Large Noise Levels Research Articles

Stochastic H∞ Filtering of the Attitude Quaternion.

Several stochastic H∞ filters for estimating the attitude of a rigid body from line-of-sight measurements and rate gyro readings are developed. The measurements are corrupted by white noise with unknown variances. Our approach consists of estimating the quaternion while attenuating the transmission gain from the unknown variances and initial errors to the current estimation error. The time-varying H∞ gain is computed by solving algebraic and differential linear matrix inequalities for a given transmission threshold, which is iteratively lowered until feasibility fails. Thanks to the bilinear structure of the quaternion state-space model, the algorithm parameters are independent of the state. The case of a gyro drift is addressed, too. Extensive Monte-Carlo simulations show that the proposed stochastic H∞ quaternion filters perform well for a wide range of noise variances. The actual attenuation, which improves with the noise variance and is worst in the noise-free case, is better than the guaranteed attenuation by one order of magnitude. The proposed stochastic H∞ filter produces smaller biases than nonlinear Kalman or unscented filters and similar standard deviations at large noise levels. An essential advantage of this H∞ filter is that the gains are independent of the quaternion, which makes it insensitive to modeling errors. This desired feature is illustrated by comparing its performances against those of unmatched nonlinear optimal filters. When provided with too high or too low noise variances, the multiplicative Kalman filter and the unscented quaternion filter are outperformed by the H∞ filter, which essentially delivers identical error magnitudes.

Enhancing the performance of coherent Ising machines in the large-noise regime with a fifth-order nonlinearity

Coherent Ising machines (CIMs), leveraging the bistable physical properties of coherent light to emulate Ising spins, exhibit great potential as hardware accelerators for tackling complex combinatorial optimization problems. Recent advances have demonstrated that the performance of CIMs can be enhanced either by incorporating large random noise or higher-order nonlinearities, yet their combined effects on CIM performance remain mainly unexplored. In this work, we develop a numerical CIM model that utilizes a tunable fifth-order polynomial nonlinear dynamic function under large noise levels, which has the potential to be implemented in all-optical platforms. We propose a normal form of a CIM model that allows for both supercritical and subcritical pitchfork bifurcation operational regimes, with fifth-order nonlinearity and tunable hyperparameters to control the Ising spin dynamics. In the benchmark studies, we simulate various sets of MaxCut problems using our fifth-order polynomial CIM model. The results show a significant performance improvement, achieving an average of 59.5% improvement in median time-to-solution (TTS) and an average of 6 times improvement in median success rate (SR) for dense Maxcut problems in the BiqMac library, compared to the commonly used third-order polynomial CIM model with low noise. The fifth-order polynomial CIM model in the large-noise regime also shows better performance trends as the problem size scales up. These findings reveal the enhancements on the computational performance of Ising machines in the large-nose regime from fifth-order nonlinearity, showing important implications for both simulation and hardware perspectives.

Overdamped Ising machine with stochastic resonance phenomena in large noise condition

Gain-dissipative Ising machines (GIMs) are dedicated devices that can rapidly solve combinatorial optimization problems. The noise intensity in traditional GIMs should be significantly smaller than its saturated fixed-point amplitude, indicating a lower noise margin. To overcome the existing limit, this work proposes an overdamped bistability-based GIM (OBGIM). Numerical test on uncoupled spin network show that the OBGIM has a different bifurcation dynamics from that of the traditional GIM. Moreover, the domain clustering dynamics on non-frustrated network proves that the overdamped bistability enables the GIM to suppress noise-induced random spin-state switching effectively; thus, it can function normally in an environment with a relatively large noise level. Besides, some prevalent frustrated graphs from the SuiteSparse Matrix Collection were adopted as MAXCUT benchmarks. The results show that the OBGIM can induce stochastic resonance phenomenon when solving difficult benchmarks. Compared with the traditional GIM, this characteristic makes the OBGIM achieve comparable solution accuracy in larger noise environment, thus achieving strong noise robustness.

Efficient Identification of Error-in-Variables Switched Systems Using a Riemannian Embedding

This paper considers the problem of error in variables identification for switched affine models. Since it is well known that this problem is generically NP hard, several relaxations have been proposed in the literature. However, while these approaches work well for low dimensional systems with few subsystems, they scale poorly with both the number of subsystems and their memory. To address this difficulty, we propose a computationally efficient alternative, based on embedding the data in the manifold of positive semidefinite matrices, and using a manifold metric there to perform the identification. Our main result shows that, under dwell-time assumptions, the proposed algorithm is convergent, in the sense that it is guaranteed to identify the system for suitably low noise. In scenarios with larger noise levels, we provide experimental results showing that the proposed method outperforms existing ones. The paper concludes by illustrating these results with academic examples and a non-trivial application: action video segmentation.

Detectability analysis of very low frequency earthquakes: methods and application in Nankai using F-net and DONET broad-band seismometers

SUMMARY For a more quantitative discussion of slow earthquake activity, we evaluated the detectable limits of very low frequency earthquakes (VLFEs), which are seismic slow earthquakes observed in very low-frequency (< 0.05 Hz) bands in the Nankai subduction zone. We performed numerical simulations using a local 3-D model and used the observed noise level of permanent broad-band seismometers. First, we investigated the effects of the source-time functions on the maximum amplitudes of the VLFE signals at a certain station. The maximum amplitudes of the VLFE signals were controlled by the VLFE moment rate. The detectable limit of VLFEs at each source location can be defined as the lowest moment rate of detectable VLFEs, which radiate signals larger than the noise levels of any component at ≥ 3 stations. For inland seismometers only, the detectable limits of VLFEs at deep (30–40 km) and shallow (≤ 10 km) depths were 1012–1012.3 and 1012.7 N·m s−1, respectively. Due to the geometrical spreading of VLFE signals and large noise levels in horizontal components, offshore seismometers improved the detectability of shallow VLFEs in regions where seismometers were densely deployed. Based on our detectability and published catalogues, shallow slow earthquakes are less active south-southwest off the Kii Peninsula, where geodetic studies expect mechanical coupling.

Deep-blur: Blind identification and deblurring with convolutional neural networks.

We propose a neural network architecture and a training procedure to estimate blurring operators and deblur images from a single degraded image. Our key assumption is that the forward operators can be parameterized by a low-dimensional vector. The models we consider include a description of the point spread function with Zernike polynomials in the pupil plane or product-convolution expansions, which incorporate space-varying operators. Numerical experiments show that the proposed method can accurately and robustly recover the blur parameters even for large noise levels. For a convolution model, the average signal-to-noise ratio of the recovered point spread function ranges from 13dB in the noiseless regime to 8dB in the high-noise regime. In comparison, the tested alternatives yield negative values. This operator estimate can then be used as an input for an unrolled neural network to deblur the image. Quantitative experiments on synthetic data demonstrate that this method outperforms other commonly used methods both perceptually and in terms of SSIM. The algorithm can process a 512 512 image under a second on a consumer graphics card and does not require any human interaction once the operator parameterization has been set up.1.

Nonlinear grey Bernoulli model with physics-preserving Cusum operator

The Cusum (cumulative sum) operator is a fundamental prerequisite for the nonlinear grey Bernoulli model. Traditionally, it is believed to visually identify the underlying dynamic pattern of the original time series. This paper presents the misconceptions concerning the Cusum operation and the over-optimization of the initial condition in the classical nonlinear grey Bernoulli model, both of which inspire the proposal of a physics-preserving Cusum operator. Under a state space framework, separable nonlinear least squares and nonlinear least squares are formulated to generate simultaneous estimates of structural parameters and initial condition. By combining the Cusum operators and parameter estimation methods, four modeling paradigms are generated and comprehensively compared. The simulation results show that (i) the physics-preserving Cusum outperforms the traditional Cusum and (ii) nonlinear least squares outperforms separable nonlinear least squares, especially in irregular sampling settings with large time intervals and high noise levels. Finally, the proposed approach is used to identify the underlying dynamics from short-term traffic flow data, and the results validate its effectiveness.

Direct Estimation of Parameters in ODE Models Using WENDy: Weak-Form Estimation of Nonlinear Dynamics

We introduce the Weak-form Estimation of Nonlinear Dynamics (WENDy) method for estimating model parameters for non-linear systems of ODEs. Without relying on any numerical differential equation solvers, WENDy computes accurate estimates and is robust to large (biologically relevant) levels of measurement noise. For low dimensional systems with modest amounts of data, WENDy is competitive with conventional forward solver-based nonlinear least squares methods in terms of speed and accuracy. For both higher dimensional systems and stiff systems, WENDy is typically both faster (often by orders of magnitude) and more accurate than forward solver-based approaches. The core mathematical idea involves an efficient conversion of the strong form representation of a model to its weak form, and then solving a regression problem to perform parameter inference. The core statistical idea rests on the Errors-In-Variables framework, which necessitates the use of the iteratively reweighted least squares algorithm. Further improvements are obtained by using orthonormal test functions, created from a set of C^{infty } bump functions of varying support sizes.We demonstrate the high robustness and computational efficiency by applying WENDy to estimate parameters in some common models from population biology, neuroscience, and biochemistry, including logistic growth, Lotka-Volterra, FitzHugh-Nagumo, Hindmarsh-Rose, and a Protein Transduction Benchmark model. Software and code for reproducing the examples is available at https://github.com/MathBioCU/WENDy.

PowerGAN: A Machine Learning Approach for Power Side‐Channel Attack on Compute‐in‐Memory Accelerators

Analog compute‐in‐memory (CIM) systems are promising candidates for deep neural network (DNN) inference acceleration. However, as the use of DNNs expands, protecting user input privacy has become increasingly important. Herein, a potential security vulnerability is identified wherein an adversary can reconstruct the user's private input data from a power side‐channel attack even without knowledge of the stored DNN model. An attack approach using a generative adversarial network is developed to achieve high‐quality data reconstruction from power leakage measurements. The analyses show that the attack methodology is effective in reconstructing user input data from power leakage of the analog CIM accelerator, even at large noise levels and after countermeasures. To demonstrate the efficacy of the proposed approach, an example of CIM inference of U‐Net for brain tumor detection is attacked, and the original magnetic resonance imaging medical images can be successfully reconstructed even at a noise level of 20% standard deviation of the maximum power signal value. This study highlights a potential security vulnerability in emerging analog CIM accelerators and raises awareness of needed safety features to protect user privacy in such systems.

An autonomous and heuristic approach for extracting bridge frequencies from passing vehicles

The Federal Highway Administration (FHWA) recognizes a need for cost-effective and practical structural health monitoring (SHM) techniques to manage the bridge network. System identification (SI) techniques are the first step in developing SHM frameworks to extract bridge dynamic properties (natural frequencies, damping ratios, and mode shapes). One promising indirect SI technique uses accelerometer-instrumented vehicles to measure the dynamic properties of bridges, such that a few instrumented vehicles could economically monitor a large network of bridges. This study proposes an autonomous framework called autonomous peak picking variational mode decomposition (APPVMD), which leverages an ensemble of signal processing techniques and heuristic models to autonomously extract bridge frequencies from instrumented vehicles. The proposed framework does not require prior information or model-informed training. The framework is tested on four vehicles and 39 unique bridge classes using finite element (FE) models to assess the feasibility of deploying it into practice. The results of this study indicate that the algorithm can make successful bridge frequency extractions in more than 69.2% of the bridge cases using any vehicle and a maximum value of 97.4% using an SUV, while considering the effects of road surface roughness. The influence of bridge stiffness, mass, and span length on the algorithm’s success rate is discussed. It is concluded that flexural rigidity and span length play a significant role in the accuracy of APPVMD. The combined effects of bridge inertia and damping cause heavier bridges to have a higher amplitude signal for a longer duration, increasing the algorithm’s successful detection rate of bridge frequency. Next, the authors examine the effect of reducing the tire stiffness in the truck model on the success of the APPVMD algorithm. The customized truck outperformed the original truck and the SUV by successfully extracting the bridge frequencies of 97.4% of the bridge cases and by having more bridge frequencies predicted in a higher confidence region than the SUV. In addition, the customized truck model is used to verify the APPVMD’s robustness to large levels of sensor noise. Even at significant levels of white noise (1% SNR), as the success rate for bridge frequency extraction using the customized truck only drops to 84.6%. Finally, the influence of vehicle speed on the APPVMD algorithm’s effectiveness is studied. Generally, slower speeds resulted in more successful predictions of bridge frequency, but minor improvements in the accuracy of the frequency predictions were observed at slightly increased velocities, 13.4 m/s (30 mph) and 17.9 m/s (40 mph), but a reduction in accuracy was observed at higher velocities, 22.3 m/s (50 mph).

Strong Noise Rejection in VLC Links under Realistic Conditions through a Real-Time SDR Front-End.

One of the main challenges in the deployment of visible light communication (VLC) in realistic application fields, such as intelligent transportation systems (ITSs), is represented by the presence of large background noise levels on top of the optical signal carrying the digital information. A versatile and effective digital filtering technique is, hence, crucial to face such an issue in an effective way. In this paper, we present an extensive experimental evaluation of a complete VLC system, embedding a software-defined-radio (SDR)-based digital signal processing (DSP) filter stage, which is tested either indoors, in the presence of strong artificial 100-Hz stray illumination, and outdoors, under direct sunlight. The system employs low-power automotive LED lamps, and it is tested for baud rates up to 1 Mbaud. We experimentally demonstrate that the use of the DSP technique improves 10× the performance of the VLC receiver over the original system without the filtering stage, reporting a very effective rejection of both 100-Hz and solar noise background. Indoors, the noise margin in the presence of strong 100-Hz noise is increased by up to 40 dB, whilst in the outdoor configuration, the system is capable of maintaining error-free communication in direct sunlight conditions, up to 7.5 m, improving the distance by a factor of 1.6 compared to the case without filtering. We believe that the proposed system is a very effective solution for the suppression of various types of noise effects in a large set of VLC applications.

Comparison of different methods to account for the plasmaspheric electron content in GNSS-derived ionospheric altimeter corrections and their impact on sea level trend estimation

Global ionospheric maps based on GNSS measurements are nowadays often used to correct satellite altimeter measurements when the instruments have only one frequency or measure over coasts and inland waters. If these corrections do not account for the free electron fraction over the altimeter satellites, this leads to systematic deviations in the range measurements and thus in the estimated sea level. This study compares and assesses different approaches to reduce GNSS-based corrections for the plasmaspheric electron content. It is shown that using a simple scaling with a constant factor of 0.881 gives the best results for the Jason-1 mission, while correcting with the commonly used model ratios leads to higher sea level trend artefacts and larger noise levels, especially for periods of lower solar activity. Using this approach, the sea level trend error for both Jason-1 and Sentinel-6A can be reduced to below 0.1 mm/year, with standard deviations of the differences from the dual-frequency altimeter corrections of 6.74 mm. A simple machine learning approach (boosted regression tree) is also investigated and shows promising results. However, due to the higher processing capacity requirements and the larger deviations from long-term trend, further improvements are recommended before such an approach can be used in routine processing of altimeter corrections.Graphical

Parameter estimation strategies for separable grey system models with comparisons and applications

Parameter estimation is a vital part of grey system models for dynamical modelling and forecasting time series. In this work, we induce a separable grey system model which covers both linear and nonlinear grey system models with separable structural parameters and propose three least squares-based strategies to estimate structural parameters and initial condition, namely two-step least squares, nonlinear least squares and separable nonlinear least squares. By using matrix computation tricks, the relationship between two-step least squares and separable nonlinear least squares estimates are quantified. Furthermore, all three strategies are comprehensively compared in terms of basic ideas, optimality, and computational efficiency. The numerical results indicate that nonlinear least squares outperforms the other two strategies, especially in the settings with large time intervals and high noise levels. Finally, we present two real applications aimed at forecasting the failure times of products and traffic flows during a given period. The results show that in each individual application, all three strategies generate reasonable estimates and the corresponding separable grey system models outperform the competitive ones.

Careful least squares active noise control with no prior secondary path model

SummaryIn feedforward active noise and vibration control (ANVC) or active noise control (ANC), with online secondary path modeling, fast converging overall modeling algorithms may give high modeling errors. These errors are due to the highly correlated inputs, namely the reference and antinoise signals. These high modeling errors can result in poor performance if ignored. However, it is possible to consider these modeling errors in the control filter design, resulting in a careful controller and good performance, as proposed in this work. Careful control is a dual controller feature, which is the solution to the optimal control problem, but this has not been proposed before in the context of ANC. The modeling error covariance matrix (Sigma(n)) is available in the Kalman filter. However, this requires the knowledge of the time‐varying measurement noise power q(n) and state noise. Instead, this work uses a different approach in which the corresponding linear system is solved in a non‐recursive manner. The resulting maximum error is used for a worst‐case estimate of q(n), and, as it turns out, this can be used to get a worst‐case estimate of Sigma(n). A lower control filter update frequency and other optimizations keep computational complexity similar to other approaches. The resulting algorithm has very few easily selected parameters, good performance, does not require any prior secondary path estimate, and adapts to slow and sudden changes in the physical paths without loss of performance or noise overshoots. However, performance can be impaired by large background noise levels.

Stochastic fluctuations promote ordered pattern formation of cells in the Notch-Delta signaling pathway.

The Notch-Delta signaling pathway mediates cell differentiation implicated in many regulatory processes including spatiotemporal patterning in tissues by promoting alternate cell fates between neighboring cells. At the multicellular level, this "lateral inhibition” principle leads to checkerboard patterns with alternation of Sender and Receiver cells. While it is well known that stochasticity modulates cell fate specification, little is known about how stochastic fluctuations at the cellular level propagate during multicell pattern formation. Here, we model stochastic fluctuations in the Notch-Delta pathway in the presence of two different noise types–shot and white–for a multicell system. Our results show that intermediate fluctuations reduce disorder and guide the multicell lattice toward checkerboard-like patterns. By further analyzing cell fate transition events, we demonstrate that intermediate noise amplitudes provide enough perturbation to facilitate “proofreading” of disordered patterns and cause cells to switch to the correct ordered state (Sender surrounded by Receivers, and vice versa). Conversely, high noise can override environmental signals coming from neighboring cells and lead to switching between ordered and disordered patterns. Therefore, in analogy with spin glass systems, intermediate noise levels allow the multicell Notch system to escape frustrated patterns and relax towards the lower energy checkerboard pattern while at large noise levels the system is unable to find this ordered base of attraction.

Robust physics discovery via supervised and unsupervised pattern recognition using the Euler Characteristic

Machine learning approaches have been widely used for discovering the underlying physics of dynamical systems from measured data. Existing approaches, however, still lack robustness, especially when the measured data contain a large level of noise. The lack of robustness is mainly attributed to the insufficient representativeness of used features. As a result, the intrinsic mechanism governing the observed system cannot be accurately identified. In this study, we propose a robust physics discovery method via pattern recognition. In this method, the Euler Characteristic (EC), an efficient topological descriptor for complex data, is used as the feature vector for characterizing the spatiotemporal data collected from dynamical systems. Unsupervised manifold learning and supervised classification results show that EC can be used to efficiently distinguish systems with different while similar governing models. We also demonstrate that the machine learning approaches using EC can improve the results of sparse regression methods of physics discovery without hard-thresholding or hyperparameter tuning.

Quantitative study of candlestick pattern & identifying candlestick patterns using deep learning for the Indian stock market

The stock market is an integral aspect of any country’s economic infrastructure. Analyzing and attempting to play the markets to maximize profits is an endeavor a large fraction of the population aspires to. Candlestick patterns are the backbone of Technical Analysis, used for trading in the stock market. There are a number of candlestick patterns in the market, each with its own benefits and downsides. Due to this, the task that befalls the hands of analysts is deciding which patterns provide the most effective gauge of the current market situation. Due to the large level of noise and widely recognized semi-strong form of market efficiency, analyzing and forecasting the stock market is infamously difficult. For traders that use Technical Analysis to trade, it's critical to be able to recognize candlestick patterns quickly. We will be attempting to determine their respective effectiveness with respect to the Indian Stock Market via exploratory analysis conducted on real-world market data. Also, we'll use candlestick charts to train neural networks and subsequently find patterns. Deep Learning will be used to recognize candlestick patterns in large-cap Indian equities.

Position control for an autonomous underwater vehicle under noisy conditions

Position tracking of an autonomous underwater vehicle is not trivial as its accuracy is affected by process noise, measurement noise, and uncertain hydrodynamic parameters. Thus, in this article, we studied the position control of an autonomous underwater vehicle that operates under largely unbounded system uncertainties and large noise levels and proposed a method that reduces the interference and thereby enhances the overall autonomous underwater vehicle position estimation. Our technique extended the ensemble Kalman filter by combining it with a time-delay estimator to compensate against extended uncertainty of the system dynamics which cannot be solved by the traditional ensemble Kalman filter. Our synthetic simulations demonstrated the effectiveness of the proposed controller, highlighting its appealing position-control accuracy under simultaneous noise and uncertain hydrodynamics parameters. In addition, our simulation results showed that the proposed controller outperforms the conventional time-delay controller by a percentage range of approximately 30.8%–92.6% in terms of root-mean-square error and requires on average less than 88.2% calculation time than the conventional model predictive control.

A Meshless Method for Retrieving Nonlinear Large External Forces on Euler-Bernoulli Beams

We retrieve unknown nonlinear large space-time dependent forces burdened with the vibrating nonlinear Euler-Bernoulli beams under varied boundary data, comprising two-end fixed, cantilevered, clamped-hinged, and simply supported conditions in this study. Even though some researchers used several schemes to overcome these forward problems of Euler-Bernoulli beams; however, an effective numerical algorithm to solve these inverse problems is still not available. We cope with the homogeneous boundary conditions, initial data, and final time datum for each type of nonlinear beam by employing a variety of boundary shape functions. The unknown nonlinear large external force can be recuperated via back-substitution of the solution into the nonlinear Euler-Bernoulli beam equation when we acquire the solution by utilizing the boundary shape function scheme and deal with a small-scale linear system to gratify an additional right-side boundary data. For the robustness and accuracy, we reveal that the current schemes are substantiated by comparing the recuperated numerical results of four instances to the exact forces, even though a large level of noise up to 50% is burdened with the overspecified conditions. The current method can be employed in the online real-time computation of unknown force functions in space-time for varied boundary supports of the vibrating nonlinear beam.

Solving Cauchy Issues of Highly Nonlinear Elliptic Equations Using a Meshless Method

In this paper, we address 3D inverse Cauchy issues of highly nonlinear elliptic equations in large cuboids by utilizing the new 3D homogenization functions of different orders to adapt all the specified boundary data. We also add the average classification as an approximate solution to the nonlinear operator part, without requiring to cope with nonlinear equations to resolve the weighting coefficients because these constructions are owned many conditions about the true solution. The unknown boundary conditions and the result can be retrieved straightway by coping with a small-scale linear system when the outcome is described by a new 3D homogenization function, which is right to find the numerical solutions with the errors smaller than the level of noise being put on the over-specified Neumann conditions on the bottom of the cuboid. Besides, note that the new homogenization functions method (HFM) does not require dealing with the regularization and highly nonlinear equations. The robustness and accuracy of the HFM are verified by comparing the recovered results of several numerical experiments to the exact solutions in the entire region, even though a very large level of noise 50% is imposed on the over specified Neumann conditions. The numerical errors of our scheme are in the order of O(10−1)–O(10−4).