Machine learning methods dealing with the spatial auto-correlation of the response variable have garnered significant attention in the context of spatial prediction.Nonetheless,under these methods,the relationship bet...Machine learning methods dealing with the spatial auto-correlation of the response variable have garnered significant attention in the context of spatial prediction.Nonetheless,under these methods,the relationship between the response variable and explanatory variables is assumed to be homogeneous throughout the entire study area.This assumption,known as spatial stationarity,is very questionable in real-world situations due to the influence of contextual factors.Therefore,allowing the relationship between the target variable and predictor variables to vary spatially within the study region is more reasonable.However,existing machine learning techniques accounting for the spatially varying relationship between the dependent variable and the predictor variables do not capture the spatial auto-correlation of the dependent variable itself.Moreover,under these techniques,local machine learning models are effectively built using only fewer observations,which can lead to well-known issues such as over-fitting and the curse of dimensionality.This paper introduces a novel geostatistical machine learning approach where both the spatial auto-correlation of the response variable and the spatial non-stationarity of the regression relationship between the response and predictor variables are explicitly considered.The basic idea consists of relying on the local stationarity assumption to build a collection of local machine learning models while leveraging on the local spatial auto-correlation of the response variable to locally augment the training dataset.The proposed method’s effectiveness is showcased via experiments conducted on synthetic spatial data with known characteristics as well as real-world spatial data.In the synthetic(resp.real)case study,the proposed method’s predictive accuracy,as indicated by the Root Mean Square Error(RMSE)on the test set,is 17%(resp.7%)better than that of popular machine learning methods dealing with the response variable’s spatial auto-correlation.Additionally,this method is not only valuable for spatial prediction but also offers a deeper understanding of how the relationship between the target and predictor variables varies across space,and it can even be used to investigate the local significance of predictor variables.展开更多
Seepage refers to the flow of water through porous materials.This phenomenon has a crucial role in dam,slope,excavation,tunnel,and well design.Performing seepage analysis usually is a challenging task,as one must cope...Seepage refers to the flow of water through porous materials.This phenomenon has a crucial role in dam,slope,excavation,tunnel,and well design.Performing seepage analysis usually is a challenging task,as one must cope with the uncertainty associated with the parameters such as the hydraulic conductivity in the horizontal and vertical directions that drive this phenomenon.However,at the same time,the data on horizontal and vertical hydraulic conductivities are typically scarce in spatial resolution.In this context,so-called non-traditional approaches for uncertainty quantification(such as intervals and fuzzy variables)offer an interesting alternative to classical probabilistic methods,since they have been shown to be quite effective when limited information on the governing parameters of a phenomenon is available.Therefore,the main contribution of this study is the development of a framework for conducting seepage analysis in saturated soils,where uncertainty associated with hydraulic conductivity is characterized using fuzzy fields.This method to characterize uncertainty extends interval fields towards the domain of fuzzy numbers.In fact,it is illustrated that fuzzy fields are an effective tool for capturing uncertainties with a spatial component,since they allow one to account for available physical measurements.A case study in confined saturated soil shows that with the proposed framework,it is possible to quantify the uncertainty associated with seepage flow,exit gradient,and uplift force effectively.展开更多
Cone penetration testing(CPT)and its variant with pore pressure measurements(CPTu)are versatile tools that have been traditionally used for in situ geotechnical site investigations.These investigations are among the m...Cone penetration testing(CPT)and its variant with pore pressure measurements(CPTu)are versatile tools that have been traditionally used for in situ geotechnical site investigations.These investigations are among the most challenging yet indispensable tasks,providing a crucial reference for infrastructure planning,design and construction.However,data obtained through the CPT/CPTu testing often exhibit significant variability,even at closely spaced test points.This variability is primarily attributed to the complex mineral compositions and sedimentary process of the Quaternary sediments.Problems induced by the scattering data include the difficulties in estimating the shear strength of the sediments and determining the appropriate bearing stratum for pile foundations.In this paper,the conventional interpretation methods of the CPT/CPTu data are enhanced with sedimentary facies knowledge.The geotechnical investigation mainly involves 42 CPTu tests(39 essential data sets available)and 4 boring samples.Sediment types are interpreted from the CPTu data and calibrated by the nearby boring samples.Sedimentary facies are derived from the interpreted sequence stratigraphy,for which the interpretation skills are summarized in the form of characteristic curves of the CPTu data.Scattering distribution of the sediment types and their mechanical parameters are well explained by the sedimentary facies.The sediments are then categorized into a few groups by their sedimentary facies,resulting in reduced uncertainties and scattering in terms of shear strength.Bearing stratum of pile foundations is also suggested based on the sedimentary regulations.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
During the manufacturing process of dielectric materials used in electromagnetic engineering, the electromagnetic parameters are often spatially uncertain due to the processing technology, environmental temperature, p...During the manufacturing process of dielectric materials used in electromagnetic engineering, the electromagnetic parameters are often spatially uncertain due to the processing technology, environmental temperature, personal operations, etc. Traditionally,the random field model can be used to measure the spatial uncertainties, but its construction requires a large number of samples.On the contrary, the interval field model only needs the upper and lower bounds of the spatially uncertain parameters, which requires much less samples and furthermore is easy to understand and use for engineers. Therefore, in this paper, the interval field model is introduced to describe the spatial uncertainties of dielectric materials, and then an interval finite element method(IFEM) is proposed to calculate the upper and lower bounds of electromagnetic responses. Firstly, the interval field of the dielectric material is represented by the interval K-L expansion and inserted into the scalar Helmholtz wave equations, and thus the interval equilibrium equations are constructed according to the node-based finite element method. Secondly, a perturbation interval finite element method is developed for calculating the upper and lower bounds of electromagnetic responses such as the electric strength and magnetic strength. Finally, the effectiveness of the proposed method is verified by three numerical examples.展开更多
Eigenvalues of the dielectric-filled waveguide are of great importance to its transmission characteristic analysis and optimization design, which could be easily affected by spatially uncertain dielectric parameters. ...Eigenvalues of the dielectric-filled waveguide are of great importance to its transmission characteristic analysis and optimization design, which could be easily affected by spatially uncertain dielectric parameters. For the sake of quantifying their influence on eigenvalues of the dielectric-filled waveguide and overcoming the limitation of less samples, an interval vector finite element method(IVFEM) is proposed to acquire the lower and upper bounds of the eigenvalues with spatial uncertainty of the medium parameters. Firstly, the uncertain dielectric material properties are described by the interval field model and the corresponding interval Karhunen-Loève(K-L) approximate method. Secondly, by inserting the interval uncertainties into the constitutive relationship of the standard generalized eigenvalue equations of the dielectric-filled waveguide, an interval standard generalized eigenvalue equation is then formulated. At last, the lower and upper bounds of the eigenvalues are calculated according to the first-order perturbation method, which can be used to estimate the transmission properties of the waveguide efficiently. Three kinds of the dielectric-filled waveguides are analyzed by the proposed IVFEM and verified by Monte Carlo simulation method.展开更多
文摘Machine learning methods dealing with the spatial auto-correlation of the response variable have garnered significant attention in the context of spatial prediction.Nonetheless,under these methods,the relationship between the response variable and explanatory variables is assumed to be homogeneous throughout the entire study area.This assumption,known as spatial stationarity,is very questionable in real-world situations due to the influence of contextual factors.Therefore,allowing the relationship between the target variable and predictor variables to vary spatially within the study region is more reasonable.However,existing machine learning techniques accounting for the spatially varying relationship between the dependent variable and the predictor variables do not capture the spatial auto-correlation of the dependent variable itself.Moreover,under these techniques,local machine learning models are effectively built using only fewer observations,which can lead to well-known issues such as over-fitting and the curse of dimensionality.This paper introduces a novel geostatistical machine learning approach where both the spatial auto-correlation of the response variable and the spatial non-stationarity of the regression relationship between the response and predictor variables are explicitly considered.The basic idea consists of relying on the local stationarity assumption to build a collection of local machine learning models while leveraging on the local spatial auto-correlation of the response variable to locally augment the training dataset.The proposed method’s effectiveness is showcased via experiments conducted on synthetic spatial data with known characteristics as well as real-world spatial data.In the synthetic(resp.real)case study,the proposed method’s predictive accuracy,as indicated by the Root Mean Square Error(RMSE)on the test set,is 17%(resp.7%)better than that of popular machine learning methods dealing with the response variable’s spatial auto-correlation.Additionally,this method is not only valuable for spatial prediction but also offers a deeper understanding of how the relationship between the target and predictor variables varies across space,and it can even be used to investigate the local significance of predictor variables.
文摘Seepage refers to the flow of water through porous materials.This phenomenon has a crucial role in dam,slope,excavation,tunnel,and well design.Performing seepage analysis usually is a challenging task,as one must cope with the uncertainty associated with the parameters such as the hydraulic conductivity in the horizontal and vertical directions that drive this phenomenon.However,at the same time,the data on horizontal and vertical hydraulic conductivities are typically scarce in spatial resolution.In this context,so-called non-traditional approaches for uncertainty quantification(such as intervals and fuzzy variables)offer an interesting alternative to classical probabilistic methods,since they have been shown to be quite effective when limited information on the governing parameters of a phenomenon is available.Therefore,the main contribution of this study is the development of a framework for conducting seepage analysis in saturated soils,where uncertainty associated with hydraulic conductivity is characterized using fuzzy fields.This method to characterize uncertainty extends interval fields towards the domain of fuzzy numbers.In fact,it is illustrated that fuzzy fields are an effective tool for capturing uncertainties with a spatial component,since they allow one to account for available physical measurements.A case study in confined saturated soil shows that with the proposed framework,it is possible to quantify the uncertainty associated with seepage flow,exit gradient,and uplift force effectively.
基金supported by the National Natural Science Foundation of China(Grant Nos.42272328 and 52108356).
文摘Cone penetration testing(CPT)and its variant with pore pressure measurements(CPTu)are versatile tools that have been traditionally used for in situ geotechnical site investigations.These investigations are among the most challenging yet indispensable tasks,providing a crucial reference for infrastructure planning,design and construction.However,data obtained through the CPT/CPTu testing often exhibit significant variability,even at closely spaced test points.This variability is primarily attributed to the complex mineral compositions and sedimentary process of the Quaternary sediments.Problems induced by the scattering data include the difficulties in estimating the shear strength of the sediments and determining the appropriate bearing stratum for pile foundations.In this paper,the conventional interpretation methods of the CPT/CPTu data are enhanced with sedimentary facies knowledge.The geotechnical investigation mainly involves 42 CPTu tests(39 essential data sets available)and 4 boring samples.Sediment types are interpreted from the CPTu data and calibrated by the nearby boring samples.Sedimentary facies are derived from the interpreted sequence stratigraphy,for which the interpretation skills are summarized in the form of characteristic curves of the CPTu data.Scattering distribution of the sediment types and their mechanical parameters are well explained by the sedimentary facies.The sediments are then categorized into a few groups by their sedimentary facies,resulting in reduced uncertainties and scattering in terms of shear strength.Bearing stratum of pile foundations is also suggested based on the sedimentary regulations.
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supported by the National Science Fund for Distinguished Young Scholars(Grant No.51725502)the Major Program of National Science Foundation of China(Grant No.51490662)
文摘During the manufacturing process of dielectric materials used in electromagnetic engineering, the electromagnetic parameters are often spatially uncertain due to the processing technology, environmental temperature, personal operations, etc. Traditionally,the random field model can be used to measure the spatial uncertainties, but its construction requires a large number of samples.On the contrary, the interval field model only needs the upper and lower bounds of the spatially uncertain parameters, which requires much less samples and furthermore is easy to understand and use for engineers. Therefore, in this paper, the interval field model is introduced to describe the spatial uncertainties of dielectric materials, and then an interval finite element method(IFEM) is proposed to calculate the upper and lower bounds of electromagnetic responses. Firstly, the interval field of the dielectric material is represented by the interval K-L expansion and inserted into the scalar Helmholtz wave equations, and thus the interval equilibrium equations are constructed according to the node-based finite element method. Secondly, a perturbation interval finite element method is developed for calculating the upper and lower bounds of electromagnetic responses such as the electric strength and magnetic strength. Finally, the effectiveness of the proposed method is verified by three numerical examples.
基金supported by the National Science Fund for Distinguished Young Scholars(Grant No.51725502)the National Natural Science Foundation of China(Grant No.11802089)the National Defense Fundamental Research Foundation of China(Grant No.JCKY2020110C105)。
文摘Eigenvalues of the dielectric-filled waveguide are of great importance to its transmission characteristic analysis and optimization design, which could be easily affected by spatially uncertain dielectric parameters. For the sake of quantifying their influence on eigenvalues of the dielectric-filled waveguide and overcoming the limitation of less samples, an interval vector finite element method(IVFEM) is proposed to acquire the lower and upper bounds of the eigenvalues with spatial uncertainty of the medium parameters. Firstly, the uncertain dielectric material properties are described by the interval field model and the corresponding interval Karhunen-Loève(K-L) approximate method. Secondly, by inserting the interval uncertainties into the constitutive relationship of the standard generalized eigenvalue equations of the dielectric-filled waveguide, an interval standard generalized eigenvalue equation is then formulated. At last, the lower and upper bounds of the eigenvalues are calculated according to the first-order perturbation method, which can be used to estimate the transmission properties of the waveguide efficiently. Three kinds of the dielectric-filled waveguides are analyzed by the proposed IVFEM and verified by Monte Carlo simulation method.
