Multi-scale Grids Research Articles

A Universal Generating Algorithm of the Polyhedral Discrete Grid Based on Unit Duplication

Based on the analysis of the problems in the generation algorithm of discrete grid systems domestically and abroad, a new universal algorithm for the unit duplication of a polyhedral discrete grid is proposed, and its core is “simple unit replication + effective region restriction”. First, the grid coordinate system and the corresponding spatial rectangular coordinate system are established to determine the rectangular coordinates of any grid cell node. Then, the type of the subdivision grid system to be calculated is determined to identify the three key factors affecting the grid types, which are the position of the starting point, the length of the starting edge, and the direction of the starting edge. On this basis, the effective boundary of a multiscale grid can be determined and the grid coordinates of a multiscale grid can be obtained. A one-to-one correspondence between the multiscale grids and subdivision types can be established. Through the appropriate rotation, translation and scaling of the multiscale grid, the node coordinates of a single triangular grid system are calculated, and the relationships between the nodes of different levels are established. Finally, this paper takes a hexagonal grid as an example to carry out the experiment verifications by converting a single triangular grid system (plane) directly to a single triangular grid with a positive icosahedral surface to generate a positive icosahedral surface grid. The experimental results show that the algorithm has good universality and can generate the multiscale grid of an arbitrary grid configuration by adjusting the corresponding starting transformation parameters.

Reverse time migration via frequency-adaptive multiscale spatial grids

Reverse time migration (RTM) is widely used because of its ability to recover complex geologic structures. However, RTM also has a drawback in that it requires significant computational cost. In RTM, wave modeling accounts for the largest part of the computing cost for calculating forward- and backward-propagated wavefields before applying an imaging condition. For this reason, we have applied a frequency-adaptive multiscale spatial grid to enhance the efficiency of the wave simulations. To implement wave modeling for different values of the spatial grid interval, we apply a model reduction technique, the generalized multiscale finite-element method (GMsFEM), which solves local spectral problems on a fine grid to simulate wave propagation on a coarser grid. We can enhance the speed of computation without sacrificing accuracy by using coarser grids for lower frequency waves, while applying a finer grid for higher frequency waves. In the proposed method, we can control the size of the coarse grid and level of heterogeneity of the wave solutions to tune the trade-off between speedup and accuracy. As we increase the expected level of complexity of the wave solutions, the GMsFEM wave modeling can capture more detailed features of waves. After computing the forward and backward wavefield on the coarse grid, we reproject the coarse wave solutions to the fine grid to construct the RTM gradient image. Although wave solutions are computed on a coarse grid, we still obtain the RTM images without reducing the image resolution by projecting coarse wave solutions to the fine grid. We determine the efficiency of the proposed imaging method using the Marmousi-2 model. We compare the RTM images using GMsFEM with a fixed coarse mesh and a multiple frequency-adaptive coarse meshes to indicate the image quality and computational speed of the new approach.

A new hyperparameters optimization method for convolutional neural networks

The use of convolutional neural networks involves hyperparameters optimization. Gaussian process based Bayesian optimization (GPEI) has proven to be an effective algorithm to optimize several hyperparameters. Then deep networks for global optimization algorithm (DNGO) that used neural network as an alternative to Gaussian process was proposed to optimize more hyperparameters.This paper presents a new algorithm that combines multiscale and multilevel evolutionary optimization (MSMLEO) with GPEI to optimize dozens of hyperparameters. These hyperparameters are divided into two groups. The first group related with the sizes of layers and kernels are discrete integers. The second group related with learning rates and so on is continuous floating-point numbers. All combinations of the first group are corresponding to the combinations of grid points on multi-scale grids and MSMLEO launches GPEI to optimize the second group of hyperparameters while the first group keeps fixed. The output of convolutional networks configured with above two groups of optimized hyperparameters is used as the fitness of MSMLEO. MSMLEO alternates with GPEI to search the optimal hyperparameters from coarsest scale to finest scale. Experimental results show that our algorithm has better performance and adaptability on optimizing dozens of hyperparameters of neural networks with a variety of numerical types.

A multi-core ready discrete element method with triangles using dynamically adaptive multiscale grids.

SummaryThe simulation of vast numbers of rigid bodies of non‐analytical shapes and of tremendously different sizes that collide with each other is computationally challenging. A bottleneck is the identification of all particle contact points per time step. We propose a tree‐based multilevel meta data structure to administer the particles. The data structure plus a purpose‐made tree traversal identifying the contact points introduce concurrency to the particle comparisons, whilst they keep the absolute number of particle‐to‐particle comparisons low. Furthermore, a novel adaptivity criterion allows explicit time stepping to work with comparably large time steps. It optimises both toward low algorithmic complexity per time step and low numbers of time steps. We study three different parallelisation strategies exploiting our traversal's concurrency. The fusion of two of them yields promising speedups once we rely on maximally asynchronous task‐based realisations. Our work shows that new computer architecture can push the boundary of rigid particle computability, yet if and only if the right data structures and data processing schemes are chosen.

Weakly sheared turbulent flows generated by multiscale inhomogeneous grids

A group of three multiscale inhomogeneous grids have been tested to generate different types of turbulent shear flows with different mean shear rate and turbulence intensity profiles. Cross hot-wire measurements were taken in a wind tunnel with Reynolds number$Re_{D}$of 6000–20 000, based on the width of the vertical bars of the grid and the incoming flow velocity. The effect of local drag coefficient$C_{D}$on the mean velocity profile is discussed first, and then by modifying the vertical bars to obtain a uniform aspect ratio the mean velocity profile is shown to be predictable using the local blockage ratio profile. It is also shown that, at a streamwise location$x=x_{m}$, the turbulence intensity profile along the vertical direction$u^{\prime }(y)$scales with the wake interaction length$x_{\ast ,n}^{peak}=0.21g_{n}^{2}/(\unicode[STIX]{x1D6FC}C_{D}w_{n})$($\unicode[STIX]{x1D6FC}$is a constant characterizing the incoming flow condition, and$g_{n}$,$w_{n}$are the gap and width of the vertical bars, respectively, at layer$n$) such that$(u^{\prime }/U_{n})^{2}\unicode[STIX]{x1D6FD}^{2}(C_{D}w_{n}/x_{\ast ,n}^{peak})^{-1}\sim (x_{m}/x_{\ast ,n}^{peak})^{b}$, where$\unicode[STIX]{x1D6FD}$is a constant determined by the free-stream turbulence level,$U_{n}$is the local mean velocity and$b$is a dimensionless power law constant. A general framework of grid design method based on these scalings is proposed and discussed. From the evolution of the shear stress coefficient$\unicode[STIX]{x1D70C}(x)$, integral length scale$L(x)$and the dissipation coefficient$C_{\unicode[STIX]{x1D716}}(x)$, a simple turbulent kinetic energy model is proposed that describes the evolution of our grid generated turbulence field using one centreline measurement and one vertical profile of$u^{\prime }(y)$at the beginning of the evolution. The results calculated from our model agree well with our measurements in the streamwise extent up to$x/H\approx 2.5$, where$H$is the height of the grid, suggesting that it might be possible to design some shear flows with desired mean velocity and turbulence intensity profiles by designing the geometry of a passive grid.

Turbulence Enhancement by Fractal Square Grids: Effects of Multiple Fractal Scales

Multi-scale fractal grids can be considered to mimic the fractal characteristic of objects of complex appearance in nature, such as branching pulmonary network and corals in biology, river network, trees, and cumulus clouds in geophysics, and the large-scale structure of the universe in astronomy. Understanding the role that multiple length scales have in momentum and energy transport is essential for effective utilization of fractal grids in a wide variety of engineering applications. Fractal square grids, consisted of the basic square pattern, have been used for enhancing fluid mixing as a passive flow control strategy. While previous studies have solidified the dominant effect of the largest scale, effects of the smaller scales and the interaction of the range of scales on the generated turbulent flow remain unclear. This research is to determine the relationship between the fractal scales (varying with the fractal iteration N), the turbulence statistics of the flow and the pressure drop across the fractal square grids using well-controlled water-tunnel experiments. Instantaneous and ensemble-averaged velocity fields are obtained by a planar Particle Image Velocimetry (PIV) method for a set of fractal square grids (N = 1, 2 and 4) at Reynolds number of 3400. The static pressure drop across the fractal square grid is measured by a differential pressure transducer. Flow fields indicate that the multiple jets, wakes and the shear layers produced by the multiple scales of bars are the fundamental flow physics that promote momentum transport in the fractal grid generated turbulence. The wake interaction length scale model is modified to incorporate the effects of smaller scales and thereof interaction, by the effective mesh size M e f f and an empirical coefficient β . Effectiveness of a fractal square grid is assessed using the gained turbulence intensity and Reynolds shear stress level at the cost of pressure loss, which varies with the distance downstream. In light of the promising capability of the fractal grids to enhance momentum and energy transport, this work can potentially benefit a wide variety of applications where energy efficient mixing or convective heat transfer is a key process.

Screening wells by multi-scale grids for multi-stage Markov Chain Monte Carlo simulation

For improved prediction of subsurface flows and representation of the uncertainties of geostatistical properties, we use the framework of Bayesian statistical interface in combination with the Markov Chain Monte Carlo (MCMC) method which needs many fine-scale simulations. Hence it is essential to apply cheap screening stages, such as coarse-scale simulation to remove irrelevant proposals of the generated Markov chain, reduce fine-scale computational cost and increase the acceptance rate of MCMC. We propose a screening step, that is examination of subsurface characteristics around injection/production wells, aiming at accurate breakthrough capturing as well as above mentioned efficiency goals. However this short time simulation needs fine-scale structure of the geological model around wells and running a fine-scale model is not as cheap as necessary for screening steps. On the other hand applying it on a coarse-scale model declines important data around wells and causes inaccurate results, particularly accurate breakthrough capturing which is important for prediction applications. Therefore we propose a multi-scale grid which preserves the fine-scale model around wells (as well as high permeable regions and fractures) and coarsens rest of the field and keeps efficiency and accuracy for the screening well stage and coarse-scale simulation, as well. A discrete wavelet transform is used as a powerful tool to generate the desired unstructured multi-scale grid efficiently. Finally an accepted proposal on coarse-scale models (screening well stage and coarse-scale simulation) will be assessed by fine-scale simulation. Accepted proposals are saved for prediction. Numerical results admit increment in acceptance rate, improvement in breakthrough capturing and significant reduction in computational cost by avoiding many forward simulations.

Heat transfer from a flat plate in inhomogeneous regions of grid-generated turbulence

Experiments on the convective heat transfer from a flat plate, vertically mounted and parallel to the flow in a wind tunnel, were carried out via Infra-Red thermography and hot-wire anemometry. The Reynolds number based on the inflow velocity and on the length of the plate was about 5×105. A step near the leading edge of the plate was used to promote transition to turbulence, with tripping effects on the heat transfer coefficients shown to be negligible for more than 90% of the plate’s length. Different types of grids, all with same blockage ratio σg=28%, were placed upstream of the plate to investigate their potential to enhance the turbulent heat transfer. These grids were of three classes: regular square-mesh grids (RGs), single-square grids (SSGs) and multi-scale inhomogeneous grids (MIGs). The heat transfer coefficients at the mid-length of the plate were correlated with the mean velocity and the turbulence intensity of the flow at a distance from the plate at which the ratio of the standard deviations of the streamwise and wall-normal velocity fluctuations began to increase. However, the heat transfer was shown to be insensitive to the turbulence intensity of the incoming flow in close proximity of the tripping step. Furthermore, the integral length scale of the streamwise turbulent fluctuations was found not to affect the heat transfer results, both near the tripping step and in the well-developed region on the plate. For the smallest plate-to-grid distance, the strongest heat transfer enhancement (by roughly 30%) with respect to the no-grid case was achieved with one of the SSGs. For the largest plate-to-grid distance, the only grid producing an appreciable increase (by approximately 10%) of the heat transfer was one of the MIGs. The present results demonstrate that MIG design can be optimised to maximise the overall heat transfer from the plate. A MIG that produces a uniform transverse mean shear, which is approximately preserved over significant downstream distances from the grid and with a velocity decreasing with distance from the plate, allows a sustained heat transfer enhancement, in contrast to all other grid designs tested here. The most efficient configuration for a MIG is one for which the section of the grid that has lower blockage and thicker bars is adjacent to the plate.

Effects of grid geometry on non-equilibrium dissipation in grid turbulence

A total of 11 grids in four families, including single- and multi-scale grids, are tested to investigate the development and decay characteristics of grid-generated turbulence. Special attention has been focused on dissipation and non-equilibrium characteristics in the decay region. A wide non-equilibrium region is observed for fractal square grids with three and four iterations. The distributions of the Taylor microscale λ, integral length scale Lu, and dissipation coefficient Cε show that a simple combination of large and small grids does not reproduce elongated non-equilibrium regions as realized by the fractal square grid. On the other hand, a new kind of grid, quasi-fractal grids, in which the region of the smaller fractal elements (N=2–4) of the fractal square grid is replaced by regular grids, successfully reproduce a similar flow field and non-equilibrium nature to that seen in the fractal square grid case. This suggests that the combination of large square grid and inhomogeneously arranged smaller grids produces an elongated non-equilibrium region. The dissipation coefficient Cε is better collapsed using Re0=t0U∞/ν (where t0 is the thickness of the largest grid bar, U∞ the inflow velocity, and ν the kinematic viscosity) as a global/inlet Reynolds number rather than ReM=MU∞/ν (where M is the mesh size) [P. C. Valente and J. C. Vassilicos, “Universal dissipation scaling for non-equilibrium turbulence,” Phys. Rev. Lett. 108, 214503 (2012)].

Geo-spatial Cognition on Human's Social Activity Space Based on Multi-scale Grids

Geo-spatial Cognition on Human's Social Activity Space Based on Multi-scale Grids

Evolution of turbulence and in-plane vortices in the near field flow behind multi-scale planar grids

In this experimental work, we carry out detailed two-dimensional particle image velocimetry investigations for the near field wakes behind a conventional and two multi-scale planar grids, using stitched camera fields of view. Statistical independent measurements are conducted focusing on the first few mesh distances downstream of the grid. It is found that the multiple integral length scales originated from the grids loose their importance on the turbulence development after about three mesh distances downstream, much earlier than the distance where the turbulence becomes homogeneous. The largest eddy size, represented by the integral length scales, does not show clear differences in its growth rate among the three grids after an initial development of three times the largest grid size downstream. Nevertheless, when examining individual vortex behaviours using conditional averaging and filtering processes, clear differences are found. The grids are found to have different decay rates of peak vorticity and projected vortex strengths. Despite these differences, the in-plane vorticity correlation function reveals that the mean vortex shape of all the grids shows a universal near-Gaussian pattern which does not change much as the turbulence decays.

Algebraic multiscale method for flow in heterogeneous porous media with embedded discrete fractures (F-AMS)

This paper introduces an Algebraic MultiScale method for simulation of flow in heterogeneous porous media with embedded discrete Fractures (F-AMS). First, multiscale coarse grids are independently constructed for both porous matrix and fracture networks. Then, a map between coarse- and fine-scale is obtained by algebraically computing basis functions with local support. In order to extend the localization assumption to the fractured media, four types of basis functions are investigated: (1) Decoupled-AMS, in which the two media are completely decoupled, (2) Frac-AMS and (3) Rock-AMS, which take into account only one-way transmissibilities, and (4) Coupled-AMS, in which the matrix and fracture interpolators are fully coupled. In order to ensure scalability, the F-AMS framework permits full flexibility in terms of the resolution of the fracture coarse grids. Numerical results are presented for two- and three-dimensional heterogeneous test cases. During these experiments, the performance of F-AMS, paired with ILU(0) as second-stage smoother in a convergent iterative procedure, is studied by monitoring CPU times and convergence rates. Finally, in order to investigate the scalability of the method, an extensive benchmark study is conducted, where a commercial algebraic multigrid solver is used as reference. The results show that, given an appropriate coarsening strategy, F-AMS is insensitive to severe fracture and matrix conductivity contrasts, as well as the length of the fracture networks. Its unique feature is that a fine-scale mass conservative flux field can be reconstructed after any iteration, providing efficient approximate solutions in time-dependent simulations.

Investigation on a micro-pin-fin based membrane separator

We proposed a micro-pin-fin based membrane separator. An enclosed membrane with micron scale holes was symmetrically populated in a rectangular duct. When gas phase interacts with the membrane, the gas–liquid interface cannot break through the pin-fin holes due to the increased surface energy. A two-dimensional numerical model simulated the separation process. The volume of fluid (VOF) method tracked the gas–liquid interface. Multiscale grids were used. When a bubble attacks the pin-fin membrane, strong liquid circulation occurs at the membrane entrance. Pressures in the side region are larger than those in the core region. Liquid plugs are shortened due to the pressure driven flow from side region to core region to cause the bubble coalescence. The separation length was shortened while increasing the gas flow rates. The bubble lengths were weakly influenced by gas flow rates. Liquid plugs are quickly shortened following the membrane entrance. The frictional pressure drop of the two-phase mixture in the side region was larger than that of liquids in the core region, even at low gas flow rates. The ultra-large gas flow rates yielded quite large bubble pressure to exceed the capillary pressure limit, causing the separator failure. Ultra-low and large gas flow rates specified the separator operation range.

Fabrication of Multi-Scale Grid Patterns as Deformation Carriers in Optical Methods

Multi-scale grid is an essential deformation carrier in optical methods for multi-scale deformation measurement. In this study, several new-type multi-scale grids were designed and fabricated by electron beam lithography. Each pattern includes several periodically distributed dots with the same spacing but different sizes. As a consequence, the grayscale of the whole grid pattern periodically changes. The peak parts of the grayscale generate a secondary grid, i.e., the large-scale grid. The ratio of the large-scale grid pitch to the small-scale grid pitch can be easily adjusted according to the requirement. The natural integration between the small-scale grid and the large-scale grid works well in eliminating the mutual disturbance between the different-scale grids. Besides, this type of grid has a very high success rate in fabrication owing to the small differences in size between the big dots and the small dots. The proposed multi-scale grid pattern is expected to serve as the deformation carrier in moiré methods and geometric phase analysis for multi-scale deformation measurement.

CLASH: THE CONCENTRATION-MASS RELATION OF GALAXY CLUSTERS

We present a new determination of the concentration-mass relation for galaxy clusters based on our comprehensive lensing analysis of 19 X-ray selected galaxy clusters from the Cluster Lensing and Supernova Survey with Hubble (CLASH). Our sample spans a redshift range between 0.19 and 0.89. We combine weak lensing constraints from the Hubble Space Telescope (HST) and from ground-based wide field data with strong lensing constraints from HST. The result are reconstructions of the surface-mass density for all CLASH clusters on multi-scale grids. Our derivation of NFW parameters yields virial masses between 0.53 x 10^15 and 1.76 x 10^15 M_sol/h and the halo concentrations are distributed around c_200c ~ 3.7 with a 1-sigma significant negative trend with cluster mass. We find an excellent 4% agreement between our measured concentrations and the expectation from numerical simulations after accounting for the CLASH selection function based on X-ray morphology. The simulations are analyzed in 2D to account for possible biases in the lensing reconstructions due to projection effects. The theoretical concentration-mass (c-M) relation from our X-ray selected set of simulated clusters and the c-M relation derived directly from the CLASH data agree at the 90% confidence level.

Influence of solid boundary conditions on the evolution of free and wall-bounded turbulent flows

The effect of the boundary conditions on the organization of vortex clusters is analyzed in two separate cases: rough channel flow and grid-generated turbulence. The aim is to understand how far the fluid structures are affected by the presence of roughness and the geometry of the grid. The grid-turbulence cases show that the single- and multi-scale geometries generate a flow strongly dominated by the shear at the beginning. The shear is initially caused by the presence of the body and, for the multi-scale grids, subsequently by the large differences between the scales. Further downstream from the grid these shear-dominated structures break up and form more isotropic clusters, whose dimensions seem to depend little on the particular geometry of the grid. For fractal grids, clusters are formed right downstream of the grid, resulting in a flow with less inhomogeneities than for single- and multi-scale grids. Eight different rough surfaces have been analyzed. In the smooth channel, both attached and detached clusters have been found and, depending on the geometry, the roughness affects the attached structures. Roughnesses made of aligned obstacles with a large separation seem to reduce the number of these structures in the flow. When the roughness elements are closely packed, both for transverse and aligned obstacles, the attached clusters are not able to reach within the roughness elements, and they seem to be anchored to the plane of the crests.

Multi-scale Graph-matching Based Kernel for Character Recognition from Natural Scenes

Recognizing characters extracted from natural scene images is quite challenging due to the high degree of intraclass variation. In this paper, we propose a multi-scale graph-matching based kernel for scene character recognition. In order to capture the inherently distinctive structures of characters, each image is represented by several graphs associated with multi-scale image grids. The similarity between two images is thus defined as the optimum energy by matching two graphs (images), which finds the best match for each node in the graph while also preserving the spatial consistency across adjacent nodes. The computed similarity is suitable to construct a kernel for support vector machine (SVM). Multiple kernels acquired by matching graphs with multi-scale grids are combined so that the final kernel is more robust. Experimental results on challenging Chars74k and ICDAR03-CH datasets show that the proposed method performs better than the state of the art methods.

Decay of homogeneous, nearly isotropic turbulence behind active fractal grids

The study of decaying isotropic turbulent flow is an important point of reference for turbulence theories and numerical simulations. For the past several decades, most experimental results appear to favor power-law decay with exponents between −1.2 and −1.4, approximately. More recently, studies of fractal-generated turbulence with multi-scale passive grids have shown increased Reynolds numbers and exponential or very fast power-law decays following an increase of kinetic energy close to the grid. Other recent studies have confirmed that such non-classical decay is limited to the region near the grid. In order to generate turbulence with multi-scale injection of kinetic energy at more elevated Reynolds numbers and with more spatially homogeneous distributions than available in prior experiments, we use an active-grid consisting of winglets with fractal shapes. We consider various types of fractal winglets, namely, Sierpinski triangle, space-filling squares, and Apollonian gasket type fractal shapes. Regular non-fractal winglets are also considered. Passive fractal grids are studied by keeping the winglets locked in place. Data are acquired using X-wire thermal anemometry and the decay is analyzed between 15 < x/M < 50 (M is the mesh-size). Results exhibit power-law decay with decay exponent approximately between −1.0 and −1.3. The precise values of the decay exponent and the coefficient \documentclass[12pt]{minimal}\begin{document}$C_{\epsilon }=\epsilon \ell /u_{rms}^3$\end{document}Cε=εℓ/urms3 depend on the geometry of the initial condition, although it is not possible to discern systematic or monotonic trends with respect to Reλ, component anisotropy, grid fractal dimension, or blockage ratio.

Why is multiscale exposure modeling essential to determine the burden of disease of pollution in Australia

Background Spatialized emission inventory are available for close to 300 point sources and 100 substances in Australia. To use these data to prioritize possible actions, it is essential to understand the spatial distribution of intakes and health impacts. Aims We aim a) to parameterize Pangea - a multiscale model of fate and exposure that determines spatially distribute exposures, and b) to apply the model to analyze population intakes for emission sources across Australia. Methods We first build multi-scale multi-media grids refined around each source and high population density area. Concentrations and multi-pathways exposures are calculated for test substances. We then analyze overall intakes as well as intake fractions for four source-to-receptor patterns: outback Alice Springs, suburban Sydney, Sydney and an offshore platform NW from Australia. Results Depending on source location, cumulated intake fractions of benzene vary from 2ppm in Alice Springs to 23 ppm at Sydney airport. For Alice Springs, 10% of the intake is local, 20% is at 2300 km - Sydney and Melbourne, the rest at more than 3000 km, in particular in highly populated Indonesia which is under dominant wind direction. For an emission 150km West of Sydney, 70% of the 5ppm taken in occur in Sydney. This proportion rises to 90% for emission at Sydney airport. The offshore platform has most of its impact in Indonesia. In contrast, benzo[a]pyrene impacts are primarily associated to deposition on local fields and subsequent bioconcentration in food, with highest impacts in regions of high agriculture production intensity. Maps of resulting concentrations, intake and burden of disease will be presented. Conclusions The multiscale approach models accurately spatial distribution of intake fraction while limiting calculation time. Prioritization schemes for intervention need to consider both emission sources and exposed receptors to take full advantage of spatialized emission inventories.

Recognition of Wind Speed Patterns Using Multi-Scale Subspace Grids with Decision Trees

The wind speed patterns are essential and indispensable requirement for the efficient utilization of the wind power generated by wind turbines. For this reason, this paper proposes a new approach in order to recognize the wind speed patterns from the multidimensional meteorological data. The meteorological dataset used in this study includes wind direction, air temperature, atmospheric pressure, relative humidity and wind speed parameters. Firstly, the proposed approach eliminated the dimensionality problem of the total dataset by means of obtaining the lower dimensional subspaces with the principal component analysis and the multiple discriminant analysis. Secondly, the proposed approach alleviated the problem of small sample sizes by means of achieving the coarse scales as generic rules at the lower dimensional subspaces. The total dataset includes 3244 observations for each meteorological parameter. In this study, 3100 data points were used for extracting the rules and 144 data points were utilized for testing the extracted rules. As a result, it is mined that the proposed approach leads to reveal the wind speed patterns in a usable and comprehensive manner.