**Outer Feedback Correction Loops in Particle Filtering-based**

Prognostic Algorithms: Statistical Performance Comparison

Prognostic Algorithms: Statistical Performance Comparison

**Marcos E. ORCHARD ^{1}**,

**Felipe A. TOBAR**

^{1}, George J. VACHTSEVANOS^{2}**Electrical Engineering Department, University of Chile**

^{1 }Av. Tupper 2007, Santiago, Chile

**School of Electrical and Computer Engineering, Georgia Institute of Technology**

^{2 }777 Atlantic Drive, Atlanta GA 30332, USA

**Abstract**: This paper presents, analyzes, and evaluates two different approaches for outer feedback correction loops (OFCL) in particle-filtering-based prognostic algorithms. These approaches incorporate information, from the short-term prediction error, back into the implementation of the estimation routine, to improve its performance in terms of both the resulting state and time-of-failure (ToF) pdf estimates. Three indicators are also proposed and used to measure the performance of the prognostic routines that result from the implementation of these OFCL in terms of precision, accuracy, and steadiness of the solution. Both approaches are tested using actual data from a seeded fault test in a critical component of rotorcraft transmission system.

**Keywords**: Particle filtering, failure prognosis, nonlinear state estimation, feedback loops.

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**CITE THIS PAPER AS**:

Marcos E. ORCHARD, Felipe A. TOBAR, George J. VACHTSEVANOS, **Outer Feedback Correction Loops in Particle Filtering-based Prognostic Algorithms: Statistical Performance Comparison**, *Studies in Informatics and Control*, ISSN 1220-1766, vol. 18 (4), pp. 295-304, 2009.

**1. Introduction**

Uncertainty management of prognostics holds the key for a successful penetration of health management strategies in industrial applications. While methods to estimate and handle uncertainty have received a reasonable amount of attention in the diagnostics domain, uncertainty management for prognostics is an area which awaits major advances.

In the field of failure prognosis, several approaches intend to solve the issue of uncertainty management. Probabilistic, soft computing methods and tools derived from evidential theory or Dempster-Shafer theory [1] have been explored for uncertainty representation in prediction. Probabilistic methods are mathematically rigorous assuming, of course, that a statistically sufficient database is available to estimate the required distributions. Possibility theory (fuzzy logic) offers an alternative when scarce data and even incomplete or contradictory data are available. Dempster’s rule of combination and such concepts from evidential theory as belief on plausibility based on mass function calculations can support uncertainty representation tasks. Probabilistic reliability analysis tools employing an inner-outer loop Bayesian update scheme have also been used to “tune” model hyper-parameters given observations [2].

In this sense, particle filters (PF) have been established as the de facto state of the art in failure prognosis and uncertainty representation [3]. PF-based algorithms are capable of combining advantages of the rigors of Bayesian estimation to nonlinear prediction while also providing uncertainty estimates for a given solution. The outcome of these algorithms – an estimate of the probability density function (pdf) of the state – allows online computation of expectations, 95% confidence intervals, and other statistics of the time of failure (ToF). All the more, PF-based algorithms provide the framework to implement corrective schemes aimed at an online performance improvement; see Figure 1.

This paper proposes, tests, and assesses a systematic method for the uncertainty management problem in failure prognosis consisting in two possible options for outer feedback correction loops.

These loops incorporate information about the short-term prediction error to improve the performance of the overall prognostic framework. The structure of the paper is as follows. Section 2 summarizes the basic concepts associated to the usage of PF in the field of failure prognosis. Section 3 presents two approaches that can be used to implement outer correction loops, while Section 4 illustrates obtained results when using these loops in several realizations of PF-based prognostic algorithms that are fed with actual fault data. Section V presents an assessment of the results on the basis of three performance indicators that help to quantify the concepts of accuracy, precision, and steadiness of prognostic results. All proposed approaches are tested using actual data from a seeded fault test in a critical component of rotorcraft transmission system [4].

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