We present here probabilistic approaches to diagnostic inference. Model-based diagnostic techniques that rely on graphical models, in particular Bayesian networks and arithmetic circuits, are emphasized. Our research includes the development of new methods and algorithms as well as development of cutting edge applications and demonstrations of importance to NASA.
As an example of a probabilistic model, consider Bayesian networks. Bayesian networks (BNs) are used to represent multivariate probability distributions for the purpose of reasoning and learning under uncertainty. In BNs, random variables are represented as nodes in directed acyclic graphs. Each node has a conditional probability table (CPT). BNs can contain both discrete and continuous random variables; the BNs discussed here currently contain discrete variables only. While a joint probability table's size is exponential in the number of discrete random variables, the BN provides a mechanism to compactly represent the joint probability table.
Bayesian networks have recently gained great popularity as an approach to representing, learning, and reasoning with multi-variate probability distributions. Bayesian networks play a central role in a wide range of automated reasoning applications, not only in model-based diagnosis but also in medical diagnosis, natural language understanding, probabilistic risk analysis, intelligent data analysis, and error correction coding.
In resource-bounded systems, including real-time avionics systems used in aircraft and spacecraft, there is an expressed need to align the resource consumption of diagnostic computation with the resource bounds imposed by the avionics system. As a consequence, approaches in which a BN is compiled, off-line, into a secondary data structure, which is then used on-line for inference are of great interest in aerospace. The main advantage of compilation is that a significant amount of the work required for inference is performed once off-line, and this work thus be amortized over many on-line diagnostic queries. Repeated online inference is often much more efficient using a compilation approach. In addition, on-line inference times may have much smaller variance. In this work we emphasize the compilation of Bayesian network into arithmetic circuits, where on-line diagnostic inference amounts to linear-time arithmetic circuit (AC) evaluation.
We illustrate the benefit of our technologies by considering an aerospace application of great interest to NASA, namely electrical power system health management. We investigate a real-world electrical power system (EPS), namely the Advanced Diagnostics and Prognostics Testbed (ADAPT). ADAPT is representative of EPSs found in aerospace vehicles. In our probabilistic approach, a Bayesian network (BN) model of the ADAPT electrical power system plays a central role. The ADAPT BN represents health of sensors and subsystem components explicitly, and is auto-generated from a high-level system model of the ADAPT EPS. This BN is compiled off-line it into an arithmetic circuit, which is then evaluated on-line. We believe that our ADAPT case study clearly demonstrates how arithmetic circuits offer a scalable inference technique with potential for real-time evaluation in aircraft and spacecraft.