Least Square QR Decomposition Method for Solving the Inverse Problem in Functional Near Infra-Red Spectroscopy

In geophysical subsurface surveys, difficulty to interpret measurement of data obtain from the equipment are risen. Data provided by the equipment did not indicate subsurface condition specifically and deviates from the expected standard due to numerous features. Generally, the data that obtained from the laws of physics computation is known as forward problem. And the process of obtaining the data from sets of measurements and reconstruct the model is known as inverse problem. Researchers have proposed multiple estimation techniques to cater the inverse problem and provide estimation that close to actual model. In this work, we investigate the feasibility of using artificial neural network (ANN) in solving two- dimensional (2-D) direct current (DC) resistivity mapping for subsurface investigation, in which the algorithms are based on the radial basis function (RBF) model and the multi-layer perceptron (MLP) model. Conventional approach of least square (LS) method is used as a benchmark and comparative study with the proposed algorithms. In order to train the proposed algorithms, several synthetic data are generated using RES2DMOD software based on hybrid Wenner-Schlumberger configurations. Results are compared between the proposed algorithms and least square method in term of its effectiveness and error variations to the actual values. It is discovered that the proposed algorithms have offered better performance in term minimum error difference to the actual model, as compared to least square method. Simulation results demonstrate that proposed algorithms can solve the inverse problem and it can be illustrated by means of the 2-D graphical mapping.

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Solution of inverse heat conduction equation with the use of Chebyshev polynomials

Archives of Thermodynamics ◽

10.1515/aoter-2016-0028 ◽

2016 ◽

Vol 37 (4) ◽

pp. 73-88 ◽

Cited By ~ 4

Author(s):

Magda Joachimiak ◽

Andrzej Frąckowiak ◽

Michał Ciałkowski

Keyword(s):

Inverse Problem ◽

Chebyshev Polynomials ◽

Direct Problem ◽

Least Square Method ◽

Least Square ◽

Random Disturbance ◽

Inverse Heat Conduction ◽

Chebyshev Nodes ◽

The Difference ◽

The Stability

AbstractA direct problem and an inverse problem for the Laplace’s equation was solved in this paper. Solution to the direct problem in a rectangle was sought in a form of finite linear combinations of Chebyshev polynomials. Calculations were made for a grid consisting of Chebyshev nodes, what allows us to use orthogonal properties of Chebyshev polynomials. Temperature distributions on the boundary for the inverse problem were determined using minimization of the functional being the measure of the difference between the measured and calculated values of temperature (boundary inverse problem). For the quasi-Cauchy problem, the distance between set values of temperature and heat flux on the boundary was minimized using the least square method. Influence of the value of random disturbance to the temperature measurement, of measurement points (distance from the boundary, where the temperature is not known) arrangement as well as of the thermocouple installation error on the stability of the inverse problem was analyzed.

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Pre-stack 5D Seismic Data Reconstruction Based on a Fast Uncoiled Randomized QR Decomposition Method

79th EAGE Conference and Exhibition 2017 ◽

10.3997/2214-4609.201701432 ◽

2017 ◽

Author(s):

J.J. Gao ◽

China University of Petroleum ◽

S. Wang

Keyword(s):

Seismic Data ◽

Decomposition Method ◽

Qr Decomposition ◽

Data Reconstruction ◽

Seismic Data Reconstruction

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Designing fuzzy logic systems for uncertain environments using a singular-value-QR decomposition method

Proceedings of IEEE 5th International Fuzzy Systems ◽

10.1109/fuzzy.1996.551757 ◽

2002 ◽

Cited By ~ 32

Author(s):

G.C. Mouzouris ◽

J.M. Mendel

Keyword(s):

Fuzzy Logic ◽

Decomposition Method ◽

Qr Decomposition ◽

Singular Value ◽

Uncertain Environments ◽

Fuzzy Logic Systems ◽

Logic Systems

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Variational approach for recovering viscoelasticity from MRE data

Journal of Physics Conference Series ◽

10.1088/1742-6596/2092/1/012001 ◽

2021 ◽

Vol 2092 (1) ◽

pp. 012001

Author(s):

Yu Jiang ◽

Gen Nakamura ◽

Kenji Shirota

Keyword(s):

Inverse Problem ◽

Cost Function ◽

Variational Approach ◽

Simulated Data ◽

Least Square ◽

Projected Gradient Method ◽

Living Body ◽

The Cost ◽

Derivatives Of ◽

Real Experimental Data

Abstract This paper deals with an inverse problem for recovering the viscoelasticity of a living body from MRE (Magnetic Resonance Elastography) data. Based on a viscoelastic partial differential equation whose solution can approximately simulate MRE data, the inverse problem is transformed to a least square variational problem. This is to search for viscoelastic coefficients of this equation such that the solution to a boundary value problem of this equation fits approximately to MRE data with respect to the least square cost function. By computing the Gateaux derivatives of the cost function, we minimize the cost function by the projected gradient method is proposed for recovering the unknown coefficients. The reconstruction results based on simulated data and real experimental data are presented and discussed.

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Determination and Prediction of Some Soil Properties using Partial Least Square (PLS) Calibration and Mid-Infra Red (MIR) Spectroscopy Analysis

Journal of Tropical Soils ◽

10.5400/jts.2011.v16i2.93-98 ◽

2013 ◽

Vol 16 (2) ◽

pp. 93-98 ◽

Cited By ~ 1

Author(s):

Irnanda Aiko Fifi Djuuna ◽

Lynette Abbott ◽

Craig Russell

Keyword(s):

Soil Properties ◽

Soil Microbial Biomass ◽

Microbial Biomass Carbon ◽

Partial Least Square ◽

Least Square ◽

Soil Extraction ◽

Soil Microbial ◽

Mir Spectroscopy ◽

Infra Red ◽

Pls Method

Soil chemical, physical and biological analyses are a crucial but often expensive and time-consuming step in the characterization of soils. Rapid and accurate predictions and relatively simple methods are ideally needed for soil analysis. The objective of this study was to predict some soil properties (e.g. pH, EC, total C, total N,C/N, NH4-N, NO3-N, P, K, clay, silt, and sand and soil microbial biomass carbon) across the Wickepin farm during summer season using a Mid-Infra Red - Partial Least Square (MIR–PLS) method. The 291 soil samples were analyzed bothwith soil extraction procedure and MIR Spectrometer. Calibrations were developed between MIR spectral data and the results of soil extraction procedures. Results using the PLS-MIR showed that MIR-predicted values were almost as highly correlated to the measured value obtained by the soil extraction method of total carbon, total nitrogen and soil pH. Values for EC, NH4-N, NO3-N, C/N, P, K, clay, silt, sand, and soil microbial biomass carbon were not successfully predicted by the MIR – PLS technique. There was a tendency for these factors to correlate with the MIR predicted value, but the correlation values were very low. This study has confirmed that the MIR-PLS method can be used to predict some soil properties based on calibrations of MIR values.Keywords: MIR-Partial Least Square, MIR-Spectroscopy, soil properties

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