ESTIMATION OF FATIGUE CURVES USING ORTHOGONAL POLYNOMIALS

Abstract

The article proposes a methodology for processing fatigue tests carried out to assess the fatigue curve of materials and structural elements, the most important design characteristic of the endurance, service life and reliability of aircraft products, transport engineering and other structures operating under conditions of both regular and irregular loading. The task of estimating the parameters of the fatigue curve is often complicated by the limited scope of fatigue tests, significant scattering of cyclic durability, uneven duplication of experiments at a given level of alternating stress amplitudes, the presence of censoring, especially at low levels, and other factors. which necessitates the use of the weighted least squares method. These circumstances lead to the violation of the conditions for using standard methods of regression analysis and the least squares method. This is especially true for the confidence assessment of the fatigue curve, the accuracy of which significantly depends on these factors. For this purpose, the article proposes to apply the procedure of orthogonalization of factor characteristics to estimate the parameters of the fatigue curve, which reduces the errors arising from standard approaches and makes it possible to obtain accurate confidence intervals for durability. A special feature of the technique is the use of orthogonal polynomials in statistical procedures, which makes it possible to modify the covariance matrix of estimates by converting it to a diagonal form, regardless of the spread of the weight parameters of the original data. These transformations make it possible to perform statistical procedures for point and confidence estimation when processing the results of fatigue tests. To test the methodology, a statistical analysis of a large volume (about 200 samples) of fatigue tests of samples with varying degrees of stress concentration from titanium alloy VT3-1 and aluminum alloy V-95 was performed, algorithms and computer programs were developed in the public domain.