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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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All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Latest Development in Radiative Transfer Models and Retrieval Algorithms Using Principal Components

The radiative transfer model (RTMs) has a wide range of applications in satellite remote sensing and atmospheric radiation applications. However, millions of line-by-line (LBL) radiative transfer calculations at fine monochromatic frequencies are needed in order to properly calculate spectral contributions of water vapor and trace gases in the atmosphere in infrared and solar spectral regions. Therefore, fast and accurate RTMs are needed to efficiently process large amount of satellite data. A Principal Component-based Radiative Transfer Model (PCRTM) was first developed in 2004 at NASA Langley Research Centre to fulfil this need. By using PC-compression, one can reduce the data dimension significantly while maintaining original information content. The PCRTM can directly compute PC-scores and their derivatives with respect to retrieved parameters. The PCRTM can simulate the top-of-atmosphere (TOA) radiance or reflectance spectra from 0.250 µm (400000 cm-1) to 2000 µm (50 cm-1) with several orders of magnitude faster speed as compared to a LBL RTM. It is also extremely accurate compared to LBL RTM benchmarks (0.03 K RMS error in IR and 0.05% in solar). The PCRTM model has been developed for hyperspectral sensors such as AIRS, CrIS, IASI, NAST-I, SHIS, FIRST, and CLARREO-IR in thermal IR spectral region and CLARREO-Solar, CPF, TEMPO, EMIT, OMI, and SCIAMACHY in solar spectral region. The PCRTM accuracy has been demonstrated via RTM intercomparisons and with real satellite observations from AIRS, CrIS, IASI, SCHIAMACHY, and EMIT etc. In this presentation, we will describe two PCRTM-based inversion algorithms to retrieve atmospheric temperature, water vapor, and trace gas profiles, as well as cloud and surface properties from hyperspectral sounders such as AIRS, CrIS, IASI, and NAST-I. The first one is called Single Fieldof-view Sounder Atmospheric Product (SiFSAP) algorithm. It provides L2 products with 9-times higher area spatial resolution as compared to current cloud-clearing sounder algorithms. The SiFSAP L2 and L3 products are available at NASA's Goddard Earth Sciences Data and Information Services Center (GES DISC) for public access. The second inversion algorithm is called Climate Fingerprinting Atmospheric Product (ClimFiSP) algorithm. It is designed to produce high quality climate products (trends, anomalies, daily, and monthly profiles of temperature, water vapor, traces, clouds, and surface properties) from multiple satellite sensors such AIRS on Aqua and CrIS on multiple satellites. This product will be available at NASA GES DISC later this year. The PCRTMbased high fidelity simulators for CLARREO and CPF have been used for sensor performance trade studies, algorithm development, and inter-satellite calibrations. We have also used PCRTM generated TOA radiance spectra to train an AI-based algorithm and successfully retrieved cloud properties from EMIT solar hyperspectral imagers.

PCRTM↗
NASA NTRSDate not supplied

Developing Fast and Accurate Radiative Transfer Models to Meet the Needs of Modern Satellite Remote Sensing Applications

Modern hyperspectral satellite remote sensors provide highly accurate measurements the Earth’s Top-of-Atmosphere (TOA) radiance, reflectance, or polarized spectra with hundreds to thousands of spectral channels and with millions of observations per day. The large data volume and high spectral dimensionality of the data pose challenges for retrieval algorithms. To process the satellite Level-1 data (e.g. calibrated TOA spectra) into Level-2 products (e.g. atmospheric and surface properties) using physical-based retrieval algorithms, accurate and fast Radiative Transfer Models (RTMs) are needed. RTMs are usually the limiting factor in determining the speed of a level-2 algorithm. For example, more than one million Line-by-Line (LBL) radiative transfer (RT) calculations are needed in order to properly capture the spectral contributions of important atmospheric molecules for an IR hyperspectral sensor with a spectral coverage from 3.5 m to 15 m or a solar hyperspectral sensor with spectral coverage from 0.25 m to 2.5 m. In this presentation, we will discuss advantages and disadvantages of different ways (e.g. correlated k and effective transmittance) to accelerate the speed of a fast RTM. We finally describe a Principal Component-based Radiative Transfer Model (PCRTM), which can calculate TOA radiance or reflectance spectra from 50 cm-1 to 40,000 cm-1 (200 m to 0.25 m). It has demonstrated very good accuracy relative to reference LBL RTMs and saves orders of magnitude in computational time. The PCRTM has been used in many satellite remote sensing applications. Examples include forward modeling in Level-2 and Level-3 retrieval algorithms, high fidelity satellite instrument simulators and instrument performance trade studies, spectral and radiometric accuracy characterizations of satellite Level-1 data, tools for inter-satellite calibrations, tools for satellite RTM lookup table generations, and tools for generating physically based training datasets for Artificial Intelligence (AI) algorithms.

climate data record↗
NASA NTRSDate not supplied

Space Flown Rodent Liver RNA Sequencing Data for Machine Learning in Space Biology Research

High-throughput nucleic acid sequencing (DNA-seq, RNA-seq) has become widespread in biomedical research due to the growing availability and affordability of these assays. Data analysis has been accelerated in recent years by the adoption of artificial intelligence (AI) and machine learning (ML) techniques by biomedical researchers. In space biology research, RNAseq datasets from space-flown experimental samples are critical for characterizing the gene expression aberrations associated with exposure to spaceflight stressors. However, space biological experiments tend to be very low sample size, so identifying proper AI/ML algorithms for sequencing data analysis is an ongoing challenge since these algorithms typically require large sample size. The NASA Science Mission Directorate (SMD) has started the “Benchmark Initiative for AI/ML”, focused on creating datasets meant for three main applications: 1) scientific benchmarking, which finds the best algorithm for a specific problem; 2) application benchmarking, which measures algorithm performance against a set of parameters; and 3) system benchmarking, which evaluates performance of hardware and software architecture. These scientific benchmarks consist of an AI-ready dataset and a reference implementation on a specific scientific question. In this work, we focused on generating standardized datasets to allow the scientific community to benchmark AI/ML algorithms in the domain of space biology. We present here a standardized, AI-ready, publicly available benchmark dataset for space biology RNA-seq data as a collaboration between the NASA AI4LS (Artificial Intelligence for Life Sciences) working group. and NASA’s SMD. This dataset consists of space-flown and ground control mouse liver found in the NASA GeneLab omics database. However, to amplify the small sample number (n=112 samples) for ML purposes, we employ Gaussian noise and a generative adversarial network to extend this dataset to 6,000 synthetic samples, matching the original gene expression characteristics.

James Casaletto↗
NASA NTRS1992

Geometry modeling and multi-block grid generation for turbomachinery configurations

An interactive 3D grid generation code, Turbomachinery Interactive Grid genERation (TIGER), was developed for general turbomachinery configurations. TIGER features the automatic generation of multi-block structured grids around multiple blade rows for either internal, external, or internal-external turbomachinery flow fields. Utilization of the Bezier's curves achieves a smooth grid and better orthogonality. TIGER generates the algebraic grid automatically based on geometric information provided by its built-in pseudo-AI algorithm. However, due to the large variation of turbomachinery configurations, this initial grid may not always be as good as desired. TIGER therefore provides graphical user interactions during the process which allow the user to design, modify, as well as manipulate the grid, including the capability of elliptic surface grid generation.

Shih, Ming H.↗
NASA NTRS2021

Surface Cancellation in Wideband Ground Penetrating Radar Employing Genetic Algorithm AI for Waveform Synthesis

This paper presents a wideband 600-1200 MHz ground penetrating radar (GPR) system for sub-surface exploration of the moon and other planetary bodies. The presented radar system uses an arbitrary waveform generator (AWG) to directly produce the frequency-modulated continuous wave (FMCW) chirp waveform. To address the key challenges of Tx-to-Rx leakage and surface reflections, the system uses a second AWG channel coupled directly to the receiver that provides a cancellation waveform to mitigate the unwanted signals. The system also uses a genetic algorithm AI engine which assesses the radar IF and iteratively improves the parameters of the cancellation waveform injected at the receiver.

Chang, Frank↗
NASA NTRS2019

Standardizing Microprocessor and GPU Radiation Test Approaches

Microprocessor, Graphics Processing Units (GPUs) and DDRx memory devices have emerged as promising next-generation technologies that enables both high performance processing and acceleration of complex algorithms for the latest challenges in human spaceflight, autonomous vehicles and artificial intelligence (AI). The feature sets of these devices offer exponential increases to throughput, calculation capability and system autonomy when compared to legacy flight systems. NASA's Electronic Part and Packaging (NEPP) Program has conducted an investigation into the radiation susceptibility of leading edge devices and process technologies by establishing standardized test approaches. Unlike most discrete devices, these require state of the art test systems to induce specific hardware activity similar to application software, thus allowing the characterization of failure modes within the system. To best characterize the tested part, NEPP eliminates variables that may impact device performance under radiation. Simplification of remaining system-level variables leads to an improved understanding of complex computational devices and their intended applications. The failure modes and error signatures that are recorded during testing are used to determine radiation sensitivity of the semiconductor process and the microcode architecture of the design. This presentation will discuss the test methodology that NASA Electronic Parts and Packaging (NEPP) is working to establish for its microprocessor, GPU and DDRx memory test programs to provide guidance on these devices and their underlying technology, in regards to their potential usage in future space flight systems.

GPU↗
NASA NTRS1994

Thunderstorm Hypothesis Reasoner

THOR is a knowledge-based system which incorporates techniques from signal processing, pattern recognition, and artificial intelligence (AI) in order to determine the boundary of small thunderstorms which develop and dissipate over the area encompassed by KSC and the Cape Canaveral Air Force Station. THOR interprets electric field mill data (derived from a network of electric field mills) by using heuristics and algorithms about thunderstorms that have been obtained from several domain specialists. THOR generates two forms of output: contour plots which visually describe the electric field activity over the network and a verbal interpretation of the activity. THOR uses signal processing and pattern recognition to detect signatures associated with noise or thunderstorm behavior in a near real time fashion from over 31 electrical field mills. THOR's AI component generates hypotheses identifying areas which are under a threat from storm activity, such as lightning. THOR runs on a VAX/VMS at the Kennedy Space Center. Its software is a coupling of C and FORTRAN programs, several signal processing packages, and an expert system development shell.

Mulvehill, Alice M.↗
NASA NTRSDate not supplied

Using Federated Learning to Overcome Data Gravity in Space

Humans intend to take longer missions to outer space. Understanding the impact that space has on human health is paramount to the success of these missions. Controlled experiments with model organisms are run to infer the impact of space conditions on human health, but the data these experiments generate are too large to transfer to Earth for building models. The same is true for space-relevant data generated on Earth. Ideally, these datasets should be combined to improve statistical power and model accuracy without having to transfer data. Federated learning is such a method which trains an algorithm across decentralized computing systems, each of which has their own local copy of training and testing data. In this research, made possible by NASA@Work, the AI for Life in Space group at NASA demonstrates the use of federated learning to train an ensemble of causality inference models on a combination of data residing on the International Space Station (ISS) and in the cloud. Our work leverages CRISP, a causal inference platform developed during the 2020 Frontier Development Lab’s “Astronaut Health Challenge.” We also leverage the OpenFL federated learning library which was collaboratively developed at Intel and UPenn. We used publicly available data from the NASA Ames Life Sciences Data Archive to identify features in ionizing radiation experiments as causal of changes in cardiac blood velocity. This research demonstrates, for the first time, the possibility of running machine learning algorithms on datasets separated by astronomical distances. In this experiment, all the data were generated in terra, half of which were transferred to the ISS and analyzed on the Spaceborne Computer. In the future, our research will leverage federated learning on data generated in situ on the ISS with data generated terrestrially to predict the impact of spaceflight on mammalian female reproductive capacity.

James Casaletto↗
NASA NTRSDate not supplied

A NASA Perspective on Quantum AI, Error Correction, and Beyond

Quantum computing is one of the most enticing computational paradigms with the potential to revolutionize diverse areas of future-generation computational systems. While quantum computing hardware has advanced rapidly, from tiny laboratory experiments to quantum chips that can outperform even the largest supercomputers on specialized computational tasks, these noisy-intermediate scale quantum (NISQ) processors are still too small and non-robust to be directly useful for any real-world applications. We discuss the prospects for quantum computing and AI, highlighting advances in algorithms, both near- and longer-term. Quantum error correction is critical to the realization of any such vision. The talk with touch on some recent exciting advanced in quantum error correction, particularly in dynamical codes. The talk will conclude with an example of how the combination of quantum computing and artificial intelligence can help probe fundamental aspect of quantum physics.

quantum optimization algorithms and sampling↗
NASA NTRS2004

The Role of Ontologies in Schema-based Program Synthesis

Program synthesis is the process of automatically deriving executable code from (non-executable) high-level specifications. It is more flexible and powerful than conventional code generation techniques that simply translate algorithmic specifications into lower-level code or only create code skeletons from structural specifications (such as UML class diagrams). Key to building a successful synthesis system is specializing to an appropriate application domain. The AUTOBAYES and AUTOFILTER systems, under development at NASA Ames, operate in the two domains of data analysis and state estimation, respectively. The central concept of both systems is the schema, a representation of reusable computational knowledge. This can take various forms, including high-level algorithm templates, code optimizations, datatype refinements, or architectural information. A schema also contains applicability conditions that are used to determine when it can be applied safely. These conditions can refer to the initial specification, to intermediate results, or to elements of the partially-instantiated code. Schema-based synthesis uses AI technology to recursively apply schemas to gradually refine a specification into executable code. This process proceeds in two main phases. A front-end gradually transforms the problem specification into a program represented in an abstract intermediate code. A backend then compiles this further down into a concrete target programming language of choice. A core engine applies schemas on the initial problem specification, then uses the output of those schemas as the input for other schemas, until the full implementation is generated. Since there might be different schemas that implement different solutions to the same problem this process can generate an entire solution tree. AUTOBAYES and AUTOFILTER have reached the level of maturity where they enable users to solve interesting application problems, e.g., the analysis of Hubble Space Telescope images. They are large (in total around 100kLoC Prolog), knowledge intensive systems that employ complex symbolic reasoning to generate a wide range of non-trivial programs for complex application do- mains. Their schemas can have complex interactions, which make it hard to change them in isolation or even understand what an existing schema actually does. Adding more capabilities by increasing the number of schemas will only worsen this situation, ultimately leading to the entropy death of the synthesis system. The root came of this problem is that the domain knowledge is scattered throughout the entire system and only represented implicitly in the schema implementations. In our current work, we are addressing this problem by making explicit the knowledge from Merent parts of the synthesis system. Here; we discuss how Gruber's definition of an ontology as an explicit specification of a conceptualization matches our efforts in identifying and explicating the domain-specific concepts. We outline the dual role ontologies play in schema-based synthesis and argue that they address different audiences and serve different purposes. Their first role is descriptive: they serve as explicit documentation, and help to understand the internal structure of the system. Their second role is prescriptive: they provide the formal basis against which the other parts of the system (e.g., schemas) can be checked. Their final role is referential: ontologies also provide semantically meaningful "hooks" which allow schemas and tools to access the internal state of the program derivation process (e.g., fragments of the generated code) in domain-specific rather than language-specific terms, and thus to modify it in a controlled fashion. For discussion purposes we use AUTOLINEAR, a small synthesis system we are currently experimenting with, which can generate code for solving a system of linear equations, Az = b.

Bures, Tomas↗
NASA NTRSDate not supplied

Multiscale Modeling of Reconstructed Tricalcium Silicate using NASA Multiscale Analysis Tool

To study microstructure characteristics of cementitious materials hydrated in space; previously, cement binder formations were processed under microgravity conditions and was further compared against ground-based experiments. For accurate estimation of process-structure-property linkage, particularly on samples hydrated in the microgravity environment, it is desired to have a high-fidelity volumetric representation of the microstructure. However, owing to small sample size and high porosity of the space-returned samples, conventional experimental characterization techniques are not viable. Hence, a deep learning-based reconstruction algorithm was employed to obtain high fidelity 3D volumes from sparse high resolution 2D Scanning Electron Microscopy (SEM) images, as inputs to micromechanics-based modeling. This machine learning-based reconstruction methodology validated against low-order statistical descriptors, captured the microstructural topology of both sample types (ground, 1g and microgravity, μg). Due to the lack of gravity, hydration products of the samples processed in space differed from those processed-on ground. Such AI-generated virtual samples were analyzed in a multiscale recursive micromechanics approach using the NASA Multiscale Analysis Tool (NASMAT). Here, we present a methodology to rapidly integrate and evaluate these AI-generated volumes in NASMAT. The synthesized microstructural volumes are directly employed as Representative Volume Elements (RVEs) to preserve the fidelity (1 pixel = 0.54 m). Invariably, analysis of such largescale problems (5123 voxels) requires huge amount of computational resources. By taking advantage of the NASMAT architecture, we also focused on systematic multiscale integration of these AI-reconstructed virtual volumes to reduce the computational demands. In this work, this methodology is demonstrated on the ground-based, 1g samples. The estimated stiffness value of 15.90 GPa is comparable to experimentally obtained modulus of hydrated tricalcium silicate sample. The workflow presented here paves the way for utilizing the NASMAT tool to perform multiscale analyses of other multi-phase material systems using either 3D virtual datasets synthesized using AI or obtained via micro-CT.

Machine Learning↗
NASA NTRSDate not supplied

Creating Benchmark Data for Artificial Intelligence and Machine Learning Space Biology Research

To identify an appropriate AI/ML approach for a specific problem, the best practice is to measure algorithm performance through the benchmarking process. A scientific benchmark consists of an AI-ready dataset and a reference implementation on a specific scientific question. The NASA Science Mission Directorate (SMD) has started the “Benchmark Initiative for AI/ML to create scientific benchmark datasets in three applications: 1) scientific benchmarking, which finds the best algorithm for a specific problem; 2) application benchmarking, which measures algorithm performance against a set of parameters; and 3) system benchmarking, which evaluates performance of hardware and software architecture. Currently, there are no standardized datasets available to benchmark AI/ML algorithms in the domain of space biology. In this work, we constructed two AI/ML-ready biological datasets from experiments in space-flown mice: cellular imaging and RNA-seq. First, radiation-exposed immune cells harbor DNA damage foci that can be fluorescently marked to visualize the amount of damage following exposure to ionizing radiation. However, such large datasets are difficult to analyze visually, due to imaging inconsistencies and human bias, and classical image processing approaches can fail on imaging artifacts. AI/ML are therefore exciting alternative, providing the speed of machines and the accuracy of humans. We have made this dataset available at https://registry.opendata.aws/bps_microscopy/. Second, high-throughput nucleic acid sequencing (DNA-seq, RNA-seq) has become widespread in biomedical research due to the growing availability and affordability of these assays. However, most sequencing datasets suffer from high dimensionality and low sample count. In this work, we used a generative adversarial network to synthesize a standardized, AI-ready, publicly available benchmark dataset for space biology RNA-seq data with sufficient space-flown and ground control mouse liver samples from NASA GeneLab. This dataset is available at https://registry.opendata.aws/bps_rnaseq/. These datasets are now fully open the Space Biology community to test their favorite AI/ML approaches.

James Casaletto↗
NASA NTRS2015

Certification Considerations for Adaptive Systems

Advanced capabilities planned for the next generation of aircraft, including those that will operate within the Next Generation Air Transportation System (NextGen), will necessarily include complex new algorithms and non-traditional software elements. These aircraft will likely incorporate adaptive control algorithms that will provide enhanced safety, autonomy, and robustness during adverse conditions. Unmanned aircraft will operate alongside manned aircraft in the National Airspace (NAS), with intelligent software performing the high-level decision-making functions normally performed by human pilots. Even human-piloted aircraft will necessarily include more autonomy. However, there are serious barriers to the deployment of new capabilities, especially for those based upon software including adaptive control (AC) and artificial intelligence (AI) algorithms. Current civil aviation certification processes are based on the idea that the correct behavior of a system must be completely specified and verified prior to operation. This report by Rockwell Collins and SIFT documents our comprehensive study of the state of the art in intelligent and adaptive algorithms for the civil aviation domain, categorizing the approaches used and identifying gaps and challenges associated with certification of each approach.

Bhattacharyya, Siddhartha↗
NASA NTRS2003

Automated Data Processing as an AI Planning Problem

NASA s vision for Earth Science is to build a "sensor web"; an adaptive array of heterogeneous satellites and other sensors that will track important events, such as storms, and provide real-time information about the state of the Earth to a wide variety of customers. Achieving his vision will require automation not only in the scheduling of the observations but also in the processing af tee resulting data. Ta address this need, we have developed a planner-based agent to automatically generate and execute data-flow programs to produce the requested data products. Data processing domains are substantially different from other planning domains that have been explored, and this has led us to substantially different choices in terms of representation and algorithms. We discuss some of these differences and discuss the approach we have adopted.

Golden, Keith↗
NASA NTRS1992

Using neural networks and Dyna algorithm for integrated planning, reacting and learning in systems

The traditional AI answer to the decision making problem for a robot is planning. However, planning is usually CPU-time consuming, depending on the availability and accuracy of a world model. The Dyna system generally described in earlier work, uses trial and error to learn a world model which is simultaneously used to plan reactions resulting in optimal action sequences. It is an attempt to integrate planning, reactive, and learning systems. The architecture of Dyna is presented. The different blocks are described. There are three main components of the system. The first is the world model used by the robot for internal world representation. The input of the world model is the current state and the action taken in the current state. The output is the corresponding reward and resulting state. The second module in the system is the policy. The policy observes the current state and outputs the action to be executed by the robot. At the beginning of program execution, the policy is stochastic and through learning progressively becomes deterministic. The policy decides upon an action according to the output of an evaluation function, which is the third module of the system. The evaluation function takes the following as input: the current state of the system, the action taken in that state, the resulting state, and a reward generated by the world which is proportional to the current distance from the goal state. Originally, the work proposed was as follows: (1) to implement a simple 2-D world where a 'robot' is navigating around obstacles, to learn the path to a goal, by using lookup tables; (2) to substitute the world model and Q estimate function Q by neural networks; and (3) to apply the algorithm to a more complex world where the use of a neural network would be fully justified. In this paper, the system design and achieved results will be described. First we implement the world model with a neural network and leave Q implemented as a look up table. Next, we use a lookup table for the world model and implement the Q function with a neural net. Time limitations prevented the combination of these two approaches. The final section discusses the results and gives clues for future work.

Lima, Pedro↗
NASA NTRS1990

Artificial Intelligence (AI) Based Tactical Guidance for Fighter Aircraft

A research program investigating the use of Artificial Intelligence (AI) techniques to aid in the development of a Tactical Decision Generator (TDG) for Within Visual Range (WVR) air combat engagements is discussed. The application of AI programming and problem solving methods in the development and implementation of the Computerized Logic For Air-to-Air Warfare Simulations (CLAWS), a second generation TDG, is presented. The Knowledge-Based Systems used by CLAWS to aid in the tactical decision-making process are outlined in detail, and the results of tests to evaluate the performance of CLAWS versus a baseline TDG developed in FORTRAN to run in real-time in the Langley Differential Maneuvering Simulator (DMS), are presented. To date, these test results have shown significant performance gains with respect to the TDG baseline in one-versus-one air combat engagements, and the AI-based TDG software has proven to be much easier to modify and maintain than the baseline FORTRAN TDG programs. Alternate computing environments and programming approaches, including the use of parallel algorithms and heterogeneous computer networks are discussed, and the design and performance of a prototype concurrent TDG system are presented.

McManus, John W.↗
NASA NTRS1988

Graph-based real-time fault diagnostics

A real-time fault detection and diagnosis capability is absolutely crucial in the design of large-scale space systems. Some of the existing AI-based fault diagnostic techniques like expert systems and qualitative modelling are frequently ill-suited for this purpose. Expert systems are often inadequately structured, difficult to validate and suffer from knowledge acquisition bottlenecks. Qualitative modelling techniques sometimes generate a large number of failure source alternatives, thus hampering speedy diagnosis. In this paper we present a graph-based technique which is well suited for real-time fault diagnosis, structured knowledge representation and acquisition and testing and validation. A Hierarchical Fault Model of the system to be diagnosed is developed. At each level of hierarchy, there exist fault propagation digraphs denoting causal relations between failure modes of subsystems. The edges of such a digraph are weighted with fault propagation time intervals. Efficient and restartable graph algorithms are used for on-line speedy identification of failure source components.

Padalkar, S.↗
NASA NTRS1981

Evaluation of the procedure 1A component of the 1980 US/Canada wheat and barley exploratory experiment

Several techniques which use clusters generated by a new clustering algorithm, CLASSY, are proposed as alternatives to random sampling to obtain greater precision in crop proportion estimation: (1) Proportional Allocation/relative count estimator (PA/RCE) uses proportional allocation of dots to clusters on the basis of cluster size and a relative count cluster level estimate; (2) Proportional Allocation/Bayes Estimator (PA/BE) uses proportional allocation of dots to clusters and a Bayesian cluster-level estimate; and (3) Bayes Sequential Allocation/Bayesian Estimator (BSA/BE) uses sequential allocation of dots to clusters and a Bayesian cluster level estimate. Clustering in an effective method in making proportion estimates. It is estimated that, to obtain the same precision with random sampling as obtained by the proportional sampling of 50 dots with an unbiased estimator, samples of 85 or 166 would need to be taken if dot sets with AI labels (integrated procedure) or ground truth labels, respectively were input. Dot reallocation provides dot sets that are unbiased. It is recommended that these proportion estimation techniques are maintained, particularly the PA/BE because it provides the greatest precision.

Chapman, G. M.↗