A New Similarity Measure of Generalized Trapezoidal Fuzzy Numbers and Its Application on Rotor Fault Diagnosis

Abstract

Fault diagnosis technology plays a vital role in the variety of critical engineering applications. Fuzzy approach is widely employed to cope with decision-making problems because it is in the simplest and most used form. This paper proposed a new similarity measure of generalized trapezoidal fuzzy numbers used for fault diagnosis. The presented similarity measure combines concepts of the geometric distance, the center of gravity point, the perimeter, and the area of the generalized trapezoidal fuzzy numbers for calculating the degree of similarity between generalized trapezoidal fuzzy numbers. This method is proposed to deal with both standardized and nonstandardized generalized trapezoidal fuzzy numbers. Some properties of the proposed similarity measure have been proved, and 12 sets of generalized fuzzy numbers have been used to compare the calculation results of the proposed similarity measures with the existing similarity measures. Comparison results indicate that the proposed similarity measure can overcome the drawbacks of existing similarity measures. Finally, a fault diagnosis experiment is carried out in laboratory based on multifunctional flexible rotor experiment bench. Experimental results demonstrate that the proposed similarity measure is more effective than other methods in terms of rotor fault diagnosis.

[WiP] A Novel Method for Big Data Analytics and Summarization Based on Fuzzy Similarity Measure

“…Hence, we choose Zuo et al's similarity measure of generalized fuzzy numbers for our data comparison (and dealing with fault diagnosis). The calculation process for the similarity of two non-standard fuzzy number and B is described in detail by Zuo et al [12]. They utilize the following (7) for measuring the similarity ofà andB:…”

“…According to the decision makers opinion, in this case, the approximate value of a one degree temperature change is equivalent to 10% humidity change and 100 lux lighting change. Therefore, the following unit changes are performed by (11) and (12):…”

“…After that, for instance, this information can be used for predictive maintenance operations [11]. We choose Zuo et al's similarity measure of generalized fuzzy numbers for data comparison cause of its good deal with non-standard fuzzy numbers and fault detection [12]. In order to show the effectiveness and efficiency of our method in realworld situations, an IoT use case is presented and analyzed utilizing the method introduced in this paper.…”

Z-TOPSIS approach for performance assessment using fuzzy similarity

“…This section focuses on the development of Z -TOPSIS using fuzzy similarity. The methodology of Z -TOPSIS using fuzzy similarity is extended from [11].…”

Hybrid fuzzy MCDM model for Z-numbers using intuitive vectorial centroid

“…Convert each generalised trapezoidal fuzzy numbers into standardised generalised fuzzy numbers using normalisation process by [26] from equation (29).…”