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Continuum and Atomic-Scale Finite Element Modeling of Multilayer Self-Positioning Nanostructures
Published in Sarhan M. Musa, Computational Finite Element Methods in Nanotechnology, 2013
In the least square approximations, unknown coefficients of a given set of polynomials are found by minimizing the sum of differences between nodal values with the set of polynomials. Typically, the least square approximation is a linear function fitting for a given data set, while the MLS approximate it in each partial region. Strains are obtained through differentiations of interpolation functions of displacements. In the moving least squares approximation, the displacement uh approximation at a position x is calculated as linear combination of fitting polynomial terms and their coefficients as follows: () uh(x)=pT(x)a(x)
Discrete topology optimization
Published in Sigrid Adriaenssens, Philippe Block, Diederik Veenendaal, Chris Williams, Shell Structures for Architecture, 2014
James N. Richardson, Sigrid Adriaenssens, Rajan Filomeno Coelho, Philippe Bouillard
Moving least squares (MLS) is a regression method used to approximate or interpolate a continuous function (such as a smooth surface) known only at a limited set of sample points. The method uses a weighted least-squares measure, assigning a higher influence to the samples belonging to the vicinity of the point to be constructed.
A segment-based filtering method for mobile laser scanning point cloud
Published in International Journal of Image and Data Fusion, 2022
In the last decade, mobile laser scanning (MLS) is a quite new technology in which the environment is mapped by laser distance measurements from moving vehicles and transformed into a georeferenced 3D point cloud using GPS/IMU data. As a state-of-the-art technology for mapping and remote sensing, MLS can serve as an effective solution for mapping in complicated environments, such as urban environment and road corridors (Lin et al. 2013). Many mature MLS systems can be found on the market (Kaartinen et al. 2012), it could be mounted on UAV (Jaakkola et al. 2017), or based on boat (Schneider and Blaskow 2021), or even backpack wearable equipment (Comesaña-Cebral et al. 2021). So the various MLS solutions could be widely used for diversified purposes, such as road inventory (Pu et al. 2011), map update (Hwang et al. 2013), façade extraction (Jochem et al. 2011, Yang et al. 2013), building reconstruction (Frueh et al. 2005, Becker and Haala 2009), road marking extraction (Yang et al. 2012a), window extraction (Wang et al. 2012), tree extraction (Wu et al. 2013), object extraction and recognition (Golovinskiy et al. 2009, Yang et al. 2012b, Yu et al. 2013), and so on.
State-varying optimal decoupled sliding mode control for the Lorenz chaotic nonlinear problem based on HEPSO and MLS
Published in International Journal of Modelling and Simulation, 2021
Moreover, to present an optimal controller, the values of the controller gains must be tuned regarding of the system parameters. Indeed, the optimal performance of a controller highly depends on the values of the plant dynamical parameters [20,21]. In this paper, the Moving Least Squares (MLS) approximation is utilized in order to provide online optimal gains for the controller in a range of system disturbances. The MLS is one of the best techniques to interpolate the random data with an appropriate accuracy. While the nodal shape functions of the MLS approach have a very intricate nature, they always preserve completeness up to the order of the selected basis, and robustly interpolate the distributed nodal information. In fact, the MLS approach is widely utilized to approximate in problems with discrete data. For example, the approximation of parametric curves by the moving least squares method was studied by Amirfakhrian and Mafikandi [22]. The learning performance of the regularized moving least square regression was reviewed in reproducing kernel Hilbert space by Tong and Wu [23]. The piece-wise moving least squares approximation with certain localized information was introduced for scattered data to reduce the computational cost of the standard MLS method by Li et al. [24]. The complex moving least squares approximation and the associated element-free Galerkin approach was analyzed by Li and Li [25]. The MLS based numerical manifold approach was suggested to solve the dynamical problems with stationary cracks in two dimensional linear elasticity subjected to dynamic loads by Li et al. [26]. Mahmoodabadi et al. utilized the MLS approximation for interpolation of nodal values to solve three dimensional Navior stocks equations by the forward finite difference and meshless Petrov-Galerkin methods [27].