Maximum entropy-based uncertainty modeling at the elemental level in linear structural and thermal problems

Song, Pengchao; Mignolet, Marc P.

doi:10.1007/s00466-019-01734-y

Cited by 8 publications

(6 citation statements)

References 15 publications

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“…For the mass matrix, the randomization is a single-physics one [41,42], i.e., it is performed with the matrix itself. For each elemental mass matrix of the mean FE model, denoted as M ðeÞ , its random sample is constructed as…”

Section: Nonparametric Maximum Entropy Approach For Uncertainty Quant...mentioning

confidence: 99%

“…Following the procedure proposed in Refs. [41], [52], and [53], each element H ij of the matrix H ðeÞ is treated as the transformation of a zero mean, unit variance Gaussian field P ij with a specified stationary autocorrelation function…”

Section: Nonparametric Maximum Entropy Approach For Uncertainty Quant...mentioning

confidence: 99%

“…Such an uncertainty modeling is proposed here based on the very recent work in Refs. [40][41][42], where the developed nonparametric approach is nonintrusive to the finite element software, requiring only the capability to output finite element mass, stiffness, electromechanical coupling, and piezoelectric capacitance matrices for the mean harvester design. The approach in Refs.…”

Section: Introductionmentioning

confidence: 99%

“…The approach in Refs. [40][41][42] follows the original work of Soize in Ref. [43], in which the maximum entropy principle is applied and the uncertainty is modeled directly at the level of a reduced-order model of the structure, not within the finite element formulation as is done with the stochastic finite element approach.…”

Section: Introductionmentioning

confidence: 99%

“…The specific formulation in Refs. [40][41][42], also used in this study, is a modification of the original methodology of Soize, in which the elemental mass and stiffness matrices are recognized as reduced order model matrices of the structure within each of the finite elements with the interpolation functions serving as basis functions inside the elements. Once the mean model elemental matrices have been obtained, uncertainty is introduced element per element for each sample of the uncertain harvester, the structural-piezoelectric matrices are reassembled and the simulation, e.g., output power determination, can be carried out.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Uncertainty Analysis of Piezoelectric Vibration Energy Harvesters Using a Finite Element Level-Based Maximum Entropy Approach

Wang

Liao

Mignolet

2021

ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering

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Quantifying effects of system-wide uncertainties (i.e., affecting structural, piezoelectric, and/or electrical components) in the analysis and design of piezoelectric vibration energy harvesters has recently been emphasized. The present investigation proposes first a general methodology to model these uncertainties within a finite element model of the harvester obtained from an existing finite element software. Needed from this software are the matrices relating to the structural properties (mass, stiffness), the piezoelectric capacitance matrix, as well as the structural-piezoelectric coupling terms of the mean harvester. The thermal analogy linking piezoelectric and temperature effects is also extended to permit the use of finite element software that do not have piezoelectric elements but include thermal effects on structures. The approach is applied to a beam energy harvester. Both weak and strong coupling configurations are considered and various scenarios of load resistance tuning are considered, i.e., based on the mean model, for each harvester sample, or based on the entire set of harvesters. The uncertainty is shown to have significant effects in all cases even at a relatively low level and these effects are dominated by the uncertainty on the structure vs. the one on the piezoelectric component. The strongly coupled configuration is shown to be better as it is less sensitive to the uncertainty and its variability in power output can be significantly reduced by the adaptive optimization, and the harvested power can even be boosted if the target excitation frequency falls into the power saturation band of the system.

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Section: Nonparametric Maximum Entropy Approach For Uncertainty Quant...mentioning

confidence: 99%

Section: Nonparametric Maximum Entropy Approach For Uncertainty Quant...mentioning

confidence: 99%