Interval model updating(IMU)methods have been widely used in uncertain model updating due to their low requirements for sample data.However,the surrogate model in IMU methods mostly adopts the one-time construction me...Interval model updating(IMU)methods have been widely used in uncertain model updating due to their low requirements for sample data.However,the surrogate model in IMU methods mostly adopts the one-time construction method.This makes the accuracy of the surrogate model highly dependent on the experience of users and affects the accuracy of IMU methods.Therefore,an improved IMU method via the adaptive Kriging models is proposed.This method transforms the objective function of the IMU problem into two deterministic global optimization problems about the upper bound and the interval diameter through universal grey numbers.These optimization problems are addressed through the adaptive Kriging models and the particle swarm optimization(PSO)method to quantify the uncertain parameters,and the IMU is accomplished.During the construction of these adaptive Kriging models,the sample space is gridded according to sensitivity information.Local sampling is then performed in key subspaces based on the maximum mean square error(MMSE)criterion.The interval division coefficient and random sampling coefficient are adaptively adjusted without human interference until the model meets accuracy requirements.The effectiveness of the proposed method is demonstrated by a numerical example of a three-degree-of-freedom mass-spring system and an experimental example of a butted cylindrical shell.The results show that the updated results of the interval model are in good agreement with the experimental results.展开更多
This study introduces a new approach utilizing an interval finite element method combined with a bilevel Kriging model to determine the bounds of structural responses in the presence of spatial uncertainties.A notable...This study introduces a new approach utilizing an interval finite element method combined with a bilevel Kriging model to determine the bounds of structural responses in the presence of spatial uncertainties.A notable benefit of this approach is its ability to determine the response bounds across all degrees of freedom with a small sample size,which means that it has high efficiency.Firstly,the spatially varying uncertain parameters are quantified using an interval field model,which is described by a series of standard interval variables within a truncated interval Karhunen-Loe`ve(K-L)series expansion.Secondly,considering that the bound of structural response is a function of spatial position with the property of continuity,a surrogate model for the response bound is constructed,namely the first-level Kriging model.The training samples required for this surrogate model are obtained by establishing the second-level Kriging model.The second-level Kriging model is established to describe the structural responses at particular locations relative to the interval variables so as to facilitate the upper and lower bounds of the node response required by the first-level Kriging model.Finally,the accuracy and effectiveness of the method are verified through examples.展开更多
In this paper, a computationally efficient optimization method for aerodynamic design has been developed. The low-fidelity model and the multi-infill strategy are utilized in this approach.Low-fidelity data is employe...In this paper, a computationally efficient optimization method for aerodynamic design has been developed. The low-fidelity model and the multi-infill strategy are utilized in this approach.Low-fidelity data is employed to provide a good global trend for model prediction, and multiple sample points chosen by different infill criteria in each updating cycle are used to enhance the exploitation and exploration ability of the optimization approach. Take the advantages of lowfidelity model and the multi-infill strategy, and no initial sample for the high-fidelity model is needed. This approach is applied to an airfoil design case and a high-dimensional wing design case.It saves a large number of high-fidelity function evaluations for initial model construction. What＇s more, faster reduction of an aerodynamic function is achieved, when compared to ordinary kriging using the multi-infill strategy and variable-fidelity model using single infill criterion. The results indicate that the developed approach has a promising application to efficient aerodynamic design when high-fidelity analyses are involved.展开更多
This paper is devoted to the probabilistic stability analysis of a tunnel face excavated in a two-layer soil. The interface of the soil layers is assumed to be positioned above the tunnel roof. In the framework of lim...This paper is devoted to the probabilistic stability analysis of a tunnel face excavated in a two-layer soil. The interface of the soil layers is assumed to be positioned above the tunnel roof. In the framework of limit analysis, a rotational failure mechanism is adopted to describe the face failure considering different shear strength parameters in the two layers. The surrogate Kriging model is introduced to replace the actual performance function to perform a Monte Carlo simulation. An active learning function is used to train the Kriging model which can ensure an efficient tunnel face failure probability prediction without loss of accuracy. The deterministic stability analysis is given to validate the proposed tunnel face failure model. Subsequently, the number of initial sampling points, the correlation coefficient, the distribution type and the coefficient of variability of random variables are discussed to show their influences on the failure probability. The proposed approach is an advisable alternative for the tunnel face stability assessment and can provide guidance for tunnel design.展开更多
In order to study the variation of machine tools’dynamic characteristics in the manufacturing space,a Kriging approximate model is proposed.Finite element method(FEM)is employed on the platform of ANSYS to establish ...In order to study the variation of machine tools’dynamic characteristics in the manufacturing space,a Kriging approximate model is proposed.Finite element method(FEM)is employed on the platform of ANSYS to establish finite element(FE)model with the dynamic characteristic of combined interface for a milling machine,which is newly designed for producing aero engine blades by a certain enterprise group in China.The stiffness and damping of combined interfaces are adjusted by using adaptive simulated annealing algorithm with the optimizing software of iSIGHT in the process of FE model update according to experimental modal analysis(EMA)results.The Kriging approximate model is established according to the finite element analysis results utilizing orthogonal design samples by taking into account of the range of configuration parameters.On the basis of the Kriging approximate model,the response surfaces between key response parameter and configuration parameters are obtained.The results indicate that configuration parameters have great effects on dynamic characteristics of machine tools,and the Kriging approximate model is an effective and rapid method for estimating dynamic characteristics of machine tools in the manufacturing space.展开更多
This paper aims to solve the resonance failure probability and develop an effective method to estimate the effects of variables and failure modes on failure probability of axially functionally graded material(FGM)pipe...This paper aims to solve the resonance failure probability and develop an effective method to estimate the effects of variables and failure modes on failure probability of axially functionally graded material(FGM)pipe conveying fluid.Correspondingly,the natural frequency of axially FGM pipes conveying fluid is calculated using the differential quadrature method(DQM).A variable sensitivity analysis(VSA)is introduced to measure the effect of each random variable,and a mode sensitivity analysis(MSA)is introduced to acquire the importance ranking of failure modes.Then,an active learning Kriging(ALK)method is established to calculate the resonance failure probability and sensitivity indices,which greatly improves the application of resonance reliability analysis for pipelines in engineering practice.Based on the resonance reliability analysis method,the effects of fluid velocity,volume fraction and fluid density of axially FGM pipe conveying fluid on resonance reliability are analyzed.The results demonstrate that the proposed method has great performance in the anti-resonance analysis of pipes conveying fluid.展开更多
Because of the randomness and uncertainty,integration of large-scale wind farms in a power system will exert significant influences on the distribution of power flow.This paper uses polynomial normal transformation me...Because of the randomness and uncertainty,integration of large-scale wind farms in a power system will exert significant influences on the distribution of power flow.This paper uses polynomial normal transformation method to deal with non-normal random variable correlation,and solves probabilistic load flow based on Kriging method.This method is a kind of smallest unbiased variance estimation method which estimates unknown information via employing a point within the confidence scope of weighted linear combination.Compared with traditional approaches which need a greater number of calculation times,long simulation time,and large memory space,Kriging method can rapidly estimate node state variables and branch current power distribution situation.As one of the generator nodes in the western Yunnan power grid,a certain wind farm is chosen for empirical analysis.Results are used to compare with those by Monte Carlo-based accurate solution,which proves the validity and veracity of the model in wind farm power modeling as output of the actual turbine through PSD-BPA.展开更多
To improve the operational efficiency of global optimization in engineering, Kriging model was established to simplify the mathematical model for calculations. Ducted coaxial-rotors aircraft was taken as an example an...To improve the operational efficiency of global optimization in engineering, Kriging model was established to simplify the mathematical model for calculations. Ducted coaxial-rotors aircraft was taken as an example and Fluent software was applied to the virtual prototype simulations. Through simulation sample points, the total lift of the ducted coaxial-rotors aircraft was obtained. The Kriging model was then constructed, and the function was fitted. Improved particle swarm optimization(PSO) was also utilized for the global optimization of the Kriging model of the ducted coaxial-rotors aircraft for the determination of optimized global coordinates. Finally, the optimized results were simulated by Fluent. The results show that the Kriging model and the improved PSO algorithm significantly improve the lift performance of ducted coaxial-rotors aircraft and computer operational efficiency.展开更多
The first order reliability method (FORM) is widely adopted for structural reliability evaluation due to its numerical efficiency. Concerning the issue of FORM often failing to converge when the limit state function (...The first order reliability method (FORM) is widely adopted for structural reliability evaluation due to its numerical efficiency. Concerning the issue of FORM often failing to converge when the limit state function (LSF) behaves high nonlinearity, a new iteration scheme called "rotated gradient algorithm (RGA)" is proposed and combined with Kriging model to evaluate the reliability of implicit performance function. In this paper, the Kriging model is applied to approximate the real LSF first. Then the scheme of RGA, constructed in terms of gradient information of two adjacent design points obtained during the process of calculation, is used to calculate the reliability index. Numerical examples show the validity in convergence and accuracy of the proposed methodfor arbitrary nonlinear performance function.展开更多
Kriging models are widely employed due to their simplicity and flexibility in a variety of fields.To gain more distributional information about the unknown parameters,we focus on constructing the fiducial distribution...Kriging models are widely employed due to their simplicity and flexibility in a variety of fields.To gain more distributional information about the unknown parameters,we focus on constructing the fiducial distribution of Kriging model parameters.To solve the challenge of constructing the fiducial marginal distribution for the spatially related parameter,we substitute the Bayesian posterior distribution for the fiducial distribution of this spatially related parameter and present a quasi-fiducial distribution for Kriging model parameters.A Gibbs sampling algorithm is given to get the samples of the quasi-fiducial distribution.Then a model selection criterion based on the quasi-fiducial distribution is proposed.Numerical studies demonstrate that the proposed method is superior to the Lasso and Elastic Net.展开更多
The main objective of this paper is to consider model averaging methods for kriging models.This paper proposes a Mallows model averaging procedure for the orthogonal kriging model and demonstrate the asymptotic optima...The main objective of this paper is to consider model averaging methods for kriging models.This paper proposes a Mallows model averaging procedure for the orthogonal kriging model and demonstrate the asymptotic optimality of the model averaging estimators in terms of mean square error.Simulation studies are conducted to evaluate the performance of the proposed method and compare it with the competitors to demonstrate its superiority.The authors also analyse a real dataset for an illustration.展开更多
In recent years,Kriging model has gained wide popularity in various fields such as space geology,econometrics,and computer experiments.As a result,research on this model has proliferated.In this paper,the authors prop...In recent years,Kriging model has gained wide popularity in various fields such as space geology,econometrics,and computer experiments.As a result,research on this model has proliferated.In this paper,the authors propose a model averaging estimation based on the best linear unbiased prediction of Kriging model and the leave-one-out cross-validation method,with consideration for the model uncertainty.The authors present a weight selection criterion for the model averaging estimation and provide two theoretical justifications for the proposed method.First,the estimated weight based on the proposed criterion is asymptotically optimal in achieving the lowest possible prediction risk.Second,the proposed method asymptotically assigns all weights to the correctly specified models when the candidate model set includes these models.The effectiveness of the proposed method is verified through numerical analyses.展开更多
Metal powder contributes to the environmental burdens of additive manufacturing(AM)substantially.Current life cycle assessments(LCAs)of metal powders present considerable variations of lifecycle environmental inventor...Metal powder contributes to the environmental burdens of additive manufacturing(AM)substantially.Current life cycle assessments(LCAs)of metal powders present considerable variations of lifecycle environmental inventory due to process divergence,spatial heterogeneity,or temporalfluctuation.Most importantly,the amounts of LCA studies on metal powder are limited and primarily confined to partial material types.To this end,based on the data surveyed from a metal powder supplier,this study conducted an LCA of titanium and nickel alloy produced by electrode-inducted and vacuum-inducted melting gas atomization,respectively.Given that energy consumption dominates the environmental burden of powder production and is influenced by metal materials’physical properties,we proposed a Bayesian stochastic Kriging model to estimate the energy consumption during the gas atomization process.This model considered the inherent uncertainties of training data and adaptively updated the parameters of interest when new environmental data on gas atomization were available.With the predicted energy use information of specific powder,the corresponding lifecycle environmental impacts can be further autonomously estimated in conjunction with the other surveyed powder production stages.Results indicated the environmental impact of titanium alloy powder is slightly higher than that of nickel alloy powder and their lifecycle carbon emissions are around 20 kg CO_(2)equivalency.The proposed Bayesian stochastic Kriging model showed more accurate predictions of energy consumption compared with conventional Kriging and stochastic Kriging models.This study enables data imputation of energy consumption during gas atomization given the physical properties and producing technique of powder materials.展开更多
Structural Reliability-Based Topology Optimization(RBTO),as an efficient design methodology,serves as a crucial means to ensure the development ofmodern engineering structures towards high performance,long service lif...Structural Reliability-Based Topology Optimization(RBTO),as an efficient design methodology,serves as a crucial means to ensure the development ofmodern engineering structures towards high performance,long service life,and high reliability.However,in practical design processes,topology optimization must not only account for the static performance of structures but also consider the impacts of various responses and uncertainties under complex dynamic conditions,which traditional methods often struggle accommodate.Therefore,this study proposes an RBTO framework based on a Kriging-assisted level set function and a novel Dynamic Hybrid Particle Swarm Optimization(DHPSO)algorithm.By leveraging the Kriging model as a surrogate,the high cost associated with repeatedly running finite element analysis processes is reduced,addressing the issue of minimizing structural compliance.Meanwhile,the DHPSO algorithm enables a better balance between the population’s developmental and exploratory capabilities,significantly accelerating convergence speed and enhancing global convergence performance.Finally,the proposed method is validated through three different structural examples,demonstrating its superior performance.Observed that the computational that,compared to the traditional Solid Isotropic Material with Penalization(SIMP)method,the proposed approach reduces the upper bound of structural compliance by approximately 30%.Additionally,the optimized results exhibit clear material interfaces without grayscale elements,and the stress concentration factor is reduced by approximately 42%.Consequently,the computational results fromdifferent examples verify the effectiveness and superiority of this study across various fields,achieving the goal of providing more precise optimization results within a shorter timeframe.展开更多
In the structural reliability analysis,the first-order reliability method(FORM)often yields significant errors when addressing nonlinear problems.Although the second-order reliability method(SORM)can provide higher ac...In the structural reliability analysis,the first-order reliability method(FORM)often yields significant errors when addressing nonlinear problems.Although the second-order reliability method(SORM)can provide higher accuracy,the additional computation of the Hessian matrix leads to lower computational efficiency.Additionally,when the dimensionality of the random variables is high,the approximation formula of SORM can result in larger errors.To address these issues,a structural reliability analysis method based on Kriging and spherical cap area integral is proposed.Firstly,this method integrates FORM with the quasi-Newton algorithm Broyden-Fletcher-Goldfarb-Shanno(BFGS),trains the Kriging model by using sample points from the algorithm’s iteration process,and combines the Kriging model with gradient information to approximate the Hessian matrix.Then,the failure surface is approximated as a rotating paraboloid,utilizing the spherical cap to replace the complex surface.For the n-dimensional case,the hyperspherical cap area expression is combined with the integral method to calculate the failure probability.Finally,the method is validated through three examples,demonstrating improved computational accuracy and efficiency compared to traditional methods.展开更多
Surrogate models offer an efficient approach to tackle the computationally intensive evaluation of performance functions in reliability analysis.Nevertheless,the approximations inherent in surrogate models necessitate...Surrogate models offer an efficient approach to tackle the computationally intensive evaluation of performance functions in reliability analysis.Nevertheless,the approximations inherent in surrogate models necessitate the consideration of surrogate model uncertainty in estimating failure probabilities.This paper proposes a new reliability analysis method in which the uncertainty from the Kriging surrogate model is quantified simultaneously.This method treats surrogate model uncertainty as an independent entity,characterizing the estimation error of failure probabilities.Building upon the probabilistic classification function,a failure probability uncertainty is proposed by integrating the difference between the traditional indicator function and the probabilistic classification function to quantify the impact of surrogate model uncertainty on failure probability estimation.Furthermore,the proposed uncertainty quantification method is applied to a newly designed reliability analysis approach termed SUQ-MCS,incorporating a proposed median approximation function for active learning.The proposed failure probability uncertainty serves as the stopping criterion of this framework.Through benchmarking,the effectiveness of the proposed uncertainty quantification method is validated.The empirical results present the competitive performance of the SUQ-MCS method relative to alternative approaches.展开更多
Precise calculation of the trajectory of store separation is critical in assess-ing whether the store can be released safely.Store ejection is the initial stage of the releasing process and any uncertainty introduced ...Precise calculation of the trajectory of store separation is critical in assess-ing whether the store can be released safely.Store ejection is the initial stage of the releasing process and any uncertainty introduced at this stage will propagate through the whole trajectory.In this work,the impact of the uncertainties in ejector modeling on the simulation of a generic store separation is investigated by using a Monte-Carlo-based approach.To reduce the extremely large computation cost resulted from the direct use CFD in Monte Carlo simulation,the CFD solutions are represented by a time-dependent Kriging model,which is constructed at each time step by using the samples from the URANS simulations.The stochastic outputs,including the distri-bution of probability density function,expected value and 95%confidence interval of store separation trajectory,are obtained by the Monte Carlo simulations.The sensitiv-ity analysis is also carried out by using the Monte-Carlo-based method to determine the most significant variables in ejector modeling,which affect the output uncertainty.Our results show that ejector modeling is one of the main uncertainty sources of store separation simulation and the approximation in ejector modeling can cause a signifi-cant deviation,especially in the angular displacement.展开更多
Multi-objective optimization of crashworthiness in automobile front-end structure was performed,and finite element model(FEM)was validated by experimental results to ensure that FEM can predict the response value with...Multi-objective optimization of crashworthiness in automobile front-end structure was performed,and finite element model(FEM)was validated by experimental results to ensure that FEM can predict the response value with sufficient accuracy.Seven design variables and four crashworthiness indicators were defined.Through orthogonal design method,18 FEMs were established,and the response values of crashworthiness indicators were extracted.By using the variable-response specimen matrix,Kriging surrogate model(KSM)was constructed to replace FEM to refect the function correlation between variables and responses.The accuracy of KSM was also validated.Finally,the simulated annealing optimization algorithm was implemented in KSM to seek optimal and reliable solutions.Based on the optimal results and comparison analysis,the 9096-th iteration point was the optimal solution.Although the intrusion of firewall and the mass of optimal structure increased slightly,the vehicle acceleration of the optimal solution decreased by 6.9%,which fectively reduced the risk of occupant injury.展开更多
To better complete various missions, it is necessary to plan an optimal trajectory or provide the optimal control law for the multirole missile according to the actual situation, including launch conditions and target...To better complete various missions, it is necessary to plan an optimal trajectory or provide the optimal control law for the multirole missile according to the actual situation, including launch conditions and target location. Since trajectory optimization struggles to meet real-time requirements, the emergence of data-based generation methods has become a significant focus in contemporary research. However, due to the large differences in the characteristics of the optimal control laws caused by the diversity of tasks, it is difficult to achieve good prediction results by modeling all data with one single model.Therefore, the modeling idea of the mixture of experts(MoE) is adopted. Firstly, the K-means clustering algorithm is used to partition the sample data set, and the corresponding neural network classification model is established as the gate switch of MoE. Then, the expert models, i.e., the mappings from the generation conditions to the optimal control law represented by the results of principal component analysis(PCA), are represented by Kriging models. Finally, multiple rounds of accuracy evaluation, sample supplementation, and model updating are conducted to improve the generation accuracy. The Monte Carlo simulation shows that the accuracy of the proposed model reaches 96% and the generation efficiency meets the real-time requirement.展开更多
The application of reliability analysis and reliability sensitivity analysis methods to complicated structures faces two main challenges:small failure probability(typical less than 10-5)and time-demanding mechanical m...The application of reliability analysis and reliability sensitivity analysis methods to complicated structures faces two main challenges:small failure probability(typical less than 10-5)and time-demanding mechanical models.This paper proposes an improved active learning surrogate model method,which combines the advantages of the classical Active Kriging–Monte Carlo Simulation(AK-MCS)procedure and the Adaptive Linked Importance Sampling(ALIS)procedure.The proposed procedure can,on the one hand,adaptively produce a series of intermediate sampling density approaching the quasi-optimal Importance Sampling(IS)density,on the other hand,adaptively generate a set of intermediate surrogate models approaching the true failure surface of the rare failure event.Then,the small failure probability and the corresponding reliability sensitivity indices are efficiently estimated by their IS estimators based on the quasi-optimal IS density and the surrogate models.Compared with the classical AK-MCS and Active Kriging–Importance Sampling(AK-IS)procedure,the proposed method neither need to build very large sample pool even when the failure probability is extremely small,nor need to estimate the Most Probable Points(MPPs),thus it is computationally more efficient and more applicable especially for problems with multiple MPPs.The effectiveness and engineering applicability of the proposed method are demonstrated by one numerical test example and two engineering applications.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.12272211,12072181,12121002)。
文摘Interval model updating(IMU)methods have been widely used in uncertain model updating due to their low requirements for sample data.However,the surrogate model in IMU methods mostly adopts the one-time construction method.This makes the accuracy of the surrogate model highly dependent on the experience of users and affects the accuracy of IMU methods.Therefore,an improved IMU method via the adaptive Kriging models is proposed.This method transforms the objective function of the IMU problem into two deterministic global optimization problems about the upper bound and the interval diameter through universal grey numbers.These optimization problems are addressed through the adaptive Kriging models and the particle swarm optimization(PSO)method to quantify the uncertain parameters,and the IMU is accomplished.During the construction of these adaptive Kriging models,the sample space is gridded according to sensitivity information.Local sampling is then performed in key subspaces based on the maximum mean square error(MMSE)criterion.The interval division coefficient and random sampling coefficient are adaptively adjusted without human interference until the model meets accuracy requirements.The effectiveness of the proposed method is demonstrated by a numerical example of a three-degree-of-freedom mass-spring system and an experimental example of a butted cylindrical shell.The results show that the updated results of the interval model are in good agreement with the experimental results.
基金co-supported by the National Key R&D Program of China(No.2022YFB3403800)the National Natural Science Foundations of China(Nos.52235005 and 52175224)the Hunan Province Agricultural Science and Technology Innovation Fund Project,China(No.2024CX117).
文摘This study introduces a new approach utilizing an interval finite element method combined with a bilevel Kriging model to determine the bounds of structural responses in the presence of spatial uncertainties.A notable benefit of this approach is its ability to determine the response bounds across all degrees of freedom with a small sample size,which means that it has high efficiency.Firstly,the spatially varying uncertain parameters are quantified using an interval field model,which is described by a series of standard interval variables within a truncated interval Karhunen-Loe`ve(K-L)series expansion.Secondly,considering that the bound of structural response is a function of spatial position with the property of continuity,a surrogate model for the response bound is constructed,namely the first-level Kriging model.The training samples required for this surrogate model are obtained by establishing the second-level Kriging model.The second-level Kriging model is established to describe the structural responses at particular locations relative to the interval variables so as to facilitate the upper and lower bounds of the node response required by the first-level Kriging model.Finally,the accuracy and effectiveness of the method are verified through examples.
基金co-supported by the National Natural Science Foundation of China(Nos.11272263 and 11302177)
文摘In this paper, a computationally efficient optimization method for aerodynamic design has been developed. The low-fidelity model and the multi-infill strategy are utilized in this approach.Low-fidelity data is employed to provide a good global trend for model prediction, and multiple sample points chosen by different infill criteria in each updating cycle are used to enhance the exploitation and exploration ability of the optimization approach. Take the advantages of lowfidelity model and the multi-infill strategy, and no initial sample for the high-fidelity model is needed. This approach is applied to an airfoil design case and a high-dimensional wing design case.It saves a large number of high-fidelity function evaluations for initial model construction. What＇s more, faster reduction of an aerodynamic function is achieved, when compared to ordinary kriging using the multi-infill strategy and variable-fidelity model using single infill criterion. The results indicate that the developed approach has a promising application to efficient aerodynamic design when high-fidelity analyses are involved.
基金Projects supported by the China Scholarship Council
文摘This paper is devoted to the probabilistic stability analysis of a tunnel face excavated in a two-layer soil. The interface of the soil layers is assumed to be positioned above the tunnel roof. In the framework of limit analysis, a rotational failure mechanism is adopted to describe the face failure considering different shear strength parameters in the two layers. The surrogate Kriging model is introduced to replace the actual performance function to perform a Monte Carlo simulation. An active learning function is used to train the Kriging model which can ensure an efficient tunnel face failure probability prediction without loss of accuracy. The deterministic stability analysis is given to validate the proposed tunnel face failure model. Subsequently, the number of initial sampling points, the correlation coefficient, the distribution type and the coefficient of variability of random variables are discussed to show their influences on the failure probability. The proposed approach is an advisable alternative for the tunnel face stability assessment and can provide guidance for tunnel design.
基金Project(2009ZX04001-073)supported by the Important National Science&Technology Specific Projects of ChinaProject(51105025)supported by the National Natural Science Foundation of China
文摘In order to study the variation of machine tools’dynamic characteristics in the manufacturing space,a Kriging approximate model is proposed.Finite element method(FEM)is employed on the platform of ANSYS to establish finite element(FE)model with the dynamic characteristic of combined interface for a milling machine,which is newly designed for producing aero engine blades by a certain enterprise group in China.The stiffness and damping of combined interfaces are adjusted by using adaptive simulated annealing algorithm with the optimizing software of iSIGHT in the process of FE model update according to experimental modal analysis(EMA)results.The Kriging approximate model is established according to the finite element analysis results utilizing orthogonal design samples by taking into account of the range of configuration parameters.On the basis of the Kriging approximate model,the response surfaces between key response parameter and configuration parameters are obtained.The results indicate that configuration parameters have great effects on dynamic characteristics of machine tools,and the Kriging approximate model is an effective and rapid method for estimating dynamic characteristics of machine tools in the manufacturing space.
基金The funding was provided by Laboratory Fund (Grant No.SYJJ200320).
文摘This paper aims to solve the resonance failure probability and develop an effective method to estimate the effects of variables and failure modes on failure probability of axially functionally graded material(FGM)pipe conveying fluid.Correspondingly,the natural frequency of axially FGM pipes conveying fluid is calculated using the differential quadrature method(DQM).A variable sensitivity analysis(VSA)is introduced to measure the effect of each random variable,and a mode sensitivity analysis(MSA)is introduced to acquire the importance ranking of failure modes.Then,an active learning Kriging(ALK)method is established to calculate the resonance failure probability and sensitivity indices,which greatly improves the application of resonance reliability analysis for pipelines in engineering practice.Based on the resonance reliability analysis method,the effects of fluid velocity,volume fraction and fluid density of axially FGM pipe conveying fluid on resonance reliability are analyzed.The results demonstrate that the proposed method has great performance in the anti-resonance analysis of pipes conveying fluid.
文摘Because of the randomness and uncertainty,integration of large-scale wind farms in a power system will exert significant influences on the distribution of power flow.This paper uses polynomial normal transformation method to deal with non-normal random variable correlation,and solves probabilistic load flow based on Kriging method.This method is a kind of smallest unbiased variance estimation method which estimates unknown information via employing a point within the confidence scope of weighted linear combination.Compared with traditional approaches which need a greater number of calculation times,long simulation time,and large memory space,Kriging method can rapidly estimate node state variables and branch current power distribution situation.As one of the generator nodes in the western Yunnan power grid,a certain wind farm is chosen for empirical analysis.Results are used to compare with those by Monte Carlo-based accurate solution,which proves the validity and veracity of the model in wind farm power modeling as output of the actual turbine through PSD-BPA.
基金Project(2013AA063903)supported by High-tech Research and Development Program of China
文摘To improve the operational efficiency of global optimization in engineering, Kriging model was established to simplify the mathematical model for calculations. Ducted coaxial-rotors aircraft was taken as an example and Fluent software was applied to the virtual prototype simulations. Through simulation sample points, the total lift of the ducted coaxial-rotors aircraft was obtained. The Kriging model was then constructed, and the function was fitted. Improved particle swarm optimization(PSO) was also utilized for the global optimization of the Kriging model of the ducted coaxial-rotors aircraft for the determination of optimized global coordinates. Finally, the optimized results were simulated by Fluent. The results show that the Kriging model and the improved PSO algorithm significantly improve the lift performance of ducted coaxial-rotors aircraft and computer operational efficiency.
文摘The first order reliability method (FORM) is widely adopted for structural reliability evaluation due to its numerical efficiency. Concerning the issue of FORM often failing to converge when the limit state function (LSF) behaves high nonlinearity, a new iteration scheme called "rotated gradient algorithm (RGA)" is proposed and combined with Kriging model to evaluate the reliability of implicit performance function. In this paper, the Kriging model is applied to approximate the real LSF first. Then the scheme of RGA, constructed in terms of gradient information of two adjacent design points obtained during the process of calculation, is used to calculate the reliability index. Numerical examples show the validity in convergence and accuracy of the proposed methodfor arbitrary nonlinear performance function.
基金supported by the National Social Science Found of China[Grant number 23BTJ064].
文摘Kriging models are widely employed due to their simplicity and flexibility in a variety of fields.To gain more distributional information about the unknown parameters,we focus on constructing the fiducial distribution of Kriging model parameters.To solve the challenge of constructing the fiducial marginal distribution for the spatially related parameter,we substitute the Bayesian posterior distribution for the fiducial distribution of this spatially related parameter and present a quasi-fiducial distribution for Kriging model parameters.A Gibbs sampling algorithm is given to get the samples of the quasi-fiducial distribution.Then a model selection criterion based on the quasi-fiducial distribution is proposed.Numerical studies demonstrate that the proposed method is superior to the Lasso and Elastic Net.
基金supported by the National Natural Science Foundation of China under Grant No.11871294。
文摘The main objective of this paper is to consider model averaging methods for kriging models.This paper proposes a Mallows model averaging procedure for the orthogonal kriging model and demonstrate the asymptotic optimality of the model averaging estimators in terms of mean square error.Simulation studies are conducted to evaluate the performance of the proposed method and compare it with the competitors to demonstrate its superiority.The authors also analyse a real dataset for an illustration.
基金supported by the National Natural Science Foundation of China under Grant Nos.71973116 and 12201018the Postdoctoral Project in China under Grant No.2022M720336+2 种基金the National Natural Science Foundation of China under Grant Nos.12071457 and 11971045the Beijing Natural Science Foundation under Grant No.1222002the NQI Project under Grant No.2022YFF0609903。
文摘In recent years,Kriging model has gained wide popularity in various fields such as space geology,econometrics,and computer experiments.As a result,research on this model has proliferated.In this paper,the authors propose a model averaging estimation based on the best linear unbiased prediction of Kriging model and the leave-one-out cross-validation method,with consideration for the model uncertainty.The authors present a weight selection criterion for the model averaging estimation and provide two theoretical justifications for the proposed method.First,the estimated weight based on the proposed criterion is asymptotically optimal in achieving the lowest possible prediction risk.Second,the proposed method asymptotically assigns all weights to the correctly specified models when the candidate model set includes these models.The effectiveness of the proposed method is verified through numerical analyses.
基金funded by the National Natural Science Foundation of China under Grant No.52305544the Project of Guangdong Science and Technology Innovation Strategy under Grant No.STKJ202209065.
文摘Metal powder contributes to the environmental burdens of additive manufacturing(AM)substantially.Current life cycle assessments(LCAs)of metal powders present considerable variations of lifecycle environmental inventory due to process divergence,spatial heterogeneity,or temporalfluctuation.Most importantly,the amounts of LCA studies on metal powder are limited and primarily confined to partial material types.To this end,based on the data surveyed from a metal powder supplier,this study conducted an LCA of titanium and nickel alloy produced by electrode-inducted and vacuum-inducted melting gas atomization,respectively.Given that energy consumption dominates the environmental burden of powder production and is influenced by metal materials’physical properties,we proposed a Bayesian stochastic Kriging model to estimate the energy consumption during the gas atomization process.This model considered the inherent uncertainties of training data and adaptively updated the parameters of interest when new environmental data on gas atomization were available.With the predicted energy use information of specific powder,the corresponding lifecycle environmental impacts can be further autonomously estimated in conjunction with the other surveyed powder production stages.Results indicated the environmental impact of titanium alloy powder is slightly higher than that of nickel alloy powder and their lifecycle carbon emissions are around 20 kg CO_(2)equivalency.The proposed Bayesian stochastic Kriging model showed more accurate predictions of energy consumption compared with conventional Kriging and stochastic Kriging models.This study enables data imputation of energy consumption during gas atomization given the physical properties and producing technique of powder materials.
基金fundings supported by Sichuan Science and Technology Program(2025YFHZ0065).
文摘Structural Reliability-Based Topology Optimization(RBTO),as an efficient design methodology,serves as a crucial means to ensure the development ofmodern engineering structures towards high performance,long service life,and high reliability.However,in practical design processes,topology optimization must not only account for the static performance of structures but also consider the impacts of various responses and uncertainties under complex dynamic conditions,which traditional methods often struggle accommodate.Therefore,this study proposes an RBTO framework based on a Kriging-assisted level set function and a novel Dynamic Hybrid Particle Swarm Optimization(DHPSO)algorithm.By leveraging the Kriging model as a surrogate,the high cost associated with repeatedly running finite element analysis processes is reduced,addressing the issue of minimizing structural compliance.Meanwhile,the DHPSO algorithm enables a better balance between the population’s developmental and exploratory capabilities,significantly accelerating convergence speed and enhancing global convergence performance.Finally,the proposed method is validated through three different structural examples,demonstrating its superior performance.Observed that the computational that,compared to the traditional Solid Isotropic Material with Penalization(SIMP)method,the proposed approach reduces the upper bound of structural compliance by approximately 30%.Additionally,the optimized results exhibit clear material interfaces without grayscale elements,and the stress concentration factor is reduced by approximately 42%.Consequently,the computational results fromdifferent examples verify the effectiveness and superiority of this study across various fields,achieving the goal of providing more precise optimization results within a shorter timeframe.
基金National Natural Science Foundation of China(No.52375236)Fundamental Research Funds for the Central Universities,China(No.23D110316)。
文摘In the structural reliability analysis,the first-order reliability method(FORM)often yields significant errors when addressing nonlinear problems.Although the second-order reliability method(SORM)can provide higher accuracy,the additional computation of the Hessian matrix leads to lower computational efficiency.Additionally,when the dimensionality of the random variables is high,the approximation formula of SORM can result in larger errors.To address these issues,a structural reliability analysis method based on Kriging and spherical cap area integral is proposed.Firstly,this method integrates FORM with the quasi-Newton algorithm Broyden-Fletcher-Goldfarb-Shanno(BFGS),trains the Kriging model by using sample points from the algorithm’s iteration process,and combines the Kriging model with gradient information to approximate the Hessian matrix.Then,the failure surface is approximated as a rotating paraboloid,utilizing the spherical cap to replace the complex surface.For the n-dimensional case,the hyperspherical cap area expression is combined with the integral method to calculate the failure probability.Finally,the method is validated through three examples,demonstrating improved computational accuracy and efficiency compared to traditional methods.
基金supported by the National Key Research and Development Program of China(No.2023YFB3406900)the National Natural Science Foundation of China(No.52075068).
文摘Surrogate models offer an efficient approach to tackle the computationally intensive evaluation of performance functions in reliability analysis.Nevertheless,the approximations inherent in surrogate models necessitate the consideration of surrogate model uncertainty in estimating failure probabilities.This paper proposes a new reliability analysis method in which the uncertainty from the Kriging surrogate model is quantified simultaneously.This method treats surrogate model uncertainty as an independent entity,characterizing the estimation error of failure probabilities.Building upon the probabilistic classification function,a failure probability uncertainty is proposed by integrating the difference between the traditional indicator function and the probabilistic classification function to quantify the impact of surrogate model uncertainty on failure probability estimation.Furthermore,the proposed uncertainty quantification method is applied to a newly designed reliability analysis approach termed SUQ-MCS,incorporating a proposed median approximation function for active learning.The proposed failure probability uncertainty serves as the stopping criterion of this framework.Through benchmarking,the effectiveness of the proposed uncertainty quantification method is validated.The empirical results present the competitive performance of the SUQ-MCS method relative to alternative approaches.
基金The work was financially supported by National Numerical Windtunnel(Grant No.NNW2019ZT7-B31)This research was also supported in part by the Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘Precise calculation of the trajectory of store separation is critical in assess-ing whether the store can be released safely.Store ejection is the initial stage of the releasing process and any uncertainty introduced at this stage will propagate through the whole trajectory.In this work,the impact of the uncertainties in ejector modeling on the simulation of a generic store separation is investigated by using a Monte-Carlo-based approach.To reduce the extremely large computation cost resulted from the direct use CFD in Monte Carlo simulation,the CFD solutions are represented by a time-dependent Kriging model,which is constructed at each time step by using the samples from the URANS simulations.The stochastic outputs,including the distri-bution of probability density function,expected value and 95%confidence interval of store separation trajectory,are obtained by the Monte Carlo simulations.The sensitiv-ity analysis is also carried out by using the Monte-Carlo-based method to determine the most significant variables in ejector modeling,which affect the output uncertainty.Our results show that ejector modeling is one of the main uncertainty sources of store separation simulation and the approximation in ejector modeling can cause a signifi-cant deviation,especially in the angular displacement.
文摘Multi-objective optimization of crashworthiness in automobile front-end structure was performed,and finite element model(FEM)was validated by experimental results to ensure that FEM can predict the response value with sufficient accuracy.Seven design variables and four crashworthiness indicators were defined.Through orthogonal design method,18 FEMs were established,and the response values of crashworthiness indicators were extracted.By using the variable-response specimen matrix,Kriging surrogate model(KSM)was constructed to replace FEM to refect the function correlation between variables and responses.The accuracy of KSM was also validated.Finally,the simulated annealing optimization algorithm was implemented in KSM to seek optimal and reliable solutions.Based on the optimal results and comparison analysis,the 9096-th iteration point was the optimal solution.Although the intrusion of firewall and the mass of optimal structure increased slightly,the vehicle acceleration of the optimal solution decreased by 6.9%,which fectively reduced the risk of occupant injury.
基金Defense Industrial Technology Development Program (JCKY2020204B016)National Natural Science Foundation of China (92471206)。
文摘To better complete various missions, it is necessary to plan an optimal trajectory or provide the optimal control law for the multirole missile according to the actual situation, including launch conditions and target location. Since trajectory optimization struggles to meet real-time requirements, the emergence of data-based generation methods has become a significant focus in contemporary research. However, due to the large differences in the characteristics of the optimal control laws caused by the diversity of tasks, it is difficult to achieve good prediction results by modeling all data with one single model.Therefore, the modeling idea of the mixture of experts(MoE) is adopted. Firstly, the K-means clustering algorithm is used to partition the sample data set, and the corresponding neural network classification model is established as the gate switch of MoE. Then, the expert models, i.e., the mappings from the generation conditions to the optimal control law represented by the results of principal component analysis(PCA), are represented by Kriging models. Finally, multiple rounds of accuracy evaluation, sample supplementation, and model updating are conducted to improve the generation accuracy. The Monte Carlo simulation shows that the accuracy of the proposed model reaches 96% and the generation efficiency meets the real-time requirement.
基金supported by National Natural Science Foundation of China(Nos.51905430,51608446)the Fundamental Research Fund for Central Universities(No.3102018zy011)+1 种基金the supports of Alexander von Humboldt Foundation of Germanythe Top International University Visiting Program for Outstanding Young scholars of Northwestern Polytechnical University。
文摘The application of reliability analysis and reliability sensitivity analysis methods to complicated structures faces two main challenges:small failure probability(typical less than 10-5)and time-demanding mechanical models.This paper proposes an improved active learning surrogate model method,which combines the advantages of the classical Active Kriging–Monte Carlo Simulation(AK-MCS)procedure and the Adaptive Linked Importance Sampling(ALIS)procedure.The proposed procedure can,on the one hand,adaptively produce a series of intermediate sampling density approaching the quasi-optimal Importance Sampling(IS)density,on the other hand,adaptively generate a set of intermediate surrogate models approaching the true failure surface of the rare failure event.Then,the small failure probability and the corresponding reliability sensitivity indices are efficiently estimated by their IS estimators based on the quasi-optimal IS density and the surrogate models.Compared with the classical AK-MCS and Active Kriging–Importance Sampling(AK-IS)procedure,the proposed method neither need to build very large sample pool even when the failure probability is extremely small,nor need to estimate the Most Probable Points(MPPs),thus it is computationally more efficient and more applicable especially for problems with multiple MPPs.The effectiveness and engineering applicability of the proposed method are demonstrated by one numerical test example and two engineering applications.
