Multi-Variate Optimization of Gen 3 CSP Falling Particle Receivers Using High-Performance Computing
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McLaughlin, Luke Patrick [Sandia National Laborato↗
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Modeling and Simulation of Upset-Inducing Disturbances for Digital Systems in an Electromagnetic Reverberation Chamber
This report describes a modeling and simulation approach for disturbance patterns representative of the environment experienced by a digital system in an electromagnetic reverberation chamber. The disturbance is modeled by a multi-variate statistical distribution based on empirical observations. Extended versions of the Rejection Samping and Inverse Transform Sampling techniques are developed to generate multi-variate random samples of the disturbance. The results show that Inverse Transform Sampling returns samples with higher fidelity relative to the empirical distribution. This work is part of an ongoing effort to develop a resilience assessment methodology for complex safety-critical distributed systems.
Torres-Pomales, Wilfredo↗
Massively parallel and universal approximation of nonlinear functions using diffractive processors
Nonlinear computation is essential for a wide range of information processing tasks, yet implementing nonlinear functions using optical systems remains a challenge due to the weak and power-intensive nature of optical nonlinearities. Overcoming this limitation without relying on nonlinear optical materials could unlock unprecedented opportunities for ultrafast and parallel optical computing systems. Here, we demonstrate that large-scale nonlinear computation can be performed using linear optics through optimized diffractive processors composed of passive phase-only surfaces. In this framework, the input variables of nonlinear functions are encoded into the phase of an optical wavefront—e.g., via a spatial light modulator (SLM)—and transformed by an optimized diffractive structure with spatially varying point-spread functions to yield output intensities that approximate a large set of unique nonlinear functions–all in parallel. We provide proof establishing that this architecture serves as a universal function approximator for an arbitrary set of bandlimited nonlinear functions, also covering wavelength-multiplexed nonlinear functions as well as multi-variate and complex-valued functions that are all-optically cascadable. Our analysis also indicates the successful approximation of typical nonlinear activation functions commonly used in neural networks, including the sigmoid, tanh, ReLU (rectified linear unit), and softplus. We numerically demonstrate the parallel computation of one million distinct nonlinear functions, accurately executed at wavelength-scale spatial density at the output of a diffractive optical processor. Furthermore, we experimentally validated this framework using in situ optical learning and approximated 35 unique nonlinear functions in a single shot using a compact setup consisting of an SLM and an image sensor. These results establish diffractive optical processors as a scalable platform for massively parallel universal nonlinear function approximation, paving the way for new capabilities in analog optical computing based on linear materials.
Rahman, Md Sadman Sakib [University of California,↗
Acoustic fatigue - A Monte Carlo approach
The present paper reviews the basic concepts of nonlinear structural response to surface flow and acoustic pressure inputs. A time domain solution and the Monte Carlo method are utilized to estimate the required statistics of the nonlinear response. Simulation procedures of multi-dimensional and multi-variate random processes are discussed. Application of these procedures to acoustic fatigue of flight structures are considered. Numerical examples are included to illustrate the applicability of this method for the solution of nonlinear problems.
Vaicaitis, R.↗
Active control of multi-dimensional random sound in ducts
Previous work has demonstrated how active control may be applied to the control of random noise in ducts. These implementations, however, have been restricted to frequencies where only plane waves are propagating in the duct. In spite of this, the need for this technology at low frequencies has progressed to the point where commercial products that apply these concepts are currently available. Extending the frequency range of this technology requires the extension of current single channel controllers to multi-variate control systems as well as addressing the problems inherent in controlling higher order modes. The application of active control in the multi-dimensional propagation of random noise in waveguides is examined. An adaptive system is implemented using measured system frequency response functions. Experimental results are presented illustrating attained suppressions of 15 to 30 dB for random noise propagating in multiple modes.
Silcox, R. J.↗
Tropical Pacific moisture variability: Its detection, synoptic structure and consequences in the general circulation
Satellite data analysis tools are developed and implemented for the diagnosis of atmospheric circulation systems over the tropical Pacific Ocean. The tools include statistical multi-variate procedures, a multi-spectral radiative transfer model, and the global spectral forecast model at NMC. Data include in-situ observations; satellite observations from VAS (moisture, infrared and visible) NOAA polar orbiters (including Tiros Operational Satellite System (TOVS) multi-channel sounding data and OLR grids) and scanning multichannel microwave radiometer (SMMR); and European Centre for Medium Weather Forecasts (ECHMWF) analyses. A primary goal is a better understanding of the relation between synoptic structures of the area, particularly tropical plumes, and the general circulation, especially the Hadley circulation. A second goal is the definition of the quantitative structure and behavior of all Pacific tropical synoptic systems. Finally, strategies are examined for extracting new and additional information from existing satellite observations. Although moisture structure is emphasized, thermal patterns are also analyzed. Both horizontal and vertical structures are studied and objective quantitative results are emphasized.
Mcguirk, James P.↗
Polytopic vector analysis in igneous petrology: Application to lunar petrogenesis
Lunar samples represent a heterogeneous assemblage of rocks with complex inter-relationships that are difficult to decipher using standard petrogenetic approaches. These inter-relationships reflect several distinct petrogenetic trends as well as thermomechanical mixing of distinct components. Additional complications arise from the unequal quality of chemical analyses and from the fact that many samples (e.g., breccia clasts) are too small to be representative of the system from which they derived. Polytopic vector analysis (PVA) is a multi-variate procedure used as a tool for exploratory data analysis. PVA allows the analyst to classify samples and clarifies relationships among heterogenous samples with complex petrogenetic histories. It differs from orthogonal factor analysis in that it uses non-orthogonal multivariate sample vectors to extract sample endmember compositions. The output from a Q-mode (sample based) factor analysis is the initial step in PVA. The Q-mode analysis, using criteria established by Miesch and Klovan and Miesch, is used to determine the number of endmembers in the data system. The second step involves determination of endmembers and mixing proportions with all output expressed in the same geochemical variable as the input. The composition of endmembers is derived by analysis of the variability of the data set. Endmembers need not be present in the data set, nor is it necessary for their composition to be known a priori. A set of any endmembers defines a 'polytope' or classification figure (triangle for a three component system, tetrahedron for a four component system, a 'five-tope' in four dimensions for five component system, et cetera).
Shervais, John W.↗
Solar Cycle Predictions Near Sunspot Minimum
Observations of solar magnetic activity and the dynamics of the solar convection zone have produced severe constraints on models of the Sun's magnetic dynamo. These constraints are so severe that, at present, we do not have numerical models that can accept the current conditions and then march forward in time to predict future activity. Given this state of solar dynamo theory we are forced to examine previous behavior to discover patterns and trends that afford us some measure of predictability. Here we examine the behavior of several indicators of solar activity near solar minimum that are well correlated with the amplitude of the following solar maximum to predict the level of solar activity over cycle 23. Sunspot numbers, areas, and positions are useful for characterizing solar cycle behavior due to the extent of the data (12 cycles or more). These data exhibit several patterns that relate future activity to past behavior. With the Odd-Even effect the odd numbered cycles have been larger than their even numbered predecessors for each of the last six cycle pairs. With the Amplitude-Period effect short period cycles have been followed by large amplitude cycles and long period cycles have been followed by small amplitude cycles for 10 of the last 13 cycles. With the Maximum-Minimum effect the sunspot number at minimum is directly correlated with the sunspot number at maximum for a given cycle. The geomagnetic indices aa and Ap are also related to solar activity by the connections between disturbances in the solar wind and variations in the Earth's magnetic field. Like the Maximum-Minimum effect for sunspots, the size of the aa and Ap indices at minimum are directly related to the amplitude of the following maximum. The number of geomagnetically disturbed days (days with Ap >= 25) over the course of a cycle is another indicator for the size of the next cycle. The aa and Ap indices can each be separated into a component in phase with the current sunspot cycle and an "extended cycle" component that is directly related to the following cycle. Individually each of these indicators provides some measure of predictive ability for the amplitudes of previous cycles. Taken in combination we find that the predictions are much more accurate. Our multi-variate analysis indicates that a maximum sunspot number of 160 +/- 20 should occur near the end of 1999 for cycle 23.
Hathaway, David H.↗
"Novel Techniques in Non-Stationary Analysis of Rotorcraft Vibration Signitures"
This research effort produced new methods to analyze the performance of linear predictors that track non-stationary processes. Specifically, prediction methods have been applied to the vibration pattern of rotorcraft drivetrains. This analysis is part or a larger rotorcraft Health and Usage Monitoring System (HUMS) that can diagnose immediate failures of the subsystems, as indicated by abrupt change in the vibration signature, and prognosticate future health, by examining the vibration patterns against long-term trends. This problem is described by a earlier joint paper co-authored by members of the funding agency and the recipient institutions prior to this grant effort. Specific accomplishments under this grant include the following: (1) Definition of a framework for analysis of non-stationary time-series estimation using the coefficients of an adaptive filter. (2) Description of a novel method of combining short-term predictor error and long-term regression error to analyze the performance of a non-stationary predictor. (3) Formulation of a multi-variate probability density function that quantifies the performance of a adaptive predictor by using the short- and long-term error variables in a Gamma function distribution. and (4) Validation of the mathematical formulations with empirical data from NASA flight tests and simulated data to illustrate the utility beyond the domain of vibrating machinery.
Meng, Teresa↗
Multiwavelength Luminosity Functions of Galaxies
I have developed a technique for measuring multi-variate luminosity functions of galaxies. Multivariate or multi-wavelength luminosity functions will reveal the interplay between star formation, chemical evolution, and absorption and re-emission of dust within evolving galaxy populations. By using principle component analysis to reduce the dimensionality of the problem, I optimally extract the relevant photometric information from large galaxy catalogs. As a demonstration of the technique, I derive the multiwavelength luminosity function for the galaxies in the released SDSS catalog, and show that the results are consistent with those obtained by traditional methods. This technique will be applicable to catalogs of galaxies from datasets obtained by the SIRTF and GALEX missions.
Gardner, Jonathan↗
Understanding the Scalability of Bayesian Network Inference using Clique Tree Growth Curves
Bayesian networks (BNs) are used to represent and efficiently compute with multi-variate probability distributions in a wide range of disciplines. One of the main approaches to perform computation in BNs is clique tree clustering and propagation. In this approach, BN computation consists of propagation in a clique tree compiled from a Bayesian network. There is a lack of understanding of how clique tree computation time, and BN computation time in more general, depends on variations in BN size and structure. On the one hand, complexity results tell us that many interesting BN queries are NP-hard or worse to answer, and it is not hard to find application BNs where the clique tree approach in practice cannot be used. On the other hand, it is well-known that tree-structured BNs can be used to answer probabilistic queries in polynomial time. In this article, we develop an approach to characterizing clique tree growth as a function of parameters that can be computed in polynomial time from BNs, specifically: (i) the ratio of the number of a BN's non-root nodes to the number of root nodes, or (ii) the expected number of moral edges in their moral graphs. Our approach is based on combining analytical and experimental results. Analytically, we partition the set of cliques in a clique tree into different sets, and introduce a growth curve for each set. For the special case of bipartite BNs, we consequently have two growth curves, a mixed clique growth curve and a root clique growth curve. In experiments, we systematically increase the degree of the root nodes in bipartite Bayesian networks, and find that root clique growth is well-approximated by Gompertz growth curves. It is believed that this research improves the understanding of the scaling behavior of clique tree clustering, provides a foundation for benchmarking and developing improved BN inference and machine learning algorithms, and presents an aid for analytical trade-off studies of clique tree clustering using growth curves.
Mengshoel, Ole Jakob↗
Translation of Bernstein Coefficients Under an Affine Mapping of the Unit Interval
We derive an expression connecting the coefficients of a polynomial expanded in the Bernstein basis to the coefficients of an equivalent expansion of the polynomial under an affine mapping of the domain. The expression may be useful in the calculation of bounds for multi-variate polynomials.
Alford, John A., II↗
Physics Mining of Multi-Source Data Sets
Powerful new parallel data mining algorithms can produce diagnostic and prognostic numerical models and analyses from observational data. These techniques yield higher-resolution measures than ever before of environmental parameters by fusing synoptic imagery and time-series measurements. These techniques are general and relevant to observational data, including raster, vector, and scalar, and can be applied in all Earth- and environmental science domains. Because they can be highly automated and are parallel, they scale to large spatial domains and are well suited to change and gap detection. This makes it possible to analyze spatial and temporal gaps in information, and facilitates within-mission replanning to optimize the allocation of observational resources. The basis of the innovation is the extension of a recently developed set of algorithms packaged into MineTool to multi-variate time-series data. MineTool is unique in that it automates the various steps of the data mining process, thus making it amenable to autonomous analysis of large data sets. Unlike techniques such as Artificial Neural Nets, which yield a blackbox solution, MineTool's outcome is always an analytical model in parametric form that expresses the output in terms of the input variables. This has the advantage that the derived equation can then be used to gain insight into the physical relevance and relative importance of the parameters and coefficients in the model. This is referred to as physics-mining of data. The capabilities of MineTool are extended to include both supervised and unsupervised algorithms, handle multi-type data sets, and parallelize it.
Helly, John↗
Does Ocean Color Data Assimilation Improve Estimates of Global Ocean Inorganic Carbon?
Ocean color data assimilation has been shown to dramatically improve chlorophyll abundances and distributions globally and regionally in the oceans. Chlorophyll is a proxy for phytoplankton biomass (which is explicitly defined in a model), and is related to the inorganic carbon cycle through the interactions of the organic carbon (particulate and dissolved) and through primary production where inorganic carbon is directly taken out of the system. Does ocean color data assimilation, whose effects on estimates of chlorophyll are demonstrable, trickle through the simulated ocean carbon system to produce improved estimates of inorganic carbon? Our emphasis here is dissolved inorganic carbon, pC02, and the air-sea flux. We use a sequential data assimilation method that assimilates chlorophyll directly and indirectly changes nutrient concentrations in a multi-variate approach. The results are decidedly mixed. Dissolved organic carbon estimates from the assimilation model are not meaningfully different from free-run, or unassimilated results, and comparisons with in situ data are similar. pC02 estimates are generally worse after data assimilation, with global estimates diverging 6.4% from in situ data, while free-run estimates are only 4.7% higher. Basin correlations are, however, slightly improved: r increase from 0.78 to 0.79, and slope closer to unity at 0.94 compared to 0.86. In contrast, air-sea flux of C02 is noticeably improved after data assimilation. Global differences decline from -0.635 mol/m2/y (stronger model sink from the atmosphere) to -0.202 mol/m2/y. Basin correlations are slightly improved from r=O.77 to r=0.78, with slope closer to unity (from 0.93 to 0.99). The Equatorial Atlantic appears as a slight sink in the free-run, but is correctly represented as a moderate source in the assimilation model. However, the assimilation model shows the Antarctic to be a source, rather than a modest sink and the North Indian basin is represented incorrectly as a sink rather than the source indicated by the free-run model and data estimates.
Gregg, Watson↗
Decadal Prediction Skill in the GEOS-5 Forecast System
A suite of decadal predictions has been conducted with the NASA Global Modeling and Assimilation Office?s GEOS-5 Atmosphere-Ocean General Circulation Model (AOGCM). The hindcasts are initialized every December from 1959 to 2010 following the CMIP5 experimental protocol for decadal predictions. The initial conditions are from a multi-variate ensemble optimal interpolation ocean and sea-ice reanalysis, and from the atmospheric reanalysis (MERRA, the Modern-Era Retrospective Analysis for Research and Applications) generated using the GEOS-5 atmospheric model. The forecast skill of a three-member-ensemble mean is compared to that of an experiment without initialization but forced with observed CO2. The results show that initialization acts to increase the forecast skill of Northern Atlantic SST compared to the uninitialized runs, with the increase in skill maintained for almost a decade over the subtropical and mid-latitude Atlantic. The annual-mean Atlantic Meridional Overturning Circulation (AMOC) index is predictable up to a 5-year lead time, consistent with the predictable signal in upper ocean heat content over the Northern Atlantic. While the skill measured by Mean Squared Skill Score (MSSS) shows 50% improvement up to 10-year lead forecast over the subtropical and mid-latitude Atlantic, however, prediction skill is relatively low in the subpolar gyre, due in part to the fact that the spatial pattern of the dominant simulated decadal mode in upper ocean heat content over this region appears to be unrealistic. An analysis of the large-scale temperature budget shows that this is the result of a model bias, implying that realistic simulation of the climatological fields is crucial for skillful decadal forecasts.
Ham, Yoo-Geun↗
Particle Filtering for Model-Based Anomaly Detection in Sensor Networks
A novel technique has been developed for anomaly detection of rocket engine test stand (RETS) data. The objective was to develop a system that postprocesses a csv file containing the sensor readings and activities (time-series) from a rocket engine test, and detects any anomalies that might have occurred during the test. The output consists of the names of the sensors that show anomalous behavior, and the start and end time of each anomaly. In order to reduce the involvement of domain experts significantly, several data-driven approaches have been proposed where models are automatically acquired from the data, thus bypassing the cost and effort of building system models. Many supervised learning methods can efficiently learn operational and fault models, given large amounts of both nominal and fault data. However, for domains such as RETS data, the amount of anomalous data that is actually available is relatively small, making most supervised learning methods rather ineffective, and in general met with limited success in anomaly detection. The fundamental problem with existing approaches is that they assume that the data are iid, i.e., independent and identically distributed, which is violated in typical RETS data. None of these techniques naturally exploit the temporal information inherent in time series data from the sensor networks. There are correlations among the sensor readings, not only at the same time, but also across time. However, these approaches have not explicitly identified and exploited such correlations. Given these limitations of model-free methods, there has been renewed interest in model-based methods, specifically graphical methods that explicitly reason temporally. The Gaussian Mixture Model (GMM) in a Linear Dynamic System approach assumes that the multi-dimensional test data is a mixture of multi-variate Gaussians, and fits a given number of Gaussian clusters with the help of the wellknown Expectation Maximization (EM) algorithm. The parameters thus learned are used for calculating the joint distribution of the observations. However, this GMM assumption is essentially an approximation and signals the potential viability of non-parametric density estimators. This is the key idea underlying the new approach.
Solano, Wanda↗
National Climate Assessment - Land Data Assimilation System (NCA-LDAS) Data and Services at NASA GES DISC
The National Climate Assessment-Land Data Assimilation System (NCA-LDAS) is an Integrated Terrestrial Water Analysis, and is one of NASAs contributions to the NCA of the United States. The NCA-LDAS has undergone extensive development, including multi-variate assimilation of remotely-sensed water states and anomalies as well as evaluation and verification studies, led by the Goddard Space Flight Centers Hydrological Sciences Laboratory (HSL). The resulting NCA-LDAS data have recently been released to the general public and include those from the Noah land-surface model (LSM) version 3.3 (Noah-3.3) and the Catchment LSM version Fortuna-2.5 (CLSM-F2.5). Standard LSM output variables including soil moistures temperatures, surface fluxes, snow cover depth, groundwater, and runoff are provided, as well as streamflow using a river routing system. The NCA-LDAS data are archived at and distributed by the NASA Goddard Earth Sciences Data and Information Services Center (GES DISC). The data can be accessed via HTTP, OPeNDAP, Mirador search and download, and NASA Earth data Search. To further facilitate access and use, the NCA-LDAS data are integrated into the NASA Giovanni, for quick visualization and analysis, and into the Data Rods system, for retrieval of time series of long time periods. The temporal and spatial resolutions of the NCA-LDAS data are, respectively, daily-averages and 0.125x0.125 degree, covering North America (25N 53N; 125W 67W) and the period January 1979 to December 2015. The data files are in self-describing, machine-independent, CF-compliant netCDF-4 format.
data assimiliation↗
Joint Assimilation of SMOS Brightness Temperature and GRACE Terrestrial Water Storage Observations for Improved Soil Moisture Estimation
Observations from recent soil moisture missions (e.g. SMOS) have been used in innovative data assimilation studies to provide global high spatial (i.e. 40 km) and temporal resolution (i.e. 3-days) soil moisture profile estimates from microwave brightness temperature observations. In contrast with microwave-based satellite missions that are only sensitive to near-surface soil moisture (0 - 5 cm), the Gravity Recovery and Climate Experiment (GRACE) mission provides accurate measurements of the entire vertically integrated terrestrial water storage column but, it is characterized by low spatial (i.e. 150,000 km2) and temporal (i.e. monthly) resolutions. Data assimilation studies have shown that GRACE-TWS primarily affects (in absolute terms) deeper moisture storages (i.e., groundwater). This work hypothesizes that unprecedented soil water profile accuracy can be obtained through the joint assimilation of GRACE terrestrial water storage and SMOS brightness temperature observations. A particular challenge of the joint assimilation is the use of the two different types of measurements that are relevant for hydrologic processes representing different temporal and spatial scales. The performance of the joint assimilation strongly depends on the chosen assimilation methods, measurement and model error spatial structures. The optimization of the assimilation technique constitutes a fundamental step toward a multi-variate multi-resolution integrative assimilation system aiming to improve our understanding of the global terrestrial water cycle.
Soil Moisture↗