Liessman Sturlaugson

Principal component analysis preprocessing with Bayesian networks for battery capacity estimation

Bayesian networks (BNs) are a common data-driven approach for representing and reasoning in the presence of uncertainty. Inference in a BN can quickly become intractable as the complexity of the network increases, specifically in the number of nodes and the number of states for each node. We demonstrate the benefit of preprocessing cyclic time-series measurements using principal component analysis (PCA), evaluating the technique with the BN to perform diagnostics on a set of lithium-ion batteries that have undergone repeated charging/discharging cycles. The results show how PCA preprocessing can result in simpler Bayesian network models than those from the raw data while still achieving higher accuracy.

Sensitivity Analysis of Continuous Time Bayesian Network Reliability Models

We show how to perform sensitivity analysis on continuous time Bayesian networks (CTBNs) as applied specifically to reliability models. Sensitivity analysis of these models can be used, for example, to measure how uncertainty in the failure rates impact the reliability of the modeled system. The CTBN can be thought of as a type of factored Markov process that separates a system into a set of interdependent subsystems. The factorization allows CTBNs to model more complex systems than single Markov processes. However, the state-space of the CTBN is exponential in the number of subsystems. Therefore, existing methods for sensitivity analysis of Markov processes, when applied directly to the CTBN, become intractable. Sensitivity analysis of CTBNs, while borrowing from techniques for Markov processes, must be adapted to take advantage of the factored nature of the network if it is to remain feasible. To address this, we show how to extend the perturbation realization method for Markov processes to the CTBN. We...

A standards-based approach to gray-scale health assessment using fuzzy fault trees

As part of a project to examine how current standards focused on test and diagnosis might be extended to address requirements for prognostics and health management, we have been exploring alternatives for incorporating facilities to represent gray-scale health information in the IEEE Std 1232 Standard for Artificial Intelligence Exchange and Service Tie to All Test Environments (AI-ESTATE). In this work, we extend the AI-ESTATE Common Element Model to provide “soft outcomes” on tests and diagnoses. We then demonstrate how to use these soft outcomes with the AI-ESTATE Fault Tree Model to implement a “fuzzy” fault tree. The resulting model then enables isolating faults within a system such that levels of degradation can also be tracked. In this paper, we describe the proposed extensions to AI-ESTATE as well as how those extensions work to implement a fuzzy fault tree using the demonstration circuit from previous Automatic Test Markup Language (ATML) demonstrations.

Implementing AI-ESTATE with prognostic extensions in Java

This paper is part of an ongoing effort to facilitate wider acceptance and further development of the IEEE Std 1232-2010 Standard for Artificial Intelligence Exchange and Service Tie to All Test Environments (AI-ESTATE). To that end, we describe a tool named SAPPHIRETM, which includes an implementation of AI-ESTATE in Java and a corresponding GUI tool that supports model creation and diagnostic inference of the standards Bayes Network Model (BNM). In addition, we describe extensions to the BNM as well as additional reasoner services that allow for representation and inference over dynamic Bayesian networks (DBNs) for standards-based prognostics.

Extending high-dimensional indexing techniques pyramid and iminmax(θ): lessons learned

Pyramid Technique and iMinMax(θ) are two popular high-dimensional indexing approaches that map points in a high-dimensional space to a single-dimensional index. In this work, we perform the first independent experimental evaluation of Pyramid Technique and iMinMax(θ), and discuss in detail promising extensions for testing k-Nearest Neighbor (kNN) and range queries. For datasets with skewed distributions, the parameters of these algorithms must be tuned to maintain balanced partitions. We show that, by using the medians of the distribution we can optimize these parameters. For the Pyramid Technique, different approximate median methods on data space partitioning are experimentally compared using kNN queries. For the iMinMax(θ), the default parameter setting and parameters tuned using the distribution median are experimentally compared using range queries. Also, as proposed in the iMinMax(θ) paper, we investigated the benefit of maintaining a parameter to account for the skewness of each dimension separately instead of a single parameter over all the dimensions.

Diagnostic Bayesian networks with Fuzzy evidence

Diagnostic Bayesian networks, one of the models supported by the Artificial Intelligence Exchange and Service Tie to All Test Environments (AI-ESTATE) standard, are an important and commonly used tool for modeling systems for fault isolation. When performing the tests specified by the diagnostic Bayesian network, the test program often maps the raw test measurements to discrete Pass or Fail outcomes. We would like to relax this hard discretization requirement and instead represent degrees of passing and failing. To do this, we propose a method for integrating fuzzy set theory and diagnostic Bayesian networks. Our proposed approach further demonstrates the extensions described in previous work to include gray-scale health information in AI-ESTATE. The previous work demonstrated the use of soft outcomes in AI-ESTATEs Fault Tree Model (FTM); however, no process was given for incorporating the soft outcomes into the other models specified by AI-ESTATE. Here, we describe how to extend the AI-ESTATE Bayesian Network Model (BNM) to incorporate the previously proposed soft outcomes. Because D-matrices and diagnostic logic models can be represented as Bayesian networks, the proposed approach can be adapted to work with AI-ESTATEs D-matrix Inference Model (DIM) and Diagnostic Logic Model (DLM) as well.

Factored performance functions and decision making in continuous time Bayesian networks

Abstract The continuous time Bayesian network (CTBN) is a probabilistic graphical model that enables reasoning about complex, interdependent, and continuous-time subsystems. The model uses nodes to denote subsystems and arcs to denote conditional dependence. This dependence manifests in how the dynamics of a subsystem changes based on the current states of its parents in the network. While the original CTBN definition allows users to specify the dynamics of how the system evolves, users might also want to place value expressions over the dynamics of the model in the form of performance functions. We formalize these performance functions for the CTBN and show how they can be factored in the same way as the network, allowing what we argue is a more intuitive and explicit representation. For cases in which a performance function must involve multiple nodes, we show how to augment the structure of the CTBN to account for the performance interaction while maintaining the factorization of a single performance function for each node. We introduce the notion of optimization for CTBNs, and show how a family of performance functions can be used as the evaluation criteria for a multi-objective optimization procedure.

Using continuous-time Bayesian networks for standards-based diagnostics and prognostics

In this paper we present a proposal for a new prognostic model to be included in a future revision of the IEEE Std 1232-2010 Standard for Artificial Intelligence Exchange and Service Tie to All Test Environments (AI-ESTATE). Specifically, we introduce the continuous time Bayesian network (CTBN) as an alternative to the previously proposed dynamic Bayesian network to provide an additional model for prognostic reasoning. We specify a semantic model capable of representing a CTBN within the standard and discuss the advantages of using such a model for prognosis. As with previous work, we demonstrate the feasibility and necessity of incorporating prognostic capabilities into the standard.

Uncertain and negative evidence in continuous time Bayesian networks

The continuous time Bayesian network (CTBN) enables reasoning about complex systems by representing the system as a factored, finite-state, continuous-time Markov process. Inference over the model incorporates evidence, given as state observations through time. The time dimension introduces several new types of evidence that are not found with static models. In this work, we present a comprehensive look at the types of evidence in CTBNs. Moreover, we define and extend inference to reason under uncertainty in the presence of uncertain evidence, as well as negative evidence, concepts extended to static models but not yet introduced into the CTBN model. Created a taxonomy of discrete-state, continuous-time evidence types.Showed generalization and combination relationships between evidence types.Demonstrated the effects of evidence types on a real-world network.Extended exact and approximate inference for CTBNs to handle new evidence types.Demonstrated convergence and scaling of CTBN approximate inference algorithm.