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Locally varying geostatistical machine learning for spatial prediction

Artificial Intelligence in Geosciences 2024年第1期5卷 28-45页

作者： Francky Fouedjio Emet Arya Rio Tinto Data&Analytics152-158 St Georges TerracePerthWA 6000Australia Kaplan Business School Pty Ltd Perth Campus1325 Hay StWest PerthWA6005Australia Edith Cowan University School of Science270 Joondalup DriveJoondalupWA 6027Australia

Machine learning methods dealing with the spatial auto-correlation of the response variable have garnered significant attention in the context of spatial ***,under these methods,the relationship between the response variable and explanatory variables is assumed to be homogeneous throughout the entire study *** assumption,known as spatial stationarity,is very questionable in real-world situations due to the influence of contextual ***,allowing the relationship between the target variable and predictor variables to vary spatially within the study region is more ***,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 ***,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 *** 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 *** 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 *** proposed method’s effectiveness is showcased via experiments conducted on synthetic spatial data with known characteristics as well as real-world spatial *** the synthetic(***)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-correla

关键词： Data augmentation Geostatistics Local stationarity Machine learning Conditional simulation spatial auto-correlation spatial non-stationarity spatial uncertainty

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An interval finite element method for electromagnetic problems with spatially uncertain parameters

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Science China(Technological Sciences) 2020年第1期63卷 25-43页

作者： WANG ZhongHua JIANG Chao NI BingYu WANG CongSi ZHONG JianFeng FANG Teng State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body College of Mechanical and Vehicle EngineeringHunan UniversityChangsha 410082China Key Laboratory of Electronic Equipment Structure Design of Ministry of Education School of Electro-Mechanical EngineeringXidian UniversityXi'an 710071China Nanjing Research Institute of Electronics Technology Nanjing 210039China

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 *** 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.

关键词： electromagnetic problems spatial uncertainty interval field model interval finite element method

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Uncertain eigenvalue analysis of the dielectric-filled waveguide by an interval vector finite element method

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Science China(Technological Sciences) 2022年第2期65卷 336-346页

作者： WANG ZhongHua JIANG Chao NI BingYu LI JinWu ZHENG Jing YAO ZhongYang State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body College of Mechanical and Vehicle EngineeringHunan UniversityChangsha 410082China

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.

关键词： dielectric-filled waveguide eigenvalue spatial uncertainty interval vector finite element method

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An interval finite element method based on bilevel Kriging model

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Chinese Journal of Aeronautics 2024年第12期37卷 1-11页

作者： Zhongyang YAO Shaohua WANG Pengge WU Bingyu NI Chao JIANG State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body College of Mechanical and Vehicle EngineeringHunan UniversityChangsha 410082China Flight Automatic Control Research Institute of AVIC Xi’an 710065China Agriculture Equipment Institute of Hunan Hunan Academy of Agricultural SciencesChangsha 410125China

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 ***,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 ***,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 *** training samples required for this surrogate model are obtained by establishing the second-level Kriging *** 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 ***,the accuracy and effectiveness of the method are verified through examples.

关键词： Interval field spatial uncertainty Kriging model Interval finite element analysis Response bounds

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