Modeling of Non-Linear Relations Among Different Design Evaluation Measures for Multi-Objective Design Optimization

2005 ◽  
Author(s):  
H. Yang ◽  
D. Xue ◽  
Y. L. Tu
Keyword(s):  
Design Optimization ◽  
Comparison Method ◽  
Least Square ◽  
Design Evaluation ◽  
Linear Relations ◽  
Evaluation Measures ◽  
Multi Objective ◽  
Fitting Method ◽  
Non Linear ◽  
Curve Fitting Method

This research introduces a new approach to model the non-linear relations among different design evaluation measures and to achieve the optimal design considering these different design evaluation measures through multi-objective optimization. In this approach, different design evaluation measures are mapped to comparable design evaluation indices. The non-linear relation between a design evaluation measure and its design evaluation index is identified based on the least-square curve-fitting method. The weighting factors for different design evaluation indices, representing the importance measures of these indices in the multi-objective design optimization, are achieved using the pair-wise comparison method. A case study example of automobile caliper disc brake design considering 4 different design evaluation measures is given to illustrate the effectiveness of the introduced approach.

A Useful Curve Fitting Method for Concrete Uniaxial Compressive Experiment Data

2011 ◽  
Vol 291-294 ◽  
pp. 1015-1020 ◽  
Author(s):  
Chong Jin ◽  
Hong Wang ◽  
Xiao Zhou Xia
Keyword(s):  
Experimental Data ◽  
Orthogonal Polynomial ◽  
Least Square ◽  
Base Function ◽  
Concrete Material ◽  
Fitting Method ◽  
Orthogonal Base ◽  
The Matrix ◽  
Uniform Function ◽  
Curve Fitting Method

Based on the superiority avoiding the matrix equation to be morbid for those fitting functions constructed by orthogonal base, the Legendre orthogonal polynomial is adopted to fit the experimental data of concrete uniaxial compression stress-strain curves under the frame of least-square. With the help of FORTRAN programming, 3 series of experimental data is fitted. And the fitting effect is very satisfactory when the item number of orthogonal base is not less than 5. What’s more, compared with those piecewise fitting functions, the Legendre orthogonal polynomial fitting function obtained can be introduced into the nonlinear harden-soften character of concrete constitute law more convenient because of its uniform function form and continuous derived feature. And the fitting idea by orthogonal base function will provide a widely road for studying the constitute law of concrete material.

Reliability and Usefulness of the Fitting of a Modified Gamma Function to Time-Activity Curves by Means of a Non-Linear Iterative Least-Square Method

1981 ◽  
Vol 20 (04) ◽  
pp. 195-197
Author(s):  
J. M. Fránquiz
Keyword(s):  
Gamma Function ◽  
Least Square Method ◽  
Least Square ◽  
Base Line ◽  
Time Activity ◽  
Appearance Time ◽  
Least Square Fitting ◽  
Fitting Method ◽  
Non Linear ◽  
Least Square Fitting Method

A non-linear iterative least-square fitting method is presented for calculating the parameters of a modified gamma function. The method permits the correction of the appearance time (AT) and the curve parameters in those situations in which AT cannot be estimated with accuracy. The reliability and accuracy of the method is studied in experimental and simulated curves by means of a computer, comparing the results with those obtained by the method of Starmer and Clark for different initial selections of AT and noise at the base line. The usefulness of the method is shown in situations where the curves are distorted in their initial part.

Improved modified moving average analysis of T-wave alternans using least squares-based curve fitting method

2014 ◽  
Vol 07 (04) ◽  
pp. 1450044 ◽  
Author(s):  
Xiang-Kui Wan ◽  
Kang-Hui Yan ◽  
Ang Li ◽  
Ming-Hu Wu
Keyword(s):  
Curve Fitting ◽  
Moving Average ◽  
Least Square Method ◽  
Least Square ◽  
T Wave ◽  
Fitting Method ◽  
Average Analysis ◽  
T Wave Alternans ◽  
Improved Performance ◽  
Curve Fitting Method

T-wave alternans (TWA) in surface electrocardiograph (ECG) signal is considered a marker of abnormal ventricular function which may be associated with ventricular tachycardia. Several methods have been developed in recent years to evaluate the important feature. One such method is known as modified moving average (MMA) analysis, which performs well for different levels of TWA, but it is sensitive to the noise in T-waves. In this paper we propose an improved MMA algorithm, which adds a stage of T-wave curve fitting for the MMA method before intermediate averaging. The curve fitting is performed by means of least square method technique. Our assessment study demonstrates the improved performance.

Simultaneous Determinations of Liver- and Bone-Type Alkaline Phosphatase by Curve-Fitting of Inhibition Kinetic Data. I. Development and Evaluation of an Absorbance-Based Method

1992 ◽  
Vol 38 (2) ◽  
pp. 238-246 ◽  
Author(s):  
Carol P Fitzpatrick ◽  
Harry L Pardue
Keyword(s):  
Alkaline Phosphatase ◽  
Curve Fitting ◽  
Comparison Method ◽  
Fitting Method ◽  
Least Squares Fit ◽  
Relative Standard ◽  
Two Component ◽  
Primary Focus ◽  
Curve Fitting Method ◽  
The Individual

Abstract We describe an approach for the simultaneous determination of isoenzymes of alkaline phosphatase (EC 3.1.3.1) based on the kinetic behavior of inhibition reactions. Data for absorbance vs time, collected while enzymes are being inhibited, are fitted with suitable models to obtain results related to activities of the individual isoenzymes. The primary focus is on two-component mixtures of the bone and liver isoenzymes of alkaline phosphatase, but some results are reported for three- and four-component mixtures. Factors studied include choices of inhibitors, buffers, pH, ionic strength, substrate concentration, kinetic models, data ranges, data densities, and data-processing approaches and programs. Criteria used to select optimal conditions include measurement times, detection limits, useful range, and agreement between expected and computed results for mixtures of isoenzymes. For two-component mixtures, a linear least-squares fit of isoenzyme content computed with the curve-fitting method (y) v a comparison method (x) gave y = 0.96 (+/- 0.05)x + 3.8 (+/- 3)% with r = 0.97 and standard error of the estimate of 9.4% for a range from 15 to 300 U/L. The pooled relative standard deviation (CV) for results was about 5%. Results were degraded for three- and four-component samples.

scholarly journals Immediacy Premium: A Simpler Measure to Estimate the Hyperbolic Delay Discounting Rate (k)

2021 ◽  
Author(s):  
Harli Berk ◽  
Tanya Gupta ◽  
Federico Sanabria
Keyword(s):  
Delay Discounting ◽  
Curve Fitting ◽  
Hyperbolic Discounting ◽  
Dependent Measure ◽  
Least Square ◽  
Published Data ◽  
Fitting Method ◽  
Subjective Value ◽  
Curve Fitting Method ◽  
The Individual

The estimation of delay discounting rates (k) typically assumes that the relative subjective value of a reinforcer declines as a reciprocal function of its delay. Nonetheless, estimates of k based on least-squares fits of the hyperbolic discounting function to relative subjective values appear to have serious limitations. This curve-fitting method yield average discounting functions that may not accurately reflect the individual subjects’ data. The present study used the hyperbolic discounting function to derive a new dependent measure, termed immediacy premium, which is a linear function of delay. By averaging linear rather than reciprocal functions, the averaged estimates obtained from immediacy premiums are more representative of individual data, and comparisons between mean estimates across treatments or samples is more meaningful. Using published data, the similarity of k estimates based on least-square fits to relative subjective values and immediacy premiums was evaluated. The assumptions of this curve-fitting method (normally-distributed error with mean of zero, independent across delays within the same subject) were evaluated for each dependent measure. Systematic species-dependent differences in estimates of k were observed when obtained from one measure or another. Violations of curve-fitting assumptions were observed regardless of measure, but primarily in human data. These violations were simulated to determine the likelihood that they emerge from the transformation between dependent measures. Taken together, the reported analysis yields a qualified support for the adoption of immediacy premiums as the basis for the estimation of k.

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