BenBales
summary
Bayesian inversion recovers elastic constants of single‑crystal superalloys from resonance modes using Stan with embedded eigenvalue solvers and custom autodiff eigen solvers wrapped around C++ PDE code. Results are computationally heavy (each run can take a day) and currently rest on one sample revealing a misorientation ridge, which sampling exposes while optimization later also finds point estimates. Workable estimates need population replicates; sampling yields a physical hypothesis (extra symmetry/columnar structure) that optimization alone misses.
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chapters (14)
- 0:00Bayesian estimation of elastic constants
- 2:09Superalloys in jet engines
- 5:00Hooke’s law basics
- 6:25Measuring resonance modes
- 8:34Single crystal complexities
- 11:22Bayesian model with eigenvalues
- 12:25Results from cobalt nickel tests
- 13:29Limitations of single-sample analysis
- 14:36Optimization versus Bayesian inference
- 16:00Non-identifiability in Stan
- 17:46Future directions in material science
- 18:09Q&A
- 19:56Future work on fatigue and creep
- 20:59Additional resources
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