scholarly journals Optimization method based on minimization m-Order central moments used in surveying engineering problems

2021 ◽  
Author(s):  
Sławomir Cellmer
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Optimization Method ◽  
Railway Track ◽  
Computational Techniques ◽  
Central Moments ◽  
Numerical Tests ◽  
Moments Method ◽  
Engineering Problems ◽  
Set Of Points

A new optimization method presented in this work – the Least m-Order Central Moments method, is a generalization of the Least Squares method. It allows fitting a geometric object into a set of points in such a way that the maximum shift between the object and the points after fitting is smaller than in the Least Squares method. This property can be very useful in some engineering tasks, e.g. in the realignment of a railway track or gantry rails. The theoretical properties of the proposed optimization method are analyzed. The computational problems are discussed. The appropriate computational techniques are proposed to overcome these problems. The detailed computational algorithm and formulas of iterative processes have been derived. The numerical tests are presented, in order to illustrate the operation of proposed techniques. The results have been analyzed, and the conclusions were then formulated.

scholarly journals Third-Octave and Bark Graphic-Equalizer Design with Symmetric Band Filters

2020 ◽  
Vol 10 (4) ◽  
pp. 1222 ◽  
Author(s):  
Jussi Rämö ◽  
Juho Liski ◽  
Vesa Välimäki
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Gain Control ◽  
Optimization Method ◽  
Maximum Magnitude ◽  
Weighted Least Squares Method ◽  
The Neural Network ◽  
Symmetric Band ◽  
Previous State

This work proposes graphic equalizer designs with third-octave and Bark frequency divisions using symmetric band filters with a prescribed Nyquist gain to reduce approximation errors. Both designs utilize an iterative weighted least-squares method to optimize the filter gains, accounting for the interaction between the different band filters, to ensure excellent accuracy. A third-octave graphic equalizer with a maximum magnitude-response error of 0.81 dB is obtained, which outperforms the previous state-of-the-art design. The corresponding error for the Bark equalizer, which is the first of its kind, is 1.26 dB. This paper also applies a recently proposed neural gain control in which the filter gains are predicted with a multilayer perceptron having two hidden layers. After the training, the resulting network quickly and accurately calculates the filter gains for third-order and Bark graphic equalizers with maximum errors of 0.86 dB and 1.32 dB, respectively, which are not much more than those of the corresponding weighted least-squares designs. Computing the filter gains is about 100 times faster with the neural network than with the original optimization method. The proposed designs are easy to apply and may thus lead to widespread use of accurate auditory graphic equalizers.

scholarly journals STUDY OF THE ALGORITHM OF PSEUDONORMAL OPTIMIZATION ON THE STABILITY OF THE SOLUTION OF THE EQUATION PROBLEM AND THE ESTIMATION OF THE ACCURACY

2021 ◽  
Vol 1 ◽  
pp. 40-48
Author(s):  
Amridon G. Barliani ◽  
Galina A. Nefedova ◽  
Irina V. Karnetova
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Experimental Studies ◽  
Network Models ◽  
Optimization Method ◽  
Equation Problem ◽  
Estimated Parameters ◽  
The Matrix ◽  
The Stability ◽  
Stability Of The Solution

In geodesic practice, when designing and adjusting geodetic networks for various purposes on a computer, it is necessary to solve poorly conditioned systems of linear normal equations. In such systems, the determinant of the matrix of equations tends to zero, so the application of the least squares method leads to large distortions of the estimated parameters. Moreover, in such situations, for the least squares algorithm, a slight distortion of the input data leads to unacceptably large distortions of the final results of the equalization and accuracy estimation. In this regard, the application of the pseudonormal optimization method is proposed. The presented work is devoted to the study of the stability of the solution of the adjustment task and the estimation of accuracy obtained on the basis of the pseudonormal optimization method. The novelty is the obtained algorithm for estimating the relative error of the pseudonormal optimization method. A comparative analysis of two competing processing methods was performed for different network models. The results of experimental studies and their analysis have shown the advantage of the pseudonormal optimization method over the least squares method.

scholarly journals Least-squares adjustment taking into account the errors in variables

2021 ◽  
Vol 65 (02) ◽  
pp. 205-218
Author(s):  
Aleš Marjetič
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Regression Line ◽  
Errors In Variables ◽  
Coordinate Systems ◽  
National Coordinate ◽  
Least Squares Adjustment ◽  
Transformation Parameters ◽  
Set Of Points ◽  
Theoretical Foundations

In this article, we discuss the procedure for computing the values of the unknowns under the condition of the minimum sum of squares of the observation residuals (least-squares method), taking into account the errors in the unknowns. Many authors have already presented the problem, especially in the field of regression analysis and computations of transformation parameters. We present an overview of the theoretical foundations of the least-squares method and extensions of this method by considering the errors in unknowns in the model matrix. The method, which can be called ‘the total least-squares method’, is presented in the paper for the case of fitting the regression line to a set of points and for the case of calculating transformation parameters for the transition between the old and the new Slovenian national coordinate systems. With the results based on relevant statistics, we confirm the suitability of the considered method for solving such tasks.

Evaluation of Minimum Zone Straightness by a Nonlinear Optimization Method

1999 ◽  
Vol 122 (4) ◽  
pp. 795-797 ◽  
Author(s):  
Elsayed Orady ◽  
Songnian Li ◽  
Yubao Chen
Keyword(s):  
Convex Hull ◽  
Least Squares ◽  
Nonlinear Optimization ◽  
Least Squares Method ◽  
Optimization Method ◽  
Measured Data ◽  
Data Sets ◽  
Minimum Zone ◽  
Nonlinear Optimization Method

In this paper, a new algorithm, based on a nonlinear optimization method (NOM), has been developed. The accuracy as well as the reliability/robustness of the new algorithm have been verified by applying it to more than 200 CMM measured data sets on differently manufactured parts. The results have been compared with that of Least Squares Method (LSM) and Convex Hull (CVH) method applied to the same data sets. A data filter is proposed to be enclosed in the new algorithm to detect and delete outliers in the data sets. [S1087-1357(00)01102-3]

‘Least squares’ method—theorem or law?

1980 ◽  
Vol 59 (9) ◽  
pp. 8
Author(s):  
D.E. Turnbull
Keyword(s):  
Least Squares ◽  
Least Squares Method

An Augmented Iteratively Re-weighted and Refined Least Squares Method for lp Minimization Problem in Inverse Modeling of Potential Field Magnetic Data

2020 ◽  
Vol 1 (3) ◽  
Author(s):  
Maysam Abedi
Keyword(s):  
Magnetic Field ◽  
Magnetic Susceptibility ◽  
Least Squares ◽  
Minimization Problem ◽  
Potential Field ◽  
Field Data ◽  
Least Squares Method ◽  
Porphyry Copper ◽  
Magnetic Data ◽  
Magnetic Field Data

The presented work examines application of an Augmented Iteratively Re-weighted and Refined Least Squares method (AIRRLS) to construct a 3D magnetic susceptibility property from potential field magnetic anomalies. This algorithm replaces an lp minimization problem by a sequence of weighted linear systems in which the retrieved magnetic susceptibility model is successively converged to an optimum solution, while the regularization parameter is the stopping iteration numbers. To avoid the natural tendency of causative magnetic sources to concentrate at shallow depth, a prior depth weighting function is incorporated in the original formulation of the objective function. The speed of lp minimization problem is increased by inserting a pre-conditioner conjugate gradient method (PCCG) to solve the central system of equation in cases of large scale magnetic field data. It is assumed that there is no remanent magnetization since this study focuses on inversion of a geological structure with low magnetic susceptibility property. The method is applied on a multi-source noise-corrupted synthetic magnetic field data to demonstrate its suitability for 3D inversion, and then is applied to a real data pertaining to a geologically plausible porphyry copper unit.  The real case study located in  Semnan province of  Iran  consists  of  an arc-shaped  porphyry  andesite  covered  by  sedimentary  units  which  may  have  potential  of  mineral  occurrences, especially  porphyry copper. It is demonstrated that such structure extends down at depth, and consequently exploratory drilling is highly recommended for acquiring more pieces of information about its potential for ore-bearing mineralization.

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