A continuous random variable is expanded as a sum of a sequence of uncorrelated random variables. These variables are principal dimensions in continuous scaling on a distance function, as an extension of classic scali...A continuous random variable is expanded as a sum of a sequence of uncorrelated random variables. These variables are principal dimensions in continuous scaling on a distance function, as an extension of classic scaling on a distance matrix. For a particular distance, these dimensions are principal components. Then some properties are studied and an inequality is obtained. Diagonal expansions are considered from the same continuous scaling point of view, by means of the chi-square distance. The geometric dimension of a bivariate distribution is defined and illustrated with copulas. It is shown that the dimension can have the power of continuum.展开更多
In deep hard rock excavation, stress plays a pivotal role in inducing stress-controlled failure. While the impact of excavation-induced stress disturbance on rock failure and tunnel stability has undergone comprehensi...In deep hard rock excavation, stress plays a pivotal role in inducing stress-controlled failure. While the impact of excavation-induced stress disturbance on rock failure and tunnel stability has undergone comprehensive examination through laboratory tests and numerical simulations, its validation through insitu stress tests remains unexplored. This study analyzes the three-dimensional stress changes in the surrounding rock at various depths, monitored during the excavation of B2 Lab in China Jinping Underground Laboratory Phase Ⅱ(CJPL-Ⅱ). The investigation delves into the three-dimensional stress variation characteristics in deep hard rock, encompassing stress components and principal stress. The results indicate changes in both the magnitude and direction of the principal stress during tunnel excavation. To quantitatively describe the degree of stress disturbance, a series of stress evaluation indexes are established based on the distances between stress tensors, including the stress disturbance index(SDI), the principal stress magnitude disturbance index(SDIm), and the principal stress direction disturbance index(SDId). The SDI indicates the greatest stress disturbance in the surrounding rock is 4.5 m from the tunnel wall in B2 Lab. SDIm shows that the principal stress magnitude disturbance peaks at2.5 m from the tunnel wall. SDId reveals that the largest change in principal stress direction does not necessarily occur near the tunnel wall but at a specific depth from it. The established relationship between SDI and the depth of the excavation damaged zone(EDZ) can serve as a criterion for determining the depth of the EDZ in deep hard rock engineering. Additionally, it provides a reference for future construction and support considerations.展开更多
In response to the challenges posed by insufficient real-time performance and suboptimal matching accuracy of traditional feature matching algorithms within automotive panoramic surround view systems,this paper has pr...In response to the challenges posed by insufficient real-time performance and suboptimal matching accuracy of traditional feature matching algorithms within automotive panoramic surround view systems,this paper has proposed a high-performance dimension reduction parallel matching algorithm that integrates Principal Component Analysis(PCA)and Dual-Heap Filtering(DHF).The algorithm employs PCA to map the feature points into the lower-dimensional space and employs the square of Euclidean distance for feature matching,which significantly reduces computational complexity.To ensure the accuracy of feature matching,the algorithm utilizes Dual-Heap Filtering to filter and refine matched point pairs.To further enhance matching speed and make optimal use of computational resources,the algorithm introduces a multi-core parallel matching strategy,greatly elevating the efficiency of feature matching.Compared to Scale-Invariant Feature Transform(SIFT)and Speeded Up Robust Features(SURF),the proposed algorithm reduces matching time by 77%to 80%and concurrently enhances matching accuracy by 5%to 15%.Experimental results demonstrate that the proposed algorithmexhibits outstanding real-time matching performance and accuracy,effectivelymeeting the feature-matching requirements of automotive panoramic surround view systems.展开更多
文摘A continuous random variable is expanded as a sum of a sequence of uncorrelated random variables. These variables are principal dimensions in continuous scaling on a distance function, as an extension of classic scaling on a distance matrix. For a particular distance, these dimensions are principal components. Then some properties are studied and an inequality is obtained. Diagonal expansions are considered from the same continuous scaling point of view, by means of the chi-square distance. The geometric dimension of a bivariate distribution is defined and illustrated with copulas. It is shown that the dimension can have the power of continuum.
基金financial support for this work from the National Natural Science Foundation of China(Nos.42202320 and 42102266)the Open Project of Engineering Research Center of Phosphorus Resources Development and Utilization of Ministry of Education(No.LKF201901).
文摘In deep hard rock excavation, stress plays a pivotal role in inducing stress-controlled failure. While the impact of excavation-induced stress disturbance on rock failure and tunnel stability has undergone comprehensive examination through laboratory tests and numerical simulations, its validation through insitu stress tests remains unexplored. This study analyzes the three-dimensional stress changes in the surrounding rock at various depths, monitored during the excavation of B2 Lab in China Jinping Underground Laboratory Phase Ⅱ(CJPL-Ⅱ). The investigation delves into the three-dimensional stress variation characteristics in deep hard rock, encompassing stress components and principal stress. The results indicate changes in both the magnitude and direction of the principal stress during tunnel excavation. To quantitatively describe the degree of stress disturbance, a series of stress evaluation indexes are established based on the distances between stress tensors, including the stress disturbance index(SDI), the principal stress magnitude disturbance index(SDIm), and the principal stress direction disturbance index(SDId). The SDI indicates the greatest stress disturbance in the surrounding rock is 4.5 m from the tunnel wall in B2 Lab. SDIm shows that the principal stress magnitude disturbance peaks at2.5 m from the tunnel wall. SDId reveals that the largest change in principal stress direction does not necessarily occur near the tunnel wall but at a specific depth from it. The established relationship between SDI and the depth of the excavation damaged zone(EDZ) can serve as a criterion for determining the depth of the EDZ in deep hard rock engineering. Additionally, it provides a reference for future construction and support considerations.
基金the National Natural Science Foundation of China(61803206)the Key R&D Program of Jiangsu Province(BE2022053-2)the Nanjing Forestry University Youth Science and Technology Innovation Fund(CX2018004)for partly funding this project.
文摘In response to the challenges posed by insufficient real-time performance and suboptimal matching accuracy of traditional feature matching algorithms within automotive panoramic surround view systems,this paper has proposed a high-performance dimension reduction parallel matching algorithm that integrates Principal Component Analysis(PCA)and Dual-Heap Filtering(DHF).The algorithm employs PCA to map the feature points into the lower-dimensional space and employs the square of Euclidean distance for feature matching,which significantly reduces computational complexity.To ensure the accuracy of feature matching,the algorithm utilizes Dual-Heap Filtering to filter and refine matched point pairs.To further enhance matching speed and make optimal use of computational resources,the algorithm introduces a multi-core parallel matching strategy,greatly elevating the efficiency of feature matching.Compared to Scale-Invariant Feature Transform(SIFT)and Speeded Up Robust Features(SURF),the proposed algorithm reduces matching time by 77%to 80%and concurrently enhances matching accuracy by 5%to 15%.Experimental results demonstrate that the proposed algorithmexhibits outstanding real-time matching performance and accuracy,effectivelymeeting the feature-matching requirements of automotive panoramic surround view systems.
