Application of Logistic Regression in Calculation of Damageability of Solid Deformable Body

Abstract

The paper proposes a logistic regression model for estimating the damageability of a solid deformable body. A training sample is randomly generated from a uniform distribution over the area containing the dangerous volume. For linear separability of the training sample, a classifying kernel is used in the form of a radial basis function. The regression parameters were estimated using the maximum likelihood method, then the system of nonlinear equations was solved by the Newton–Raphson method. To determine the quality of the classifier, a ROC analysis was performed, which consists in constructing the ROC curve and calculating the area between the ROC curve and the specificity axis. For adequate assessment of the work, the logistic regression model is used to calculate the damage of a half-plane when a normally distributed load acts on its boundary. The paper also analyzes the stability of the model parameter estimation algorithms when generating a random sample of training sample.

Keywords

• mechanics of damageability
• machine learning
• logistic regression
• logit model
• discriminant function