scholarly journals Approximation of continuous random variables for the evaluation of the reliability parameter of complex stress–strength models

2021 ◽  
Author(s):  
Alessandro Barbiero ◽  
Asmerilda Hitaj
Keyword(s):  
Order Approximation ◽  
Linear Optimization ◽  
Closed Form Solution ◽  
Random Variables ◽  
Discrete Distribution ◽  
Computation Time ◽  
Form Solution ◽  
Engineering Problem ◽  
Approximation Technique ◽  
Reliability Parameter

AbstractIn many management science or economic applications, it is common to represent the key uncertain inputs as continuous random variables. However, when analytic techniques fail to provide a closed-form solution to a problem or when one needs to reduce the computational load, it is often necessary to resort to some problem-specific approximation technique or approximate each given continuous probability distribution by a discrete distribution. Many discretization methods have been proposed so far; in this work, we revise the most popular techniques, highlighting their strengths and weaknesses, and empirically investigate their performance through a comparative study applied to a well-known engineering problem, formulated as a stress–strength model, with the aim of weighting up their feasibility and accuracy in recovering the value of the reliability parameter, also with reference to the number of discrete points. The results overall reward a recently introduced method as the best performer, which derives the discrete approximation as the numerical solution of a constrained non-linear optimization, preserving the first two moments of the original distribution. This method provides more accurate results than an ad-hoc first-order approximation technique. However, it is the most computationally demanding as well and the computation time can get even larger than that required by Monte Carlo approximation if the number of discrete points exceeds a certain threshold.

scholarly journals Deep learning for a space-variant deconvolution in galaxy surveys

2020 ◽  
Vol 641 ◽  
pp. A67
Author(s):  
F. Sureau ◽  
A. Lechat ◽  
J.-L. Starck
Keyword(s):  
Deep Learning ◽  
Network Architecture ◽  
Signal To Noise Ratio ◽  
Closed Form Solution ◽  
Computation Time ◽  
Form Solution ◽  
High Signal ◽  
Galaxy Surveys ◽  
Point Spread ◽  
Space Variant

The deconvolution of large survey images with millions of galaxies requires developing a new generation of methods that can take a space-variant point spread function into account. These methods have also to be accurate and fast. We investigate how deep learning might be used to perform this task. We employed a U-net deep neural network architecture to learn parameters that were adapted for galaxy image processing in a supervised setting and studied two deconvolution strategies. The first approach is a post-processing of a mere Tikhonov deconvolution with closed-form solution, and the second approach is an iterative deconvolution framework based on the alternating direction method of multipliers (ADMM). Our numerical results based on GREAT3 simulations with realistic galaxy images and point spread functions show that our two approaches outperform standard techniques that are based on convex optimization, whether assessed in galaxy image reconstruction or shape recovery. The approach based on a Tikhonov deconvolution leads to the most accurate results, except for ellipticity errors at high signal-to-noise ratio. The ADMM approach performs slightly better in this case. Considering that the Tikhonov approach is also more computation-time efficient in processing a large number of galaxies, we recommend this approach in this scenario.

Fast laser scan matching approach based on adaptive curvature estimation for mobile robots

Robotica ◽  
2009 ◽  
Vol 27 (3) ◽  
pp. 469-479 ◽  
Author(s):  
P. Núñez ◽  
R. Vázquez-Martín ◽  
A. Bandera ◽  
F. Sandoval
Keyword(s):  
Dynamic Environment ◽  
Closed Form Solution ◽  
Computation Time ◽  
Form Solution ◽  
Local Alignment ◽  
Curvature Function ◽  
Scan Matching ◽  
Characteristic Points ◽  
Curvature Estimation ◽  
Three Stages

SUMMARYThis paper describes a complete laser-based approach for tracking the pose of a robot in a dynamic environment. The main novelty of this approach is that the matching between consecutively acquired scans is achieved using their associated curvature-based representations. The proposed scan matching algorithm consists of three stages. Firstly, the whole raw laser data is segmented into groups of consecutive range readings using a distance-based criterion and the curvature function for each group is computed. Then, this set of curvature functions is matched to the set of curvature functions associated to the previously acquired laser scan. Finally, characteristic points of pairwise curvature functions are matched and used to correctly obtain the best local alignment between consecutive scans. A closed form solution is employed for computing the optimal transformation and minimizing the robot pose shift error without iterations. Thus, the system is outstanding in terms of accuracy and computation time. The implemented algorithm is evaluated and compared to three state of the art scan matching approaches.

REFINED BEAM THEORIES BASED ON A UNIFIED FORMULATION

2010 ◽  
Vol 02 (01) ◽  
pp. 117-143 ◽  
Author(s):  
ERASMO CARRERA ◽  
GAETANO GIUNTA
Keyword(s):  
Differential Equations ◽  
Cross Section ◽  
Cross Sections ◽  
Order Approximation ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Approximation Order ◽  
Form Solution ◽  
Geometrical Parameters ◽  
Beam Theories

This paper proposes several axiomatic refined theories for the linear static analysis of beams made of isotropic materials. A hierarchical scheme is obtained by extending plates and shells Carrera's Unified Formulation (CUF) to beam structures. An N-order approximation via Mac Laurin's polynomials is assumed on the cross-section for the displacement unknown variables. N is a free parameter of the formulation. Classical beam theories, such as Euler-Bernoulli's and Timoshenko's, are obtained as particular cases. According to CUF, the governing differential equations and the boundary conditions are derived in terms of a fundamental nucleo that does not depend upon the approximation order. The governing differential equations are solved via the Navier type, closed form solution. Rectangular and I-shaped cross-sections are accounted for. Beams undergo bending and torsional loadings. Several values of the span-to-height ratio are considered. Slender as well as deep beams are analysed. Comparisons with reference solutions and three-dimensional FEM models are given. The numerical investigation has shown that the proposed unified formulation yields the complete three-dimensional displacement and stress fields for each cross-section as long as the appropriate approximation order is considered. The accuracy of the solution depends upon the geometrical parameters of the beam and loading conditions.

Thermomechanical Stress Analysis of Multi-Layered Electronic Packaging

2003 ◽  
Vol 125 (1) ◽  
pp. 134-138 ◽  
Author(s):  
Yujun Wen ◽  
Cemal Basaran
Keyword(s):  
Analytical Model ◽  
Material Properties ◽  
Orthotropic Material ◽  
Thermal Stresses ◽  
Order Approximation ◽  
Closed Form Solution ◽  
Accurate Estimate ◽  
Form Solution ◽  
Element Analysis ◽  
Thermomechanical Stress

An accurate estimate of thermal stresses in multilayered microelectronics structures along the bonded interfaces is crucial for design and prediction of delamination-related failures. Compared with a numerical method, analytical closed-form solution can offer a more rapid method to obtain the stresses at the interfaces. An analytical model for ply-level sub-laminate analysis is investigated in this paper. The theory presented treats each layer as a beam-type plate with orthotropic material properties. As an example, the results are shown for a three-layer beam problem with special orthotropic material properties. Analytical model results are compared with the finite element analysis results, as a first order approximation.

Efficient Closed-Form Solution of the Kinematics of a Tunnel Digging Machine

2017 ◽  
Vol 9 (3) ◽  
Author(s):  
Paolo Boscariol ◽  
Alessandro Gasparetto ◽  
Lorenzo Scalera ◽  
Renato Vidoni
Keyword(s):  
Numerical Solution ◽  
Closed Form ◽  
Closed Form Solution ◽  
Computation Time ◽  
Form Solution ◽  
Large Size ◽  
Closure Equation ◽  
Class 1 ◽  
Spherical Mechanism ◽  
Kinematic Solution

In this work, the kinematics of a large size tunnel digging machine is investigated. The closed-loop mechanism is made by 13 links and 13 class 1 couplings, seven of which are actuated. This kind of machines are commonly used to perform ground drilling for the placement of reinforcement elements during the construction of tunnels. The direct kinematic solution is obtained using three methods: the first two are based on the numerical solution of the closure equation written using the Denavit–Hartenberg convention, while the third is based on the definition and solution in closed form of an equivalent spherical mechanism. The procedures have been tested and implemented with reference to a real commercial tunnel digging machine. The use of the proposed method for the closed-form solution of direct kinematics allows to obtain a major reduction of the computation time in comparison with the standard numerical solution of the closure equation.

scholarly journals Location and Shape Reconstruction of 2D Dielectric Objects by Means of a Closed-Form Method: Preliminary Experimental Results

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Gian Luigi Gragnani ◽  
Maurizio Diaz Mendez
Keyword(s):  
Closed Form ◽  
Cross Sections ◽  
Complete Solution ◽  
Closed Form Solution ◽  
Computation Time ◽  
Shape Reconstruction ◽  
Form Solution ◽  
Scattering Data ◽  
Equivalent Sources ◽  
Value Decomposition

An analytical approach to location and shape reconstruction of dielectric scatterers, that was recently proposed, is tested against experimental data. Since the cross-sections of the scatterers do not depend on the z coordinate, a 2D problem can be formulated. A closed-form singular value decomposition of the scattering integral operator is derived and is used to determine the radiating components of the equivalent source density. This is a preliminary step toward a more complete solution, which will take into account the incident field inside the investigation domain in order to provide the dielectric features of the scatterer and also the nonradiating sources. Reconstructions of the equivalent sources, performed on some scattering data belonging to the Fresnel database, show the capabilities of the method and, thanks to the closed-form solution, results are obtained in a very short computation time.

scholarly journals Analytical-Numerical Solution of a Parabolic Diffusion Equation Under Uncertainty Conditions Using DTM with Monte Carlo Simulations

2015 ◽  
Vol 11 (22) ◽  
pp. 49-72 ◽  
Author(s):  
Gilberto González Parra ◽  
Abraham J Arenas ◽  
Miladys Cogollo
Keyword(s):  
Monte Carlo ◽  
Diffusion Coefficient ◽  
Hybrid Method ◽  
Source Term ◽  
Closed Form Solution ◽  
Random Variables ◽  
Form Solution ◽  
Mean Values ◽  
The Monte Carlo Method ◽  
Condi Tions

A numerical method to solve a general random linear parabolic equationwhere the diffusion coefficient, source term, boundary and initial condi-tions include uncertainty, is developed. Diffusion equations arise in manyfields of science and engineering, and, in many cases, there are uncertaintiesdue to data that cannot be known, or due to errors in measurements andintrinsic variability. In order to model these uncertainties the correspon-ding parameters, diffusion coefficient, source term, boundary and initialconditions, are assumed to be random variables with certainprobabilitydistributions functions. The proposed method includes finite differenceschemes on the space variable and the differential transformation methodfor the time. In addition, the Monte Carlo method is used to deal withthe random variables. The accuracy of the hybrid method is investigatednumerically using the closed form solution of the deterministic associated equation. Based on the numerical results, confidence intervals and ex-pected mean values for the solution are obtained. Furthermore, with theproposed hybrid method numerical-analytical solutions are obtained.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

Plane Wave Resonance in the Tire Air Cavity as a Vehicle Interior Noise Source

1995 ◽  
Vol 23 (1) ◽  
pp. 2-10 ◽  
Author(s):  
J. K. Thompson
Keyword(s):  
Closed Form Solution ◽  
Form Solution ◽  
Interior Noise ◽  
Cavity Resonance ◽  
Test Results ◽  
Vehicle Interior ◽  
Air Cavity ◽  
Vehicle Interior Noise ◽  
Wave Resonance ◽  
Resonance Frequencies

Abstract Vehicle interior noise is the result of numerous sources of excitation. One source involving tire pavement interaction is the tire air cavity resonance and the forcing it provides to the vehicle spindle: This paper applies fundamental principles combined with experimental verification to describe the tire cavity resonance. A closed form solution is developed to predict the resonance frequencies from geometric data. Tire test results are used to examine the accuracy of predictions of undeflected and deflected tire resonances. Errors in predicted and actual frequencies are shown to be less than 2%. The nature of the forcing this resonance as it applies to the vehicle spindle is also examined.

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