A regularized approach to linear regression of fatigue life measurements

2016 ◽  
Vol 7 (1) ◽  
pp. 95-105 ◽  
Author(s):  
S. Ali Faghidian
Keyword(s):  
Experimental Data ◽  
Fatigue Life ◽  
Linear Regression ◽  
Tikhonov Regularization ◽  
Regularization Method ◽  
Initial Guess ◽  
Measurement Noise ◽  
Attractive Alternative ◽  
Life Distribution ◽  
Content Type

Purpose – The linear regression technique is widely used to determine empirical parameters of fatigue life profile while the results may not continuously depend on experimental data. Thus Tikhonov-Morozov method is utilized here to regularize the linear regression results and consequently reduces the influence of measurement noise without notably distorting the fatigue life distribution. The paper aims to discuss these issues. Design/methodology/approach – Tikhonov-Morozov regularization method would be shown to effectively reduce the influences of measurement noise without distorting the fatigue life distribution. Moreover since iterative regularization methods are known to be an attractive alternative to Tikhonov regularization, four gradient iterative methods called as simple iteration, minimum error, steepest descent and conjugate gradient methods are examined with an appropriate initial guess of regularized coefficients. Findings – It has been shown that in case of sparse fatigue life measurements, linear regression results may not have continuous dependence on experimental data and measurement error could lead to misinterpretations of the solution. Therefore from engineering safety point of view, utilizing regularization method could successfully reduce the influence of measurement noise without significantly distorting the fatigue life distribution. Originality/value – An excellent initial guess for mixed iterative-direct algorithm is introduced and it has been shown that the combination of Newton iterative approach and Morozov discrepancy principle is one of the interesting strategies for determination of regularization parameter having an excellent rate of convergence. Moreover since iterative methods are known to be an attractive alternative to Tikhonov regularization, four gradient descend methods are examined here for regularization of the linear regression problem. It has been found that all of gradient decent methods with an appropriate initial guess of regularized coefficients have an excellent convergence to Tikhonov-Morozov regularization results.

scholarly journals A modified Tikhonov regularization method based on Hermite expansion for solving the Cauchy problem of the Laplace equation

2020 ◽  
Vol 18 (1) ◽  
pp. 1685-1697
Author(s):  
Zhenyu Zhao ◽  
Lei You ◽  
Zehong Meng
Keyword(s):  
Cauchy Problem ◽  
Laplace Equation ◽  
Tikhonov Regularization ◽  
Regularization Method ◽  
Regularization Parameter ◽  
Solution Process ◽  
Tikhonov Regularization Method ◽  
Hermite Expansion ◽  
The Cauchy Problem ◽  
Ill Posed

Abstract In this paper, a Cauchy problem for the Laplace equation is considered. We develop a modified Tikhonov regularization method based on Hermite expansion to deal with the ill posed-ness of the problem. The regularization parameter is determined by a discrepancy principle. For various smoothness conditions, the solution process of the method is uniform and the convergence rate can be obtained self-adaptively. Numerical tests are also carried out to verify the effectiveness of the method.

scholarly journals Fatigue Modeling and Numerical Analysis of Re-Filling Probe Hole of Friction Stir Spot Welded Joints in Aluminum Alloys

Materials ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2171
Author(s):  
Armin Yousefi ◽  
Ahmad Serjouei ◽  
Reza Hedayati ◽  
Mahdi Bodaghi
Keyword(s):  
Experimental Data ◽  
Tensile Strength ◽  
Fatigue Life ◽  
Fatigue Strength ◽  
Fatigue Behavior ◽  
Element Model ◽  
Plastic Strain Amplitude ◽  
Friction Stir ◽  
Probe Hole ◽  
Good Agreement

In the present study, the fatigue behavior and tensile strength of A6061-T4 aluminum alloy, joined by friction stir spot welding (FSSW), are numerically investigated. The 3D finite element model (FEM) is used to analyze the FSSW joint by means of Abaqus software. The tensile strength is determined for FSSW joints with both a probe hole and a refilled probe hole. In order to calculate the fatigue life of FSSW joints, the hysteresis loop is first determined, and then the plastic strain amplitude is calculated. Finally, by using the Coffin-Manson equation, fatigue life is predicted. The results were verified against available experimental data from other literature, and a good agreement was observed between the FEM results and experimental data. The results showed that the joint’s tensile strength without a probe hole (refilled hole) is higher than the joint with a probe hole. Therefore, re-filling the probe hole is an effective method for structures jointed by FSSW subjected to a static load. The fatigue strength of the joint with a re-filled probe hole was nearly the same as the structure with a probe hole at low applied loads. Additionally, at a high applied load, the fatigue strength of joints with a refilled probe hole was slightly lower than the joint with a probe hole.

The IRS eyes professor's movie: a taxation case exercise

2013 ◽  
Vol 9 (2) ◽  
pp. 58-64
Author(s):  
Jayanti Bandyopadhyay ◽  
Paul F. McGee ◽  
Linda A. Hall
Keyword(s):  
Foreign Country ◽  
Attractive Alternative ◽  
Sufficient Information ◽  
Case Description ◽  
Red Flags ◽  
Content Type ◽  
Accounting Rules ◽  
The Individual ◽  
Tax Accounting

Case description This case illustrates the tax implications of a movie produced in a foreign country that resulted in a loss. Teaching opportunities include the application of tax rules to a Schedule C business loss and a resulting net operating loss (NOL) deduction, the consideration of hobby and passive activity losses, the tax treatment of funds received in a divorce settlement, and how an individual might handle a possible IRS examination. Students are asked to prepare a revised Form 1040 for the movie business loss and the individual NOL deduction based on evidence provided in the case. Sufficient information is provided in the case to identify audit “red flags” in a tax return. Using the tale of an actual movie production in a foreign country and its consequent tax implications can provide an attractive alternative to teaching tax accounting rules that are often considered by students as “dry”.

Fatigue Reliability Functions in Semilogarithmic Coordinates

1991 ◽  
Author(s):  
Vladimir A. Avakov
Keyword(s):  
Fatigue Life ◽  
Coordinate System ◽  
Strength Distribution ◽  
Fatigue Reliability ◽  
Life Distribution ◽  
Similar Transformation ◽  
Asymptotic Type ◽  
Life Distributions ◽  
Strength Distributions

Abstract In the previous publication [2], the transformation between fatigue life and strength distribution was established using double-logarithmic coordinate system (lnN-lnS). Here, a similar transformation is established using a semi logarithmic (lnN-S) coordinate system. With the aid of the developed orthogonal relations, lognormal, Weibull and three-parameter logweibull life distributions have been transformed into normal, asymptotic type 1 of smallest value, and three-parameter Weibull strength distributions, respectively. This procedure may be applied to other types of fatigue life distribution.

Sign in / Sign up

Export Citation Format

Share Document