Two-layer Problem Research Articles

Coordinated optimization of configuration and operation of a photovoltaic integrated building cooling system with electricity and ice storages under source-load uncertainties

Solar photovoltaic integration into buildings provides an effective and attractive method to decrease fossil energy consumption and reduce greenhouse gases emission. This study proposes a flexible photovoltaic integrated building cooling system with electricity and ice storages to address the challenges posed by the instability of solar energy and the integration and coordination of multiple components. Uncertainties in solar irradiance, ambient temperature, and cooling load are characterized using a scenario analysis method that combines Latin Hypercube Sampling and the K-Means++ algorithm. Then, aiming to achieve the minimal total cost, including investment, operational, and CO2 emission costs, a two-layer stochastic optimization model is developed to simultaneously determine the optimal capacities and operational strategies for each device. Genetic algorithm and mixed integer linear programming are, respectively, used to solve the two-layer optimization problem. The comparisons between optimum schemes with and without CO2 emission cost demonstrates that when the base chiller’s capacities are 1179 kW and 1081 kW in cases 1 and 2 respectively, it can independently meet 72.37 % and 61.27 % of the cooling load demand throughout the cooling season. In addition, the optimal capacity of photovoltaics, considering CO2 emission, increases by 109.7 %, and its penetration rate reaches 18.3 %, which is 9.7 % higher than the optimal scheme not considering CO2 emission. However, the annualized investment cost increases by 52.3 %. The developed methods provide effective tools for the system design and operation management of solar energy integrated building cooling system.

Heat transfer in shear flow over a still nanofluid: A direct integration approach

Heat transfer in a two-layer fluid system, including shear-driven viscous fluid in the upper layer and still nanofluid in the lower layer, is investigated in this work. Following single phase model for nanofluid, three different types of nanofluids are considered. Different from existing literatures on two-layer fluid flow problem, this work introduces the heat transfer of shear-driven viscous fluid over a still nanofluid which makes this investigation new. The main equations which are partial in nature are reduced to a set of coupled nonlinear ordinary differential equation (ODE) by employing suitable similarity transformations. These ODEs together with the coupled interfacial boundary conditions are supplied to MATLAB software to get the solution numerically. Comparing the results obtained in this study with the previous authoritative research results, the accuracy and correctness of the present research methodology are ensured. The results show that the temperature of the upper fluid and the lower fluid are controlled by the thermophysical properties of different types of nanofluids. Also, opposite behavior of temperature distribution for the upper and the lower fluid are observed.

Hierarchically Distributed Charge Control of Plug-In Hybrid Electric Vehicles in a Future Smart Grid

Plug-in hybrid electric vehicles (PHEVs) are becoming increasingly widespread due to their environmental benefits. However, PHEV penetration can overload distribution systems and increase operational costs. It is a major challenge to find an economically optimal solution under the condition of flattening load demand for systems. To this end, we formulate this problem as a two-layer optimization problem, and propose a hierarchical algorithm to solve it. For the upper layer, we flatten the load demand curve by using the water-filling principle. For the lower layer, we minimize the total cost for all consumers through a consensus-like iterative method in a distributed manner. Technical constraints caused by consumer demand and power limitations are both taken into account. In addition, a moving horizon approach is used to handle the random arrival of PHEVs and the inaccuracy of the forecast base demand. This paper focuses on distributed solutions under a time-varying switching topology so that all PHEV chargers conduct local computation and merely communicate with their neighbors, which is substantially different from the existing works. The advantages of our algorithm include a reduction in computational burden and high adaptability, which clearly has its own significance for the future smart grid. Finally, we demonstrate the advantages of the proposed algorithm in both theory and simulation.

Heat and concentration analysis of two-layered muco-ciliary third grade fluid flow in human airways

Understanding the mechanisms involved in the movement and clearance of mucus within the human airways is important from a physiological perspective. A mathematical model of muco-ciliary two-layered fluid flow in a finite two-dimensional channel is proposed. Due to the presence of both the airway ciliary layer (ACL) and the periciliary liquid layer (PCL) in airways epithelial cells, the two-layered model is adopted. The third grade fluid models is used to characterize the viscoelastic nature of mucus secreted in the airways. The mathematical modeling of two-layer flow problem is simplified by using long wavelength and small Reynolds number approximation. A formulated set of partial differential equations (PDEs) is solved for series-form solutions of velocity, temperature, concentration, and pressure gradient by using the Adomian decomposition method (ADM). The analysis delineated that with an increase in pressure gradient at airways entrance ξ the velocity and temperature increases while concentration decreases. Deborah numbers impact ACL and PCL velocities differently, with De(A) influencing flow direction and De(P) causing fluid to flow faster in the forward direction. It also emphasizes the significance of the rate of thermal diffusion, viscous dissipation, and relaxation time. The results showed that the suggested two-layered muco-ciliary model provides a better description of mucus transport in the human airways. The pressure gradient at the airways entrance has a significant impact on mucus transport through the airways.

Two-Layer Optimization Strategy of Electric Vehicle and Air Conditioning Load Considering the Benefit of Peak-to-Valley Smoothing

To satisfy the interests of multiple agents and those of comprehensive indicators such as peak-to-valley differences and load fluctuations occurring on the network side, this paper presents a flexible load demand-side response optimization method that considers the benefits of peak-to-valley smoothing. First, load aggregation modelling of air conditioning and electric vehicles was conducted, and the complementarity of the power consumption behavior of different types of flexible loads was used to improve the responsiveness of the load aggregator. Second, considering demand-side responses and taking into account the interests of both supply and demand, the load fluctuation and peak-to-valley difference on the network side are reduced, and a flexible load double-layer optimization model incorporating the peak-to-valley smoothing benefit is established. Finally, the effectiveness of the proposed optimization model is verified by using the KKT condition and the big M method to evaluate this two-layer optimization problem as a single-layer optimization problem. Comparative examples show that the proposed two-layer optimization method can take advantage of the complementarity of air conditioning and electric vehicles to improve the income of load aggregators. Moreover, the proposed method can effectively reduce the load peak-to-valley difference and load fluctuation of the distribution network by introducing the peak-to-valley smoothing benefit model.

An efficient branch and bound reduction algorithm for globally solving linear fractional programming problems

This paper investigates a class of linear fractional programs (LFP) with linear constraints, which are widely applied in transportation, economic investment and so on. We start with transforming LFP into its equivalent two-layer problem. Subsequently, we introduce a novel linear relaxation approach and integrate it within the branch and bound framework, and a new global optimization algorithm is presented in cooperation with a region deleting rule. Additionally, we discuss the convergence and complexity of this algorithm. Preliminary numerical results validate the practicality and effectiveness of our proposed method.

A new branch and bound method for solving linear multiplicative programming problems

ABSTRACT This paper studies a class of linear multiplicative problems (LMP). To find a global optimal solution of problem (LMP), we first convert problem (LMP) into an equivalent problem (EP) via auxiliary variables, then problem (EP) is expressed as a two-layer problem (EP1). On the basis of problems (EP) and (EP1), a new bounding technique which integrates two linear relaxation processes is proposed to obtain a valid lower bound for the optimal value of (LMP). Combining the bounding technique with the bisection branching rule, a novel branch and bound algorithm is designed. Also, we establish the global convergence of the proposed algorithm and estimate its computational complexity. Preliminary numerical results verify the feasibility and effectiveness of the presented method.

The Solution and Numerical Verification of the Two-Layer Spherical Symmetric Heat Conduction Problem

The Solution and Numerical Verification of the Two-Layer Spherical Symmetric Heat Conduction Problem

Two-layer intelligent deployment of capsule airports and unmanned aerial vehicles for providing emergency communication services

The utilization of Unmanned Aerial Vehicles (UAVs) as base stations for emergency communication services has garnered significant attention due to their lightness and agility. To increase the capacity and coverage of UAVs, the Capsule Airport (CA) is developed, which serves as a recharging and retrieval station for UAVs. Meanwhile, deploying CAs and UAVs in appropriate positions is crucial for ensuring high-quality and efficient service provision. To address this challenge, we propose the Two-Layer Maximum Deployment Problem for Capsule Airports and Unmanned Aerial Vehicles (2L-MCDP-C&U). The objective of the 2L-MCDP-C&U is to maximize the number of served users by determining the ground locations for opening a given number of CAs and deploying their UAVs in 3D space, while considering the connectivity of UAV-to-UAV, UAV-to-CA, and UAV-to-user. An improved variable neighborhood search algorithm is designed based on the k-means (VNS-K) to solve the 2L-MCDP-C&U. To further validate its efficacy, we conduct experiments on random instances of various sizes and a practical case study of Zhulin town in China. Our work paves the way for more efficient and effective emergency communication services using CAs and UAVs.

A micro-economic model of the market uptake of truck platooning

Truck platooning is a technology allowing trucks to travel in convoy formation using wireless communications and advanced driver assistance systems. This technology is expected to increase road safety and capacity, and to decrease fuel consumption and GHG emissions; it comes with apparently important financial benefits and positive externalities. However, forecasting the market uptake of platooning is a complex economic issue, requiring a dedicated methodology.From a micro-economic standpoint, several features of truck platooning are important. First, forming a platoon implies a coordination cost. Second, platooning requires trucks with specific and costly equipment. That makes platooning a two-layer problem. Third, the decision of one carrier depends on those of other carriers: truck platooning, as a market, is characterized with network externalities. Fourth, road freight transportation is a heterogeneous system: different vehicles follow different operation patterns.This paper submits a micro-economic model of the uptake of platooning which accounts for all of the above points. First, a conditional sub-model of platoon formation is designed, where two trucks decide whether to form a platoon or not based on the net monetary benefits of doing so. Then, platoon formation is modeled in a simplified, single road context, as a Markov chain. At that stage, the share of platoonable trucks entering the market is obtained with a numerical, dynamic model. Upgrading conventional trucks to become compatible with platooning is assumed impossible.The paper concludes that due to the positive feedback loop of network externalities, market uptake is very sensitive to the economic assumptions. In addition, due to the equipment and coordination costs induced by platooning, the overall financial benefits for carriers are much lower than what they would initially appear to be; third, energy savings can be significant on the long run if the technology spreads widely.

(Invited) Multiscale Diffusion-Reaction Heat Transfer Analysis for Predicting Thermal Runaway in Li-Ion Cells and Battery Packs

Thermal runaway in Li-ion cells and battery packs remains a topic of much importance for ensuring the safety of electrochemical energy conversion and storage systems. Thermal runaway also indirectly affects performance, as conservative overdesign to reduce the risk of thermal runaway affects system-level performance metrics such as energy storage density. Given the considerable challenges in experimental investigation of thermal runaway, theoretical models to predict thermal runaway characteristics of a cell or battery pack are critically needed. Such models can help guide the design of experiments, and ensure that practical systems are reasonably safe without being needlessly overdesigned.This talk will summarize ongoing work on theoretical analysis of multilayer diffusion-reaction heat transfer problems for predicting thermal runaway in Li-ion cells and battery packs. Following a linearization of heat generation terms, the governing energy conservation equation is solved in a multilayer geometry representative of a Li-ion cell comprising multiple electrode and separator layers, or of a battery pack containing several cells. It is mathematically shown that under certain conditions, this problem may admit a finite number of imaginary eigenvalues, which are shown to cause thermal runaway. It is shown that the occurrence of imaginary eigenvalues is governed by a delicate balance between heat generation, thermal conduction within the multilayer body and heat removal from the boundaries, based on which, an explicit threshold condition for thermal runaway is derived. This threshold condition is interpreted in the context of parameter values relevant to Li-ion cells. For example, it is shown that boundary cooling is severely limited in its role to prevent thermal runaway, whereas improving thermal transport within the cell is likely to be a lot more effective. This theoretical model is also extended to a two-layer problem comprising a finite layer adjoined by a semi-infinite body that may model immersion cooling of a Li-ion cell or battery pack. It is shown that while this diffusion-reaction problem is, in principle, unconditionally unstable, the finite time period of any discharge process may allow the temperature field to still remain within a safe envelope, if designed appropriately. Based on this mathematical model, scenarios related to immersion cooling of pouch cells are investigated.The theoretical work described in this talk is broadly relevant to several diffusion-reaction systems. In the particular context of Li-ion cells, these results may form the foundation of techniques to proactively predict and prevent thermal runaway in Li-ion cells and battery packs.

Opportunistic CR-NOMA Transmissions for Zero-Energy Devices: A DRL-Driven Optimization Strategy

To efficiently accommodate RF energy-harvesting (EH) capable device in a wireless network with prescheduled devices, this letter designs the deep reinforcement learning (DRL)-driven energy-efficient transmission strategy. The transmission strategy handles the EH-device uplink transmissions opportunistically using cognitive radio-inspired non-orthogonal multiple access (CR-NOMA) scheme while maximizing energy efficiency (EE). In this respect, firstly, we formulate the EE optimization problem of the EH-device while considering its RF circuit power consumption. Secondly, we divide the original, non-convex problem into a two-layer optimization problem, and solve it sequentially as i) we theoretically derive the optimal transmit power and time-sharing coefficient parameters from the first layer, and ii) using the derived parameters in the second layer, we solve the one-dimensional continuous space optimization problem through a DRL technique, recognized as a combined experience replay deep deterministic policy gradient (CER-DDPG). Finally, the numerical results show that, under different operational scenarios, the proposed approach outperforms benchmark DDPG and Stochastic algorithms in terms of EE.

Fourier spectral theory of pulsed photothermal radiometry, signal analysis, and parametric measurements in two-layered media

A theoretical model of pulsed photothermal radiometry based on conduction-radiation theory is introduced for a two-layered medium with a first layer having optical and thermal properties different from those of the semi-infinite substrate. This geometry closely represents the optical and thermal properties of biotissues, a major intended application. The theory derives the spatial distribution of the frequency spectrum of the pulsed photothermal signal from the composite two-layer boundary-value problem and matches the spectral frequency domain results to the measured photothermal transients through an efficient inverse Fourier transformation algorithm, which involves the optical, thermal, and geometric parameters of the experimental system. This approach avoids the complicated and computationally expensive analytical Laplace transform approach usually adopted in similar studies and yields a complete conduction–radiation description of photothermal signals without simplifying, yet restrictive, approximations encountered in the literature. Numerical and experimental tests of the model using intralipid solution as layer 1 and semi-infinite solid samples such black rubber and anodized aluminum as layer 2 of the medium are described. The radiation heat transfer coefficients from the air–intralipid and intralipid–solid interfaces were introduced to complement the conductive blackbody-radiated infrared signal component at the detecting camera. The best-fitted parameters and heat transfer coefficients are compared to theoretical and experimental data, and the results of these tests were found to be consistent with the theoretical model.

Joint Offloading Scheduling and Resource Allocation in Vehicular Edge Computing: A Two Layer Solution

Vehicular Edge Computing (VEC) is a promising paradigm for autonomous driving. It can reduce delay and energy consumption of tasks. The problem of joint task offloading scheduling and resource allocation in VEC is a challenge issue. In this paper, we investigate the problem of joint task offloading, task scheduling, and resource allocation in VEC, and the fast changing channel between a vehicle and an edge server. A target problem of joint considering task offloading scheduling, resource allocation and time-varying channel in VEC is formulated. The goal is to minimize the delay and energy consumption of tasks to guarantee the Quality of Service (QoS) of VEC. Constraints on the completion time, the energy consumption, and the computing capability are considered for each task. The resulting mixed integer optimization problem is decomposed into a two-layer optimization problem. In the upper layer, we use a Deep Q-Network (DQN) to solve the task offloading scheduling problem. In the lower level, the CPU frequency allocation is determined using the Gradient Descent (GD) method. Numerical results illustrate that the proposed algorithm can minimize the delay and energy consumption of VEC for different network parameter settings.

Two-layer spherical rubber-metal joints and problems of their calculation features

Introduction. The article analyses the methods for calculating the characteristics of spherical rubber-metal joints. The authors consider a verified calculation model for determining the stiffness characteristics of spherical rubber-metal joints, both single-layer and double-layer.Materials and methods. The researchers used computer modelling and the finite element method to determine the features of the spherical rubber-metal joints. The possibility of neglecting the deformation of the metal parts of the joint for the modelling purposes was substantiated, which enabled to simplify the calculation model. Moreover, the authors proposed the method for measuring the effect of the elastic layer precompression and determined the values of radial stiffness for single-layer and double-layer rubber-metal joints at different hardness of materials, which coincided with the experimental results. Results. As a result, the authors revealed that with a decrease in the thickness of the rubber layer by assessing the rigidity of the joint, its features were significantly affected by the accuracy of setting the Poisson's ratio. A satisfactory convergence of the radial stiffness of the joint found through the modelling and experimental studies was achieved at a Poisson's ratio equal to 0.499999 (the discrepancy is about 5 %, which is less than the technological spread of rigidity during manufacture). The authors also found out that the rigidity of two-layer rubber-metal joints, similar in size and compensatory capacity to those used in the design of domestic locomotives, should be 6.3 times higher than for existing single-layer ones. Such features would reduce the deformation of rubber by loads exsposion during operation and thereby would solve the problems with the reliability of traction motors suspension units.Discussion and conclusion. Due to the fact that the shape of the free surface of the side faces of two-layer rubber-metal joints before assembly should have small radii of the recesses curvature, further research is needed to select the rational geometry of the free surface of the side faces. The researchers got a utility model patent for the proposed design and manufacturing technology of two-layer rubber-metal joints.

Derivation of multiple but finite number of imaginary eigenvalues for a two-layer diffusion-reaction problem

Diffusion-reaction problems occur commonly in heat and mass transfer analysis. In the particular case of a multilayer body under certain conditions, such problems are known to result in imaginary eigenvalues that indicate divergence in the temperature/concentration field at large times. For small values of the reaction coefficient, past work has derived conditions in which an imaginary eigenvalue may exist. This work generalizes this result by showing that more than one, but not infinite imaginary eigenvalues may exist under certain conditions in a one-dimensional two-layer diffusion-reaction problem. A systematic investigation of the eigenequation in the imaginary space is carried out in order to derive a closed form expression for the number of imaginary eigenvalues for any given problem. It is shown that, for other parameters being fixed, the larger the values of the reaction coefficients, the greater is the number of imaginary eigenvalues. However, unlike real eigenvalues, it is shown that the number of imaginary eigenvalues is never infinite. While presented for a two-layer body, similar techniques may be applied for a more general multilayer body, although the derivation of explicit equations may be more challenging. Besides its theoretical importance, accounting for imaginary eigenvalues in the problem discussed here is clearly important to ensure accuracy of the mathematical model. The present work contributes towards this by systematically identifying the number and nature of imaginary eigenvalues that occur in multilayer diffusion-reaction heat and mass transfer problems.

Beyond the Quadratic Approximation: The Multiscale Structure of Neural Network Loss Landscapes

A quadratic approximation of neural network loss landscapes has been extensively used to study the optimization process of these networks. Though, it usually holds in a very small neighborhood of the minimum, it cannot explain many phenomena observed during the optimization process. In this work, we study the structure of neural network loss functions and its implication on optimization in a region beyond the reach of a good quadratic approximation. Numerically, we observe that neural network loss functions possesses a multiscale structure, manifested in two ways: (1) in a neighborhood of minima, the loss mixes a continuum of scales and grows subquadratically, and (2) in a larger region, the loss shows several separate scales clearly. Using the subquadratic growth, we are able to explain the Edge of Stability phenomenon [5] observed for the gradient descent (GD) method. Using the separate scales, we explain the working mechanism of learning rate decay by simple examples. Finally, we study the origin of the multiscale structure and propose that the non-convexity of the models and the non-uniformity of training data is one of the causes. By constructing a two-layer neural network problem we show that training data with different magnitudes give rise to different scales of the loss function, producing subquadratic growth and multiple separate scales.

Evaluation of accuracy and convergence of numerical coupling approaches for poroelasticity benchmark problems

Accurate modeling of subsurface flow and transport processes is vital as the prevalence of subsurface activities such as carbon sequestration, geothermal recovery, and nuclear waste disposal increases. Computational modeling of these problems leverages poroelasticity theory, which describes coupled fluid flow and mechanical deformation. Although fully coupled monolithic schemes are accurate for coupled problems, they can demand significant computational resources for large problems. In this work, a fixed stress scheme is implemented into the Sandia Sierra Multiphysics toolkit. Two implementation methods, along with the fully coupled method, are verified with one-dimensional (1D) Terzaghi, 2D Mandel, and 3D Cryer sphere benchmark problems. The impact of a range of material parameters and convergence tolerances on numerical accuracy and efficiency was evaluated. Overall the fixed stress schemes achieved acceptable numerical accuracy and efficiency compared to the fully coupled scheme. However, the accuracy of the fixed stress scheme tends to decrease with low permeable cases, requiring the finer tolerance to achieve a desired numerical accuracy. For the fully coupled scheme, high numerical accuracy was observed in most of cases except a low permeability case where an order of magnitude finer tolerance was required for accurate results. Finally, a two-layer Terzaghi problem and an injection–production well system were used to demonstrate the applicability of findings from the benchmark problems for more realistic conditions over a range of permeability. Simulation results suggest that the fixed stress scheme provides accurate solutions for all cases considered with the proper adjustment of the tolerance. This work clearly demonstrates the robustness of the fixed stress scheme for coupled poroelastic problems, while a cautious selection of numerical tolerance may be required under certain conditions with low permeable materials.

Minimum Dinamik İletim Hat Derecelendirmesi Kullanarak Güç Sistemin Güvenilirliğini Artırma

Due to increase in electricity demand and renewable resources penetration, power transmission infrastructure is utilized close to its technical limits. Dynamic line rating is one of the new practices in power transmission management by which existing transmission lines can be more efficiently utilized. In the literature, dynamic rating is usually applied to all lines of the power system which is not desirable as it is risky to simultaneously monitor a high number of transmission lines. In this paper we propose to apply dynamic rating on few and most suitable lines to effectively increase the system N–K reliability. We develop a robust min-max-min three-layer optimization model to find minimum number of lines for dynamic rating. We use duality theory and convert the three-layer problem into a two-layer min-max problem and then we develop a benders decomposition framework to solve the two-layer problem. We use two test power systems to demonstrate our solution approach and analyze the results.

A multi-product multi-layer urban freight distribution problem solved using a hybrid metaheuristic procedure

The pick-up and delivery routing problem has received special attention thanks to its application to urban freight distribution processes. However, due to the multiple levels involved in those processes, modeling and analyzing urban distribution networks in urban contexts are complex tasks. As a result, efficient and robust solution methods should be proposed according to the dynamic and uncertain conditions that characterize this type of problems. This article presents a new formulation for the pick-up and delivery problem in a logistics distribution network composed of 3 levels: n: 1: m (n suppliers, 1 urban consolidation center, and m customers). In addition, an algorithm based on GRASP heuristic and 2-opt algorithm was implemented here to find solutions to problem, which were compared with the results of the same algorithm for a two-layer vehicle routing problem in several instances. Thus, the proposed procedure achieved a 22% improvement over such algorithm.