Abstract: Disclosed herein are representative embodiments of methods, apparatus, and systems for performing radiography analysis. For example, certain embodiments perform radiographic analysis using mixed variable computation techniques. One exemplary system comprises a radiation source, a two-dimensional detector for detecting radiation transmitted through a object between the radiation source and detector, and a computer. In this embodiment, the computer is configured to input the radiographic image data from the two-dimensional detector and to determine one or more materials that form the object by using an iterative analysis technique that selects the one or more materials from hierarchically arranged solution spaces of discrete material possibilities and selects the layer interfaces from the optimization of the continuous interface data.

Abstract: A control system for controlling the output of at least one plant process output parameter is implemented by adaptive model predictive control using a neural network. An improved method and apparatus provides for sampling plant output and control input at a first sampling rate to provide control inputs at the fast rate. The MPC system is, however, provided with a network state vector that is constructed at a second, slower rate so that the input control values used by the MPC system are averaged over a gapped time period. Another improvement is a provision for on-line training that may include difference training, curvature training, and basis center adjustment to maintain the weights and basis centers of the neural in an updated state that can follow changes in the plant operation apart from initial off-line training data.