China
Africa
Explore chapters and articles related to this topic
Estimation from Measurements
Published in Clarence W. de Silva, Sensor Systems, 2016
Clearly, linear least-squares fit is an estimation method, which “estimates” the two parameters of an input/output model (process model), the straight line. It fits a given set of data to a straight line such that the squared error is a minimum. The estimated straight line is known as the “linear regression line.” In the context of sensing and instrumentation, it is also known as the “mean calibration curve.” Instrument linearity may be represented by the largest deviation of the input/output data (or the actual calibration curve, which can be nonlinear) from the least-squares straight-line fit of the data (or the mean calibration curve). LSE comes under the general subject of “model identification,” “system identification,” or “experimental modeling,” where a model (static or dynamic) is fitted to the data. Essentially, the parameters of the model are estimated. A treatment of estimating the parameters of a dynamic (nonalgebraic) model is beyond the scope of the present treatment.
Flow Injection Determination of Aqueous Sulfate (Methylthymol Blue Method)
Published in James P. Lodge, Methods of Air Sampling and Analysis, 2017
Measure mean peak heights obtained for each concentration and plot against the concentration of the sample injected. A linear plot should result. Compute the best fit of the data to a straight line using standard linear least-squares regression. A typical equation obtained is peak height (A.U.) = (0.0383 ± 0.0003) × µg/mL (S042−) + (−0.0009 ± 0.0006)
Data regression and curve fitting
Published in Edwin Zondervan, A Numerical Primer for the Chemical Engineer, 2019
In this chapter we have seen how fit parameters of a model can be fitted to a data set using the linear least squares method. We found out how to calculate the regression coefficients and how to perform a statistical analysis of the model using ANOVA. We also postulated expressions for the confidence limits for the fit parameters and the predicted points.
Remarks on the experimental behaviour of curved surface sliders of the new Polcevera Bridge in Genoa
Published in Structure and Infrastructure Engineering, 2023
Andrea Miano, Marcello Cademartori, Antimo Fiorillo, Angelo Figundio, Marco Di Ludovico, Andrea Prota
In order to maximize the available information about the static and dynamic frictional coefficients, all the results (from both certification and acceptance tests performed according to EN 15129) have been used and discussed in this section. Regressions laws have been derived from the data, by also comparing them with the outcomes of previous literature studies. Linear least squares fitting is a mathematical procedure for finding the best-fitting line to a given set of points by minimizing the sum of the squares of the residuals (offsets) of the data from the line. Herein, linear regression is used to find the relationship between the (logarithm of) frictional coefficient, lnμ, and the (logarithm of) contact pressure, lnσ. Logarithmic linear regression in structural reliability is a widely used approach in literature (see e.g. Cornell, Jalayer, Hamburger, & Foutch, 2002; Jalayer, Ebrahimian, & Miano, 2020; Jalayer et al. 2021; Miano, Sezen, Jalayer, & Prota, 2017). This is equivalent to fitting a power-law curve to the μ−σ response in the arithmetic scale that predicts the conditional median of μ for a given value of the contact pressure σ, denote as ημ |σ, as follows: where ln a and b are the logarithmic linear regression parameters; βμ|σ is the logarithmic standard deviation of regression (i.e. the standard error of regression); {σi, μi}, i = 1: n, are the n outcomes of the tests.
Dynamic analysis and identification of multiple fault parameters in a cracked rotor system equipped with active magnetic bearings: a physical model based approach
Published in Inverse Problems in Science and Engineering, 2020
Real part consisting of multi harmonic (ith) response is represented as, Imaginary part consisting multi-harmonic (ith) response is represented as, The superscripts: Re and Im represent the real and imaginary responses, respectively. The linear least-square regression is a primary tool for finding out the best fit data between the data and the system model. The regression form of estimation equation for the general multi-harmonic (i = −n,, −1, 0, 1,, n) for backward components and forward components with zeroth component which represents the DC point for static force signal consisting the forward and backward whirls, is expressed as The identifiables of the least-square estimator are expressed, in matrix form as, The A matrix, known as the design matrix, is a rectangular matrix, which often suffers from ill-conditioning during its pseudo-inverse process. Often, it is convenient to use a linear least-squares prediction technique to estimate the parameters. The estimation of the unknown parameters obtained from linear least-squares regression is the optimal estimates from a wide-range class of possible parameter estimates under the usual assumptions used for the system modelling. In the present case, the A matrix has the number of equations larger than the number of unknowns to be estimated {(2n + 1) > 8}, where n is the number of harmonics to be considered, thus the system is overdetermined and in general have no exact solution. Hence, the least-squares approach aims to minimize the residual vector to find out the estimation. The regression matrix and the regressor matrix obtained are given in Appendix A.