scholarly journals On some Chebyshev type inequalities for thecomplex integral

2019 ◽  
Vol 37 (2) ◽  
pp. 307-317
Author(s):  
Silvestru Sever Dragomir
Keyword(s):  
Chebyshev Inequality

Assume thatfandgare continuous onγ,γ⊂Cis a piecewisesmooth path parametrized byz(t), t∈[a, b]fromz(a) =utoz(b) =wwithw6=u, and thecomplex Chebyshev functionalis defined byDγ(f, g) :=1w−u∫γf(z)g(z)dz−1w−u∫γf(z)dz1w−u∫γg(z)dz.In this paper we establish some bounds for the magnitude of the functionalDγ(f, g)under Lipschitzian assumptions for the functionsfandg,and pro-vide a complex version for the well known Chebyshev inequality.

scholarly journals Data-based polyhedron model for optimization of engineering structures involving uncertainties

2021 ◽  
Vol 2 ◽  
Author(s):  
Zhiping Qiu ◽  
Han Wu ◽  
Isaac Elishakoff ◽  
Dongliang Liu
Keyword(s):  
Linear Programming ◽  
Convex Polyhedron ◽  
Linear Optimization ◽  
Optimal Solution ◽  
Composite Plates ◽  
Convex Polyhedra ◽  
Chebyshev Inequality ◽  
Engineering Structures ◽  
Load Bearing ◽  
Polyhedron Model

Abstract This paper studies the data-based polyhedron model and its application in uncertain linear optimization of engineering structures, especially in the absence of information either on probabilistic properties or about membership functions in the fussy sets-based approach, in which situation it is more appropriate to quantify the uncertainties by convex polyhedra. Firstly, we introduce the uncertainty quantification method of the convex polyhedron approach and the model modification method by Chebyshev inequality. Secondly, the characteristics of the optimal solution of convex polyhedron linear programming are investigated. Then the vertex solution of convex polyhedron linear programming is presented and proven. Next, the application of convex polyhedron linear programming in the static load-bearing capacity problem is introduced. Finally, the effectiveness of the vertex solution is verified by an example of the plane truss bearing problem, and the efficiency is verified by a load-bearing problem of stiffened composite plates.

Type–reduction of Interval Type–2 fuzzy numbers via the Chebyshev inequality

2021 ◽  
Author(s):  
Juan Carlos Figueroa-García ◽  
Heriberto Román-Flores ◽  
Yurilev Chalco-Cano
Keyword(s):  
Fuzzy Numbers ◽  
Chebyshev Inequality ◽  
Type Reduction ◽  
Interval Type

scholarly journals New Chebyshev type inequalities via a general family of fractional integral operators with a modified Mittag-Leffler kernel

2021 ◽  
Vol 6 (10) ◽  
pp. 11167-11186
Author(s):  
Hari M. Srivastava ◽  
◽  
Artion Kashuri ◽  
Pshtiwan Othman Mohammed ◽  
Abdullah M. Alsharif ◽  
...  
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integrals ◽  
Chebyshev Inequality ◽  
Fractional Integral Operators ◽  
General Family ◽  
Chebyshev Functional ◽  
Bounded Below

<abstract><p>The main goal of this article is first to introduce a new generalization of the fractional integral operators with a certain modified Mittag-Leffler kernel and then investigate the Chebyshev inequality via this general family of fractional integral operators. We improve our results and we investigate the Chebyshev inequality for more than two functions. We also derive some inequalities of this type for functions whose derivatives are bounded above and bounded below. In addition, we establish an estimate for the Chebyshev functional by using the new fractional integral operators. Finally, we find similar inequalities for some specialized fractional integrals keeping some of the earlier results in view.</p></abstract>

scholarly journals Performance Degradation Assessment of Concrete Beams Based on Acoustic Emission Burst Features and Mahalanobis—Taguchi System

Sensors ◽  
2020 ◽  
Vol 20 (12) ◽  
pp. 3402 ◽  
Author(s):  
Md Arafat Habib ◽  
Akhand Rai ◽  
Jong-Myon Kim
Keyword(s):  
Acoustic Emission ◽  
Concrete Beams ◽  
Early Stage ◽  
Concrete Structures ◽  
Feature Selection Method ◽  
Noise Removal ◽  
Performance Degradation ◽  
Reinforced Concrete Beams ◽  
Chebyshev Inequality ◽  
Degradation Indicator

Acoustic emission (AE) has been used extensively for structural health monitoring based on the stress waves generated due to evolution of cracks in concrete structures. A major concern while using AE features is that each of them responds differently to the fractures in concrete structures. To tackle this problem, Mahalanobis—Taguchi system (MTS) is utilized, which fuses the AE feature space to provide comprehensive and reliable degradation indicator with a feature selection method to determine useful features. Further, majority of the existing investigations gave little attention to naturally occurring cracks, which are actually more difficult to detect. In this study, a novel degradation indicator (DI) based on AE features and MTS is proposed to indicate the performance degradation in reinforced concrete beams. The experimental results confirm that the MTS can successfully distinguish between healthy and faulty conditions. To alleviate the noise from the DI obtained through MTS, a noise-removal strategy based on Chebyshev inequality is suggested. The results show that the proposed DI based on AE features and MTS is capable of detecting early stage cracks as well as development of damage in concrete beams.

Chebyshev inequality for q-integrals

2019 ◽  
Vol 106 ◽  
pp. 146-154 ◽  
Author(s):  
Tingsu Yan ◽  
Yao Ouyang
Keyword(s):  
Chebyshev Inequality

scholarly journals Failure Prediction of the Rotating Machinery Based on CEEMDAN-ApEn Feature and AR-UKF Model

2020 ◽  
Vol 10 (6) ◽  
pp. 2056 ◽  
Author(s):  
Jingli Yang ◽  
Yongqi Chang ◽  
Tianyu Gao ◽  
Jianfeng Wang
Keyword(s):  
Unscented Kalman Filter ◽  
Failure Prediction ◽  
Prediction Method ◽  
Degradation Process ◽  
Rotating Machinery ◽  
Remaining Useful Life ◽  
Ar Model ◽  
Chebyshev Inequality ◽  
Intrinsic Mode Functions ◽  
Maximal Information Coefficient

A novel failure prediction method of the rotating machinery is presented in this paper. Firstly, the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) is applied to decompose the vibration signals of the rotating machinery into a number of intrinsic mode functions (IMFs) and a residual (Res), and the metric of maximal information coefficient (MIC) is used to select eligible IMFs to reconstruct signals. Then, the approximate entropy (ApEn)-weighted energy value of the reconstructed signals are calculated to track the degradation process of the rotating machinery. Furthermore, the Chebyshev inequality is introduced to determine the prediction starting time (PST). Finally, the auto regress (AR) model and unscented Kalman filter (UKF) algorithm are used to predict the remaining useful life (RUL) of the rotating machinery. The method is fully evaluated in a test-to-failure experiment. The obtained results show that the proposed method outperforms its counterparts on failure prediction of the rotating machinery.

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