Input Selection for Modeling and Diagnostics With Application to Diesel Engines

[+] Author and Article Information
Brett Martin

Textron Marine and Land Systems, Division of Textron, Inc., New Orleans, LA 70129

Peter Meckl

Ray W. Herrick Laboratories, School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907

J. Dyn. Sys., Meas., Control 129(1), 114-120 (Jul 24, 2006) (7 pages) doi:10.1115/1.2397161 History: Received April 28, 2004; Revised July 24, 2006

A theoretical and experimental approach to the use of information theory in input space selection for modeling and diagnostic applications is examined. The assumptions and test cases used throughout the paper are specifically tailored to diesel engine diagnostic and modeling applications. This work seeks to quantify the amount of information about an output contained within an input space. The information theoretic quantity, conditional entropy, is shown to be an accurate predictor of model and diagnostic algorithm performance and therefore is a good choice for an input vector selection metric. Methods of estimating conditional entropy from collected data, including the amount of needed data, are also discussed.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Conditional entropy estimate versus data sufficiency parameter. As increasing numbers of data points are collected, and the data sufficiency parameter increases, the estimation of conditional entropy approaches a constant value.

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Figure 2

RBF performance versus conditional entropy. In this case, a radial basis function with 100 input nodes and a spread of 0.04 was used. The plot shows normalized mean squared error versus conditional entropy.

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Figure 3

Comparison of predicted error bound versus actual mean absolute error. The solid curve corresponds to the average length needed to contain all of the probability on the conditional domain as computed using the AEP property. The data points correspond to two times the mean absolute error of the model from Table 2.

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Figure 4

LVQ and prediction error lower bound versus H(Y∣X) for failure diagnostics. The above figure compares the fault diagnosis error probability using a LVQ classifier to its conditional entropy. Also plotted is the predicted lower bound on error probability of any diagnostic algorithm built on input vectors of differing conditional entropies.

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Figure 5

More and less informative input vectors. (a) The output data when plotted against a more informative input vector with H(Y∣X)=0.0317 nats. (b) The same output data when plotted against a less informative input vector with H(Y∣X)=0.2772 nats.




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