Acoustic Emission Signal Entropy as a Means to Estimate Loads in Fiber Reinforced Polymer Rods

Fibre reinforced polymer (FRP) rods are widely used as corrosion-resistant reinforcing in civil structures. However, developing a method to determine the loads on in-service FRP rods remains a challenge. In this study, the entropy of acoustic emission (AE) emanating from FRP rods is used to estimate the applied loads. As loads increased, the fraction of AE hits with higher entropy also increased. High entropy AE hits are defined using the one-sided Chebyshev’s inequality with parameter k = 2 where the histogram of AE entropy up to 10–15% of ultimate load was used as a baseline. According to the one-sided Chebyshev’s inequality, when more than 20% (k = 2) of AE hits that fall further than two standard deviations away from the mean are classified as high entropy events, a new distribution of high entropy AE hits is assumed to exist. We have found that the fraction of high AE hits. In glass FRP and carbon FRP rods, a high entropy AE hit fraction of 20% was exceeded at approximately 40% and 50% of the ultimate load, respectively. This work demonstrates that monitoring high entropy AE hits may provide a useful means to estimate the loads on FRP rods.

New General Variants of Chebyshev Type Inequalities via Generalized Fractional Integral Operators

In this study, new and general variants have been obtained on Chebyshev’s inequality, which is quite old in inequality theory but also a useful and effective type of inequality. The main findings obtained by using integrable functions and generalized fractional integral operators have generalized many existing results as well as iterating the Chebyshev inequality in special cases.

Inequalities in Triangular Norm-Based ∗-fuzzy ( L + ) p Spaces

In this article, we introduce the ∗-fuzzy (L+)p spaces for 1≤p<∞ on triangular norm-based ∗-fuzzy measure spaces and show that they are complete ∗-fuzzy normed space and investigate some properties in these space. Next, we prove Chebyshev’s inequality and Hölder’s inequality in ∗-fuzzy (L+)p spaces.

A Review on Issues of Settling the Sample-size in Surveys: Two Approaches—Equal and Varying Probability Sampling—Crises in Sensitive Cases

“How many units to take in a sample to choose” is a classical problem in sample surveys addressed by numerous predecessors. Chebyshev’s inequality provides a tool in simple random sampling as may as well be extended to varying probability sampling. Two approaches are presented. But critically, in indirect surveys to cover sensitive issues, problems seem to be insurmountable, as illustrated.