In this paper we study the problem of predictability in partially observable discrete event systems, i.e., the question whether an observer can predict the occurrence of a fault. We extend the definition of predictability to consider the time interval where the fault will occur: the @math -predictability does not only specify that the fault will be predicted before it occurs, but also that the predictor will be able to predict that its occurrence will occur in @math to @math observations from now. We also provide a quadratic algorithm that decides predictability of the system.
Predictability as presented in this paper was introduced by Genc and Lafortune @cite_13 . Their approach was however only Boolean: they addressed the question can the fault be predicted before it occurs?'' They presented an exponential space algorithm using a structure similar to our optimal predictor. They also announced the existence of a polytime algorithm, similar to the twin plant used for diagnosability and formally presented in an extension of their work @cite_3 .
@cite_13 @cite_3
1455915656 2141676918 2339807279 2329723054
The exponential growth of computational power of the extreme scale machines over the past few decades has led to a corresponding decrease in reliability and a sharp increase of the frequency of hardware faults. Our research focuses on the mathematical challenges presented by the silent hardware faults; i.e., faults that can perturb the result of computations in an inconspicuous way. Using the approach of selective reliability, we present an analytic fault mode that can be used to study the resilience properties of a numerical algorithm. We apply our approach to the classical fixed point iteration and demonstrate that in the presence of hardware faults, the classical method fails to converge in expectation. We preset a modified resilient algorithm that detects and rejects faults resulting in error with large magnitude, while small faults are negated by the natural self-correcting properties of the algorithm. We show that our method is convergent (in first and second statistical moments) even in the presenc... To facilitate proactive fault management in large-scale systems such as IBM Blue Gene P, online failure prediction is of paramount importance. While many techniques have been presented for online failure prediction, questions arise regarding two commonly used approaches: period-based and event-driven. Which one has better accuracy? What is the best observation window (i.e., the time interval used to collect evidence before making a prediction)? How does the lead time (i.e., the time interval from the prediction to the failure occurrence) impact prediction arruracy? To answer these questions, we analyze and compare period-based and event-driven prediction approaches via a Bayesian prediction model. We evaluate these prediction approaches, under a variety of testing parameters, by means of RAS logs collected from a production supercomputer at Argonne National Laboratory. Experimental results show that the period-based Bayesian model and the event-driven Bayesian model can achieve up to 65.0 and 83.8 prediction accuracy, respectively. Furthermore, our sensitivity study indicates that the event-driven approach seems more suitable for proactive fault management in large-scale systems like Blue Gene P. This paper introduces a framework for inference of timed temporal logic properties from data. The dataset is given as a finite set of pairs of finite-time system traces and labels, where the labels indicate whether the traces exhibit some desired behavior (e.g., a ship traveling along a safe route). We propose a decision-tree based approach for learning signal temporal logic classifiers. The method produces binary decision trees that represent the inferred formulae. Each node of the tree contains a test associated with the satisfaction of a simple formula, optimally tuned from a predefined finite set of primitives. Optimality is assessed using heuristic impurity measures, which capture how well the current primitive splits the data with respect to the traces' labels. We propose extensions of the usual impurity measures from machine learning literature to handle classification of system traces by leveraging upon the robustness degree concept. The proposed incremental construction procedure greatly improves the execution time and the accuracy compared to existing algorithms. We present two case studies that illustrate the usefulness and the computational advantages of the algorithms. The first is an anomaly detection problem in a maritime environment. The second is a fault detection problem in an automotive powertrain system. A discrete event system that is predictable can anticipate faults and act accordingly. However, bare predictability (as found in the literature) has some drawbacks. One does not know exactly when a fault occurs (it could be immediately or long after it is predicted). We propose lower and upper bound refinements of predictability, called (lb; ub)-predictability. A lower bound guarantees a fault to occur after certain execution steps, whereas an upper bound guarantees a fault to occur, in the future, but before some steps. This information can be exploited by the system to adopt the best contingency plan. We formally define the notions of lb-predictability and ub-predictability, present a decision algorithm to verify it on arbitrary systems, and illustrate them with examples.