scholarly journals Research on Iterative Calibration Method of Linear Model Parameters of Gravity Sensor

2020 ◽  
Vol 474 ◽  
pp. 042011
Author(s):  
Shuhai Lu ◽  
Juliang Cao ◽  
Cai Shaokun ◽  
Ruihang Yu ◽  
Bainan Yang
Keyword(s):  
Linear Model ◽  
Calibration Method ◽  
Model Parameters ◽  
Gravity Sensor

scholarly journals Least Squares Estimations for the General Linear Model Parameters with Epsilon Skew Normal Error Term

2020 ◽  
pp. 636-645
Author(s):  
Hussain Karim Nashoor ◽  
Ebtisam Karim Abdulah
Keyword(s):  
Least Squares ◽  
Linear Model ◽  
Least Squares Method ◽  
General Linear Model ◽  
Ordinary Least Squares ◽  
Skewed Distribution ◽  
General Linear ◽  
Average Error ◽  
Model Parameters ◽  
Skew Normal

Examination of skewness makes academics more aware of the importance of accurate statistical analysis. Undoubtedly, most phenomena contain a certain percentage of skewness which resulted to the appearance of what is -called "asymmetry" and, consequently, the importance of the skew normal family . The epsilon skew normal distribution ESN (μ, σ, ε) is one of the probability distributions which provide a more flexible model because the skewness parameter provides the possibility to fluctuate from normal to skewed distribution. Theoretically, the estimation of linear regression model parameters, with an average error value that is not zero, is considered a major challenge due to having difficulties, as no explicit formula to calculate these estimates can be obtained. Practically, values for these estimates can be obtained only by referring to numerical methods. This research paper is dedicated to estimate parameters of the Epsilon Skew Normal General Linear Model (ESNGLM) using an adaptive least squares method, as along with the employment of the ordinary least squares method for estimating parameters of the General Linear Model (GLM). In addition, the coefficient of determination was used as a criterion to compare the models’ preference. These methods were applied to real data represented by dollar exchange rates. The Matlab software was applied in this work and the results showed that the ESNGLM represents a satisfactory model. 

scholarly journals Generalized Exponentiated Weibull Linear Model in the Presence of Covariates

2017 ◽  
Vol 6 (3) ◽  
pp. 75
Author(s):  
Tiago V. F. Santana ◽  
Edwin M. M. Ortega ◽  
Gauss M. Cordeiro ◽  
Adriano K. Suzuki
Keyword(s):  
Regression Model ◽  
Linear Model ◽  
Goodness Of Fit ◽  
Likelihood Function ◽  
Confidence Bands ◽  
Model Parameters ◽  
Random Component ◽  
Monte Carlo Simulation Study ◽  
New Model ◽  
Exponentiated Weibull

A new regression model based on the exponentiated Weibull with the structure distribution and the structure of the generalized linear model, called the generalized exponentiated Weibull linear model (GEWLM), is proposed. The GEWLM is composed by three important structural parts: the random component, characterized by the distribution of the response variable; the systematic component, which includes the explanatory variables in the model by means of a linear structure; and a link function, which connects the systematic and random parts of the model. Explicit expressions for the logarithm of the likelihood function, score vector and observed and expected information matrices are presented. The method of maximum likelihood and a Bayesian procedure are adopted for estimating the model parameters. To detect influential observations in the new model, we use diagnostic measures based on the local influence and Bayesian case influence diagnostics. Also, we show that the estimates of the GEWLM are  robust to deal with the presence of outliers in the data. Additionally, to check whether the model supports its assumptions, to detect atypical observations and to verify the goodness-of-fit of the regression model, we define residuals based on the quantile function, and perform a Monte Carlo simulation study to construct confidence bands from the generated envelopes. We apply the new model to a dataset from the insurance area.

scholarly journals Generalized Born radii computation using linear models and neural networks

2019 ◽  
Vol 36 (6) ◽  
pp. 1757-1764
Author(s):  
Saida Saad Mohamed Mahmoud ◽  
Gennaro Esposito ◽  
Giuseppe Serra ◽  
Federico Fogolari
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Linear Model ◽  
Correlation Coefficient ◽  
Linear Models ◽  
Reference Method ◽  
Supplementary Information ◽  
Model Parameters ◽  
Generalized Born ◽  
Supplementary Material

Abstract Motivation Implicit solvent models play an important role in describing the thermodynamics and the dynamics of biomolecular systems. Key to an efficient use of these models is the computation of generalized Born (GB) radii, which is accomplished by algorithms based on the electrostatics of inhomogeneous dielectric media. The speed and accuracy of such computations are still an issue especially for their intensive use in classical molecular dynamics. Here, we propose an alternative approach that encodes the physics of the phenomena and the chemical structure of the molecules in model parameters which are learned from examples. Results GB radii have been computed using (i) a linear model and (ii) a neural network. The input is the element, the histogram of counts of neighbouring atoms, divided by atom element, within 16 Å. Linear models are ca. 8 times faster than the most widely used reference method and the accuracy is higher with correlation coefficient with the inverse of ‘perfect’ GB radii of 0.94 versus 0.80 of the reference method. Neural networks further improve the accuracy of the predictions with correlation coefficient with ‘perfect’ GB radii of 0.97 and ca. 20% smaller root mean square error. Availability and implementation We provide a C program implementing the computation using the linear model, including the coefficients appropriate for the set of Bondi radii, as Supplementary Material. We also provide a Python implementation of the neural network model with parameter and example files in the Supplementary Material as well. Supplementary information Supplementary data are available at Bioinformatics online.

Experimental Non-Linear Model Updating Applied in Cylindrical Journal Bearings

2001 ◽  
Author(s):  
Katia Lucchesi Cavalca ◽  
Sérgio Junichi Idehara ◽  
Franco Giuseppe Dedini ◽  
Robson Pederiva
Keyword(s):  
Linear Model ◽  
Model Updating ◽  
Optimization Method ◽  
Model Parameters ◽  
Numeric Model ◽  
Rotating Systems ◽  
Non Linear ◽  
Symmetric Rotor ◽  
Set Up ◽  
Experimental Values

Abstract The present paper proposes the use of non linear model updating applying unrestricted optimization method, in order to obtain a methodology, which allows the calibration of mathematical models in rotating systems. An experimental set up for this purpose consists of a symmetric rotor, on a rigid foundation supported by two hidrodynamic cylindrical bearings and with a central disk of considerable mass, working as na unbalancing excitation force. Once the numeric and experimental values are obtained, error vectors are defined, which are the minimization parameters, through the variation of the numeric model parameters. The method presented satisfactory results, as it was able to calibrate the mathematical model, and then to obtain reliable responses for the physical system studied. The research also presents a contribution for the rotating machine desing area as it presents a relatively simple methodology on the updating and revalidation of computacional models for machines and structures.

scholarly journals DoF-Dependent and Equal-Partition Based Lens Distortion Modeling and Calibration Method for Close-Range Photogrammetry

Sensors ◽  
2020 ◽  
Vol 20 (20) ◽  
pp. 5934
Author(s):  
Xiao Li ◽  
Wei Li ◽  
Xin’an Yuan ◽  
Xiaokang Yin ◽  
Xin Ma
Keyword(s):  
Optical Axis ◽  
Focal Length ◽  
Calibration Method ◽  
Depth Of Field ◽  
Model Parameters ◽  
Lens Distortion ◽  
Camera Model ◽  
Distortion Model ◽  
Manual Adjustment ◽  
Close Range

Lens distortion is closely related to the spatial position of depth of field (DoF), especially in close-range photography. The accurate characterization and precise calibration of DoF-dependent distortion are very important to improve the accuracy of close-range vision measurements. In this paper, to meet the need of short-distance and small-focal-length photography, a DoF-dependent and equal-partition based lens distortion modeling and calibration method is proposed. Firstly, considering the direction along the optical axis, a DoF-dependent yet focusing-state-independent distortion model is proposed. By this method, manual adjustment of the focus and zoom rings is avoided, thus eliminating human errors. Secondly, considering the direction perpendicular to the optical axis, to solve the problem of insufficient distortion representations caused by using only one set of coefficients, a 2D-to-3D equal-increment partitioning method for lens distortion is proposed. Accurate characterization of DoF-dependent distortion is thus realized by fusing the distortion partitioning method and the DoF distortion model. Lastly, a calibration control field is designed. After extracting line segments within a partition, the de-coupling calibration of distortion parameters and other camera model parameters is realized. Experiment results shows that the maximum/average projection and angular reconstruction errors of equal-increment partition based DoF distortion model are 0.11 pixels/0.05 pixels and 0.013°/0.011°, respectively. This demonstrates the validity of the lens distortion model and calibration method proposed in this paper.

DefVolc: Interface and web service for fast computation of volcano displacement

2020 ◽  
Author(s):  
Valerie Cayol ◽  
Farshid Dabaghi ◽  
Yo Fukushima ◽  
Marine Tridon ◽  
Delphine Smittarello ◽  
...  
Keyword(s):  
Web Service ◽  
Linear Model ◽  
Web Server ◽  
Model Parameters ◽  
Magma Reservoirs ◽  
Surface Displacements ◽  
Stress Changes ◽  
Speed Up ◽  
Source Geometry ◽  
Volcano Observatories

<div> <div> <div> <p>DefVolc is a suite of programs and a web service intended to help the rapid interpretation of InSAR data, acquired on volcanoes at an increased frequency thanks to the various dedicated satellites. Our objective is to help to rapidely inverse volcano displacements, whether these displacements result from fractures (sheet intrusions or faults) or massive magma reservoirs. These sources may have complex geometries, and they may deform simultaneously. Moreover, volcanoes are associated with prominent topographies. This makes the analysis of surface displacements complex. To appropriately analyse the InSAR displacements, we conduct inverse modelling, using 3D elastostatic boundary element models and a neighbourhood optimization algorithm . We simultaneously invert non-linear model parameters (source geometry and location) and linear model parameters (source stress changes), and further assess mean model parameters and confidence intervals. In order to speed up the setting up of inversions, we developed a users friendly graphical interface. In order to accelerate the inversions, they run on clusters. A web server is proposed to registered users in order to run the inversions on University Clermont Auvergne clusters. Because the web server was developped in the framework of the Eurovolc project framework, European volcano observatories are priority users.</p> </div> </div> </div>

Experimental Validation of a Nonlinear Model Calibration Method Based on Multiharmonic Frequency Responses

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Yousheng Chen ◽  
Andreas Linderholt ◽  
Thomas J. S. Abrahamsson
Keyword(s):  
Steady State ◽  
Frequency Response ◽  
Test Data ◽  
Nonlinear Model ◽  
Model Calibration ◽  
Experimental Validation ◽  
Calibration Method ◽  
Model Parameters ◽  
Response Data ◽  
Starting Point

Correlation and calibration using test data are natural ingredients in the process of validating computational models. Model calibration for the important subclass of nonlinear systems which consists of structures dominated by linear behavior with the presence of local nonlinear effects is studied in this work. The experimental validation of a nonlinear model calibration method is conducted using a replica of the École Centrale de Lyon (ECL) nonlinear benchmark test setup. The calibration method is based on the selection of uncertain model parameters and the data that form the calibration metric together with an efficient optimization routine. The parameterization is chosen so that the expected covariances of the parameter estimates are made small. To obtain informative data, the excitation force is designed to be multisinusoidal and the resulting steady-state multiharmonic frequency response data are measured. To shorten the optimization time, plausible starting seed candidates are selected using the Latin hypercube sampling method. The candidate parameter set giving the smallest deviation to the test data is used as a starting point for an iterative search for a calibration solution. The model calibration is conducted by minimizing the deviations between the measured steady-state multiharmonic frequency response data and the analytical counterparts that are calculated using the multiharmonic balance method. The resulting calibrated model's output corresponds well with the measured responses.

scholarly journals Urban development trend analysis and spatial simulation based on time series remote sensing data: A case study of Jinan, China

PLoS ONE ◽  
2021 ◽  
Vol 16 (10) ◽  
pp. e0257776
Author(s):  
Yanghua Zhang ◽  
Liang Zhao ◽  
Hu Zhao ◽  
Xiaofeng Gao
Keyword(s):  
Time Series ◽  
Urban Development ◽  
Linear Model ◽  
Urban Growth ◽  
Vegetation Type ◽  
Development Trend ◽  
Practical Significance ◽  
Model Parameters ◽  
Growth Trend ◽  
Development Trends

Uncontrolled urban growth detracts from healthy urban development. Understanding urban development trends and predicting future urban spatial states is of great practical significance. In order to comprehensively analyze urbanization and its effect on vegetation cover, we extracted urban development trends from time series DMSP/OLS NTL and NDVI data from 2000 to 2015, using a linear model fitting method. Six urban development trend types were identified by clustering the linear model parameters. The identified trend types were found to accurately reflect the on-ground conditions and changes in the Jinan area. For example, a high-density, stable urban type was found in the city center while a stable dense vegetation type was found in the mountains to the south. The SLEUTH model was used for urban growth simulation under three scenarios built on the urban development analysis results. The simulation results project a gentle urban growth trend from 2015 to 2030, demonstrating the prospects for urban growth from the perspective of environmental protection and conservative urban development.

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