Optimization and Engineering最新文献

The circumferential nonuniform clearance of the rotor blade tip significantly impacts aerodynamic stability. Therefore, in the assembly process, the clearance distribution of rotor blade tips at all levels should be as uniform as possible. The aim of this paper is to minimize the non-uniformity of the clearance distribution by optimizing the assembly process parameters of the rotor–stator assembly. The prediction model for clearance non-uniformity was first established using spatial geometric transformation. Then, the influence of factors on clearance non-uniformity was quantified using the Morris method. The normalized sensitivities of the main factors were 0.1242 for the runouts of the rotor blade tips, 0.0998 for the runouts of the runners of the casing, and 0.7759 for the eccentricity of the rear pivot. Therefore, the eccentricity of the rear pivot was the main factor. Furthermore, a process optimization strategy was established based on the sensitivity analysis results. The process optimization of the rotor–stator assembly was completed by considering the rear pivot, rotor blade tips, and casing runners as optimization objects. The test results demonstrated that, by optimizing the assembly state of the rotor–stator assembly based on the optimal process parameters, the overall clearance non-uniformity was reduced by an average of about 85.06% compared to the initial clearance non-uniformity. Specifically, the optimization of the rear pivot and the rotor blade tips reduced the clearance non-uniformity by about 83.3% and 11.65%, respectively, compared to clearance non-uniformity before their respective optimizations. Despite efforts to optimize the runners of the casing, clearance non-uniformity remained largely unchanged.

This article presents a mathematical analysis of the effects of shortages in an integrated inventory model that considers energy utilization in manufacturing and warehousing. A Non-Linear Programming model is proposed for the Energy-Economic Production Quantity with Shortages problem. A solution procedure is proposed to minimize total cost by analyzing different shortage policies (full backorder, partial backorder, and full lost sale). Numerical examples illustrate the significance of integrating energy consumption components in inventory modeling, particularly in the context of rising energy prices. Accepting shortages reduces average inventory levels, decreases warehousing energy costs and achieves overall cost minimization. Full backorder policy do not reduce energy consumption in production, highlighting partial backorder policy as the optimal choice from both economic and environmental perspectives. Sensitivity analysis highlights the significant influence of model parameters on total costs and energy components. The impact of energy unit cost is particularly noteworthy given increasing energy demand and supply disruptions. These findings underscore the importance of considering energy consumption and associated costs in supply chain operations, emphasizing the study’s role in addressing these challenges.

Energy communities (ECs) are a promising solution to integrate renewable local production with buildings’ systems and services. To exploit renewable energy sources, ECs should be carefully designed, identifying an appropriate mix of prosumers and consumers. In this research, the electrical energy loads of eight dwellings have been monitored for a year. Then, each dwelling is evaluated either as a mere consumer, maintaining its monitored electrical consumption profile as it is, or as a prosumer, thus simulating a photovoltaic system on the roof, sized to provide a given fraction of its energy needs and sharing the surplus with other EC participants. Genetic optimization is employed to seek the optimal mix of consumers and prosumers within the community to optimize the shared energy within the EC. Results show that dwellings with night-time energy requirements are included as prosumers to maximize photovoltaic power sharing during daylight time, and dwellings with regular daily loads are included as consumers.

For nuclear power plants to remain competitive in energy markets increasingly penetrated by variable renewable energy sources, designs that allow flexible operation or incorporate additional revenue streams should be considered. This study models a nuclear reactor decoupled from a supercritical steam Rankine cycle through a two-tank thermal storage system using molten salt as the heat transfer fluid. The model allows steam extraction from the power cycle’s low-pressure turbine to provide thermal energy to a thermal desalination facility. The desalination facility likewise includes a two-tank thermal storage system. This study aims to determine the conditions under which thermal storage integrated with nuclear-desalination systems increases economic competitiveness compared to standalone nuclear power plants. We built a mixed-integer linear program that determines optimal dispatch schedules and subsystem sizing of the energy storage components given current price parameters in the literature. We then performed sensitivity analyses to turbine size, thermal storage system cost, and desalinated water price. We found that multi-effect distillation increased the revenue generation of the system beyond standalone conditions except when the price of desalinated water decreased beyond 30% of its nominal 2021 price. We also found that when the turbine is oversized, high-temperature and low-temperature thermal storage is dispatched in a complementary fashion that allows for load-following and continuous distillate production.

The Stackelberg prediction game (SPG) is an effective model that formulates the strategic interaction between the learner and data generator in a competition situation in which the learner controls the predictive model while the data generator reacts on the learner’s move. Recently, SPG has received increasing interests, especially, in the binary class Stackelberg prediction game with least squares loss (SPG-LS) as it was shown in Wang et al. (in: International conference on machine learning, 2022) that an (epsilon ) optimal solution can be computed in (O(N/sqrt{epsilon })) flops where N is the number of non-zeros in the data matrix. Concerning that many practical problems involve multi-class situation, in this paper, we extend the current SPG-LS model as well as its computational approach to the multi-class case. In particular, by relying on a special nonlinear transformation, we show that the multi-class SPG-LS can be equivalently transformed to a special unbalanced Procrustes problem, and we propose an efficient numerical approach based on the unbalanced Procrustes problem to approximately tackle the multi-class SPG-LS. We particularly introduce two methods: the self-consistent-field (SCF) iteration and the Riemannian trust-region method (RTR), and conduct on numerical experiments to demonstrate the performance of the multi-class SPG-LS on synthetic and real data. The existence of the Stackelberg equilibrium of SPG-LS is also discussed.

The aerodynamic performance characteristics of an unmanned aerial vehicle airfoil and wing are optimized in the low Reynolds number regime using a variable-fidelity Multi-Level Hierarchical Kriging (MHK) surrogate modeling framework. This methodology employs aerodynamic data obtained from computational grids of varying grid resolution. This approach results in an efficient framework for optimizing expensive aerodynamic functions with the aid of lower fidelity data. The MHK-based optimization framework is first applied to enhance the aerodynamic properties of an Eppler E214 airfoil. The endurance factor of the airfoil is improved by 28%. Next, the aerodynamic characteristics of a small unmanned aerial vehicle wing is optimized. The endurance factor of the optimal wing is improved by 12.5%, with a substantial 45 drag count reduction. The optimal wing is of a swept wing design with a leading edge sweep of 13.6°. The evolution of a swept wing as the optimal wing design is an interesting outcome of the present study. Though the effect of wing sweep is well studied in high-subsonic and supersonic flows, its effect in the incompressible low Reynolds number regime is quantified in the present study. The wing sweep increases the suction on the outboard portion of the wing leading to a higher lift coefficient of the optimal wing. Further, the drag coefficient of the optimal wing is also reduced compared to the baseline wing. Much of this drag reduction comes from the reduction in the pressure drag component. Thus the wing sweep not only increases the lift coefficient, but also decreases the drag coefficient. This leads to a significant increase in the lift-to-drag ratio and the endurance factor of the optimal wing design. The present results demonstrate the optimization efficiency of the MHK modeling approach in the sensitive low Reynolds number regime.

This paper investigates an energy-efficient distributed blocking hybrid flowshop scheduling problem, constrained by the makespan upper-bound criterion. This problem is an extension of the distributed hybrid flowshop scheduling problem and closely resembles practical production scenarios, denoted as (DHF_{m} left| {block} right|varepsilon left( {{{TEC} mathord{left/ {vphantom {{TEC} {C_{{max}} }}} right. kern-nulldelimiterspace} {C_{{max}} }}} right)). Initially, we formulate the issue into a mixed integer linear programming (MILP) model that reflects its unique characteristics and leverage the Gurobi solver for validation purposes. Building upon this groundwork, we develop a self-regulating iterative greedy (SIG) algorithm, designed to autonomously fine-tune its strategies and parameters in response to the quality of solutions derived during iterative processes. Within the SIG, we design a double-layer destruction-reconstruction, accompanied by a self-regulating variable neighborhood descent strategy, to facilitate the exploration of diverse search spaces and augment the global search capability of the algorithm. To evaluate the performance of the proposed algorithm, we implement an extensive series of simulation experiments. Based on the experimental result, the average total energy consumption and relative percentage increase obtained by SIG are 2.12 and 82% better than the four comparison algorithms, respectively. These statistics underscore SIG’s superior performance in addressing (DHF_{m} left| {block} right|varepsilon left( {{{TEC} mathord{left/ {vphantom {{TEC} {C_{{max}} }}} right. kern-nulldelimiterspace} {C_{{max}} }}} right)) compared to the other algorithms, thus offering a novel reference for decision-makers.

Abstract

The shape of a hydrodynamic particle separator has been optimized using a parallelized and robust formulation of Bayesian optimization, with data from an unsteady Eulerian flow field coupled with Lagrangian particle tracking. The uncertainty due to the mesh, initial conditions, and stochastic dispersion in the Eulerian-Lagrangian simulations was minimized and quantified. This was then translated across to the error term in the Gaussian process model and the minimum probability of improvement infill criterion. An existing parallelization strategy was modified for the infill criterion and customized to prefer exploitation in the decision space. In addition, a new strategy was developed for hidden constraints using Voronoi penalization. In the approximate Pareto Front, an absolute improvement over the base design of (14%) in the underflow collection efficiency and (10%) in the total collection efficiency was achieved, which resulted in the filing of a patent.* The corresponding designs were attributed to the effective distribution of residence time between the trays via the removal of a vertical plume. The plume also reduced both efficiencies by creating a flow path in a direction that acted against effective settling. The concave down and offset tray shapes demonstrated the value of Bayesian optimization in producing useful and non-intuitive designs.

Graphic abstract

The determination of free technical capacities belongs to the core tasks of a gas network owner. Since gas loads are uncertain by nature, it makes sense to understand this as a probabilistic problem provided that stochastic modeling of available historical data is possible. Future clients, however, do not have a history or they do not behave in a random way, as is the case, for instance, in gas reservoir management. Therefore, capacity maximization becomes an optimization problem with uncertainty-related constraints which are partially of probabilistic and partially of robust (worst case) type. While previous attempts to solve this problem were devoted to models with static (time-independent) gas flow, we aim at considering here transient gas flow subordinate to the isothermal Euler equations. The basic challenge addressed in the manuscript is two-fold: first, a proper way of formulating probabilistic constraints in terms of the differential equations has to be provided. This will be realized on the basis of the so-called spherical-radial decomposition of Gaussian random vectors. Second, a suitable characterization of the worst-case load behaviour of future customers has to be found. It will be shown, that this is possible for quasi-static flow and can be transferred to the transient case. The complexity of the problem forces us to constrain ourselves in this first analysis to simple pipes or to a V-like structure of the network. Numerical solutions are presented and show that the differences between quasi-static and transient solutions are small, at least in these elementary examples.

We present a novel approach for solving time fractional Black-Scholes partial differential equations (tfBSPDEs) using Physics Informed Neural Network (PINN) approach. Traditional numerical methods are faced with challenges in solving fractional PDEs due to the non-locality and non-differentiability nature of fractional derivative operators. By leveraging the ideas of Riemann sums and the refinement of tagged partitions of the time domain, we show that fractional derivatives can directly be incorporated into the loss function when applying the PINN approach to solving tfBSPDEs. The approach allows for the simultaneous learning of the underlying process dynamics and the involved fractional derivative operator without a need for the use of numerical discretization of the fractional derivatives. Through some numerical experiments, we demonstrate that, the PINN approach is efficient, accurate and computationally inexpensive particularly when dealing with high frequency and noisy data. This work augments the understanding between advanced mathematical modeling and machine learning techniques, contributing to the body of knowlege on the advancement of accurate derivative pricing models.