Posing probability problems related to continuous and discrete sample space

Abstract The pearceite-polybasite group of minerals, general formula [M6T2S7][Ag9CuS4] with M = Ag, Cu; and T = As, Sb, show a crystal structure which can be described as the succession, along the c axis, of two pseudo-layer modules: a [M6T2S7]2– A module layer and a [Ag9CuS4]2+ B module layer. Copper is present in one structural position of the B module layer and replaces Ag in the only fully occupied M position of the A module layer. When the Cu content is >4.00 a.p.f.u., the structural position of the A module layer becomes Cu-dominant and, consequently, the mineral deserves its own name. In this paper we report the crystal-chemical characterization of two Cu-rich members exhibiting the 111 unitcell type (corresponding to the Tac polytype). One sample (space group (P )m1, a 7.3218(8), c 11.8877(13) Å, V 551.90(10) Å3, Z = 1) having As >Sb and with the structural position of the A module layer dominated by Cu, has been named cupropearceite and the other sample (space group (P3̄)m1, a 7.3277(3), c 11.7752(6) Å, V 547.56(8) Å3, Z = 1) having Sb >As has been named cupropolybasite. Both the new minerals and mineral names have been approved by the IMA-CNMNC.

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Optimization of a vacuum cleaner fan suction and shaft power using Kriging surrogate model and MIGA

Proceedings of the Institution of Mechanical Engineers Part A Journal of Power and Energy ◽

10.1177/09576509211049613 ◽

2021 ◽

pp. 095765092110496

Author(s):

Soheil Almasi ◽

Mohammad Mahdi Ghorani ◽

Mohammad Hadi Sotoude Haghighi ◽

Seyed Mohammad Mirghavami ◽

Alireza Riasi

Keyword(s):

Optimization Design ◽

Optimization Technique ◽

Internal Flow ◽

Latin Hypercube Sampling ◽

Sample Space ◽

Geometrical Parameters ◽

Vacuum Cleaner ◽

Time Saving ◽

Design Variables ◽

Shaft Power

Optimization of vacuum cleaner fan components is a low-cost and time-saving solution to satisfy the increasing requirement for compact energy-efficient cleaners. In this study, surrogate-based optimization technique is used and for the first time it is focused on maximization of Airwatt parameter, which describes the fan suction power, as an objective function (Case II). Besides, the shaft power is minimized (Case I) as another optimization target in order to reduce the power consumption of the vacuum cleaner. 11 geometrical variables of 3 fan components including impeller, diffuser and return channel are selected as the optimization design variables. 80 training points are distributed in the sample space using Advanced Latin Hypercube Sampling (ALHS) technique and the outputs of sample points are calculated by means of CFD simulations. Kriging and RSA surrogate models have been fitted to the outputs of the sample space. Through coupling of constructed Kriging models and Multi-Island Genetic Algorithm (MIGA), the optimal design for each of the optimization cases is presented and evaluated using numerical simulations. A 20.22% reduction in shaft power in Case I and an improvement of 27.73% in Airwatt in Case II have been achieved as the overall results of this study. Despite achieving goals in both optimization cases, a slight decrease in Airwatt in Case I (−6.20%) and a slight increase in shaft power in Case II (+4.82%) are observed relative to primary fan. Furthermore, the Analysis of Variance (ANOVA) determines the importance level of design variables and their 2-way interactions on the objective functions. It was concluded that geometrical parameters related to all of the fan components must be considered simultaneously to conduct a comprehensive optimization. The reasons of enhancement in optimal cases compared with the reference design have been further investigated by analysis of the fan internal flow field. Post-processing of the CFD results demonstrates that the applied geometrical modifications cause a more uniform flow through the flow passages of the optimal fan components.

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