Optimal Designs for Multiple-Mixture by Process Variable Experiments

2013 ◽  
pp. 45-53 ◽  
Author(s):  
Roelof L. J. Coetzer ◽  
Linda M. Haines
Keyword(s):  
Process Variable ◽  
Optimal Designs

Using a genetic algorithm to generate D‐optimal designs for mixture‐process variable experiments

2019 ◽  
Vol 35 (8) ◽  
pp. 2657-2676
Author(s):  
Wasinee Pradubsri ◽  
Boonorm Chomtee ◽  
John J. Borkowski
Keyword(s):  
Genetic Algorithm ◽  
Process Variable ◽  
Optimal Designs

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.

Constrained optimal designs

1984 ◽  
Author(s):  
Moun-Shen Carl Lee
Keyword(s):  
Optimal Designs

Habitability: a process versus a state variable framework with observational tests and theoretical implications

2021 ◽  
pp. 1-8
Author(s):  
A. Lenardic ◽  
J. Seales
Keyword(s):  
Process Variable ◽  
State Variable ◽  
Modelling Framework ◽  
Meta Level ◽  
Planetary Habitability

The term habitable is used to describe planets that can harbour life. Debate exists as to specific conditions that allow for habitability but the use of the term as a planetary variable has become ubiquitous. This paper poses a meta-level question: What type of variable is habitability? Is it akin to temperature, in that it is something that characterizes a planet, or is something that flows through a planet, akin to heat? That is, is habitability a state or a process variable? Forth coming observations can be used to discriminate between these end-member hypotheses. Each has different implications for the factors that lead to differences between planets (e.g. the differences between Earth and Venus). Observational tests can proceed independent of any new modelling of planetary habitability. However, the viability of habitability as a process can influence future modelling. We discuss a specific modelling framework based on anticipating observations that can discriminate between different views of habitability.

Dynamic modeling and power optimization of a 4RPSP+PS parallel flight simulator machine

Robotica ◽  
2021 ◽  
pp. 1-26
Author(s):  
Soheil Zarkandi
Keyword(s):  
Power Consumption ◽  
Dynamic Modeling ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Pareto Front ◽  
Essential Role ◽  
Power Optimization ◽  
Optimal Designs ◽  
Flight Simulator ◽  
Lagrange Method

Abstract Reducing consumed power of a robotic machine has an essential role in enhancing its energy efficiency and must be considered during its design process. This paper deals with dynamic modeling and power optimization of a four-degrees-of-freedom flight simulator machine. Simulator cabin of the machine has yaw, pitch, roll and heave motions produced by a 4RPSP+PS parallel manipulator (PM). Using the Euler–Lagrange method, a closed-form dynamic equation is derived for the 4RPSP+PS PM, and its power consumption is computed on the entire workspace. Then, a newly introduced optimization algorithm called multiobjective golden eagle optimizer is utilized to establish a Pareto front of optimal designs of the manipulator having a relatively larger workspace and lower power consumption. The results are verified through numerical examples.

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