Divergence Error Research Articles

Observability Decomposition-Based Decentralized Kalman Filter and Its Application to Resilient State Estimation under Sensor Attacks.

This paper considers a discrete-time linear time invariant system in the presence of Gaussian disturbances/noises and sparse sensor attacks. First, we propose an optimal decentralized multi-sensor information fusion Kalman filter based on the observability decomposition when there is no sensor attack. The proposed decentralized Kalman filter deploys a bank of local observers who utilize their own single sensor information and generate the state estimate for the observable subspace. In the absence of an attack, the state estimate achieves the minimum variance, and the computational process does not suffer from the divergent error covariance matrix. Second, the decentralized Kalman filter method is applied in the presence of sparse sensor attacks as well as Gaussian disturbances/noises. Based on the redundant observability, an attack detection scheme by the test and a resilient state estimation algorithm by the maximum likelihood decision rule among multiple hypotheses, are presented. The secure state estimation algorithm finally produces a state estimate that is most likely to have minimum variance with an unbiased mean. Simulation results on a motor controlled multiple torsion system are provided to validate the effectiveness of the proposed algorithm.

Pinning Impulsive Synchronization of Stochastic Delayed Neural Networks via Uniformly Stable Function.

This article investigates the synchronization of stochastic delayed neural networks under pinning impulsive control, where a small fraction of nodes are selected as the pinned nodes at each impulsive moment. By proposing a uniformly stable function as a new tool, some novel mean square decay results are presented to analyze the error system obtained from the leader and the considered neural networks. For the divergent error system without impulsive effects, the impulsive gains of pinning impulsive controller can admit destabilizing impulse and the number of destabilizing impulse may be infinite. However, if the error system without impulsive effects is convergent, to achieve the synchronization of the stochastic neural networks, the growth exponent of the product of impulsive gains can not exceed some positive constant. It is shown that the obtained results increase the flexibility of the impulsive gains compared with the existing results. Finally, a numerical example is given to illustrate the practicality of synchronization criteria.

Anomaly Detection of Gas-Insulated Switchgear (GIS) Equipment Based on Embedding Position Variational Auto-Encoder

Gas-insulated switchgear (GIS) is one of the most important power devices in the power system. Once a fault occurs, it is difficult to determine and locate the fault due to its fully enclosed nature, which may lead to greater accidents and huge losses. Many GIS anomaly detection methods based on vibration and deep learning (DL) have been developed in recent years. However, these DL-based methods only utilize one single sampling point data on GIS, while not all faults are reflected at the points currently in use due to the signal attenuation. In this paper, an embedded position variational auto-encoder (EP-VAE) model for anomaly detection of GIS devices is presented, which can model multipoint vibration signals. We fuse the position information and the corresponding one dimension vibration signal to the two dimension grayscale images by Gram matrix. Then, the normal grayscale images are feed into the EP-VAE model, which is optimized by KL divergence and reconstruction error jointly. In the test phase, when one of these two losses is higher than the normal images, it is identified as an abnormal fault. We use the vibration data from the actual operation of GIS to carry out the anomaly detection experiments. The results show that our model EP-VAE has a detection accuracy of 93.12% for normal vibration grayscale images, and an abnormality detection accuracy of 87.94%.

Surface measurement of silicon wafer using harmonic phase-iterative analysis and wavelength-scanning Fizeau interferometer

Wavelength-scanning interferometry has been widely used for surface measurements of silicon wafers with a high reflection factor owing to its non-contact and high-resolution measurement. However, the measurement results are degraded by the second-order harmonics of the signal and nonlinearity of phase modulation in wavelength scanning. In this study, a harmonic phase-iterative technique using five-frame experimental interferograms was developed for the surface measurement of a silicon wafer, while simultaneously compensating for the second-order harmonics and nonlinear phase modulation. Considering the reflection factor of the silicon wafer and the harmonics of the signal, a harmonic phase-iterative technique was derived. Furthermore, by combining the proposed iterative technique with the harmonic convergence condition and the selected pixel technique, the harmonic phase-iterative technique was insensitive to divergence errors and considerably reduced the computational time of phase extraction. The surface of the silicon wafer was measured using the harmonic phase-iterative technique and five-frame interferograms obtained using a wavelength-scanning Fizeau interferometer. The repeatability error of the silicon wafer surface measurement was 2.617 nm. Finally, it was confirmed that the harmonic phase-iterative technique had superior phase-extraction ability in terms of residual ripples and repeatability errors compared to the conventional iterative technique and phase-modulation technique.

Three-Dimensional Hydrostatic Curved Channel Flow Simulations Using Non-Staggered Triangular Grids

Non-staggered triangular grids have many advantages in performing river or ocean modeling with the finite-volume method. However, horizontal divergence errors may occur, especially in large-scale hydrostatic calculations with centrifugal acceleration. This paper proposes an unstructured finite-volume method with a filtered scheme to mitigate the divergence noise and avoid further influencing the velocities and water elevation. In hydrostatic pressure calculations, we apply the proposed method to three-dimensional curved channel flows. Approximations reduce the numerical errors after filtering the horizontal divergence operator, and the approximation is second-order accurate. Numerical results for the channel flow accurately calculate the velocity profile and surface elevation at different Froude numbers. Moreover, secondary flow features such as the vortex pattern and its movement along the channel sections are also well captured.

Divergence Error Based p-adaptive Discontinuous Galerkin Solution of Time-domain Maxwell's Equations

A $p$-adaptive discontinuous Galerkin time-domain method is developed to obtain high-order solutions to electromagnetic scattering problems. A novel feature of the proposed method is the use of divergence error to drive the $p$-adaptive method. The nature of divergence error is explored and that it is a direct consequence of the act of discretization is established. Its relation with relative truncation error is formed which enables the use of divergence error as an inexpensive proxy to truncation error. Divergence error is used as an indicator to dynamically identify and assign spatial operators of varying accuracy to substantial regions in the computational domain. This results in a reduced computational cost than a comparable discontinuous Galerkin time-domain solution using uniform degree piecewise polynomial bases throughout.

A Provably Positive, Divergence-free Constrained Transport Scheme for the Simulation of Solar Wind

Abstract In this paper, we present a provably positive, divergence-free constrained transport (CT) scheme to simulate the steady-state solar wind ambient with the three-dimensional magnetohydrodynamics numerical model. The positivity can be lost in two ways: one way is in the reconstruction process, and the other is in the updating process when the variables are advanced to the next time step. We adopt a self-adjusting strategy to bring the density and pressure into the permitted range in the reconstruction process, and use modified wave speeds in the Harten–Lax–van Leer flux to ensure the positivity in the updating process. The CT method can keep the magnetic fields divergence-free if the magnetic fields are divergence-free initially. Thus, we combine the least-squares reconstruction of the magnetic fields with the divergence-free constraints to make the magnetic fields globally solenoidal initially. Furthermore, we adopt a radial basis function method to interpolate variables at boundaries that can keep the magnetic field locally divergence-free. To verify the capability of the model in producing structured solar wind, the modeled results are compared with Parker Solar Probe (PSP) in situ observations during its first two encounters, as well as Wind observations at 1 au. Additionally, a solar maximum solar wind background is simulated to show the property of the model’s ability to preserve the positivity. The results show that the model can provide a relatively satisfactory comparison with PSP or Wind observations, and the divergence error is about 10−10 for all of the tests in this paper.

An Entropy-stable Ideal EC-GLM-MHD Model for the Simulation of the Three-dimensional Ambient Solar Wind

Abstract The main aim of the current work is to apply the Roe+Lax–Friedrichs (LF) hybrid entropy-stable scheme to the simulation of the three-dimensional ambient solar wind. The governing equations for the solar wind flow and magnetic field utilize the entropy-consistent nine-wave magnetic field divergence diminishing ideal magnetohydrodynamics (MHD) equations, which are symmetric and Galilean invariant with some nonconservative terms proportional to the divergence of magnetic field or the gradient of the Lagrange multiplier ψ. By using solenoidality-preserving and non-negativity-preserving reconstruction, the divergence error is further constrained, and the densities and pressures are reliably guaranteed. Moreover, the entropy is used as an auxiliary equation to completely avoid the appearance of negative pressure, which is independent of any numerical flux and can be retrofit into any MHD equations straightforwardly. All the properties referred to above make the newly developed scheme more handy and robust to cope with the high Mach number or low plasma β situations. After the experiments of the entropy consistency and the robustness of the proposed entropy-stable scheme through two simple tests, we carry out the simulation of the large-scale solar wind structures for Carrington Rotation 2183 (CR 2183) in a six-component grid system with the initial potential field obtained from the Helioseismic and Magnetic Imager magnetogram by retaining spherical harmonics of degree 50. The comparisons of the numerical results with the remote sensing observations and in situ data show that the new model has the capability to produce structured solar wind.

THE COMBINATION OF SHAPE SENSING ROBOTIC BRONCHOSCOPY WITH MOBILE 3D IMAGING TO VERIFY TOOL-IN-LESION AND ASSESS DIVERGENCE

TOPIC: Procedures TYPE: Late Breaking PURPOSE: With recent advances in robotic bronchoscopy for peripheral pulmonary nodule sampling, there has been notable improvements in reach, stability, and precision. However, barriers such as CT to body divergence and sampling error remain. Traditional cone beam systems have been shown to overcome these hurdles, however, this imaging modality is expensive and can have limited availability. The combination of shape-sensing robotic bronchoscopy (SSRAB) and mobile C-arm with CT capabilities could not only enhance the confidence of the pathology results with confirmation of tool-in-lesion for peripheral pulmonary nodules but may also overcome diaphragmatic motion through real-time 3D image feedback to make precise micro-adjustments and optimize outcomes in a transportable fashion. METHODS: A single-center prospective study was conducted to evaluate the combined use of SSRAB with portable cone beam computed tomography to visualize tool-in-lesion as a correlate to diagnostic yield (NCT# 04740047). Fluoroscopy and radiation data were captured. Additionally, data regarding nodule motion during navigation and breath holds were captured to quantify nodule motion and divergence. RESULTS: Twenty-two lesions were captured in 12 males (54.5%) and 10 females (45.5%). The median lesion size was 15 mm (range 10 – 27 mm) with the median airway generation being 7 (range 5-11) and median distance from pleura of 13 mm (range 1 - 45.8 mm). Most lesions were in the left upper lobe (8, 34.8%). Tool-in-lesion was visualized at the time of the procedure in 21 lesions (95.5%). Based on immediate histopathologic review, 14 (63.63%) nodules were malignant and 6 (27.3%) were benign. Two specimens were suggestive of inflammation and are awaiting follow up imaging. Mean number of spins was 2.6 (± 1.8 spins) with a mean fluoroscopy time of 9.1 minutes (± 6.6 minutes) and a mean Dose Area Product of 51.1 Gy*cm2 (± 33.9 Gy*cm2). There were no episodes of bleeding or pneumothorax. Observed CT-body divergence was overcome using the combination of both technologies as evidenced by the tool-in-lesion rate and will be quantified when the entire dataset is available. CONCLUSIONS: The combination of SSRAB and mobile 3D imaging allows for adequate visualization of tool in lesion without the need for a fixed cone beam CT and may improve diagnostic yield. CLINICAL IMPLICATIONS: Shape-sensing robotic technology combined with mobile CT imaging allows for accurate placement of the biopsy tool in the lesion. This combination may enhance diagnostic ability for sampling of peripheral pulmonary nodules and translate well in the applications of therapeutics in the future. Mobile 3D imaging allows for flexibility and maneuverability without the need for an expensive fixed cone beam CT room with adequate image quality. DISCLOSURES: No relevant relationships by Jennifer Duke, source=Web Response No relevant relationships by Eric Edell, source=Web Response No relevant relationships by Sebastian Fernandez-Bussy, source=Web Response No relevant relationships by Ryan Kern, source=Web Response Research grant relationship with Intuitive Surgical Please note: $5001 - $20000 by Janani Reisenauer, source=Web Response, value=Grant/Research Support

A new locally divergence-free WLS-ENO scheme based on the positivity-preserving finite volume method for ideal MHD equations

In this paper, the WLS-ENO (Weighted-Least-Squares based Essentially Non-Oscillatory) reconstruction is modified to maintain the conservation of the cell average values. Furthermore, the divergence-free constraint is combined with the conservative WLS-ENO reconstruction, which can make the magnetic field locally divergence-free. The main merit of the proposed reconstruction scheme is that it can keep both the divergence-free constraint and ENO property for the magnetic field without using any limiter. We apply the scheme to the simulations of ideal MHD equations within the framework of a positivity-preserving finite volume method. The convergence, the magnetic field divergence error and the capability for low plasma-beta of the scheme are tested by some MHD benchmark problems.

On Generative-Adversarial-Network-Based Underwater Acoustic Noise Modeling

Noise fitting plays a key role in underwater acoustic communications. Traditional approximate models can fit global heavy-tail distribution of the impulsive noise with fixed parameters. These models are unable to cover local distributions with arbitrary lengths. In this paper, we propose a generative-adversarial-network-based underwater noise simulator (GUNS), which constructs a deep-neural-network-based generator and a convolutional-neural-network-based discriminator are constructed to learn the heavy-tail distribution of the impulsive noise. Based on the noise collected in the Wuyuanwan Bay, Xiamen, probability distribution function of the underwater acoustic noise simulated by the proposed GUNS performs lower Kullback-Leibler divergence, Jensen-Shannon divergence and mean square error than that employed traditional approximate models.

Closed-form approximation of BPSK bit error rate over strong scintillation channel induced by solar wind turbulence

The signal strength fluctuations on the spacecraft-to-earth link caused by solar wind turbulence will reduce telemetry performance. It is essential to establish a reliable deep-space communication link. The K-distribution model of the solar wind turbulence and strong scintillation channel of the telemetry link is established by analyzing the characteristics of the telemetry signal amplitude scintillation caused by the solar wind. Using the Laguerre orthogonal polynomial, the channel K distribution is approximated and studied, and a closed-form approximation of the binary phase shift keying (BPSK) bit error rate under the strong scintillation channel of solar wind turbulence is given. Numerical calculations show that the scintillation index has tremendous influence on the bit error rate, and the parameter β affects the K-distribution approximation and bit error rate of the strong scintillation channel of the strong wind, and choosing a smaller value is beneficial to reduce the KL divergence and bit error rate of the K-distribution approximation. At the same time, choosing a smaller parameter b, that is a smaller β as well, is helpful to reduce the bit error rate of the telemetry system.

Numerical Study of Divergence Cleaning and Coronal Heating/Acceleration Methods in the 3D COIN-TVD MHD Model

In the solar coronal numerical simulation, the coronal heating/acceleration and the magnetic divergence cleaning techniques are very important. The coronal–interplanetary total variation diminishing (COIN-TVD) magnetohydrodynamic (MHD) model is developed in recent years that can effectively realize the coronal–interplanetary three-dimensional (3D) solar wind simulation. In this study, we focus on the 3D coronal solar wind simulation by using the COIN-TVD MHD model. In order to simulate the heating and acceleration of solar wind in the coronal region, the volume heating term in the model is improved efficiently. Then, the influence of the different methods to reduce the ∇⋅B constraint error on the coronal solar wind structure is discussed. Here, we choose Carrington Rotation (CR) 2199 as a study case and try to make a comparison of the simulation results among the different magnetic divergence cleaning methods, including the diffusive method, the Powell method, and the composite diffusive/Powell method, by using the 3D COIN-TVD MHD model. Our simulation results show that with the different magnetic divergence cleaning methods, the ∇⋅B error can be reduced in different levels during the solar wind simulation. Among the three divergence cleaning methods we used, the composite diffusive/Powell method can maintain the divergence cleaning constraint better to a certain extent, and the relative magnetic field divergence error can be controlled in the order of 10−9. Although these numerical simulations are performed for the background solar corona, these methods are also suitable for the simulation of CME initiation and propagation.

Provably physical-constraint-preserving discontinuous Galerkin methods for multidimensional relativistic MHD equations

We propose and analyze a class of robust, uniformly high-order accurate discontinuous Galerkin (DG) schemes for multidimensional relativistic magnetohydrodynamics (RMHD) on general meshes. A distinct feature of the schemes is their physical-constraint-preserving (PCP) property, i.e., they are proven to preserve the subluminal constraint on the fluid velocity and the positivity of density, pressure, and internal energy. This is the first time that provably PCP high-order schemes are achieved for multidimensional RMHD. Developing PCP high-order schemes for RMHD is highly desirable but remains a challenging task, especially in the multidimensional cases, due to the inherent strong nonlinearity in the constraints and the effect of the magnetic divergence-free condition. Inspired by some crucial observations at the PDE level, we construct the provably PCP schemes by using the locally divergence-free DG schemes of the recently proposed symmetrizable RMHD equations as the base schemes, a limiting technique to enforce the PCP property of the DG solutions, and the strong-stability-preserving methods for time discretization. We rigorously prove the PCP property by using a novel “quasi-linearization” approach to handle the highly nonlinear physical constraints, technical splitting to offset the influence of divergence error, and sophisticated estimates to analyze the beneficial effect of the additional source term in the symmetrizable RMHD system. Several two-dimensional numerical examples are provided to further confirm the PCP property and to demonstrate the accuracy, effectiveness and robustness of the proposed PCP schemes.

Key parameter analysis of the DRESOR method for calculating the radiative heat transfer in three-dimensional absorbing, emitting and scattering media

The Distribution of Ratios of Energy Scattered by the medium Or Reflected by the boundary surface (DRESOR) method based on the Monte Carlo method is an important new approach to solve the radiative transfer equation accurately and efficiently. This method has been applied extensively for the detection and analysis of the furnace flame temperature. However, the discrete method, the number of direct incident radiation directions (DIRDs), and the number of scattered or reflected energy beams (SREBs) lack quantitative references. Therefore, in this paper, the effects of different discrete methods, the number of DIRDs, and the number of SREBs on the radiative heat flux, divergence error, and computational efficiency of three-dimensional homogeneous absorbing, emitting, and scattering media are analyzed. The results show that the random discrete method of the DIRD for the space element substantially reduces the divergence error of the radiation heat flux. The uniform discrete method of the DIRD should be used for the surface element to minimize the error of the radiation heat flux error. In addition, the relative error of the DRESOR method is reduced to 0.004, and the figure of merit reaches the maximum when the number of DIRDs is about 1000, the number of SREB is 500, and the scattering albedo is less than 0.8. The fitted equations describing the relationship between the calculation errors and the number of SREBs for the surface and space elements are obtained for different scattering albedos. An increase in the number of DIRDs and SREBs does not significantly reduce the calculation error. The results provide a quantitative reference for determining the parameters of the DRESOR method in radiant heat analysis.

A Conditional Generative adversarial Network for energy use in multiple buildings using scarce data

Building consumption data is integral to numerous applications including retrofit analysis, Smart Grid integration and optimization, and load forecasting. Still, due to technical limitations, privacy concerns and the proprietary nature of the industry, usable data is often unavailable for research and development. Generative adversarial networks (GANs) - which generate synthetic instances that resemble those from an original training dataset - have been proposed to help address this issue. Previous studies use GANs to generate building sequence data, but the models are not typically designed for time series problems, they often require relatively large amounts of input data (at least 20,000 sequences) and it is unclear whether they correctly capture the temporal behaviour of the buildings. In this work we implement a conditional temporal GAN that addresses these issues, and we show that it exhibits state-of-the-art performance on small datasets. 22 different experiments that vary according to their data inputs are benchmarked using Jensen-Shannon divergence (JSD) and predictive forecasting validation error. Of these, the best performing is also evaluated using a curated set of metrics that extends those of previous work to include PCA, deep-learning based forecasting and measurements of trend and seasonality. Two case studies are included: one for residential and one for commercial buildings. The model achieves a JSD of 0.012 on the former data and 0.037 on the latter, using only 396 and 156 original load sequences, respectively.

An arbitrary high-order Spectral Difference method for the induction equation

We study in this paper three variants of the high-order Discontinuous Galerkin (DG) method with Runge-Kutta (RK) time integration for the induction equation, analysing their ability to preserve the divergence-free constraint of the magnetic field. To quantify divergence errors, we use a norm based on both a surface term, measuring global divergence errors, and a volume term, measuring local divergence errors. This leads us to design a new, arbitrary high-order numerical scheme for the induction equation in multiple space dimensions, based on a modification of the Spectral Difference (SD) method [1] with ADER time integration [2]. It appears as a natural extension of the Constrained Transport (CT) method. We show that it preserves ∇⋅B→=0 exactly by construction, both in a local and a global sense. We compare our new method to the 3 RKDG variants and show that the magnetic energy evolution and the solution maps of our new SD-ADER scheme are qualitatively similar to the RKDG variant with divergence cleaning, but without the need for an additional equation and an extra variable to control the divergence errors.

IMU Data and GPS Position Information Direct Fusion Based on LSTM.

In recent years, the application of deep learning to the inertial navigation field has brought new vitality to inertial navigation technology. In this study, we propose a method using long short-term memory (LSTM) to estimate position information based on inertial measurement unit (IMU) data and Global Positioning System (GPS) position information. Simulations and experiments show the practicability of the proposed method in both static and dynamic cases. In static cases, vehicle stop data are simulated or recorded. In dynamic cases, uniform rectilinear motion data are simulated or recorded. The value range of LSTM hyperparameters is explored through both static and dynamic simulations. The simulations and experiments results are compared with the strapdown inertial navigation system (SINS)/GPS integrated navigation system based on kalman filter (KF). In a simulation, the LSTM method’s computed position error Standard Deviation (STD) was 52.38% of what the SINS computed. The biggest simulation radial error estimated by the LSTM method was 0.57 m. In experiments, the LSTM method computed a position error STD of 23.08% using only SINSs. The biggest experimental radial error the LSTM method estimated was 1.31 m. The position estimated by the LSTM fusion method has no cumulative divergence error compared to SINS (computed). All in all, the trained LSTM is a dependable fusion method for combining IMU data and GPS position information to estimate position.

Computational general relativistic force-free electrodynamics

General relativistic force-free electrodynamics is one possible plasma-limit employed to analyze energetic outflows in which strong magnetic fields are dominant over all inertial phenomena. The amazing images of black hole (BH) shadows from the Galactic Center and the M87 galaxy provide a first direct glimpse into the physics of accretion flows in the most extreme environments of the universe. The efficient extraction of energy in the form of collimated outflows or jets from a rotating BH is directly linked to the topology of the surrounding magnetic field. We aim at providing a tool to numerically model the dynamics of such fields in magnetospheres around compact objects, such as BHs and neutron stars. To do so, we probe their role in the formation of high energy phenomena such as magnetar flares and the highly variable teraelectronvolt emission of some active galactic nuclei. In this work, we present numerical strategies capable of modeling fully dynamical force-free magnetospheres of compact astrophysical objects. We provide implementation details and extensive testing of our implementation of general relativistic force-free electrodynamics in Cartesian and spherical coordinates using the infrastructure of the EINSTEINTOOLKIT. The employed hyperbolic/parabolic cleaning of numerical errors with full general relativistic compatibility allows for fast advection of numerical errors in dynamical spacetimes. Such fast advection of divergence errors significantly improves the stability of the general relativistic force-free electrodynamics modeling of BH magnetospheres.

The properties of clusters, and the orientation of magnetic fields relative to filaments, in magnetohydrodynamic simulations of colliding clouds

ABSTRACT We have performed Smoothed Particle Magneto-Hydrodynamics (SPMHD) calculations of colliding clouds to investigate the formation of massive stellar clusters, adopting a timestep criterion to prevent large divergence errors. We find that magnetic fields do not impede the formation of young massive clusters (YMCs), and the development of high star formation rates, although we do see a strong dependence of our results on the direction of the magnetic field. If the field is initially perpendicular to the collision, and sufficiently strong, we find that star formation is delayed, and the morphology of the resulting clusters is significantly altered. We relate this to the large amplification of the field with this initial orientation. We also see that filaments formed with this configuration are less dense. When the field is parallel to the collision, there is much less amplification of the field, dense filaments form, and the formation of clusters is similar to the purely hydrodynamical case. Our simulations reproduce the observed tendency for magnetic fields to be aligned perpendicularly to dense filaments, and parallel to low density filaments. Overall our results are in broad agreement with past work in this area using grid codes.