جستجوی مقالات مرتبط با کلیدواژه « Radial basis functions » در نشریات گروه « عمران »

The computational centers in the multiquadric radial basis functions meshless method have high adaptability considering the lack of geometric and physical connection between the centers. In this research, a new adaptive algorithm is proposed based on the gradients of the physical variables of the problem with the aim of creating an optimal distribution. The resulted adaptive distribution generated by this algorithm improves significantly the accuracy and speed of the multiquadric method compared to the uniform distribution in steady and unsteady problems. In this approach, firstly, the domains with low and high physical variations are identified in a known time step, then the number of computational centers decreases and increases in these areas, respectively. Thus, the centers will be distributed more compact where needed and will be eliminated where not. Facing another important challenge of the multiquadric method, i.e. determining the optimal shape parameter, a simple and efficient method is introduced in such a way that there is no need to optimize the shape parameter at each time step and the computational costs are controlled. Finally, the effectiveness of the proposed method is shown by solving examples of diffusion, convection and convection-diffusion equations. The results are compared to their uniform distributions by measuring their efficiency and to the exact solution by evaluating the accuracy.

The Multiquadric Radial Basis Function (MQ-RBF) method, despite its advantages, has not yet been developed to be used for Dam-Reservoir-Foundation Interaction (DRFI) problems. In this study, this mesh-less method was developed for solving the DRFI systems in the frequency domain. A new domain decomposition technique was also used for analyzing dynamic interaction problems for the first time in MQ-RBF. In this regard, the computational domain is divided into dam, reservoir, and foundation subdomains. Then, the MQ-RBF method is separately applied to each subdomain. For applying the dynamic interaction between two adjacent subdomains, two Multiquadric shape functions must be considered for each computational center on their interaction boundary. Besides, each shape function is also defined using the computational centers in the subdomain. One of the important challenging issues in RBFs is the determination of the Optimal Shape Parameter (OSP). Thereafter, some new relations in terms of the earthquake frequencies are proposed for the OSPs in different cases of the interaction systems. In this regard, a few frequency magnitudes were considered and, consequently, different relations were presented for all frequencies using the obtained OSPs. It is found that, the OSP does not depend on the shear modulus of neither the dam nor the foundation. Moreover, the OSP value are not sensitive to the fluid compressibility and do not depend on the number of subdomains. Apparently, these properties reduce the computational costs and facilitate the MQ-RBF application. In order to validate the capabilities of the approach, nine numerical examples are solved in which the Roots Mean Square Error (RMSE) criterion has been evaluated for comparing the results with those of the exact and FD methods. Results show that the proposed method is of acceptable accuracy, i.e. more accurate than FD even with much more FD computational nodes. Also, it is shown that the errors increase by increasing the earthquake frequency value while the FD errors seem to be unacceptable in frequency values close to the resonance frequency, unlike those of the MQ-RBF.

Porous materials are widely applied in different engineering fields such as chemical engineering, materials engineering, environmental geomechanics, biomechanics, soil structure interaction and geomechanics. For this reason, dynamic and static analysis of the stress and strain of structures and continuum made of these materials have attracted the attention of researchers. To analyze these structures, numerical methods are required due to the fact that the governing equations are complicated. The meshless method was well implied for many structural problems in recent decades. In this method, the scattered nodes with regular or irregular distributions are used to discretize the field functions in local sub-domains. Because of using the nodes rather than the elements, the application of meshless method in some problems yields to more accurate results. To interpolate the fields' variables in terms of its nodal values, the radial point interpolation method (RPIM) with radial basis function (RBF) is used. The radial point interpolation method (RPIM) is employed to construct the shape functions. Because of the fact the interpolation function type affects the results of meshless approach, various interpolation functions are investigated. Then, the most proper one is selected for analyzing the porous material structure. To verify the presented method, the result of cylinders made of saturated porous materials using MLPG method under dynamic loading is compared to the analytical results. A good agreement between the presented method and analytical result is achieved. It is worthwhile to mention that damping should be included in dynamic analysis. Hence, the modeling of damping effect on the behavior of porous material is conducted. According to the obtained results, for the usual damping ratios of the porous materials, increasing the damping ratio leads to reduction in the displacement amplitude and stress. Also, it is observed that the period of the porous material are independent from its damping ratio.

Management and exploitation in mines require a continuous and relatively smooth surface of the mineral grades. While assessing the various mineral elements, the scattered exploratory cavities are irregularly excavated. Producing a continuous surface from measured data requires interpolation methods. Several factors, including the characteristics of the data, affect the efficiency of the interpolation methods. For this reason, the efficiency of different methods in various cases is inconsistence, and choosing the appropriate interpolation method is also challenging. Interpolation methods can be categorized into two groups of mesh-based and meshless methods. Despite the efficiency and capabilities of meshless methods, they have a fundamental shortcoming due to the fixed size of the support domain. On the one hand, the distribution of exploratory cavities in mines is usually irregular, and in some areas, it is very dense, and in others, it is very sparse. On the other hand, the grade values of minerals at the surface of the region can be very variable with high changes. Conventional interpolation methods do not have sufficient efficiency and flexibility in confronting these two aforementioned issues. In this study, a precise, reliable, and flexible method is developed for interpolation of minerals through integrating the moving least squares and recursive least squares methods. In the proposed method for crack detection, the residuals statistical test of least squares computations is used.  In this method, for the central point, a continuity threshold (non-continuity) is determined based on the standard deviation of field values, so that points with crack are revealed and removed from the calculation of the value of the central point. Moreover, the size of the support domain is determined dynamically based on the recursive property of the method. In this method, an individual radius for the support domain is assigned to each central point according to the values and distributions of the surrounding field points. The dynamic size of the support domain allows a precise and reliable estimation of polynomial coefficients and the values of the central points. The efficiency of the proposed method is evaluated by applying it to simulated data as well as comparing it with the results of conventional interpolation methods on real mineral data. The results of the simulation data indicate the ability of the proposed method to reveal the non-continuity and fractures of surfaces with determining the dynamics size of the support domain based on the data structure. To compare the results of the proposed method with conventional interpolation methods including LPI, IDW, Kriging, and RBF, the root mean square error (RMSE), mean and median of errors are used. In this way, in addition to the overall accuracy of each method, the distribution of errors is also determined. The RMSE, mean and median errors of the proposed method, using the 10-fold cross-validation method for chromium (Cr), are 28.020, 0.2.201 and 2.874, respectively, and for iron (Fe) are 1.074, 0.017 and 0.094, respectively. Comparison of these results with conventional interpolation methods indicates the efficiency of the proposed method for both groups of high concentration and significant changes in the values and low concentration and almost uniform level of values. The results indicate the ability of the proposed method in detecting the jumps and non-continuity in the support domain and removal of some field points within the dynamic process, lead to a significant increase in the efficiency of the method compared to conventional methods.