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At least 379 records · Page 21

NASA Tech Briefs, December 2007

Topics include: Ka-Band TWT High-Efficiency Power Combiner for High-Rate Data Transmission; Reusable, Extensible High-Level Data-Distribution Concept; Processing Satellite Imagery To Detect Waste Tire Piles; Monitoring by Use of Clusters of Sensor-Data Vectors; Circuit and Method for Communication Over DC Power Line; Switched Band-Pass Filters for Adaptive Transceivers; Noncoherent DTTLs for Symbol Synchronization; High-Voltage Power Supply With Fast Rise and Fall Times; Waveguide Calibrator for Multi-Element Probe Calibration; Four-Way Ka-Band Power Combiner; Loss-of-Control-Inhibitor Systems for Aircraft; Improved Underwater Excitation-Emission Matrix Fluorometer; Metrology Camera System Using Two-Color Interferometry; Design and Fabrication of High-Efficiency CMOS/CCD Imagers; Foam Core Shielding for Spacecraft CHEM-Based Self-Deploying Planetary Storage Tanks Sequestration of Single-Walled Carbon Nanotubes in a Polymer PPC750 Performance Monitor Application-Program-Installer Builder Using Visual Odometry to Estimate Position and Attitude Design and Data Management System Simple, Script-Based Science Processing Archive Automated Rocket Propulsion Test Management Online Remote Sensing Interface Fusing Image Data for Calculating Position of an Object Implementation of a Point Algorithm for Real-Time Convex Optimization Handling Input and Output for COAMPS Modeling and Grid Generation of Iced Airfoils Automated Identification of Nucleotide Sequences Balloon Design Software Rocket Science 101 Interactive Educational Program Creep Forming of Carbon-Reinforced Ceramic-Matrix Composites Dog-Bone Horns for Piezoelectric Ultrasonic/Sonic Actuators Benchtop Detection of Proteins Recombinant Collagenlike Proteins Remote Sensing of Parasitic Nematodes in Plants Direct Coupling From WGM Resonator Disks to Photodetectors Using Digital Radiography To Image Liquid Nitrogen in Voids Multiple-Parameter, Low-False-Alarm Fire-Detection Systems Mosaic-Detector-Based Fluorescence Spectral Imager Plasmoid Thruster for High Specific-Impulse Propulsion Analysis Method for Quantifying Vehicle Design Goals Improved Tracking of Targets by Cameras on a Mars Rover Sample Caching Subsystem Multistage Passive Cooler for Spaceborne Instruments GVIPS Models and Software Stowable Energy-Absorbing Rocker-Bogie Suspensions

Source record↗

Cloud-Precipitation Hybrid Regimes and their Projection onto IMERG Precipitation Data

We extend and enhance the concept of the Cloud Regimes (CRs) developed from two-dimensional joint histograms of cloud optical thickness and cloud top pressure from the Moderate Resolution Imaging Spectroradiometer (MODIS), by adding precipitation information in order to better understand cloud-precipitation relationships. Taking advantage of the high-resolution Integrated Multi-satellitE Retrievals for GPM (IMERG) precipitation dataset, cloud-precipitation “hybrid” regimes are derived by implementing the k-means clustering algorithm with advanced initialization and objective measures to determine the most optimal clusters. By expressing precipitation rates within 1-degree grid cell as histograms and making choices on the relative weight of cloud and precipitation, we could obtain several editions of hybrid cloud-precipitation regimes (CPRs), and examine their characteristics. In the deep tropics, when precipitation is weighted weakly, the cloud part of the hybrid entroids resembles the centroid of cloud-only regimes, but still tightens the cloud-precipitation relationship by decreasing the precipitation variability of each regime. As precipitation weight progressively increases, the shape of the cloudy part of the hybrid centroids becomes blunter, while the precipitation part of the centroids sharpens. In the case where cloud and precipitation are weighted equally, the CPRs representing high clouds with intermediate to heavy precipitation exhibit distinct features in the precipitation parts of the centroids, which allows us to project them onto the 30-minly IMERG domain. Such a projection can be used to overcome the temporal sparseness of MODIS cloud observations, which leads to great application potential for various convection-focused studies, including diurnal cycle analysis.

cloud-precipitation↗

Advanced Flexible Transformers

Advanced grid solutions are comprised of advanced transmission technologies and grid enhancing technologies. In this webinar, experts will provide participants with insights into eight advanced grid solutions. The advanced transmission technologies that will be discussed include point-to-point high voltage direct current and advanced conductoring and the grid enhancing technologies that experts will explore include topology optimization, advanced power flow control, dynamic line rating, energy storage, virtual power plants, and advanced flexible transformers

flexible power transformer, power flow controller,↗

Topology Optimization of Curved Electrodes with Suggested Simplified Corrugated Designs

The demand for space-efficient energy storage, from grid to device scale, has soared with the rapid electrification of society. To increase energy density while maintaining high rate performance, shaping electrodes has been shown to be an effective strategy. Computational optimization can suggest designs that improve energy storage performance; however, generated designs are often complex, leading to manufacturing challenges. Additionally, most optimization is typically conducted in standard rectangular domains, whereas some applications, such as in the aerospace industry or in consumer electronics, may benefit from optimized electrodes that fit in a nonstandard form factor. Here, in this work, we use topology optimization to design capacitive full-cell electrodes in a curved domain. We propose a simplified corrugated electrode design based on the optimization results and show that the energy stored in the simplified design is only reduced by about 5–27% when compared to that in the fully optimized design, with more deviation occurring when ionic transport in the porous electrode is particularly impeded. Overall, we find that these simplified designs are promising, particularly given the more conventional manufacturing techniques required, and have a 42–369% increase in energy stored compared to monolithic electrodes.

Energy - Storage↗

Large Scale Bilevel Optimization for N-K SCOPF Using Adversarial Robustness

Ensuring a secure dispatch against multiple simultaneous outages has long been desired to maintain grid security in the presence of severe events, such as extreme weather phenomena. Traditionally denoted as N-k security constrained optimal power flow (N-k SCOPF), this problem is intractable to solve due to its size being combinatorial in the number of simultaneous outages and due to the non-convex nature of the AC network constraints. This hinders the use of N-k SCOPF for operating realistic-scale systems. In this paper, we introduce a methodology to scalably solve an AC-feasible dispatch that improves security over k simultaneous outages. Our methodology poses N-k SCOPF as a bilevel optimization problem and solves it using an adversarial robustness approach. We develop new efficient methods to solve each level of the bilevel optimization by employing knowledge of the physics of the underlying system. This yields significant improvements in speed and convergence that enable us to address the N-k SCOPF problem at scale. We demonstrate the effectiveness of our method by conducting a comprehensive analysis of an N-3 SCOPF for a 500-bus network. Furthermore, we emphasize the ability of our physics-driven techniques to handle larger systems by successfully scaling up to 12,000 buses.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Large-scale simulation-based parametric analysis of an optimal precooling strategy for demand flexibility in a commercial office building

Achieving success with grid-interactive efficient buildings (GEBs) is closely tied to the utilization of flexible loads. A valuable strategy involves the implementation of precooling techniques before high-demand events, such as peak hours, by adjusting zone air temperature setpoints. This leads to a reduction in thermal loads and peak electricity demand during these times, as the building’s thermal mass stores and subsequently releases thermal energy. However, the effectiveness of the pre-cooling optimization is highly contingent on specific conditions such as building thermal properties, weather conditions, utility rate structure, HVAC equipment sizing, etc. Therefore, investigating the impacts of these condition-specific factors is crucial, especially when considering precooling strategies that utilize thermal mass in commercial buildings. In this paper, we first devised a novel heuristic control approach that incorporates parameterized optimal precooling thermostat schedules to enhance demand flexibility in a commercial office building. Subsequently, we conducted a thorough performance evaluation of this control strategy. Here, the optimal thermostat schedule was parameterized using three optimization variables: the precooling start time, the precooling end time, and the precooling temperature setpoint. Utilizing the DOE medium-sized office building as the virtual testbed, we showed that the parameterized schedule effectively approximates model predictive control and requires drastically reduced computational overhead. In addition, we investigated the impact of different influencing factors on the optimal precooling strategy. These factors include building thermal mass, outdoor air conditions, and energy price profiles. Using high-performance computing, we simulated a total of 225 scenarios, consisting of three levels of thermal mass, five typical outdoor air temperature profiles, and fifteen time-of-use price plans. The results demonstrate that optimal thermostat scheduling could save substantial energy cost in medium-sized office buildings with heavy thermal mass but with some energy penalty. Although the potential for cost savings is lower in buildings with low and medium thermal mass, the energy penalty remains consistent in all three thermal mass scenarios. The study also highlights the need to account for zone diversity and recognize that a one-size-fits-all-zone setpoint schedule may not be suitable for all zones and can lead to unnecessary energy wastage. Furthermore, the results highlight that while outdoor air conditions play a role in cost and energy performance, the cooling load exerts a more immediate and substantial influence on cost savings in precooling strategies. Although cost savings are comparable under certain conditions with the same cooling load, observed deviations in energy penalty indicate potential disparities in the efficiency of the HVAC system during the load-shifting process. In addition, the duration of peak pricing and the ratio between peak and off-peak times exhibit clear correlations with cost savings and energy consumption, aligning with intuitive expectations. These findings offer valuable insights for optimizing precooling strategies in office buildings.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

S3D: An interactive surface grid generation tool

S3D, an interactive software tool for surface grid generation, is described. S3D provides the means with which a geometry definition based either on a discretized curve set or a rectangular set can be quickly processed towards the generation of a surface grid for computational fluid dynamics (CFD) applications. This is made possible as a result of implementing commonly encountered surface gridding tasks in an environment with a highly efficient and user friendly graphical interface. Some of the more advanced features of S3D include surface-surface intersections, optimized surface domain decomposition and recomposition, and automated propagation of edge distributions to surrounding grids.

Luh, Raymond Ching-Chung↗

An Empirical Validation of a Constrained Bin Packing Algorithm for a Home Energy Management System

The increasing number of intelligent electrical appliances and home energy management systems provide a big opportunity for demand response services from residential and small commercial buildings to the grid. Simultaneously, direct control of individual devices by utilities can cause communication bottlenecks, as well as coordination and privacy concerns. These challenges can be addressed by combining the constituent devices into a single house battery equivalent for the purposes of demand response, using Minkowski sum and a 2d bin packing problem. However, the well-studied traditional problems have not been tested in a real house, as implementation carries significant challenges of its own. We deploy the packing problem on residential devices in a controllable house. We report the barriers we found, such as charge forecast and scalability of the algorithm, and discuss our solutions. The study serves as an intermediate step between existing theoretical research and possible future steps, such as prototype deployments of systems that provide residential demand response.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Overview of Sensitivity Analysis and Shape Optimization for Complex Aerodynamic Configurations

This paper presents a brief overview of some of the more recent advances in steady aerodynamic shape-design sensitivity analysis and optimization, based on advanced computational fluid dynamics (CFD). The focus here is on those methods particularly well-suited to the study of geometrically complex configurations and their potentially complex associated flow physics. When nonlinear state equations are considered in the optimization process, difficulties are found in the application of sensitivity analysis. Some techniques for circumventing such difficulties are currently being explored and are included here. Attention is directed to methods that utilize automatic differentiation to obtain aerodynamic sensitivity derivatives for both complex configurations and complex flow physics. Various examples of shape-design sensitivity analysis for unstructured-grid CFD algorithms are demonstrated for different formulations of the sensitivity equations. Finally, the use of advanced, unstructured-grid CFDs in multidisciplinary analyses and multidisciplinary sensitivity analyses within future optimization processes is recommended and encouraged.

Newman, James C., III↗

Influence of structural and aerodynamic modeling on optimization with flutter constraint

The influences of structural and aerodynamic modeling on multidisciplinary optimization in an aeroelastic environment are not well understood. Therefore, optimizations with flutter and frequency constraints were performed to investigate the effects these modeling factors have on various representative wings. To this end, the Automated Structural Optimization System (ASTROS) was used as a tool to minimize the weight of various fully built-up finite element wing models in subsonic and supersonic flow under given flutter and frequency constraints. First, the performance of the optimization module was tested against results from other codes on a straight and uniform wing widely used for optimization with flutter constraints. Then, fully built-up finite element models of various wings with different aspect ratios were investigated for the influence on the structural optimization for minimum weight of the following modeling factors: finite element selection, structural grid refinement; number of selected modes, retention of breathing modes; selection of reduced frequencies to be used in flutter analysis; aerodynamic panel size and placement; splining of the aerodynamic grid to the structural grid selection of extra points of the structural wing box for splining; and number of constraints to be retained. Knowledge of these influences as well as of the program behavior is important, since optimization can be made more efficient by the selection of reasonable initial models. Also, it was shown previously that modeling has an impact on the results of modal and aeroelastic analyses. Thus, if modeling errors can negatively affect the analyses, a minimum weight optimization can be jeopardized and result in an optimal design that is rather unreliable. In the following, selected results are presented and the influences of some modeling parameters on optimization are pointed out.

Striz, Alfred G.↗

An Examination of the Impact of Grid Spacing on WRF Simulations of Wintertime Precipitation in the Mid-Atlantic United States

A large set of deterministic and ensemble forecasts was produced to identify the optimal spacing for forecasting U.S. East Coast snowstorms. WRF forecasts were produced on cloud-allowing (~1-km grid spacing) and convection-allowing (3–4 km) grids, and compared against forecasts with parameterized convection (>~10 km). Performance diagrams were used to evaluate 19 deterministic forecasts from the winter of 2013–14. Ensemble forecasts of five disruptive snowstorms spanning the years 2015–18 were evaluated using various methods to evaluate probabilistic forecasts. While deterministic forecasts using cloud-allowing grids were not better than convection-allowing forecasts, both had lower bias and higher success ratios than forecasts with parameterized convection. All forecasts were underdispersive. Nevertheless, forecasts on the higher-resolution grids were more reliable than those with parameterized convection. Forecasts on the cloud-allowing grid were best able to discriminate areas that received heavy snow and those that did not, while the forecasts with parameterized convection were least able to do so. It is recommended to use convection-resolving and (if computationally possible) to use cloud-allowing forecast grids when predicting East Coast winter storms.

Snowstorms↗

Navier-Stokes simulations of rotor-stator interaction using patched and overlaid grids

An accurate numerical analysis of the flows associated with rotor-stator configurations in turbomachinery can be very helpful in optimizing the performance of turbomachinery. In this study the unsteady, thin-layer, Navier-Stokes equations are solved using a system of patched and overlaid grids for a rotor-stator configuration of an axial turbine. The equations necessary for an accurate transfer of information between the several grids are briefly described within the framework of an iterative, implicit algorithm. Results in the form of Mach number contours, time-averaged pressures, unsteady pressures, amplitudes, and phase are presented. The numerical results are also compared with experimental data and the agreement is found to be good.

Rai, M. M.↗

Bayesian image reconstruction - The pixon and optimal image modeling

In this paper we describe the optimal image model, maximum residual likelihood method (OptMRL) for image reconstruction. OptMRL is a Bayesian image reconstruction technique for removing point-spread function blurring. OptMRL uses both a goodness-of-fit criterion (GOF) and an 'image prior', i.e., a function which quantifies the a priori probability of the image. Unlike standard maximum entropy methods, which typically reconstruct the image on the data pixel grid, OptMRL varies the image model in order to find the optimal functional basis with which to represent the image. We show how an optimal basis for image representation can be selected and in doing so, develop the concept of the 'pixon' which is a generalized image cell from which this basis is constructed. By allowing both the image and the image representation to be variable, the OptMRL method greatly increases the volume of solution space over which the image is optimized. Hence the likelihood of the final reconstructed image is greatly increased. For the goodness-of-fit criterion, OptMRL uses the maximum residual likelihood probability distribution introduced previously by Pina and Puetter (1992). This GOF probability distribution, which is based on the spatial autocorrelation of the residuals, has the advantage that it ensures spatially uncorrelated image reconstruction residuals.

Pina, R. K.↗

Building a standardized Observing System Simulation Experiment (OSSE) framework for Mars

We advocate that the Decadal Survey recommends the NASA Science Mission Directorate to develop a rigorous Observing System Simulation Experiment (OSSE) framework for Mars, to optimize future atmospheric observations. Atmospheric conditions on Mars are a potential hazard source for landing missions. Errors in the estimates of atmospheric density profiles, inadequate knowledge of wind vertical structure and dust concentration as a function of height are likely causes of uncertainty at the landing site on the order of kilometers. An operational real-time weather forecasting capability for Mars would reduce such uncertainties, carrying enormous benefits to future robotic missions, and would be an invaluable prerequisite for human missions.A real-time forecasting capability relies upon three fundamental components: a critical mass of observing systems, a data assimilation system (DAS), and a global forecast model. The DAS allows the model to ingest the data effectively, optimizing the observational information content,and transforming them into a gridded representation of the atmosphere at a given time, called an ‘analysis’. The analysis is the best estimate of the atmospheric state for that time, and also represents a set of ‘initial conditions’ from which a global model can be initialized, to predict a future state of the atmosphere. The connection between analysis and forecast represents the foundation of modern weather forecasting. However, from the point of view of a forecast system,not all observations are equally impactful, partially because of the problem of “observational error correlation”, one important research topic in data assimilation development. For the Earth, partly due to the spontaneous and deregulated development of observations and forecast capabilities worldwide for more than half a century,the use of observations in contemporary operational forecast systems is suboptimal, with many potentially useful data being underutilized. On the contrary, Mars atmospheric scientists are in the unique situation of designing the next-generation observing systems by learning from the experience gathered on the Earth, so as to assure that the future instruments are specifically optimized to give the maximum benefit to a future weather forecast capability.An immensely powerful tool that has been firmly established by atmospheric scientists on the Earth is represented by a properly designed OSSE framework. A realistic OSSE framework cannot only quantify the benefit of future data types, be them surface based or space borne, but can also help design and optimize an entire observational network. Furthermore, OSSEs can provide deep insights into an atmosphere’s behavior, by addressing conceptual problems of its intrinsic predictability and delineating the regions or features of the atmosphere which are more sensitive to additional data and would benefit from a denser sampling. The difficulties posed by OSSEs are fundamentally different for Earth and Mars. For Earth, the enormous data volume imposes a tremendous constraint on any innovation in the observing systems: it is very hard for a single sensor to impact the skill. For Mars, the problem is the opposite: almost any additional instrument will exert some impact. However, OSSEs can help to evaluate the cost/benefit for every sensor and suggest optimal data configuration and density.The purpose of this white paper is to provide an introduction to a rigorously designed OSSE framework, explain the underlying problems and challenges, and engage the Mars community to collaborate with Earth Atmospheric scientists in order to develop a joint-OSSE framework for Mars with the largest consensual basis possible. An OSSE infrastructure would increase the understanding of the Martian atmosphere, would help NASA to optimize instrument specifications and orbit choice, providing the maximium benefit for a given expenditure of resources, and could even help establishing a roadmap for a future real-time weather forecasting capability.

Oreste Reale↗

Acoustic analysis using numerical solutions of the Navier-Stokes equations

Numerical solutions of the time-dependent compressible Navier-Stokes equations are employed to analyze the unsteady features of jet flows which contribute to jet noise. The turbulent-mass flux spectra are examined in detail in the numerical analysis, and MacCormack's explicit finite difference algorithm is used to solve the governing equations. The computational grid is based on an axisymmetric jet with simple exponential stretching used to optimize the resolution of critical unsteady flow features. The time-varying numerical data are analyzed, and the time averages of the velocity and turbulence-intensity profiles are shown to agree with experimental data. Grid refinement and longer run times improved the prediction of the experimental mass-flux spectra. The numerical procedure can be extended to 3D jet-flow configurations to study the related 3D unsteady flow features.

Scott, James N.↗

Alternating Direction Decomposition with Strong Bounding and Convexification (ADDSBC) for Solving Security Constrained AC Unit Commitment Problems

This project aims to develop efficient and robust computational methods for solving the security-constrained unit commitment and alternating current optimal power flow problem (SC-UC-ACOPF). The SC-UC-ACOPF problem is at the center of the short-term operation of the U.S. Power Grid. It is solved every week, every day, and every 10 minutes to plan for the optimal action of electricity generation and consumption by minimizing the generation cost and maintaining power system reliability against potential disruptions of equipment failures. In mathematical terms, SC-UC-ACOPF is a challenging large-scale mixed-integer nonlinear optimization model. This means that the decisions involve both discrete variables, e.g. the turning on and off of generators and switching of transmission lines and transformers, and continuous decisions, e.g. the amount of energy generated by each generator and the power flows in the power grid. The physics of the power flow is described by nonlinear equations involving real and reactive power and bus voltages. Another key feature is the large number of contingencies, i.e. the system needs to stay reliable in face of failure of any one equipment, such as transmission lines and generators. The U.S. power grids are extremely complicated and large scale with more than 5,000 generators, 50,000 buses, and 100,000 high-voltage transmission lines, making the SC-UC-ACOPF a very large-scale computation challenge. The research developed in this project aims to solve the SC-UC-ACOPF problems in the three timescales, i.e. weekly, daily, and every 10-min. The proposed computational methods are built on a principled algorithmic approach of decomposition and penalization. More specifically, the algorithm develops spatial and temporal decomposition by exploiting the strong temporal coupling and weak spatial coupling of the UC problem and the complementary feature, i.e. weak temporal coupling and strong spatial coupling of the ACOPF problem. The algorithm also leverages recent progresses in strong convex relaxation of ACOPF. A unique feature of the proposed approach is that it generates a valid, global upper bound on the optimal maximum profit. In this way, a global optimality gap is available to measure the quality of the solution. To further speed up computation, the research team has developed a plethora of effective heuristics to strengthen the iterative penalty-based decomposition framework. For instance, a heuristic is developed to construct inner approximations of the time coupling constraints within the time decoupled problems. Contingencies are pre-screened and low-rank matrix computation is exploited to find the almost unique solution to each contingency. A novel heuristic for line switching is proposed and tested with positive impacts on instances where line switching is beneficial. Taking a systematic approach and carefully handling every detail of the problem pays off. The TIM-GO’s performance throughout the trials and the final event was stellar. TIM-GO garnered the second highest total prize money and is ranked in the top three positions across all categories of comparison.

97 MATHEMATICS AND COMPUTING↗

CHARGE-MAP: An integrated framework to study the multicriteria EV charging infrastructure expansion problem

The widespread adoption of electric vehicles (EVs) in recent years has necessitated the development of effective charging infrastructures. However, charging infrastructure expansion is a multifaceted problem that requires careful consideration of the existing infrastructure, spatiotemporal distribution of charging demands, power-grid capacity, and budget constraints. Here, to approach this complex problem, we present CHARGE-MAP, a data-driven simulation-optimization framework, focused on ensuring meaningful charging experience for individual EV owners. CHARGE-MAP integrates three modules: an agent-based simulation module that estimates spatiotemporal distribution of charging demands by modeling EV adopter mobility and charging behavior; an optimization module that determines optimal new charging station/charger locations and capacities, while minimizing expected detour distances and wait-times with a limited number of new stations; and a power module that determines how to connect the stations to the power grid while maintaining its stability. Using the state of Virginia (consisting of 95 counties and 38 independent cities) as a case study, our results show that CHARGE-MAP can meet the demand of ~198,600 predicted EVs with 1,305 new public charging stations and 2,164 new chargers. It reduces average detour distances for charging by 66% and wait-times at stations by 72% compared to the existing infrastructure. Furthermore, transformer capacity requirement analysis reveals that only 1.8% of residential transformers require upgrades, while over 80% of commercial charging locations can be supported with modest transformer infrastructure (25 to 50 kVA). This indicates that targeted investments can facilitate cost-effective EV integration. Consequently, CHARGE-MAP provides policymakers and urban planners with crucial data-driven insights for effective EV charging infrastructure expansion. Sign up for PNAS alerts.

charging infrastructure↗

Faster solutions to the interdiction defense problem using suboptimal solutions

The interdiction defense (ID) problem solves a defender-attacker-defender model where the defender and attacker share the same set of components to harden and target. Here, we build upon the best response intersection (BRI) algorithm by developing the BRI with suboptimal solutions (BRI-SS) algorithm to solve the ID problem. The BRI-SS algorithm utilizes off-the-shelf optimization solvers that return suboptimal solutions at no additional computation cost. We derive novel cuts from suboptimal solutions, reducing the number of iterations required for the algorithm to converge while maintaining optimality guarantees. We also present a heuristic that utilizes all obtained suboptimal solutions to select the next defense to evaluate at each iteration. We perform computational experiments applied to power grid interdiction on standard test cases. Our results demonstrate that the BRI-SS algorithm consistently outperforms the BRI algorithm across all test cases.

Computer science↗