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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 487 records · Page 27

AI-Based Analytics and Energy Modeling Framework for Characterizing Urban Energy Systems

Developing location-specific district energy models is essential for understanding energy patterns and supporting efficient management and planning decisions. However, accurately characterizing these models remains challenging due to gaps in building characteristics and labor-intensive traditional modeling workflows. To address these challenges, we develop an AI-based framework that integrates top-down and bottom-up building energy data to automate urban energy model characterization. The framework trains multimodal deep learning models using heterogeneous ResStockTM datasets to infer missing building characteristics from varying levels of known information and generate simulation-ready inputs for district-scale energy modeling. It also employs a conditioning-based injection approach to generate ”what-if” scenarios, enabling users to explore retrofit, efficiency, and technology-upgrade pathways. Integrated within URBANoptTM, a bottom-up district energy modeling platform for simulating co-located buildings, the framework infers detailed building-level inputs required for bottom-up simulations. Both localized and generalized AI models are developed to learn relationships across categorical, numerical, and time-series data, enabling reconstruction of missing attributes and generation of targeted upgrade scenarios. We demonstrate this methodology on a residential neighborhood in Baltimore, MD, assessing internal consistency against ResStock reference data and URBANopt simulation, and comparing selected attributes against real-world building characteristics. Results show strong overall predictive accuracy in data completion and scenario generation, with localized and generalized models offering complementary trade-offs between precision and scalability. Overall, our automated framework streamlines energy modeling and provides a reliable framework for urban building energy characterization.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Behavior of composite bolted joints at elevated temperature

Experimental results from an investigation which examines the combined effects of temperature, joint geometry and out-of-plane constraint upon the response of mechanically fastened composite joints are presented. Data are presented for simulated mechanically fastened joint conditions in two laminate configurations fabricated from Hercules AS/3501-6 graphite-epoxy. Strength and failure mode results are presented for the test temperatures of 21 C, 121 C and 177 C and for a range of the geometric parameters W/D and e/D from 3.71 to 7.43 and 1.85 to 3.69, respectively. A hole diameter, D of 5.16 mm was utilized for all tests. Pin bearing tests with out-of-plane constraint were conducted at room temperature only. All elevated temperature data were generated for pin bearing conditions. Ultrasonic C scan inspection of the failed specimens was employed to assess the damage region and to determine failure mode. Comparative data are presented for pin bearing and out-of-plane constraint conditions for the above mentioned joint configurations. The joint under pin loading was modeled by two dimensional finite element methods. Predicted net section strain concentrations were compared with experimental results.

Wilson, D. W.↗

Guidance and control requirements for high-speed Rollout and Turnoff (ROTO)

This report defines the initial requirements for designing a research high-speed rollout and turnoff (ROTO) guidance and control system applicable to transport class aircraft whose purpose is to reduce the average runway occupancy time (ROT) for aircraft operations. The requirements will be used to develop a ROTO system for both automatic and manual piloted operation under normal and reduced visibility conditions. Requirements were determined for nose wheel/rudder steering, braking/reverse thrust, and the navigation system with the aid of a non-real time, three degree-of-freedom MD-11 simulation program incorporating airframe and gear dynamics. The requirements were developed for speeds up to 70 knots using 30 ft exit geometries under dry and wet surface conditions. The requirements were generated under the assumptions that the aircraft landing system meets the current Category III touchdown dispersion requirements and that aircraft interarrival spacing is 2 nautical miles. This effort determined that auto-asymmetric braking is needed to assist steering for aft center-of-gravity aircraft. This report shows various time-history plots of the aircraft performance for the ROTO operation. This effort also investigated the state-of-the-art in the measurement of the runway coefficient of friction for various runway conditions.

Goldthorpe, Steve H.↗

Exhausted Plume Flow Field Prediction Near the Afterbody of Hypersonic Flight Vehicles in High Altitudes

A two-dimensional computer code to solve the Burnett equations has been developed which computes the flow interaction between an exhausted plume and hypersonic external flow near the afterbody of a flight vehicle. This Burnett-2D code extends the capability of Navier-Stokes solver (RPLUS2D code) to include high-order Burnett source terms and slip-wall conditions for velocity and temperature. Higher-order Burnett viscous stress and heat flux terms are discretized using central-differencing and treated as source terms. Blocking logic is adopted in order to overcome the difficulty of grid generation. The computation of exhaust plume flow field is divided into two steps. In the first step, the thruster nozzle exit conditions are computed which generates inflow conditions in the base area near the afterbody. Results demonstrated that at high altitudes, the computations of nozzle exit conditions must include the effects of base flow since significant expansion exists in the base region. In the second step, Burnett equations were solved for exhaust plume flow field near the afterbody. The free stream conditions are set at an altitude equal to 80km and the Mach number is equal to 5.0. The preliminary results show that the plume expansion, as altitude increases, will eventually cause upstream flow separation.

Chou, Lynn Chen↗

New High-Temperature Turbine Seal Rig Fabricated

Current NASA program goals for aircraft engines and vehicle performance include reducing direct operating costs for commercial aircraft by 3 percent in large engines and 5 percent in regional engines, reducing engine fuel burn up to 10 percent, and reducing engine oxides of nitrogen emissions by more than 50 percent. Significant advancements in current gas turbine engines and engine components, such as seals, are required to meet these goals. Specifically, advanced seals have been identified as critical in meeting engine goals for specific fuel consumption, thrust-to-weight ratio, emissions, durability, and operating costs. In a direct effort to address and make progress toward these goals, researchers at the NASA Glenn Research Center at Lewis Field have developed a unique high-temperature, high-speed engine seal test rig to evaluate seals under the temperature, speed, and pressure conditions anticipated for next generation turbine engines. This new seal test rig has capabilities beyond those of any existing seal rigs. It can test air seals (i.e., labyrinth, brush, and new seal concepts) at temperatures of up to 1500 F and pressures up to 100 psid (even higher pressures are possible at lower temperatures), and at all surface speeds anticipated in future NASA (Ultra Efficient Engine Technology, UEET, and Integrated High-Performance Turbine Engine Technology, IHPTET) engine programs. In addition, seals can be tested offset from the rotor centerline, in the rotor runout condition, and with simulated mission profiles. Support for this new rig was provided by NASA Glenn, the U.S. Air Force, and the U.S. Army.

Delgado, Irebert R.↗

Hall Magnetohydrodynamic Power Generation and Drag Augmentation Using A Coaxial-Electrode Configuration During Hypersonic Entry

For interplanetary missions, a spacecraft must reduce its relative velocity from orbital speeds of multiple kilometers per second to zero in order to safely land on the surface of a planetary body. During this phase known as planetary reentry, the spacecraft undergoes high speed above Mach 5 up to Mach 30. This hyper-sonic flight regime imposes a strong bow shock in front of the vehicle that imparts extreme aerodynamic and thermal effects. In addition, during portions of this regime, a plasma is formed in the post-shock flow-field around the vehicle due to these high temperatures. Interaction between an applied magnetic field with this electrically conductive fluid, or magnetohydrodynamic (MHD) interaction, can be utilized to convert kinetic energy from the flow into storable electrical energy. Onboard MHD energy generation can benefit the spacecraft by increasing the power of active thermal control components and vehicle control systems during reentry. MHD interaction also exerts a Lorentz body force on the plasma flow that can be manipulated to act as an additional drag force through the vehicle body. MHD drag augmentation can benefit the spacecraft with an additional control mechanism that operates without moving parts. This can be utilized at higher altitudes and subsequently reduce convective heat transfer to the vehicle. MHD interaction with plasma flow suggests that both power generation and drag augmentation can be integrated together in one design. Modern numerical studies have only demonstrated the viability and potential of MHD energy generation and drag modulation separately for implementation into future spacecraft designs [1] [2] [3]. Steeves et. al. presented one possible generator design specifically for reentry vehicles that utilized a modular panel with two embedded electromagnets and two extruding electrodes for air plasma to flow between. Fujino et. al. presented results that indicated increased total drag with a permanent magnet embedded in the blunt body of the Orbital Reentry Experiment (OREX) trajectory. Furthermore, experimental investigations of these two MHD applications have been limited and separate due to the difficult technical nature of experimental de-sign and analysis. For MHD energy generation, there have been two designs which used a cylindrical fore-body with two embedded permanent magnets and two outward facing curved electrodes for tangency to an artificially ionized plasma that flowed along the body length [4] [5]. The first design was studied using an air microwave (MW) ionized supersonic plasma wind tunnel and the second design used radio frequency (RF) ionization of Argon, but both physically demonstrated the feasibility of MHD energy generation in reentry plasma conditions. For MHD drag modulation, one study involved a small-scale cylindrical blunt body embedded with permanent magnets immersed in plasma flow in an arcjet tunnel [6], and another utilized a spherical permanent magnet enclosed with a spherical forebody that was evaluated in a shock expansion tunnel [7]. Both experimental studies provided physical evidence of drag augmentation due to MHD interactions. Therefore, because of the multi-faceted effects of MHD along with both applications having been deemed feasible and beneficial during reentry, this indicates that a coupled power generation and drag modulation design could be achievable. The axi-symmetric nature of blunt bodies for reentry suggests that a spherical set of two ring electrodes near the nose along the body axis. Based on first principles, flow along the walls of the spherical body can then produce MHD interactions between the electrodes. As a result, two currents are generated: a Hall current that produces power and a primary inductive current that augments the drag force. The goal of this work is to provide a simulated design of a coaxial-electrode con-figuration for power generation and drag modulation for experimental testing.

E. Leong↗

Project Fog Drops. Part 2: Laboratory investigations

Measurements of the total nucleus concentration and cloud condensation nuclei (CCN) were acquired for several conditions representing both high normal and severe pollution levels for the Los Angeles Basin as well as clean filtered air. The data show that in filtered air there is a large photochemically induced increase in the total particle content within a few minutes after starting the lamp. The concentration of CCN remains near zero, until sufficient coagulation and condensation occurs on the smaller Aitken particles. The addition of gaseous pollutants to filtered air results in large increases in the photochemical production of both the cloud and Aitken nucleus concentration. Fogs were also generated under controlled, reproducible conditions in the cloud chamber and seeded with aerosols of various compounds which form monomolecular surface films at air-water interfaces. Visibility characteristics and droplet data were obtained. The data suggest that droplet growth on treated nuclei can be retarded but fog formation was not significantly altered by the chemical seeding.

Kocmond, W. C.↗

Laboratory Shock Experiments on Basalt - Iron Sulfate Mixes at Approximately 40-50 GPa and Their Relevance to the Martian Regolith Component Present in Shergottites

Basaltic shergottites such as Shergotty, Zagami and EET79001 contain impact melt glass pockets that are rich in Martian atmospheric gases [1] and are known as gas-rich impact-melt (GRIM) glasses. These glasses show evidence for the presence of a Martian regolith component based on Sm and Kr isotopic studies [2]. The GRIM glasses are sometimes embedded with clusters of innumerable micron-sized iron-sulfide blebs associated with minor amounts of iron sulfate particles [3, 4]. These sulfide blebs are secondary in origin and are not related to the primary igneous sulfides occurring in Martian meteorites. The material comprising these glasses arises from the highly oxidizing Martian surface and sulfur is unlikely to occur as sulfide in the Martian regoilith. Instead, sulfur is shown to occur as sulfate based on APXS and Mossbauer results obtained by the Opportunity and Spirit rovers at Meridiani and Gusev [5]. We have earlier suggested that the micron-sized iron sulfide globules in GRIM glasses were likely produced by shock-reduction of iron sulfate occurring in the regolith at the time when the GRIM glasses were produced by the meteoroid impact that launched the Martian meteorites into space [6]. As a result of high energy deposition by shock (approx. 40-60 GPa), the iron sulfate bearing phases are likely to melt along with other regolith components and will get reduced to immiscible sulfide fluid under reducing conditions. On quenching, this generates a dispersion of micron-scale sulfide blebs. The reducing agents in our case are likely to be H2 and CO which were shock-implanted from the Martian atmosphere into these glasses along with the noble gases. We conducted lab simulation experiments in the Lindhurst Laboratory of Experimental Geophysics at Caltech and the Experimental Impact Laboratory at JSC to test whether iron sulfide globules can be produced by impact-driven reduction of iron sulfate by subjecting Columbia River Basalt (CRB) and ferric sulfate mixtures to shock pressures between 40 and 50 GPa under reducing conditions. The experimental products from the recovered samples were analyzed by SEM and microprobe techniques at JSC.

Rao, M. N.↗

Dynamics of magnetosphere-ionosphere coupling including turbulent transport

The dynamics of magnetosphere-ionosphere coupling has been investigated by means of a two-dimensional two-fluid MHD model including anomalous resistivity. When field-aligned current is generated on auroral field lines, the disturbance propagates toward the ionosphere in the form of a kinetic Alfven wave. When the current exceeds a critical value, microscopic turbulence is produced, which modifies the propagation of the Alfven wave. This process is modeled by a nonlinear collision frequency, which increases with the excess of the drift velocity over the critical value. The system evolves toward an electrostatic structure, with the perpendicular electric field having a shorter scale than the field-aligned current. The approach to a steady state is strongly dependent on the presence or absence of the turbulence and on the boundary conditions imposed in the generator. As current is increased or scale size is decreased, the turbulent region reflects and absorbs most of the Alfven wave energy, decoupling the generator from the ionosphere.

Lysak, R. L.↗

Skin microvascular flow during hypobaric exposure with and without a mechanical counter-pressure space suit glove

INTRODUCTION: Current space suits are rigid, gas-pressurized shells that protect astronauts from the vacuum of space. A tight elastic garment or mechanical-counter-pressure (MCP) suit generates pressure by compression and may have several advantages over current space suit technology. In this study, we investigated local microcirculatory effects produced with and without a prototype MCP glove. METHODS: The right hand of eight normal volunteers was studied at normal ambient pressure and during exposure to -50, -100 and -150 mm Hg with and without the MCP glove. Measurements included the pressure against the hand, skin microvascular flow, temperature on the dorsum of the hand, and middle finger girth. RESULTS: Without the glove, skin microvascular flow and finger girth significantly increased with negative pressure, and the skin temperature decreased compared with the control condition. The MCP glove generated approximately 200 mm Hg at the skin surface; all measured values remained at control levels during exposure to negative pressure. DISCUSSION: Without the glove, skin microvascular flow and finger girth increased with negative pressure, probably due to a blood shift toward the hand. The elastic compression of the material of the MCP glove generated pressure on the hand similar to that in current gas-pressurized space suit gloves. The MCP glove prevented the apparent blood shift and thus maintained baseline values of the measured variables despite exposure of the hand to negative pressure.

NASA Discipline Cardiopulmonary↗

Drawbar Pull (DP) Procedures for Off-Road Vehicle Testing

As NASA strives to explore the surface of the Moon and Mars, there is a continued need for improved tire and vehicle development. When tires or vehicles are being designed for off-road conditions where significant thrust generation is required, such as climbing out of craters on the Moon, it is important to use a standard test method for evaluating their tractive performance. The drawbar pull (DP) test is a way of measuring the net thrust generated by tires or a vehicle with respect to performance metrics such as travel reduction, sinkage, or power efficiency. DP testing may be done using a single tire on a traction rig, or with a set of tires on a vehicle; this report focuses on vehicle DP tests. Though vehicle DP tests have been used for decades, there are no standard procedures that apply to exploration vehicles. This report summarizes previous methods employed, shows the sensitivity of certain test parameters, and provides a body of knowledge for developing standard testing procedures. The focus of this work is on lunar applications, but these test methods can be applied to terrestrial and planetary conditions as well. Section 1.0 of this report discusses the utility of DP testing for off-road vehicle evaluation and the metrics used. Section 2.0 focuses on test-terrain preparation, using the example case of lunar terrain. There is a review of lunar terrain analogs implemented in the past and a discussion on the lunar terrain conditions created at the NASA Glenn Research Center, including methods of evaluating the terrain strength variation and consistency from test to test. Section 3.0 provides details of the vehicle test procedures. These consist of a review of past methods, a comprehensive study on the sensitivity of test parameters, and a summary of the procedures used for DP testing at Glenn.

wheel↗

Shuttle filter study. Volume 2: Contaminant generation and sensitivity studies

Contaminant generation studies were conducted at the component level using two different methods, radioactive tracer technique and gravimetric analysis test procedure. Both of these were reduced to practice during this program. In the first of these methods, radioactively tagged components typical of those used in spacecraft were studied to determine their contaminant generation characteristics under simulated operating conditions. Because the purpose of the work was: (1) to determine the types and quantities of contaminants generated; and (2) to evaluate improved monitoring and detection schemes, no attempt was made to evaluate or qualify specific components. The components used in this test program were therefore not flight hardware items. Some of them had been used in previous tests; some were obsolete; one was an experimental device. In addition to the component tests, various materials of interest to contaminant and filtration studies were irradiated and evaluated for use as autotracer materials. These included test dusts, plastics, valve seat materials, and bearing cage materials.

Source record↗

Electrochemical Hydrogen Peroxide Generator

Two-electron reduction of oxygen to produce hydrogen peroxide is a much researched topic. Most of the work has been done in the production of hydrogen peroxide in basic media, in order to address the needs of the pulp and paper industry. However, peroxides under alkaline conditions show poor stabilities and are not useful in disinfection applications. There is a need to design electrocatalysts that are stable and provide good current and energy efficiencies to produce hydrogen peroxide under acidic conditions. The innovation focuses on the in situ generation of hydrogen peroxide using an electrochemical cell having a gas diffusion electrode as the cathode (electrode connected to the negative pole of the power supply) and a platinized titanium anode. The cathode and anode compartments are separated by a readily available cation-exchange membrane (Nafion 117). The anode compartment is fed with deionized water. Generation of oxygen is the anode reaction. Protons from the anode compartment are transferred across the cation-exchange membrane to the cathode compartment by electrostatic attraction towards the negatively charged electrode. The cathode compartment is fed with oxygen. Here, hydrogen peroxide is generated by the reduction of oxygen. Water may also be generated in the cathode. A small amount of water is also transported across the membrane along with hydrated protons transported across the membrane. Generally, each proton is hydrated with 3-5 molecules. The process is unique because hydrogen peroxide is formed as a high-purity aqueous solution. Since there are no hazardous chemicals or liquids used in the process, the disinfection product can be applied directly to water, before entering a water filtration unit to disinfect the incoming water and to prevent the build up of heterotrophic bacteria, for example, in carbon based filters. The competitive advantages of this process are: 1. No consumable chemicals are needed in the process. The only raw materials needed are water and oxygen or air. 2. The product is pure and can therefore be used in disinfection applications directly or after proper dilution with water. 3. Oxygen generated in the anode compartment is used in the electrochemical reduction process; in addition, external oxygen is used to establish a high flow rate in the cathode compartment to remove the desired product efficiently. Exiting oxygen can be recycled after separation of liquid hydrogen peroxide product, if so desired. 4. The process can be designed for peroxide generation under microgravity conditions. 5. High concentrations of the order of 6-7 wt% can be generated by this method. This method at the time of this reporting is superior to what other researchers have reported. 6. The cell design allows for stacking of cells to increase the hydrogen peroxide production. 7. The catalyst mix containing a diquaternary ammonium compound enabled not only higher concentration of hydrogen peroxide but also higher current efficiency, improved energy efficiency, and catalyst stability. 8. The activity of the catalyst is maintained even after repeated periods of system shutdown. 9. The catalyst system can be extended for fuel-cell cathodes with suitable modifications.

Tennakoon, Charles L. K.↗

Learning and discovering multiple solutions using physics-informed neural networks with random initialization and deep ensemble

In this work we explore the capability of physics-informed neural networks (PINNs) to discover multiple solutions. Many real-world phenomena governed by nonlinear differential equations (DEs), such as fluid flow, exhibit multiple solutions under the same conditions, yet capturing this solution multiplicity remains a significant challenge. A key difficulty lies in providing appropriate initial conditions or guesses, as widely used time-marching schemes and Newton’s method are highly sensitive to these choices when solving complex computational problems. While machine learning models, particularly PINNs, have shown promise in solving DEs, their ability to capture multiple solutions remains underexplored. In this work, we propose a simple and practical approach using PINNs to learn and discover multiple solutions. We first demonstrate that PINNs, when combined with random initialization and deep ensemble method—originally developed for uncertainty quantification—can effectively uncover multiple solutions to nonlinear ordinary and partial DEs. Although training large ensembles of PINNs may appear computationally demanding, this can be done efficiently using vectorization techniques supported by modern deep learning frameworks, allowing many networks to be trained simultaneously. Our approach highlights the critical role of initialization in shaping solution diversity, addressing an often-overlooked aspect of machine learning for scientific computing. Furthermore, we propose utilizing PINN-generated solutions as initial conditions or initial guesses for conventional numerical solvers to enhance accuracy and efficiency in capturing multiple solutions. Extensive numerical experiments, including the Allen–Cahn equation and cavity flow, where our approach successfully identifies both stable and unstable solutions, validate the effectiveness of our method. These findings establish a general and efficient framework for addressing solution multiplicity in nonlinear DEs.

97 MATHEMATICS AND COMPUTING↗

Stochastic Estimation and Non-Linear Wall-Pressure Sources in a Separating/Reattaching Flow

Simultaneous wall-pressure and PIV measurements are used to study the conditional flow field associated with surface-pressure generation in a separating/reattaching flow established over a fence-with-splitter-plate geometry. The conditional flow field is captured using linear and quadratic stochastic estimation based on the occurrence of positive and negative pressure events in the vicinity of the mean reattachment location. The results shed light on the dominant flow structures associated with significant wall-pressure generation. Furthermore, analysis based on the individual terms in the stochastic estimation expansion shows that both the linear and non-linear flow sources of the coherent (conditional) velocity field are equally important contributors to the generation of the conditional surface pressure.

Naguib, A.↗

Ionization and temperature measurements in warm dense copper using x-ray absorption spectroscopy

We detail experimental results inferring ionization and temperature for warm dense copper plasmas at several times solid density (15–25 g/cm 3 ) and temperatures of 10–21 eV. Experiments performed at the OMEGA Laser Facility generate uniform warm dense matter conditions via symmetric shock compression of a buried copper layer. The plasma is probed with a laser-generated x-ray source to collect the K-shell x-ray absorption spectrum. Fitting bound-bound absorption contributions from constituent charge states of copper provides an estimated $\overline{Z}$ of approximately 4–7 for these warm dense copper plasmas. We find that these partially ionized plasmas have K-edge shifts of 12–30 eV and bound-bound resonance 1s → 3p absorption shifts of 4–26 eV with respect to the cold K edge. This study provides necessary experimental data to improve ionization and opacity models in the warm dense matter regime.

42 ENGINEERING↗

Critical review of the trailing edge condition in steady and unsteady flow. Blade flutter in compressors and fans: Numerical simulation of the aerodynamic loading

Existing interpretations of the trailing edge condition, addressing both theoretical and experimental works in steady, as well as unsteady flows are critically reviewed. The work of Kutta and Joukowski on the trailing edge condition in steady flow is reviewed. It is shown that for most practical airfoils and blades (as in the case of most turbomachine blades), this condition is violated due to rounded trailing edges and high frequency effects, the flow dynamics in the trailing edge region being dominated by viscous forces; therefore, any meaningful modelling must include viscous effects. The question of to what extent the trailing edge condition affects acoustic radiation from the edge is raised; it is found that violation of the trailing edge condition leads to significant sound diffraction at the tailing edge, which is related to the problem of noise generation. Finally, various trailing edge conditions in unsteady flow are discussed, with emphasis on high reduced frequencies.

Radwan, S. F.↗

Model-Based Approaches to Generate Knowledge from Data in a Plant Reliability Context

One challenge that nuclear power plant system engineers are facing is continuous generation of an extremely large amount of equipment reliability (ER) data. These data elements come in textual (e.g., condition reports) and numeric (e.g., generated by monitoring systems) forms. They provide system engineers with valuable insights and information by discovering anomalous behaviors or degradation trends, identifying possible causes behind such behaviors and trends, and predicting their direct consequences. This paper directly targets the knowledge generation from ER data by putting “data into context.” We employ model-based system engineering (MBSE) of systems and assets to represent and capture their architecture and functional (i.e., cause-effect) relations. ER data elements are processed by first identifying which of the developed MBSE elements they are referring to. This task is harder for textual data since the information contained in issue or maintenance reports needs to be “understood” by a computational tool. We called this process “knowledge extraction” since our methods extract knowledge from textual data. Last, once numeric and textual ER data elements have been processed and “understood,” we discover possible cause-effect relations among them. This is performed by observing whether a logical connection through the MBSE models exists, and if there is a temporal relationship among them. The logic and temporal are the two main ingredients to perform “machine reasoning” from ER data.

97 - MATHEMATICS AND COMPUTING↗