Distribution modeling of nonlinear inverse controllers under a Bayesian framework

The inverse controller is traditionally assumed to be a deterministic function. This paper presents a pedagogical methodology for estimating the stochastic model of the inverse controller. The proposed method is based on Bayes' theorem. Using Bayes' rule to obtain the stochastic model of the inverse controller allows the use of knowledge of uncertainty from both the inverse and the forward model in estimating the optimal control signal. The paper presents the methodology for general nonlinear systems and is demonstrated on nonlinear single-input-single-output (SISO) and multiple-input-multiple-output (MIMO) examples. © 2006 IEEE.

A Bayesian approach to modeling the conditional density of the inverse controller

The inverse controller is traditionally assumed to be a deterministic function. This paper presents a pedagogical methodology for estimating the stochastic model of the inverse controller. The proposed method is based on Bayes' theorem. Using Bayes' rule to obtain the stochastic model of the inverse controller allows the use of knowledge of uncertainty from both the inverse and the forward model in estimating the optimal control signal. The paper presents the methodology for general nonlinear systems. For illustration purposes, the proposed methodology is applied to linear Gaussian systems. © 2004 IEEE.

General bounds on Bayes errors for regression with Gaussian processes

Based on a simple convexity lemma, we develop bounds for different types of Bayesian prediction errors for regression with Gaussian processes. The basic bounds are formulated for a fixed training set. Simpler expressions are obtained for sampling from an input distribution which equals the weight function of the covariance kernel, yielding asymptotically tight results. The results are compared with numerical experiments.

Real-time process plant fault diagnosis

Operators can become confused while diagnosing faults in process plant while in operation. This may prevent remedial actions being taken before hazardous consequences can occur. The work in this thesis proposes a method to aid plant operators in systematically finding the causes of any fault in the process plant. A computer aided fault diagnosis package has been developed for use on the widely available IBM PC compatible microcomputer. The program displays a coloured diagram of a fault tree on the VDU of the microcomputer, so that the operator can see the link between the fault and its causes. The consequences of the fault and the causes of the fault are also shown to provide a warning of what may happen if the fault is not remedied. The cause and effect data needed by the package are obtained from a hazard and operability (HAZOP) study on the process plant. The result of the HAZOP study is recorded as cause and symptom equations which are translated into a data structure and stored in the computer as a file for the package to access. Probability values are assigned to the events that constitute the basic causes of any deviation. From these probability values, the a priori probabilities of occurrence of other events are evaluated. A top-down recursive algorithm, called TDRA, for evaluating the probability of every event in a fault tree has been developed. From the a priori probabilities, the conditional probabilities of the causes of the fault are then evaluated using Bayes' conditional probability theorem. The posteriori probability values could then be used by the operators to check in an orderly manner the cause of the fault. The package has been tested using the results of a HAZOP study on a pilot distillation plant. The results from the test show how easy it is to trace the chain of events that leads to the primary cause of a fault. This method could be applied in a real process environment.

The evolution of learning systems:to Bayes or not to be

Bayesian algorithms pose a limit to the performance learning algorithms can achieve. Natural selection should guide the evolution of information processing systems towards those limits. What can we learn from this evolution and what properties do the intermediate stages have? While this question is too general to permit any answer, progress can be made by restricting the class of information processing systems under study. We present analytical and numerical results for the evolution of on-line algorithms for learning from examples for neural network classifiers, which might include or not a hidden layer. The analytical results are obtained by solving a variational problem to determine the learning algorithm that leads to maximum generalization ability. Simulations using evolutionary programming, for programs that implement learning algorithms, confirm and expand the results. The principal result is not just that the evolution is towards a Bayesian limit. Indeed it is essentially reached. In addition we find that evolution is driven by the discovery of useful structures or combinations of variables and operators. In different runs the temporal order of the discovery of such combinations is unique. The main result is that combinations that signal the surprise brought by an example arise always before combinations that serve to gauge the performance of the learning algorithm. This latter structures can be used to implement annealing schedules. The temporal ordering can be understood analytically as well by doing the functional optimization in restricted functional spaces. We also show that there is data suggesting that the appearance of these traits also follows the same temporal ordering in biological systems. © 2006 American Institute of Physics.