Mathematical Modeling Methods in Designing Onboard Laser-Ranging Systems of Spacecraft

To perform rendezvous and docking of spacecraft (SC), it is necessary to detect and measure the coordinates of a passive space vehicle (SV) using the onboard aids of an active SV. For this purpose, in addition to radio engineering systems, laser-ranging systems (LRS) are used. A designing process of the onboard LRS for promising spacecraft is currently becoming more complicated and requires taking into account a lot of factors.The authors have developed the PC software to assess capabilities of onboard pulse LRS of spacecraft when working on the nearby or distant space objects that have a diffusely scattering surface, as well as are equipped with the corner reflectors. The software also allows us to calculate the LRS parameters, which, according to GOST R 50723-94, ensure eye-safety in the spectral range of 0.81 ... 1.5 microns in case of accidental irradiation.The energy of the intensifier pulse and the divergence of a sensing beam determine the LRS range and the distance of eye-safe observation, which are the most important indicators to characterize the onboard LRS capabilities. To ensure the best LRS range and safety characteristics simultaneously, it is necessary to solve the problem of multi-criteria optimization.The paper solves the problem of multi-criteria optimization for the maximum LRS range and the eye-safe observation distance by Pareto sets the use of which allows us to avoid uncertainty in choosing a significance of criteria.The results obtained show that the proposed methods can be successfully applied in designing onboard LRS of spacecraft.

Multiobjective Monotonicity Analysis: Pareto Set Dependency and Tradeoffs Causality in Configuration Design

Multiobjective design optimization studies typically derive Pareto sets or use a scalar substitute function to capture design trade-offs, leaving it up to the designer's intuition to use this information for design refinements and decision making. Understanding the causality of trade-offs more deeply, beyond simple post-optimality parametric studies, would be particularly valuable in configuration design problems to guide configuration redesign. This paper presents the method of Multiobjective Monotonicity Analysis to identify root causes for the existence of trade-offs and the particular shape of Pareto sets. This analysis process involves reducing optimization models through constraint activity identification to a point where dependencies specific to the Pareto set and the constraints that cause them are revealed. The insights gained can then be used to target configuration design changes. We demonstrate the proposed approach in the preliminary design of a medical device for oral drug delivery

A Multi-Objective Hybrid Genetic Algorithm for Sizing and Siting of Renewable Distributed Generation

Renewable generation has been addressed in several aspects but it still represents a new paradigm for the expansion of the electricity supply. This paper aims to propose a new model for the sizing and siting problem of distributed generation (DG), based on renewable sources and considering three main aspects: technical, from the distribution utility viewpoint; economical, from the DG owner’s viewpoint, and environmental, from a sustainability perspective. A multi-objective Genetic Algorithm and the Maximin metric are implemented to obtain optimal Pareto sets; also, three decision criteria, considering the concept of preference, are applied to select a final solution from Pareto sets. Case-studies are carried out in medium voltage systems: the 69-bus distribution test system, known from literature, and a 918-bus Brazilian distribution system. Diversity of alternatives in the obtained Pareto sets testify algorithm effectiveness in searching for solutions to the distributed generation sizing and siting problem, in order to ensure power loss reductions, investment return, and environmental benefits. The proposed methodology contributes to the discussions and perspectives among electricity utilities, DG owners, society, and regulators regarding planning and decision making tools.

Multi-criteria Optimization for Parameterization of SAFT-type Equations of State for Water

Finding appropriate parameter sets for a given equation of state (EoS) to describe different properties of a certain substance is an optimization problem with conflicting objectives. Such problem is commonly addressed by single-criteria optimization in which the different objectives are lumped into a single goal function. We show how multi-criteria optimization (MCO) can be beneficially used for parameterizing equations of state. The Pareto set, which comprises a set of optimal solutions of the MCO problem, is determined. As an example, the perturbed-chain statistical associating fluid theory (PC-SAFT) EoS is used and applied to the description of the thermodynamic properties of water, focusing on saturated liquid density and vapor pressure. Different options to describe the molecular nature of water by the PC-SAFT EoS are studied and for all variants, the Pareto sets are determined, enabling a comprehensive assessment. When compared to literature models, Pareto optimization yields improved models.

Generating minimal Pareto sets in multi-objective topology optimisation: an application to the wing box structural layout

Multi-objective topology optimisation problems are often tackled by compromising the cost functions according to the designer’s knowledge. Such an approach however has clear limitations and usually requires information which especially at the preliminary design stage could be unavailable. This paper proposes an alternative multi-objective approach for the generation of minimal Pareto sets in combination with density-based topology optimisation. Optimised solutions are generated integrating a recently revised method for a posteriori articulation of preferences with the Method of Moving Asymptotes. The methodology is first tested on an academic two-dimensional structure and eventually employed to optimise a full-scale aerospace structure with the support of the commercial software Altair OptiStructⓇ. For the academic benchmark, the optimised layouts with respect to static and dynamic objectives are visualised on the Pareto frontier and reported with the corresponding density distribution. Results show a progressive and consistent transition between the two extreme single-objective layouts and confirm that the minimum number of evaluations was required to fill the smart Pareto front. The multi-objective strategy is then coupled with Altair OptiStruct and used to optimise a full-scale wing box, with the clear purpose to fill a gap in multi-objective topology optimisation applied to the wing primary structure. The proposed methodology proved that it can generate efficiently non-dominated optimised configurations, at a computational cost that is mainly driven by the model complexity. This strategy is particularly indicated for the preliminary design phase, as it releases the designer from the burden to assign preferences. Furthermore, the ease of integration into a commercial design tool makes it available for industrial applications.

Impact of Social Welfare Metrics on Energy Allocation in Multi-Objective Optimization

Resource allocation problems are at the core of the smart grid where energy supply and demand must match. Multi-objective optimization can be applied in such cases to find the optimal allocation of energy resources among consumers considering energy domain factors such as variable and intermittent production, market prices, or demand response events. In this regard, this paper considers consumer energy demand and system-wide energy constraints to be individual objectives and optimization variables to be the allocation of energy over time to each of the consumers. This paper considers a case in which multi-objective optimization is used to generate Pareto sets of solutions containing possible allocations for multiple energy intensive consumers constituted by commercial greenhouse growers. We consider the problem of selecting a final solution from these Pareto sets, one of maximizing the social welfare between objectives. Social welfare is a set of metrics often applied to multi-agent systems to evaluate the overall system performance. We introduce and apply social welfare ordering using different social welfare metrics to select solutions from these sets to investigate the impact of the type of social welfare metric on the optimization outcome. The results of our experiments indicate how different social welfare metrics affect the optimization outcome and how that translates to general resource allocation strategies.

Propeller Selection by Means of Pareto-Optimal Sets Applied to Flight Performance

Selection process of the propeller for short take-off and landing (STOL) category aircraft is described. The aim is to achieve the highest possible performance with fixed propeller, i.e., high maximal horizontal and cruise speed, short take-off and high rate of climb. These requirements are contradictory and so Pareto sets were used in order to find the optimal propeller. The method is applied to a family of geometrically similar propellers that are suitable for 73.5 kW (100 hp) piston engine designed for ultralight category aircraft with maximal take-off weight of 472.5 kg. The propellers have from two to eight blades, blade angle settings from 15° to 40° and diameter from 1.1 m to 2.65 m. Pareto frontier is designed for each pair of flight conditions, and the optimal propeller is selected according to these results. For comparison, the optimal propeller selection from the propeller family by means of a standard single-optimal process based on the speed power coefficient cs is also used. Use of Pareto sets leads to considerable performance increase for the set of contradictory requirements. Therefore, high performance for a low price for the given aircraft can be achieved. The described method can be used for propeller optimization in similar cases.