Abstract: In the mining environment, tailings dam embankment is among the hazards and risk areas. The tailings dam embankment could fail and result to damages to facilities, human injuries or even fatalities. Periodic monitoring of the dam embankment is needed to help assess the safety of the tailings dam embankment. Artificial intelligence techniques such as fractals can be used to analyse the stability of the monitored dataset from survey measurement techniques. In this paper, the fractal dimension (D) was determined using D = 2-H. The Hurst parameters (H) of each monitored prism were determined by using a time domain of rescaled range programming in MATLAB software. The fractal dimensions of each monitored prism were determined based on the values of H. The results reveal that the values of the determined H were all within the threshold of 0 ≤ H ≤ 1 m. The smaller the H, the bigger the fractal dimension is. Fractal dimension values ranging from 1.359 x 10-4 m to 1.8843 x 10-3 m were obtained from the monitored prisms on the based on the tailing dam embankment dataset used. The ranges of values obtained indicate that the tailings dam embankment is stable.
Abstract: In the present work, we consider one category of curves
denoted by L(p, k, r, n). These curves are continuous arcs which are
trajectories of roots of the trinomial equation zn = αzk + (1 − α),
where z is a complex number, n and k are two integers such that
1 ≤ k ≤ n − 1 and α is a real parameter greater than 1. Denoting
by L the union of all trinomial curves L(p, k, r, n) and using the
box counting dimension as fractal dimension, we will prove that the
dimension of L is equal to 3/2.
Abstract: Soil moisture content is a key variable in many environmental sciences. Even though it represents a small proportion of the liquid freshwater on Earth, it modulates interactions between the land surface and the atmosphere, thereby influencing climate and weather. Accurate modeling of the above processes depends on the ability to provide a proper spatial characterization of soil moisture. The measurement of soil moisture content allows assessment of soil water resources in the field of hydrology and agronomy. The second parameter in interaction with the radar signal is the geometric structure of the soil. Most traditional electromagnetic models consider natural surfaces as single scale zero mean stationary Gaussian random processes. Roughness behavior is characterized by statistical parameters like the Root Mean Square (RMS) height and the correlation length. Then, the main problem is that the agreement between experimental measurements and theoretical values is usually poor due to the large variability of the correlation function, and as a consequence, backscattering models have often failed to predict correctly backscattering. In this study, surfaces are considered as band-limited fractal random processes corresponding to a superposition of a finite number of one-dimensional Gaussian process each one having a spatial scale. Multiscale roughness is characterized by two parameters, the first one is proportional to the RMS height, and the other one is related to the fractal dimension. Soil moisture is related to the complex dielectric constant. This multiscale description has been adapted to two-dimensional profiles using the bi-dimensional wavelet transform and the Mallat algorithm to describe more correctly natural surfaces. We characterize the soil surfaces and sub-surfaces by a three layers geo-electrical model. The upper layer is described by its dielectric constant, thickness, a multiscale bi-dimensional surface roughness model by using the wavelet transform and the Mallat algorithm, and volume scattering parameters. The lower layer is divided into three fictive layers separated by an assumed plane interface. These three layers were modeled by an effective medium characterized by an apparent effective dielectric constant taking into account the presence of air pockets in the soil. We have adopted the 2D multiscale three layers small perturbations model including, firstly air pockets in the soil sub-structure, and then a vegetable canopy in the soil surface structure, that is to simulate the radar backscattering. A sensitivity analysis of backscattering coefficient dependence on multiscale roughness and new soil moisture has been performed. Later, we proposed to change the dielectric constant of the multilayer medium because it takes into account the different moisture values of each layer in the soil. A sensitivity analysis of the backscattering coefficient, including the air pockets in the volume structure with respect to the multiscale roughness parameters and the apparent dielectric constant, was carried out. Finally, we proposed to study the behavior of the backscattering coefficient of the radar on a soil having a vegetable layer in its surface structure.
Abstract: In this paper, we present a neural approach for
unsupervised natural color-texture image segmentation, which is
based on both Kohonen maps and mathematical morphology, using
a combination of the texture and the image color information of the
image, namely, the fractal features based on fractal dimension are
selected to present the information texture, and the color features
presented in RGB color space. These features are then used to train
the network Kohonen, which will be represented by the underlying
probability density function, the segmentation of this map is made
by morphological watershed transformation. The performance of our
color-texture segmentation approach is compared first, to color-based
methods or texture-based methods only, and then to k-means method.
Abstract: The purpose of this study is the discrimination of 28
postmenopausal with osteoporotic femoral fractures from an agematched
control group of 28 women using texture analysis based on
fractals. Two pre-processing approaches are applied on radiographic
images; these techniques are compared to highlight the choice of the
pre-processing method. Furthermore, the values of the fractal
dimension are compared to those of the fractal signature in terms of
the classification of the two populations. In a second analysis, the
BMD measure at proximal femur was compared to the fractal
analysis, the latter, which is a non-invasive technique, allowed a
better discrimination; the results confirm that the fractal analysis of
texture on calcaneus radiographs is able to discriminate osteoporotic
patients with femoral fracture from controls. This discrimination was
efficient compared to that obtained by BMD alone. It was also
present in comparing subgroups with overlapping values of BMD.
Abstract: Applications of the Hausdorff space and its mappings
into tangent spaces are outlined, including their fractal dimensions
and self-similarities. The paper details this theory set up and further
describes virtualizations and atomization of manufacturing processes.
It demonstrates novel concurrency principles that will guide
manufacturing processes and resources configurations. Moreover,
varying levels of details may be produced by up folding and breaking
down of newly introduced generic models. This choice of layered
generic models for units and systems aspects along specific aspects
allows research work in parallel to other disciplines with the same
focus on all levels of detail. More credit and easier access are granted
to outside disciplines for enriching manufacturing grounds. Specific
mappings and the layers give hints for chances for interdisciplinary
outcomes and may highlight more details for interoperability
standards, as already worked on the international level. The new rules
are described, which require additional properties concerning all
involved entities for defining distributed decision cycles, again on the
base of self-similarity. All properties are further detailed and assigned
to a maturity scale, eventually displaying the smartness maturity of a
total shopfloor or a factory. The paper contributes to the intensive
ongoing discussion in the field of intelligent distributed
manufacturing and promotes solid concepts for implementations of
Cyber Physical Systems and the Internet of Things into
manufacturing industry, like industry 4.0, as discussed in German-speaking
countries.
Abstract: Modeling and forecasting dynamics of rainfall
occurrences constitute one of the major topics, which have been
largely treated by statisticians, hydrologists, climatologists and many
other groups of scientists. In the same issue, we propose, in the
present paper, a new hybrid method, which combines Extreme
Values and fractal theories. We illustrate the use of our methodology
for transformed Emberger Index series, constructed basing on data
recorded in Oujda (Morocco).
The index is treated at first by Peaks Over Threshold (POT)
approach, to identify excess observations over an optimal threshold u.
In the second step, we consider the resulting excess as a fractal object
included in one dimensional space of time. We identify fractal
dimension by the box counting. We discuss the prospect descriptions
of rainfall data sets under Generalized Pareto Distribution, assured by
Extreme Values Theory (EVT). We show that, despite of the
appropriateness of return periods given by POT approach, the
introduction of fractal dimension provides accurate interpretation
results, which can ameliorate apprehension of rainfall occurrences.
Abstract: BCI (Brain Computer Interface) is a communication machine that translates brain massages to computer commands. These machines with the help of computer programs can recognize the tasks that are imagined. Feature extraction is an important stage of the process in EEG classification that can effect in accuracy and the computation time of processing the signals. In this study we process the signal in three steps of active segment selection, fractal feature extraction, and classification. One of the great challenges in BCI applications is to improve classification accuracy and computation time together. In this paper, we have used student’s 2D sample t-statistics on continuous wavelet transforms for active segment selection to reduce the computation time. In the next level, the features are extracted from some famous fractal dimension estimation of the signal. These fractal features are Katz and Higuchi. In the classification stage we used ANFIS (Adaptive Neuro-Fuzzy Inference System) classifier, FKNN (Fuzzy K-Nearest Neighbors), LDA (Linear Discriminate Analysis), and SVM (Support Vector Machines). We resulted that active segment selection method would reduce the computation time and Fractal dimension features with ANFIS analysis on selected active segments is the best among investigated methods in EEG classification.
Abstract: Shot boundary detection is a fundamental step for the organization of large video data. In this paper, we propose a new method for video gradual shots detection and classification, using advantages of fractal analysis and AIS-based classifier. Proposed features are “vertical intercept" and “fractal dimension" of each frame of videos which are computed using Fourier transform coefficients. We also used a classifier based on Clonal Selection Algorithm. We have carried out our solution and assessed it according to the TRECVID2006 benchmark dataset.
Abstract: Fractal analyses of successive event of explosion
earthquake and harmonic tremor recorded at Semeru volcano were
carried out to investigate the dynamical system regarding to their
generating mechanism. The explosive eruptions accompanied by
explosion earthquakes and following volcanic tremor which are
generated by continuous emission of volcanic ash. The fractal
dimension of successive event of explosion and harmonic tremor was
estimated by Critical Exponent Method (CEM). It was found that the
method yield a higher fractal dimension of explosion earthquakes and
gradually decrease during the occurrence of harmonic tremor, and can
be considerably as correlated complexity of the source mechanism
from the variance of fractal dimension.
Abstract: This paper proposes fractal patterns for power quality
(PQ) detection using color relational analysis (CRA) based classifier.
Iterated function system (IFS) uses the non-linear interpolation in the
map and uses similarity maps to construct various fractal patterns of
power quality disturbances, including harmonics, voltage sag, voltage
swell, voltage sag involving harmonics, voltage swell involving
harmonics, and voltage interruption. The non-linear interpolation
functions (NIFs) with fractal dimension (FD) make fractal patterns
more distinguishing between normal and abnormal voltage signals.
The classifier based on CRA discriminates the disturbance events in a
power system. Compared with the wavelet neural networks, the test
results will show accurate discrimination, good robustness, and faster
processing time for detecting disturbing events.
Abstract: Semiconductor nanomaterials like TiO2 nanoparticles
(TiO2-NPs) approximately less than 100 nm in diameter have become
a new generation of advanced materials due to their novel and
interesting optical, dielectric, and photo-catalytic properties. With the
increasing use of NPs in commerce, to date few studies have
investigated the toxicological and environmental effects of NPs.
Motivated by the importance of TiO2-NPs that may contribute to the
cancer research field especially from the treatment prospective
together with the fractal analysis technique, we have investigated the
effect of TiO2-NPs on colony morphology in the dark condition
using fractal dimension as a key morphological characterization
parameter. The aim of this work is mainly to investigate the cytotoxic
effects of TiO2-NPs in the dark on the growth of human cervical
carcinoma (HeLa) cell colonies from morphological aspect. The in
vitro studies were carried out together with the image processing
technique and fractal analysis. It was found that, these colonies were
abnormal in shape and size. Moreover, the size of the control
colonies appeared to be larger than those of the treated group. The
mean Df +/- SEM of the colonies in untreated cultures was
1.085±0.019, N= 25, while that of the cultures treated with TiO2-NPs
was 1.287±0.045. It was found that the circularity of the control
group (0.401±0.071) is higher than that of the treated group
(0.103±0.042). The same tendency was found in the diameter
parameters which are 1161.30±219.56 μm and 852.28±206.50 μm
for the control and treated group respectively. Possible explanation of
the results was discussed, though more works need to be done in
terms of the for mechanism aspects. Finally, our results indicate that
fractal dimension can serve as a useful feature, by itself or in
conjunction with other shape features, in the classification of cancer
colonies.
Abstract: In this paper, we study FPGA implementation of a
novel supra-optimal receiver diversity combining technique,
generalized maximal ratio combining (GMRC), for wireless
transmission over fading channels in SIMO systems. Prior
published results using ML-detected GMRC diversity signal
driven by BPSK showed superior bit error rate performance to
the widely used MRC combining scheme in an imperfect
channel estimation (ICE) environment. Under perfect channel
estimation conditions, the performance of GMRC and MRC
were identical. The main drawback of the GMRC study was
that it was theoretical, thus successful FPGA implementation
of it using pipeline techniques is needed as a wireless
communication test-bed for practical real-life situations.
Simulation results showed that the hardware implementation
was efficient both in terms of speed and area. Since diversity
combining is especially effective in small femto- and picocells,
internet-associated wireless peripheral systems are to
benefit most from GMRC. As a result, many spinoff
applications can be made to the hardware of IP-based 4th
generation networks.
Abstract: The objective of this paper is to characterize the spontaneous Electroencephalogram (EEG) signals of four different motor imagery tasks and to show hereby a possible solution for the present binary communication between the brain and a machine ora Brain-Computer Interface (BCI). The processing technique used in this paper was the fractal analysis evaluated by the Critical Exponent Method (CEM). The EEG signal was registered in 5 healthy subjects,sampling 15 measuring channels at 1024 Hz.Each channel was preprocessed by the Laplacian space ltering so as to reduce the space blur and therefore increase the spaceresolution. The EEG of each channel was segmented and its Fractaldimension (FD) calculated. The FD was evaluated in the time interval corresponding to the motor imagery and averaged out for all the subjects (each channel). In order to characterize the FD distribution,the linear regression curves of FD over the electrodes position were applied. The differences FD between the proposed mental tasks are quantied and evaluated for each experimental subject. The obtained results of the proposed method are a substantial fractal dimension in the EEG signal of motor imagery tasks and can be considerably utilized as the multiple-states BCI applications.
Abstract: The present paper deals with problems related to the
possibilities to use fractal systems to solve some important scientific
and practical problems connected with filtering and separation of
aqueous phases from organic ones. For this purpose a special
separator have been designed. The reactor was filled with a porous
material with fractal dimension, which is an integral part of the set
for filtration and separation of emulsions. As a model emulsion
hexadecan mixture with water in equal quantities (1:1) was used. We
examined the hydrodynamics of the separation of the emulsion at
different rates of submission of the entrance of the reactor.
Abstract: Successive event of explosion earthquake and harmonic tremor recorded at Semeru volcano were analyzed to investigate the dynamical system regarding to their eruptive mechanism. The eruptive activity at Semeru volcano East Java, Indonesia is intermittent emission of ash and bombs with Strombolian style which occurred at interval of 15 to 45 minutes. The explosive eruptions accompanied by explosion earthquakes and followed by volcanic tremor which generated by continuous emission of volcanic ash. The spectral and Lyapunov exponent of successive event of explosion and harmonic tremor were analyzed. Peak frequencies of explosion earthquakes range 1.2 to 1.9 Hz and those of the harmonic tremor have peak frequency range 1.5 — 2.2 Hz. The phase space is reconstructed and evaluated based on the Lyapunov exponents. Harmonic tremors have smaller Lyapunov exponent than explosion earthquakes. It can be considerably as correlated complexity of the mechanism from the variance of spectral and fractal dimension and can be concluded that the successive event of harmonic tremor and explosions are chaotic.
Abstract: The colonic tissue is a complicated dynamic system
and the colonic activities it generates are composed of irregular
segmental waves, which are referred to as erratic fluctuations or spikes.
They are also highly irregular with subunit fractal structure. The
traditional time-frequency domain statistics like the averaged
amplitude, the motility index and the power spectrum, etc. are
insufficient to describe such fluctuations. Thus the fractal
box-counting dimension is proposed and the fractal scaling behaviors
of the human colonic pressure activities under the physiological
conditions are studied. It is shown that the dimension of the resting
activity is smaller than that of the normal one, whereas the clipped
version, which corresponds to the activity of the constipation patient,
shows with higher fractal dimension. It may indicate a practical
application to assess the colonic motility, which is often indicated by
the colonic pressure activity.
Abstract: A nucleotide sequence can be expressed as a numerical sequence when each nucleotide is assigned its proton number. A resulting gene numerical sequence can be investigated for its fractal dimension in terms of evolution and chemical properties for comparative studies. We have investigated such nucleotide fluctuation in the 16S rRNA gene of archaea thermophiles. The studied archaea thermophiles were archaeoglobus fulgidus, methanothermobacter thermautotrophicus, methanocaldococcus jannaschii, pyrococcus horikoshii, and thermoplasma acidophilum. The studied five archaea-euryarchaeota thermophiles have fractal dimension values ranging from 1.93 to 1.97. Computer simulation shows that random sequences would have an average of about 2 with a standard deviation about 0.015. The fractal dimension was found to correlate (negative correlation) with the thermophile-s optimal growth temperature with R2 value of 0.90 (N =5). The inclusion of two aracheae-crenarchaeota thermophiles reduces the R2 value to 0.66 (N = 7). Further inclusion of two bacterial thermophiles reduces the R2 value to 0.50 (N =9). The fractal dimension is correlated (positive) to the sequence GC content with an R2 value of 0.89 for the five archaea-euryarchaeota thermophiles (and 0.74 for the entire set of N = 9), although computer simulation shows little correlation. The highest correlation (positive) was found to be between the fractal dimension and di-nucleotide Shannon entropy. However Shannon entropy and sequence GC content were observed to correlate with optimal growth temperature having an R2 of 0.8 (negative), and 0.88 (positive), respectively, for the entire set of 9 thermophiles; thus the correlation lacks species specificity. Together with another correlation study of bacterial radiation dosage with RecA repair gene sequence fractal dimension, it is postulated that fractal dimension analysis is a sensitive tool for studying the relationship between genotype and phenotype among closely related sequences.
Abstract: The dispersion of heavy particles line in an isotropic
and incompressible three-dimensional turbulent flow has been
studied using the Kinematic Simulation techniques to find out the
evolution of the line fractal dimension. In this study, the fractal
dimension of the line is found for different cases of heavy particles
inertia (different Stokes numbers) in the absence of the particle
gravity with a comparison with the fractal dimension obtained in the
diffusion case of material line at the same Reynolds number. It can
be concluded for the dispersion of heavy particles line in turbulent
flow that the particle inertia affect the fractal dimension of a line
released in a turbulent flow for Stokes numbers 0.02 < St < 2. At the
beginning for small times, most of the different cases are not affected
by the inertia until a certain time, the particle response time τa, with
larger time as the particles inertia increases, the fractal dimension of
the line increases owing to the particles becoming more sensitive to
the small scales which cause the change in the line shape during its
journey.
Abstract: Biological reactions of individuals of a testing animal
to toxic substance are unique and can be used as an indication of the
existing of toxic substance. However, to distinguish such phenomenon
need a very complicate system and even more complicate to analyze
data in 3 dimensional. In this paper, a system to evaluate in vitro
biological activities to acute toxicity of stochastic self-affine
non-stationary signal of 3D goldfish swimming by using fractal
analysis is introduced. Regular digital camcorders are utilized by
proposed algorithm 3DCCPC to effectively capture and construct 3D
movements of the fish. A Critical Exponent Method (CEM) has been
adopted as a fractal estimator. The hypothesis was that the swimming
of goldfish to acute toxic would show the fractal property which
related to the toxic concentration. The experimental results supported
the hypothesis by showing that the swimming of goldfish under the
different toxic concentration has fractal properties. It also shows that
the fractal dimension of the swimming related to the pH value of FD Ôëê
0.26pH + 0.05. With the proposed system, the fish is allowed to swim
freely in all direction to react to the toxic. In addition, the trajectories
are precisely evaluated by fractal analysis with critical exponent
method and hence the results exhibit with much higher degree of
confidence.