Uncertainty Quantification in Computational Science

Iaccarino, Gianluca

doi:10.2514/5.9781624102714.0113.0148

Cited by 7 publications

(7 citation statements)

References 28 publications

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“…Intrusive methods require the formulation and solution of a stochastic version of the original model. Non-intrusive methods only require multiple solutions of the original (deterministic) model 18 . This work focuses only in non-intrusive methods.…”

Section: Uncertainty Quantification Methodsmentioning

confidence: 99%

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Monte Carlo based Robust MDO applied to Aircraft Conceptual Design: a technical-financial coupling optimization strategy

Bianchi

Orra

Paglione

2015

15th AIAA Aviation Technology, Integration, and Operations Conference

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Aircraft Conceptual Design is a challenging task that requires not only the understanding of many different disciplines, but also how they interact with each other, leading to many trade-off analyses. The complexity of these interactions grows fast with the number of variables, disciplines and goals of the problem. Multidisciplinary Analysis and Optimization tools can be very helpful to explore the design space, but it is up to the engineering team to define the objective function: optimal with respect to what? For commercial aircraft segment there are two well defined objectives that mostly represent what costumers of this segment desire: minimization of block fuel or minimization of direct operating costs. The objective function is not so clear for the Executive Jets segment and it is usual to apply minimization of MTOW. This paper proposes an architecture that includes Costs, Market Share and Finances disciplines in the optimization loop, treating the market specifications provided by company's intelligence as constraints and maximizes the financial return to the shareholders. This way, the conceived solution complies with all customer needs and also provides the most attractive investment to the shareholders. A comparison is made with the traditional optimization strategy and the results shows that, although both strategies are not exactly conflicting objectives, to maximize the financial return can lead to a different design with significant improvement in financial return. Another key optimization issue treated in this work is the reliability and robustness of the design. Estimation methods have inherent model uncertainties that can not be mitigated even with in-house data calibration. Uncertainty quantification and Robust Design is held in this work by the use of Monte Carlo simulations using triangular distributions and superposition of effects. Results for the Robust Optimization showed that slight changes in the design can improve robustness in the outcomes of interest. Also, the proposed methodology reduces the computational cost of the Robust Design to almost the level of a deterministic design, presenting a significant improvement to this process. Engine Inoperative RC = Rate of Climb Re = Reynolds number Ri = Range for the i-th mission Sref, Sw = Wing reference area SRi = Specific Range for the i-th mission t/c = Thickness-to-Chord ratio TLR = Top Level Requirements TO = Take-off TOFL = Take-Off Field Length TSFC = Thrust Specific Fuel Consumption TSLS = Engine's Sea-Level Static Thrust V, TAS = True Airspeed Vfuel = Fuel Volume VH = Horizontal Tail Volume coefficient VT = Vertical Tail VV = Vertical Tail Volume coefficient Wresf = Fuel reserves weight α, AoA = Angle of Attack β = Sideslip angle Λ = Sweep angle λ = Taper-Ratio Financial acronyms and symbols DOC = Direct Operating Costs IRR = Internal Rate of Return NPV = Net Present Value Optimization acronyms and symbols MDO = Multidisciplinary Design Optimization VDD = Value-Driven Design MOGA = Multi-Objective Genetic Algorithm φ(.) = Vector of O...

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Section: Uncertainty Quantification Methodsmentioning

confidence: 99%

“…Latin Hypercube Sampling assumes an input vector and instead of picking Nsamples random stochastic vectors, the realizations are chosen in a way to maximize the spacing between samples, i.e. to maximize the exploration of the parameter space18 .…”

mentioning

confidence: 99%

Monte Carlo based Robust MDO applied to Aircraft Conceptual Design: a technical-financial coupling optimization strategy

Bianchi

Orra

Paglione

2015

15th AIAA Aviation Technology, Integration, and Operations Conference

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“…However, in practice, we may have only a limited number of samples available and it consequently would be difficult, if not impossible, to obtain an accurate probability for any proposition A (e.g., A = {Y |Y < θ}, where θ is a fixed value). In such a situation, it is suggested to represent the random variable Y "as a mixture of natural variability (aleatory) and estimation errors (epistemic)" since "a finite number of samples from a population leads to epistemic uncertainty [23]." We consider such a situation in the current work and build a fuzzy set for a probability measure: using a probability measure to represent the random nature in the quantity of interest Y ; and a fuzzy set to represent the epistemic uncertainty (due to the incompleteness of the information) in the probability measure.…”

Section: Problem Setupmentioning

confidence: 99%

Mixed aleatory and epistemic uncertainty quantification using fuzzy set theory

Mirzargar

Kirby

2015

International Journal of Approximate Reasoning

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This paper proposes algorithms to construct fuzzy probabilities to represent or model the mixed aleatory and epistemic uncertainty in a limited-size ensemble. Specifically, we discuss the possible requirements for the fuzzy probabilities in order to model the mixed types of uncertainty, and propose algorithms to construct fuzzy probabilities for both independent and dependent datasets. The effectiveness of the proposed algorithms is demonstrated using one-dimensional and high-dimensional examples. After that, we apply the proposed uncertainty representation technique to isocontour extraction, and demonstrate its applicability using examples with both structured and unstructured meshes.

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“…There are also analytical studies done in [21], [22], [23], [24], [25] and [26] to model thin conducting layers using finite element method. However, the conducting layers formed by burrs within the stacks are uncertain, since they are formed by a stochastic process which depends on a large number of parameters, such as the age of punching die, stacking pressure, short circuit's geometry, thickness of the insulating layer and the number of sheets [27], [28].…”

Section: Effects Of Burrs On Laminated Sheetsmentioning

confidence: 99%

Modeling of Losses Due to Inter-Laminar Short-Circuit Currents in Lamination Stacks

Shah

Rasilo

Belahcen

et al. 2013

Electrical, Control and Communication Engineering

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-The cores of electrical machines are generally punched and laminated to reduce the eddy current losses. These manufacturing processes such as punching and cutting deform the electrical sheets and deteriorate its magnetic properties. Burrs are formed due to plastic deformation of electrical sheets. Burr formed due to punching on the edges of laminated sheets impairs the insulation of adjacent sheet and make random galvanic contacts during the pressing of stacked sheets. The effect of circulating current occurs if the burrs occur on the opposite edges of the stacks of laminated sheets and incase of bolted or wielded sheets, induced current return through it. This induced current causes the additional losses in electrical machine. The existence of surface current on the boundary between two insulated regions causes discontinuity of tangential component of magnetic field. Hence, based on this principle, the boundary layer model was developed to study the additional losses due to galvanic contacts formed by burred edges. The boundary layer model was then coupled with 2-D finite element vector potential formulation and compared with fine mesh layer model. Fine mesh layer model consists of finely space discretized 950028 second order triangular elements. The losses were computed from two models and were obtained similar at 50 Hz. The developed boundary layer model can be further used in electrical machines to study additional losses due to galvanic contacts at the edges of stator cores.

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Uncertainty Quantification in Computational Science

Cited by 7 publications

References 28 publications

Monte Carlo based Robust MDO applied to Aircraft Conceptual Design: a technical-financial coupling optimization strategy

Monte Carlo based Robust MDO applied to Aircraft Conceptual Design: a technical-financial coupling optimization strategy

Mixed aleatory and epistemic uncertainty quantification using fuzzy set theory

Modeling of Losses Due to Inter-Laminar Short-Circuit Currents in Lamination Stacks

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