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Study on Damage Process and Damage Degree of Recycled Aggregate Concrete Using Improved differential box-counting method and BFEM Based on Complementary Energy Principle

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INTERNATIONAL JOURNAL OF COMPUTATIONAL methodS 2025年

作者： Su, Zongming Wang, Yao Peng, Yijiang Beijing Univ Technol Key Lab Urban Secur & Disaster Engn Minist Educ Beijing 100124 Peoples R China

The quantification of the damage process and damage degree in recycled aggregate concrete (RAC) holds significant importance due to the challenges associated with capturing the initiation and propagation of internal cracks in conventional macroscopic tests. The fractal dimension can quantitatively define the irregularity of meso-damage in RAC. Based on this, the study applied the base force element method (BFEM) and the improved differential box-counting (DBC) method to analyze the damage process and damage degree in RAC. This study developed two two-dimensional models of RAC using the BFEM, both with identical circular aggregate distribution patterns. Then, the two models were subjected to uniaxial compression simulation experiment to obtain damage images at different strain stages. To analyze these images, an improved DBC method was proposed to calculate fractal dimensions. The results indicated that when reaching the ultimate strain, the fractal dimension of the 100% replacement ratio is 0.0259 higher than that of the 0% replacement ratio. The variation in fractal dimensions can be attributed to the differing damage process modes inherent in RAC, with which the growth rate of the fractal dimension significantly decreases as strain increases. The main reason is that the propagation of mesocracks in RAC exhibits fractal characteristics. Moreover, a distinct univariate cubic function relationship emerges between strain and fractal dimension, which indicates that the fractal dimension can effectively characterize the variation in strain. Finally, the severity of injury (D-si) is proposed to more intuitively and quantitatively analyze the damage process and damage degree of RAC.

关键词： Fractal dimension differential box-counting method base force element method recycled aggregate concrete damage

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An Improved differential box-counting method of Image Segmentation 7

An Improved Differential Box-counting Method of Image Segmen...

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7th International Symposium on Precision Mechanical Measurements (ISPMM)

作者： Li, Cancan Cheng, Longfei He, Tao Chen, Lang Yu, Fei Yang, Liangen Hubei Univ Technol Hubei Key Lab Modern Manufacture Qual Engn Wuhan 430068 Peoples R China Hubei Univ Technol Sch Mech Engn Wuhan 430068 Peoples R China Hubei Railway Profess Technol Coll Wuhan 430068 Peoples R China

ISBN: (纸本)9781510601673

Fractal dimension is an important quantitative characteristic of a image, which can be widely used in image analysis. differential box-counting method which is one of many calculation methods of a fractal dimension has been frequently used due to its simple calculation. In differential box-counting method, a window size M is limited in the integer power of 2. It leads to inaccurate calculation results of a fractal dimension. Aiming at solving the issues, in this paper, an improved algorithm is discussed that the window size M has been improved to be able to accommodate non-integer power of 2, and making the calculated fractal dimension error smaller. In order to verify superiority of the improved algorithm, the values of fractal dimension are regarded as parameters, and are applied for image segmentation combined with Ostu algorithm. Both traditional and improved differential box-counting methods are respectively used to estimate fractal dimensions and do threshold segmentation for a thread image. The experimental results show that image segmentation details by improved differential box-counting method are more obvious than that by traditional differential box-counting method, with less impurities, clearer target outline and better segmentation effect.

关键词： fractal dimension differential box-counting method Ostu algorithm

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Edge detection of optical subaperture image based on improved differential box-counting method

Edge detection of optical subaperture image based on improve...

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International Conference on Optical Instruments and Technology (OIT) at the Topical Meeting on Optoelectronic Imaging/Spectroscopy and Signal Processing Technology

作者： Li, Yi Hui, Mei Liu, Ming Dong, Liquan Kong, Lingqin Zhao, Yuejin Beijing Inst Technol Sch Optoelect Beijing Key Lab Precis Optoelect Measurement Inst Beijing 100081 Peoples R China

ISBN: (数字)9781510617520

ISBN: (纸本)9781510617520;9781510617513

Optical synthetic aperture imaging technology is an effective approach to improve imaging resolution. Compared with monolithic mirror system, the image of optical synthetic aperture system is often more complex at the edge, and as a result of the existence of gap between segments, which makes stitching becomes a difficult problem. So it is necessary to extract the edge of subaperture image for achieving effective stitching. Fractal dimension as a measure feature can describe image surface texture characteristics, which provides a new approach for edge detection. In our research, an improved differential box-counting method is used to calculate fractal dimension of image, then the obtained fractal dimension is mapped to grayscale image to detect edges. Compared with original differential box-counting method, this method has two improvements as follows: by modifying the box-counting mechanism, a box with a fixed height is replaced by a box with adaptive height, which solves the problem of over-counting the number of boxes covering image intensity surface;an image reconstruction method based on super-resolution convolutional neural network is used to enlarge small size image, which can solve the problem that fractal dimension can't be calculated accurately under the small size image, and this method may well maintain scale invariability of fractal dimension. The experimental results show that the proposed algorithm can effectively eliminate noise and has a lower false detection rate compared with the traditional edge detection algorithms. In addition, this algorithm can maintain the integrity and continuity of image edge in the case of retaining important edge information.

关键词： Optical subaperture Edge detection Fractal dimension differential box-counting method Super-resolution convolutional neural network

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Research on A Precise differential box-counting method of Eliminating Image Background 7

Research on A Precise Differential Box-Counting Method of El...

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7th International Symposium on Precision Mechanical Measurements (ISPMM)

作者： Lai, Kexue He, Tao Li, Cancan Zhou, Weisong Yang, Liangen Hubei Univ Technol Hubei Key Lab Modern Mfg Qual Engn Wuhan 430068 Peoples R China Hubei Univ Technol Sch Mech Engn Wuhan 430068 Peoples R China

ISBN: (纸本)9781510601673

differential box-counting (DBC) method has been widely used to calculate fractal dimension. analyzing the result of fractal dimension with background image by estimating this traditional method, we find that this algorithm has the limitation to estimate fractal dimension of images with background accurately. In order to solve this issue, in this paper, an improved differential box-counting(IDBC) method has been proposed to eliminate influence of background on fractal dimension. The mainly improved steps of IDBC as follow: firstly, the background pixels values G(b) of image need to be found out using probability. Secondly, the n(q) (n(q) is the numbers of boxes in a grid) is set to zero when the maximum and minimum in a grid are equal to image background values. To validate IDBC method's performance, we designed an experiment that the fractal dimension of both original texture images and these ones put in different size frame with black-background are estimated and compared through four different algorithms, including DBC, relevant differential box-counting (RDBC) method, shifting differential box-counting (SDBC) method and IDBC method. The experimental results demonstrate that the IDBC method developed in this work has the ability to improve the measurement accuracy by avoiding the influence caused by background.

关键词： fractal dimension differential box-counting method improved differential box-counting method

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box Height-Independent differential Bar Cumulation (DBC) for 3D Raster Surface Fractal Dimension Analysis

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JOURNAL OF GEOVISUALIZATION AND SPATIAL ANALYSIS 2025年第1期9卷 1-19页

作者： Malleswar, S. D. Isoda, Yuzuru Nakaya, Tomoki Tohoku Univ Grad Sch Sci Dept Earth Sci Sendai Japan Tohoku Univ Grad Sch Environm Studies Dept Frontier Sci Adv Environm Sendai Japan

The box-counting method is the predominant technique for calculating fractal dimensions (FD) for raster data. However, past studies focused primarily on measuring the FD of 2D binary raster. While fields like image analysis have advanced with methods such as differential box counting (DBC) to measure the FD of 3D surfaces, this approach has yet to be applied to geographical raster data, mainly due to challenges like various data depth formats, choice of box height, and type of distribution of raster values within data. In this study, we address these challenges, particularly focusing on selecting an appropriate box height which is also a methodological issue even for images. The difficulties in DBC, such as too-small and too-large box height problems, appear on finer and coarser scales of log-log plots, respectively, and there are optimal scales that represent the accurate FD somewhere in the middle. We proposed key modifications to the conventional DBC method theoretically to reduce the number of inappropriate scales due to the difficulties in DBC. To identify the effective scales in log-log plot, we introduced a novel visualization technique which can be used to detect subtle variations in log-log plots by visual inspection, aiding in the identification of box height problems and related difficulties. We applied and compared both the conventional and modified DBC method to two empirical datasets, population data and digital elevation model data, across the USA. Our results demonstrate that the log-log plots display greater consistency, and the FD values converge to a larger value as the box height decreases. The enhanced log-log plots from the results showed that there is no too-small box height problem at all, and the box height is smaller the better. Based on the empirical results, we proposed a derived method that eliminates the need for selecting a specific box height, addressing all three difficulties of DBC identified in this study. Since the derived method

关键词： Fractal dimension Raster analysis differential box-counting method Log-log plot Scale invariance

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Fractal dimension of synthesized and natural color images in Lab space

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PATTERN ANALYSIS AND APPLICATIONS 2020年第2期23卷 819-836页

作者： Panigrahy, Chinmaya Seal, Ayan Mahato, Nihar Kumar PDPM Indian Inst Informat Technol Design & Mfg Jabalpur 482005 India

Fractal dimension (FD) is a useful metric for the analysis of natural images that exhibit a high degree of complexity, randomness and irregularity in color and texture. Several approaches exist in the literature to measure FD of gray-scale images. The aim of this study is to introduce a FD estimation method for color images with color proximity in Lab space. The proposed method uses a xy-plane partitioning-shifting mechanism, where the divisors of image size are used as grid sizes. The proposed method simulates on synthesized color fractal Brownian motion (FBM) images, publicly available Brodatz database, Google color fractal images and noisy Brodatz database. The random midpoint displacement algorithm for the formation of gray-scale images is extended in this work to synthesize color FBM images. Noisy Brodatz database is obtained by adding salt-and-pepper noise with different noise densities to understand the behavior of FD. The experimental results illustrate that the proposed method is effective and efficient and outperforms the three state-of-the-art methods by observing the values of two proposed metrics, namely average error and average computed FD. A new mathematical expression for estimating FD of a color image is demonstrated, which relies on the number of edge pixels of individual color channel using multiple linear regression.

关键词： Fractal dimension differential box-counting method Fractal Brownian motion Lab color space Multiple linear regression

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Image Classification and Recognition method to Mechanical Parts Based on Fractal Dimension

Image Classification and Recognition Method to Mechanical Pa...

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International Conference on Mechanical, System and Control Engineering (ICMSC)

作者： He, Tao Yu, Kun Chen, Lang Lai, Kexue Yang, Liangen Wang, Xuanze Zhai, Zhongsheng Hubei Univ Technol Hubei Key Lab Modern Manufacture Qual Engn Wuhan 430068 Peoples R China

ISBN: (纸本)9781509065301

Complex mechanical parts have characteristics of irregularity and certain statistical self-similarity, which can be described by fractal dimension. And the values of their fractal dimension can be used as an measurement to classify and recognize the mechanical parts. In addition, the values can guide robots to grab parts. However, the image obtained by a vision system, which contains part images main image and image background will affect the calculation of fractal dimension of main images. In order to solve the problem, an improved differential box-counting method is designed in this paper. The fractal dimension of part images which has been cut and rotated can be calculated using this differential boxcounting method. The experimental result shows that the improved differential box-counting method can calculate the fractal dimension of different size-length images, and the values are more stable. The improved method solves the problem that traditional algorithm can only calculate the fractal dimension of image which side length is integer power of 2.

关键词： fractal dimension differential box-counting method background improved differential box-counting method

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Improved Image Analysis method to Evaluate Tracking Property under Successive Flashover Based on Fractal Theory

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ENERGIES 2021年第24期14卷 8253页

作者： Li, Xiaolong Cao, Chen Lin, Xin Shenyang Univ Technol Sch Elect Engn Shenyang 110870 Peoples R China

Successive flashover would result in carbonized tracking on insulator surface and cause deterioration to the insulation. Thus, investigation of the tracking can be beneficial in understanding flashover characteristics during long-term operation. In this paper, DC flashover was operated on the insulator, and the image of tracking after successive discharge were captured. Improved differential box-counting method (IDBM) was applied to analyze these images based on fractal theory. Weighted item was suggested during the counting procedure for rectangle image with margin covered by cut-size box. Fractal dimension of the tracking was calculated according to the suggested method. It is claimed that the suggested method could estimate the discharge propagation property and deterioration characteristics on the insulator surface. Moreover, IDBM showed advantages in image pre-processing and deterioration property revealed compared to traditional box-counting method attributing to the consideration of color depth. This image analysis method shows universality in dealing with tracking image and could provide additional information to flashover voltage. This paper suggested a potential approach for the investigation of discharge mechanism and corresponding deterioration in future research.

关键词： fractal dimension flashover tracking differential box-counting method insulator epoxy resin

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Fractal Analysis of Tunnel Structural Damage Caused by High-Temperature and Explosion Impact

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BUILDINGS 2022年第9期12卷 1410-1410页

作者： Yang, Zhaopeng Wang, Linbing Univ Sci & Technol Beijing Natl Ctr Mat Serv Safety Beijing 100083 Peoples R China Univ Georgia Sch Environm Civil Agr & Mech Engn Sensing & Percept Lab Athens GA 30602 USA

The tunnel is one of the most important components in modern underground engineering. Due to long and narrow shape constraints, it very easily results in large-scale fire and explosion when deflagration is caused by the accidents of vehicles that transport dangerous goods in the tunnel. Previously, the studies on the damage to tunnel lining caused by high-temperature impacts in these kinds of disasters were often limited to a discussion of only one influencing factor, either fire or explosion, but they rarely considered the two factors simultaneously. In this work, the damage properties of full-size tunnel lining induced by high temperature and impact were evaluated, and the concrete samples from the whole lining arch were selected for CT scanning. The improved differential box-counting method was used for the fractal analysis of the CT images to obtain the damage-distribution properties of the tunnel lining structure under the two coupled influencing factors: the high temperature caused by fire, and the impact caused by deflagration.

关键词： high temperature concrete impact test CT scan fractal-dimension analysis differential box-counting method

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