Limiting performance characteristics of randomly disturbed dynamic systems, a survey
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Pilkey, W. D.↗
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Results for “Random Systems”
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The Steady State Behavior of Randomly Perturbed Dynamical Systems
The statistical behavior of nonlinear systems near stable.
steady state behavior dynamic systems stable equil↗
Randomness fault detection system
A method and apparatus are provided for detecting a fault on a power line carrying a line parameter such as a load current. The apparatus monitors and analyzes the load current to obtain an energy value. The energy value is compared to a threshold value stored in a buffer. If the energy value is greater than the threshold value a counter is incremented. If the energy value is greater than a high value threshold or less than a low value threshold then a second counter is incremented. If the difference between two subsequent energy values is greater than a constant then a third counter is incremented. A fault signal is issued if the counter is greater than a counter limit value and either the second counter is greater than a second limit value or the third counter is greater than a third limit value.
Russell, B. Don↗
Response of linear systems to magnitude limited random excitation.
Magnitude limited random excitation effect on linear system response, using single degrees of freedom model representing idealized mechanical structure
Hu, P. Y.↗
Systems and methods for randomized, packet-based power management of conditionally-controlled loads and bi-directional distributed energy storage systems
The present disclosure provides a distributed and anonymous approach to demand response of an electricity system. The approach conceptualizes energy consumption and production of distributed-energy resources (DERs) via discrete energy packets that are coordinated by a cyber computing entity that grants or denies energy packet requests from the DERs. The approach leverages a condition of a DER, which is particularly useful for (1) thermostatically-controlled loads, (2) non-thermostatic conditionally-controlled loads, and (3) bi-directional distributed energy storage systems. In a first aspect of the present approach, each DER independently requests the authority to switch on for a fixed amount of time (i.e., packet duration). The coordinator determines whether to grant or deny each request based electric grid and/or energy or power market conditions. In a second aspect, bi-directional DERs, such as distributed-energy storage systems (DESSs) are further able to request to supply energy to the grid.
Frolik, Jeff↗
Detecting hidden transient events in noisy nonlinear time-series
The information impulse function (IIF), running Variance, and local Hölder Exponent are three conceptually different time-series evaluation techniques. These techniques examine time-series for local changes in information content, statistical variation, and point-wise smoothness, respectively. Using simulated data emulating a randomly excited nonlinear dynamical system, this study interrogates the utility of each method to correctly differentiate a transient event from the background while simultaneously locating it in time. Computational experiments are designed and conducted to evaluate the efficacy of each technique by varying pulse size, time location, and noise level in time-series. Our findings reveal that, in most cases, the first instance of a transient event is more easily observed with the information-based approach of IIF than with the Variance and local Hölder Exponent methods. While our study highlights the unique strengths of each technique, the results suggest that very robust and reliable event detection for nonlinear systems producing noisy time-series data can be obtained by incorporating the IIF into the analysis.
42 ENGINEERING↗
A pseudo random-access synchronous meteorological satellite system
Communications satellite system uses pseudo-random time frequency multiplexing technique for extracting real-time meteorological data from great number of isolated weather stations /data collection platforms/ situated randomly throughout the world.
Darcey, R. J.↗
Linear growth of circuit complexity from Brownian dynamics
How rapidly can a many-body quantum system generate randomness? Using path integral methods, we demonstrate that Brownian quantum systems have circuit complexity that grows linearly with time. In particular, we study Brownian clusters of N spins or fermions with time-dependent all-to-all interactions, and calculate the Frame Potential to characterize complexity growth in these models. In both cases the problem can be mapped to an effective statistical mechanics problem which we study using path integral methods. Within this framework it is straightforward to show that the kth Frame Potential comes within ϵ of the Haar value after a time of order t ~ kN + k log k + log ϵ –1 . Using a bound on the diamond norm, this implies that such circuits are capable of coming very close to a unitary k-design after a time of order t ~ kN. We also consider the same question for systems with a time-independent Hamiltonian and argue that a small amount of time-dependent randomness is sufficient to generate a k-design in linear time provided the underlying Hamiltonian is quantum chaotic. These models provide explicit examples of linear complexity growth that are analytically tractable and are directly applicable to practical applications calling for unitary k-designs.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
A Procedure for Accurately Measuring the Shaker Overturning Moment During Random Vibration Tests
Motivation: For large system level random vibration tests, there may be some concerns about the shaker's capability for the overturning moment. It is the test conductor's responsibility to predict and monitor the overturning moment during random vibration tests. If the predicted moment is close to the shaker's capability, test conductor must measure the instantaneous moment at low levels and extrapolate to higher levels. That data will be used to decide whether it is safe to proceed to the next test level. Challenge: Kistler analog formulation for computing the real-time moment is only applicable to very limited cases in which we have 3 or 4 load cells installed at shaker interface with hardware. Approach: To overcome that limitation, a simple procedure was developed for computing the overturning moment time histories using the measured time histories of the individual load cells.
predict overturning↗
GenMod: A generative modeling approach for spectral representation of PDEs with random inputs
Here, we propose a method for quantifying uncertainty in high-dimensional PDE systems with random parameters, where the number of solution evaluations is small. Parametric PDE solutions are often approximated using a spectral decomposition based on polynomial chaos expansions. For the class of systems we consider (i.e., high dimensional with limited solution evaluations) the coefficients are given by an underdetermined linear system in a regression formulation. This implies additional assumptions, such as sparsity of the coefficient vector, are needed to approximate the solution. Here, we present an approach where we assume the coefficients are close to the range of a generative model that maps from a low to a high dimensional space of coefficients. Our approach is inspired be recent work examining how generative models can be used for compressed sensing in systems with random Gaussian measurement matrices. Using results from PDE theory on coefficient decay rates, we construct an explicit generative model that predicts the polynomial chaos coefficient magnitudes. The algorithm we developed to find the coefficients, which we call GenMod, is composed of two main steps. First, we predict the coefficient signs using Orthogonal Matching Pursuit. Then, we assume the coefficients are within a sparse deviation from the range of a sign-adjusted generative model. This allows us to find the coefficients by solving a nonconvex optimization problem, over the input space of the generative model and the space of sparse vectors. We obtain theoretical recovery results for a Lipschitz continuous generative model and for a more specific generative model, based on coefficient decay rate bounds. We examine three high-dimensional problems and show that, for all three examples, the generative model approach outperforms sparsity promoting methods at small sample sizes.
97 MATHEMATICS AND COMPUTING↗
Estimates of the Statistics of Randomly Varying Parameters of Linear Systems
Mathematical model used in estimating statistics of randomly varying parameters of linear systems
IDENTIFICATION↗
A system identification technique based on the random decrement signatures. Part 1: Theory and simulation
Identification of the system parameters of a randomly excited structure may be treated using a variety of statistical techniques. Of all these techniques, the Random Decrement is unique in that it provides the homogeneous component of the system response. Using this quality, a system identification technique was developed based on a least-squares fit of the signatures to estimate the mass, damping, and stiffness matrices of a linear randomly excited system. The mathematics of the technique is presented in addition to the results of computer simulations conducted to demonstrate the prediction of the response of the system and the random forcing function initially introduced to excite the system.
Bedewi, Nabih E.↗
Digital servo control of random sound test excitation
A digital servocontrol system for random noise excitation of a test object in a reverberant acoustic chamber employs a plurality of sensors spaced in the sound field to produce signals in separate channels which are decorrelated and averaged. The average signal is divided into a plurality of adjacent frequency bands cyclically sampled by a time division multiplex system, converted into digital form, and compared to a predetermined spectrum value stored in digital form. The results of the comparisons are used to control a time-shared up-down counter to develop gain control signals for the respective frequency bands in the spectrum of random sound energy picked up by the microphones.
Nakich, R. B.↗
Hardware implementation for direct digital control of random excitation environmental testing
Direct digital control system for random excitation environmental testing, discussing interfacing of TIME/DATA time series processor and minicomputer
Chapman, C. P.↗
Petabyte mass memory system using the Newell Opticel(TM)
A random access system is proposed for digital storage and retrieval of up to a Petabyte of user data. The system is comprised of stacked memory modules using laser heads writing to an optical medium, in a new shirt-pocket-sized optical storage device called the Opticel. The Opticel described is a completely sealed 'black box' in which an optical medium is accelerated and driven at very high rates to accommodate the desired transfer rates, yet in such a manner that wear is virtually eliminated. It essentially emulates a disk, but with storage area up to several orders of magnitude higher. Access time to the first bit can range from a few milliseconds to a fraction of a second, with time to the last bit within a fraction of a second to a few seconds. The actual times are dependent on the capacity of each Opticel, which ranges from 72 Gigabytes to 1.25 Terabytes. Data transfer rate is limited strictly by the head and electronics, and is 15 Megabits per second in the first version. Independent parallel write/read access to each Opticel is provided using dedicated drives and heads. A Petabyte based on the present Opticel and drive design would occupy 120 cubic feet on a footprint of 45 square feet; with further development, it could occupy as little as 9 cubic feet.
Newell, Chester W.↗
A system identification technique based on the random decrement signatures. Part 2: Experimental results
Identification of the system parameters of a randomly excited structure may be treated using a variety of statistical techniques. Of all these techniques, the Random Decrement is unique in that it provides the homogeneous component of the system response. Using this quality, a system identification technique was developed based on a least-squares fit of the signatures to estimate the mass, damping, and stiffness matrices of a linear randomly excited system. The results of an experiment conducted on an offshore platform scale model to verify the validity of the technique and to demonstrate its application in damage detection are presented.
Bedewi, Nabih E.↗
Photoionization of Atomic Systems Using the Random-Phase Approximation Including Relativistic Interactions
Approximation methods are unavoidable in solving a many-electron problem. One of the most successful approximations is the random-phase approximation (RPA). Miron Amusia showed that it can be used successfully to describe atomic photoionization processes of many-electron atomic systems. In this article, the historical reasons behind the term “random-phase approximation” are revisited. A brief introduction to the relativistic RPA (RRPA) developed by Walter Johnson and colleagues is provided and some of its illustrative applications are presented.
74 ATOMIC AND MOLECULAR PHYSICS↗
Systems and methods for randomized energy draw or supply requests
The present disclosure can provide a distributed and anonymous approach to demand response of an electricity system. The approach can conceptualize energy consumption and production of distributed-energy resources (DERs) via discrete energy packets that are coordinated by a cyber computing entity that grants or denies energy packet requests from the DERs. The approach leverages a condition of a DER, which is particularly useful for (1) thermostatically-controlled loads, (2) non-thermostatic conditionally-controlled loads, and (3) bi-directional distributed energy storage systems, among others. In a first aspect of the present approach, each DER independently requests the authority to switch on for a fixed amount of time (i.e., packet duration). The coordinator determines whether to grant or deny each request based electric grid and/or energy or power market conditions. In a second aspect, bi-directional DERs, such as distributed-energy storage systems (DESSs) are further able to request to supply energy to the grid.
Frolik, Jeff↗