Errors Incurred in the Reduction and Mathematical Modeling of Process Dynamic Data Final Report
Errors incurred in reduction and mathematical modeling of process dynamic data
DATA REDUCTION↗
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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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Detection of digital FSK using a phase-locked loop
A theory is presented for the design of a digital FSK receiver which employs a phase-locked loop to set up the desired matched filter as the arriving signal frequency switches. The developed mathematical model makes it possible to establish the error probability performance of systems which employ a class of digital FM modulations. The noise mechanism which accounts for decision errors is modeled on the basis of the Meyr distribution and renewal Markov process theory.
Lindsey, W. C.↗
Explicit least squares system parameter identification for exact differential input/output models
The equation error for a class of systems modeled by input/output differential operator equations has the potential to be integrated exactly, given the input/output data on a finite time interval, thereby opening up the possibility of using an explicit least squares estimation technique for system parameter identification. The paper delineates the class of models for which this is possible and shows how the explicit least squares cost function can be obtained in a way that obviates dealing with unknown initial and boundary conditions. The approach is illustrated by two examples: a second order chemical kinetics model and a third order system of Lorenz equations.
Pearson, A. E.↗
Conflict Probability Estimation for Free Flight
The safety and efficiency of free flight will benefit from automated conflict prediction and resolution advisories. Conflict prediction is based on trajectory prediction and is less certain the farther in advance the prediction, however. An estimate is therefore needed of the probability that a conflict will occur, given a pair of predicted trajectories and their levels of uncertainty. A method is developed in this paper to estimate that conflict probability. The trajectory prediction errors are modeled as normally distributed, and the two error covariances for an aircraft pair are combined into a single equivalent covariance of the relative position. A coordinate transformation is then used to derive an analytical solution. Numerical examples and Monte Carlo validation are presented.
Paielli, Russell A.↗
Boosting with Averaged Weight Vectors
AdaBoost is a well-known ensemble learning algorithm that constructs its constituent or base models in sequence. A key step in AdaBoost is constructing a distribution over the training examples to create each base model. This distribution, represented as a vector, is constructed to be orthogonal to the vector of mistakes made by the previous base model in the sequence. The idea is to make the next base model's errors uncorrelated with those of the previous model. Some researchers have pointed out the intuition that it is probably better to construct a distribution that is orthogonal to the mistake vectors of all the previous base models, but that this is not always possible. We present an algorithm that attempts to come as close as possible to this goal in an efficient manner. We present experimental results demonstrating significant improvement over AdaBoost and the Totally Corrective boosting algorithm, which also attempts to satisfy this goal.
Oza, Nikunj C.↗
Methodology for Validation of Unsteady Pressure-Sensitive Paint Measurements using Pressure Transducers
Unsteady Pressure-Sensitive Paint (uPSP) technology provides simultaneously high-frequency and high-spatial resolution surface pressure fluctuation measurements. It has demonstrated value in wind tunnel test facilities to evaluate aerospace vehicle unsteady aerodynamics. The calibration of measurements from digital pixel counts into corresponding physical units relies on both lab-based and in-situ calibration steps, and its validation is both challenging and critical to adoption of the technology. We present a rigorous methodology for direct comparison of uPSP-derived surface pressure measurements to reference pressure transducer data based on a model of the camera-based measurement error, a model of the flow field pressure signal, and their propagation through the uPSP data reduction algorithm. The methodology is demonstrated on data collected in a small-scale, subsonic wind tunnel test as well as data collected from a Space Launch System unsteady aerodynamics characterization test at the NASA Ames Research Center Unitary Plan Wind Tunnel Complex.
Pressure-Sensitive Paint↗
Validating uPSP with Transducers
Unsteady Pressure-Sensitive Paint (uPSP) technology provides simultaneously high-frequency and high-spatial resolution surface pressure fluctuation measurements. It has demonstrated value in wind tunnel test facilities to evaluate aerospace vehicle unsteady aerodynamics. The calibration of measurements from digital pixel counts into corresponding physical units relies on both lab-based and in-situ calibration steps, and its validation is both challenging and critical to adoption of the technology. We present a rigorous methodology for direct comparison of uPSP-derived surface pressure measurements to reference pressure transducer data based on a model of the camera-based measurement error, a model of the flow field pressure signal, and their propagation through the uPSP data reduction algorithm. The methodology is demonstrated on data collected in a small-scale, subsonic wind tunnel test as well as data collected from a Space Launch System unsteady aerodynamics characterization test at the NASA Ames Research Center Unitary Plan Wind Tunnel Complex.
Pressure-Sensitive Paint↗
Comparison of plug flow and multi-node stratified tank modeling approaches regarding computational efficiency and accuracy
Residential water heaters contain water stratified by temperature-driven density differences. This implies that a water tank can reach a state in which the top and bottom sections have different temperatures, unless mixing happens. A high degree of thermal stratification can improve the efficiency of some water heaters, by saving the amount of energy required for the heat-up process. Studies of stratification became popular in the 1970s and it remains an active research topic today. The research has led to the development of different models and techniques to better predict and define a stratified tanks behavior. By comparing these models and techniques used previously to describe thermal stratification, the phenomenon could be better understood, exploited, and used to increase efficiency and thermal energy capacity in modern water tanks. From the existing models, we found the one-dimensional standard plug-flow and a multi node model to be appropriate for analyzing the processes of the heat up and cool-down in a water tank. These two models are based on energy balances. This work involved comparing the accuracy and computational effort needed to implement these models. To assess accuracy, we compared both types of existing models to experimental data (also collected in this work) which included a heat up process using an external heat pump. This external process included a layering process that has an eddy diffusivity at five times the rate of thermal diffusion. For this project, we implemented the models in MATLAB, the multi-paradigm numerical computing environment. We quantified model accuracy using the root mean squared error between modeled data and experimental data for six measured tank temperatures. Comparing the accuracy and the computational time taken to run the simulation provides a method to contrast the performance of each model and a way to rate it. The multi node model was run using from 6 to 96 spatial nodes; the plug flow model was run using 1 to 0.001 º C temperature bin sizes. Additionally, timesteps were varied from 4 to 236 s. The results quantify the tradeoff between accuracy and computational time, providing guidance for simulations to intelligently select the best model type and simulation parameters. This research can be used to validate the pre-existing models and possibly improve the modern water tank.
Bulnes, Fernando Karg↗
Integration of system identification and robust controller designs for flexible structures in space
A novel approach is developed using experimental data from the structural testing of a physical system to identify a reduced-order model and its error for a robust controller design. There are three steps involved in the approach. First, an approximately balanced model is identified using the eigensystem realization algorithm, which is an identification algorithm. Second, the model error is calculated and described in frequency domain in terms of the H(infinity) norm. Third, a pole-placement technique in combination with an H(infinity) control method is applied to design a controller for the system. A set of experimental data from an existing setup, namely the Mini-Mast system, is used to illustrate and verify the approach development in this paper.
Juang, Jer-Nan↗
Comparison of interlaminar damage modeling strategies for hybrid composite/aluminum laminates subjected to low-velocity impact
Low-velocity impact of hybrid metal-composite structures was investigated experimentally and computationally. Composite laminates consisting of 2D woven glass fiber reinforced polymer (GFRP) and carbon fiber reinforced polymer (CFRP) were joined with a 6061-T6 aluminum plate using an epoxy adhesive. Two variations of the structure were studied; one consisting of all plies oriented at 0° and one consisting of all plies oriented at 45°. A drop tower was used to impact structures at a range of energies, including energies above and below the threshold at which the aluminum layer was perforated. Numerical simulations were implemented using Sierra/SM, an in-house transient dynamics finite element code developed at Sandia National Laboratories. A Hosford plasticity model was used to describe the response of the aluminum layer. A newly implemented orthotropic continuum damage mechanics (CDM) constitutive model was used to represent the composite laminate. This 3D-CDM model was compared to a cohesive zone model (2D-CDM/CZM) to investigate efficacy of aluminum perforation energy prediction, delamination prediction, and computational cost. Accuracy of each model was evaluated using the experimental results. Each showed good agreement with the tests for both the force and velocity histories, as well as the observed damage mechanisms. The 2D-CDM/CZM model was marginally more accurate in capturing both the composite and aluminum behavior — this model averaged error percentages of -11.2% and 10.8% for residual velocity and peak force, respectively. Meanwhile, the 3D-CDM model predictions yielded average error percentages of -35.5% (velocity) and 22.6% (force). However, the 3D-CDM model generally resulted in a decreased computational cost; the average run time was 14% shorter than the 2D-CDM/CZM model and 3x as many timesteps per hour were computed using the same computational resources. In conclusion, new experimental data on the impact and perforation resistance of metal-composite laminates is presented in addition to numerical predictions of the impact behavior.
Carbon fiber↗
Probabilistic failure assessment with application to solid rocket motors
A quantitative methodology is being developed for assessment of risk of failure of solid rocket motors. This probabilistic methodology employs best available engineering models and available information in a stochastic framework. The framework accounts for incomplete knowledge of governing parameters, intrinsic variability, and failure model specification error. Earlier case studies have been conducted on several failure modes of the Space Shuttle Main Engine. Work in progress on application of this probabilistic approach to large solid rocket boosters such as the Advanced Solid Rocket Motor for the Space Shuttle is described. Failure due to debonding has been selected as the first case study for large solid rocket motors (SRMs) since it accounts for a significant number of historical SRM failures. Impact of incomplete knowledge of governing parameters and failure model specification errors is expected to be important.
Jan, Darrell L.↗
Parameter estimation for terrain modeling from gradient data
A method is developed for modeling terrain surfaces for use on an unmanned Martian roving vehicle. The modeling procedure employs a two-step process which uses gradient as well as height data in order to improve the accuracy of the model's gradient. Least square approximation is used in order to stochastically determine the parameters which describe the modeled surface. A complete error analysis of the modeling procedure is included which determines the effect of instrumental measurement errors on the model's accuracy. Computer simulation is used as a means of testing the entire modeling process which includes the acquisition of data points, the two-step modeling process and the error analysis. Finally, to illustrate the procedure, a numerical example is included.
Dangelo, K. R.↗
A stochastic-dynamic model for the spatial structure of forecast error statistics
The present investigation is concerned with the presentation of a simplified model of the spatial structure of forecast error statistics, a comparison of the model with actual numerical weather prediction results, and the extent to which simplifying assumptions made in the model are justified. A stochastic-dynamic model is derived for the spatial structure of the global atmospheric mass-field forecast error. The model states that the relative potential vorticity of the forecast error is random. The covariance function of the model's solutions is found to be governed by a simple deterministic equation. The agreement between the stochastic model and actual mass-field forecast errors fields for 12-36 h periods validates the assumptions on which the model is derived. Within this period, the difference between the potential voriticity fields of the atmosphere and of the numerical forecasts used in the comparison is well represented by white noise.
Balgovind, R.↗
Fusion of Multiple Models for Improving Gross Primary Production Estimation With Eddy Covariance Data Based on Machine Learning
Abstract Terrestrial gross primary production (GPP) represents the magnitude of CO 2 uptake through vegetation photosynthesis, and is a key variable for carbon cycles between the biosphere and atmosphere. Light use efficiency (LUE) models have been widely used to estimate GPP for its physiological mechanisms and availability of data acquisition and implementation, yet each individual GPP model has exhibited large uncertainties due to input errors and model structure, and further studies of systematic validation, comparison, and fusion of those models with eddy covariance (EC) site data across diverse ecosystem types are still needed in order to further improve GPP estimation. We here compared and fused five GPP models (VPM, EC‐LUE, GOL‐PEM, CHJ, and C‐Fix) across eight ecosystems based on FLUXNET2015 data set using the ensemble methods of Bayesian Model Averaging (BMA), Support Vector Machine (SVM), and Random Forest (RF) separately. Our results showed that for individual models, EC‐LUE gave a better performance to capture interannual variability of GPP than other models, followed by VPM and GLO‐PEM, while CHJ and C‐Fix were more limited in their estimation performance. We found RF and SVM were superior to BMA on merging individual models at various plant functional types (PFTs) and at the scale of individual sites. On the basis of individual models, the fusion methods of BMA, SVM, and RF were examined by a five‐fold cross validation for each ecosystem type, and each method successfully improved the average accuracy of estimation by 8%, 18%, and 19%, respectively.
Environmental Sciences & Ecology↗
Field-Array Benchmark of Commercial Bifacial PV Technologies with Publicly Available Data
We present results for a 75-kW field array deployed with rows of 5 different commercially available bifacial technologies. Four PERC (multi and mono) and 1 Silicon Heterojunction manufacturers are represented. Reference strings of equivalent monofacial PV modules are also installed in the 10-row field. High accuracy string-level DC monitoring and module-level measurements have been recorded for six months. Analysis indicates performance within expectation, with a cumulative model mean error within +/- 2% for both bifacial and monofacial models and cumulative bifacial energy gain between 6-9%. A custom-module to measure shading loss from the torque-tube was installed. One month data shows up to 6% irradiance non-uniformity. A fixed-tilt test-site with 3 years of bifacial data is also presented, with a bifacial gain of 3%.
41 EE - Solar Energy Technologies Office (EE-4S)↗
On-line Generation and Error Handling for Surrogate Models within Multifidelity Uncertainty Quantification
Uncertainty quantification is recognized as a fundamental task to obtain predictive numerical simulations. However, many realistic engineering applications require complex and computationally expensive high-fidelity numerical simulations for the accurate characterization of the system responses. Moreover, complex physical models and extreme operative conditions can easily lead to hundreds of uncertain parameters that need to be propagated through high-fidelity codes. Under these circumstances, a single fidelity approach, i.e. a workflow that only uses high-fidelity simulations to perform the uncertainty quantification task, is unfeasible due to the prohibitive overall computational cost. In recent years, multifidelity strategies have been introduced to overcome this issue. The core idea of this family of methods is to combine simulations with varying levels of fidelity/accuracy in order to obtain the multifidelity estimators or surrogates with the same accuracy of their single fidelity counterparts at a much lower computational cost. This goal is usually accomplished by defining a prioria sequence of discretization levels or physical modeling assumptions that can be used to decrease the complexity of a numerical realization and thus its computational cost. However ,less attention has been dedicated to low-fidelity models that can be built directly from the small number of high-fidelity simulations available. In this work we focus our attention on Reduced-Order Models that can be considered a particular class of data-driven approaches. Our main goal is to explore the combination of multifidelity uncertainty quantification and reduced-order models to obtain an efficient framework for propagating uncertainties through expensive numerical codes.
97 MATHEMATICS AND COMPUTING↗