Abstract
pantograph–catenary system is one of the critical components used in electrical trains. It ensures the transmission of the electrical energy to the train taken from the substation that is required for electrical trains. The condition monitoring and early diagnosis for pantograph–catenary systems are very important in terms of rail transport disruption. In this study, a new method is proposed for arc detection in the pantograph–catenary system based signal processing and S-transform. Arc detection and condition monitoring were achieved by using current signals received from a real pantograph–catenary system. Firstly, model based current data for pantograph–catenary system is obtained from Mayr arc model. The method with S-transform is developed by using this current data. Noises on the current signal are eliminated by applying a low pass filter to the current signal. The peak values of the noiseless signals are determined by taking absolute values of these signals in a certain frequency range. After the data of the peak points has been normalized, a new signal will be obtained by combining these points via a linear interpolation method. The frequency-time analysis was realized by applying S-transform on the signal obtained from peak values. Feature extraction that obtained by S-matrix was used in the fuzzy system. The current signal is detected the contdition as healthy or faulty by using the outputs of the fuzzy system. Furthermore the real-time processing of the proposed method is examined by applying to the current signal received from a locomotive.
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This work was supported by the TUBITAK (The Scientific and Technological Research Council of Turkey) under Grant No: 112E067.
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Appendix: Fuzzy sets and fuzzy inference systems
Appendix: Fuzzy sets and fuzzy inference systems
Schematic representation of a fuzzy set and its components
Block diagram of a fuzzy inference system
The membership value to a set of an element in the fuzzy set theory can be taken a value between 0 and 1, while state whether or not belong to a set of an element in the classical set theory and conventional logic is expressed with 1 or 0. These fuzzy values obtained with the various membership functions are characterized by linguistic variables such as medium, very large, short, and large used for concepts in real life. A fuzzy set and its components are shown in Fig. 19. Two fuzzy values for actual input value have been calculated with the four linguistic variables defined for the height as shown in Fig. 19. The height value of 6 meter belongs to Medium set with 0.2 and to Low set with 0.8 according to these fuzzy set. As well known, an element cannot belong to more than one set at a time in the classical set theory. However, 6 meter height can be expressed as both Medium and Low in fuzzy set theory for real-life applications and human reasoning. Gaussian, sigmoidal, and trapezoidal type membership functions outside of triangular function showed in Fig. 19 can be used for obtaining of fuzzy values.
Fuzzy inference for Mamdani
Fuzzy inference systems for control, decision-making, or classification purposes in the real-world problems are used for fuzzy sets. A fuzzy inference system consists of four basic steps as fuzzification, rule base, inference mechanism, and defuzzification as shown in Fig. 20. Fuzzy inference systems that require maximum information about the system are used to solve of white box problems. There are Mamdani, Sugeno, and Tsukamoto type fuzzy inference systems and structure of Mamdani fuzzy inference system that is most preferred type can be shown in Figs. 20 and 21. If output processing is defined as a function of input instead of inference and defuzzification, this type fuzzy inference systems is known as Sugeno-type fuzzy inference systems. Short explanations for components of the Mamdani fuzzy inference system are given below.
Fuzzification: At this stage, the actual values are converted to fuzzy values between 0 and 1 separately defined by fuzzy sets for each input. Most preferred membership functions for fuzzy sets are the triangular membership functions because of it has low mathematical complexity. The type, base values, and the number of membership functions selected for fuzzy sets affect the performance of the system.
Rule table: The number of the rules in fuzzy inference systems are defined by multiplying of the number of membership functions used for each input. These rules is defined by IF-THEN expressions. For example, IF input1 is zero and input2 is big, THEN output is hot.
Inference mechanism: The most preferred operator is min-max operator although there are different operators used for inference mechanism in a fuzzy system. Firstly, the minimum operator is applied to fuzzy values obtained by fuzzification at this stage, then maximum operator is applied for same linguistic variables and process is completed. Figure 21 summarizes this process.
Defuzzification: The defuzzification stage that is the final stage of fuzzy inference system provides converting to actual output value from fuzzy values. The most widely used method for the defuzzification process is center of gravity. There are other algorithms such as the largest, smallest, and average of the maximum.
A numerical example for fuzzy inference system designed in this paper has been given in Table 6 with all stages.
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Karakose, E., Gencoglu, M.T., Karakose, M. et al. A new arc detection method based on fuzzy logic using S-transform for pantograph–catenary systems. J Intell Manuf 29, 839–856 (2018). https://doi.org/10.1007/s10845-015-1136-3
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DOI: https://doi.org/10.1007/s10845-015-1136-3