Iterative Calculation Research Articles

Constructive Approximate Nash Equilibrium for In-Orbit Target Enclosing with Collision Avoidance and Full-state Constraint via Nonzero-Sum Differential Games

The problem of in-orbit cooperative target enclosing involving N thrust-limited satellites under collision avoidance and maneuver amplitude constraints is studied. In order to find global optimal trajectories for target enclosing task with all constraints above, by integrating the collision threat and maneuver boundaries into a novel nonlinear cost functional, the studied target enclosing problem is described as a nonlinear nonzero-sum differential game. Further, to avoid iterative calculations caused by traditional nonlinear-game-solving methods, an approximate solution which can be constructed directly is designed. Then the approximate Nash equilibrium strategies can be educed by the constructive approximate solution for the proposed nonzero-sum game. Analysis shows that the proposed control strategies can asymptotically approach the exact one and can ensure a zero-error tracking of the enclosing configuration. Simulation results illustrate lower time costs and better enclosing accuracy while the collision avoidance and maneuver amplitude constraints are satisfied simultaneously.

A study of options to enhance the operation of a H2 direct reduction shaft furnace using a two-dimensional model

With the intent to explore techno-economically feasible options for improving the performance of the hydrogen (H2) -operated direct reduction shaft furnace for iron ores, a two-dimensional computational fluid dynamics model was applied to assess the potential of a new top gas recycling system featuring dual-row injection. A special numerical routine was developed to bridge data communication during the iterative calculation, where the composition of the gas injected in the upper (tuyere) row varies with the conditions. The results showed that a poor gas utilization is inevitable for a (conventional) single-row recycling system since it cannot properly address the strong heat demand of the process. For dual-row top gas recycling with a reduced lower-row feed rate, the in-furnace thermochemical state is inappropriate if the upper-row feed rate is low, but is gradually improved as the upper-row feed rate increases, since more thermal energy is supplied to the part of the furnace where it is needed. With an appropriate configuration of the upper- and lower-row feed rates, the overall furnace performance can be substantially improved particularly with respect to gas utilization degree. The findings of this work are expected to aid the future design of more efficient operation of H2-based direct reduction of iron ores.

Enhancing short-circuit current calculation in active distribution networks through Fusing superposition theorem and Data-Driven approach

In the realm of active distribution networks, the Inverter Interfaced Distributed Generator (IIDG) poses a challenge with its diverse non-linear fault outputs stemming from varied control strategies and objectives. This presents a dilemma, balancing computational precision and speed in short-circuit current calculation. To address this issue, a novel methodology is proposed, utilizing a Graph Attention Network (GAT)-based model. This model is designed for rapid and precise computation of IIDG fault outputs, thereby enhancing the efficiency of the iterative calculation process. Integration of the superposition theorem significantly boosts the efficiency of short-circuit current calculation in active distribution networks. Moreover, the proposed approach successfully overcomes common problems, such as reduced accuracy and non-convergence, often encountered due to the dynamic nature of network structures. The utility and adaptability of this method are illustrated through various examples, showcasing its ability to accommodate networks with unknown structures and increased branch circuits, while ensuring consistent and reliable computational results.

Saline water treatment coupled with carbon dioxide capture by bipolar membrane electrodialysis in a continuous feed-bleed mode: The effect of proton leakage

Bipolar membrane electrodialysis (BMED) has emerged as a promising technology for integrating saline water treatment with CO2 capture systems. However, a significant challenge remains in the form of proton leakage, which depletes the OH− ions generated by the bipolar membrane (BPM), thereby directly hindering CO2 absorption efficiency. To unravel the underlying mechanism of proton leakage and optimize BMED performance, a continuous feed-bleed BMED system for both saline water treatment and CO2 capture was proposed. A comprehensive investigation was conducted to assess the influence of key parameters, including current density, alkalinity ion concentration, feedstock salinity, and product concentration on the extent of H+ leakage. Notably, it’s found that increasing current density from 150 to 300 A/m2, the proportion of H+ leakage through the anion exchange membrane (AEM) rose from 65.53 % to 74.77 %, while alkalinity ion concentration has a relatively minor impact. To manage the feedstock salinity and product concentration, the NaCl and H2O feeding rates were precisely regulated in this feed-bleed system. By adjusting these rates to 8–15 mL/min for NaCl and 3–8 mL/min for H2O, respectively, a notable reduction in the H+ leakage rate was achieved, from 71.37 % down to 57.97 %. Furthermore, through the integration of iterative calculations with experimental data, it was discovered that proton leakage predominantly occurs via concentration diffusion mechanisms. This insight into the intricate regulation of proton leakage not only deepens our understanding of the underlying mechanism but also provides valuable guidance for the effective deployment and optimization of BMED technology.

Distance-reconstructed dependency enhanced aspect-based sentiment analysis with sentiment strength

Aspect-based sentiment analysis (ABSA) is a fine-grained sentiment analysis task that requires the detection of sentiment polarity towards specific aspects. Dependency tree-based graph convolutional network models (GCN) have been widely applied in ABSA. These studies utilize syntactic analysis tools to derive syntactic dependency graphs, which are then inputted into GCN. It enables iterative learning of sentiment dependency information from contextual words to aspect terms. However, directly using syntactic dependency graphs can lead to two shortcomings. First, the long-distance sentiment information in long sentences will be weakened during GCN iterative computations. Second, the syntactic dependency graphs of short sentences lack sentiment strength information. To address these two shortcomings, we propose a Distance-Reconstructed Dependency Enhanced Sentiment analysis approach with Sentiment Strength based on GCN (DRD-SE-GCN) approach, in which the syntactic dependency graph of long sentences is reconstructed based on distance, thus narrowing the gap between sentiment words and target aspect words. It ensures that the sentiment dependency information carried by the long-distance sentiment words will not be weakened or lost during the GCN iteration. Additionally, the weights of the syntactic dependency graph for short sentences are reassigned so as to carry the strength information of sentiment words. Experimental results on four standard datasets show that our proposed model can effectively improve the accuracy of aspect-level sentiment analysis.

A probabilistic model for real-time quantification of building energy flexibility

Buildings have great energy flexibility potential to manage supply-demand imbalance in power grids with high renewable penetration. Accurate and real-time quantification of building energy flexibility is essential not only for engaging buildings in electricity and grid service markets, but also for ensuring the reliable and optimal operation of power grids. This paper proposes a probabilistic model for rapidly quantifying the aggregated flexibility of buildings under uncertainties. An explicit equation is derived as the analytical solution of a commonly used second-order building thermodynamic model to quantify the flexibility of individual buildings, eliminating the need of time-consuming iterative and finite difference computations. A sampling-based uncertainty analysis is performed to obtain the distribution of aggregated building flexibility, considering major uncertainties comprehensively. Validation tests are conducted using 150 commercial buildings in Hong Kong. The results show that the proposed model not only quantifies the aggregated flexibility with high accuracy, but also dramatically reduces the computation time from 3605 s to 6.7 s, about 537 times faster than the existing probabilistic model solved numerically. Moreover, the proposed model is 8 times faster than the archetype-based model and achieves significantly higher accuracy.

Efficient magnetic forward modeling for strongly magnetized bodies: An iterative integral equation approach

Magnetic surveying encounters challenges in high-precision detection and inversion on strongly magnetized bodies. Nonuniform magnetization caused by self-demagnetization and mutual magnetization makes magnetic field calculation using analytical formulas impractical. The previous discrete numerical methods have suffered from computational inefficiency or low accuracy. To resolve this issue, we develop an algorithm to solve the magnetic field integral equation for calculating the magnetization state of high-susceptibility bodies, combining the improved spatial convolution forward approach with the adaptive relaxation iteration method. To address the excessive computational burden in the magnetization field between 3D voxel arrays of the discrete model, we construct the circular convolution kernel matrix directly when the subsurface space is divided with an equidistant grid, significantly reducing redundant computations. Then, the fast Fourier transform is used to accelerate the forward discrete circular convolution operation. In addition, we derive an iterative computation scheme that adaptively adjusts the relaxation factor based on magnetic field changes to correct the effective magnetization for algorithm convergence. From a pragmatic perspective, equating the cuboid to equal-volume sphere subdivisions is developed to enhance computational efficiency further by approximately 50% despite sacrificing slight accuracy. The sphere and spherical shell models validate the algorithm accuracy, efficiency, and convergence. Furthermore, we analyze the characteristics of the mutual magnetization effect among magnetic bodies under different magnetization conditions. Finally, the applicability of the algorithm is demonstrated with a realistic example. Our algorithm shows promise for precisely exploring highly magnetized minerals, underground pipelines, and unexploded ordnance.

An Enhanced Numerical Calculation Method to Study the Anchorage Performance of Rebars.

When modelling the anchorage performance of rebars with the tri-linear law, the calculation process of the load-deformation relation is complicated. The reason is that when the rebar-grout interface entered the elastic-softening-debonding stage, the softening section length and debonding section length vary simultaneously. To solve this issue, this paper proposes an enhanced numerical calculation method. When the rebar-grout interface entered the elastic-softening-debonding stage, the softening section length was fixed to a specific value. One loop function was created to calculate the debonding section length. With this method, the number of iteration calculations significantly decreased. The credibility of this calculation method was confirmed with experimental results. Two case studies were conducted to compare the load-deformation relation obtained with the original calculation method and enhanced calculation method. The results showed that good consistency existed between the results obtained by those two methods. This finding can significantly improve the calculation efficiency when studying the anchorage performance of rebars. Moreover, this paper provides new insight for users to optimise the modelling process of rebars.

The effective thermal conductivity of random isotropic porous media analysis and prediction

Effective thermal conductivity of porous media is a crucial parameter for heat transfer within them. Many studies have characterized various porous media by adjusting the control parameters generated through the Quartet Structure Generation Set method. The porous media effective thermal conductivity is then determined through Computational Fluid Dynamics calculations, which, however, necessitate significant computational resources and time. Thus, following an exploration of the influence of control parameters (i.e., porosity, core growth probability, and their coupling) on the effective thermal conductivity of isotropic porous media generated by the Quartet Structure Generation Set method, this study developed a multi-layer perceptron prediction model. The aim was to establish a prediction model from the porous media control parameters to effective thermal conductivity, thereby reducing the time spent on iterative calculations. The findings indicate that the effective thermal conductivity does not uniformly increase with the growth of core probability, and instead fluctuates after a certain threshold. Notably, the trained model exhibits a high prediction accuracy, with average deviations of 0.0887 and 0.0748 for the training and testing datasets, respectively.

Effect of Heat Exchange Area Margins on Thermal Characteristics of the Heat Exchange System in the Pressurized Water Test Loop during Fuel Assembly Irradiation

The performance of heat exchangers in the pressurized water test loop is a critical factor in ensuring the achievement of irradiation parameters for fuel assemblies and the safety of experimental operations. The effect of the heat exchange area margin on the heat exchangers in the pressurized water test loop for the fuel assembly during the steady-state irradiation is analyzed. Additionally, optimization methods for determining the margin of heat exchange area and corresponding design strategies are further investigated. It shows that the effect of the heat exchange area margin on the heat exchange power is less affected by the inlet temperature of the primary water and is primarily influenced by the flow rate of the primary water. A decrease in the flow rate of the primary water reduces the compensatory effect of the cooling section on power and enhances the weakening effect of the regeneration section on power. Meanwhile, the correspondence between the margin of the regeneration section and the cooling section, established based on design conditions, can be applicable when there are changes in the inlet temperature of the primary water, but it is not suitable when there are changes in the flow rate of the primary water. When the flow rate of the primary water decreases, the cooling section margin required to compensate for the decrease in power caused by the regeneration section margin will increase significantly. In addition, short-circuiting the heat exchange tubes in the regeneration section can effectively enhance the heat transfer capability. Furthermore, setting the heat exchange area margins of the regeneration and cooling sections to zero can serve as a termination condition for iterative calculations in the verification of regenerative heat exchangers under off-design conditions.

Data-Driven Entrepreneurship in Green Hydrogen Economy: An Integrated Framework for Entrepreneurial Enterprises in the Era of Big Data

In the era of big data, in order to improve the aggregation effect of start-ups, a digital framework with a promoting role has been formed. This paper proposes a data-driven approach in the context of the green hydrogen economy. Firstly, the data function was used to collect, classify and sort out the entrepreneurial data to form an orderly data set. Then, with the help of data-driven functions, the nonlinear reorganization of start-ups is carried out to verify their discreteness, the correlation between the hydrogen economy and start-up data is mined, and an integrated framework is formed through iterative calculation. The results show that there is a significant correlation between the hydrogen economy and start-ups, and big data can drive the integrated development of start-ups, and the data-driven method proposed in this paper can accurately identify start-up data, with a recognition rate of 90%, which is better than the previous machine learning methods and decision tree methods, and has strong big data mining capabilities. Therefore, there is a significant correlation between the hydrogen economy, big data, and start-ups, and a data-driven approach can identify the relationship between the two and facilitate the construction of an integrated framework.

Spatial positioning method based on range-only measurement of multi-station radar

Aiming at the characteristics that affect the high ranging accuracy of shipborne radar, a multi station radar spatial positioning method based on ranging is proposed. This method is based on the ECEF (Earth Centered Earth Fixed) coordinate system, and adopts the method of intersecting the detection distances of multiple radars to the target, and directly calculates the spatial position of the target. This method only needs the geodetic coordinates of each radar station and the detection range of the target to calculate the geodetic coordinates of the target, which can effectively solve the coordinate conversion problem caused by the curvature of the earth, and does not involve higher-order equations and multi-value solutions, and it does not involve iterative initial value calculation. The positioning system can not only obtain high positioning accuracy, but also has a long operating distance, which can better solve the multi-radar range measurement intersection positioning problem.

Centrifugal failure mechanism analysis for ferrofluid seals based on a bidirectional coupled multi-physics model

In this paper, we propose a bidirectional coupled multi-physics (BCM) model to study the centrifugal failure mechanism of ferrofluid seals, employing a hybrid finite volume–finite element method. In this model, the evolution of the flow field is described by the two-phase incompressible Navier-Stokes (NS) equations with Kelvin force. The volume of fluid (VOF) method is used to capture the gas-ferrofluid interface. Magnetic scalar potential is introduced to solve for the magnetostatic field. We conducted secondary development on the OpenFOAM and Elmer software packages, which are based on the finite volume method (FVM) and finite element method (FEM), respectively, to calculate the flow field and magnetic field in ferrofluid seals. By developing interpolation methods between FEM and FVM grids based on the parallel bidirectional coupler EOF-Library[1], field information exchange between the flow field and magnetic field is achieved. The BCM model executes iterative computations on the flow and magnetic fields in an alternating way, continuously synchronizing the information of each, thus facilitating bidirectional coupling between the FVM and FEM frameworks. We employ the BCM model to investigate the failure mechanisms of ferrofluid seals under different conditions, including various load pressure and rotational velocity. The results indicate that the ferrofluid will leave the surface of the shaft along the pole teeth under the action of centrifugal forces, with the highest radial velocity occurring at the boundary of the liquid film. Under varying conditions of rotational velocity and pressure drop, the centrifugal failure modes of ferrofluid seals exhibit distinct differences. Moreover, two dimensionless numbers are proposed to quantitatively evaluate the effects of load pressure and centrifugal force, thereby augmenting the efficacy of seal design.

Assessment of groundwater vulnerability using GOD index and Dar Zarrouk parameters: A case study of OAUSTECH main campus, Okitipupa, Ondo State

Groundwater is essential for efficient management of groundwater to prevent the deterioration of its quality. The objective of this study is to evaluate the vulnerability of the primary campus of (Olusegun Agagu University of Science and Technology) OAUSTECH in Okitipupa, Ondo State, Nigeria. This was done by analysing the GOD index and the Dar Zarrouk parameters of conductance and transverse resistance. A total of 24 Vertical Electrical Sounding (VES) data points were gathered, with AB/2 values varying from 200 to 225. These data points were then analysed utilising partial curve matching and computer iteration techniques to determine geoelectric characteristics, including resistivity and thickness. The computed characteristics, longitudinal conductance and transverse resistance, suggest that the aquifer's ability to defend against contamination in the research area is generally insufficient. The longitudinal conductance values range from 0.02 to 0.6, with most values below 0.1. Using the GOD method, the study shows that the GOD index value varies from 0.2 to 0.6, with an average of 0.325, suggesting a moderate to high level of vulnerability in the groundwater. The association between the GOD index and longitudinal conductance results in a 60 % accuracy in predicting groundwater susceptibility. This research emphasises that the groundwater within the main campus of OAUSTECH is moderately to highly vulnerable.

Multi-Criteria Decision-Making Method for Simple and Fast Dimensioning and Selection of Glass Tube Collector Type Based on the Iterative Thermal Resistance Calculation Algorithm with Experimental Validation

This paper presents an analytical method for the dimensioning and selection of the four glass tube collector types: single-glazed with an air layer, single-glazed with a vacuum layer, double-glazed with an air layer, and double-glazed with a vacuum layer. In the first part of the paper (dimensioning phase), the iterative thermal resistance calculation algorithms were developed for all glass tube collector types, whereby the iterative thermal resistance calculation algorithm of the single-glazed tube collector with an air layer was experimentally tested and validated. The second part of the paper (selection phase) uses a multi-criteria decision-making method to determine the optimal glass tube collector design. Unlike other papers, three indicator groups are taken into account in this case: geometric (mass, surface occupation, total surface occupation, volume occupation), economic (manufacturing and exploitation costs), and ecological (embodied energy and greenhouse gas emission). The proposed method is characterized by simple and fast calculations with satisfactory accuracy, which avoids high investment costs (experimental research), approximation and discretization of physical models (numerical research), and a large number of input parameters with boundary conditions (theoretical research). It should be noted that, with certain additions and changes, it can also be applied to other solar thermal collectors, so the authors believe such tools are handy for the global scientific public.

Research on computationally generative design of woven braced structure based on fiber composite material in architectural design industry

ABSTRACT With the intervention of computer algorithm-assisted design in the realm of contemporary architectural design, architectural spatial forms and corresponding design methods have improved significantly. However, the limitations of material strength and plasticity impose certain constraints on the architectural design of the new century. Based on this occurrence, this paper studies the development of a computational generative design system for woven braced structure composed of fiber-reinforced materials. Through experimental data of material performance, the research firstly argues feasibility of employing fiber composite materials to braced structure. The conclusion is that the structure designed and generated could produce a support of 1 ton per ㎡. Moreover, based on the ant colony algorithm and the algorithm principle of cellular automata on the Java platform, the study designs a generative system with iterative computing of force as the major axis to achieve the self-organization and adaptability of the braced structure. Above all, this paper proposes a design strategy engaging with computational generative design approach, as well as a design attempt for the material and form of architecture.

A fast numerical method for calculating SPND space charge effect at steady state

To address the issue of low efficiency and long computation times in calculating the space charge effect in Self-Powered Neutron Detectors (SPNDs), we developed a fast and efficient numerical method to calculate the steady-state electric fields in SPND insulators. Previous calculations have shown that even when the electric field in the SPND insulator reaches 1 GV/m, its effect on electron transport is negligible. Therefore, we assume that the electric field has a negligible effect on electron transport. Based on this assumption, we developed a one-step numerical method for calculating the steady-state electric field in the insulator. This fast method is based on the charge conservation equation in equilibrium, thus requiring only a single charge deposition result without an electric field to obtain the distribution of the electric field under steady-state conditions. We validated our method by comparing it with precise iterative calculation results and experiments. The computational results indicate that, for three typical experimental scenarios, the fast method only takes up to one percent, or even less, of the time required by the iterative method. At the same time, the Mean Relative Error (MRE) in the electric field distribution between the fast method and iterative calculations are 1.48%, 0.31%, and 5.12%, respectively; whereas the relative errors in sensitivity calculations based on the electric field compared to iterative calculations are all less than 2%. Therefore, the fast method can significantly reduce computation time and ensure sufficient accuracy of steady state electric field distribution when the electric field is less than 1 GV/m. The introduction of this method has made it possible to conduct space charge effect assessments and precise sensitivity calculations for the placement of detectors throughout the entire reactor core.

Analysis of the Effect of Sampling Probe Geometry on Measurement Accuracy in Supersonic Gas Flow

The accuracy of sampling of gas components has a significant impact on the measurement of various performance parameters in the combustion chamber of an aero-engine. In order to investigate the effect of the probe geometry of a six-point gas sampling probe on sampling accuracy in supersonic gas flow, a three-dimensional probe gas flow characteristic solution model is established through numerical simulation methods of components of transport and fluid–solid coupling. Probes with three angles of 28°, 30°, and 32° and an optimized conical probe are constructed. The sampling accuracy of the probes with different geometries is compared and evaluated by the deviation of the component volume fraction before and after sampling and the resulting combustion efficiency error. This paper presents a set of calculation methods for solving the relative deviation of volume fraction by an iterative method based on the ideal gas law and the Redlich–Kwong equation (R-K equation). The method is designed to solve the exact component volume fraction problem in the simulation calculation. The study results demonstrate that the 28° and optimized conical probes improve sampling accuracy more effectively than the original 30° structure. The deviation of the volume fractions of the two structures is less than 1.7%, and the combustion efficiency error is less than 0.09%. The developed iterative calculation method can significantly reduce the theoretical calculation error to less than 0.06%. The experimental data of the test bench are in good agreement with the simulation results, thereby demonstrating the reliability and accuracy of the sampling probe following structural optimization.

Research on the mechanism of severe unsteadiness of PAT braking condition during the power failure

The Pump-As-Turbine (PAT) technology has become popular in micro hydropower stations due to its simple installation and cost-effectiveness. Nevertheless, power failures present a substantial risk to the secure and steady functioning of PAT’s braking system. The commercial CFD code (ANSYSCFX) is improved by incorporating a secondary development to model the power-off transition using Fortran accurately. This enhancement allows for real-time iterative calculations of angular momentum equations for mixed-flow PAT at different speeds. Meanwhile, the time–frequency domain analysis is utilized to analyze pressure pulsation signals and the evolution of the internal flow field in mixed-flow PAT. An investigation was conducted to have a deeper understanding of braking circumstances. The results revealed that the main frequency of the pressure pulsation aligns with the blade frequency at various flow rates, and there is a sudden change in pressure amplitude during the braking phase. The impeller experienced the majority of energy losses, with the draft tube being the subsequent area of concern. In addition, a thorough examination and comparison of the changes in the internal flow field during braking were carried out. This analysis revealed a distinct double helix structure within the draft tube, with a slower inner helix and a faster outer helix. Furthermore, it was observed that there is a strong correlation between wall shear stresses and hydraulic losses on the blade surface. This research enhanced understanding of the flow characteristics of mixed-flow PAT can help improve system safety and provide valuable guidance for future optimization efforts.

Application of efficient algorithm based on block Newton method to elastoplastic problems with nonlinear kinematic hardening

PurposeThe purpose of this study is to present the effectiveness and robustness of a numerical algorithm based on the block Newton method for the nonlinear kinematic hardening rules adopted in modeling ductile materials.Design/methodology/approachElastoplastic problems can be defined as a coupled problem of the equilibrium equation for the overall structure and the yield equations for the stress state at every material point. When applying the Newton method to the coupled residual equations, the displacement field and the internal variables, which represent the plastic deformation, are updated simultaneously.FindingsThe presented numerical scheme leads to an explicit form of the hardening behavior, which includes the evolution of the equivalent plastic strain and the back stress, with the internal variables. The features of the present approach allow the displacement field and the hardening behavior to be updated straightforwardly. Thus, the scheme does not have any local iterative calculations and enables us to simultaneously decrease the residuals in the coupled boundary value problems.Originality/valueA pseudo-stress for the local residual and an algebraically derived consistent tangent are applied to elastic-plastic boundary value problems with nonlinear kinematic hardening. The numerical procedure incorporating the block Newton method ensures a quadratic rate of asymptotic convergence of a computationally efficient solution scheme. The proposed algorithm provides an efficient and robust computation in the elastoplastic analysis of ductile materials. Numerical examples under elaborate loading conditions demonstrate the effectiveness and robustness of the numerical scheme implemented in the finite element analysis.