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TECHNICAL PAPERS: Gas Turbines: Controls, Diagnostics, and Instrumentation

# Fuzzy Logic Estimation Applied to Newton Methods for Gas Turbines

[+] Author and Article Information
Dan Martis

J. Eng. Gas Turbines Power 129(1), 88-96 (Mar 01, 2004) (9 pages) doi:10.1115/1.2360597 History: Received October 01, 2003; Revised March 01, 2004

## Abstract

This method, based on fuzzy logic principles, is intended to find the most likely solution of an over-determined system, in specific conditions. The method addresses typical problems encountered in gas turbine performance analysis and, more specifically, to the alignment of a synthesis model with measured data. Generally speaking, the relatively low accuracy of measurements introduces a random noise around the true value of a performance parameter and distorts any deterministic solution of a square matrix-based linear system. The fuzzy logic estimator is able to get very close to the real solution by using additional (pseudo-redundant) parameters and by building the most likely solution based on each of the measurement accuracies. The accuracy—or “quality”—of a measurement is encapsulated within an extra dimension which is defined as fuzzy and which encompasses the whole range of values, between 0 (false) and 1 (true). The value of the method is shown in two examples. The first simulates compressor fouling, the other deals with actual engine test data following a hardware modification. Both examples experience noisy measurements. The method is stable and effective even at high level of noise. The results are within the close vicinity of the expected levels (within 0.2% accuracy) and the accuracy is about ten times lower than the noise level.

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## Figures

Figure 1

Normal distribution applied to measurement pj

Figure 2

Input fuzzy domain—normal distribution

Figure 3

Input fuzzy domain—normal distribution; scalar representation

Figure 4

Intersection of uncertainty domains

Figure 5

Output fuzzy domain—normal distribution

Figure 6

Output fuzzy domain—normal distribution; scalar representation

Figure 7

Output fuzzy domain—trapezoidal distribution

Figure 8

Output fuzzy domain—trapezoidal distribution; scalar representation

Figure 9

The solution of system 13—no noise

Figure 10

System 13 with seeded noise

Figure 11

The fuzzy solution migration toward ideal solution

Figure 12

Error function level versus number of measured parameters

Figure 13

Comparison of FLE and least squares error stability with increasing measurement noise

## Errata

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