scholarly journals ON EFFICIENCY OF SOME METHODS FOR DETERMINING THE AZIMUTHAL STRUCTURE OF NOISE IN CYLINDRICAL DUCT

Akustika ◽  
2019 ◽  
Vol 32 ◽  
pp. 130-134
Author(s):  
Vadim Palchikovskiy ◽  
Yuliy Bersenev ◽  
Ivan Korin
Keyword(s):  
Least Squares ◽  
Dynamic Range ◽  
Least Squares Method ◽  
Microphone Array ◽  
Aircraft Engine ◽  
Circular Array ◽  
Noise Measurements ◽  
Air Intake ◽  
Experimental Values ◽  
Cylindrical Duct

The determination of azimuthal sound modes propagating in a cylindrical duct is considered based on the results of noise measurements on experimental setup with a duct diameter of 1.8 m, which corresponds to the air intake of aircraft engine. The experiments were carried out in PNRPU anechoic chamber. Spinning modes were generated by a circular array of 40 acoustic drivers. Noise in duct was recorded with circular array of 100 microphones with optimized arrangement to reach maximum dynamic range. The following methods for determining the azimuthal structure of noise were compared: modal decomposition method, cross-correlation with a reference channel method; least-squares method. The mathematical foundations and specifics of these methods are briefly outlined. According to the results of the azimuthal structure extraction, it was found that the least-squares method provides the best agreement between the generated and extracted modes and the distribution of the computed and experimental values of acoustic pressures on microphone array.

‘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.

CALCULATION-EXPERIMENTAL METHOD FOR DEFINITION OF LOWEST FREQUENCY IN BENDING VIBRATIONS OF COACH CAR BODY IN VERTICAL PLANE BASED ON IDENTIFICATION OF ITS BENDING STIFFNESS

2020 ◽  
Vol 2020 (9) ◽  
pp. 35-46
Author(s):  
Aleksandr Skachkov ◽  
Viktor Vasilevskiy ◽  
Aleksey Yuhnevskiy
Keyword(s):  
Least Squares Method ◽  
Vertical Plane ◽  
Bending Stiffness ◽  
Dimensional Problem ◽  
Euler Beam ◽  
Bending Vibrations ◽  
Car Body ◽  
Variable Function ◽  
Experimental Values ◽  
Definition Of

The consideration of existing methods for a modal analysis has shown a possibility for the lowest frequency definition of bending vibrations in a coach car body in a vertical plane based on an indirect method reduced to the assessment of the bending stiffness of the one-dimensional model as a Bernoulli-Euler beam with fragment-constant parameters. The assessment mentioned can be obtained by means of the comparison of model deflections (rated) and a prototype (measured experimentally upon a natural body) with the use of the least-squares method that results in the necessity of the solution of the multi-dimensional problem with the reverse coefficient. The introduction of the hypothesis on ratability of real bending stiffness of the prototype and easily calculated geometrical stiffness of a model reduces a multi-dimensional problem incorrect according to Adamar to the simplest search of the extremum of one variable function. The procedure offered for the indirect assessment of bending stiffness was checked through the solution of model problems. The values obtained are offered to use for the assessment of the lowest frequency of bending vibrations with the aid of Ritz and Grammel methods. In case of rigid poles it results in formulae for frequencies into which there are included directly the experimental values of deflections.

Theoretical accuracy of the last squares method in the isotope dilution analysis

1984 ◽  
Vol 49 (4) ◽  
pp. 805-820
Author(s):  
Ján Klas
Keyword(s):  
Least Squares ◽  
Isotope Dilution ◽  
Least Squares Method ◽  
Isotope Dilution Analysis ◽  
Straight Line ◽  
The One ◽  
Two Parameter ◽  
Theoretical Accuracy

The accuracy of the least squares method in the isotope dilution analysis is studied using two models, viz a model of a two-parameter straight line and a model of a one-parameter straight line.The equations for the direct and the inverse isotope dilution methods are transformed into linear coordinates, and the intercept and slope of the two-parameter straight line and the slope of the one-parameter straight line are evaluated and treated.

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