On the use of the simplex algorithm for the absolute deviation curve fitting problem

1984 ◽  
Vol 15 (3) ◽  
pp. 393-399
Author(s):  
J.T. Buchanan ◽  
J. Hammerton
Keyword(s):  
Curve Fitting ◽  
Simplex Algorithm ◽  
Absolute Deviation ◽  
The Absolute ◽  
Fitting Problem

scholarly journals A Novel Statistical Optimization Algorithm for Estimating Perfusion Curves in Susceptibility Contrast-Enhanced MRI

2021 ◽  
Vol 15 ◽  
Author(s):  
Zhenghui Hu ◽  
Fei Li ◽  
Junhui Shui ◽  
Yituo Tang ◽  
Qiang Lin
Keyword(s):  
Gamma Distribution ◽  
Curve Fitting ◽  
Attractive Alternative ◽  
Dynamic Susceptibility ◽  
Brain Physiology ◽  
Initial Values ◽  
Concentration Time ◽  
Contrast Enhanced ◽  
Susceptibility Contrast ◽  
Fitting Problem

Dynamic susceptibility contrast-enhanced magnetic resonance imaging is an important tool for evaluating intravascular indicator dynamics, which in turn is valuable for understanding brain physiology and pathophysiology. This procedure usually involves fitting a gamma-variate function to observed concentration-time curves in order to eliminate undesired effects of recirculation and the leakage of contrast agents. Several conventional curve-fitting approaches are routinely applied. The nonlinear optimization methods typically are computationally expensive and require reliable initial values to guarantee success, whereas a logarithmic linear least-squares (LL-LS) method is more stable and efficient, and does not suffer from the initial-value problem, but it can show degraded performance, especially when a few data or outliers are present. In this paper, we demonstrate, that the original perfusion curve-fitting problem can be transformed into a gamma-distribution-fitting problem by treating the concentration-time curves as a random sample from a gamma distribution with time as the random variable. A robust maximum-likelihood estimation (MLE) algorithm can then be readily adopted to solve this problem. The performance of the proposed method is compared with the nonlinear Levenberg-Marquardt (L-M) method and the LL-LS method using both synthetic and real data. The results show that the performance of the proposed approach is far superior to those of the other two methods, while keeping the advantages of the LL-LS method, such as easy implementation, low computational load, and dispensing with the need to guess the initial values. We argue that the proposed method represents an attractive alternative option for assessing intravascular indicator dynamics in clinical applications. Moreover, we also provide valuable suggestions on how to select valid data points and set the initial values in the two traditional approaches (LL-LS and nonlinear L-M methods) to achieve more reliable estimations.

The Curve Fitting Problem: A Bayesian Rejoinder

1999 ◽  
Vol 66 ◽  
pp. S390-S402 ◽  
Author(s):  
Prasanta S. Bandyopadhyay ◽  
Robert J. Boik
Keyword(s):  
Curve Fitting ◽  
Fitting Problem

scholarly journals The iAssist Navigation System Demonstrated Superior Radiological Outcomes in Restoring Mechanical Alignment and Component Sagittal Positioning in Total Knee Arthroplasty

2020 ◽  
Author(s):  
Jiaxiang Gao ◽  
Yunfei Hou ◽  
Zhichang Li ◽  
Runjun Li ◽  
Yan Ke ◽  
...  
Keyword(s):  
Total Knee Arthroplasty ◽  
Clinical Outcomes ◽  
Knee Arthroplasty ◽  
Navigation System ◽  
Clinical Parameters ◽  
Mechanical Alignment ◽  
Absolute Deviation ◽  
Total Knee ◽  
The Absolute

Abstract Background: This study aimed to determine whether the iAssist navigation system (NAV) could improve the accuracy of restoring mechanical axis (MA), component positioning, and clinical outcomes compared to conventional (CON) total knee arthroplasty (TKA). Methods: A total of 301 consecutive patients (NAV: 27, CON: 274) were included. A 1:4 propensity score matching (PSM) was performed between the two groups according to preoperative demographic and clinical parameters. The postoperative MA, femoral coronal angle (FCA), femoral sagittal angle (FSA), tibial coronal angle (TCA) and tibial sagittal angle (TSA) were compared. Absolute deviations of aforementioned angles were calculated as the absolute value of difference between the exact and ideal value and defined as appropriate if within 3°, otherwise regarded as outliers. Additional clinical parameters, including the Knee Society knee and function scores (KSKS and KSFS) and range of motion (ROM), were assessed at the final follow-up (mean follow-up time was 21.88 and 21.56 months respectively for NAV and CON group). Results: A total of 98 patients/102 knees were analyzed after the PSM (NAV: 21 patients/24 knees, CON: 77 patients/78 knees). In the NAV group, the mean MA, FCA and TSA were significantly improved (p = 0.019, 0.006, <0.001, respectively). Proportions of TKAs within a ±3°deviation were significantly improved in all the postoperative radiological variables except for TCA (p = 0.003, 0.021, 0,017, 0.013, respectively for MA, FCA, FSA, and TSA). The absolute deviations of FSA and TSA were also significantly lower in the NAV group (p = 0.016, 0.048, respectively). In particular, no significant differences were found in either mean value, absolute deviation or outlier ratio of TCA between two groups. For the clinical outcomes, there were no significant differences between two groups, although KSKS, KSFS and ROM (p<0.01, respectively) dramatically improved compared to baseline. Conclusions: We suggested that the iAssist system could improve the accuracy and precision of mechanical alignment and component positioning without significant improvement of clinical outcomes. Further long-term high-quality studies are necessary to validate the results.

The Method of Least Squares

2011 ◽  
pp. 181-185 ◽  
Author(s):  
Bernd Jaeger
Keyword(s):  
Least Squares ◽  
Curve Fitting ◽  
Method Of Least Squares ◽  
Unknown Parameters ◽  
Nonlinear Curve Fitting ◽  
Nonlinear Curve ◽  
Fitting Problem

The method of least squares is a geometric principle of curve fitting. The unknown parameters of a function are calculated in such a way that the sum of squared differences between function values and measurements gets minimal. Examples are given for a linear and a nonlinear curve fitting problem. Consequences of model linearizations are explained.

scholarly journals The Absolute Deviation Rank Diagnostic Approach to Gear Tooth Composite Fault

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Guangbin Wang ◽  
Wenhui Deng ◽  
Xiaoyang Du ◽  
Xuejun Li
Keyword(s):  
Gear Tooth ◽  
Frequency Doubling ◽  
Diagnostic Approach ◽  
Dynamics Model ◽  
Absolute Deviation ◽  
Single Fault ◽  
Simulating Analysis ◽  
Gear Fault ◽  
The Absolute ◽  
Set Up

Aiming at nonlinear and nonstationary characteristics of the different degree with single fault gear tooth broken, pitting, and composite fault gear tooth broken-pitting, a method for the diagnosis of absolute deviation of gear faults is presented. The method uses ADAMS, respectively, set-up dynamics model of single fault gear tooth broken, pitting, and composite fault gear tooth broken-pitting, to obtain the result of different degree of broken teeth, pitting the single fault and compound faults in the meshing frequency, and the amplitude frequency doubling through simulating analysis. Through the comparison with the normal state to obtain the sensitive characteristic of the fault, the absolute value deviation diagnostic approach is used to identify the fault and validate it through experiments. The results show that absolute deviation rank diagnostic approach can realize the recognition of gear single faults and compound faults with different degrees and provide quick reference to determine the degree of gear fault.

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