PATTERN RECOGNITION OF MINE MICROSEISMIC AND BLASTING EVENTS BASED ON WAVE FRACTAL FEATURES

A microseismic (MS) monitoring system in a mine can monitor the MS signals generated by coal rock rupture and blasting waves and can distinguish the two types of waves more clearly to monitor and analyze the rupture and evolution process of coal rock. According to the nonlinearity characteristics of the waveform, the fractal characteristics of a mine’s MS and blasting waves are analyzed by simple fractal and multifractal theory, and the simple fractal dimension [Formula: see text] and multifractal parameters are obtained, respectively. Results show that the simple fractal dimension [Formula: see text] reflects the complexity and frequency structure of the wave. The simple fractal dimension [Formula: see text] of a blasting wave is larger than that of a mine MS wave, which indicates that the blasting wave is relatively complex with higher frequency, while the mine MS wave is relatively simple with lower frequency. However, the simple fractal dimension [Formula: see text] can only describe the wave integrity features, not the local features. The multifractal parameters can describe the local characteristics of the wave more finely, and the multifractal spectrum describes the probability information of the singularity exponent [Formula: see text]. The singularity exponential range and multifractal spectral width [Formula: see text] of the blasting wave are smaller than those of the mine MS wave, which indicates that the probability measure of distribution unevenness and the degree of partial parameter fluctuation of the blasting wave are more severe than those of the mine MS wave. Wave signal analysis based on simple fractal and multifractal methods can not only obtain the characteristics of the wave strength and spectral structure but also other important information, such as local singularity. Therefore, it is possible to more clearly and conspicuously identify mine MS and blasting waves, so that coal rock rupture can be monitored more accurately.

The Effect of the Free Surface on the Singular Stress Field at the Fatigue Crack Front

Description of stress singularity in the vicinity of a free surface is presented. Its presence causes the retardation of the fatigue crack growth in that region and fatigue crack is being curved. Numerical model is used to study dependence of the stress singularity exponent on Poisson’s ratio. Estimated values are compared to those already published. Experimentally measured angles of fatigue crack on SENB specimens confirm the relation between Poisson’s ratio and the angle between crack front and free surface.

EXPERIMENTAL STUDY ON THE MULTIFRACTAL EVOLUTION OF FRICTION TEMPERATURE

The experiments were performed by sliding a pin against a plate under lubricated sliding condition. The friction temperature signal was measured by a thermocouple through the wear life. The multifractal spectrum was utilized to study the dynamic evolution of the friction temperature. The width of the multifractal spectrum, [Formula: see text], and the difference between the fractal dimensions of the subset with the largest singularity exponent and that with the smallest singularity exponent, [Formula: see text], are computed for qualitative analysis. The results demonstrate that the friction temperature signal possesses multifractal properties. In the running-in period, both [Formula: see text] and [Formula: see text] decrease gradually, and the spectrum changes from a wide, hook-like shape to a narrow, bell-like shape. In the steady state, [Formula: see text] maintains at a small value, [Formula: see text] fluctuates slightly around 0, and the narrow, bell-like shape of the spectrum persists. In the increasing friction, [Formula: see text] and [Formula: see text] increase gradually, and the spectrum changes from the narrow, bell-like shape to the wide, hook-like shape. The results provided insight into the dynamic behavior of friction system.

Multifractal and singularity analysis of weighted road networks

Road is an important element of modern traffic infrastructures in national economic construction. Accurately, road networks might be multifractal systems. The mathematics of multifractal can be used to provide a quantitative signature in many fields. The roads in this paper are endowed with weights according to their respective traffic abilities. With the aim in mind, the weighted road networks in three country-level cities (Danyang, Yangzhong and Jurong) which belong to Zhenjiang, China, are studied. We analyze the heterogeneities of the three weighted road networks with multifractal spectrum, which correspond to their socio-geographical contexts. Besides, we extract the singularity regions of three country-level cities with the annular segmentation method and the singularity exponent method, which can be helpful in further transportation planning.

Influence of the V-Notch Opening Angle on Critical Applied Force Values for the Crack Initiation from the Sharp V-Notch

The aim of this paper is to estimate a value of the critical applied force for a crack initiation from the sharp V-notch tip. The classical approach of the linear elastic fracture mechanics (LELM) was generalized, because the stress singularity exponent differs from 0.5 in studied case. The value of the stress singularity exponent depends on the V-notch opening angle. The finite element method was used for a determination of stress distribution in the vicinity of the sharp V-notch tip and for the estimation of the generalized stress intensity factor depending on the V-notch opening angle. Critical value of generalized stress intensity factor was obtained by using stability criterion based on the tangential stress component averaged over a critical distancedfrom the V-notch tip. Calculated values of the critical applied force were compared with experimental data taken from the literature.

Critical Value for Crack Propagation from Sharp V-Notch

The contribution is focused on estimation of a critical value of generalized stress intensity factor for crack propagation from sharp V-notches. Stress distribution around the tip of the V-notch is described on the base of generalized linear elastic fracture mechanics, because V-notch is a singular stress concentrator with stress singularity exponent different from 0.5 (depending on V-notch opening angle). Then also stability criteria based on strain energy density factor and average critical stress are generalized for the stress singularity different from 0.5. Using FE analysis the critical stresses for crack initiation was estimated and compared with experimental data from the literature.

WAVELET MULTIFRACTAL DETRENDED FLUCTUATION ANALYSIS OF ENCRYPTION AND DECRYPTION MATRICES

In this paper, we study in detail the multifractal features of the main matrices of an encryption system based on a rule-90 cellular automaton. For this purpose, we consider the scaling method known as the wavelet transform multifractal detrended fluctuation analysis (WT-MFDFA). In addition, we analyze the multifractal structure of the matrices of different dimensions, and find that there are minimal differences in all the examined multifractal quantities such as the multifractal support, the most frequent singularity exponent, and the generalized Hurst exponent.