The rate of a class of random processes
Algorithm applied to specific classes of random processes for calculating minimum channel capacity required by transmission system for sources in each class
Sakrison, D. J.↗
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Bandelier Ecological Conservation: Mapping Invasive Species Along the Rio Grande Corridor in Bandelier National Monument
The Southwest U.S. has experienced a growth of invasive riparian species, specifically Elaeagnus angustifolia (Russian olive), Tamarix ramosissima (saltcedar), and Ulmus pumila (Siberian elm), which alter local soil chemistry and outcompete native species. Locating these exotic species is critical for ecological conservation; however, field identification can be resource intensive. NASA DEVELOP partnered with the National Park Service (NPS) at Bandelier National Monument (BAND) to assess the feasibility of using Earth observation data to map invasive species along the Rio Grande corridor of the park. The team used Landsat 8 OLI, Sentinel-2 MSI, and ISS DESIS imagery to compute principal components based on spectral bands, vegetation indices, and terrain indices. Using the first five principal components, the team created classification maps using both a k-means classification algorithm and a random forest algorithm to differentiate between native and non-native species. The team derived maps for the three invasive riparian species in the region for the last five years. The team found that invasive species covered 33% of the park's river corridor in 2023, and the invasive species extent has increased by 5.7% from 2019 to 2023. The methods will serve as a guide for aiding historic and present invasive species identification in riparian regions, and the NPS staff at BAND will use the results to inform local mitigation practices and advocate for invasive species removal.
Evan Barrett↗
Relabeling of finite element meshes using a random process
An algorithm is presented to relabel automatically the nodes of an arbitrary finite-element mesh. The purpose of such relabeling is to reduce the bandwidth of the master stiffness matrix produced by the finite-element method. The algorithm uses a random process for the relabeling. Computing time is reduced substantially, compared to systematic methods.
Roberts, E., Jr.↗
Study of a global search algorithm for optimal control.
Adaptive random search algorithm utilizing boundary cost-function hypersurfaces measurement to implement Pontryagin maximum principle, discussing hybrid computer use, iterative solution and convergence properties
Brocker, D. H.↗
Global search algorithm for optimal control
Random-search algorithm employs local and global properties to solve two-point boundary value problem in Pontryagin maximum principle for either fixed or variable end-time problems. Mixed boundary value problem is transformed to an initial value problem. Mapping between initial and terminal values utilizes hybrid computer.
Brocker, D. H.↗
Determination of optimal stock level for a group of customers under conditions of random demand
Optimal stock level with algorithm for random distribution
Gipsh, L. A.↗
Recursive Branching Simulated Annealing Algorithm
This innovation is a variation of a simulated-annealing optimization algorithm that uses a recursive-branching structure to parallelize the search of a parameter space for the globally optimal solution to an objective. The algorithm has been demonstrated to be more effective at searching a parameter space than traditional simulated-annealing methods for a particular problem of interest, and it can readily be applied to a wide variety of optimization problems, including those with a parameter space having both discrete-value parameters (combinatorial) and continuous-variable parameters. It can take the place of a conventional simulated- annealing, Monte-Carlo, or random- walk algorithm. In a conventional simulated-annealing (SA) algorithm, a starting configuration is randomly selected within the parameter space. The algorithm randomly selects another configuration from the parameter space and evaluates the objective function for that configuration. If the objective function value is better than the previous value, the new configuration is adopted as the new point of interest in the parameter space. If the objective function value is worse than the previous value, the new configuration may be adopted, with a probability determined by a temperature parameter, used in analogy to annealing in metals. As the optimization continues, the region of the parameter space from which new configurations can be selected shrinks, and in conjunction with lowering the annealing temperature (and thus lowering the probability for adopting configurations in parameter space with worse objective functions), the algorithm can converge on the globally optimal configuration. The Recursive Branching Simulated Annealing (RBSA) algorithm shares some features with the SA algorithm, notably including the basic principles that a starting configuration is randomly selected from within the parameter space, the algorithm tests other configurations with the goal of finding the globally optimal solution, and the region from which new configurations can be selected shrinks as the search continues. The key difference between these algorithms is that in the SA algorithm, a single path, or trajectory, is taken in parameter space, from the starting point to the globally optimal solution, while in the RBSA algorithm, many trajectories are taken; by exploring multiple regions of the parameter space simultaneously, the algorithm has been shown to converge on the globally optimal solution about an order of magnitude faster than when using conventional algorithms. Novel features of the RBSA algorithm include: 1. More efficient searching of the parameter space due to the branching structure, in which multiple random configurations are generated and multiple promising regions of the parameter space are explored; 2. The implementation of a trust region for each parameter in the parameter space, which provides a natural way of enforcing upper- and lower-bound constraints on the parameters; and 3. The optional use of a constrained gradient- search optimization, performed on the continuous variables around each branch s configuration in parameter space to improve search efficiency by allowing for fast fine-tuning of the continuous variables within the trust region at that configuration point.
Bolcar, Matthew↗
Simulation of multicorrelated random processes using the FFT algorithm
A technique for the digital simulation of multicorrelated Gaussian random processes is described. This technique is based upon generating discrete frequency functions which correspond to the Fourier transform of the desired random processes, and then using the fast Fourier transform (FFT) algorithm to obtain the actual random processes. The main advantage of this method of simulation over other methods is computation time; it appears to be more than an order of magnitude faster than present methods of simulation. One of the main uses of multicorrelated simulated random processes is in solving nonlinear random vibration problems by numerical integration of the governing differential equations. The response of a nonlinear string to a distributed noise input is presented as an example.
Wittig, L. E.↗
System Design under Uncertainty: Evolutionary Optimization of the Gravity Probe-B Spacecraft
This paper discusses the application of evolutionary random-search algorithms (Simulated Annealing and Genetic Algorithms) to the problem of spacecraft design under performance uncertainty. Traditionally, spacecraft performance uncertainty has been measured by reliability. Published algorithms for reliability optimization are seldom used in practice because they oversimplify reality. The algorithm developed here uses random-search optimization to allow us to model the problem more realistically. Monte Carlo simulations are used to evaluate the objective function for each trial design solution. These methods have been applied to the Gravity Probe-B (GP-B) spacecraft being developed at Stanford University for launch in 1999, Results of the algorithm developed here for GP-13 are shown, and their implications for design optimization by evolutionary algorithms are discussed.
Pullen, Samuel P.↗
Exhaustive Versus Randomized Searchers for Nonlinear Optimization in 21st Century Computing: Solar Application
We present a simple multi-dimensional exhaustive search method to obtain, in a reasonable time, the optimal solution of a nonlinear programming problem. It is more relevant in the present day non-mainframe computing scenario where an estimated 95% computing resources remains unutilized and computing speed touches petaflops. While the processor speed is doubling every 18 months, the band width is doubling every 12 months, and the hard disk space is doubling every 9 months. A randomized search algorithm or, equivalently, an evolutionary search method is often used instead of an exhaustive search algorithm. The reason is that a randomized approach is usually polynomial-time, i.e., fast while an exhaustive search method is exponential-time i.e., slow. We discuss the increasing importance of exhaustive search in optimization with the steady increase of computing power for solving many real-world problems of reasonable size. We also discuss the computational error and complexity of the search algorithm focusing on the fact that no measuring device can usually measure a quantity with an accuracy greater than 0.005%. We stress the fact that the quality of solution of the exhaustive search - a deterministic method - is better than that of randomized search. In 21 st century computing environment, exhaustive search cannot be left aside as an untouchable and it is not always exponential. We also describe a possible application of these algorithms in improving the efficiency of solar cells - a real hot topic - in the current energy crisis. These algorithms could be excellent tools in the hands of experimentalists and could save not only large amount of time needed for experiments but also could validate the theory against experimental results fast.
Sen, Syamal K.↗
Computationally Efficient Motion Planning Algorithms for Agile Autonomous Vehicles in Cluttered Environments
Fast, real-time motion planning of an agile, autonomous vehicle in a cluttered environment, with many geometrically-fixed obstacles, is a very complex problem, especially because of the vehicle dynamics constraints and resource constrained computational capabilities onboard the vehicle. In this paper, we present computationally-efficient versions of our novel motion planning algorithm called the Spherical Expansion and Sequential Convex Programming (SE–SCP) algorithm. The SE–SCP algorithm first uses a spherical-expansion-based randomized sampling algorithm to explore the workspace. Oncea path is found from the start position to the goal position, the algorithm computes a locally optimal trajectory, within its homotopy class for a desired cost function, by solving a sequence of convex optimization problems. Thus, the SE–SCP algorithm is anytime locally optimal and the trajectory is globally optimal if the number of samples tends to infinity. In this paper, we further enhance the computational efficiency of the SE–SCP algorithm using uni-directional and bi-directional rewiring techniques. We also present a detailed proof of the local optimality characteristics of the new SE–SCP algorithms for aspecial case of vehicle dynamics. Simulation examples involving quadrotor and spacecraft help demonstrate the effectiveness of our new algorithms.
Bandyopadhyay, Saptarshi↗
A construction technique for random error correcting convolutional codes
Algorithm for constructing random error correcting convolutional codes
Costello, D. J., Jr.↗
A construction technique for random-error- correcting convolutional codes.
Algorithm for constructing random error correcting convolutional codes
Costello, D. J., Jr.↗
The generation of a random sample-covariance matrix
Algorithm for generation of random sample covariance matrix - trajectory analysis
TRAJECTORY ANALYSIS↗
Supervised Machine Learning Approach for Classifying Earth Science Publications
The data collections archived and distributed by the GES DISC NASA data center are widely utilized for various Earth Science studies. As these collections are created, many research works are published regarding these collections' algorithms, their validation, and their applications. As NASA data centers collect these publications for public use, it is helpful to categorize them based on how they relate to their associated datasets. Specifically, whether the publication linked to the GES DISC dataset is using it for applicational research, describing the algorithm used for the dataset creation, validating the dataset, or providing a general overview of the data collection. Currently, this process requires simple manual labeling, and as such, it may be possible to solve via automation. To approach this problem, machine learning classifiers were developed to predict a publication's category. Manually labeled publications were used as the training data for the supervised machine learning algorithms, specifically Random Forest and Multinomial Naïve Bayes. After balancing the dataset and implementing the Multinomial Naïve Bayes algorithm, the classification accuracy achieved was substantially higher than the baseline accuracy, thus significantly improving the efficiency of publication labeling.
Rohan Dayal↗
Hybrid computer methods for direct functional optimization
Control and trajectory optimization involves the minimization of a performance index (PI) of integral form where some optimal control law exists in a dynamic system. In this paper, a hybrid minicomputer with an adaptive random-search algorithm implements an iterative search for the optimal control. The search assumes that some initial control is randomly perturbed and a fast analog computer generates respective PI from the analog response of the dynamic system. An improved PI informs the digital computer to utilize the perturbed control as a basis for the next iteration; otherwise a new perturbation replaces the old perturbation in the next iteration. The search terminates when no further improvements occur.
Andrews, M.↗
Development of a Climatology of Vertically Complete Wind Profiles from Doppler Radar Wind Profiler Systems
This paper describes in detail the QC and splicing methodology for KSC's 50- and 915-MHz DRWP measurements that generates an extensive archive of vertically complete profiles from 0.20-18.45 km. The concurrent POR from each archive extends from April 2000 to December 2009. MSFC NE applies separate but similar QC processes to each of the 50- and 915-MHz DRWP archives. DRWP literature and data examination provide the basis for developing and applying the automated and manual QC processes on both archives. Depending on the month, the QC'ed 50- and 915-MHz DRWP archives retain 52-65% and 16-30% of the possible data, respectively. The 50- and 915-MHz DRWP QC archives retain 84-91% and 85-95%, respectively, of all the available data provided that data exist in the non- QC'ed archives. Next, MSFC NE applies an algorithm to splice concurrent measurements from both DRWP sources. Last, MSFC NE generates a composite profile from the (up to) five available spliced profiles to effectively characterize boundary layer winds and to utilize all possible 915-MHz DRWP measurements at each timestamp. During a given month, roughly 23,000-32,000 complete profiles exist from 0.25-18.45 km from the composite profiles' archive, and approximately 5,000- 27,000 complete profiles exist from an archive utilizing an individual 915-MHz DRWP. One can extract a variety of profile combinations (pairs, triplets, etc.) from this sample for a given application. The sample of vertically complete DRWP wind measurements not only gives launch vehicle customers greater confidence in loads and trajectory assessments versus using balloon output, but also provides flexibility to simulate different DOL situations across applicable altitudes. In addition to increasing sample size and providing more flexibility for DOL simulations in the vehicle design phase, the spliced DRWP database provides any upcoming launch vehicle program with the capability to utilize DRWP profiles on DOL to compute vehicle steering commands, provided the program applies the procedures that this report describes to new DRWP data on DOL. Decker et al. (2015) details how SLS is proposing to use DRWP data and splicing techniques on DOL. Although automation could enhance the current DOL 50-MHz DRWP QC process and could streamline any future DOL 915-MHz DRWP QC and splicing process, the DOL community would still require manual intervention to ensure that the vehicle only uses valid profiles. If a program desires to use high spatial resolution profiles, then the algorithm could randomly add high-frequency components to the DRWP profiles. The spliced DRWP database provides lots of flexibility in how one performs DOL simulations, and the algorithms that this report provides will assist the aerospace and atmospheric communities that are interested in utilizing the DRWP.
Barbre, Robert E., Jr.↗
Development of Algorithms and Error Analyses for the Short Baseline Lightning Detection and Ranging System
NASA, at the John F. Kennedy Space Center (KSC), developed and operates a unique high-precision lightning location system to provide lightning-related weather warnings. These warnings are used to stop lightning- sensitive operations such as space vehicle launches and ground operations where equipment and personnel are at risk. The data is provided to the Range Weather Operations (45th Weather Squadron, U.S. Air Force) where it is used with other meteorological data to issue weather advisories and warnings for Cape Canaveral Air Station and KSC operations. This system, called Lightning Detection and Ranging (LDAR), provides users with a graphical display in three dimensions of 66 megahertz radio frequency events generated by lightning processes. The locations of these events provide a sound basis for the prediction of lightning hazards. This document provides the basis for the design approach and data analysis for a system of radio frequency receivers to provide azimuth and elevation data for lightning pulses detected simultaneously by the LDAR system. The intent is for this direction-finding system to correct and augment the data provided by LDAR and, thereby, increase the rate of valid data and to correct or discard any invalid data. This document develops the necessary equations and algorithms, identifies sources of systematic errors and means to correct them, and analyzes the algorithms for random error. This data analysis approach is not found in the existing literature and was developed to facilitate the operation of this Short Baseline LDAR (SBLDAR). These algorithms may also be useful for other direction-finding systems using radio pulses or ultrasonic pulse data.
Starr, Stanley O.↗