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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS2011

Bayesian Software Health Management for Aircraft Guidance, Navigation, and Control

Modern aircraft, both piloted fly-by-wire commercial aircraft as well as UAVs, more and more depend on highly complex safety critical software systems with many sensors and computer-controlled actuators. Despite careful design and V&V of the software, severe incidents have happened due to malfunctioning software. In this paper, we discuss the use of Bayesian networks (BNs) to monitor the health of the on-board software and sensor system, and to perform advanced on-board diagnostic reasoning. We will focus on the approach to develop reliable and robust health models for the combined software and sensor systems.

Schumann, Johann↗
DOE OSTI2025

Automated and highly parallelized Bayesian optimization scheme for direct drive fusion experiments on OMEGA

Finding the optimal implosion design on existing experimental facilities for inertial confinement fusion requires an exhaustive search of the vast design parameter space. This is infeasible both with experiments and with simulations. Consequently, a large fraction of the experimentally realizable design space remains unexplored, and new design schemes are challenging to optimize in a reasonable time frame. On the OMEGA laser facility, predictive machine learning models have been developed to accurately forecast the result of an experiment using only inexpensive simulations and the large dataset of prior experimental data. However, the full design space remains vast enough to be unassailable with simple optimization techniques. Here we develop an automated and optimally parallel Bayesian optimization algorithm that can entirely optimize the target and pulse shape of a direct-drive ICF implosion under a given design paradigm. We use this algorithm to find a markedly improved design for the performance implosions on OMEGA that is predicted to hydroequivalently scale to ignition at 2.15 MJ.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2011

Towards Measurement of Confidence in Safety Cases

Arguments in safety cases are predominantly qualitative. This is partly attributed to the lack of sufficient design and operational data necessary to measure the achievement of high-dependability targets, particularly for safety-critical functions implemented in software. The subjective nature of many forms of evidence, such as expert judgment and process maturity, also contributes to the overwhelming dependence on qualitative arguments. However, where data for quantitative measurements is systematically collected, quantitative arguments provide far more benefits over qualitative arguments, in assessing confidence in the safety case. In this paper, we propose a basis for developing and evaluating integrated qualitative and quantitative safety arguments based on the Goal Structuring Notation (GSN) and Bayesian Networks (BN). The approach we propose identifies structures within GSN-based arguments where uncertainties can be quantified. BN are then used to provide a means to reason about confidence in a probabilistic way. We illustrate our approach using a fragment of a safety case for an unmanned aerial system and conclude with some preliminary observations

Denney, Ewen↗
NASA NTRS2015

R2U2: Monitoring and Diagnosis of Security Threats for Unmanned Aerial Systems

We present R2U2, a novel framework for runtime monitoring of security properties and diagnosing of security threats on-board Unmanned Aerial Systems (UAS). R2U2, implemented in FPGA hardware, is a real-time, REALIZABLE, RESPONSIVE, UNOBTRUSIVE Unit for security threat detection. R2U2 is designed to continuously monitor inputs from the GPS and the ground control station, sensor readings, actuator outputs, and flight software status. By simultaneously monitoring and performing statistical reasoning, attack patterns and post-attack discrepancies in the UAS behavior can be detected. R2U2 uses runtime observer pairs for linear and metric temporal logics for property monitoring and Bayesian networks for diagnosis of security threats. We discuss the design and implementation that now enables R2U2 to handle security threats and present simulation results of several attack scenarios on the NASA DragonEye UAS.

Formal Methods↗
NASA NTRS2009

A Method for Retrieving Ground Flash Fraction from Satellite Lightning Imager Data

A general theory for retrieving the fraction of ground flashes in N lightning observed by a satellite-based lightning imager is provided. An "exponential model" is applied as a physically reasonable constraint to describe the measured optical parameter distributions, and population statistics (i.e., mean, variance) are invoked to add additional constraints to the retrieval process. The retrieval itself is expressed in terms of a Bayesian inference, and the Maximum A Posteriori (MAP) solution is obtained. The approach is tested by performing simulated retrievals, and retrieval error statistics are provided. The ability to retrieve ground flash fraction has important benefits to the atmospheric chemistry community. For example, using the method to partition the existing satellite global lightning climatology into separate ground and cloud flash climatologies will improve estimates of lightning nitrogen oxides (NOx) production; this in turn will improve both regional air quality and global chemistry/climate model predictions.

Koshak, William J.↗
NASA NTRS1995

Learning In networks

Intelligent systems require software incorporating probabilistic reasoning, and often times learning. Networks provide a framework and methodology for creating this kind of software. This paper introduces network models based on chain graphs with deterministic nodes. Chain graphs are defined as a hierarchical combination of Bayesian and Markov networks. To model learning, plates on chain graphs are introduced to model independent samples. The paper concludes by discussing various operations that can be performed on chain graphs with plates as a simplification process or to generate learning algorithms.

Buntine, Wray L.↗
NASA NTRS2010

A Ground Flash Fraction Retrieval Algorithm for GLM

A Bayesian inversion method is introduced for retrieving the fraction of ground flashes in a set of N lightning observed by a satellite lightning imager (such as the Geostationary Lightning Mapper, GLM). An exponential model is applied as a physically reasonable constraint to describe the measured lightning optical parameter distributions. Population statistics (i.e., the mean and variance) are invoked to add additional constraints to the retrieval process. The Maximum A Posteriori (MAP) solution is employed. The approach is tested by performing simulated retrievals, and retrieval error statistics are provided. The approach is feasible for N greater than 2000, and retrieval errors decrease as N is increased.

Koshak, William J.↗
NASA NTRS1990

Probabilistic reasoning for intelligent wind shear avoidance

A computerized intelligent cockpit aid can increase flight-crew awareness of wind shear, improving avoidance decisions. The FAA Windshear Training Aid (WTA) provides guidelines for assessing the risk of wind shear encounter from meteorological evidence. Use of these guidelines in the cockpit is complicated by uncertainty surrounding meteorological knowledge of wind shear. Bayesian network representation is discussed as a means of modeling this uncertain knowledge in a computer. A probabilistic model of the WTA guidelines using Bayesian network representation is presented. This model combines evidence from sources of varying reliability and incorporates results from meteorological studies of wind shear. The probabilistic model can provide flight crews with meaningful estimates of risk to aid their decisions, using evidence from a variety of sources and a base of meteorological knowledge.

Stratton, D. Alexander↗
NASA NTRS2015

A Massively Parallel Bayesian Approach to Planetary Protection Trajectory Analysis and Design

The NASA Planetary Protection Office has levied a requirement that the upper stage of future planetary launches have a less than 10(exp -4) chance of impacting Mars within 50 years after launch. A brute-force approach requires a decade of computer time to demonstrate compliance. By using a Bayesian approach and taking advantage of the demonstrated reliability of the upper stage, the required number of fifty-year propagations can be massively reduced. By spreading the remaining embarrassingly parallel Monte Carlo simulations across multiple computers, compliance can be demonstrated in a reasonable time frame. The method used is described here.

parallel computing↗
NASA NTRS2008

Sensor Selection and Data Validation for Reliable Integrated System Health Management

For new access to space systems with challenging mission requirements, effective implementation of integrated system health management (ISHM) must be available early in the program to support the design of systems that are safe, reliable, highly autonomous. Early ISHM availability is also needed to promote design for affordable operations; increased knowledge of functional health provided by ISHM supports construction of more efficient operations infrastructure. Lack of early ISHM inclusion in the system design process could result in retrofitting health management systems to augment and expand operational and safety requirements; thereby increasing program cost and risk due to increased instrumentation and computational complexity. Having the right sensors generating the required data to perform condition assessment, such as fault detection and isolation, with a high degree of confidence is critical to reliable operation of ISHM. Also, the data being generated by the sensors needs to be qualified to ensure that the assessments made by the ISHM is not based on faulty data. NASA Glenn Research Center has been developing technologies for sensor selection and data validation as part of the FDDR (Fault Detection, Diagnosis, and Response) element of the Upper Stage project of the Ares 1 launch vehicle development. This presentation will provide an overview of the GRC approach to sensor selection and data quality validation and will present recent results from applications that are representative of the complexity of propulsion systems for access to space vehicles. A brief overview of the sensor selection and data quality validation approaches is provided below. The NASA GRC developed Systematic Sensor Selection Strategy (S4) is a model-based procedure for systematically and quantitatively selecting an optimal sensor suite to provide overall health assessment of a host system. S4 can be logically partitioned into three major subdivisions: the knowledge base, the down-select iteration, and the final selection analysis. The knowledge base required for productive use of S4 consists of system design information and heritage experience together with a focus on components with health implications. The sensor suite down-selection is an iterative process for identifying a group of sensors that provide good fault detection and isolation for targeted fault scenarios. In the final selection analysis, a statistical evaluation algorithm provides the final robustness test for each down-selected sensor suite. NASA GRC has developed an approach to sensor data qualification that applies empirical relationships, threshold detection techniques, and Bayesian belief theory to a network of sensors related by physics (i.e., analytical redundancy) in order to identify the failure of a given sensor within the network. This data quality validation approach extends the state-of-the-art, from red-lines and reasonableness checks that flag a sensor after it fails, to include analytical redundancy-based methods that can identify a sensor in the process of failing. The focus of this effort is on understanding the proper application of analytical redundancy-based data qualification methods for onboard use in monitoring Upper Stage sensors.

Garg, Sanjay↗
DOE OSTI2025

Propagating synthetic populations with dynamic Bayesian networks: a framework for long-horizon demographic forecasting

This study presents a dynamic demographic microsimulator using dynamic Bayesian networks to forecast long–term changes in household and individual life events. Leveraging longitudinal Panel Study of Income Dynamics (PSID) data, two networks for individuals and households were modeled to simulate transitions in employment, income, education, marriage, childbirth, leaving the parental home, home ownership, mortality, and household formation or dissolution. Across 1,000 simulation runs spanning 24 years, household–level outcomes remain highly accurate and individual–level predictions reasonable. Although accuracy naturally declines with projection horizon, performance remains promising at both levels. This study addresses a key limitation of existing population synthesis models, which typically generate only a single static snapshot of the population. In conclusion, by introducing a framework that propagates cross-sectional outputs into the future, the microsimulator enables the tracking of demographic evolution over time, enhances realism in population-based simulations, and supplies credible inputs to agent-based travel demand models.

Demographic modeling↗
DOE OSTI2025

Mechanistic within-host mathematical model of inhalational anthrax

We present a mathematical model of the dynamics of Bacillus anthracis bacteria within the lymph nodes and blood of a host, following inhalation of an initial dose of spores. We also incorporate the dynamics of protective antigen, which is the binding component of the anthrax toxin produced by the bacteria. The model offers a mechanistic description of the early infection dynamics of inhalational anthrax, while its stochastic nature allows us to study the probabilities of different outcomes (for example, how likely it is that the infection will be cleared for a given inhaled dose of spores) in order to explain dose-response data for inhalational anthrax. The model is calibrated via a Bayesian approach, using in vivo data from New Zealand white rabbit and guinea pig infection studies, enabling within-host parameters to be estimated. We also leverage incubation-period data from the Sverdlovsk 1979 anthrax outbreak to show that the model can accurately describe human time-to-symptoms data under reasonable parameter regimes. Finally, we derive a simple approximate formula for the probability of symptom onset before time t, assuming that the number of inhaled spores has a Poisson distribution.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS2019

Health Management and Prognostics for Electric Aircraft Powertrain

W and c Any air borne vehicle needs incorporating safety as key parameter of measure, and inclusion of autonomy raises the critical need for safety under autonomous operations. Management of faults and component degradation is key as complexity in autonomous operations grow over the period of time. Therefore, in addition to basic operational requirements, an autonomous electric vehicle should be able to make accurate estimates of its current system health and take the correct decisions to complete its mission successfully. Real-time safety and state-awareness tools are therefore essential for the vehicle to be able to reach its destination in a safe and successful manner. The need for safety assurance and health management capabilities is particularly relevant for aircraft electric propulsion systems, which are relatively new and with limited historical to learn. They are critical systems requiring high power density along with reliability, resilience, efficient management of weight, and operational costs. A model- based fault diagnosis and prognostics approach of complex critical systems can successfully accomplish the safety and state awareness goal for such electric propulsion systems, enabling autonomous decision making capability for safe and efficient operation. To identify critical components in the system a Qualitative Bayesian approach using FMECA is implemented. This requires the assessment of some quantities representing the state of the electric unmanned aerial systems (e-UAS), as well as look-ahead forecasts of such states during the entire flight, presented in form of safety metrics (SM). In-service data and performance data gathered from degraded components sup- ports diagnostic and prognostic methods for these systems, but this data can be difficult to obtain as weight and packaging restrictions reduce redundancy and instrumentation on-board the vehicle. Therefore, an model-based framework should be capable or operating with limited data. In addition to data scarcity, the variability of such complex critical systems re- quires the model-based framework to reason in the presence of uncertainty, such as sensor noise, and modeling imperfections. Quantification of errors and uncertainties in the measured states and quantities is therefore a fundamental step for a precise estimation of such SMs; un-modeled uncertainty may result in erroneous state assessment and un- reliable predictions of future states of e-UAVs. Typical, centralized model-based schemes suffer from inherent disadvantages such as computational complexity, single point of failure, and scalability issues, and therefore may fail in such a complex scenario. This paper presents a methodology for developing a system level diagnostics and prognostics approach using a Qualitative Bayesian FMECA approach along with a formal uncertainty management framework for an e-UAS. In this work we demonstrate the efficacy of the framework to predict effects of sub-system level degradation on vehicle operation incorporating uncertainty management to predict future behavior under different operating conditions.

Kulkarni, Chetan↗
DOE OSTI2025

Rapid Bayesian High Entropy Alloy Designs Fabricated via Wire Arc Additive Manufacturing

Purpose: This project seeks to demonstrate a new high-throughput (rapid) alloy design technique applied to creating new high entropy alloys (HEAs) for extreme environments. High entropy alloys shift the design paradigm from being focused on a single principal element (e.g. nickel-based alloys) to target alloys that include high atomic fractions (X >10%) of multiple elements. These HEA materials can exhibit sluggish diffusion and enhanced corrosion resistance, ideal for potential applications in advanced ultra supercritical (A-USC) steam cycles for power generation. Scope: The addition of multiple elements in high atomic fractions creates an enormous design space that cannot easily be investigated by traditional material design strategies such as designed of experiments (DOE). This project utilizes a Bayesian machine learning algorithm that has been modified to work with calculation of phase diagrams (CALPHAD) software. This Bayesian algorithm reduces manual inputs and increase the likelihood of achieving an optimal solution. Compositional inputs to this algorithm will be assessed using existing material property models for high temperature strength and corrosion resistance. The target for alloy performance will be a 15% (~100 ⁰C) increase in allowable service temperature beyond heat-resistant stainless steels while maintaining or improving alloy cost and corrosion resistance. Haynes 230 was selected as a baseline, which is 57 wt% Ni with 22 wt% Cr 14 wt% W, and 2 wt% Mo as solid solution strengtheners. In addition to rapid design via Bayesian machine learning, the alloys were rapidly fabricated using a multi-wire arc additive manufacturing (mWAAM) technique which allows for precise control of alloy composition and assessing of alloy design “windows” to study composition effects. Build speeds for wire-arc additive processes are among the highest for additive technologies enabling rapid and reliable sample fabrication when compared to conventional methods such as arc button melting. The mWAAM samples will be rapidly characterized via instrumented indentation for room temperature modulus and strength and for elevated temperature strength via hot hardness tests. After being screened with hardness testing, potential alloys will be further evaluated with conventional microscopy techniques including scanning electron microscopy (SEM) and transmission electron microscopy (TEM) to assess agreement with modeling results. The most promising compositions will also be evaluated by printing full sized tensile specimens for mechanical behavior tests at elevated temperatures. Results: Bayesian machine learning of a single performance function was initially used to optimize five performance metrics: 1) single phase stability, 2) yield strength, 3) creep resistance (low diffusion coefficient), 4) freezing range (weldability), and 5) material cost. The single performance function was suboptimal as assumptions had to be made about the results while formulating the optimization. A goal-oriented Bayesian optimization strategy (Hanaoka, 2021) was implemented with CALPHAD for use with the five metrics above. This multi-objective Bayesian optimization (MOBO) enabled the design of NiCrCoFe alloys with V and W additions. A base composition of NiCoCr was selected as Ni provides a stable FCC matrix, Cr aids corrosion/oxidation resistance, and Co is a solid-solutions strengthener that also improves creep by increasing the activation energy. Fe helps reduce diffusion coefficients and cost. Finally, V and W were selected for their reasonable solubility and high atomic misfit to aid in solid solution strengthening. Cracking of the mWAAM specimens was an early issue, and the Easton solidification cracking model (Easton et al., 2014a) was selected for addition to the MOBO function. High performing alloys fabricated by mWAAM included Ni 28 Cr 25 Co 26 Fe 15 V 8 and Ni 62 Cr 18 Co 1 Fe 3 W 15 . It was observed that even after adapting the mWAAM process for W, the W did not fully dissolve. To fully evaluate the Ni 62 Cr 18 Co 1 Fe 3 W 15 composition, a cored wire (80-20 NiCr sheath/powder core) was manufactured and printed via WAAM, and HIP’ing was utilized to homogenize and densify the printed alloy. The V and W alloys produced met metrics 1 (solid solution), 4 (solidification cracking), and 5 (cost). However, an unmodeled mechanism of thermal stress cracking was identified in the WAAM produced materials, perhaps exacerbated by the lack of grain boundary strengthening elements (B, C). Conclusions & Recommendations: A high-throughput (rapid) alloy design technique was applied to designing and manufacturing new high entropy alloys (HEAs) for extreme environments utilizing MOBO and mWAAM. The developed process was rapid and effective in addressing the mechanisms included in the model. The lack of grain boundary strengthening element additions (e.g., B, C) was a simplification that likely produced thermal stress cracking that turned into a large part of the investigation. Additions on the order of 0.005 wt% B and 0.05 wt% C likely would have minimized thermal stress grain boundary cracking. Overall, the high throughput design strategy is promising for rapid design of metrics-driven alloys for advanced ultra supercritical (A-USC) steam cycles for power generation. The MOBO and mWAAM process could be commercialized to accelerate metrics-driven alloy design. In addition, the cored-wire process utilized for scale-up is a promising high-volume process for WAAM alloy development and scale-up.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Boron Coordination in Multicomponent Glasses: Analytical Models and Machine Learning With Uncertainty

Borosilicate glasses are extensively used in a variety of applications from kitchenware to nuclear waste immobilization due to the strong network formed by the Si-O-B bond that makes it resistant to chemical corrosion and gives it a low thermal expansion. Boron, however, exists in both trigonal BO3 and tetrahedral BO4 bonds in glass systems, which impacts the chemical durability and thermal resistance of the glass, amongst other properties. Boron coordination (N4), or the ratio of the amount of BO4 to BO3 within a glass, may aid in predicting these properties but is difficult to derive without experimental data due to the complexity of impacts from varied glass compositions and processing factors. For this reason, compositional models have been developed to predict boron coordination, but the models typically include a limited number of glass components. To help fill this gap in the models, in this work, a diverse multicomponent glass dataset of 809 glasses is compiled from a literature search, and then a number of analytical and machine learning (ML) models are trained on the dataset. Previously developed modified Bernstein and modified Du Stebbins analytical models were fitted to update parameters with the new dataset. Then, partially Bayesian neural networks, Gaussian process regressor, and heteroskedastic deterministic neural networks were evaluated. The ML models examined all have different strategies to overcome the potential for overfitting as a result of a limited training dataset, and return results that account for model uncertainty, which can be valuable for understanding model reliability. For the first time, cooling rate is introduced as an input parameter for ML models, showing consistent improvements in performance and solidifying the importance of including parameters outside of composition alone for N4 prediction. The machine learning models examined here show promise in accurate predictions of boron coordination in borosilicate glasses, all achieving R2 values of 0.91.

boron coordination↗
NASA NTRS2017

R2U2: Tool Overview

R2U2 (Realizable, Responsive, Unobtrusive Unit) is an extensible framework for runtime System HealthManagement (SHM) of cyber-physical systems. R2U2 can be run in hardware (e.g., FPGAs), or software; can monitorhardware, software, or a combination of the two; and can analyze a range of different types of system requirementsduring runtime. An R2U2 requirement is specified utilizing a hierarchical combination of building blocks: temporal formula runtime observers (in LTL or MTL), Bayesian networks, sensor filters, and Boolean testers. Importantly, the framework is extensible; it is designed to enable definitions of new building blocks in combination with the core structure. Originally deployed on Unmanned Aerial Systems (UAS), R2U2 is designed to run on a wide range of embedded platforms, from autonomous systems like rovers, satellites, and robots, to human-assistive ground systems and cockpits. R2U2 is named after the requirements it satisfies; while the exact requirements vary by platform and mission, the ability to formally reason about realizability, responsiveness, and unobtrusiveness is necessary for flight certifiability, safety-critical system assurance, and achievement of technology readiness levels for target systems. Realizability ensures that R2U2 is suficiently expressive to encapsulate meaningful runtime requirements while maintaining adaptability to run on different platforms, transition between different mission stages, and update quickly between missions. Responsiveness entails continuously monitoring the system under test, real-time reasoning, reporting intermediate status, and as-early-as-possible requirements evaluations. Unobtrusiveness ensures compliance with the crucial properties of the target architecture: functionality, certifiability, timing, tolerances, cost, or other constraints.

Rozier, Kristin Y.↗
DOE OSTI2025

Sharp detection of low-dimensional structure in probability measures via dimensional logarithmic Sobolev inequalities

Identifying low-dimensional structure in high-dimensional probability measures is an essential pre-processing step for efficient sampling. To identify this structure, we approximate the target measure as a perturbation of an arbitrary reference measure along a few directions in $\mathbb{R}^{d}$. These directions are determined by minimizing an upper bound on the Kullback–Leibler (KL) divergence between the target and its approximation. Our contribution improves upon previous works by leveraging dimensional logarithmic Sobolev inequalities to refine the bound on the KL divergence. These inequalities lead to a uniformly tighter bound on the KL divergence, thereby enhancing the identification of the most significant perturbation directions. In particular, when the target and reference are both Gaussian, minimizing the resulting bound is equivalent to minimizing the KL divergence. We further demonstrate the applicability of this analysis to the squared Hellinger distance, where analogous reasoning shows that the dimensional Poincaré inequality offers improved bounds.

Bayesian inference↗
NASA NTRS2002

Hierarchies of Models: Toward Understanding Planetary Nebulae

Stars like our sun (initial masses between 0.8 to 8 solar masses) end their lives as swollen red giants surrounded by cool extended atmospheres. The nuclear reactions in their cores create carbon, nitrogen and oxygen, which are transported by convection to the outer envelope of the stellar atmosphere. As the star finally collapses to become a white dwarf, this envelope is expelled from the star to form a planetary nebula (PN) rich in organic molecules. The physics, dynamics, and chemistry of these nebulae are poorly understood and have implications not only for our understanding of the stellar life cycle but also for organic astrochemistry and the creation of prebiotic molecules in interstellar space. We are working toward generating three-dimensional models of planetary nebulae (PNe), which include the size, orientation, shape, expansion rate and mass distribution of the nebula. Such a reconstruction of a PN is a challenging problem for several reasons. First, the data consist of images obtained over time from the Hubble Space Telescope (HST) and spectra obtained from Kitt Peak National Observatory (KPNO) and Cerro Tololo Inter-American Observatory (CTIO). These images are of course taken from a single viewpoint in space, which amounts to a very challenging tomographic reconstruction. Second, the fact that we have two disparate and orthogonal data types requires that we utilize a method that allows these data to be used together to obtain a solution. To address these first two challenges we employ Bayesian model estimation using a parameterized physical model that incorporates much prior information about the known physics of the PN. In our previous works we have found that the forward problem of the comprehensive model is extremely time consuming. To address this challenge, we explore the use of a set of hierarchical models, which allow us to estimate increasingly more detailed sets of model parameters. These hierarchical models of increasing complexity are akin to scientific theories of increasing sophistication, with each new model/theory being a refinement of a previous one by either incorporating additional prior information or by introducing a new set of parameters to model an entirely new phenomenon. We apply these models to both a simulated and a real ellipsoidal PN to initially estimate the position, angular size, and orientation of the nebula as a two-dimensional object and use these estimates to later examine its three-dimensional properties. The efficiency/accuracy tradeoffs of the techniques are studied to determine the advantages and disadvantages of employing a set of hierarchical models over a single comprehensive model.

Knuth, Kevin H.↗