Multiple Changepoint Analysis of Noisy Nonlinear Data with an Application to Modeling Crack Growth in Additively Manufactured Titanium

• Activity Number: 504 - The Future of Statistical Consulting and Collaboration
• Type: Topic Contributed
• Date/Time: Wednesday, July 31, 2019 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Consulting
• Author(s): Lucas Koepke* and Jolene Splett and Tim Quinn and Nik Hrabe and Jake Benzing and Michael Frey
• Companies: University of Colorado, NIST and National Institute of Standards and Technology and National Institute of Standards and Technology and National Institute of Standards and Technology and National Institute of Standards and Technology and National Institute of Standards and Technology
• Keywords: changepoint; isotonic regression; nonlinear least squares; pool-adjacent-violators algorithm

Abstract

Noisy measurement data pose a challenge for changepoint analysis, especially in the presence of multiple changepoints and when the model is nonlinear. We explore various approaches to estimating changepoints and their standard errors under these conditions. We consider whether adding a monotonicity constraint improves the changepoint estimates and reduces their standard errors. We finish with a novel application to material science using crack growth data from additively manufactured titanium. As cyclic loading is applied to a test specimen, crack growth can be partitioned into three regimes: slow-growth, mid-growth, and high-growth. We improve estimates of the transition points between these regimes versus those made by experts in the field by adding confidence bounds to the changepoint locations, allowing for designed experiments to study treatment effects on changepoint location.