Linear Combination Of Orthogonal Functions Research Articles

Robust topology optimization of structures under uncertain propagation of imprecise stochastic-based uncertain field

This study introduces a novel computational framework for Robust Topology Optimization (RTO) considering imprecise random field parameters. Unlike the worst-case approach, the present method provides upper and lower bounds for the mean and standard deviation of compliance as well as the optimized topological layouts of a structure for various scenarios. In the proposed approach, the imprecise random field variables are determined utilizing parameterized p-boxes with different confidence intervals. The Karhunen–Loève (K–L) expansion is extended to provide a spectral description of the imprecise random field. The linear superposition method in conjunction with a linear combination of orthogonal functions is employed to obtain explicit mathematical expressions for the first and second order statistical moments of the structural compliance. Then, an interval sensitivity analysis is carried out, applying the Orthogonal Similarity Transformation (OST) method with the boundaries of each of the intermediate variable searched efficiently at every iteration using a Combinatorial Approach (CA). Finally, the validity, accuracy, and applicability of the work are rigorously checked by comparing the outputs of the proposed approach with those obtained using the particle swarm optimization (PSO) and Quasi-Monte-Carlo Simulation (QMCS) methods. Three different numerical examples with imprecise random field loads are presented to show the effectiveness and feasibility of the study.

A Spline Finite Point Method for Nonlinear Bending Analysis of FG Plates in Thermal Environments Based on a Locking-free Thin/Thick Plate Theory

A spline finite point method (SFPM) based on a locking-free thin/thick plate theory, which is suitable for analysis of both thick and thin plates, is developed to study nonlinear bending behavior of functionally graded material (FGM) plates with different thickness in thermal environments. In the proposed method, one direction of the plate is discretized with a set of uniformly distributed spline nodes instead of meshes and the other direction is expressed with orthogonal functions determined by the boundary conditions. The displacements of the plate are constructed by the linear combination of orthogonal functions and cubic B-spline interpolation functions with high efficiency for modeling. The locking-free thin/thick plate theory used by the proposed method is based on the first-order shear deformation theory but takes the shear strains and displacements as basic unknowns. The material properties of the FG plate are assumed to vary along the thickness direction following the power function distribution. By comparing with several published research studies based on the finite element method (FEM), the correctness, efficiency, and generality of the new model are validated for rectangular plates. Moreover, uniform and nonlinear temperature rise conditions are discussed, respectively. The effect of the temperature distribution, in-plane temperature force, and elastic foundation on nonlinear bending under different parameters are discussed in detail.

The Trigonometrical Series of Fourier: A Visual Approximation

This work gives an account of the staging of a didactic proposal for the construction of the notion of Trigonometric Fourier Series (TFS), with the aim of promoting in the student that the mathematical object has meaning and significance to the engineer in training. The theoretical perspective is the social construction of knowledge, identified through the institutional and social context to the analysis of signals as a driving force of knowledge throughout the across the academic career, due to the fact that any physical phenomenon to be studied is a signal. Hence the proposal promotes visual thinking and the development of advanced mathematical thinking. Given the academic background and content of the subjects prior to the issue is considered the TFS as a linear combination of orthogonal functions and aims to visually characterize the concepts involved correlating the physical phenomenon in this case the signals are linear time-invariant. Research has established that the construction of knowledge and the development of mathematical visualization achieved by students is encouraged by the interaction of different registers of representation, with the help of a technological medium, the computer in this case.

Extraction of Aerosol-Size Distributions from Multispectral Light Extinction Data

An algorithm for inverting remote sensing measurements to determine particle concentration and size distribution, proposed by Nguyen and Cox in 1989, is described and evaluated. This determination uses extinction measurements at multiple wavelengths with the solution of the Fredholm integral equation. The solution represents the second derivative of the particle-size distribution as a linear combination of orthogonal functions chosen so that the resulting solution is smooth and positive everywhere. We used this algorithm to reconstruct concentrations and size distributions for simulated and experimental measurements of light extinction caused by different test aerosols. An “information content parameter” was used to measure how well each size distribution could be reconstructed from its corresponding measurements. For a wavelength range of 340–940 nm, aerosols in the accumulation mode (300 nm < d 50 < 2500 nm) were reconstructed well. The algorithm was good at reconstructing moderately polydisperse aeroso...

Effective bandwidth of 2-D functions that can be expressed as a linear combination of orthogonal functions

The authors investigate bounds on the two-dimensional function f(x,y) that can be expressed as a linear combination of an orthogonal set of functions (q/sub nm/(x,y)) in the mean. Each function q/sub nm/(x,y) has the property of being separable. Each of these functions is bandlimited. Effective bandwidth expressions are derived on the basis of a given error criterion.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Principal components of monsoon rainfall

Monsoon rainfall over India during the 120-day period from the beginning of June to the end of September exhibits interesting oscillations over the country. According to an analysis by Sub-bramayya (1968), there is a negative correlation in rainfall between the north-eastern and west-central parts of India. But his analysis does not indicate how much of the total variance of rainfall is explained by different rainfall patterns. We examined this aspect by expressing rainfall as a linear combination of orthogonal functions. This technique was suggested by Lorenz (1956). It was later used by Kutzbach (1967) and Weare (1977) to evaluate the principal components of sea-level pressure over the northern hemisphere, and sea surface temperature over the Atlantic Ocean. DOI: 10.1111/j.2153-3490.1980.tb00956.x

Principal components of monsoon rainfall

Monsoon rainfall over India during the 120-day period from the beginning of June to the end of September exhibits interesting oscillations over the country. According to an analysis by Sub-bramayya (1968), there is a negative correlation in rainfall between the north-eastern and west-central parts of India. But his analysis does not indicate how much of the total variance of rainfall is explained by different rainfall patterns. We examined this aspect by expressing rainfall as a linear combination of orthogonal functions. This technique was suggested by Lorenz (1956). It was later used by Kutzbach (1967) and Weare (1977) to evaluate the principal components of sea-level pressure over the northern hemisphere, and sea surface temperature over the Atlantic Ocean.