Morphological Fractal Dimension Research Articles

Research on Analog Circuit Soft Fault Diagnosis Method Based on Mathematical Morphology Fractal Dimension

It is difficult for traditional circuit-fault feature-extraction methods to accurately distinguish between nonlinear analog-circuit faults and analog-circuit faults with high fault rates and high diagnostic costs. To solve this problem, this paper proposes a method of mathematical morphology fractal dimension (VMD-MMFD) based on variational mode decomposition for soft-fault feature extraction in analog circuits. First, the signal is decomposed into variational modes to suppress the influence of environmental noise, and multiple high-dimensional eigenmode functions with different center frequencies are obtained. The fractal dimension of the signal feature information component IMF is calculated, and then, KPCA (Kernel Principal Component Analysis) is used to remove the overlapping and redundant parts of the data. The fault set obtained is used as the basis for judging the working state and the fault type of the circuit. The experimental results of the simulation circuits show that this method can be effectively used for circuit-fault diagnosis.

Online Distributed Denial of Service (DDoS) intrusion detection based on adaptive sliding window and morphological fractal dimension

Distributed Denial of Service (DDOS) attacks are important threats to network services and applications. Studies in literature have proposed various approaches including Intrusion Detection Systems (IDS) based on the application of machine learning and deep learning, but their computational cost can be significant. For this reason, other studies have proposed efficient IDS algorithms based on the online real-time analysis of the network traffic with a sliding window and entropy or other statistical measures. This paper proposes an online algorithm based on a sliding window with the novel application of the Morphological Fractal Dimension (MFD) to this problem. The results presented in this study show that the application of MFD to the recent CICIDS2017 public data set can obtain a significant improvement in the detection of the DDoS attack in comparison to entropy based approaches. In addition, this paper proposes a novel algorithm for the automatic definition of the sliding window size. This paper reports the impact of the different hyper-parameters, including the parameters present in the definition of MFD and the evaluation of the distance measures, where the Chebyschev distance provides the optimal detection accuracy. The results show a detection accuracy of 99.30%, which performs better than similar approaches on the same data set.

Superior control for physical properties of sputter deposited ITO thin-films proper for some transparent solar applications

Superior control of sputtering deposition of ITO thin-films to enhance the physical properties of the ITO thin-films has been investigated. The effect of different sputter deposition conditions and the thermal post-annealing on the physical properties of the transparent-conductive indium tin oxide (ITO) thin-films deposited on a glass substrate have been studied. The power varied from 20 to 210 W with argon (Ar) gas flowing at a rate from 20 to 80 sccm. Thermal post-annealing of deposited thin-films at 200–450 °C in vacuum and air has been carried out as well. The physical properties were monitored using XRD, STM, four-point probe electrometer, and UV–Vis spectrometer. The change of the Ar flow rates influences the deposited films surface roughness, electrical sheet resistance (Rs), average optical transmittance (Tavg) with no apparent change in the morphology fractal dimension. At the Ar flow rate of 30 sccm and the critical power of 120 W, the deposited thin-films transform from amorphous to semi-crystalline structure mostly up 170 W. Optimal thin-films with fairly the highest Tavg at 97.7% and good Rs with 158.3 Ω/sq could be obtained under a residual Ar gas flow rate of 50 sccm and at 20 W. The critical post-annealing temperature at 350 ℃ (air) and 450 °C (vacuum) could initiate the semi-crystalline structure of the previously amorphous deposited thin-films. For the first time, ITO thin-films with Tavg and Tmax up to 97.7% and 99.9% respectively have been achieved. Besides, the Rs value is controlled from 6 to 3981 Ω/sq with excellent average transparency. These prove viable candidates in transparent solar applications.

Feature extraction and identification of gas–liquid two-phase flow based on fractal theory

Due to the gas–liquid two-phase flow system with nonlinear characteristics, the fractal theory has a significant impact on nonlinear analysis, so the paper proposes applying the fractal theory to characterize the fractal characteristics of two-phase flow. Firstly, it performs the mathematical morphology fractal dimension (MMFD) to analyse the fractal dimension of typical signals, and the box-counting dimension is employed as a comparison. The results indicate that the MMFD has better accuracy in estimating the fractal dimension of the typical signals. The MMFD can reflect the complexity and nonlinear of a chaotic system; Finally, it applies the MMFD to extract features and analyse two-phase flow characteristics. The experimental results show that the MMFD can effectively identify signals of different flow patterns, especially the transitional flow pattern, and reflect the complexity of gas–liquid two phases.

Relationships between shear strength parameters and microstructure of alkaline-contaminated red clay.

The leachate (pH = 14) from alumina production changes the mechanical properties of red clay, and the shear strength parameters of the system vary due to the multiple-dimensional interactions of the microscopic parameters. In this paper, the alumina production liquid and the concentrations of the NaOH solution were designed to contaminate the red clay during 80days. The cohesion and friction angle of the alkaline-contaminated red clay were obtained from direct shear tests. Through qualitative and quantitative analyses using scanning electron microscopy (SEM), the microstructure was observed. Based on the rock engineering systems (RES) theory, interactions among microscopic parameters were analysed, and the relationships between shear strength parameters and microscopic parameters of alkaline-contaminated red clay were established. Results show that both of the cohesion and friction angle of alkaline-contaminated red clay are increased in general; the adsorption in alumina production liquid and dispersing effect of 0.7% NaOH concentration are noticeable, and the interactions of the microscopic parameters are intense; the ratio of the intra-aggregate pore number, the probability distribution index and the number of particles can significantly influence cohesion; the particle morphology fractal dimension, aspect and probability entropy have a severe effect on friction angle. This work is expected to serve as a reference for future research on the relationship between macroscopic properties and microcosmic structure of soil.

A Chaotic Feature Extraction Based on SMMF and CMMFD for Early Fault Diagnosis of Rolling Bearing

Various failure mechanisms of rolling bearing under different working conditions involve important nonlinear dynamic characteristics. And the incipient fault detection of the complex and non-stationary rolling bearing signal is difficult, especially with multiple interference source components. To address this issue, a novel fault feature extraction method which integrates chaos theory and mathematical morphology is proposed. Firstly, the smooth multi-scale morphological filtering (SMMF) is adopted to reduce the noise in chaotic rolling bearing signals without destroying its original nonlinear dynamic structure. In addition, a method of generalized estimation of morphological fractal dimension called composite multi-scale morphological fractal dimension (CMMFD) is proposed, and applied to quantify the complexity of those orbits reconstructed from rolling bearing signals. The CMMFD improves the identification ability of the original morphological fractal dimension (MFD). Then, CMMFD features are extracted from SMMF denoised signal. Different conditions of rolling bearing signals are distinguished in this feature space. Finally, the CMMFD features are input into a Hidden Markov Model (HMM) training and diagnosis to distinguish different faults of rolling bearing signals. The new diagnosis approach based on SMMF and CMMFD is compared with some existing methods in analysis of simulated signals and experimental rolling bearing signals. Accuracy and efficiency of different approaches are contrasted by analyzing the results of simulation and experiments. Comparative results demonstrate that the proposed diagnosis approach based on SMMF and CMMFD can reliably recognize different fault types at the early stage and have more accurate results.

Feature extraction of non-linearity and low noise-signal ratio signals and its application to engine fault diagnosis

Since the vibration signals of engine cylinder head come from different interference sources, it is difficult to detect weak but useful signals in the background of noise. Aiming at nonlinear and low noise characteristics of engine vibration signals, a method based on integrated empirical mode decomposition (EMD) and fractal dimension is proposed. Firstly, the integrated EMD method is used to decompose the nonlinear low noise signal into a set of intrinsic mode functions from high to low. Then the morphological fractal dimension is applied to the intrinsic mode function (IMFs). The fractal dimension of the characteristic IMF is calculated. The vibration signals of a diesel engine exhaust valve under normal and leakage conditions are analysed. The results show that this method can extract fault features of diesel engine exhaust valve.

Fracture Toughness and Fracture Surface Morphology of Concretes Modified with Selected Additives of Pozzolanic Properties

Modern methods of designing and testing concrete must be extended to appropriate material engineering approaches. It is then crucial to link the properties of concrete with its structure described in a quantitative way. The aim of the article was to present the results of research on concretes modified with three additives: Silica fume (SF), activated fluidal ash (FA), and metakaolinite (MK). The concretes were tested for compressive strength, fracture toughness (determining critical stress intensity factor KIcS and elastic modulus E). Also, stereological and fractal tests were performed. The research program covered three separate experiment plans, adopting the water/binder ratio and the additive/binder mass ratio as the independent variables. The results of experiments and their analysis proved a statistically significant relationship between fracture morphology (fractal dimension D) and concrete composition and fracture toughness. A higher fractal dimension was found in concretes with a higher content of cement paste and a lower content of additive. No significant effect of the type of additive used in the above dependence was found. An original method enabling the determination of mechanical properties of concrete with no need for destructive testing has been developed.

An Online Degradation Feature Extraction Technique for Shore Bridge Gearbox Based on Morphological Fractal Dimension and Sliding Window Weibull Fitting

Shore bridge and other port cranes have some working condition characters including high speed, heavy load, and large impact. In order to solve the degradation feature extraction issue of hoisting mechanism gearbox, an online degradation feature extraction technique based on morphological fractal dimension and sliding window Weibull fitting is proposed. Firstly, taking the vibration energy spectrum collecting from the gearbox as the online data source, the fractal dimension of the vibration energy spectrum during an analysis period is calculated and a fractal evolution curve is obtained. A three‐parameter Weibull fitting on the fractal curve within a sliding window after setting the window’s width and step size is performed. The scale parameter of the Weibull fitting model is introduced as the performance degradation feature. The effectiveness of the technique is verified by the full‐life vibration data of hoisting gearbox from Shanghai Port Group. The results show that the morphological fractal dimension is able to describe the fractal complexity of the vibration energy spectrum. The scale parameter of Weibull distribution is able to reflect the performance degradation trend of fractal curve smoothly, which lays a theoretical foundation for further solving the problem of online health assessment.

Fractal dimensions and morphological characteristics of aggregates formed in different physico-chemical and mechanical flocculation environments

Flocculation experiments were performed in a Taylor-Couette reactor in turbulent conditions characterized by the mean shear rate. A sequenced hydrodynamic protocol was applied which consists in low and high shear rates steps allowing to promote respectively aggregation and breakage processes. The particle size distribution and the 3D fractal dimension were determined on line by laser diffraction while morphological parameters were characterized off line using an automated microscope coupled with image processing. After a first aggregation-breakage cycle, the flocs formed by charge neutralization have smaller sizes than during the first aggregation step when the main aggregation mechanism is the charge neutralization whereas coarser but more resistant aggregates can be produced by bridging mechanism. During the flocculation process, high shear rates calibrate the flocs, creating small flocs having a size close to the Kolmogorov microscale. These small flocs serve as bricks to form larger flocs when lower shear rates are applied and a full reproducibility is observed after one or two cycles of the sequence depending on the aggregation mechanism. A clear correspondence was put in evidence between the shear rate conditions and the volume base mean size or fractal dimension of flocs. The morphological fractal dimension, as well as the fractal dimension derived from laser measurements, are in good agreement with the mean trend of the morphological data but cannot represent the whole diversity of floc sizes and shapes. The 3D surface base area and perimeter distributions appear as a promising tool allowing a deeper analysis of the impact of physico-chemical and shear conditions on aggregate properties during a flocculation process.

Investigation of the pore structures and fractal characteristics of marine shale reservoirs using NMR experiments and image analyses: A case study of the Lower Cambrian Niutitang Formation in northern Guizhou Province, South China

The pore structures and fractal characteristics of the organic-rich marine shales of the Lower Cambrian Niutitang Formation in northern Guizhou Province were investigated using nuclear magnetic resonance (NMR) and field emission scanning electron microscopy (FE-SEM). In this paper, the NMR fractal dimensions and pore morphology fractal dimensions were calculated based on NMR T2 spectra and SEM image analyses. The relationships among the total organic carbon (TOC) contents, mineral compositions, porosities, permeabilities, CH4 adsorptions and NMR fractal dimensions (DN1 and DN2) of the shales are discussed, and the properties of the different pores are quantitatively analyzed using pore extraction based on SEM images. Moreover, the geological significances of fractal dimensions are discussed. The results reveal that DN1 is positively correlated with TOC contents, whereas DN2 does not have an apparent relationship with TOC contents. The quartz content presents a positive linear correlation with DN1 and DN2, whereas the clay content is positively correlated with DN1 but is not correlated with DN2. DN1 increases with decreases in porosity and permeability, and DN2 increases with increases in porosity but is not correlated with permeability. The organic matter (OM) pores are smaller in size and have a larger number than the interparticle pores and intraparticle pores. The interparticle pores have the smallest average roundness values, implying that their roundness is the worst. Moreover, the fractal dimension of the OM pores is the largest, whereas the fractal dimension of the intraparticle pores is the smallest. The pore morphology fractal dimension has no apparent relationship with the roundness but shows a negative correlation with pore size. Shale samples with larger surface fractal dimensions have higher methane adsorption capacities.

Rolling bearing performance degradation condition recognition based on mathematical morphological fractal dimension and fuzzy C-means

In allusion to performance degradation condition recognition issue for rolling bearing, a method based on mathematical morphological fractal dimension (MMFD as abbreviation) and fuzzy C-means algorithm (FCM as abbreviation) is proposed in this paper. MMFD of vibrating signal is able to describe the complexity and irregularity from the perspective of fractal, its effectiveness and stability is justified by means of signal simulation. On this basis, considering fuzzy character of performance degradation condition boundary, FCM is introduced in degradation condition recognition. Rolling bearing fatigue life enhancement testing was carried out in Hangzhou Bearing Test & Research Center, the whole life data was gathered and applied in this paper, the result shows that the proposed technique of MMFD-FCM has an excellent effect.

Investigation on the surface morphology of Si3N4 ceramics by a new fractal dimension calculation method

Rotary ultrasonic grinding machining (RUGM) has been employed in Si3N4 ceramics parts machining widely, and the surface morphology is related with surface friction and wear properties directly. It is necessary to investigation on the surface morphology characterization to improve surface quality. Surface morphology of Si3N4 ceramics for rotary ultrasonic grinding machining was investigated based on fractal theory in the paper. The fractal features of surface morphology have been proved with qualitative and quantitative investigation. Differential box-counting method and peleg-blanket method was applied to calculate fractal dimension, but low calculation accuracy was found. So a new fractal dimension calculation method called perimeter-volume method has been proposed. The results show that the calculation deviation rate of morphology fractal dimension is only 2.5%. Meanwhile, the influence of spindle speed, cutting depth, feed rate and cutting force on fractal dimension has also been investigated. The investigation results provide the support for surface morphology optimization.

Influence of Textural Properties and Surface Fractal Dimensions on the Cobalt Adsorption Behavior of Rice Hull Ash Prepared via Solid Combustion

Rice hull ash was prepared via a fast chemical combustion method with ammonium nitrate, urea and milled rice hull. Urea was used as the chemical fuel. The mixture was heated to various temperatures (100 to 1000 °C), and the resulting products were compared with products obtained via calcination, in which samples were heated to the same temperatures for 2 hours. Changes in the structure, morphology, texture and surface fractal dimensions with respect to temperature were examined and found to be highly relevant for adsorption applications. The prepared powders were characterized physicochemically by X-ray diffraction and N2-physisorption measurements. The surface fractal dimensions of the prepared materials were calculated from N2-adsorptiondesorption isotherms. The results indicate that the fast combustion samples have larger surface fractal dimensions than calcined samples. A correlation between fractal dimensions and Co 2+ ion adsorption was found. The present study demonstrates the importance of textural properties and surface fractal dimensions in the adsorption performance of adsorbents.

Validation of Lepidopteran Classification by Morphological Fractal Dimension Analysis

The paper uses fractal geometry through the fractal dimension of photos of theLepidopteran species, the commonly named butterflies, collected from the regions of Central Visayas, Philippines to determine if the morphological dimensions can discriminate one species over the other for classification purposes. The images of species were converted into a binary image using the simplest form of image processing known as thresholding effect. The binary images provide a simple view and ease for computing its fractal dimension. The fractal dimension explains the space – filling property of the image. The species available for use were the Cethosia, Idea, Pachliopta, Catopsilia, Troides where 10 subspecies of each were chosen. Also, the male species were isolated and tallied separately from the females. Empirical results revealed that the fractal dimensions can differentiate the species from one another with a general p – value of 0.000 and F – value of 6.483. All sample pairwise comparisons were tested for the significant differences and still differentiates one over the other as evidenced by the corresponding p - values of all equal to 0.000, respectively. Moreover, the fractal dimensions, in relation to the species gender, were tested for possible significant differences, and findings showed that it could differentiate across butterfly’s gender with a p – value of 0.000 and F- value of 8.037. The empirical probability of wrong classification using the fractal dimension is less than 1%.

FDG uptake heterogeneity evaluated by fractal analysis improves the differential diagnosis of pulmonary nodules

PurposeThe present study aimed to determine whether fractal analysis of morphological complexity and intratumoral heterogeneity of FDG uptake can help to differentiate malignant from benign pulmonary nodules. Materials and methodsWe retrospectively analyzed data from 54 patients with suspected non-small cell lung cancer (NSCLC) who were examined by FDG PET/CT. Pathological assessments of biopsy specimens confirmed 35 and 19 nodules as NSCLC and inflammatory lesions, respectively. The morphological fractal dimension (m-FD), maximum standardized uptake value (SUVmax) and density fractal dimension (d-FD) of target nodules were calculated from CT and PET images. Fractal dimension is a quantitative index of morphological complexity and tracer uptake heterogeneity; higher values indicate increased complexity and heterogeneity. ResultsThe m-FD, SUVmax and d-FD significantly differed between malignant and benign pulmonary nodules (p<0.05). Although the diagnostic ability was better for d-FD than m-FD and SUVmax, the difference did not reach statistical significance. Tumor size correlated significantly with SUVmax (r=0.51, p<0.05), but not with either m-FD or d-FD. Furthermore, m-FD combined with either SUVmax or d-FD improved diagnostic accuracy to 92.6% and 94.4%, respectively. ConclusionThe d-FD of intratumoral heterogeneity of FDG uptake can help to differentially diagnose malignant and benign pulmonary nodules. The SUVmax and d-FD obtained from FDG-PET images provide different types of information that are equally useful for differential diagnoses. Furthermore, the morphological complexity determined by CT combined with heterogeneous FDG uptake determined by PET improved diagnostic accuracy.

Analysis of electron microscope images of soil pore structure for the study of land subsidence in centrifuge model tests of high-rise building groups

The scanning electron microscopy (SEM) images of soil pore structures were quantitatively analyzed for the study of land subsidence in the centrifuge model tests of high-rise building groups in this paper. The changes of the macrostructure and microstructure characteristics of the soils before and after centrifuge model test were studied, including the void ratio, the equivalent diameter, the circularity, the shape factor, the distribution of the orientation angle and the morphological fractal dimension of pores. The results demonstrated that the real filling rate can be estimated by 115% of the filling rate calculated by the Otsu method or be estimated by the normalized threshold of the SEM images between [0.34, 0.36]. Variations of the calculated filling rate with the adopted threshold showed the Gaussian function relationship. After the consolidation, 28.0% and 29.6% of the total pore area of the silty clay of layer No. 4 and the clayey soil of layer No. 8 were reduced, respectively, which illustrated the great compressibility and showed good agreement with the large macroscopic subsidence. The pores with radii more than 1μm occupied the vast majority of the total pore area. The fractal dimension of the pore shapes decreased after the consolidation. Considering the changes of the average eccentricity and the average shape factor, during the soil consolidation, the pores were not simply flattened but parts of the boundaries of pores were compressed to be closed, which made the shape of pores more regular.

Determination of fractal dimension of physiologically characterized neurons in two and three dimensions

Although there is a growing interest in the application of fractal analysis in neurobiology, questions about the methodology have restricted its wider application. In this report we discuss some of the underlying principles for fractal analysis, we propose the cumulative-mass method as a standard method and we extend the applicability of fractal analysis to both 2 and 3 dimensions. We have examined the relationship between the method of log-log Sholl analysis and fractal analysis and have found that they correlate well. Measurements of physiologically characterized retinal ganglion cells indicate that different cell types can have significantly different fractal dimensions. Such differences may allow the correlation of the physiological type of a neuron with its morphological fractal dimension.