Wednesday, December 23, 2015

Hamiltonian Monte Carlo with Stan

Stan is a library for doing Bayesian statistical inference. One of the really cool capabilities it has is the Hamiltonian Monte Carlo (HMC) method rather than the more common Markov Chain approaches. There are interfaces for using the library from Python, R or the command line:
Stan is based on a probabilistic programming language for specifying models in terms of probability distributions. Stan’s modeling language is is portable across all interfaces (PyStan, RStan, CmdStan).

I found this video from the documentation page a very understandable description of the Hamiltonian Monte Carlo approach used by Stan. It's neat to see how using a deterministic dynamics can improve on random walks. I'm reminded of Jaynes: "It appears to be a quite general principle that, whenever there is a randomized way of doing something, then there is a nonrandomized way that delivers better performance but requires more thought."

Wednesday, September 23, 2015

A One-Equation Local Correlation-Based Transition Model

Here's the Abstract:
A model for the prediction of laminar-turbulent transition processes was formulated. It is based on the LCTM (‘Local Correlation-based Transition Modelling’) concept, where experimental correlations are being integrated into standard convection-diffusion transport equations using local variables. The starting point for the model was the γ-Re θ model already widely used in aerodynamics and turbomachinery CFD applications. Some of the deficiencies of the γ-Re θ model, like the lack of Galilean invariance were removed. Furthermore, the Re θ equation was avoided and the correlations for transition onset prediction have been significantly simplified. The model has been calibrated against a wide range of Falkner-Skan flows and has been applied to a variety of test cases.
Keywords: Laminar-turbulent transition, Correlation, Local variables
Authors: Florian R. Menter, Pavel E. Smirnov , Tao Liu, Ravikanth Avancha

Transition location, and subsequent turbulence modeling remain the largest source of uncertainty for most engineering flows. Even for chemically reacting flows the source of uncertainty is often less the parameters and reactions for the chemistry, and more the uncertainty in the fluid state driven by shortcomings in turbulence and transition modeling.

Sunday, March 22, 2015

Reliability Growth: Enhancing Defense System Reliability

This report (pdf) from the National academies on reliability growth is interesting. There's a lot of good stuff on design for reliability, physics of failure, highly accelerated life testing, accelerated life testing and reliability growth modeling. Especially useful is the discussion about the suitability of assumptions underlying some of the different reliability growth models.

The authors provide a thorough critique of MIL-HDBK-217, Reliability Prediction of Electronic Equipment, in Appendix D, which is probably worth the price of admission by itself. If you're concerned with product reliability you should read this report (lots of good pointers to the lit).

Tuesday, January 13, 2015

Guidelines for Planning and Evidence for Assessing a Well-Designed Experiment

This paper is full of great guidance for planning a campaign of experimentation, or assessing the sufficiency of a plan that already exists. The authors break up the effort into four phases:
1. Plan a Series of Experiments to Accelerate Discovery
1. Design Alternatives to Span the Factor Space
2. Decide on a Design Strategy to Control the Risk of Wrong Conclusions
2. Execute the Test
3. Analyze the Experimental Design
They give a handy checklist for each phase (reproduced below). The checklists are comprehensive (significantly more than my little list of questions) and I think they stand-alone, but the whole paper is well worth a read. Design of experiments is more than just math, as this paper stresses it is a strategy for discovery.