General Chebyshev type inequalities for universal integral

“…The differences within the internal structure of same material lead to the instability and unknown distribution of AE hits. Due to the unknown distribution of AE hits, Chebyshev's inequality [10,11] which can be used for any unknown distribution is used to calculate the threshold of detection criteria. Based on this detection criteria, the safe status of rail can be determined.…”

Section: B Chebyshev's Inequalitymentioning

confidence: 99%

An investigation on rail health monitoring using acoustic emission technique by tensile test

Xin

Feng

Zou

et al. 2015

2015 IEEE International Instrumentation and Measurement Technology Conference (I2MTC) Proceedings

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In order to detect the health status of high-speed railway, various studies have been examined by Acoustic Emission (AE) method. However, little work has been done on studying the relationship between rail status and features of AE signals, and this relationship can be used to establish a detection criterion for rail health monitoring. This paper presents a methodology on rail health monitoring by AE signals and establishing a detection criterion. AE signals in different safe status are obtained by tensile testing machine and AE data acquisition system. The safe and unsafe region of rail steel is analyzed by stress-strain curve. Based on the Chebyshev's inequality and the variation rate of AE hits, a detection criteria is established to detect the safe status of rail, and the corresponding detection procedure are provided. The results clearly illustrate that the proposed method can detect the safe status of rail effectively.

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“…We will give first a main inequality, see [5], and then the Minkowski and Chebyshev type inequalities appear as special cases.…”

Section: A General Inequality For Universal Integralmentioning

confidence: 99%

“…Recently, Mesiar, Li, and Pap [17] have given an approach to the Choquet integral as Lebesgue integral and in this way they obtained the related inequalities. Inequalities with respect to the universal integral (introduced in [12]) were obtained in [5].…”

Section: Introductionmentioning

confidence: 99%

Inequalities for integrals based on nonadditive measures

Pap

2011

2011 IEEE 12th International Symposium on Computational Intelligence and Informatics (CINTI)

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There are considered generalizations of the classical integral inequalities as Hölder, Minkowski, Chebishev, Berwald to fuzzy integrals, e.g., Choquet and Sugeno integrals. For the universal integral, as generalization of Choquet and Sugeno integral, there are given a general inequality which cover Hölder and Minkowski type inequalities. There are given generalizations of the Hölder, Minkowski and Chebyshev's inequalities for two important cases of the pseudo-integral.

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General Chebyshev type inequalities for universal integral

Cited by 30 publications

References 23 publications

Integrals based on monotone set functions

Integrals based on monotone set functions

An investigation on rail health monitoring using acoustic emission technique by tensile test

Inequalities for integrals based on nonadditive measures

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