Gaussian Signals Research Articles

Identification methodology for MIMO Hammerstein nonlinear model with process noise

In this paper, we present a methodology for identifying the multi-input–multi-output (MIMO) Hammerstein nonlinear model under colored noise. The Hammerstein model presented comprises neural fuzzy models (NFMs) as its static nonlinear block and rational transfer functions (RTF) model as its dynamic linear block. The hybrid signals consisting of separable signals and random signals are utilized to deal with the MIMO Hammerstein model identification issue, and the separable signals to implement separation identification of MIMO Hammerstein model is introduced, that is, the two blocks are separately identified. First, parameters of the linear block are estimated applying correlation function-based least squares method in the presence of measurable input–output of Gaussian signals, which can efficiently weaken the process noise interference. Second, estimate of noise parameters vector is introduced to solve the unknown noise vector in the information matrix, then a recursive extended least squares method is developed for identifying parameters of nonlinear block and colored noise model based on available input–output of random signals. The validity and precision of the presented methodology are demonstrated applying a numerical simulation and a nonlinear process, and it is known from the research results that compared with existing identification techniques, the methodology utilized achieved higher identification accuracy.

Advanced Data Augmentation Techniques for Enhanced Fault Diagnosis in Industrial Centrifugal Pumps

This study presents an advanced data augmentation framework to enhance fault diagnostics in industrial centrifugal pumps using vibration data. The proposed framework addresses the challenge of insufficient defect data in industrial settings by integrating traditional augmentation techniques, such as Gaussian noise (GN) and signal stretching (SS), with advanced models, including Long Short-Term Memory (LSTM) networks, Autoencoders (AE), and Generative Adversarial Networks (GANs). Our approach significantly improves the robustness and accuracy of machine learning (ML) models for fault detection and classification. Key findings demonstrate a marked reduction in false positives and a substantial increase in fault detection rates, particularly in complex operational scenarios where traditional statistical methods may fall short. The experimental results underscore the effectiveness of combining these augmentation techniques, achieving up to a 30% improvement in fault detection accuracy and a 25% reduction in false positives compared to baseline models. These improvements highlight the practical value of the proposed framework in ensuring reliable operation and the predictive maintenance of centrifugal pumps in diverse industrial environments.

Estimate non-Gaussian road roughness from international roughness index

Gaussian model is commonly used to characterize road roughness, while field measured data is usually non-Gaussian. A new method based on the amplitude modulation and International Roughness Index is proposed in this paper to estimate non-Gaussian road roughness. A modified Gamma distribution is proposed to describe the International Roughness Index and to create the amplitude modulation signal. To ensure that the high kurtosis of the amplitude-modulated non-Gaussian profile is correctly transferred to the vehicle response, the method is further developed to fulfill the specifications for the fatigue damage spectrum by controlling the spectral content of the amplitude modulation signal. Herein, a Gaussian amplitude modulation signal with a cutoff frequency is firstly generated, and then converted to a modified Gamma distribution amplitude modulation signal based on the cumulative distribution function transform. Field data are used to verify the proposed method. The results show that a good match is obtained between the estimated and measured non-Gaussian road roughness. The estimated International Roughness Index and fatigue damage potential of vehicle response are well represented using the proposed method.

A model is worth tens of thousands of examples for estimation and thousands for classification

Traditional signal processing methods relying on mathematical data generation models have been cast aside in favour of deep neural networks, which require vast amounts of data. Since the theoretical sample complexity is nearly impossible to evaluate, these amounts of examples are usually estimated with crude rules of thumb. However, these rules only suggest when the networks should work, but do not relate to the traditional methods. In particular, an interesting question is: how much data is required for neural networks to be on par or outperform, if possible, the traditional model-based methods? In this work, we empirically investigate this question in three simple examples covering estimation and classification, where the data is generated according to precisely defined mathematical models, and where well-understood optimal or state-of-the-art mathematical data-agnostic solutions are known. A first problem is deconvolving one-dimensional Gaussian signals, a second one is estimating a circle’s radius and location in random grayscale images of disks, and a third one both classifies the presence of a line and locates it when present in a binary random dot image. By training various networks, either naive custom designed or well-established ones, with various amounts of training data, we find that networks require tens of thousands of examples for estimation in comparison to the traditional methods and thousands for classification, whether the networks are trained from scratch or even with transfer-learning or finetuning.

Gaussian bistable cascade double feedback stochastic resonance weak signal enhancement detection

Stochastic resonance (SR), as a nonlinear weak signal enhancement detection method, has found extensive applications in fields like fault diagnosis and biological information processing. However, further research has revealed that single stochastic resonance systems often fail to meet the requirements of practical engineering applications, leading to a growing interest in multi-system collaborative stochastic resonance. This article first constructs a cascaded SR system based on the Gaussian bistable model, and introduces the idea of feedback into the cascaded system. A Gaussian bistable cascaded dual feedback SR system is proposed to improve the output signal enhancement performance of the system. This system effectively utilizes the memory characteristics inherent in the output feedback and enables multi-level particle transitions and energy transfers in noisy input signals, thereby reducing noise and enhancing the extraction of weak signal features. Furthermore, the BSO optimization algorithm was utilized to optimize the system parameters of the model, resulting in an adaptive Gaussian bistable cascaded double feedback stochastic resonance (GBCDFSR) system. This system is applied to the processing of noisy periodic signals across various noise types. Simulation experiments and engineering applications show that the proposed model has stronger signal detection capabilities.

Parameter learning for Wiener systems with time‐delay state‐space model

AbstractThis paper discusses a novel scheme for learning the Wiener output error nonlinear system with time‐delay state‐space model. In the Wiener system, the dynamic linear block is approximated by time‐delay state‐space model, and the static nonlinear block is established using neural fuzzy network. Combined signals designed including separable signal and random signal are devoted to achieving parameters separation learning of the Wiener system, that is, the two blocks are learned independently. Firstly, using the properties of shift operator and transforming state‐space model with time‐delay into a representation with input and output, then linear dynamic block parameters are learned by the virtue of correlation analysis method in the condition of Gaussian signals. Moreover, a recursive extended least squares estimation is carried out to learn parameters of static nonlinear block and colored noise model under the condition of random signals. The efficiency and accuracy of proposed scheme are confirmed on experiment results of a numerical simulation and a typical practical nonlinear process, and experimental simulation results demonstrate that the learning scheme proposed obtains good learning precision.

A hierarchical signal detection model with unequal variance for binary responses.

Gaussian signal detection models with equal variance are commonly used in simple yes-no detection and discrimination tasks whereas more flexible models with unequal variance require additional information. Here, a hierarchical Bayesian model with equal variance is extended to an unequal-variance model by exploiting variability of hit and false-alarm rates in a random sample of participants. This hierarchical model is investigated analytically, in simulations and in applications to existing data sets. The results suggest that signal variance and other parameters can be accurately estimated if plausible assumptions are met. It is concluded that the model provides a promising alternative to the ubiquitous equal-variance model for binary data.

A High-Resolution Defect Location Method for Medium-Voltage Cables Based on Gaussian Narrow-Band Envelope Signals and the S-Transform

A High-Resolution Defect Location Method for Medium-Voltage Cables Based on Gaussian Narrow-Band Envelope Signals and the S-Transform

Generalized Gaussian signal detection theory: A unified signal detection framework for confidence data analysis.

Human decision behavior entails a graded awareness of its certainty, known as a feeling of confidence. Until now, considerable interest has been paid to behavioral and computational dissociations of decision and confidence, which has raised an urgent need for measurement frameworks that can quantify the efficiency of confidence rating relative to decision accuracy (metacognitive efficiency). As a unique addition to such frameworks, we have developed a new signal detection theory paradigm utilizing the generalized Gaussian distribution (GGSDT). This framework evaluates the observer's metacognitive efficiency and internal standard deviation ratio through shape and scale parameters, respectively. The shape parameter quantifies the kurtosis of internal distributions and can practically be understood in reference to the proportion of the Gaussian ideal observer's confidence being disrupted with random guessing (metacognitive lapse rate). This interpretation holds largely irrespective of the contaminating effects of decision accuracy or operating characteristic asymmetry. Thus, the GGSDT enables hitherto unexplored research protocols (e.g., direct comparison of yes/no vs. forced-choice metacognitive efficiency), expected to find applications in various fields of behavioral science. This article provides a detailed walkthrough of the GGSDT analysis with an accompanying R package (ggsdt). (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Numerical Simulation and Influence of Non-Gaussian Vibrations on Flexible Robotic Systems

Random vibration excitation is a standard method for obtaining the dynamic properties of aerospace structures and simulating loading conditions. Shaker-based random excitation and traditional finite element analysis techniques use random vibrations, assuming a Gaussian distribution of excitation impulse magnitudes. While Gaussian signals may sufficiently describe some vibrational environments, many real-world excitations have non-Gaussian distributions. These signals may contain vibrational impulses larger than those observed in a Gaussian signal and could cause damage if not considered. This paper examines the influence of non-Gaussian signals on flexible vs. rigid robotic architectures using NASA JPL’s Pop-Up Flat Folding Explorer Robot (PUFFER) and Cooperative Autonomous Distributed Robotic Explorer (CADRE). The results indicate that flexible systems can be significantly impacted by a non-Gaussian excitation profile and that neither a typical enveloping of a Gaussian excitation nor a superposition of the responses to a worst-case impulse load with the response to a Gaussian signal was sufficient to bound the response due to non-Gaussian excitation. The driving mechanism for increased sensitivity of flexible robotic systems appears to be inertial, and designers may consider shifting the relative flexibility of the system or its constraints to force particular deformation modes or designing hinge mechanisms with increased damping to minimize the influence of non-Gaussian signals on the response of a flexible robotic structure.

Supplemental Material for Generalized Gaussian Signal Detection Theory: A Unified Signal Detection Framework for Confidence Data Analysis

Supplemental Material for Generalized Gaussian Signal Detection Theory: A Unified Signal Detection Framework for Confidence Data Analysis

Identifying temporal pathways using biomarkers in the presence of latent non-Gaussian components.

Time-series data collected from a network of random variables are useful for identifying temporal pathways among the network nodes. Observed measurements may contain multiple sources of signals and noises, including Gaussian signals of interest and non-Gaussian noises, including artifacts, structured noise, and other unobserved factors (eg, genetic risk factors, disease susceptibility). Existing methods, including vector autoregression (VAR) and dynamic causal modeling do not account for unobserved non-Gaussian components. Furthermore, existing methods cannot effectively distinguish contemporaneous relationships from temporal relations. In this work, we propose a novel method to identify latent temporal pathways using time-series biomarker data collected from multiple subjects. The model adjusts for the non-Gaussian components and separates the temporal network from the contemporaneous network. Specifically, an independent component analysis (ICA) is used to extract the unobserved non-Gaussian components, and residuals are used to estimate the contemporaneous and temporal networks among the node variables based on method of moments. The algorithm is fast and can easily scale up. We derive the identifiability and the asymptotic properties of the temporal and contemporaneous networks. We demonstrate superior performance of our method by extensive simulations and an application to a study of attention-deficit/hyperactivity disorder (ADHD), where we analyze the temporal relationships between brain regional biomarkers. We find that temporal network edges were across different brain regions, while most contemporaneous network edges were bilateral between the same regions and belong to a subset of the functional connectivity network.

Accurate Parameter Estimation for Safety-Critical Systems with Unmodeled Dynamics (Abstract Reprint)

Analysis and synthesis of safety-critical autonomous systems are carried out using models which are often dynamic. Two central features of these dynamic systems are parameters and unmodeled dynamics. Much of feedback control design is parametric in nature and as such, accurate and fast estimation of the parameters in the modeled part of the dynamic system is a crucial property for designing risk-aware autonomous systems. This paper addresses the use of a spectral lines-based approach for estimating parameters of the dynamic model of an autonomous system. Existing literature has treated all unmodeled components of the dynamic system as sub-Gaussian noise and proposed parameter estimation using Gaussian noise-based exogenous signals. In contrast, we allow the unmodeled part to have deterministic unmodeled dynamics, which are almost always present in physical systems, in addition to sub-Gaussian noise. In addition, we propose a deterministic construction of the exogenous signal in order to carry out parameter estimation. We introduce a new tool kit which employs the theory of spectral lines, retains the stochastic setting, and leads to non-asymptotic bounds on the parameter estimation error. Unlike the existing stochastic approach, these bounds are tunable through an optimal choice of the spectrum of the exogenous signal leading to accurate parameter estimation. We also show that this estimation is robust to unmodeled dynamics, a property that is not assured by the existing approach. Finally, we show that under ideal conditions with no deterministic unmodeled dynamics, the proposed approach can ensure a Õ(√t) Regret, matching existing literature. Experiments are provided to support all theoretical derivations, which show that the spectral lines-based approach outperforms the Gaussian noise-based method when unmodeled dynamics are present, in terms of both parameter estimation error and Regret obtained using the parameter estimates with a Linear Quadratic Regulator in feedback.

ROC curve measurements using euro-rack modules (and some DIY)

Acoustic signal processing projects encourage DIY electronics as well as hardware designed to expose principles found either in nature or from man-made sources. Searching within the Eurorack format of the modular synthesis community, functional equivalents to more common DIY units are identified. Some signal generators and measurements are still underrepresented commercially and require DIY Eurorack modules to be built. One goal is to use existing Eurorack components where DIY modules are designed as necessary in this format. A Receiver Operating Characteristic curve (ROC) is calculated for three cases using analog energy detection and probability density function (pdf) circuitry. The hypothesis for noise (N) is a fixed Gaussian noise distribution. The three hypotheses for the signal plus noise (S+N) have signals characterized as; a constant sinusoid with random phase, a broadband unknown Gaussian signal, and an unknown narrow band Gaussian signal utilizing a narrow band carrier frequency. Our classroom demonstration involves two loudspeakers, one for noise, the other for signal. The detected microphone’s voltage is bandpass filtered, amplified, squared, integrated and then fed into the pdf circuitry where pulses are counted for 4 seconds in each voltage window. Increasing the signal amplitude will increase the detection index.

FlexKnot as a generalized model of the sky-averaged 21-cm signal at z ∼ 6–30 in the presence of systematics

ABSTRACT Global 21-cm experiments are built to study the evolution of the Universe between the cosmic dawn and the epoch of reionization. FlexKnot is a function parametrized by freely moving knots stringed together by splines. Adopting the FlexKnot function as the signal model has the potential to separate the global 21-cm signal from the foregrounds and systematics while being capable of recovering the crucial features given by theoretical predictions. In this paper, we implement the FlexKnot method by integrating twice over a function of freely moving knots interpolated linearly. The function is also constrained at the lower frequencies corresponding to the dark ages by theoretical values. The FlexKnot model is tested in the framework of the realistic data analysis pipeline of the REACH global signal experiment using simulated antenna temperature data. We demonstrate that the FlexKnot model performs better than existing signal models, e.g. the Gaussian signal model, at reconstructing the shape of the true signals present in the simulated REACH data, especially for injected signals with complex structures. The capabilities of the FlexKnot signal model is also tested by introducing various systematics and simulated global signals of different types. These tests show that four to five knots are sufficient to recover the general shape of most realistic injected signals, with or without sinusoidal systematics. We show that true signals whose absorption trough is of amplitude between 120 and 450 mK can be well recovered with systematics up to about 50 mK.

Search for New Phenomena in Two-Body Invariant Mass Distributions Using Unsupervised Machine Learning for Anomaly Detection at sqrt[s]=13 TeV with the ATLAS Detector.

Searches for new resonances are performed using an unsupervised anomaly-detection technique. Events with at least one electron or muon are selected from 140 fb^{-1} of pp collisions at sqrt[s]=13 TeV recorded by ATLAS at the Large Hadron Collider. The approach involves training an autoencoder on data, and subsequently defining anomalous regions based on the reconstruction loss of the decoder. Studies focus on nine invariant mass spectra that contain pairs of objects consisting of one light jet or b jet and either one lepton (e,μ), photon, or second light jet or b jet in the anomalous regions. No significant deviations from the background hypotheses are observed. Limits on contributions from generic Gaussian signals with various widths of the resonance mass are obtained for nine invariant masses in the anomalous regions.

Seismic Station Monitoring Using Deviation from the Gaussianity

Abstract Degradation of the seismic signal quality sometimes occurs at permanent and temporary stations. Although the most likely cause is a high level of humidity, leading to corrosion of the connectors, environmental changes can also alter recording conditions in different frequency ranges and not necessarily for all three components in the same way. Assuming that the continuous seismic signal can be described by a normal distribution, we present a new approach to quantify the seismogram quality and to point out any time sample that deviates from this Gaussian assumption. We introduce the notion of background Gaussian signal (BGS) to characterize a set of samples that follows a normal distribution. The discrete function obtained by sorting the samples in ascending order of amplitudes is compared with a modified Probit function to retrieve the elements composing the BGS, and its statistical properties (mostly its standard deviation σG). As soon as there is any amplitude perturbation, σG deviates from the standard deviation of all samples composing the time window (σ). Hence, the parameter log(σσG) directly quantifies the alteration level. For a single day, a given frequency range and a given component, the median of all log(σσG) that can be computed using short-time windows, reflects the overall gaussianity of the continuous seismic signal. We demonstrate that it can be used to efficiently monitor the quality of seismic traces using this approach at four broadband permanent stations. We show that the daily log(σσG) is sensitive to both subtle changes on one or two components as well as the signal signature of a sensor’s degradation. Finally, we suggest that log(σσG) and other parameters that are computed from the BGS bring useful information for station monitoring in addition to existing methods.

Blind Polarization Demultiplexing of Shaped QAM Signals Assisted by Temporal Correlations.

While probabilistic constellation shaping (PCS) enables rate and reach adaption with finer granularity [1], it imposes signal processing challenges at the receiver. Since the distribution of PCS-quadrature amplitude modulation (QAM) signals tends to be Gaussian, conventional blind polarization demultiplexing algorithms are not suitable for them [2]. It is known that independently and identically distributed (iid) Gaussian signals, when mixed, cannot be recovered/separated from their mixture. For PCS-QAM signals, there are algorithms such as [3], [4] which are designed by extending conventional blind algorithms used for uniform QAM signals. In these algorithms, an initialization point is obtained by processing only a part of the mixed signal, which have non-Gaussian statistics. In this paper, we propose an alternative method wherein we add temporal correlations at the transmitter, which are subsequently exploited at the receiver in order to separate the polarizations. We will refer to the proposed method as frequency domain (FD) joint diagonalization (JD) probability aware-multi modulus algorithm (pr-MMA), and it is suited to channels with moderate polarization mode dispersion (PMD) effects. Furthermore, we extend our previously proposed JD-MMA [5] by replacing the standard MMA with a pr-MMA, improving its performance. Both FDJD-pr-MMA and JD-pr-MMA are evaluated for a diverse range of PCS (entropy ) over a first-order PMD channel that is simulated in a proof-of-concept setup. A MMA initialized with a memoryless constant modulus algorithm (CMA) is used as a benchmark. We show that at a differential group delay (DGD) of 10% of symbol period and 18 dB SNR/pol., JD-pr-MMA successfully demultiplexes the PCS signals, while CMA-MMA fails drastically. Furthermore, we demonstrate that the newly proposed FDJD-pr-MMA is robust against moderate PMD effects by evaluating it over a DGD of up to 40% of . Our results show that the proposed FDJD-pr-MMA successfully equalizes PMD channels with a DGD up to 20% of .

Superimposed imaging of acoustic wave reflections for the detection of underground nonmetallic pipelines

Due to the non-conductive and non-magnetic properties, nonmetallic pipelines are difficult to be detected by traditional pipe location technologies. This paper presents a superimposed imaging method of acoustic wave reflections for pipe location, which operates on the propagation of elastic waves. The propagation and attenuation model of elastic waves in soil are constructed according to the geometric relationship between the acoustic source, geophone array and pipelines. The two-dimensional and three-dimensional acoustic field diagrams of underground pipeline are generated by superimposed imaging of the cross-correlation coefficients between the signals from the sound source and geophone array, with the attenuation caused by hysteretic damping and geometric dissipation considered in the imaging process. In order to suppress clutter interference on the imaging results, the strategy of ‘multi-point transmit, multi-point receive and cross-correlation coefficient superposition’ is adopted. In the simulation, comparison is made to demonstrate the influences of different excitation sources on the detection imaging results, including the single frequency signal, multi-frequency signal, Gaussian pulse signal and sweep signal. It is found that the excitation signals with rich frequency components are more conducive to improving the resolution of detection images. The effectiveness of the proposed imaging method is further verified in the experimental work, which may be beneficial for the visualization and determination of the location, depth and orientation of underground non-metallic pipelines.

A Comparative Study of the Perceptual Sensitivity of Topological Visualizations to Feature Variations.

Color maps are a commonly used visualization technique in which data are mapped to optical properties, e.g., color or opacity. Color maps, however, do not explicitly convey structures (e.g., positions and scale of features) within data. Topology-based visualizations reveal and explicitly communicate structures underlying data. Although our understanding of what types of features are captured by topological visualizations is good, our understanding of people's perception of those features is not. This paper evaluates the sensitivity of topology-based isocontour, Reeb graph, and persistence diagram visualizations compared to a reference color map visualization for synthetically generated scalar fields on 2-manifold triangular meshes embedded in 3D. In particular, we built and ran a human-subject study that evaluated the perception of data features characterized by Gaussian signals and measured how effectively each visualization technique portrays variations of data features arising from the position and amplitude variation of a mixture of Gaussians. For positional feature variations, the results showed that only the Reeb graph visualization had high sensitivity. For amplitude feature variations, persistence diagrams and color maps demonstrated the highest sensitivity, whereas isocontours showed only weak sensitivity. These results take an important step toward understanding which topology-based tools are best for various data and task scenarios and their effectiveness in conveying topological variations as compared to conventional color mapping.