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Bayesian Neural Network

The software implemented for the neural networks with Bayesian framework is developed by Dr.Mackey. Bayesian formalism utilizes learning from data and uncertainty about the relationship being learned is represented by probability. We have prior belief about the data and this is expressed as probability distribution over the networks of weights. After seeing data our revised belief is expressed in terms of posterior distribution over network weights.

Database used to implement the neural network on titanium alloys developed by CAMM standard stereological procedures. The database used to model the network is normalized and divided into training data set and test data set. The training data set is used to train the network and test data set is used to test the network trained by training data set. Database is trained with different seeds and hidden nodes. The network which has minimum test error generalizes data better. This model which has the minimum test set error is used to predict the outputs. Mackay developed Bayesian frame work in which uncertainty in predictions are represented with error bars. These error bars are large when the data is sparse or locally noisy.

Advantages of Bayesian approach [2]:

  1. Complexity of the non linear models is automatically controlled.
  2. Reliability of the model prediction is represented with the error bars.
  3. Automatic relevance determination of the various input variables

Applications of BNN in CAMM

  1. Prediction of tensile properties of titanium alloys (alternate chemistry and base line composition, b-processed and a-b processed)
  2. Prediction of fracture toughness of b processed and a-b processed titanium alloys
  3. Prediction of fatigue life cycles of titanium alloys

Input variables:

  • Volume fraction of total alpha
  • Volume fraction of equiaxed alpha
  • Size of the equiaxed alpha,
  • Thickness of the alpha laths
  • Grain boundary alpha
  • Colony scale factor
  • Composition (Aluminum, Vanadium, Oxygen , and Iron)


CompuTherm LLC - Pandat

Computherm LLC’s Pandat® software is a versatile software program for calculating thermodynamic properties and phase diagrams in multi-component systems. It combines a powerful calculation engine with a user-friendly Microscope Windows based graphical interface. The resulting program is easy for a novice to use and effective for the expert. The user interface of the Pandat® workspace consists of five components: Menus, Toolbars, Statusbar, Explorer window and Main display window.
The calculations performed by Pandat® are based on models for Gibbs free energy for every phase in a particular system. The thermodynamic parameters required for such calculations are optimized so that the model fits the available experimental data for a given phase. Such optimization was achieved by data mining from published journals and other commercial thermodynamic databases.

Applications of Pandat at CAMM

The different types of calculations done with Pandat® version 5.0 are Point (0D), Line (1D), Section (2D), Liquidus projection and Solidification Simulation. Although Pandat® does not require the users to supply initial values for stable phase equilibrium calculation, the basic calculation conditions have to be set up by users. Pandat® uses temperature-composition as a calculation space. For each calculation, one or more points in the temperature-composition space are defined. For example, one point defines the calculation condition for point calculations (0D) and solidification simulations, two points define the two ends for a line calculation (1D), and three non-collinear points define the 2D section for a section calculation (2D). Depending on the definition of these points, one or more variables in temperature and composition can change simultaneously along one direction. A liquidus projection calculation uses a special calculation space that is the liquid surface hyperspace.

One of the great features of Pandat® 5.0 is that one can run a series of calculations by defining them in a text file and letting them run over an extended period without having to wait on it. Such batch processes create a batch file after each calculation so that the user can easily create and modify them without memorizing their syntax. Last but not least, one can create and edit customized tables and graphs from the data collected from running the Pandat® 5.0 software.

CAMM Example Pandat Results