**1. Introduction**

134 Fuzzy Inference System – Theory and Applications

[14] Jamaludin J., Wahyudi, Iswaini and Suhaimi A, "Development of Automatic Gantry

Electronics Seminar 2004, Surabaya, 11 October 2004.

Crane Part2:Controller Design and Implementation", in Proc. The 5th Industrial

Within industry, the concept of maintenance can be handled in different ways. It can be done periodically at predefined times, according to the type of machine, and according to the manufacturers' recommendations. In this case, it is referred to as scheduled preventive maintenance. Maintenance done when there is faulty equipment is commonly called corrective maintenance. Employing electrical machines' operating signals may be useful for diagnosis purposes.

Three-phase electrical machines such as induction motors or generators are used in a wide variety of applications. In order to increase the productivity and to reduce maintenance costs, condition monitoring and diagnosis is often desired. A wide variety of conditioning monitoring techniques has been introduced over the last decade. These include the electric current signature and stator vibrations analysis (Cusido & Romeral & Ortega & Espinoza, 2008; Blodt & Granjon & Raison & Rostaing, 2008; Blodt & Regnier & Faucher, 2009; Riera & Daviu & Fulch, 2008).

Nowadays, industry demands solutions to provide more flexible alternatives for maintenance, avoiding waste of time in case of major requirements to unforeseen failures, as well as time of scheduled maintenance. This creates the necessity to propose and implement predictive technologies, which ensure that machinery receive attention only when they present some evidence of their mechanical properties deterioration (Taylor, 2003). Vibrations have been one of the usual machinery's physical state indicators.

Some issues related to failures in machinery are as follows:


Fuzzy Inference Systems Applied to the Analysis of Vibrations in Electrical Machines 137

quantitative analyses. The fuzzy modeling or fuzzy identification, was first explored systematically by Takagi and Sugeno (Takagi & Sugeno, 1985). There are some basic aspects

1. Vibration signals in electrical machines have information, which can be used to predict

2. Patterns captured under different conditions may be similar, therefore it is necessary an

Fuzzy *if-then* rules or fuzzy conditional statements are expressions of the form *IF* A *THEN* B, where A and B are labels of fuzzy sets (Zadeh, 1965) characterized by appropriate membership functions. Due to their concise form, fuzzy *if-then* rules are often employed to capture the imprecise modes of reasoning that play an essential role in the human ability to make decisions in an environment of uncertainty and imprecision. An example that

*If vibration is high, it is possible the bars' failure*  where *vibration* and *failure* are linguistic variables (Jang, 1994); *high* (*small*) are linguistic

A different form of fuzzy *if-then* rules, proposed by (Omar, 2010; Takagi & Sugeno, 1985, as cited in Jang, 1993), have fuzzy sets involved only in the premise part. Both types of fuzzy *if-then* rules have been used extensively in both modeling and control. Through the use of linguistic labels and membership functions, a fuzzy *if-then* rule can easily capture the spirit of a "*rule of thumb*" used by humans. From another point of view, due to the qualifiers on the premise parts, each fuzzy *if-then* rule can be viewed as a local description of the system under consideration. Fuzzy *if-then* rules form a core part of the fuzzy inference system

values or labels that are characterized by membership functions.

the machine's state. Figure 1, shows the basic inference composition.

of this approach that require some comments. In particular:

Fig. 1. Basic inference system

**2.2 Fuzzy i***f-then* **rules** 

describes a simple fact is:

described in the following.

inference system that facilitates the identification process.

3. The precise analysis of a problem at a given frequency depends on the presence of one or more related frequencies. In the current methods, an important difficulty is the need to monitor through sophisticated sensors. Additionally, failures detection depends on the load's inertia.

Different detection techniques for machines' state monitoring have been studied. Some techniques are based on analyzing electrical signals, some others are based on vibration measurements, and some combine them. In this paper, vibration measurements are used for monitoring purposes.

Vibrations must be properly evaluated, especially those associated to rotating machinery. Capturing vibration patterns, using identification techniques and signal processing, distinctive signatures for failures detection can be set. This could help to anticipate the occurrence of equipment damage, and therefore, corrective actions can be taken to avoid the high cost of a partial or total machinery replacement, as well as economic expenses caused by their unavailability.
