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At least 307 records · Page 17

Time Series Dimension Reduction for Surrogate Models of Port Scanning Cyber Emulations

Surrogate model development is a key resource in the scientific modeling community for providing computational expedience when simulating complex systems without loss of great fidelity. The initial step to development of a surrogate model is identification of the primary governing components of the system. Principal component analysis (PCA) is a widely used data science technique that provides inspection of such driving factors, when the objective for modeling is to capture the greatest sources of variance inherent to a dataset. Although an efficient linear dimension reduction tool, PCA makes the fundamental assumption that the data is continuous and normally distributed. Thus, it provides ideal performance when these conditions are met. In the case for which cyber emulations provide realizations of a port scanning scenario, the data to be modeled follows a discrete time series function comprised of monotonically increasing piece-wise constant steps. The sources of variance are related to the timing and magnitude of these steps. Therefore, we consider using XPCA, an extension to PCA for continuous and discrete random variates. This report provides the documentation of the trade-offs between the PCA and XPCA linear dimension reduction algorithms, for the intended purpose to identify key components of greatest variance in our time series data. These components will ultimately provide the basis for future surrogate models of port scanning cyber emulations.

97 MATHEMATICS AND COMPUTING↗

Exploratory Study for Continuous-time Parameter Estimation of Ankle Dynamics

Recently, a parallel pathway model to describe ankle dynamics was proposed. This model provides a relationship between ankle angle and net ankle torque as the sum of a linear and nonlinear contribution. A technique to identify parameters of this model in discrete-time has been developed. However, these parameters are a nonlinear combination of the continuous-time physiology, making insight into the underlying physiology impossible. The stable and accurate estimation of continuous-time parameters is critical for accurate disease modeling, clinical diagnosis, robotic control strategies, development of optimal exercise protocols for longterm space exploration, sports medicine, etc. This paper explores the development of a system identification technique to estimate the continuous-time parameters of ankle dynamics. The effectiveness of this approach is assessed via simulation of a continuous-time model of ankle dynamics with typical parameters found in clinical studies. The results show that although this technique improves estimates, it does not provide robust estimates of continuous-time parameters of ankle dynamics. Due to this we conclude that alternative modeling strategies and more advanced estimation techniques be considered for future work.

neuromuscular systems↗

On the advantages of exploiting memory in Markov state models for biomolecular dynamics

Biomolecular dynamics play an important role in numerous biological processes. Markov State Models (MSMs) provide a powerful approach to study these dynamic processes by predicting long time scale dynamics based on many short molecular dynamics (MD) simulations. In an MSM, protein dynamics are modeled as a kinetic process consisting of a series of Markovian transitions between different conformational states at discrete time intervals (called “lag time”). To achieve this, a master equation must be constructed with a sufficiently long lag time to allow interstate transitions to become truly Markovian. This imposes a major challenge for MSM studies of proteins since the lag time is bound by the length of relatively short MD simulations available to estimate the frequency of transitions. Here, we show how one can employ the generalized master equation formalism to obtain an exact description of protein conformational dynamics both at short and long time scales without the time resolution restrictions imposed by the MSM lag time. Using a simple kinetic model, alanine dipeptide, and WW domain, we demonstrate that it is possible to construct these quasi-Markov State Models (qMSMs) using MD simulations that are 5–10 times shorter than those required by MSMs. These qMSMs only contain a handful of metastable states and, thus, can greatly facilitate the interpretation of mechanisms associated with protein dynamics. A qMSM opens the door to the study of conformational changes of complex biomolecules where a Markovian model with a few states is often difficult to construct due to the limited length of available MD simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Analysis of Phase-Type Stochastic Petri Nets With Discrete and Continuous Timing

The Petri net formalism is useful in studying many discrete-state, discrete-event systems exhibiting concurrency, synchronization, and other complex behavior. As a bipartite graph, the net can conveniently capture salient aspects of the system. As a mathematical tool, the net can specify an analyzable state space. Indeed, one can reason about certain qualitative properties (from state occupancies) and how they arise (the sequence of events leading there). By introducing deterministic or random delays, the model is forced to sojourn in states some amount of time, giving rise to an underlying stochastic process, one that can be specified in a compact way and capable of providing quantitative, probabilistic measures. We formalize a new non-Markovian extension to the Petri net that captures both discrete and continuous timing in the same model. The approach affords efficient, stationary analysis in most cases and efficient transient analysis under certain restrictions. Moreover, this new formalism has the added benefit in modeling fidelity stemming from the simultaneous capture of discrete- and continuous-time events (as opposed to capturing only one and approximating the other). We show how the underlying stochastic process, which is non-Markovian, can be resolved into simpler Markovian problems that enjoy efficient solutions. Solution algorithms are provided that can be easily programmed.

Jones, Robert L.↗

On model reduction

Three model reduction methods are described. These are the discrete balanced realizations of Mullis and Roberts (1976) where a characterization of the reduction error is given and a previously unknown L(infinity) norm bound on the reduction error, is obtained. Another method is a new model reduction technique for discrete time systems which has the advantage that the reduced order model is balanced and has an L(infinity) norm bound on the reduction error. The last method derived is a frequency weighting technique for continuous and discrete systems where it is possible to specify the approximation accuracy with frequency and also, for this method, an L(infinity) norm on the weighted reduction error is obtained.

Al-Saggaf, Ubaid M.↗

Generalized covariance analysis for partially autonomous deep space missions

A new covariance analysis method is presented that is suitable for the evaluation of multiple impulsive controllers acting on some stochastic process x. The method accommodates batch and sequential estimators with equal ease and accounts for time-delay effects in a natural manner. The formalism is developed in terms of a generalized state vector that is formed from the system state vector x, augmented by various fixed epoch estimates, and a data vector formed from discrete time observations of the system. Recursions are developed for time transition, measurement incorporation, and impulsive control updating of the generalized covariance matrix. Means of limiting the dimensional growth of the generalized state vector via the processes of estimator epoch adjustment and measurement vector deflation are described and the application of numerically stable matrix factorization methods to the generalized covariance recursions is outlined. The method is applied to the Magellan spacecraft to demonstrate the capability of ground-based optimal estimation and control of gyro/star scanner misalignment.

Boone, Jack N.↗

Modelling and computationally efficient time domain linear equalisation of nonlinear bandlimited QPSK satellite channels

The problem of modeling and equalization of a nonlinear satellite channel is considered. The channel is assumed to be bandlimited and exhibits both amplitude and phase nonlinearities. In traditional models, computations are usually performed in the frequency domain and solutions are based on complex numerical techniques. A discrete time model is used to represent the satellite link with both uplink and downlink white Gaussian noise. Under conditions of practical interest, a simple and computationally efficient time-domain design technique for the minimum mean square error linear equalizer is presented. The efficiency of this technique is enhanced by the use of a fast and simple iterative algorithm for the computation of the autocorrelation coefficients of the output of the nonlinear channel. Numerical results on the evaluations of bit error probability and other relevant parameters needed in the design and analysis of a nonlinear bandlimited QPSK system demonstrate the simplicity and computational efficiency of the proposed approach.

Konstantinides, K.↗

Enhanced Fuel-Optimal Trajectory-Generation Algorithm for Planetary Pinpoint Landing

An enhanced algorithm is developed that builds on a previous innovation of fuel-optimal powered-descent guidance (PDG) for planetary pinpoint landing. The PDG problem is to compute constrained, fuel-optimal trajectories to land a craft at a prescribed target on a planetary surface, starting from a parachute cut-off point and using a throttleable descent engine. The previous innovation showed the minimal-fuel PDG problem can be posed as a convex optimization problem, in particular, as a Second-Order Cone Program, which can be solved to global optimality with deterministic convergence properties, and hence is a candidate for onboard implementation. To increase the speed and robustness of this convex PDG algorithm for possible onboard implementation, the following enhancements are incorporated: 1) Fast detection of infeasibility (i.e., control authority is not sufficient for soft-landing) for subsequent fault response. 2) The use of a piecewise-linear control parameterization, providing smooth solution trajectories and increasing computational efficiency. 3) An enhanced line-search algorithm for optimal time-of-flight, providing quicker convergence and bounding the number of path-planning iterations needed. 4) An additional constraint that analytically guarantees inter-sample satisfaction of glide-slope and non-sub-surface flight constraints, allowing larger discretizations and, hence, faster optimization. 5) Explicit incorporation of Mars rotation rate into the trajectory computation for improved targeting accuracy. These enhancements allow faster convergence to the fuel-optimal solution and, more importantly, remove the need for a "human-in-the-loop," as constraints will be satisfied over the entire path-planning interval independent of step-size (as opposed to just at the discrete time points) and infeasible initial conditions are immediately detected. Finally, while the PDG stage is typically only a few minutes, ignoring the rotation rate of Mars can introduce 10s of meters of error. By incorporating it, the enhanced PDG algorithm becomes capable of pinpoint targeting.

Acikmese, Behcet↗

Space Shuttle Redesigned Solid Rocket Motor nozzle natural frequency variations with burn time

The effects of erosion and thermal degradation on the Space Shuttle Redesigned Solid Rocket Motor (RSRM) nozzle's structural dynamic characteristics were analytically evaluated. Also considered was stiffening of the structure due to internal pressurization. A detailed NASTRAN finite element model of the nozzle was developed and used to evaluate the influence of these effects at several discrete times during motor burn. Methods were developed for treating erosion and thermal degradation, and a procedure was developed to account for internal pressure stiffening using differential stiffness matrix techniques. Results were verified using static firing test accelerometer data. Fast Fourier Transform and Maximum Entropy Method techniques were applied to the data to generate waterfall plots which track modal frequencies with burn time. Results indicate that the lower frequency nozzle 'vectoring' modes are only slightly affected by erosion, thermal effects and internal pressurization. The higher frequency shell modes of the nozzle are, however, significantly reduced.

Lui, C. Y.↗

Computer graphic visualization of orbiter lower surface boundary-layer transition

Computer graphic techniques are applied to the processing of Shuttle Orbiter flight data in order to create a visual presentation of the extent and movement of the boundary-layer transition front over the orbiter lower surface during entry. Flight-measured surface temperature-time histories define the onset and completion of the boundary-layer transition process at any measurement location. The locus of points which define the spatial position of the boundary-layer transition front on the orbiter planform is plotted at each discrete time for which flight data are available. Displaying these images sequentially in real-time results in an animated simulation of the in-flight boundary-layer transition process.

Throckmorton, D. A.↗

Stable feedback control of distributed parameter systems: Time and frequency domain conditions

Large space structures, or any mechanically flexible structures, are inherently distributed parameter systems (DPS) whose dynamics are modeled by partial, rather than ordinary, differential equations. Such DPS are described by operator equations on an infinite-dimensional Hilbert (or Banach) space. However, any feedback controller for such a DPS must be a finite-dimensional (and discrete-time) system in order to be implemented with on-line digital computers and a finite (small) number of actuators and sensors. There are many ways to synthesize such controllers; the Galerkin or finite-element approach is emphasized.

Balas, M. J.↗

Parallelized Quadrupole Simulations of Thermographic Responses of Composites

Thermography has been shown to be a viable technique for inspection of composites. Model inversion of the thermography data requires a fast method for performing the forward problem. Viable numerical methods for the thermal response forward problem are finite element, finite difference and the quadrupole method. Normally both the finite element and finite difference methods solve for the thermal response in the time domain which limits one’s ability to increase the speed of the simulation by parallelization. In contrast, the quadrupole method solves for the Laplace transform of the thermal response. One of the features of the Laplace transform methodology is the solution at any discrete time is independent of the solution at all other times. Therefore, it is easy to separate into a set of independent calculations with each of the times of interest being performed in parallel. Additionally, the numeric inversion of the Laplace transform typically involves numerically solving for the Laplace transform at multiple Laplace frequencies. Each of those solutions are also independent of solutions at other frequencies and can be calculated in parallel. By parallelization of this method, it is possible to perform the simulations of three-dimensional configurations in seconds. When the input stimulus for thermal response is a delta function heat flux (a reasonable approximation for flash heating), the thermal response is smooth. For this case, it is possible to accurately estimate the thermal response at any time within a given time interval from a set of simulations separated by exponentially increasing time steps. From these simulations, it is possible to accurately interpolate to find the response at intermediate times by a spline interpolation of the logarithm of time versus logarithm of temperature. The thermal response with exponential time stepping is shown to produce values for the thermal response which are within 1% of values within the time interval. The simulations are compared to finite element simulations of the same inspection configurations. The simulations are also compared to the thermographic measurements on composites where shape and depth of the delaminations are obtained from other inspection methods.

Thermography↗

Parallelized Quadrupole Simulations of Thermographic Responses of Composites

Thermography has been shown to be a viable technique for inspection of composites. Model inversion of the thermography data requires a fast method for performing the forward problem. Viable numerical methods for the thermal response forward problem are finite element, finite difference and the quadrupole method. Normally both the finite element and finite difference methods solve for the thermal response in the time domain which limits one’s ability to increase the speed of the simulation by parallelization. In contrast, the quadrupole method solves for the Laplace transform of the thermal response. One of the features of the Laplace transform methodology is the solution at any discrete time is independent of the solution at all other times. Therefore, it is easy to separate into a set of independent calculations with each of the times of interest being performed in parallel. Additionally, the numeric inversion of the Laplace transform typically involves numerically solving for the Laplace transform at multiple Laplace frequencies. Each of those solutions are also independent of solutions at other frequencies and can be calculated in parallel. By parallelization of this method, it is possible to perform the simulations of three-dimensional configurations in seconds. When the input stimulus for thermal response is a delta function heat flux (a reasonable approximation for flash heating), the thermal response is smooth. For this case, it is possible to accurately estimate the thermal response at any time within a given time interval from a set of simulations separated by exponentially increasing time steps. From these simulations, it is possible to accurately interpolate to find the response at intermediate times by a spline interpolation of the logarithm of time versus logarithm of temperature. The thermal response with exponential time stepping is shown to produce values for the thermal response which are within 1% of values within the time interval. The simulations are compared to finite element simulations of the same inspection configurations. The simulations are also compared to the thermographic measurements on composites where shape and depth of the delaminations are obtained from other inspection methods.

Thermography↗

Variable Structure PID Control to Prevent Integrator Windup

PID controllers are frequently used to control systems requiring zero steady-state error while maintaining requirements for settling time and robustness (gain/phase margins). PID controllers suffer significant loss of performance due to short-term integrator wind-up when used in systems with actuator saturation. We examine several existing and proposed methods for the prevention of integrator wind-up in both continuous and discrete time implementations.

Hall, C. E.↗

The behavior of quantization spectra as a function of signal-to-noise ratio

An expression for the spectrum of quantization error in a discrete-time system whose input is a sinusoid plus white Gaussian noise is derived. This quantization spectrum consists of two components: a white-noise floor and spurious harmonics. The dithering effect of the input Gaussian noise in both components of the spectrum is considered. Quantitative results in a discrete Fourier transform (DFT) example show the behavior of spurious harmonics as a function of the signal-to-noise ratio (SNR). These results have strong implications for digital reception and signal analysis systems. At low SNRs, spurious harmonics decay exponentially on a log-log scale, and the resulting spectrum is white. As the SNR increases, the spurious harmonics figure prominently in the output spectrum. A useful expression is given that roughly bounds the magnitude of a spurious harmonic as a function of the SNR.

Flanagan, M. J.↗

WRLES: Wave Resolving Large-Eddy Simulation Code, Theory and Usage

A computational fluid dynamics code has been developed for large-eddy simulations (LES) of turbulent flow. The code uses high-order of accuracy and high-resolution numerical methods to minimize solution error and maximize the resolution of the turbulent structures. Spatial discretization is performed using explicit central differencing. The central differencing schemes in the code include 2nd- to 12th-order standard central difference methods as well as 7-, 9-, 11- and 13-point dispersion relation preserving schemes. Solution filtering and high-order shock capturing are included for stability. Time discretization is performed using multistage Runge-Kutta methods that are up to 4th order accurate. Several options are available to model turbulence including: Baldwin-Lomax and Spalart-Allmaras Reynolds-averaged Navier-Stokes turbulence models, and Smagorinsky, Dynamic Smagorinsky and Vreman sub-grid scale models for LES. This report presents the theory behind the numerical and physical models used in the code and provides a user's manual to the operation of the code.

High-Order↗

Numerically Relevant Timescales in the MG2 Microphysics Model

Climate models rely on parameterizations of a variety of processes in the atmospheric physics, but a common concern is that the temporal resolution is too coarse to consistently resolve the behavior that individual parameterizations are designed to capture. This study examines timescales numerically derived from the Morrison-Gettelman (MG2) microphysics as implemented within the Energy Exascale Earth System Model, version 1 (E3SMv1). Numerically relevant timescales in MG2 are derived by computing the eigenspectrum of its Jacobian. These timescales are found to often be smaller than the default 5 min time step used for MG2. The fast timescales are then heuristically connected to individual microphysics processes. By substepping a few particular rain processes within MG2, the time discretization error for those processes was considerably reduced with minimal additional expense to the overall microphysics. While this improvement has a substantial effect on the target processes and on the vertical distribution of stratiform-derived rain within E3SMv1, the overall model climate is found to not be sensitive to MG2 time step. Here, we hypothesize that this is because the surface climate does not depend strongly on certain process rates, especially MG2's rain evaporation rate.

58 GEOSCIENCES↗

Newly found evidence of Sun-climate relationships

Solar radiation cycles drive climatic changes intercyclically. These interdecadal changes were detected as variations in solar total irradiances over the time period of recorded global surface-air-temperature (SAT) and have been restored utilizing Earth Radiation Budget Channel 10C measurements (1978-1990), Greenwich Observatory faculae data (1874-1975), and Taipei Observatory Active Region data (1964-1991). Analysis of the two separate events was carried out by treating each as a discrete time series determined by the length of each solar cycle. The results show that the global SAT responded closely to the input of solar cyclical activities, S, with a quantitative relation of T = 1.62 * S with a correlation coefficient of 0.61. This correlation peaks at 0.71 with a built-in time lag of 32 months in temperature response. Solar forcing in interannual time scale was also detected and the derived relationship of T = 0.17 * S with a correlation coefficient of 0.66 was observed. Our analysis shows derived climate sensitivities approximately fit the theoretical feedback slope, 4T(sup 3).

Kim, Hongsuk H.↗