Deterministic Signals Research Articles

Toward a Self-Powered Vibration Sensor: The Signal Processing Strategy

This paper, for the first time, investigates the possibility of exploiting a nonlinear bistable snap-through buckling structure employing piezoelectric transducers, to implement an autonomous sensor of mechanical vibrations, with an embedded energy harvesting functionality. The device is operated in the presence of noisy vibrations superimposed on a subthreshold deterministic (sinusoidal) input signal. While the capability of the device to harvest a significant amount of energy has been demonstrated in previous works, here, we focus on the signal processing methodology aimed to extract from the sensor output the information about the noise level (in terms of the standard deviation) and the root mean square amplitude of the deterministic component. The developed methodology, supported by experimental evidence, removes the contribution to the overall piezoelectric output voltage ascribable to the deterministic component using a thresholding and windowing algorithm. The contribution to the output voltage due to the noise can be used to unambiguously estimate the noise level. Moreover, an analytical model to estimate, from the measurement of the output voltage, the RMS amplitude of the deterministic input and the noise-related component is proposed.

The spectrogram, method of reassignment, and frequency-domain beamforming.

A smeared spectrogram is a result of the smoothing kernel in the short-time Fourier-transform (STFT). Besides the smeared energy, time and frequency phase information is also smeared, i.e., spectral components may contain imprecise phase information. The STFT is also used as the basis for more advanced signal processing techniques such as frequency-domain beamforming and cross correlation (CC). Both methods seek the delay time between signals by exploring phase-shifts in the frequency domain. Due to the inexact phase information in some of the time-frequency elements, their phase shifts are incorrect. This study re-introduces the reassigned spectrogram (RS) as a measure to fix the STFT artifacts. Moreover, it is shown that by using the RS, phase shifts can be optimized and improve beamforming and CC results. Synthetic and recorded data are used to show the advantage of using the RS in time-frequency analysis, CC, and beamforming. Results show that, subject to certain constraints, the RS provides exact time-frequency representation of deterministic signals and significantly improve CC and beamforming results. Array analysis of infrasonic signals shows that better results are obtained by either the RS- or STFT-based analysis depending on the signals' spectral components and noise levels.

Singular vector and singular subspace distribution for the matrix denoising model

In this paper, we study the matrix denoising model $Y=S+X$, where $S$ is a low rank deterministic signal matrix and $X$ is a random noise matrix, and both are $M\times n$. In the scenario that $M$ and $n$ are comparably large and the signals are supercritical, we study the fluctuation of the outlier singular vectors of $Y$, under fully general assumptions on the structure of $S$ and the distribution of $X$. More specifically, we derive the limiting distribution of angles between the principal singular vectors of $Y$ and their deterministic counterparts, the singular vectors of $S$. Further, we also derive the distribution of the distance between the subspace spanned by the principal singular vectors of $Y$ and that spanned by the singular vectors of $S$. It turns out that the limiting distributions depend on the structure of the singular vectors of $S$ and the distribution of $X$, and thus they are nonuniversal. Statistical applications of our results to singular vector and singular subspace inferences are also discussed.

Calibration for Parameter Estimation of Signals with Complex Noise via Nonstationarity Measure

The signals in numerous complex systems of engineering can be regarded as nonlinear parameter trend with noise which is identically distributed random signals or deterministic stationary chaotic signals. The commonly used methods for parameter estimation of nonlinear trend in signals are mainly based on least squares. It can cause inaccurate estimation results when the noise is complex (such as non-Gaussian noise, strong noise, and chaotic noise). This paper proposes a calibration method for this issue in the case of single parameter via nonstationarity measure from the perspective of the stationarity of residual sequence. Some numerical studies are conducted for validation. Results of numerical studies show that the proposed calibration method performs well for various models with different noise strengths and types (including random noise and chaotic noise) and can significantly improve the accuracy of initial estimates obtained by least squares method. This is the first time that the nonstationarity measure is applied to the parameter calibration. All these results will be a guide for future studies of other parameter calibrations.

Интегральная оценка параметров усилителя мощности радиопередатчика с автоматической регулировкой режима двухчастотным тестовым сигналом

Comparative estimation of energy parameters of power amplifiers of single-band radio transmitters using automatic mode adjustment using a deterministic two-frequency test signal instead of a random single-band signal modulated by speech is investigated in the work. Relationships are found that allow judging the power consumption of the terminal stage of the power amplifier with automatic mode adjustment under various types of modulation based on the results of measurements obtained during tests. The ratios between the power consumption of the output stage when amplifying the random speech signal and amplifying the deterministic two-frequency test signal are obtained both without taking into account losses in the controlled power supply and taking into account such losses. Method is proposed for calculation of energy gain and efficiency factor (efficiency) when applying automatic control of supply voltage of output cascades of shortwave transmitters intended for modulation with speech signals. The loss in the regulated power supply has been estimated. The advantage of power amplifier circuits with automatic mode adjustment is justified

Damage indices evaluation for one-dimensional guided wave-based structural health monitoring

Damage detection in structures and systems is essential for monitoring parameters that can affect their integrity. This paper evaluates the efficiency of four damage indices (DIs) commonly used with temporal wave signals. The root mean square deviation, mean absolute percentage deviation, covariance, and correlation coefficient deviation DIs are presented, and a normalization is then proposed. An Euler-Bernoulli beam is used as a guided wave modelled with the spectral element method and excited by a toneburst signal. It includes the theoretical background of the throw-off beam, undamaged and cracked beam spectral elements. The DIs for a single crack position and a map varying crack depth and positions are calculated with deterministic and random temporal signal responses derived from noise addition. Results showed that DIs could identify and quantify the damage conditioned to the pulse location point and the influence of noise in the estimation, which leads in an analysis comparable to practical applications.

Adaptation of Fluctuating Magnetoacoustic System to External Signals

The adaptation of systems to external influences is of broad interest. We study the influence of microwave signals of different shapes on the magnetoacoustic wave system with a giant nonlinearity in canted antiferromagnet FeBO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> at room temperature, which is close to its phase transition to the paramagnetic state. The classical nonlinear system obeys external deterministic signals; the modulation response describes the shape of these signals. In response to a noisy spectrum, the system shows self-organization, and mode competition selects one excited mode while suppressing others. With an increase in the power of the external signal, another self-organization is observed in the form of a narrow peak at the frequency of the fundamental minimum. This represents the first observation of the macroscopic quantum statistical phenomenon, Bose-Einstein condensation of magnetoacoustic wave quanta in a wave system with a high level of thermal fluctuations. The resulting picture of adaptation can analogously be transferred to many other adaptive wave systems, including large scale adaptive wave systems in the natural environment.

Optimal Sparse Sampling for Detection of a Known Signal in Nonwhite Gaussian Noise

We address the problem of sparse sampling pattern design to maximize detection for a deterministic signal in colored noise. We model a colored noise as a continuous-time autoregressive process, which is obtained by passing a white noise through a causal linear-time invariant filter. This noise modeling is crucial to the development of the optimal sampling pattern design for a given number of sensors. We obtain a closed form expression for the whitening filter and consequently, for the Kullback-Leibler divergence at the whitening filter output, which is the detection index. The optimum sampling pattern is obtained by evaluating the detection index at Nyquist sampling rate, rank ordering the samples, and selecting the maximum values. We present some examples to illustrate the proposed procedure. We also extend our method to two-dimensional sampling. The advantage of our approach is its low computational complexity for both one-dimensional and two-dimensional cases and that optimality is guaranteed.

Synthesis of Differentiators to Estimate Derivatives of Target Signals in the UAV Control System

Abstract The paper deals with tracking systems for unmanned aerial vehicle under external disturbances. Within the framework of the block approach, the combined control law is developed that provides invariance with respect to external disturbances in a closed system via linear control with saturation. Under the assumption that the analytical form of the target signals is not known, dynamic differentiators with piecewise linear correcting influences are designed to estimate unknown derivatives of target signals. These differentiators are replicas of canonical virtual models with unknown inputs and provide estimates of the derivatives of deterministic signals with a given accuracy in a given time. The simulation results are presented, confirming the effectiveness of the developed algorithms.

Random response of a simple system with stochastic uncertainty and noise in parameters

The paper is concerned with the analysis of the simultaneous effect of a random perturbation and white noise in the coefficient of the system on its response. The excitation of the system of the 1st order is described by the sum of a deterministic signal and additive white noise, which is partly correlated with a parametric noise. The random perturbation in the parameter is considered statistics in a set of realizations. It reveals that the probability density of these perturbations must be limited in the phase space, otherwise the system would lose the stochastic stability in probability, either immediately or after a certain time. The width of the permissible zone depends on the intensity of the parametric noise, the extent of correlation with the additive excitation noise, and the type of probability density. The general explanation is demonstrated on cases of normal, uniform, and truncated normal probability densities.

Using a learned algorithm for detecting a deterministic signal in a noise of unknown intensity

The main sources of noise and interference, the features of detecting signals in noises, methods of dealing with them during transmission over various distances are considered. Passive methods of dealing with noise and interference are to reduce the length of cable networks to a reasonable minimum and reduce the number of cables; using only high quality cables and connectors from well-known manufacturers; laying cables with large bending radii to avoid interference from the so-called triboelectric effect; separation of signal and power cable trunks; using matched loads; in such a use of equipment so that its operating conditions are significantly lower than the limiting ones; in using the most interference-resistant interface. Active methods of dealing with noise and interference consist in the use of intermediate signal amplifiers that compensate for their attenuation in the line due to ohmic resistance and losses at high frequencies due to cable reactivity; switching to a twisted pair; switching to fiber-optic cable when it is necessary to transmit a signal over long distances. In a number of problems of signal reception in the presence of noise, one cannot be limited by such a general criterion as the signal-to-noise ratio. There is a need to use more subtle statistical properties of processes that allow one to quantify the reliability of the data. Noise is an important problem in science and technology because it defines lower limits both in terms of the accuracy of any measurement and in terms of the magnitude of signals that can be processed electronically. An adaptive detection of signals in noise is defined, using an optimal detection algorithm for analysis. An algorithm is proposed for detecting a signal in noise both in discrete observation and in the transition to continuous observation of signals. Probabilistic characteristics of signal detection in noise of unknown and known intensity of the learning algorithm are constructed.

Adaptive Internal Model Theory of the Oculomotor System and the Cerebellum

In this article, we present a computational model of the oculomotor system and the cerebellum. In contrast with prevailing theories of cerebellar function, we propose the cerebellum embodies adaptive internal models of all persistent, exogenous, deterministic signals acting on the body and observable through the error signals it receives. Our model is validated by simulations, recovering results from a number of oculomotor experiments.

Correlation dimension and approximate entropy for machine condition monitoring: Revisited

The sparsity of signals is of great concern in various research domains. In mechanical systems and signal processing, repetitive transients are the symptoms of localized gear and bearing faults and they are sparse signals. During the recent years, sparsity measures, such as kurtosis and Shannon entropy, have been thoroughly studied to quantify repetitive transients for machine condition monitoring. Spectral kurtosis and spectral negative Shannon entropy are two typical examples of sparsity measures for machine condition monitoring. Besides sparsity measures, complexity measures including correlation dimension (CD) and approximate entropy (AE) have been experimentally studied during the recent years. However, theoretical investigations on these two complexity measures for machine condition monitoring are seldom reported. This paper aims to fill this research gap and propose some new theorems and proofs to show that CD and AE have a “bilateral reduction” effect, which is a proper measure of entropy. Specifically, CD with any dimension and AE with smaller dimension become smaller when a signal is getting sparser or more deterministic, which is significantly different from sparsity measures that are monotonically increasing when a signal is getting from more deterministic to sparser. This new discovery is able to help readers fully understand the main difference between sparsity measures and complexity measures. In view of this discovery, it is suggested that the concept of blind fault component separation should be used to separate low-frequency periodic components (a deterministic signal) from high-frequency repetitive transients (a sparse signal) before complexity measures are used for machine condition monitoring. This suggestion aims to avoid the uncertainty of machine condition monitoring caused by low-frequency periodic components and high-frequency repetitive transients.

Adaptive prescribed performance neural network control for switched stochastic pure-feedback systems with unknown hysteresis

This paper investigates the problem of neural network (NN) prescribed performance tracking control for a class of switched stochastic nonlinear pure-feedback systems which contain unknown nonlinear functions, unmeasured state variables, and unknown hysteresis input. It provides an adaptive NN controller which is not restricted to a particular type of hysteresis input. A general mathematical model is introduced to describe two kinds of hysteresis nonlinearities and to utilize in the control design producer. Other focus of this paper is on the performance constraint problem to avoid performance degradation and system damage in practical control systems. Prescribed performance control (PPC) and backstepping technique are thus synthesized to develop an adaptive NN output feedback tracking control scheme under deterministic switching signal. Regarding this concern, to cope with the cause of non-differentiable difficulties and complex deductions in traditional PPC, a new asymmetry error transformation is employed. Moreover, radial basis function NNs (RBFNNs) are applied to approximate the unknown nonlinear functions and to construct a NN nonlinear observer to estimate the immeasurable state variables. Based on Lyapunov stability theory, it is demonstrated that the proposed controller can guarantee that all signals in the closed-loop system are semiglobally uniformly ultimately bounded in probability and the tracking error converges to a small neighborhood of the origin with the prescribed performance bounds. Finally, two simulation examples are provided to confirm the advantages of the presented control design approach.

AF-MNS: A Novel AM-FM Based Measure of Non-Stationarity

Robust signal processing in any application depends on the representation and the understanding of the signals in hand. There is a plethora of signal processing methods, wherein choosing a method over others would depend on the attributes of the signals and their intended application. As of now, only spectral stationarity is discussed for the deterministic signals. This letter presents a novel amplitude-modulation-frequency-modulation (AM-FM) based measure of non-stationarity of the deterministic signals by extracting AM-FM components using the Fourier decomposition method (FDM). FDM generates analytic signal representation, where the real and imaginary parts are the Hilbert transform pairs. Simple and intuitive measures of amplitude and frequency non-stationarity are presented to quantitatively assess the extent of non-stationarity. Both these measures are zero for stationary signals, while at least one of them is positive for the non-stationary signals. Important observations regarding the stationarity of a signal are made with the help of some examples. The utility of the concept is demonstrated via an application of EEG signal classification.

Cluster analysis based fringe-activity range detector

A novel clustering-analysis approach is proposed in this work. This approach addresses the fringe-activity range-detection issue often encountered in vertical-scanning wideband interferometry. The proposed approach exploits the fact that the fringe signal formed by a wideband light source, which is composed of deterministic signals and a random noise signal. As a result, the number of clusters in the proposed clustering method can be easily specified as 2, in advance. The proposed analysis procedure and its development using a k-means method-based clustering scheme are described in this paper. To the best of the authors’ knowledge, this is the first investigation report regarding fringe-activity range detection. The details of the proposed approach are introduced within the framework of femtosecond optical frequency comb-based interferometry. Experimental results demonstrate the efficiency of the proposed algorithm with respect to the fringe-activity range detection.

Complex-valued neural networks for machine learning on non-stationary physical data

Deep learning has become an area of interest in most scientific areas, including physical sciences. Modern networks apply real-valued transformations on the data. Particularly, convolutions in convolutional neural networks discard phase information entirely. Many deterministic signals, such as seismic data or electrical signals, contain significant information in the phase of the signal. We explore complex-valued deep convolutional networks to leverage non-linear feature maps. Seismic data commonly has a lowcut filter applied, to attenuate noise from ocean waves and similar long wavelength contributions. In non-stationary data, the phase content can stabilize training and improve the generalizability of neural networks. While it has been shown that phase content can be restored in deep neural networks, we show how including phase information in feature maps improves both training and inference from deterministic physical data. Furthermore, we show that smaller complex networks outperform larger real-valued networks.

Hand Gesture Recognition for Smart Devices by Classifying Deterministic Doppler Signals

Personal devices such as smartphones and tablets are rapidly becoming personal communication, information, and control centers. Apart from multitouch screens, human gestures are considered as a new interactive human–smart device interface. In this work, we propose a noncontact solution to implement hand gesture recognitions for smart devices. It is based on a continuous wave, time-division-multiplexing (TDM), single-input multiple-output (SIMO) Doppler radar sensor that can be realized by slightly modifying existing RF front ends of smart devices, and a machine-learning algorithm to recognize predefined gestures by classifying deterministic Doppler signals. An experimental setup emulating a smartphone-based radar sensor was implemented, and the experimental results verified the robustness and the accuracy of the proposed approach.

Digital Root-mean-square Signal Meter

This paper introduces a meter of the root-mean-square value of deterministic and stochastic signals of an arbitrary shape that are generated over the set time interval. Such a meter involves only the minimum number of simple arithmetic operations to obtain results, and it ensures a high degree of measurement accuracy. For this purpose, the direct calculation of the signal root-mean-square value is applied while the measurement of the half-period average straightened signal value is carried out by means of the traditional measurement devices. Implementation of this meter requires neither the knowledge of what the signal period is, nor the synchronization with the processed sampling. Simulation is then carried out demonstrating the high efficiency of the proposed measurement algorithm. We analyze the characteristics of the meter operating within a wide frequency range of the measurable signals. The recommendations concerning the hardware implementation of such a meter by means of the field programmable gate arrays are considered. The meter can be used when designing digital high-frequency AC voltmeters and ammeters and it can provide the readings that do not depend upon the signal waveform.

Random Walk of Foraging

The model of vibration driven random walk is adapted to description of foraging performed by simple organisms. Stochastic properties of foraging are described by the Gaussian random number generator, while the attraction of food is represented by a deterministic signal that directs walkers from surroundings to the food. This attraction causes transition from the Gaussian random walk to the Levy flight.