In this paper we study the Freidlin-Wentzell's large deviation principle for the following nonlinear fractional stochastic heat equation driven by Gaussian noise∂/∂tu^(ε)=D_(δ)^(α)(t,x)+√εσ(u^(ε)(t,x))W(t,x...In this paper we study the Freidlin-Wentzell's large deviation principle for the following nonlinear fractional stochastic heat equation driven by Gaussian noise∂/∂tu^(ε)=D_(δ)^(α)(t,x)+√εσ(u^(ε)(t,x))W(t,x),(t,x)∈[0,T]×R,where D_(δ)^(α)is a nonlocal fractional differential operator and W is the Gaussian noise which is white in time and behaves as a fractional Brownian motion with Hurst index H satisfying 3-α/4<H<1/2,in the space variable.The weak convergence approach plays an important role.展开更多
In this work, we first derive the one-point large deviations principle (LDP) for both the stochastic Cahn–Hilliard equation with small noise and its spatial finite difference method (FDM). Then, we focus on giving th...In this work, we first derive the one-point large deviations principle (LDP) for both the stochastic Cahn–Hilliard equation with small noise and its spatial finite difference method (FDM). Then, we focus on giving the convergence of the one-point large deviations rate function (LDRF) of the spatial FDM, which is about the asymptotical limit of a parametric variational problem. The main idea for proving the convergence of the LDRF of the spatial FDM is via the Γ-convergence of objective functions. This relies on the qualitative analysis of skeleton equations of the original equation and the numerical method. In order to overcome the difficulty that the drift coefficient is not one-sided Lipschitz continuous, we derive the equivalent characterization of the skeleton equation of the spatial FDM and the discrete interpolation inequality to obtain the uniform boundedness of the solution to the underlying skeleton equation. These play important roles in deriving the T-convergence of objective functions.展开更多
The angular deviations and influential factors of Burgers orientation relationship(BOR)in Ti-6Al-4V and Ti-6.5Al-2Zr-1Mo-1V alloys were investigated by optical microscope(OM),scanning electron microscope(SEM),electron...The angular deviations and influential factors of Burgers orientation relationship(BOR)in Ti-6Al-4V and Ti-6.5Al-2Zr-1Mo-1V alloys were investigated by optical microscope(OM),scanning electron microscope(SEM),electron backscattered diffraction(EBSD)and high-angle annular dark-field scanning transmission electron microscope(HAADF-STEM).A spherical center angle model was introduced to calculate the angular deviations from the ideal BOR between α and β phases.The results indicate thatαand β phases in α colonies of both alloys do not follow the perfect BOR during β→α phase transformation,with angular deviation values less than 3°.Through detailed microstructure characterization,the broad face of α/β interfaces viewed along two different electron incident directions shows the atomic-scale terrace-ledge structure,and many dislocations are observed within α and β phases and near α/β interfaces.Further studies reveal that the angular deviations mainly originate from lattice distortions caused by dislocations in α and β phases and lattice mismatches at α/β interfaces.展开更多
In this paper, we use sample average approximation with adaptive multiple importance sampling to explore moderate deviations for the optimal values. Utilizing the moderate deviation principle for martingale difference...In this paper, we use sample average approximation with adaptive multiple importance sampling to explore moderate deviations for the optimal values. Utilizing the moderate deviation principle for martingale differences and an appropriate Delta method, we establish a moderate deviation principle for the optimal value. Moreover, for a functional form of stochastic programming, we obtain a functional moderate deviation principle for its optimal value.展开更多
利用CMA-MESO和SWC-WARMS高分辨率模式2023年5—9月小时降水预报产品,四川自动站小时降水资料及CLDAS(CMA Land Data Assimilation System)三源融合小时降水资料,采用“点对点”和“点对面”检验方法,对两家高分辨率模式小时降水产品在...利用CMA-MESO和SWC-WARMS高分辨率模式2023年5—9月小时降水预报产品,四川自动站小时降水资料及CLDAS(CMA Land Data Assimilation System)三源融合小时降水资料,采用“点对点”和“点对面”检验方法,对两家高分辨率模式小时降水产品在四川地区的预报性能进行评估。主要结论如下:①小时降水10 mm以下和50 mm以上的极端降水,CMA-MESO的预报参考性显著优于SWC-WARMS;小时降水10~30 mm,5—6月以SWC-WARMS表现更优,7—9月则以CMA-MESO表现更佳。②空间偏差特征分析表明,两家模式的小时降水平均绝对误差空间分布整体较为一致,在盆周山区、川西高原及凉山州北部误差较大,模式误差和实况降水强度、海拔高度呈一定正相关,且SWC-WARMS的空间误差更大。③时间偏差特征分析表明,CMA-MESO的短时强降水站点频次峰值时间偏差为1~2 h,而SWC-WARMS达3~4 h。④为优化TS评分,针对CMA-MESO和SWC-WARMS模式,在空间上,预报时可分别考虑邻域半径9 km和12 km内出现对应量级降水的可能性;在时间上,对于5~30 mm小时降水,预报时可考虑预报时刻前后1 h和2 h发生的可能性,其他量级可考虑前后1 h。展开更多
声学多普勒流速剖面仪(Acoustic Doppler Current Profiler,ADCP)是目前海洋、江河流速测量的最主要仪器之一。已有对于ADCP的安装偏差分析大多是针对其安装在船上后,基阵发生偏移的安装偏差。针对5个超声换能器集成为五波束Janus结构A...声学多普勒流速剖面仪(Acoustic Doppler Current Profiler,ADCP)是目前海洋、江河流速测量的最主要仪器之一。已有对于ADCP的安装偏差分析大多是针对其安装在船上后,基阵发生偏移的安装偏差。针对5个超声换能器集成为五波束Janus结构ADCP后,由于机械加工、安装工艺造成的安装偏差,提出将安装偏差分为安装位置偏差和安装角度偏差两部分进行研究。证明了在100 m探测距离内,毫米级安装位置偏差等效于10^(-3)~10^(-2)度级安装角度偏差,得出了安装角度偏差是安装偏差中最主要部分的结论。设计了基于回波延时测距搭配高精度姿态仪的安装偏差校准方法,并通过仿真分析了校准过程中不同因素对校准精度的影响,以针对不同校准精度需求选取不同的校准环境。结果表明该校准方法有一定实用价值,可以用来对超声换能器集成为五波束Janus结构后的安装偏差进行校准。展开更多
This paper presents a small perturbation Cramer method for obtaining the large deviation principle of a family of measures (β,ε> 0) on a topological vector space. As an application, we obtain the moderate deviati...This paper presents a small perturbation Cramer method for obtaining the large deviation principle of a family of measures (β,ε> 0) on a topological vector space. As an application, we obtain the moderate deviation estimations for uniformly ergodic Markov processes.展开更多
Although machine learning models have achieved high enough accuracy in predicting shield position deviations,their“black box”nature makes the prediction mechanisms and decision-making processes opaque,leading to wea...Although machine learning models have achieved high enough accuracy in predicting shield position deviations,their“black box”nature makes the prediction mechanisms and decision-making processes opaque,leading to weaker explanations and practicability.This study introduces a novel explainable deep learning framework comprising the Informer model with enhanced attention mechanisms(EAMInfor)and deep learning important features(DeepLIFT),aimed at improving the prediction accuracy of shield position deviations and providing interpretability for predictive results.The EAMInfor model attempts to integrate channel attention,spatial attention,and simple attention modules to improve the Informer model's performance.The framework is tested with the four different geological conditions datasets generated from the Xiamen metro line 3,China.Results show that the EAMInfor model outperforms the traditional Informer and comparison models.The analysis with the DeepLIFT method indicates that the push thrust of push cylinder and the earth chamber pressure are the most significant features,while the stroke length of the push cylinder demonstrated lower importance.Furthermore,the variation trends in the significance of data points within input sequences exhibit substantial differences between single and composite strata.This framework not only improves predictive accuracy but also strengthens the credibility and reliability of the results.展开更多
Most edge-detection methods rely on calculating gradient derivatives of the potential field, a process that is easily affected by noise and is therefore of low stability. We propose a new edge-detection method named c...Most edge-detection methods rely on calculating gradient derivatives of the potential field, a process that is easily affected by noise and is therefore of low stability. We propose a new edge-detection method named correlation coefficient of multidirectional standard deviations（CCMS） that is solely based on statistics. First, we prove the reliability of the proposed method using a single model and then a combination of models. The proposed method is evaluated by comparing the results with those obtained by other edge-detection methods. The CCMS method offers outstanding recognition, retains the sharpness of details, and has low sensitivity to noise. We also applied the CCMS method to Bouguer anomaly data of a potash deposit in Laos. The applicability of the CCMS method is shown by comparing the inferred tectonic framework to that inferred from remote sensing（RS） data.展开更多
基金Partially supported by NSFC(No.11701304)the K.C.Wong Education Foundation。
文摘In this paper we study the Freidlin-Wentzell's large deviation principle for the following nonlinear fractional stochastic heat equation driven by Gaussian noise∂/∂tu^(ε)=D_(δ)^(α)(t,x)+√εσ(u^(ε)(t,x))W(t,x),(t,x)∈[0,T]×R,where D_(δ)^(α)is a nonlocal fractional differential operator and W is the Gaussian noise which is white in time and behaves as a fractional Brownian motion with Hurst index H satisfying 3-α/4<H<1/2,in the space variable.The weak convergence approach plays an important role.
基金supported by the National Natural Science Foundation of China(12201228,12171047)the Fundamental Research Funds for the Central Universities(3034011102)supported by National Key R&D Program of China(2020YFA0713701).
文摘In this work, we first derive the one-point large deviations principle (LDP) for both the stochastic Cahn–Hilliard equation with small noise and its spatial finite difference method (FDM). Then, we focus on giving the convergence of the one-point large deviations rate function (LDRF) of the spatial FDM, which is about the asymptotical limit of a parametric variational problem. The main idea for proving the convergence of the LDRF of the spatial FDM is via the Γ-convergence of objective functions. This relies on the qualitative analysis of skeleton equations of the original equation and the numerical method. In order to overcome the difficulty that the drift coefficient is not one-sided Lipschitz continuous, we derive the equivalent characterization of the skeleton equation of the spatial FDM and the discrete interpolation inequality to obtain the uniform boundedness of the solution to the underlying skeleton equation. These play important roles in deriving the T-convergence of objective functions.
基金supported by the National Natural Science Foundation of China(Nos.51971009,12002013,51831006)the Natural Science Foundation of Zhejiang Province,China(No.LZ23E010004).
文摘The angular deviations and influential factors of Burgers orientation relationship(BOR)in Ti-6Al-4V and Ti-6.5Al-2Zr-1Mo-1V alloys were investigated by optical microscope(OM),scanning electron microscope(SEM),electron backscattered diffraction(EBSD)and high-angle annular dark-field scanning transmission electron microscope(HAADF-STEM).A spherical center angle model was introduced to calculate the angular deviations from the ideal BOR between α and β phases.The results indicate thatαand β phases in α colonies of both alloys do not follow the perfect BOR during β→α phase transformation,with angular deviation values less than 3°.Through detailed microstructure characterization,the broad face of α/β interfaces viewed along two different electron incident directions shows the atomic-scale terrace-ledge structure,and many dislocations are observed within α and β phases and near α/β interfaces.Further studies reveal that the angular deviations mainly originate from lattice distortions caused by dislocations in α and β phases and lattice mismatches at α/β interfaces.
基金Supported by the National Natural Science Foundation of China(Grant No.12071175)。
文摘In this paper, we use sample average approximation with adaptive multiple importance sampling to explore moderate deviations for the optimal values. Utilizing the moderate deviation principle for martingale differences and an appropriate Delta method, we establish a moderate deviation principle for the optimal value. Moreover, for a functional form of stochastic programming, we obtain a functional moderate deviation principle for its optimal value.
文摘声学多普勒流速剖面仪(Acoustic Doppler Current Profiler,ADCP)是目前海洋、江河流速测量的最主要仪器之一。已有对于ADCP的安装偏差分析大多是针对其安装在船上后,基阵发生偏移的安装偏差。针对5个超声换能器集成为五波束Janus结构ADCP后,由于机械加工、安装工艺造成的安装偏差,提出将安装偏差分为安装位置偏差和安装角度偏差两部分进行研究。证明了在100 m探测距离内,毫米级安装位置偏差等效于10^(-3)~10^(-2)度级安装角度偏差,得出了安装角度偏差是安装偏差中最主要部分的结论。设计了基于回波延时测距搭配高精度姿态仪的安装偏差校准方法,并通过仿真分析了校准过程中不同因素对校准精度的影响,以针对不同校准精度需求选取不同的校准环境。结果表明该校准方法有一定实用价值,可以用来对超声换能器集成为五波束Janus结构后的安装偏差进行校准。
文摘This paper presents a small perturbation Cramer method for obtaining the large deviation principle of a family of measures (β,ε> 0) on a topological vector space. As an application, we obtain the moderate deviation estimations for uniformly ergodic Markov processes.
基金supported by the National Natural Science Foundation of China(Grant Nos.52378392,52408356)the Foal Eagle Program Youth Top-notch Talent Project of Fujian Province,China(Grant No.00387088).
文摘Although machine learning models have achieved high enough accuracy in predicting shield position deviations,their“black box”nature makes the prediction mechanisms and decision-making processes opaque,leading to weaker explanations and practicability.This study introduces a novel explainable deep learning framework comprising the Informer model with enhanced attention mechanisms(EAMInfor)and deep learning important features(DeepLIFT),aimed at improving the prediction accuracy of shield position deviations and providing interpretability for predictive results.The EAMInfor model attempts to integrate channel attention,spatial attention,and simple attention modules to improve the Informer model's performance.The framework is tested with the four different geological conditions datasets generated from the Xiamen metro line 3,China.Results show that the EAMInfor model outperforms the traditional Informer and comparison models.The analysis with the DeepLIFT method indicates that the push thrust of push cylinder and the earth chamber pressure are the most significant features,while the stroke length of the push cylinder demonstrated lower importance.Furthermore,the variation trends in the significance of data points within input sequences exhibit substantial differences between single and composite strata.This framework not only improves predictive accuracy but also strengthens the credibility and reliability of the results.
基金supported by the National Hi-Tech Research and Development Program of China(863 Program)(No.2006AA06Z107)the National Natural Science Foundation of China(No.40930314)
文摘Most edge-detection methods rely on calculating gradient derivatives of the potential field, a process that is easily affected by noise and is therefore of low stability. We propose a new edge-detection method named correlation coefficient of multidirectional standard deviations（CCMS） that is solely based on statistics. First, we prove the reliability of the proposed method using a single model and then a combination of models. The proposed method is evaluated by comparing the results with those obtained by other edge-detection methods. The CCMS method offers outstanding recognition, retains the sharpness of details, and has low sensitivity to noise. We also applied the CCMS method to Bouguer anomaly data of a potash deposit in Laos. The applicability of the CCMS method is shown by comparing the inferred tectonic framework to that inferred from remote sensing（RS） data.
