Bayesian Statistical Methods

Centre of Excellence in Computational Complex Systems Research

 

Bayesian Modeling of the Concrete Quality

Researchers: Aki Vehtari, Jouko Lampinen, and Hanna Järvenpää (Lohja Rudus)

The goal of the project was to develop models for predicting how the aggregate characteristics affect quality properties of concrete, as a part of a large quality control program of the industrial partner of the project. Need for such models is significant as conventional concrete aggregate supplies are becoming depleted, and environmental aspects limit the use of existing sources.

Based on the expert knowledge and preliminary analysis it was known that there were nonlinear effects, strong interactions and dependencies in the covariates. Useful model in such situations is a non-linear nonparametric Gaussian process model, which can handle interactions implicitly. Student's t-distribution with unknown number of degrees of freedom was used as a robust residual model. Posterior and predictive distributions were computed with MCMC methods.

Although the model used can handle irrelevant covariates implicitly, it was useful to make explicit covariate selection to make models more explainable by removing the covariates which were irrelevant in predictive sense. Covariate selection was made using a decision theoretic approach aided by using posterior probabilities of the models to guide the search for the good models. The expected predictive likelihoods needed in the decision theoretic approach were computed using cross-validation predictive densities and the posterior probabilities were computed with reversible jump MCMC. The marginal posterior probabilities of the covariates were also used to communicate the relative importance of the covariates in the final selected models. Cross-validation predictive densities were also used to compute expected predictive accuracy of the models in units of quality measurements, and thus the concrete expert could better assess the usefulness of the models.

By using the models and conclusions based on them it is possible to reduce the proportion of the natural gravel from 50% to 5%-20% and achieve 5-15% savings in concrete manufacturing.

See also

Bayesian Model Assessment and Selection Using Expected Utilities

References

  • Ilkka Kalliomäki, Aki Vehtari and Jouko Lampinen (2005). Shape analysis of concrete aggregates for statistical quality modeling. Machine Vision and Applications, 16(3):197-201. (PDF)

  • Aki Vehtari, Jouko Lampinen and Hanna Järvenpää (2002). Bayesian modelling of the concrete quality. Oral presentation in the Practical Bayesian Statistics 5. (Slides in PDF)

  • Aki Vehtari and Jouko Lampinen (2003). Expected utility estimation via cross-validation. In J. M. Bernardo, et al., editors, Bayesian Statistics 7, 701-710. Oxford University Press. (PostScript) (PDF)

  • Aki Vehtari and Jouko Lampinen (2002). Bayesian model assessment and comparison using cross-validation predictive densities. Neural Computation, 14(10):2439-2468. (PostScript) (PDF)

  • Aki Vehtari and Jouko Lampinen (2002). Bayesian input variable selection using posterior probabilities and expected utilities. Report B31, Laboratory of Computational Engineering, Helsinki University of Technology. (PostScript) (PDF)

  • Hanna Järvenpää (2001). Quality Characteristics of Fine Aggregates and Controlling their Effects on Concrete. Acta Polytechnica Scandinavica, Civil Engineering and Building Construction Series No. 122 (Abstract and PDF)