Columnist: June 8, 1995

Call me starry-eyed, but certain parts of fuzzy theory made complete sense to me the first time I encountered them. Consider thresholds. A crisp set indicates when an event falls within a set of boundaries, say, when a pitched baseball travels between 95 and 100 mph. A fuzzy set also provides this information, and, in addition, tells you when the event was close to, but just outside of, a boundary, as well as how close. A crisp set would have completely missed a pitch traveling at 93 mph; a fuzzy set would have caught it, with a degree of membership of, say, 0.5. Perhaps I am only interested in pitches in the range 95 mphóspeedó100 mph. But, I bet that I wouldn't send a pitcher back to the minor leagues for consistently throwing 93-mph (or 102-mph) fastballs. Regardless of the old saying, "close" counts in more than merely horseshoes and dancing.

Let's take a look at a product where fuzzy sets have replaced sets-with improved performance. Delta-X Research of Victoria, BC, Canada, has developed the Transformer Oil Analyst, a Windows-based program that stores and interprets gas-in-oil data for mineral-oil-filled, paper-insulated, electrical-power transformers. Fuzzy membership functions strengthen the tool's ability to diagnose subtle changes in its input data. The Transformer Oil Analyst is currently used by more than 40 electric-utility companies, industrial plants, testing laboratories, and electric-power consultants throughout North America.

Most large power transformers use mineral oil as a dielectric fluid and coolant and have oil-impregnated paper insulation between winding layers. As a transformer ages or becomes stressed by overloading, lightning, or switching transients, it typically experiences overheating of oil and paper. If left unattended, these "faults" can lead to complete transformer failure. Because of the cost and economic importance of large transformers, it is desirable to detect and identify faults as early as possible.

Depending on a number of parameters, each fault "cooks" the oil or paper to varying degrees, generating characteristic relative amounts of dissolved gases. Periodic transformer maintenance includes chromatographic analysis to measure concentrations of dissolved hydrogen, methane, ethane, ethylene, acetylene, carbon monoxide, and carbon dioxide in the insulating oil. An ANSI/IEEE standard (IEEE STD C57.104-1991: IEEE Guide for the Interpretation of Gases Generated in Oil Immersed Transformers) specifies three dissolved-gas analysis methods used to diagnose faults: Key Gas Analysis, Rogers Ratio Method, and Doernenberg Ratio Method.

Although each test diagnoses power-transformer faults, the three tests differ in

• the parameters upon which a diagnosis is based
• the diagnostic rules used
• the specific diagnoses supported.

These methods tend to work well in diagnosing severe faults but often fail on those that are intermittent or just starting to develop. Common to all three tests, and, at least in part responsible for their shortcomings, is the use of multiple thresholds to classify features of the dissolved-gas data into various intervals. By replacing crisp thresholds with fuzzy membership functions, diagnoses that would have previously been missed due to inputs falling near (but outside) indicated intervals can now be seen, accompanied by a confidence factor or "strength of opinion," ranging from 0 to 1.

Having limited space, I opted to discuss only one of the three diagnostic methods, the Rogers Ratio Method, with emphasis on the use of fuzzy membership functions to replace crisp thresholds.

The Rogers Ratio Method accepts as inputs three gas-concentration ratios, calculated from chromatographic data: methane/hydrogen (MH), acetylene/ ethylene (AE), and ethylene/ethane (EE). The Rogers Ratio Method segments them into intervals (see ). By Table 1looking for logical combinations of these conditions, which the rule matrix in Fig 1 shows, the method provides diagnosis of partial discharge, various kinds of overheating, and arcing. Maintenance engineers consider the Rogers Ratio Method to be accurate; however, its usefulness is limited because it often fails to yield any diagnosis at all.

Delta-X Research has replaced the standard-defined, crisp thresholds listed in Table 1 with the fuzzy membership functions shown in Fig 2. The intent was to recognize when an input is close to, but not quite within, the crisply defined region and to represent the gradual transition from entirely outside the interval to entirely inside the interval, as indicated by a confidence factor, cf. When passed to the rule output, cf is a measure of how strongly the given diagnosis is supported by the particular method. It is not a truth value, but rather a "strength of opinion."

In selecting membership-function shapes, Delta-X desired to have the fuzzy transitions correspond closely with the crisp thresholds, thereby maintaining a deterministic mapping between the fuzzy implementation and the industry-standard-defined tests. To achieve this goal, the points at which the membership-function values equal 0.5 are the same as the crisp thresholds.

The extension to fuzzy logic strengthens the tool in two principal ways. First, it preserves information about borderline cases in an intuitive manner. An engineer reading the diagnosis results with confidence factors can obtain the same "feel" for the calculated diagnosis (specifically concerning data points near the thresholds) as she or he would have developed if calculating the results by hand. The second enhancement concerns the combination of results from several individual methods into an overall diagnosis. Confidence factors accompanying the individual diagnoses greatly enhance the ability to form a meaningful overall diagnosis when compared with using the "fault/no fault" diagnoses obtained using crisp thresholds.

This column is based on information provided by Delta-X Research; conversations with Dr James Dukarm, the tool's author; and a paper, "Transformer Oil Diagnosis Using Fuzzy Logic and Neural Networks," which Dr Dukarm presented at the 1993 Canadian Conference on Electrical and Computer Engineering. If you would like additional information on the Transformer Oil Analyst, phone Dr Dukarm at (604) 592-2998.