Novel parameterized intervals may lead to sharp bounds

Purpose High-energy interwell oscillations of the bistable energy harvester (BEH) lead to large-amplitude output voltage. For processing and manufacturing of the BEH, small errors and deviations in the final structure cannot be totally eliminated in practice, which will make the output voltage to be apart away from the design value. Therefore, the geometrical variables, material properties and other parameters should be treated as uncertainties in analysis and are bound to their design. Method This paper presents uncertainty analysis of the BEH to reveal the influence of the uncertain system parameters on the energy harvesting performance. The improved interval extension based on the first-order Taylor series is used to predict the lower and upper bounds of the stable high-energy interwell output voltage of the BEH. In detail, uncertain mass, nonlinear stiffness term, damping, capacitance and electromechanical coupling coefficient are considered. Meanwhile, the Monte Carlo simulation is employed to verify the suitability and the accuracy of this method. Especially, this method allows researchers to define the number of the parameter α j according to the categories of uncertain variables. Results The research works show that interval of the output voltage of the BEH can be limited by reducing the number of uncertain variables, and the uncertainty of the output voltage is more sensitive to the electrical uncertain variables than the structural uncertainties. Conclusion Designers of the BEH should pay enough attention to the errors and tolerances of the electrical output design variables. Specifically, in the design of the BEH, it is more effective to improve the accuracy of the output voltage by limiting the uncertainties of electric parameters than structural parameters. Reducing the number of uncertain parameters through increasing processing precision in production of the BEH can also improve the accuracy of the output voltage.

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“…3 Equation (16) can be rewritten based on the parameterized interval analysis (PIA) [40,41], as follows:…”

Section: Improved Interval Extension Based On the First-order Taylor mentioning

confidence: 99%

Uncertainty Analysis of Bistable Vibration Energy Harvesters Based on the Improved Interval Extension

Zhou

Litak

2019

J. Vib. Eng. Technol.

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“…Many methods have been proposed to deal with the overestimation problem, such as parameterized interval, affine interval, modal interval, and so on. In this work, overestimation reduction is addressed via an optimization approach.…”

Section: Interval Analysismentioning

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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“…Generally, the convex model can be divided into three types: interval set convex model, single-ellipsoid convex and multi-ellipsoid convex models. Since the traditional interval set convex model may overestimate the range enclosure, Elishakoff [32,33] suggested using the parameterization method to overcome this problem. Compared to the interval set convex model, the single-ellipsoid convex model can obtain a more lightweight design, and thus it is attractive for engineering applications.…”

Section: Introductionmentioning

confidence: 99%

Non-probabilistic reliability-based design optimization of stiffened shells under buckling constraint

Meng

Hao

et al. 2015

Thin-Walled Structures

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Novel parameterized intervals may lead to sharp bounds

Cited by 49 publications

References 2 publications

Uncertainty Analysis of Bistable Vibration Energy Harvesters Based on the Improved Interval Extension

Uncertainty Analysis of Bistable Vibration Energy Harvesters Based on the Improved Interval Extension

Structural damage diagnosis with uncertainties quantified using interval analysis

Non-probabilistic reliability-based design optimization of stiffened shells under buckling constraint

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