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All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

Optimal estimation for discrete time jump processes

Optimum estimates of nonobservable random variables or random processes which influence the rate functions of a discrete time jump process (DTJP) are obtained. The approach is based on the a posteriori probability of a nonobservable event expressed in terms of the a priori probability of that event and of the sample function probability of the DTJP. A general representation for optimum estimates and recursive equations for minimum mean squared error (MMSE) estimates are obtained. MMSE estimates are nonlinear functions of the observations. The problem of estimating the rate of a DTJP when the rate is a random variable with a probability density function of the form cx super K (l-x) super m and show that the MMSE estimates are linear in this case. This class of density functions explains why there are insignificant differences between optimum unconstrained and linear MMSE estimates in a variety of problems.

Vaca, M. V.↗
NASA NTRS1978

Optimal estimation for discrete time jump processes

Optimum estimates of nonobservable random variables or random processes which influence the rate functions of a discrete time jump process (DTJP) are derived. The approach used is based on the a posteriori probability of a nonobservable event expressed in terms of the a priori probability of that event and of the sample function probability of the DTJP. Thus a general representation is obtained for optimum estimates, and recursive equations are derived for minimum mean-squared error (MMSE) estimates. In general, MMSE estimates are nonlinear functions of the observations. The problem is considered of estimating the rate of a DTJP when the rate is a random variable with a beta probability density function and the jump amplitudes are binomially distributed. It is shown that the MMSE estimates are linear. The class of beta density functions is rather rich and explains why there are insignificant differences between optimum unconstrained and linear MMSE estimates in a variety of problems.

Vaca, M. V.↗
NASA NTRS2012

Integration of the Total Lightning Jump Algorithm into Current Operational Warning Environment Conceptual Models

Key points that this analysis will begin to address are: 1)What physically is going on in the cloud when there is a jump in lightning? - Updraft variations, ice fluxes. 2)How do these processes fit in with severe storm conceptual models? 3)What would this information provide an end user (i.e., the forecaster)? - Relate LJA to radar observations, like changes in reflectivity, MESH, VIL, etc. based multi-Doppler derived physical relationships 4) How do we best transistionthis algorithm into the warning decision process. The known relationship between lightning updraft strength/volume and precipitation ice mass production can be extended to the concept of the lightning jump. Examination of the first lightning jump times from 329 storms in Schultz et al. shows an increase in the mean reflectivity profile and mixed phase echo volume during the 10 minutes prior to the lightning jump. Limited dual-Doppler results show that the largest lightning jumps are well correlated in time with increases in updraft strength/volume and precipitation ice mass production; however, the smaller magnitude lightning jumps appear to have more subtle relationships to updraft and ice mass characteristics.

Schultz, Christopher J.↗
NASA NTRS2004

Stochastic Stability of Nonlinear Sampled Data Systems with a Jump Linear Controller

This paper analyzes the stability of a sampled- data system consisting of a deterministic, nonlinear, time- invariant, continuous-time plant and a stochastic, discrete- time, jump linear controller. The jump linear controller mod- els, for example, computer systems and communication net- works that are subject to stochastic upsets or disruptions. This sampled-data model has been used in the analysis and design of fault-tolerant systems and computer-control systems with random communication delays without taking into account the inter-sample response. To analyze stability, appropriate topologies are introduced for the signal spaces of the sampled- data system. With these topologies, the ideal sampling and zero-order-hold operators are shown to be measurable maps. This paper shows that the known equivalence between the stability of a deterministic, linear sampled-data system and its associated discrete-time representation as well as between a nonlinear sampled-data system and a linearized representation holds even in a stochastic framework.

Gonzalez, Oscar R.↗
NASA NTRS2004

Stochastic Stability of Sampled Data Systems with a Jump Linear Controller

In this paper an equivalence between the stochastic stability of a sampled-data system and its associated discrete-time representation is established. The sampled-data system consists of a deterministic, linear, time-invariant, continuous-time plant and a stochastic, linear, time-invariant, discrete-time, jump linear controller. The jump linear controller models computer systems and communication networks that are subject to stochastic upsets or disruptions. This sampled-data model has been used in the analysis and design of fault-tolerant systems and computer-control systems with random communication delays without taking into account the inter-sample response. This paper shows that the known equivalence between the stability of a deterministic sampled-data system and the associated discrete-time representation holds even in a stochastic framework.

Gonzalez, Oscar R.↗
NASA NTRS2009

Rover Attitude and Pointing System Simulation Testbed

The MER (Mars Exploration Rover) Attitude and Pointing System Simulation Testbed Environment (RAPSSTER) provides a simulation platform used for the development and test of GNC (guidance, navigation, and control) flight algorithm designs for the Mars rovers, which was specifically tailored to the MERs, but has since been used in the development of rover algorithms for the Mars Science Laboratory (MSL) as well. The software provides an integrated simulation and software testbed environment for the development of Mars rover attitude and pointing flight software. It provides an environment that is able to run the MER GNC flight software directly (as opposed to running an algorithmic model of the MER GNC flight code). This improves simulation fidelity and confidence in the results. Further more, the simulation environment allows the user to single step through its execution, pausing, and restarting at will. The system also provides for the introduction of simulated faults specific to Mars rover environments that cannot be replicated in other testbed platforms, to stress test the GNC flight algorithms under examination. The software provides facilities to do these stress tests in ways that cannot be done in the real-time flight system testbeds, such as time-jumping (both forwards and backwards), and introduction of simulated actuator faults that would be difficult, expensive, and/or destructive to implement in the real-time testbeds. Actual flight-quality codes can be incorporated back into the development-test suite of GNC developers, closing the loop between the GNC developers and the flight software developers. The software provides fully automated scripting, allowing multiple tests to be run with varying parameters, without human supervision.

Vanelli, Charles A.↗
NASA NTRS1986

Discrete-time Markovian-jump linear quadratic optimal control

This paper is concerned with the optimal control of discrete-time linear systems that possess randomly jumping parameters described by finite-state Markov processes. For problems having quadratic costs and perfect observations, the optimal control laws and expected costs-to-go can be precomputed from a set of coupled Riccati-like matrix difference equations. Necessary and sufficient conditions are derived for the existence of optimal constant control laws which stabilize the controlled system as the time horizon becomes infinite, with finite optimal expected cost.

Chizeck, H. J.↗
NASA NTRS1993

Dynamics and control of coherent structures in the turbulent wall layer: An overview

We expand the velocity field in the vicinity of the wall in empirical eigenfunctions obtained from experiment. Truncating our system and using Galerkin projection, we obtain a closed set of non-linear ordinary differential equations with ten degrees of freedom. We find a rich dynamical behavior, including in particular a heteroclinic attracting orbit giving rise to intermittency. The intermittent jump from one attracting point to the other resembles in many respects the bursts observed in experiments. Specifically, the time between jumps and the duration of the jumps, is approximately that observed in a burst; the jump begins with the formation of a narrowed and intensified updraft, like the ejection phase of a burst, and is followed by a gentle, diffuse downdraft like the sweep phase of a burst. The magnitude of the Reynolds stress spike produced during a burst is limited by our truncation. The behavior is quite robust, much of it being due to the symmetries present (Aubry's group has examined dimensions up to 128 with persistence of the global behavior). We have examined eigenvalues and coefficients obtained from experiment, and from exact simulation, which differ in magnitude. Similar behavior is obtained in both cases; in the latter case, the heteroclinic orbits connect limit cycles instead of fixed points, corresponding to cross-stream waving of the streamwise rolls. The bifurcation diagram remains structurally similar, but somewhat distorted. The role of the pressure term is made clear - it triggers the intermittent jumps, which otherwise would occur at longer and longer intervals, as the system trajectory is attracted closer and closer to the heteroclinic cycle. The pressure term results in the jumps occurring at essentially random times, and the magnitude of the signal determines the average timing. Stretching of the wall region shows that the model is consistent with observations of polymer drag reduction. Change of the third order coefficients, corresponding to acceleration or deceleration of the mean flow, changes the heteroclinic cycles from attracting to repelling, increasing or decreasing the stability, in agreement with observations. The existence of fixed points is an artifact introduced by the projection; however, a decoupled model still displays the rich dynamics. Numerous assumptions made in Aubry et al. (1988) can now be proved exactly. Feeding back eigenfuncitons with the proper phase can delay the bursting, (the heteroclinic jump to the other fixed point), decreasing the drag. It is also possible to speed up the bursting, increasing mixing to control separation. Our approach is optimal for short time tracking in control.

Berkooz, Gal↗
NASA NTRS2002

Time-Variable Gravity Signal Due to Extratropic Pacific Water Mass Redistribution

Cox and Chao [2002] reported the detection of a large anomaly in the form of a positive "jump" in the time series of Earth's lowest-degree gravity harmonic J2, or the dynamic oblateness, during 1998. This prompted us to examine the mass redistribution in the global oceans. We report here a seesaw of the sea-surface height (SSH) in the extratropic north + south Pacific basins -- the leading (nonseasonal) EOF/PC mode in SSH derived from the 10-year TOPEX/Poseidon altimetry data in the extratropic Pacific region. The mode underwent a step-like jump with time evolution that match remarkably well with the observed J2 anomaly. However, the magnitude is several times too small to explain the observed J2, even if assuming the SSH jump was all mass-induced (as opposed to any steric effect which causes no time-variable gravity signal). If one accepts the notion that this extratropic Pacific seesaw is part of the geophysical process that produced the observed 1998 J2 anomaly, then this finding suggests strong geophysical connection of the interannual-to-decadal variation of J2 with the Pacific Decadal Oscillation (PDO), as the time series of the above EOF/PC mode is actually a formally defined PDO Index series.

Chao, Benjamin F.↗
NASA NTRS2011

An Overview of the Total Lightning Jump Algorithm: Past, Present and Future Work

Rapid increases in total lightning prior to the onset of severe and hazardous weather have been observed for several decades. These rapid increases are known as lightning jumps and can precede the occurrence of severe weather by tens of minutes. Over the past decade, a significant effort has been made to quantify lightning jump behavior in relation to its utility as a predictor of severe and hazardous weather. Based on a study of 34 thunderstorms that occurred in the Tennessee Valley, early work conducted in our group at Huntsville determined that it was indeed possible to create a reasonable operational lightning jump algorithm (LJA) based on a statistical framework relying on the variance behavior of the lightning trending signal. We the expanded this framework and tested several variance-related LJA configurations on a much larger sample of 87 severe and non severe thunderstorms. This study determined that a configuration named the "2(sigma)" algorithm had the most promise in development of the operational LJA with a probability of detection (POD) of 87%, a false alarm rate (FAR) of 33%, a Heidke Skill Score (HSS) of 0.75. The 2(sigma) algorithm was then tested on an even larger sample of 711 thunderstorms of all types from four regions of the country where total lightning measurement capability existed. The result was very encouraging.Despite the larger number of storms and the inclusion of different regions of the country, the POD remained high (79%), the FAR was low (36%) and HSS was solid (0.71). Average lead time from jump to severe weather occurrence was 20.65 minutes, with a standard deviation of +/- 15 minutes. Also, trends in total lightning were compared to cloud to ground (CG) lightning trends, and it was determined that total lightning trends had a higher POD (79% vs 66%), lower FAR (36% vs 54 %) and a better HSS (0.71 vs 0.55). From the 711-storm case study it was determined that a majority of missed events were due to severe weather producing thunderstorms in low flashing environments. The latest efforts have been geared toward examining these low flashing storms in order to adjust the algorithm for such storms, thus enhancing the capability of the LJA. Future work will test the algorithm in real time using current satellite and radar based cell tracking methods, as well as, comparing total lightning jump occurrence to both satellite based and ground base observations of thunderstorms to create correlations between lightning jumps and the observed structures within thunderstorms. Finally this algorithm will need to be tested using Geostationary Lightning Mapper proxy data to transition the algorithm from VHF ground based lightning measurements to lower frequency space-based lightning measurements.

Schultz, Christopher J.↗
NASA NTRS2014

Lightning Jump Algorithm Development for the GOES·R Geostationary Lightning Mapper

Current work on the lightning jump algorithm to be used in GOES‐R Geostationary Lightning Mapper (GLM)'s data stream is multifaceted due to the intricate interplay between the storm tracking, GLM proxy data, and the performance of the lightning jump itself. This work outlines the progress of the last year, where analysis and performance of the lightning jump algorithm with automated storm tracking and GLM proxy data were assessed using over 700 storms from North Alabama. The cases analyzed coincide with previous semi‐objective work performed using total lightning mapping array (LMA) measurements in Schultz et al. (2011). Analysis shows that key components of the algorithm (flash rate and sigma thresholds) have the greatest influence on the performance of the algorithm when validating using severe storm reports. Automated objective analysis using the GLM proxy data has shown probability of detection (POD) values around 60% with false alarm rates (FAR) around 73% using similar methodology to Schultz et al. (2011). However, when applying verification methods similar to those employed by the National Weather Service, POD values increase slightly (69%) and FAR values decrease (63%). The relationship between storm tracking and lightning jump has also been tested in a real‐time framework at NSSL. This system includes fully automated tracking by radar alone, real‐time LMA and radar observations and the lightning jump. Results indicate that the POD is strong at 65%. However, the FAR is significantly higher than in Schultz et al. (2011) (50‐80% depending on various tracking/lightning jump parameters) when using storm reports for verification. Given known issues with Storm Data, the performance of the real‐time jump algorithm is also being tested with high density radar and surface observations from the NSSL Severe Hazards Analysis & Verification Experiment (SHAVE).

Schultz. E.↗
NASA NTRS1997

Limits to the Stability of Phase Transfer from Ground to Space

An alternative to having a primary frequency standard on board a spacecraft is to phase lock a simple oscillator on the spacecraft to a microwave tone transmitted from the ground. The received tone is transponded and rebroadcast to the ground. The round trip phase is measured, and used to correct for effects on time scales longer than the round trip light travel time. This method is used with the TDRSS relay satellites, and will be used for the Japanese space VLBI mission VSOP. There are several sources of error introduced by this process. The most important error source is a loss of the on board standard for all times that the satellite is out of contact with a ground tracking station. The fractional loss will be greater than 10% for almost any orbit, even with a network of several ground tracking stations, and it will be considerably worse for a low earth orbit. Only a geostationary orbit can eliminate this problem. Another error source is connected to the previous one. Round trip phase tracking can remove, after the fact, link effects during a tracking pass on time scales greater than the round trip light travel time. However, there will be a jump in the spacecraft clock when multiple passes are connected (e.g. when the spacecraft is reacquired after passing out of sight). These jumps will be equal in magnitude (except for a geometrical factor) to the accuracy with which the spacecraft orbit is known. With a GPS receiver and GPS-like beacon on a spacecraft, the orbit can be known to a few cm, giving timing jumps on the order of 100 picoseconds. Even with a geostationary orbit, these jumps would occur any time the link was interrupted due to mechanical or electrical problems.

Linfield, Roger P.↗
NASA NTRS1986

Crack growth in single-crystal silicon

Crack growth in single-crystal silicon at room temperature in air was evaluated by double torsion (DT) load-relaxation method and monitored by acoustic emission (AE) technique. Both DT and AE methods indicated lack of subcritical crack growth in silicon. At the critical stress intensity factor, the crack front was found to be jumping several times in a 'mirror' region and then followed by fast crack growth in a 'hackle' region. Hackle marks were found to be associated with plastic deformation at the tip of the fast moving crack. No dislocation etch pits were found in the 'mirror' region, in which crack growth may result from interatomic bonds broken at the crack tip under stress without any plastic deformation. Acoustic emission appears to be spontaneously generated from both interatomic bonds broken and dislocation generation at the moving crack tip during the crack growth in single-crystal silicon.

Chen, C. P.↗
NASA NTRS2009

Preliminary Development and Evaluation of Lightning Jump Algorithms for the Real-Time Detection of Severe Weather

Previous studies have demonstrated that rapid increases in total lightning activity (intracloud + cloud-to-ground) are often observed tens of minutes in advance of the occurrence of severe weather at the ground. These rapid increases in lightning activity have been termed "lightning jumps." Herein, we document a positive correlation between lightning jumps and the manifestation of severe weather in thunderstorms occurring across the Tennessee Valley and Washington D.C. A total of 107 thunderstorms were examined in this study, with 69 of the 107 thunderstorms falling into the category of non-severe, and 38 into the category of severe. From the dataset of 69 isolated non-severe thunderstorms, an average peak 1 minute flash rate of 10 flashes/min was determined. A variety of severe thunderstorm types were examined for this study including an MCS, MCV, tornadic outer rainbands of tropical remnants, supercells, and pulse severe thunderstorms. Of the 107 thunderstorms, 85 thunderstorms (47 non-severe, 38 severe) from the Tennessee Valley and Washington D.C tested 6 lightning jump algorithm configurations (Gatlin, Gatlin 45, 2(sigma), 3(sigma), Threshold 10, and Threshold 8). Performance metrics for each algorithm were then calculated, yielding encouraging results from the limited sample of 85 thunderstorms. The 2(sigma) lightning jump algorithm had a high probability of detection (POD; 87%), a modest false alarm rate (FAR; 33%), and a solid Heidke Skill Score (HSS; 0.75). A second and more simplistic lightning jump algorithm named the Threshold 8 lightning jump algorithm also shows promise, with a POD of 81% and a FAR of 41%. Average lead times to severe weather occurrence for these two algorithms were 23 minutes and 20 minutes, respectively. The overall goal of this study is to advance the development of an operationally-applicable jump algorithm that can be used with either total lightning observations made from the ground, or in the near future from space using the GOES-R Geostationary Lightning Mapper.

Schultz, Christopher J.↗
NASA NTRS1990

Weak shock propagation through a turbulent atmosphere

Consideration is given to the propagation through turbulence of transient pressure waveforms whose initial onset at any given point is an abrupt shock. The work is motivated by the desire to eventually develop a mathematical model for predicting statistical features, such as peak overpressures and spike widths, of sonic booms generated by supersonic aircraft. It is argued that the transient waveform received at points where x greater than 0 will begin with a pressure jump and a formulation is developed for predicting the amount of this jump and the time derivatives of the pressure waveform immediately following the jump.

Pierce, Allan D.↗
NASA NTRS1991

A continuous mixing model for pdf simulations and its applications to combusting shear flows

The problem of time discontinuity (or jump condition) in the coalescence/dispersion (C/D) mixing model is addressed in this work. A C/D mixing model continuous in time is introduced. With the continuous mixing model, the process of chemical reaction can be fully coupled with mixing. In the case of homogeneous turbulence decay, the new model predicts a pdf very close to a Gaussian distribution, with finite higher moments also close to that of a Gaussian distribution. Results from the continuous mixing model are compared with both experimental data and numerical results from conventional C/D models.

Hsu, A. T.↗
NASA NTRS1992

PDF turbulence modeling and DNS

The problem of time discontinuity (or jump condition) in the coalescence/dispersion (C/D) mixing model is addressed in probability density function (pdf). A C/D mixing model continuous in time is introduced. With the continuous mixing model, the process of chemical reaction can be fully coupled with mixing. In the case of homogeneous turbulence decay, the new model predicts a pdf very close to a Gaussian distribution, with finite higher moments also close to that of a Gaussian distribution. Results from the continuous mixing model are compared with both experimental data and numerical results from conventional C/D models. The effect of Coriolis forces on compressible homogeneous turbulence is studied using direct numerical simulation (DNS). The numerical method used in this study is an eight order compact difference scheme. Contrary to the conclusions reached by previous DNS studies on incompressible isotropic turbulence, the present results show that the Coriolis force increases the dissipation rate of turbulent kinetic energy, and that anisotropy develops as the Coriolis force increases. The Taylor-Proudman theory does apply since the derivatives in the direction of the rotation axis vanishes rapidly. A closer analysis reveals that the dissipation rate of the incompressible component of the turbulent kinetic energy indeed decreases with a higher rotation rate, consistent with incompressible flow simulations (Bardina), while the dissipation rate of the compressible part increases; the net gain is positive. Inertial waves are observed in the simulation results.

Hsu, A. T.↗