scholarly journals How Design Quality Improves with Increasing Computational Abilities: General Formulas and Case Study of Aircraft Fuel Efficiency

2015 ◽  
Vol 19 (5) ◽  
pp. 581-584
Author(s):  
Joe Lorkowski ◽  
◽  
Olga Kosheleva ◽  
Vladik Kreinovich ◽  
Sergei Soloviev ◽  
...  
Keyword(s):  
Optimal Design ◽  
Fuel Efficiency ◽  
Optimal Designs ◽  
Theoretical Formula ◽  
Np Hard ◽  
Design Quality ◽  
Aircraft Fuel ◽  
Feasible Algorithm

It is known that the problems of optimal design are NP-hard – meaning that, in general, a feasible algorithm can only produce close-to-optimal designs. The more computations we perform, the better design we can produce. In this paper, we theoretically derive quantitative formulas describing how the design qualities improves with the increasing computational abilities. We then empirically confirm the resulting theoretical formula by applying it to the problem of aircraft fuel efficiency.

Q-optimal experimental designs and close to them experimental designs for polynomial regression on the interval

2020 ◽  
Vol 86 (5) ◽  
pp. 65-72
Author(s):  
Yu. D. Grigoriev
Keyword(s):  
Optimal Design ◽  
Polynomial Regression ◽  
Direct Consequence ◽  
Experimental Designs ◽  
Optimal Designs ◽  
Software Systems ◽  
General Character ◽  
Support Points ◽  
Optimal Weights ◽  
Universal Expression

The problem of constructing Q-optimal experimental designs for polynomial regression on the interval [–1, 1] is considered. It is shown that well-known Malyutov – Fedorov designs using D-optimal designs (so-called Legendre spectrum) are other than Q-optimal designs. This statement is a direct consequence of Shabados remark which disproved the Erdős hypothesis that the spectrum (support points) of saturated D-optimal designs for polynomial regression on a segment appeared to be support points of saturated Q-optimal designs. We present a saturated exact Q-optimal design for polynomial regression with s = 3 which proves the Shabados notion and then extend this statement to approximate designs. It is shown that when s = 3, 4 the Malyutov – Fedorov theorem on approximate Q-optimal design is also incorrect, though it still stands for s = 1, 2. The Malyutov – Fedorov designs with Legendre spectrum are considered from the standpoint of their proximity to Q-optimal designs. Case studies revealed that they are close enough for small degrees s of polynomial regression. A universal expression for Q-optimal distribution of the weights pi for support points xi for an arbitrary spectrum is derived. The expression is used to tabulate the distribution of weights for Malyutov – Fedorov designs at s = 3, ..., 6. The general character of the obtained expression is noted for Q-optimal weights with A-optimal weight distribution (Pukelsheim distribution) for the same problem statement. In conclusion a brief recommendation on the numerical construction of Q-optimal designs is given. It is noted that in this case in addition to conventional numerical methods some software systems of symbolic computations using methods of resultants and elimination theory can be successfully applied. The examples of Q-optimal designs considered in the paper are constructed using precisely these methods.

Optimal Design of Two-Sided Market Platforms: An Empirical Case Study of Ebay

2013 ◽  
Author(s):  
Aaron Bodoh-Creed ◽  
JJrn Boehnke ◽  
Brent Richard Hickman
Keyword(s):  
Optimal Design

CAEP/9-agreed certification requirement for the Aeroplane CO2Emissions Standard: a comment on ICAO Cir 337

2016 ◽  
Vol 120 (1226) ◽  
pp. 693-723 ◽  
Author(s):  
J.E. Green ◽  
J.A. Jupp
Keyword(s):  
Fuel Efficiency ◽  
Scientific Basis ◽  
Civil Aviation ◽  
Aircraft Emissions ◽  
Current Form ◽  
Fuel Burn ◽  
Aircraft Fuel ◽  
Starting Point ◽  
Range Equation ◽  
Main Criticism

ABSTRACTThe International Civil Aviation Organization (ICAO) Circular Cir 337 is the first step towards ICAO establishing an Aeroplane CO2Emissions Standard to form part of Annex 16, Volume III to the Chicago Convention. It describes itself as ‘a work in progress’. This paper reviews Cir 337 against the background of flight physics, the published literature on aircraft fuel burn and CO2emissions and the current practices of the aircraft and engine manufacturers and the airline operators. We have taken, as our starting point, the aim of ICAO to reduce the fuel used per revenue tonne-kilometre performed and argue that the Breguet range equation, which captures all the relevant flight physics, should be the basis of the metric system underpinning the standard. Our overall conclusion is that Cir 337 provides an excellent basis for the initial regulation of aviation's CO2emissions and, further in the future, for developing measures to increase the fuel efficiency of the operational side of civil aviation. Our main criticism of the circular in its current form is that it does not address the ICAO goal of reducingfuel used per revenue tonne-kilometre performedand makes no reference to payload. This defect could be eliminated simply by omission of the exponent 0.24 of the Reference Geometric Factor (RGF) in the formula for the metric given in Chapter 2 (paragraph 2.2) of the circular. Retaining theRGFto the power unity in the metric and multiplying it by an appropriate value of the effective floor loading would convert it to what the 37thAssembly of ICAO called for – a statement of fuel used per revenue tonne-kilometre performed. Finally, correlating the amended metric against design range, as determined from the measured specific air range and the key certificated masses, provides a sound scientific basis for an initial regulation to cap passenger aircraft emissions.

scholarly journals Case study on optimal design and operation of detached house energy system: Solar, battery, and ground source heat pump

2022 ◽  
Vol 308 ◽  
pp. 118370
Author(s):  
Ellen Nordgård-Hansen ◽  
Nand Kishor ◽  
Kirsti Midttømme ◽  
Vetle Kjær Risinggård ◽  
Jan Kocbach
Keyword(s):  
Optimal Design ◽  
Heat Pump ◽  
Energy System ◽  
Ground Source Heat Pump ◽  
Ground Source ◽  
Solar Battery ◽  
Detached House

scholarly journals Investigation of spillway rating curve via theoretical formula, laboratory experiment, and 3D numerical modeling: A case study of the Riam Kiwa Dam, Indonesia

2021 ◽  
Vol 930 (1) ◽  
pp. 012030
Author(s):  
J Zulfan ◽  
B M Ginting
Keyword(s):  
Numerical Modeling ◽  
Laboratory Experiment ◽  
Water Depth ◽  
Laboratory Model ◽  
Theoretical Formula ◽  
Rating Curve ◽  
3D Numerical Modeling ◽  
Construction Costs ◽  
3D Software

Abstract The spillway rating curve of the Riam Kiwa Dam was investigated via theoretical formula, laboratory experiment, and 3D numerical modeling. It is an ogee type with two uncontrolled and five gated spillways with a total length of 77.5 m. The experiment was performed with a scale of 1:50, while the numerical modeling was conducted using FLOW-3D software. Several discharge values (16.67–2,652.7 m3/s) were tested and observed for two different scenarios of gate openings. For the low discharge in Scenario 1, the theoretical formula and FLOW-3D computed the rating curve less accurately with the error values greater than 10%. A similar phenomenon was observed in Scenario 2, where both theoretical formula and FLOW-3D predicted the rating curve accurately with error values less than 10% for the higher discharge. The discharges tend to be overestimated for the water depth values greater than 2 m giving the average discharge deviation of 6% for the PMF condition. FLOW-3D was found to calculate water depth for all scenarios accurately. It shows a promising approach between numerical simulation and physical modeling, to minimize laboratory model construction costs.

scholarly journals A Highly D‑efficient Spring Balance Weighing Design for an Even Number of Objects

2019 ◽  
Vol 5 (344) ◽  
pp. 17-27
Author(s):  
Małgorzata Graczyk ◽  
Bronisław Ceranka
Keyword(s):  
Optimal Design ◽  
Sufficient Conditions ◽  
Optimality Criteria ◽  
Point Of View ◽  
Necessary And Sufficient Conditions ◽  
Optimal Designs ◽  
Efficient Design ◽  
Spring Balance ◽  
Experimental Errors ◽  
Necessary And Sufficient

The problem of determining unknown measurements of objects in the model of spring balance weighing designs is presented. These designs are considered under the assumption that experimental errors are uncorrelated and that they have the same variances. The relations between the parameters of weighing designs are deliberated from the point of view of optimality criteria. In the paper, designs in which the product of the variances of estimators is possibly the smallest one, i.e. D‑optimal designs, are studied. A highly D‑efficient design in classes in which a D‑optimal design does not exist are determined. The necessary and sufficient conditions under which a highly efficient design exists and methods of its construction, along with relevant examples, are introduced.

Optimal Design of Plastic Structures for Fixed and Shakedown Loadings

1973 ◽  
Vol 40 (2) ◽  
pp. 595-599 ◽  
Author(s):  
M. Z. Cohn ◽  
S. R. Parimi
Keyword(s):  
Optimal Design ◽  
Loading Condition ◽  
Minimum Weight ◽  
Optimal Solution ◽  
Failure Criteria ◽  
Optimal Designs ◽  
Design Solution ◽  
Variable Loading ◽  
Framed Structures ◽  
A Value

Optimal (minimum weight) solutions for plastic framed structures under shakedown conditions are found by linear programming. Designs that are optimal for two failure criteria (collapse under fixed loads and collapse under variable repeated loads) are then investigated. It is found that these designs are governed by the ratio of the specified factors defining the two failure criteria, i.e., for shakedown, λs and for collapse under fixed loading, λ. Below a certain value (λs/λ)min the optimal solution under fixed loading is also optimal for fixed and shakedown loading. Above a value (λs/λ)max the optimal design for variable loading is also optimal under the two loading conditions. For intermediate values of λs/λ the optimal design that simultaneously satisfies the two criteria is different from the optimal designs for each independent loading condition. An example illustrates the effect of λs/λ on the nature of the design solution.

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