking algorithm based on labeled random finite set and variational Bayesian （VB） approximation is proposed. The variational approximation technique is introduced to the labeled multi-Bernoulli （LMB） filter to jointly estimate the states of targets and sensor noise variances. Simulation results show that the proposed method can give unbiased estimation of cardinality and has better performance than the VB probability hypothesis density （VB-PHD） filter and the VB cardinality balanced multi-target multi-Bernoulli （VB-CBMeMBer） filter in harsh situations. The simulations also confirm the robustness of the proposed method against the time-varying noise variances. The computational complexity of proposed method is higher than the VB-PHD and VB-CBMeMBer in extreme cases, while the mean execution times of the three methods are close when targets are well separated.
基金This work is supported by the National Nature Science Founda-tion of China(Nos.11972019 and 12102237).
文摘In this paper,the approximate Bayesian computation combines the particle swarm optimization and se-quential Monte Carlo methods,which identify the parameters of the Mathieu-van der Pol-Duffing chaotic energy harvester system.Then the proposed method is applied to estimate the coefficients of the chaotic model and the response output paths of the identified coefficients compared with the observed,which verifies the effectiveness of the proposed method.Finally,a partial response sample of the regular and chaotic responses,determined by the maximum Lyapunov exponent,is applied to detect whether chaotic motion occurs in them by a 0-1 test.This paper can provide a reference for data-based parameter iden-tification and chaotic prediction of chaotic vibration energy harvester systems.
基金supported by the MOE(Ministry of Education)Project of Humanities and Social Science of China[23YJA190007]the Natural Science Foundation of Guangdong Province[2022A1515010367]the Key Research and Development Plan of Yunnan Province,China[202203AC100003].
文摘Bayesian structural equation model(BSEM)integrates the advantages of the Bayesian methods into the framework of structural equation modeling and ensures the identification by assigning priors with small variances.Previous studies have shown that prior specifications in BSEM influence model parameter estimation,but the impact on model fit indices is yet unknown and requires more research.As a result,two simulation studies were carried out.Normal distribution priors were specified for factor loadings,while inverse Wishart distribution priors and separation strategy priors were applied for the variance-covariance matrix of latent factors.Conditions included five sample sizes and 24 prior distribution settings.Simulation Study 1 examined the model-fitting performance of BCFI,BTLI,and BRMSEA proposed by Garnier-Villarreal and Jorgensen(Psychol Method 25(1):46-70,2020)and the PPp value.Simulation Study 2 compared the performance of BCFI,BTLI,BRMSEA,and DIC in model selection between three data generation models and three fitting models.The findings demonstrated that prior settings would affect Bayesian model fit indices in evaluating model fitting and selecting models,especially in small sample sizes.Even under a large sample size,the highly improper factor loading priors resulted in poor performance of the Bayesian model fit indices.BCFI and BTLI were less likely to reject the correct model than BRMSEA and PPp value under different prior specifications.For model selection,different prior settings would affect DIC on selecting the wrong model,and BRMSEA preferred the parsimonious model.Our results indicate that the Bayesian approximate fit indices perform better when evaluating model fitting and choosing models under the BSEM framework.
文摘Many properties of natural fractures are uncertain,such as their spatial distribution,petrophysical properties,and fluid flow performance.Bayesian theorem provides a framework to quantify the uncertainty in geological modeling and flow simulation,and hence to support reservoir performance predictions.The application of Bayesian methods to fractured reservoirs has mostly been limited to synthetic cases.In field applications,however,one of the main problems is that the Bayesian prior is falsified,because it fails to predict past reservoir production data.In this paper,we show how a global sensitivity analysis(GSA)can be used to identify why the prior is falsified.We then employ an approximate Bayesian computation(ABC)method combined with a tree-based surrogate model to match the production history.We apply these two approaches to a complex fractured oil and gas reservoir where all uncertainties are jointly considered,including the petrophysical properties,rock physics properties,fluid properties,discrete fracture parameters,and dynamics of pressure and transmissibility.We successfully identify several reasons for the falsification.The results show that the methods we propose are effective in quantifying uncertainty in the modeling and flow simulation of a fractured reservoir.The uncertainties of key parameters,such as fracture aperture and fault conductivity,are reduced.
文摘Due to the flexibility and feasibility of addressing ill-posed problems,the Bayesian method has been widely used in inverse heat conduction problems(IHCPs).However,in the real science and engineering IHCPs,the likelihood function of the Bayesian method is commonly computationally expensive or analytically unavailable.In this study,in order to circumvent this intractable likelihood function,the approximate Bayesian computation(ABC)is expanded to the IHCPs.In ABC,the high dimensional observations in the intractable likelihood function are equalized by their low dimensional summary statistics.Thus,the performance of the ABC depends on the selection of summary statistics.In this study,a machine learning-based ABC(ML-ABC)is proposed to address the complicated selections of the summary statistics.The Auto-Encoder(AE)is a powerful Machine Learning(ML)framework which can compress the observations into very low dimensional summary statistics with little information loss.In addition,in order to accelerate the calculation of the proposed framework,another neural network(NN)is utilized to construct the mapping between the unknowns and the summary statistics.With this mapping,given arbitrary unknowns,the summary statistics can be obtained efficiently without solving the time-consuming forward problem with numerical method.Furthermore,an adaptive nested sampling method(ANSM)is developed to further improve the efficiency of sampling.The performance of the proposed method is demonstrated with two IHCP cases.
基金supported by the National Natural Science Foundation of China(No.31471987)approved by College of Life Sciences,Beijing Normal University:No.CLSEAW-2013-007。
文摘Understanding speciation has long been a fundamental goal of evolutionary biology.It is widely accepted that speciation requires an interruption of gene flow to generate strong reproductive isolation between species.The mechanism of how speciation in sexually dichromatic species operates in the face of gene flow remains an open question.Two species in the genus Chrysolophus,the Golden Pheasant(C.pictus)and Lady Amherst’s Pheasant(C.amherstiae),both of which exhibit significant plumage dichromatism,are currently parapatric in southwestern China with several hybrid recordings in field.In this study,we estimated the pattern of gene flow during the speciation of the two pheasants using the Approximate Bayesian Computation(ABC)method based on data from multiple genes.Using a newly assembled de novo genome of Lady Amherst’s Pheasant and resequencing of widely distributed individuals,we reconstructed the demographic history of the two pheasants by the PSMC(pairwise sequentially Markovian coalescent)method.The results provide clear evidence that the gene flow between the two pheasants was consistent with the predictions of the isolation with migration model during divergence,indicating that there was long-term gene flow after the initial divergence(ca.2.2 million years ago).The data further support the occurrence of secondary contact between the parapatric populations since around 30 kya with recurrent gene flow to the present,a pattern that may have been induced by the population expansion of the Golden Pheasant in the late Pleistocene.The results of the study support the scenario of speciation between the Golden Pheasant and Lady Amherst’s Pheasant with cycles of mixing-isolation-mixing,possibly due to the dynamics of geographical context in the late Pleistocene.The two species provide a good research system as an evolutionary model for testing reinforcement selection in speciation.
基金Scientific research fund of North University of China(No.XJJ201803).
文摘Approximate Bayesian Computation(ABC)is a popular approach for Bayesian modeling,when these models exhibit an intractable likelihood.However,during each proposal of ABC,a great number of simulators are required and each simulation is always time-consuming.The overall goal of this work is to avoid inefficient computational cost of ABC.A pre-judgment rule(PJR)is proposed,which mainly aims to judge the acceptance condition using a small fraction of simulators instead of the whole simulators,thus achieving less computational complexity.In addition,it provided a theoretical study of the error bounded caused by PJR Strategy.Finally,the methodology was illustrated with various examples.The empirical results show both the effectiveness and efficiency of PJR compared with the previous methods.
基金Anusandhan National Research Foundation(ANRF)via grant no.CRG/2023/007667 and from the Ministry of Port,Shipping,and Waterways via letter no.ST-14011/74/MT(356529).
文摘Constitutive modeling is crucial for engineering design and simulations to accurately describe material behavior.However,traditional phenomenological models often struggle to capture the complexities of real materials under varying stress conditions due to their fixed forms and limited parameters.While recent advances in deep learning have addressed some limitations of classical models,purely data-driven methods tend to require large data sets,lack interpretability,and struggle to generalize beyond their training data.To tackle these issues,we introduce“Fusion-based Constitutive model(FuCe):Toward model-data augmentation in constitutive modeling.”This approach combines established phenomenological models with an Input Convex Neural Network architecture,designed to train on the limited and noisy force-displacement data typically available in practical applications.The hybrid model inherently adheres to necessary constitutive conditions.During inference,Monte Carlo dropout is employed to generate Bayesian predictions,providing mean values and confidence intervals that quantify uncertainty.We demonstrate the model's effectiveness by learning two isotropic constitutive models and one anisotropic model with a single fiber direction,across six different stress states.The framework's applicability is also showcased in finite element simulations across three geometries of varying complexities.Our results highlight the framework's superior extrapolation capabilities,even when trained on limited and noisy data,delivering accurate and physically meaningful predictions across all numerical examples.
基金supported by the National Natural Science Foundation of China[grant numbers 12131001 and 12101333]the startup fund of ShanghaiTech University,the Fundamental Research Funds for the Central Universities,LPMC,and KLMDASR.
文摘We introduce a new Python package glabcmcmc,which implements an approximate Bayesiancomputation Markovchain Monte Carlo(ABCMCMC)algorithm that combines global and local proposal strategies to address the limitations of standard ABC-MCMC.The proposed package includes key innovations such as the determination of global proposal frequencies,the implementation of a hybrid ABC-MCMC algorithm integrating global and local proposals,and an adaptive version that utilizes normalizing flows and gradient-based computations for enhanced proposal mechanisms.The functionality of the software package is demonstrated through illustrative examples.
