Comment on Joe's "Comment on Overall And Spiegel's 'Least squares analysis of experimental data.'"

1973 ◽  
Vol 79 (3) ◽  
pp. 170-171 ◽  
Author(s):  
I. Leon Smith
Keyword(s):  
Experimental Data ◽  
Least Squares

scholarly journals Determination of parameters for Cauchy’s problem for systems of ODEs with application to biological modelling

BIOMATH ◽  
2016 ◽  
Vol 5 (1) ◽  
pp. 1604231
Author(s):  
A.N. Pete ◽  
Peter Mathye ◽  
Igor Fedotov ◽  
Michael Shatalov
Keyword(s):  
Experimental Data ◽  
Mathematical Models ◽  
Least Squares ◽  
Numerical Method ◽  
Least Squares Method ◽  
Algebraic Equations ◽  
Systems Of Odes ◽  
Determination Of Parameters ◽  
Biological Modelling

An inverse numerical method that estimate parameters of dynamic mathematical models given some information about unknown trajectories at some time is applied to examples taken from Biology and Ecology. The method consisting of determining an over-determined system of algebraic equations using experimental data. The solution of the over-determined system is then obtained using, for example the least-squares method. To illustrate the effectiveness of the method an analysis of examples and corresponding numerical example are presented.

scholarly journals METHOD OF FORECASTING THE TERMS OF SETTLING OF STRUCTURES ON SOILS WITH SILT LAYERS

2019 ◽  
Vol 2 (53) ◽  
pp. 107-114
Author(s):  
Yevhen Oksen
Keyword(s):  
Experimental Data ◽  
Data Processing ◽  
Least Squares ◽  
Method Of Least Squares ◽  
Filtration Consolidation

The method of forecasting the size and timing of sedimentation of structures on soils with silt layers, based on the results offield observations, has been developed. It is suggested to use a set of exponential dependencies with a constant component.The algorithm and software for calculation of the envelope by experimental data by a stepwise approximation are developed.The process of consolidation of soils is considered as a combination of simultaneous and independent flow of phases of primary filtration consolidation and secondary consolidation of creep. According to the results of data processing of observations by direct iterative calculations by finding the minimum nonconnectedness by the method of least squares.

Theory of the rocket-grenade method of measuring temperature, pressure, density and wind velocity in the upper atmosphere

1966 ◽  
Vol 290 (1420) ◽  
pp. 44-73 ◽  
Keyword(s):  
Experimental Data ◽  
Least Squares ◽  
Wind Velocity ◽  
Speed Of Sound ◽  
Vertical Component ◽  
Second Order ◽  
Upper Atmosphere ◽  
Lower Atmosphere ◽  
Travel Times ◽  
Sound Waves

A theory is presented for deriving the speed of sound and wind velocity as a function of height in the upper atmosphere from observations on the travel times of sound waves from accurately located grenades, released during rocket flight, to microphones at surveyed positions on the ground. The theory is taken to a second order of approximation, which can be utilized in practice if lower atmosphere (balloon) measurements are available. By means of the gas law and the vertical equation of motion of the atmosphere, formulae are obtained for deriving temperature, pressure and density from the speed-of-sound profile, and these also may be evaluated to a higher accuracy if lower atmosphere measurements are available. An outline is given of the computational procedure followed in the processing of data on the basis of this theory by means of the Pegasus computer. Methods of calculating the correction to travel times due to the finite wave amplitude are discussed and compared, and the effect of neglecting this correction in a particular set of experimental data is examined. Other errors which may affect the determination of pressure are also discussed. Consistency between the theory and experimental data obtained in 13 Skylark rocket flights at Woomera is checked in two ways: by examining least squares residuals associated with the sound arrivals at various microphones; and by treating the vertical component of air motion as unknown and examining its distribution about zero. The reduction in the least squares residuals which occurs when account is taken of second order terms is evaluated on the basis of these sets of experimental data.

Guided wave tomography based on least-squares reverse-time migration

2019 ◽  
Vol 19 (4) ◽  
pp. 1237-1249 ◽  
Author(s):  
Jiaze He ◽  
Daniel C Rocha ◽  
Paul Sava
Keyword(s):  
Experimental Data ◽  
Least Squares ◽  
Guided Wave ◽  
Circular Array ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Damage Site ◽  
Time Migration ◽  
Damage Imaging ◽  
Wave Tomography

A key to successful damage diagnostics and quantification is damage imaging through ultrasonic guided wave tomography. We propose the implementation of least-squares reverse-time migration in a circular array for damage imaging in an aluminum plate. The theory of least-squares reverse-time migration is formulated for guided wave applications along with the summary of an efficient optimization algorithm: the conjugate gradient method. Numerical simulation and laboratory experiments are used to evaluate its performance with a circular array setup. In order to improve the data processing efficiency, the concept of using a limited number of actuators but a relatively large number of sensors is tested. Studies are conducted on three numerical cases, including a rectangular-shaped damage site, a complex-shaped damage site, and six other damage sites varying in size. As an inversion-based method, least-squares reverse-time migration shows significantly improved shape reconstruction with the amplitude quantification capability, compared to conventional reverse-time migration. Our experimental data are generated by piezoelectric wafers as actuators, measured by a scanning laser Doppler vibrometer to form a circular array on an aluminum plate, with a rectangular notch located in the inner region of the array. The damage images using experimental data show consistency in both the simulations using Born scattering and in altered material properties in the damaged region. According to the comparison, least-squares reverse-time migration for guided wave tomography is a promising technology to provide high-resolution large area damage imaging for plate-like structures.

Characteristics of statistical parameters used to interpret least-squares results.

1978 ◽  
Vol 24 (4) ◽  
pp. 611-620 ◽  
Author(s):  
R B Davis ◽  
J E Thompson ◽  
H L Pardue
Keyword(s):  
Experimental Data ◽  
Least Squares ◽  
Confidence Intervals ◽  
Standard Error ◽  
Statistical Parameters ◽  
Average Value ◽  
Data Points ◽  
Independent Variable ◽  
Highly Correlated

Abstract This paper discusses properties of several statistical parameters that are useful in judging the quality of least-squares fits of experimental data and in interpreting least-squares results. The presentation includes simplified equations that emphasize similarities and dissimilarities among the standard error of estimate, the standard deviations of slopes and intercepts, the correlation coefficient, and the degree of correlation between the least-squares slope and intercept. The equations are used to illustrate dependencies of these parameters upon experimentally controlled variables such as the number of data points and the range and average value of the independent variable. Results are interpreted in terms of which parameters are most useful for different kinds of applications. The paper also includes a discussion of joint confidence intervals that should be used when slopes and intercepts are highly correlated and presents equations that can be used to judge the degree of correlation between these coefficients and to compute the elliptical joint confidence intervals. The parabolic confidence intervals for calibration cures are also discussed briefly.

scholarly journals The application of NIR spectroscopy in moisture determining of vegetable seeds

2020 ◽  
Vol 38 (No. 2) ◽  
pp. 131-136
Author(s):  
Wojciech Poćwiardowski ◽  
Joanna Szulc ◽  
Grażyna Gozdecka
Keyword(s):  
Experimental Data ◽  
Least Squares ◽  
Partial Least Squares ◽  
Partial Least Squares Regression ◽  
Near Infrared ◽  
Nir Spectroscopy ◽  
Calibration Model ◽  
Least Squares Regression ◽  
Moisture Analysis ◽  
Non Destructive

The aim of the study was to elaborate a universal calibration for the near infrared (NIR) spectrophotometer to determine the moisture of various kinds of vegetable seeds. The research was conducted on the seeds of 5 types of vegetables – carrot, parsley, lettuce, radish and beetroot. For the spectra correlation with moisture values, the method of partial least squares regression (PLS) was used. The resulting qualitative indicators of a calibration model (R = 0.9968, Q = 0.8904) confirmed an excellent fit of the obtained calibration to the experimental data. As a result of the study, the possibilities of creating a calibration model for NIR spectrophotometer for non-destructive moisture analysis of various kinds of vegetable seeds was confirmed.<br /><br />

Interpretation of the optical rotatory dispersion in tellurium

2002 ◽  
Vol 35 (1) ◽  
pp. 96-102 ◽  
Author(s):  
Ivo Vyšín ◽  
Kamila Sváčková ◽  
Jan Říha
Keyword(s):  
Crystal Structure ◽  
Experimental Data ◽  
Mathematical Method ◽  
Least Squares ◽  
Coupled Oscillators ◽  
Polarized Light ◽  
Optical Rotatory Dispersion ◽  
Rotatory Dispersion ◽  
Recent Experimental Data ◽  
Optical Rotatory

An interpretation of the most recent experimental data on the optical rotatory dispersion of tellurium is presented. The experimental data are approximated by theoretical equations which were derived using the model of three coupled oscillators. The applied mathematical method is based on the sum of least squares. The derived equations are also helpful when modelling the circular dichroism of tellurium and discussing the sense of the rotation of the linear polarized light with regard to the crystal structure.

Détermination directe des coefficients du potentiel de Dunham par une méthode de moindres carrés non linéaire appliquée aux nombres d'ondes des raies. Application au cas de la molécule HBr

1977 ◽  
Vol 55 (21) ◽  
pp. 1829-1834 ◽  
Author(s):  
P. Niay ◽  
P. Bernage ◽  
C. Coquant ◽  
A. Fayt
Keyword(s):  
Experimental Data ◽  
Least Squares ◽  
Iterative Process ◽  
Nonlinear Least Squares ◽  
Theoretical Framework ◽  
New Method

In this paper, the Dunham potential coefficients are numerically determined by using a nonlinear least squares routine applied directly to the line experimental wave numbers.The results are compared to the ones obtained when using the usual iterative process applied to the H81Br Yi0 and Yi1 equilibrium constants.The al determination new method assumes a theoretical framework (B.O., adiabatic or non-adiabatic) to be valid. One can test this assumption by comparing the experimental data to the calculated ones.

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