scholarly journals Sensitivity analysis of electromagnetic quantities in time domain by means of fem

2004 ◽  
Vol 1 (2) ◽  
pp. 167-174 ◽  
Author(s):  
Konstanty Gawrylczyk ◽  
Mateusz Kugler
Keyword(s):  
Sensitivity Analysis ◽  
Finite Elements ◽  
Objective Function ◽  
Time Domain ◽  
Optimization Theory ◽  
Computational Effort ◽  
Physical Parameters ◽  
Mass Matrices ◽  
Electromagnetic Quantities ◽  
Measurement Coil

Sensitivity analysis belongs to the most important tools in optimization theory. It determines the dependence of global or local electromagnetic quantities on geometrical and physical parameters expressed in the form of an objective function. For several objective functions the sensitivity may be directly calculated differentiating the objective function versus one of material or geometric parameters. Such approach needs large computational effort, especially while evaluating in time domain. This paper presents effective methods for computing of sensitivity of nodal potentials in finite elements versus perturbations in conductivity of analyzed model in time domain. Derived equations are based on the method of stiffness and mass matrices derivative and Tellegen?s theorem known from circuit theory and have been expanded on field theory. Numerical example presented in the paper shows sensitivity of voltage induced in measurement coil versus variation of electrical conductivity in single finite element as function of time. The proposed methods calculate the sensitivity versus all finite elements in area of analysis at once. On the basis of sensitivity information the iterative algorithm for identification of shape and conductivity distribution of material flaws could be applied.

Electromagnetic methods in nondestructive testing of materials

2003 ◽  
Vol 16 (1) ◽  
pp. 1-23
Author(s):  
Konstanty Gawrylczyk
Keyword(s):  
Sensitivity Analysis ◽  
Finite Elements ◽  
Nondestructive Testing ◽  
Eddy Current ◽  
Quality Evaluation ◽  
Leakage Flux ◽  
Electromagnetic Methods ◽  
Conducting Materials ◽  
Inductive Methods ◽  
Flux Probe

The article deals with progress in electromagnetic methods used for quality evaluation of conducting materials. The term "electromagnetic methods" covers the following areas: magneto-inductive methods, magnetic leakage flux probe method, magnetometer principle and eddy-current methods. For the aim of numerical cracks recognition the sensitivity analysis with finite elements was shown.

Inversion of induced polarization data

Geophysics ◽  
1994 ◽  
Vol 59 (9) ◽  
pp. 1327-1341 ◽  
Author(s):  
Douglas W. Oldenburg ◽  
Yaoguo Li
Keyword(s):  
Inverse Problem ◽  
Objective Function ◽  
Effective Conductivity ◽  
Optimization Theory ◽  
Induced Polarization ◽  
Dc Resistivity ◽  
Earth Structure ◽  
Nonlinear Inverse Problem ◽  
Polarization Data ◽  
The Earth

We develop three methods to invert induced polarization (IP) data. The foundation for our algorithms is an assumption that the ultimate effect of chargeability is to alter the effective conductivity when current is applied. This assumption, which was first put forth by Siegel and has been routinely adopted in the literature, permits the IP responses to be numerically modeled by carrying out two forward modelings using a DC resistivity algorithm. The intimate connection between DC and IP data means that inversion of IP data is a two‐step process. First, the DC potentials are inverted to recover a background conductivity. The distribution of chargeability can then be found by using any one of the three following techniques: (1) linearizing the IP data equation and solving a linear inverse problem, (2) manipulating the conductivities obtained after performing two DC resistivity inversions, and (3) solving a nonlinear inverse problem. Our procedure for performing the inversion is to divide the earth into rectangular prisms and to assume that the conductivity σ and chargeability η are constant in each cell. To emulate complicated earth structure we allow many cells, usually far more than there are data. The inverse problem, which has many solutions, is then solved as a problem in optimization theory. A model objective function is designed, and a “model” (either the distribution of σ or η)is sought that minimizes the objective function subject to adequately fitting the data. Generalized subspace methodologies are used to solve both inverse problems, and positivity constraints are included. The IP inversion procedures we design are generic and can be applied to 1-D, 2-D, or 3-D earth models and with any configuration of current and potential electrodes. We illustrate our methods by inverting synthetic DC/IP data taken over a 2-D earth structure and by inverting dipole‐dipole data taken in Quebec.

Truss and Beam Finite Elements Revisited: A Derivation Based on Displacement-Field Decomposition

1996 ◽  
Vol 11 (4) ◽  
pp. 371-380 ◽  
Author(s):  
Alphose Zingoni
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Symmetry Group ◽  
Displacement Field ◽  
Three Dimensional ◽  
Beam Elements ◽  
Symmetry Properties ◽  
Mass Matrices ◽  
General Displacement

Where a finite element possesses symmetry properties, derivation of fundamental element matrices can be achieved more efficiently by decomposing the general displacement field into subspaces of the symmetry group describing the configuration of the element. In this paper, the procedure is illustrated by reference to the simple truss and beam elements, whose well-known consistent-mass matrices are obtained via the proposed method. However, the procedure is applicable to all one-, two- and three-dimensional finite elements, as long as the shape and node configuration of the element can be described by a specific symmetry group.

scholarly journals Machine learning-based feature importance approach for sensitivity analysis of steel frames

2021 ◽  
Author(s):  
Hyeyoung Koh ◽  
Hannah Beth Blum
Keyword(s):  
Machine Learning ◽  
Sensitivity Analysis ◽  
Feature Selection ◽  
Large Scale ◽  
Failure Modes ◽  
Model Development ◽  
Predictive Performance ◽  
Computational Effort ◽  
Structural Systems ◽  
Feature Importance

This study presents a machine learning-based approach for sensitivity analysis to examine how parameters affect a given structural response while accounting for uncertainty. Reliability-based sensitivity analysis involves repeated evaluations of the performance function incorporating uncertainties to estimate the influence of a model parameter, which can lead to prohibitive computational costs. This challenge is exacerbated for large-scale engineering problems which often carry a large quantity of uncertain parameters. The proposed approach is based on feature selection algorithms that rank feature importance and remove redundant predictors during model development which improve model generality and training performance by focusing only on the significant features. The approach allows performing sensitivity analysis of structural systems by providing feature rankings with reduced computational effort. The proposed approach is demonstrated with two designs of a two-bay, two-story planar steel frame with different failure modes: inelastic instability of a single member and progressive yielding. The feature variables in the data are uncertainties including material yield strength, Young’s modulus, frame sway imperfection, and residual stress. The Monte Carlo sampling method is utilized to generate random realizations of the frames from published distributions of the feature parameters, and the response variable is the frame ultimate strength obtained from finite element analyses. Decision trees are trained to identify important features. Feature rankings are derived by four feature selection techniques including impurity-based, permutation, SHAP, and Spearman's correlation. Predictive performance of the model including the important features are discussed using the evaluation metric for imbalanced datasets, Matthews correlation coefficient. Finally, the results are compared with those from reliability-based sensitivity analysis on the same example frames to show the validity of the feature selection approach. As the proposed machine learning-based approach produces the same results as the reliability-based sensitivity analysis with improved computational efficiency and accuracy, it could be extended to other structural systems.

scholarly journals Optimasi OPTIMASI BIAYA TRANSPORTASI PADA UKM DI KOTA BATAM

2021 ◽  
Vol 9 (1) ◽  
pp. 1-19
Author(s):  
Welly Sugianto ◽  
Elva Susanti
Keyword(s):  
Sensitivity Analysis ◽  
Objective Function ◽  
Approximation Method ◽  
Minimum Cost ◽  
Transportation Cost ◽  
Product Distribution ◽  
Mathematical Form ◽  
Total Production ◽  
Calculation Results ◽  
Iteration Methods

This research was conducted at UKM Jovelyn in Batam city. Jovelyn's UKM produces various kinds of cakes and is marketed in markets in Batam City. The UKM opened 4 branches and marketed its products to 7 markets in the city of Batam. Product distribution is still random and not properly regulated. This resulted in a very large transportation cost, up to 1/3 of the total production cost. This shows that product transportation is still not carried out effectively and efficiently. The transportation problem is converted into a mathematical form so that the problem can be solved by the transportation method. The transportation method aims to minimize the objective function which is a function of transportation costs. The transportation method is basically the same as the linear program where at each iteration a selection is made to enter the basic variabel and leave the basic variabel. There are several iteration methods, namely the northwest corner method, minimum cost method, genetic algorithm, Vogel's approximation method, minimum row method, Russell's approximation method and column minimum method. Previous research has shown that the Vogel's approximation method, and Russell's approximation method are more efficient and accurate. This study uses both methods and a sensitivity analysis is performed to optimize the calculation results. The sensitivity analysis aims to determine the extent to which the objective function constants and the constraint function constants can change Keywords: Transportation, Sensitivity, SME  

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