Stochastic Noise Source Research Articles

Stochastic Noise Sources for Computational Aeroacoustics of a Vehicle Side Mirror

<div>The broadband aeroacoustics of a side mirror is investigated with a stochastic noise source method and compared to scale-resolving simulations. The setup based on an already existing work includes two geometrical variants with a plain series side mirror and a modified mirror with a forward-facing step mounted on the inner side. The aeroacoustic near- and farfield is computed by a hydrodynamic–acoustic splitting approach by means of a perturbed convective wave equation. Aeroacoustic source terms are computed by the Fast Random Particle-Mesh method, a stochastic noise source method modeling velocity fluctuations in time domain based on time-averaged turbulence statistics. Three RANS models are used to provide input data for the Fast Random Particle-Mesh method with fundamental differences in local flow phenomena. Results of aeroacoustics simulations excited by the Fast Random Particle-Mesh method based on well-matching RANS data are in good agreement to the scale-resolving simulations in the integral acoustic Delta on the side window induced by the different side mirror geometries. For relative levels in between the variations, the robustness of the Fast Random Particle-Mesh method can be shown with secondary influences on the choice of the integral length scale. Absolute levels are only achieved with an adaptation of the length scale from literature. Two different RANS models with a missing separation bubble on the mirror or an overestimated wake flow show a good agreement with the plain series side mirror. However, they fail at computing the Delta to the step variant due to the missing amplification of the local turbulent kinetic energy interacting with the step and downstream mirror surfaces. Computational aeroacoustics simulations excited by the Fast Random Particle-Mesh method method based on RANS data only needs 14% of the computational effort compared to the conventional hybrid RANS-LES approach. This reveals its enormous potential for aeroacoustic broadband noise optimization purposes.</div>

Analytical solutions in amplitude and time measurements from discrete sampling of pseudo-Gaussian signals

Analytical solutions for amplitude and time measurements from digitized signals of the pseudo-Gaussian shape are considered. The least squares method (l.s.m.) is chosen as the algorithm to determine amplitude A and timestamp t0. For a profile with an uncorrelated sampling the l.s.m. is reduced to analytical formulas consistent with the experiment. This permits to estimate the desired number of points Ns on a profile. The obtained results for Ns are illustrated with qualitative estimates in accordance with the Nyquist–Shannon–Kotelnikov sampling theorem. The optimality of the electronic filters forming the waveform is analyzed in terms of the excess noise factor. An analytical solution is found for the autocorrelation function from stochastic noise sources. It permits to define non-diagonal weight matrix elements in the l.s.m. with formulation of requirements for neglecting sampling correlations.

Dynamic performance estimation: A design tool for mechatronic scanners

This paper presents an integrated framework for the dynamic performance estimation (DPE) of mechatronic scanners in the design phase, which is based on frequency domain models of system components and signals in the system. It considers stochastic noise sources (e.g. sensor noise) as well as deterministic signals (e.g. reference trajectory) and propagates each signal to the desired performance output (e.g. actuator current) via obtained transfer functions. The framework is evaluated for a 2 inch fast steering mirror (FSM) dedicated as optical scanner by comparing estimated and measured values for positioning uncertainty, rms coil current and rms tracking error. The estimated positioning uncertainty for the FSM with a range of 52.4 mrad deviates only 0.74 µrad from the measured value. The estimated values for three tested raster trajectories also show good agreement with the measurements resulting in averaged relative deviations of 12% for the rms current values and between 15-17% for the rms tracking error.

Design of high-throughput and low-power true random number generator utilizing perpendicularly magnetized voltage-controlled magnetic tunnel junction

A true random number generator based on perpendicularly magnetized voltage-controlled magnetic tunnel junction devices (MRNG) is presented. Unlike MTJs used in memory applications where a stable bit is needed to store information, in this work, the MTJ is intentionally designed with small perpendicular magnetic anisotropy (PMA). This allows one to take advantage of the thermally activated fluctuations of its free layer as a stochastic noise source. Furthermore, we take advantage of the voltage dependence of anisotropy to temporarily change the MTJ state into an unstable state when a voltage is applied. Since the MTJ has two energetically stable states, the final state is randomly chosen by thermal fluctuation. The voltage controlled magnetic anisotropy (VCMA) effect is used to generate the metastable state of the MTJ by lowering its energy barrier. The proposed MRNG achieves a high throughput (32 Gbps) by implementing a 64×64 MTJ array into CMOS circuits and executing operations in a parallel manner. Furthermore, the circuit consumes very low energy to generate a random bit (31.5 fJ/bit) due to the high energy efficiency of the voltage-controlled MTJ switching.

Investigation of the distance error induced by cycle-to-cycle jitter in a correlating time-of-flight distance measurement system

Time-of-flight (TOF) range sensors acquire distances by means of an optical signal delay measurement. As the signal travels at the speed of light, distance resolutions in the subcentimeters range require a time measurement resolution that is in the picoseconds range. However, typical clock synthesizers and digital buffers possess cycle-to-cycle jitter values of up to hundreds of picoseconds, which can potentially have a noticeable impact on the TOF system performances. In this publication, we investigate the influence of two common types of cycle-to-cycle jitter distributions on the measured distance. This includes a random Gaussian distribution, which is caused by, e.g., stochastic noise sources, and a discrete jitter distribution, which is found when timing constraints fail in synchronous digital designs. It was demonstrated that a Gaussian cycle-to-cycle jitter has only a negligible impact on the performance of the TOF distance sensors up to a standard deviation of 1 ns of the Gaussian jitter distribution. However, even the discrete cycle-to-cycle jitter investigated in its simplest form lowers the distance precision of the TOF sensor by a factor of 2.86, i.e., the standard deviation increases from 2.9 to 8.3 mm.

On the Problem of Reconstructing an Unknown Topology via Locality Properties of the Wiener Filter

Determining interrelatedness structure of various entities from multiple time series data is of significant interest to many areas. Knowledge of such a structure can aid in identifying cause and effect relationships, clustering of similar entities, identification of representative elements and model reduction. The majority of existing results are based on correlation based indices which effectively assume a static relationship between the time series data and are not suitable for detecting interrelatedness when the time series are dynamically related or when the time series involve loops. In this paper, a methodology for identifying the interrelatedness structure of dynamically related time series data is presented that also allows for the presence of loops in the connectivity structure. A linear dynamic graph model is presented where it is assumed that each time series data is the sum of an independent stochastic noise source and a dynamically weighted sum of other time series data. A link is assumed to be present between two time series if the weight of a time series, which is a linear time-invariant filter, is nonzero in the formation of the other. Reconstruction of the link connectivity structure under various scenarios is considered. It is shown that when the linear dynamic graph is allowed to admit non-causal weights, then the links structure can be recovered with the possibility of identifying spurious connections. However, it is shown that the spurious links remain local, where, a spurious link is restricted to be within one hop of a true link. Furthermore, strategies for exact reconstruction of the link structure when the weights are restricted to be causal are developed. The main tools for determining the network topology are based on variations of Wiener filtering. A significant insight provided by the article is that, in the class of network models considered in the paper, the Wiener filter estimating a stochastic process based on other processes remains local in the sense that the Wiener filter utilizes only measurements local to the node being estimated.

Entanglement dynamics in a non-Markovian environment: An exactly solvable model

We study the non-Markovian effects on the dynamics of entanglement in an exactly-solvable model that involves two independent oscillators each coupled to its own stochastic noise source. First, we develop Lie algebraic and functional integral methods to find an exact solution to the single-oscillator problem which includes an analytic expression for the density matrix and the complete statistics, i.e., the probability distribution functions for observables. For long bath time-correlations, we see non-monotonic evolution of the uncertainties in observables. Further, we extend this exact solution to the two-particle problem and find the dynamics of entanglement in a subspace. We find the phenomena of `sudden death' and `rebirth' of entanglement. Interestingly, all memory effects enter via the functional form of the energy and hence the time of death and rebirth is controlled by the amount of noisy energy added into each oscillator. If this energy increases above (decreases below) a threshold, we obtain sudden death (rebirth) of entanglement.

Decentralized identification for multivariable integrating processes with time delays from closed-loop step tests

In order to identify those multivariable processes with integrating factors in their transfer function matrices, a simple yet robust decentralized identification method from closed-loop step tests is proposed. By the frequency response matrix computed from the closed-loop system data and the knowledge of the decentralized controller, the structural information of the multivariable integrating process is determined firstly and then the continuous parametric model with dead times is approximated similarly with the parameterization of the open-loop stable process. Computer simulations and an application to a 3×3 integrating multiple-tank water level system verify the validation of the proposed method even if the closed-loop system is affected by some stochastic noise sources.

Study of current fluctuations in deep-submicron Si/SiGe n-channel MOSFET: impact of relevant technological parameters on the thermal noise performance

We present a study of the thermal noise locally generated in a Si/SiGe MOSFET. We use a Langevin stochastic noise source model in order to obtain the noise generated locally by random velocity fluctuations. Physical magnitudes governing local noise have been obtained using a two-dimensional device simulator that implements the hydrodynamic transport model for majority carriers. Local calculation of the spectral density of noise current, Sin, pinpoints the importance of an accurate physics-based noise model in order to fully understand the impact of technological parameters on the device noise performance. Our study shows that a reduction in the channel length will increase the local value of the noise sources across the channel. Results also suggest that a reverse doping of the channel could lead to significant reduction of Sin.

On the role of subthreshold dynamics in neuronal signaling.

The role of subthreshold dynamics in neuronal signaling is examined using periodic pulse train stimulation of the Fitzhugh-Nagumo (FN) model of nerve membrane excitability and results from the squid giant axon as an experimental data base. For a broad range of stimulus conditions the first pulse in a pulse train elicited an action potential, whereas all subsequent pulses elicited subthreshold responses, both in the axon and in the FN model. These results are not well described by the Hodgkin and Huxley 1952 model. Various different patterns of subthreshold responses, including chaotic dynamics, can be observed in both systems-the FN model and the axon-depending upon stimulus conditions. For some conditions action potentials are occasionally interspersed among the subthreshold events with randomly occurring interspike intervals. The randomness is directly attributable to the underlying subthreshold chaos-deterministic chaos-rather than to a stochastic noise source. We conclude that this mechanism may contribute to multimodal interspike interval histograms which have been observed from individual neurons throughout the nervous system.