Statistical methods in fatigue testing

The course provides an introduction to statistical methods in the context of durability testing, in particular high-cycle fatigue.

The lifetime of a component under low stress is best described by a statistical distribution with a high variance (scatter). In the interest of safety, the lower quantiles of this distribution – e.g. the minimum lifetime that is reached by all but 1% of the parts – need to be estimated accurately. As fatigue tests are time consuming and expensive, we have to draw conclusions on rare events from a small number of observations. An additional problem is that some of the data is usually censored, as tests are stopped after a certain time or number of cycles, even if the component is still intact.

The course consists of two modules:

• Module 1 gives an overview of the statistical methods used in Module 2. We consider descriptive statistics, inferential (model-based) statistics, and some important properties of parametric models. For the latter, we introduce the notion of maximum-likelihood estimators for the parameters and touch briefly on confidence intervals and hypothesis tests.
• Module 2 deals with statistical solutions to common problems in fatigue testing, in particular parameter estimation in the presence of censored data, confidence intervals for extreme quantiles, planning of life tests (a few long tests vs. a larger number of shorter tests), and the estimation of Wöhler curves (S-N curves).

The content of each module is split into two multimedia sessions of approximately 25 minutes length.

Training Objectives

The course is aimed at researchers and engineers working in the field of durability testing who want to get a better understanding of the capabilities and limitations of statistics with regards to their subject. This is necessary to develop more efficient processes and avoid methodical errors.

Prerequisites

The course requires a basic knowledge of calculus. It does not assume any statistical background, but students familiar with the subject can skip Module 1.

About the Authors:

The course is based on a training seminar for engineers that covers modern statistical methods in fatigue testing and load data analysis. The content was developed by

• Dr. Klaus Dreßler
• Dr. Michael Speckert
• Dipl.-Math. Sascha Feth
• Dipl.-Math. Nikolaus Ruf

All authors are members of the Department of Mathematical Methods for Dynamics and Durability (MDF) Fraunhofer Institute for Industrial and Financial Mathematics (ITWM) Fraunhofer-Platz 1 67663 Kaiserslautern Germany

The Fraunhofer society supports applied research in many areas of engineering and technology in direct cooperation with industrial partners. The focus of the MDF group at ITWM lies on the mathematical modelling and simulation of the dynamics and durability of mechanical and mechatronical systems. On the methodical side, this involves multibody simulation (MBS), dynamic finite element methods (FEM), statistics, and optimization. Many applications deal with functional performance engineering for vehicles or vehicle components. Another important area of activity is the simulation of the manufacturing process in order to obtain the desired functionality, e.g. the simulation of metal casting and the resulting durability properties.

As there is a large demand by engineers working in industry to keep up with current methods in computer-based simulation and modelling, the MDF group also offers training seminars related to MBS, FEM, load data analysis, and statistics. The latter serves as the basis for this introductory course, which tries to address some of the problems and questions commonly encountered by engineers working in the field of durability testing.

Topic list

• Module 1: Basic Methods in Statistics, Part I Methods and limitations of descriptive statistics; advantages of model-based statistics; important properties of continuous statistical models. Lecturer: N. Ruf
• Module 1: Basic Methods in Statistics, Part II Properties of the (log-)normal, Weibull, and binomial distribution; maximum-likelihood estimation in parametric models; confidence intervals and tests. Lecturer: N. Ruf
• Module 2: Design and Analysis of Fatigue Experiments, Part I Censored data and parameter estimation; confidence intervals for extreme quantiles. Lecturer: N. Ruf
• Module 2: Design and Analysis of Fatigue Experiments, Part II Test planning using a binomial model (number of components vs. duration); estimation of Wöhler curves (S-N curves). Lecturer: N. Ruf

This course is an outcome of the ILTOF project [4], Innovative Learning and Training on Fracture: the course is maintained free of charge by the TCN Consortium for higher education. The ILTOF project has been funded with support from the European Commission. This publication reflects the views only of the Author(s), and the Commission cannot be held responsible for any use which may be made of the information contained therein.