Overestimation-free Computational Version of Interval Analysis

Elishakoff, Isaac; Miglis, Yohann

doi:10.1080/15502287.2012.683134

Cited by 28 publications

(7 citation statements)

References 11 publications

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“…The reason for this drastic overestimation is, in the process of combination computation, each variable is treated independently. [23] For example, x 2 is regarded as two independent x's; and without considering the correlation between variables, a huge overestimation may occur. In addition, some of the algebraic laws may only hold in a weaker form in interval computation.…”

Section: Interval Combination Methodsmentioning

confidence: 99%

Structural damage diagnosis with uncertainties quantified using interval analysis

Liu

Mao

2017

Struct. Control Health Monit.

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Summary The in situ structural assessment by means of structural health monitoring (SHM) has received a great attention in all sorts of civil engineering applications. However, SHM implementations especially damage detections for real‐world infrastructures are always overwhelmed with uncertainties of high dimensionality. A nonprobabilistic uncertainty‐quantification‐enhanced damage diagnosis method is proposed in this study with respect to interval analysis on SHM features. The diagonal elements of the vector auto‐regressive model, constructed from the data measurements, are firstly extracted to form a vector, and this vector's Mahalanobis distance between pristine and unknown conditions is used as a damage‐sensitive feature. Subsequently, the uncertainty sources, such as measurement inaccuracy and physical variability, are considered as influencing variables. A differential evolution algorithm is thereby introduced to convert the fluctuating interval of those variables into the uncertainty interval of Mahalanobis distance estimation. Finally, inspired by the idea of receiver operating characteristics when probability of detection is available, a modified mathematic metric is defined suited for interval analysis, and area under the modified receiver operating characteristics curve is employed to detect and localize damages. A contrived numerical mass‐spring system and a laboratory‐scale frame structure are used to validate the proposed framework; and in addition, the damage severity is able to be quantified via a proposed interval distance between pristine and inspection conditions.

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Section: Interval Combination Methodsmentioning

confidence: 99%

Structural damage diagnosis with uncertainties quantified using interval analysis

Liu

Mao

2017

Struct. Control Health Monit.

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“…Then the arithmetic sum of the two intervals S = A + B = [6,8] and the corresponding interval-valued functional form in parametric and symmetrical parametric from are given by s ( 1,3] and the interval-valued function in two different forms are specified by d (…”

Section: Numerical Examplementioning

confidence: 99%

“…Interval arithmetic operations [3,[6][7][8]12,29,30] studied by several researches in various approaches and form for investigation their problem with interval in real or complex domain. Interval arithmetic is an important and helpful tool in numerical analysis and modeling.…”

Section: Introductionmentioning

confidence: 99%

“…Let A =[4,5] and B =[2,3], then find the arithmetic operation using convex combination form of A + B, A − B, AB, A/B.Solution:The interval-valued function in convex combination form of A and B can be written as a ( p)= 5 p + 4 (1 − p) , b ( p) = 3 p + 2 (1 − p) .The addition A + B =[6,8] and the interval-valued function in convex combination form of the sum is s ( p) = 8 p + 6 (1 − p) .The subtraction A − B =[1,3] and convex combination form of the interval-valued function is d (p) = 5 p + 4 (1 − p) − {2 p + 3 (1 − p)} = 2 p + 1.The multiplication A × B =[8,15] and convex combination form of the interval-valued function for multiplication is m ( p) = (5 p + 4 (1 − p))(3 p …”

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confidence: 99%

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Parametric Functional Representation of Interval Number with Arithmetic Operations

Pal¹,

Mahapatra

2015

Int. J. Appl. Comput. Math

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The objective of this paper is to represent the interval number in different functional forms. We have represented the interval number by parametric product functional form, symmetric functional form, asymmetric functional form and convex combination functional form. We represent positive interval number in parametric product functional form, symmetric and asymmetric functional forms. However any interval number can be represented by a convex combination functional form. We also study the arithmetic operations of interval numbers based on the different forms of functional representation. Numerical examples are given to illustrate our proposed approach for arithmetic operations of the interval number in different functional form. Finally some open problems are mentioned at the end of the paper.

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“…Researchers developed several interval analysis method, such as the general interval analysis [31][32][33], the Parameterized Interval Analysis (PIA) [34,35]which has the optimization and anti-optimization problems [33]. Among interval analysis methods, the Taylor Expansion [36][37][38][39][40] is popular since it is not required to alter the governing functions of system dynamics. Especially, there is a nonlinear relation between the output response of the system and uncertainties.…”

Section: Introductionmentioning

confidence: 99%

Robust design optimization of a nonlinear monostable energy harvester with uncertainties

Zhou

Litak

2020

Meccanica

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Based on the improved interval extension, a robust optimization method for nonlinear monostable energy harvesters with uncertainties is developed. In this method, the 2nd order terms in the interval extension formula of the objective function (output voltage) are kept so this approach is suitable for a nonlinear energy harvesting system. To illustrate this method, uncertain mass, uncertain capacitance and uncertain electromechanical coupling coefficient are optimized to maximize the central point of output voltage whose deviation of which is simultaneously minimized. Then, an optimal design with different robustness is obtained. The results also show that the robustness of the optimal design of nonlinear monostable energy harvesters is increased, but the cost of performance has to be paid for. Overall, the framework provides the optimal design for nonlinear energy harvesters (monostable, bistable, tristable, multistable harvesters).

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Overestimation-free Computational Version of Interval Analysis

Cited by 28 publications

References 11 publications

Structural damage diagnosis with uncertainties quantified using interval analysis

Structural damage diagnosis with uncertainties quantified using interval analysis

Parametric Functional Representation of Interval Number with Arithmetic Operations

Robust design optimization of a nonlinear monostable energy harvester with uncertainties

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