Solution Method Research Articles

Enhanced resilience in urban stormwater management through model predictive control and optimal layout schemes under extreme rainfall events

Optimizing the layout of urban stormwater management systems is an effective method for mitigating the risk of urban flooding under extreme storms. However, traditional approaches that consider only economic costs or annual runoff control rates cannot dynamically respond to the uncertainties of extreme weather, making it difficult to completely avoid large accumulations of water and flooding in a short period. This study proposes an integrated method combining system layout optimization and Model Predictive Control(MPC)to enhance the system's resilience and effectiveness in flood control. An optimization framework was initially built to identify optimal system layouts, balancing annual average life cycle cost (AALCC) and resilience index. The MPC was then applied to the optimal layout selected using the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method, aiming to alleviate inundation cost-effectively. The adaptability of MPC to varying sets of control horizons and its efficacy in managing the hydrograph and flood dynamics of urban drainage system were examined. Conducted in Yubei, Chongqing, this study revealed patterns in optimal layout fronts among various extreme design rainfalls, showing that peak position rate and return period significantly influence system resilience. The contribution of MPC to the optimal system layout was particularly notable, resulting in improved instantaneous and overall flood mitigation. The application of MPC increased the resilience index by an average of 0.0485 and offered cost savings of 0.0514 million yuan in AALCC. Besides, our findings highlighted the importance of selecting an optimal set of control horizons for MPC, which could reduce maximum flood depth from 0.43m to 0.19m and decrease conduit peak flow by up to 14% at a flood-prone downstream location.

High-Temperature Resistance of Anchorage System for Carbon Fiber-Reinforced Polymer Composite Cable—A Review

Unidirectional carbon fiber-reinforced polymer (CFRP) may exhibit significant mechanical softening in the transverse direction at an elevated temperature. While significant transverse compressive stress exists on CFRP due to the clamping force from anchorage, a CFRP cable may exhibit anchorage failure when suffering an accidental fire disaster. The high-temperature resistance of a CFRP cable anchorage is critical, and clarifying the performance deterioration and failure mechanism of a CFRP cable anchorage system at elevated temperature is fundamental for clarifying its fire resistance. This paper reviews the current research status of the high-temperature resistance of CFRP cable anchorage systems from two aspects, including the high-temperature resistance of the comprising materials and the anchorage system. The reviews on the high-temperature properties of the comprising materials are summarized from two aspects. Firstly, the mechanical performance degradation of bonding epoxy resin at elevated temperatures and the effect of a filler on its mechanical–thermal properties are analyzed. Secondly, the mechanical performances of CFRP composites at elevated temperatures are summarized, with consideration of the stress state of the CFRP cable under the constraint of an anchorage device. The reviews on the high-temperature resistance of the anchorage system also include two aspects. Firstly, the temperature field solution method for the anchorage system is summarized and discussed. Secondly, the current research status of the anchorage performance at elevated temperatures is also summarized and discussed. Based on these reviews, the research shortage of the high-temperature resistance of CFRP cable anchorage systems is summarized, and further research is recommended.

Integrating topographic factors for effective urban sponge construction in mountainous regions: A case study

The construction of sponge cities in mountainous areas is crucial to achieving high-quality development in these regions. Owing to rugged terrain, significant changes in elevation, and uneven distribution of cities, the construction of sponge cities in mountainous areas faces challenges such as difficulties in clearing mountains and roads, high cost, and varying regional development requirements. However, there is currently limited research focusing on the impact of terrain on sponge city construction plans. In this study, we developed an optimal low impact development (LID) system layout method based on the annual runoff control rate. This study suggests implementing LID plans in stages to balance cost-effectiveness and enhance resilience. The optimized case1_100 scheme, which takes regional differences into account, can effectively achieve a runoff control coefficient of less than 0.25 in 98.86% of the area. Remarkably, this achievement comes at a significantly lower total cost of only 1.22 billion RMB compared to the unoptimized case2_100 scheme (which does not consider regional differences) with a cost of 3.03 billion RMB. Interestingly, the optimized case1_100 plan, selected using the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method, has an LID layout that is closely related to the surface terrain. Structural equation modeling analysis indicates that terrain affects land types, which in turn impacts the surface impermeability and runoff coefficients, ultimately influencing the corresponding LID deployment plan. The coefficients of relative elevation and slope on the final plan are determined as −0.13 and −0.77, respectively, with a high overall explanatory power of 0.84. This indicates that terrain characteristics have a significant impact on the spatial patterns and surface features of typical mountainous cities in China and the optimal LID strategy largely depends on the initial terrain conditions. This study provides valuable insights for optimizing LID construction in sponge cities, particularly in the context of new mountainous urban planning.

Innovative Strategies for Bio-Waste Collection in Major Cities during the COVID-19 Pandemic: A Comprehensive Model for Sustainable Cities—The City of Athens Experience

This paper introduces an innovative model for the organization and management of municipal bio-waste collection networks in major cities, particularly relevant in the context of the COVID-19 pandemic. Embracing circular economy principles and sustainable city practices, the proposed model addresses the urgent need for sustainable urban bio-waste management systems. Delving into the dynamic urban landscape, with a focus on the city of Athens, the study highlights the necessity of a robust decision-making methodology, the implementation of resilient processes, and the evaluation of their efficacy, especially during challenging times. The model centers on the effective collection, transportation, and monitoring of bio-waste, with a strategic aim to moderate environmental impacts, limit greenhouse gas emissions, and advance sustainable development goals. Utilizing the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method, this paper thoroughly examines critical components of an innovative bio-waste collection network, including infrastructure, technology, and human resources. By merging best practices from global urban centers and accounting for the unique characteristics of Athens, the model envisions a transition toward a circular economy. Notably, the proposed municipal bio-waste collection network at the source anticipates substantial contributions to achieving Sustainable Development Goals in major cities. The study concludes by showcasing the successful application of these methodologies in the Municipality of Athens, providing tangible evidence of their positive impact.

Donor-acceptor bulk-heterojunction sensitizer for efficient solid-state infrared-to-visible photon up-conversion.

Solid-state infrared-to-visible photon up-conversion is important for spectral-tailoring applications. However, existing up-conversion systems not only suffer from low efficiencies and a need for high excitation intensity, but also exhibit a limited selection of materials and complex fabrication processes. Herein, we propose a sensitizer with a bulk-heterojunction structure, comprising both an energy donor and an energy acceptor, for triplet-triplet annihilation up-conversion devices. The up-conversion occurs through charge separation at the donor-acceptor interface, followed by the formation of charge transfer state between the energy donor and annihilator following the spin statistics. The bulk-heterojunction sensitizer ensures efficient charge generation and low charge recombination. Hence, we achieve a highly efficient solid-state up-conversion device with 2.20% efficiency and low excitation intensity (10 mW cm-2) through a one-step solution method. We also demonstrate bright up-conversion devices on highly-flexible large-area substrates. This study introduces a simple and scalable platform strategy for fabricating efficient up-conversion devices.

Hazard Identification and Risk Assessment for Sustainable Shipyard Floating Dock Operations: An Integrated Spherical Fuzzy Analytical Hierarchy Process and Fuzzy CoCoSo Approach

Background: This study investigated the process of selecting sustainable safety protocols for floating dock operations in shipyards by identifying potential workplace risks in emergency situations. Thirteen occupational hazards for shipyard floating dock operations were identified through a literature review and expert discussions. Methods: We incorporated four risk elements (consequence: C, frequency: F, probability: P, and number of people at risk: NP) from the Fine–Kinney and Hazard Rating Number System (HRNS) approaches as the risk assessment criteria. We obtained the importance weights of the risk assessment criteria via the Spherical Fuzzy Analytical Hierarchy Process (SF-AHP) and extended the Combined Compromise Solution (CoCoSo) method within the fuzzy framework to prioritize occupational hazards. This study demonstrated the practicality and efficiency of the proposed emergency risk assessment model for shipyard floating dock operations through a case example of occupational risk assessment. Results: The analysis results show that H4 is the occupational hazard with the highest priority, with a score of 3.553. H4 represents the hazard associated with insufficient access to the entire pool area. The second and third most important hazards are the inability of cranes to move freely in and out of the berthing dock and the inability to dispatch emergency teams. These hazards, denoted H1 and H12, follow closely behind with scores of 3.391 and 3.344, respectively. H10 is deemed the least concerning hazard, with a score of 1.802. Conclusions: Professionals can handle complex and uncertain risk assessment data more flexibly using the proposed system, which excels in accurately organizing occupational hazards.

Evaluation of Age-Friendly Retrofits for Urban Communities in China Using a Social–Ecological–Technological Systems Framework

To address the problem of accurately evaluating age-friendly retrofit indicators in urban communities, this study constructs an evaluation model that takes into account user preferences and their interaction needs based on the social–ecological–technological systems (SETS) theory. The model aims to establish a set of precise community retrofit indicators, covering aspects such as public participation level, public ancillary facilities, green space layout, living environment building, health service support, and accessible design. By employing prioritization strategies, the model seeks to maximize resident satisfaction and promote harmonious coexistence between the community and the environment. Firstly, the retrofit evaluation indicators are formulated using the SETS theory. The entropy weight method (EWM) is then applied to determine the initial weights of these evaluation indicators, followed by the use of the Decision-Making Trial and Evaluation Laboratory (DEMATEL) method to analyze the interrelationships among the indicators. The Kano model is integrated to adjust the weights, reflecting their importance. The final weights of the indicators are determined through normalization. Based on this, the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method is employed to rank and analyze the importance of age-friendly retrofits in the community. Finally, six communities in Dalian, Liaoning Province, China, are selected as samples to evaluate and analyze the age-friendly retrofit indicators. Different methods are compared, and their advantages and disadvantages are ranked to validate the effectiveness and feasibility of the proposed approach. Based on the analysis results, specific design schemes for improving the identified shortcomings in age-friendly aspects of these communities are proposed, considering the needs of aging populations and taking into account community public facilities, accessible design renovations, and the enhancement of green space layouts. This study aims to explore the comprehensive benefits of an age-friendly retrofit in urban communities and provide reference for the deep integration of social, ecological, and technological benefits in urban renewal. The evaluation indicators, methods, and conclusions presented can serve as a decision-making basis for the renovation and renewal of aging urban communities, particularly in terms of age-friendly updates.

Special Methods Controllability and Observability in Optimal Control Systems

This article explores a specific case study that examines controllability and observability in general and in specific so that it is easy for the reader to understand these two concepts, which are fundamental in optimal control theory. Algorithms have been written to determine the controllability and observability of optimal control systems using the MATLAB programming language, and new techniques have been developed to deal with them. In addition, a critical test was created in which the state variables of the system or, more precisely, their corresponding states were split together, illustrating this with more than one example. Divided into four groups in a linear manner, as the article explains. To understand the controllability and observability of some more complex systems, this article is a starting point for the future expansion of these two concepts through the development of new algorithms or other applied solution methods or the creation of new algorithms.

Location Selection Methods for Urban Terminal Co-Distribution Centers with Air–Land Collaboration

Urban terminal logistics and distribution enterprises face the problems of duplicated network layouts, high costs, and inefficient urban environments. Recently, collaborative distribution using unmanned aerial vehicles (UAVs) and ground vehicles has been considered as a means of reducing costs and enhancing efficiency, thus overcoming the issues created by the high-density layout of enterprises’ relatively independent networks. This essentially involves constructing an air–ground collaborative common distribution network. To optimize the economic cost and distribution time of network operations, we established a site selection planning model for air–ground cooperative urban co-distribution centers and designed a solution method based on gray wolf optimization with K-means clustering. Taking the Wangsheren area of Jinan City, China, as an example, 15 UAV co-distribution centers and 13 vehicle co-distribution centers were identified. Although the average distribution cost of the network rose by 35–50% compared to traditional terminal distribution, the time saving was 80–85%, greatly improving the high-value-added service capacity. The end-distribution efficiency and customer satisfaction were also enhanced, which fully verifies the feasibility, validity, and applicability of the proposed model. Our approach can be applied to landing sites and the planning and optimization of large-scale commercial operations using logistics UAVs in urban areas.

Capacitated Mobile Facility Location Problem with Mobile Demand: Efficient relief aid provision to en route refugees

As a humanity crisis, the tragedy of forced displacement entails relief aid distribution efforts among en route refugee to alleviate their migration hardships. This study aims to assist humanitarian organizations in cost-efficiently optimizing the logistics of capacitated mobile facilities utilized to deliver relief aid to transiting refugees in a multi-period setting. The problem is referred to as the Capacitated Mobile Facility Location Problem with Mobile Demands (CMFLP-MD). In CMFLP-MD, refugee groups follow specific paths, and meanwhile, they receive relief aid at least once every fixed number of consecutive periods, maintaining continuity of service. To this end, the overall costs associated with capacitated mobile facilities, including fixed, service provision, and relocation costs, are minimized. We formulate a mixed integer linear programming (MILP) model and propose two solution methods to solve this complex problem: an accelerated Benders decomposition approach as an exact solution method and a matheuristic algorithm that relies on an enhanced fix-and-optimize agenda. We evaluate our methodologies by designing realistic instances based on the Honduras migration crisis that commenced in 2018. Our numerical results reveal that the accelerated Benders decomposition excels MILP with a 46% run time improvement on average while acquiring solutions at least as good as the MILP across all instances. Moreover, our matheuristic acquires high-quality solutions with a 2.4% average gap compared to best-incumbents rapidly. An in-depth exploration of the solution properties underscores the robustness of our relief distribution plans under varying migration circumstances. Across several metrics, our sensitivity analyses also highlight the managerial advantages of implementing CMFLP-MD solutions.

A simple numerical simulation model can elucidate the key factors for designing a miniaturized ion trap mass spectrometer

BackgroundMiniature ion trap mass spectrometer enables mass-to-charge ratio analysis of ions via quadrupole field in a low vacuum environment. It plays an important role in on-site detection due to its portability and specificity. In order to gain a deeper understanding of the analysis mechanism of miniature ion trap mass spectrometers, a quadrupole MS ion trajectory numerical simulation model (QITNS) is established in this paper for ions trajectory calculation under the action of quadrupole field, exciting field and neutral gas molecule collision. Compared with the existing methods, the model in this paper is simpler and more direct, which effectively explored the effects of dipole excitation and quadrupole excitation on ion manipulation under high background pressure. ResultsThe simulation results demonstrate that high RF amplitude, low auxiliary AC amplitude and quadrupole excitation can effectively improve the isolation resolution. Besides, it clarified the difference between the analysis mechanism of ion trap mass spectrometers under high background pressure (above 13.332 Pa) and absolute vacuum conditions. The relevant results are consistent with the conclusions of previous experiments and other theories, proving the applicability and accuracy of the proposed calculation model and solution method. SignificanceThis research bears the guiding significance for further understanding the mechanism of quadrupole mass spectrometry as well as designing and developing miniature mass spectrometers.

Distributionally robust chance-constrained kernel-based support vector machine

Support vector machine (SVM) is a powerful model for supervised learning. This article addresses the nonlinear binary classification problem using kernel-based SVM with uncertainty involved in the input data specified by the first- and second-order moments. To achieve a robust classifier with small probabilities of misclassification, we investigate a distributionally robust chance-constrained kernel-based SVM model. Since the moment information in the original problem becomes unclear/unavailable in the feature space via kernel transformation, we develop a data-driven approach utilizing empirical moments to provide a second-order cone programming (SOCP) reformulation for efficient computation. To speed up the required computations for solving large-size problems in higher dimensional space and/or with more sampling points involved in estimating empirical moments, we further design an alternating direction multipliers-based algorithm for fast computations. Extensive computational results support the effectiveness and efficiency of the proposed model and solution method. Results on public benchmark datasets without any moment information indicate that the proposed approach still works and, surprisingly, outperforms some commonly used state-of-the-art kernel-based SVM models.

Computation of three-dimensional incompressible flows using high-order weighted essentially non-oscillatory finite-difference lattice Boltzmann method

In the present work, an accurate and robust solution methodology based on the high-order weighted essentially non-oscillatory (WENO) finite-difference lattice Boltzmann method (LBM) in the three-dimensional generalized curvilinear coordinates is presented and applied for simulating the three-dimensional incompressible flows over complicated configurations with curved boundaries. Here, the incompressible form of the lattice Boltzmann equation in three dimensions is considered and the discretization of the spatial derivative terms is performed with the fifth-order WENO finite-difference method and the temporal derivative term is discretized with the fourth-order Runge–Kutta scheme to ensure the accuracy and stability of the solution method for both the steady and unsteady problems. The three-dimensional lattice Boltzmann equation applied here is based on a nineteen discrete velocity model for transforming the microscopic properties to the macroscopic ones. To assess the accuracy and robustness of the present three-dimensional high-order finite-difference LBM solver, different incompressible flow benchmarks and practical test cases are studied that are the cavity flow, the Beltrami flow, the flow in the curved ducts of rectangular cross sections, and the flow over a sphere for different flow conditions. The decay of the homogeneous isotropic turbulence is also computed to examine the suitability of the present solution method to be applied as the direct numerical simulation of turbulent flows. It is demonstrated that the solution methodology presented based on the high-order WENO finite-difference LBM in the three-dimensional generalized curvilinear coordinate can be used for accurately and effectively computing the three-dimensional practical incompressible flow problems.

Methods and algorithms of swarm intelligence for the problems of nonlinear regression analysis and optimization of complex processes, objects, and systems: review and modification of methods and algorithms

The development of high-speed methods and algorithms for global multidimensional optimization and their modifications in various fields of science, technology, and economics is an urgent problem that involves reducing computing costs, accelerating, and effectively searching for solutions to such problems. Since most serious problems involve the search for tens, hundreds, or thousands of optimal parameters of mathematical models, the search space for these parameters grows non-linearly. Currently, there are many modern methods and algorithms of swarm intelligence that solve today's scientific and applied problems, but they require modifications due to the large spaces of searching for optimal model parameters. Modern swarm intelligence has significant potential for application in the energy industry due to its ability to optimize and solve complex problems. It can be used to solve scientific and applied problems of optimizing energy consumption in buildings, industrial complexes, and urban systems, reducing energy losses, and increasing the efficiency of resource use, as well as for the construction of various elements of energy systems in general. Well-known methods and algorithms of swarm intelligence are also actively applied to forecast energy production from renewable sources, such as solar and wind energy. This allows better management of energy sources and planning of their use. The relevance of modifications of methods and algorithms is due to the issues of speeding up their work when solving machine learning problems, in particular, in nonlinear regression models, classification, and clustering problems, where the number of observed data can reach tens and hundreds of thousands or more. The work considers and modifies well-known effective methods and algorithms of swarm intelligence (particle swarm optimization algorithm, bee optimization algorithm, differential evolution method) for finding solutions to multidimensional extremal problems with and without restrictions, as well as problems of nonlinear regression analysis. The obtained modifications of the well-known classic effective methods and algorithms of swarm intelligence, which are present in the work, effectively solve complex scientific and applied tasks of designing complex objects and systems. A comparative analysis of methods and algorithms will be conducted in the next study on this topic. Keywords: optimization, swarm intelligence, mathematical modelling, nonlinear regression, complex objects and systems.

A local meshless method for the numerical solution of multi-term time-fractional generalized Oldroyd-B fluid model

This work presents an accurate and efficient method, for solving a two dimensional time-fractional Oldroyd-B fluid model. The proposed method couples the Laplace transform (LT) with a radial basis functions based local meshless method (LRBFM). The suggested numerical scheme first uses the LT which transform the given equation to an elliptic equation in LT space, and then it utilizes the LRBFM to solve transformed equation in LT space, and then the solution is converted back into the time domain via the improved Talbot's scheme. The local meshless methods are widely recognized for scattered data interpolation and for solving PDEs in complex shaped domains. The adaptability, simplicity, and ease of use are features that have led to the popularity of local meshless methods. The local meshless methods are easy and straightforward, they only requires to solve linear system of equations. The main objective of using the LT is to avoid the computation of costly convolution integral in time-fractional derivative and the effect of time stepping on accuracy and stability of numerical solution. The stability and the convergence of the proposed numerical scheme are discussed. Further, the Ulam-Hyers (UH) stability of the proposed model is discussed. The accuracy and efficiency of the suggested numerical approach have been demonstrated using numerical experiments on five different domains with regular nodes distribution.

Slagging tendency analysis and evaluation of biomass and coal during co-firing

Co-firing of biomass and coal may cause slagging and fouling and impact the operational lifespan of the boilers. In this paper, eucalyptus bark (EB) and four kinds of coal were used as raw materials, and the degree of slagging was experimentally investigated by scanning electron microscope (SEM), X-ray fluorescence (XRF), and X-ray diffraction (XRD). Moreover, the technique for order preference by similarity to ideal solution (TOPSIS) method and the entropy weight (EW) method were used to establish a slagging evaluation model E-TOPSIS. The results showed that the co-firing of EB and coal caused an increase in ash particle size, particle sintering, and adhesion. XRD analysis confirmed that EB promoted the reaction of calcium compounds with quartz and enhanced the diffraction intensity of muscovite, anorthite, and calcite. The evaluation results of the E-TOPSIS showed that the slagging tendency of EB, IC, and ICEB was severe, which is aligned with the experimental results, and proves the accuracy of this method. The research results can provide a reference for predicting the slagging tendency of biomass and coal during co-firing.

Transparent boundary condition and its effectively local approximation for the Schrödinger equation on a rectangular computational domain

The transparent boundary condition for the free Schrödinger equation on a rectangular computational domain requires implementation of an operator of the form ∂t−i△Γ where △Γ is the Laplace-Beltrami operator. It is known that this operator is nonlocal in time as well as space which poses a significant challenge in developing an efficient numerical method of solution. The computational complexity of the existing methods scale with the number of time-steps which can be attributed to the nonlocal nature of the boundary operator. In this work, we report an effectively local approximation for the boundary operator such that the resulting complexity remains independent of number of time-steps. At the heart of this algorithm is a Padé approximant based rational approximation of certain fractional operators that handles corners of the domain adequately. For the spatial discretization, we use a Legendre-Galerkin spectral method with a new boundary adapted basis which ensures that the resulting linear system is banded. A compatible boundary-lifting procedure is also presented which accommodates the segments as well as the corners on the boundary. The proposed novel scheme can be implemented within the framework of any one-step time marching schemes. In particular, we demonstrate these ideas for two one-step methods, namely, the backward-differentiation formula of order 1 (BDF1) and the trapezoidal rule (TR). For the sake of comparison, we also present a convolution quadrature based scheme conforming to the one-step methods which is computationally expensive but serves as a golden standard. Finally, several numerical tests are presented to demonstrate the effectiveness of our novel method as well as to verify the order of convergence empirically.

A method for calculating two-phase equilibrium: Constrained gray prediction evolutionary algorithm with a surrogate model based on quadratic interpolation

Traditional methods, including direct solution methods based on Newton's method and indirect solution methods based on thermodynamic principles, are the mainstream methods used to solve the volume-temperature flash calculation (called NVT-flash), even though they suffer from drawbacks such as sensitivity to initial value and complexity of derivative calculations. A constrained backtracking search algorithm (CBSA), proposed in 2024, was the first and only metaheuristic algorithm to successfully tackle the NVT-flash problem, which overcomes shortcomings of traditional methods. Considering the advantages of metaheuristic algorithms, a constrained gray prediction evolutionary algorithm with a surrogate model based on quadratic interpolation (CGPE-QI) is proposed in this paper to deal with the NVT-flash problem. CGPE-QI considers total Helmholtz free energy as the objective function, moles vector, and volume of a single phase as variables. Constraints to solve the NVT-flash problem are addressed by using a direct search method and an exterior point method. Numerical experiments on two-phase equilibrium of pure substance and mixtures are carried out employing CGPE-QI. Experimental results are the same as those obtained by traditional methods, which confirms that CGPE-QI can effectively tackle the NVT-flash problem and possesses energy decay property. In particular, the results demonstrate that CGPE-QI is more competitive than CBSA in terms of convergence speed, stability, and calculation cost. CGPE-QI proposed in this paper is the second metaheuristic algorithm to successfully solve the NVT-flash problem, illustrating that metaheuristic algorithms have great potential in solving phase equilibrium calculation problems.

Assessing hydropower capability for accommodating variable renewable energy considering peak shaving of multiple power grids

Hydropower can play a transformative role in supporting the substantial increase in variable renewable energy (VRE) via flexible regulation ability, but the capability of cascade hydropower to buffer VRE is indistinct. This study proposes a systematic framework to assess hydropower capability for integrating VRE considering the peak shaving demands of multiple power grids. A chance-constrained multi-time aggregate model for the integrated hydro-wind-solar operation is established to determine the optimal wind and solar capacity and coordinated operational strategies. An independent hydropower peak shaving operation model is proposed for comparison. The proposed models are recast as mixed integer linear programming formulations based on the proposed solution method. Comparative situation experiments divided by different influencing factors are implemented to analyze hydropower capability for integrating VRE. The results revealed the following: (1) Integrating VRE would reduce the peak shaving effectiveness of hydropower—the lowest load rate decreases to 0.899. (2) Hydropower capability for integrating wind and solar power is affected by hydrological conditions. Hydropower capability is limited under fixed hydrological conditions, and it prioritizes expanding wind power and restricting solar power. (3) Expanding the transmission capacity will increase hydropower capability from 13300 to 17000 MW and enhance peak shaving performance through the increased hydropower contribution.

Developing a scalable analytical framework for predicting the contact behavior of elastic rings against rigid surfaces

An elastic ring interacting with rigid surfaces is a fundamental engineering challenge with vast practical implications in various disciplines. However, the exploration of closed-form solutions for this issue has been limited, and existing studies often present complex, numerically unstable solution methods influenced by specific boundary conditions. Furthermore, the lack of scalable design principles for the ring-in-contact scenario has hindered its broader application across different geometries and materials. This study introduces a streamlined analytical and numerical approach to predict the contact behavior of orthotropic rings against centrosymmetric rigid surfaces, encompassing both flat and curved surfaces. Our approach, which simplifies the closed-form solution for extensible Timoshenko curved beams coupled with a contact algorithm that prevents penetration, yields robust and accurate predictions of nonlinear contact behaviors in elastic rings, including deformation patterns, contact angles, stresses, and stiffness. Additionally, we present a design map that serves as a scalable guideline for engineering elastic rings in contact, facilitating the choice of geometry and materials, such as ring radius, thickness, and elastic moduli. This research enhances the theoretical underpinnings of elasticity concerning ring contact and expands the engineering viewpoint on designing elastic rings in various contact scenarios.