Velocity Estimation Research Articles

Novel techniques for in situ estimation of shear-wave velocity and damping ratio through MASW testing – I: a beamforming procedure for extracting Rayleigh-wave phase velocity and phase attenuation

SUMMARY A robust, in situ estimate of shear-wave velocity VS and the small-strain damping ratio DS (or equivalently, the quality factor QS) is crucial for the design of buildings and geotechnical systems subjected to vibrations or earthquake ground shaking. A promising technique for simultaneously obtaining both VS and DS relies on the Multichannel Analysis of Surface Waves (MASW) method. MASW can be used to extract the Rayleigh wave phase velocity and phase attenuation data from active-source seismic traces recorded along linear arrays. Then, these data can be inverted to obtain VS and DS profiles. This paper introduces two novel methodologies for extracting the phase velocity and attenuation data. These new approaches are based on an extension of the beamforming technique which can be combined with a modal filter to isolate different Rayleigh propagation modes. Thus, the techniques return reliable phase velocity and attenuation estimates even in the presence of a multimode wavefield, which is typical of complex stratigraphic conditions. The reliability and effectiveness of the proposed approaches are assessed on a suite of synthetic wavefields and on experimental data collected at the Garner Valley Downhole Array and Mirandola sites. The results reveal that, under proper modelling of wavefield conditions, accurate estimates of Rayleigh wave phase velocity and attenuation can be extracted from active-source MASW wavefields over a broad frequency range. Eventually, the estimation of soil mechanical parameters also requires a robust inversion procedure to map the experimental Rayleigh wave parameters into soil models describing VS and DS with depth. The simultaneous inversion of phase velocity and attenuation data is discussed in detail in the companion paper.

Improving Thermospheric Density Predictions in Low‐Earth Orbit With Machine Learning

AbstractThermospheric density is one of the main sources of uncertainty in the estimation of satellites' position and velocity in low‐Earth orbit. This has negative consequences in several space domains, including space traffic management, collision avoidance, re‐entry predictions, orbital lifetime analysis, and space object cataloging. In this paper, we investigate the prediction accuracy of empirical density models (e.g., NRLMSISE‐00 and JB‐08) against black‐box machine learning (ML) models trained on precise orbit determination‐derived thermospheric density data (from CHAMP, GOCE, GRACE, SWARM‐A/B satellites). We show that by using the same inputs, the ML models we designed are capable of consistently improving the predictions with respect to state‐of‐the‐art empirical models by reducing the mean absolute percentage error (MAPE) in the thermospheric density estimation from the range of 40%–60% to approximately 20%. As a result of this work, we introduce Karman: an open‐source Python software package developed during this study. Karman provides functionalities to ingest and preprocess thermospheric density, solar irradiance, and geomagnetic input data for ML readiness. Additionally, it facilitates developing and training ML models on the aforementioned data and benchmarking their performance at different altitudes, geographic locations, times, and solar activity conditions. Through this contribution, we offer the scientific community a comprehensive tool for comparing and enhancing thermospheric density models using ML techniques.

Minimum-entropy velocity estimation from GPS position time series

Minimum-entropy velocity estimation from GPS position time series

Enhancing hydrofoil velocity estimation through residual learning

Recovering flow states from limited observations provides supports for flow control and super-resolution. Advances in deep learning have made it possible to construct precise state estimators. In this work, a deep learning estimator with an initialization branch and a residual branch is proposed to predict velocity fields from sparse pressure on the hydrofoil surface. In detail, on the one hand, the pre-trained proper orthogonal decomposition-based model as an initialization branch is employed to generate initial predictions. On the other hand, the U-shaped neural network-based model as the residual branch is trained to learn the residual between the initial predictions and the ground truth. Compared to previous models, the proposed model not only enhances prediction accuracy but also improves the interpretability of the model. Furthermore, the incorporation of the initialization branch has little influence on training and inference speed. Test results illustrate that residual learning provides additional model capacity for improving the prediction of transverse velocity fields and flow details. Moreover, even in the presence of intense velocity fluctuations near the trailing edge, predictions from the improved model are more consistent with ground truth. Visualization of feature maps underscores a significant advantage of the improved model over the baseline model in terms of structural features and increased distinctiveness among features, thereby facilitating interpretability enhancements.

Vision-based collective motion: A locust-inspired reductionist model.

Naturally occurring collective motion is a fascinating phenomenon in which swarming individuals aggregate and coordinate their motion. Many theoretical models of swarming assume idealized, perfect perceptual capabilities, and ignore the underlying perception processes, particularly for agents relying on visual perception. Specifically, biological vision in many swarming animals, such as locusts, utilizes monocular non-stereoscopic vision, which prevents perfect acquisition of distances and velocities. Moreover, swarming peers can visually occlude each other, further introducing estimation errors. In this study, we explore necessary conditions for the emergence of ordered collective motion under restricted conditions, using non-stereoscopic, monocular vision. We present a model of vision-based collective motion for locust-like agents: elongated shape, omni-directional visual sensor parallel to the horizontal plane, and lacking stereoscopic depth perception. The model addresses (i) the non-stereoscopic estimation of distance and velocity, (ii) the presence of occlusions in the visual field. We consider and compare three strategies that an agent may use to interpret partially-occluded visual information at the cost of the computational complexity required for the visual perception processes. Computer-simulated experiments conducted in various geometrical environments (toroidal, corridor, and ring-shaped arenas) demonstrate that the models can result in an ordered or near-ordered state. At the same time, they differ in the rate at which order is achieved. Moreover, the results are sensitive to the elongation of the agents. Experiments in geometrically constrained environments reveal differences between the models and elucidate possible tradeoffs in using them to control swarming agents. These suggest avenues for further study in biology and robotics.

An Eulerian finite element method for the linearized Navier–Stokes problem in an evolving domain

Abstract The paper addresses an error analysis of an Eulerian finite element method used for solving a linearized Navier–Stokes problem in a time-dependent domain. In this study, the domain’s evolution is assumed to be known and independent of the solution to the problem at hand. The numerical method employed in the study combines a standard backward differentiation formula-type time-stepping procedure with a geometrically unfitted finite element discretization technique. Additionally, Nitsche’s method is utilized to enforce the boundary conditions. The paper presents a convergence estimate for several velocity–pressure elements that are inf-sup stable. The estimate demonstrates optimal order convergence in the energy norm for the velocity component and a scaled $L^{2}(H^{1})$-type norm for the pressure component.

Improved beamforming schemes for estimation of multimode surface wave dispersion curves from seismic noise with reducing effect of the irregular array geometry and/or anisotropic source distribution

SUMMARY Dense array observation and seismic interferometry have revolutionized the imaging schemes of the earth structure. It is becoming possible to directly obtain the lateral variation of the earth's structure by applying array-based methods such as the cross-correlation beamforming (CBF) of the ambient noise to the subsets of the dense array, without tomography. CBF has been proven to extract the azimuth-averaged multimode surface wave dispersion curves. However, the resolution of the dispersion image generated by conventional CBF is low at high frequencies in the frequency–velocity (f-v) domain. Moreover, the irregular array geometry and uneven source distribution would bias the result of CBF, especially for the estimation of azimuth-dependent velocity. In this paper, two beamforming (BF) es are suggested to improve the resolution of multimode dispersion images in the f-v domain. First, the geometrical spreading of the wavefield is corrected to enhance the amplitude at high frequency (or large distance) and thereby improve the resolution of the dispersion image at high frequency. We call this scheme weighted correlation beamforming (WCBF). The azimuth-averaged velocity can be estimated with sufficient resolution using WCBF by stacking the BF output at each azimuth. We show that WCBF is the 2-D Fourier transform of the spatial wavefield from the viewpoint of the wavefield transform. Secondly, a modified beamforming scheme (MCBF) is suggested to reduce the effect of uneven source and/or irregular array geometry. The delay and summation in MCBF are performed only for plane waves incident from the stationary phase region. The azimuth-dependent velocity can therefore be estimated by MCBF with less dependence on the array geometry, as well as on the uneven source distribution. In terms of the estimation of azimuth-averaged phase velocity, we show the F-J method, another array-based method for extracting multimode surface waves from ambient noise using the Fourier–Bessel transform, is the azimuth-averaged version of WCBF. The reliability of WCBF and MCBF is verified based on the synthetic and field data using the array with different geometry. The dispersion image of multimode Rayleigh wave phase velocity at local and regional scales can be generated by WCBF or MCBF with high resolution. In particular, multimode dispersion curves at the local scale can be measured by MCBF with sufficient accuracy using quite short recordings from hours to days. This offers the possibility of a rapid assessment of the media properties.

Using delta channel width to estimate paleodischarge in the rock record: geometric scaling and practical sampling criteria

Abstract Quantifying paleodischarge from geological field observations remains a key research challenge. Several scaling relationships between paleodischarge and channel morphology (width, depth) have been developed for rivers and river deltas. Previous paleodischarge scaling relationships were based on discharge–catchment-area scaling and an empirical flow-velocity estimate (e.g., the Chézy equation, the Manning equation) multiplied by channel cross-sectional area to derive discharge. In deltas, where marine (wave, tide) energy causes bidirectional flow in distributary-channels, the available paleodischarge scaling relationships are not applicable due to their unidirectional-flow assumption. Here, the spatial variability of distributary-channel widths from a database of 114 global modern river deltas is assessed to understand the limit of marine influence on distributary-channel widths. Using measured 6,213 distributary-channel widths, the median channel widths of distributary-channels for each delta were correlated with bankfull discharge for river-, tide- and wave-dominated deltas, the latter two including the effect of bidirectional flow. Statistically significant width–discharge scaling relationships are derived for river- and wave-dominated deltas, with no significant relationships identified for tide-dominated deltas. By reverse bootstrapping the channel widths measured from modern deltas, the minimum number of width measurements needed to apply width–discharge scaling relationships to ancient deltaic deposits is estimated as 3 and 4 for the upstream parts of river- and wave-dominated deltas, respectively, increasing to 30 in the downstream parts of river-dominated deltas. These estimates will guide sedimentological studies that often have limited numbers of distributary-channel widths exposed in the rock record. To test the reliability of these alternative width–discharge scaling relationships in the rock record, paleodischarges were estimated for the well-studied Cretaceous lower Mesa Rica Sandstone Formation, USA. Comparison of these results with the more complex Chézy-derived method suggests that these new scaling relationships are accurate. Hence, it is proposed that the scaling relationships obtained from modern deltas can be applied to the rock record, requiring fewer, and easier-to-measure, data inputs than previously published methods.

Machine learning approach for GNSS geodetic velocity estimation

This study aimed to investigate the performance of machine learning (ML) algorithms in determining horizontal velocity at specific points using the current Global Navigation Satellite System (GNSS) velocity field. To achieve this objective, the analysis utilized the most comprehensive velocity field available for Turkey, where 70% of the GNSS velocities was allocated for training the ML algorithms, while the remaining 30% was used for testing. Contrary to the previous research, the significance of considering the tectonic structure within the study area was emphasized at this point. To determine the tectonic structure of the horizontal velocity field in the region, a preliminary clustering procedure was conducted. Subsequently, distinct ML algorithms were trained using velocity fields associated with different tectonic plates. Moreover, to investigate the impact of the tectonic domain, the entire velocity field was also tested using ML algorithms without considering the tectonic structure. Four different ML algorithms, namely, Gradient Boosting Machines (GBM), LightGBM, Random Forest (RF), and eXtreme Gradient Boosting Machines (XGBoost), were employed to estimate the horizontal velocities (east and north components). The findings imply that incorporating the tectonic structure improved the performance of machine learning predictions, as indicated by the GBM algorithm's decreased root-mean-square error values. In addition, when the tectonic structure was taken into account, the accuracy assessment values for the RF and XGBoost algorithms in the east component decreased significantly. In terms of predicting GNSS velocities, the RF algorithm exhibited the lowest root-mean-square error values compared to other algorithms. The horizontal velocity differences between averages of the reference velocity field and the RF velocity estimates are maximum 0.4 mm/yr.

Four-Wheeled Vehicle Sideslip Angle Estimation: A Machine Learning-Based Technique for Real-Time Virtual Sensor Development

In the last few decades, the role of vehicle dynamics control systems has become crucial. In this complex scenario, the correct real-time estimation of the vehicle’s sideslip angle is decisive. Indeed, this quantity is deeply linked to several aspects, such as traction and stability optimization, and its correct understanding leads to the possibility of reaching greater road safety, increased efficiency, and a better driving experience for both autonomous and human-controlled vehicles. This paper aims to estimate accurately the sideslip angle of the vehicle using different neural network configurations. Then, the proposed approach involves using two separate neural networks in a dual-network architecture. The first network is dedicated to estimating the longitudinal velocity, while the second network predicts the sideslip angle and takes the longitudinal velocity estimate from the first network as input. This enables the creation of a virtual sensor to replace the real one. To obtain a reliable training dataset, several test sessions were conducted on different tracks with various layouts and characteristics, using the same reference instrumented vehicle. Starting from the acquired channels, such as lateral and longitudinal acceleration, steering angle, yaw rate, and angular wheel speeds, it has been possible to estimate the sideslip angle through different neural network architectures and training strategies. The goodness of the approach was assessed by comparing the estimations with the measurements obtained from an optical sensor able to provide accurate values of the target variable. The obtained results show a robust alignment with the reference values in a great number of tested conditions. This confirms that the adoption of artificial neural networks represents a reliable strategy to develop real-time virtual sensors for onboard solutions, expanding the information available for controls.

A framework to facilitate development and testing of image‐based river velocimetry algorithms

AbstractImage‐based methods have compelling, demonstrated potential for characterizing flow fields in rivers, but algorithms like particle image velocimetry (PIV) must be further tested and improved to enable more effective use of these techniques. This paper presents a framework designed for this exact purpose: Simulating Hydraulics and Images for Velocimetry Evaluation and Refinement (SHIVER). The approach involves coupling a hydrodynamic model with a synthetic particle generator to advect particles between frames, as dictated by local velocity vectors and thus construct a plausible image sequence specific to the reach of interest. The resulting time series can then be used as input to a velocimetry algorithm to compare image‐derived estimates with known (modelled) velocities to perform an exhaustive, spatially distributed accuracy assessment. As an example application of SHIVER, we examined the effects of interrogation area (IA) size, frame rate, flow velocity, and image sequence duration on the performance of a standard PIV algorithm. This analysis indicated that image‐derived velocities were generally in close agreement with those from the flow model (root mean square error <10% and mean bias <3%), except when small IAs were coupled with low frame rates. Velocity estimates were most accurate for the lowest modelled discharge ( at baseflow) and became less reliable as the mean flow velocity increased ( for an intermediate discharge and at bankfull). Accuracy was essentially independent of image sequence duration, implying that long occupations might not be necessary. Errors were concentrated along channel margins, where PIV‐based velocities tended to be greater than those from the flow model. Small IAs led to underpredictions of velocity, while larger IAs led to overpredictions. SHIVER is highly modular and could be updated to make use of different hydrodynamic models or image simulators. The framework could also facilitate more thorough sensitivity analyses and comparison of various velocimetry algorithms.

Hydrodynamic Modeling for Flow and Velocity Estimation from an Arduino Ultrasonic Sensor

Flow is a crucial variable in water resources, although its determination is challenging. Rating curves are standard but have conceptual limitations, leading to significantly high uncertainties. Hydrodynamic models offer a more precise alternative, but they necessitate continuous measurements of velocities, which are complex and expensive to obtain. Thus, this article aimed to validate a hydrodynamic model that estimates flows and velocities in transient conditions based on water levels measured using a low-cost ultrasonic sensor. The results indicated that these estimates can be reliable if (1) hydrodynamic models are used to represent the flow, (2) the channel bed slope is well represented in the geometric data, and (3) Manning’s coefficients are accurately estimated during calibration. The calculated flow and velocity showed a maximum variation of 40% for the same water level compared to estimates using the rating curve. The model exhibited higher sensitivity in terms of the flow when varying the channel bed slope, highlighting the importance of topographic surveys for the estimates. The validity of the implemented model was assessed with experimental data, indicating precision and reliability for practical applications in natural channels.

A novel four phase slug single-well push–pull test with regional flux: forward modeling and parameter estimation

The single-well push–pull (SWPP) test has been widely used for several applications, including determination of transport parameters such as regional groundwater flux velocity, effective porosity and dispersivity. A complete SWPP test usually includes four phases of injection, chase, rest, and extraction, while previous models mostly ignore the chase phase for the sake of simplification. Actually, the chase phase is important to minimize the impact of well skins and wellbore storage on the shape of the breakthrough curves (BTCs), thus is necessary and should be included in the model. To this end, two simplified methods are proposed in this study based on two different time tp and ta during a four-phase SWPP test to estimate the parameters related to transport, where tp and ta correspond to the time of the peak concentration during the injection phase and the time when the center of tracer mass returns to the wellbore during the extraction phase, respectively. Specifically, the tp method can be used to estimate the regional groundwater flow velocity and dispersivity (transverse and longitudinal), while the ta method is used to estimate the regional groundwater flow velocity and the effective porosity. Finite-element numerical modeling of the SWPP test based on the coupling of two-dimensional transient groundwater flow and solute transport is employed to test the applicability of the proposed methods. Results indicate that both the tp and ta methods proposed in this study perform satisfactorily in estimation of regional groundwater flow velocity, effective porosity and dispersivity, and these two methods require fewer observations than traditional curve fitting methods and do not require any optimization algorithms. We have also compared the proposed two methods with several previous methods, and conclude that these two new methods generally perform better than those of previous studies in terms of parameter estimation reliability.

Performance analysis of joint range and velocity estimation in OFDM-IM-based RadCom system

Modulation symbol domain (MSD) method is usually applied in range and velocity estimation for the radar-communication (RadCom) shared system based on orthogonal frequency-division multiplexing with index modulation (OFDM-IM). Nevertheless, the deterioration of sidelobe characteristics significantly impairs the efficacy of both range and velocity estimation. In this paper, we propose a modulation symbol domain-spatial sparsity-compressed sensing (MSD-SS-CS) method to realize super resolution joint range and velocity estimation for the RadCom shared system based on OFDM-IM. The compressed sensing theory is used in MSD method to solve the problem of detection targets that meet spatial sparsity application scenarios. Simulation outcomes illustrate that the bit error rate (BER) performance of the RadCom shared system, leveraging OFDM-IM, surpasses that of the RadCom shared system relying solely on OFDM. The proposed MSD-SS-CS method not only solves the degradation of sidelobe caused by blank sub-carriers in the RadCom shared system based on OFDM-IM, but also achieves good super resolution joint range and velocity estimation.

DeepVelo: deep learning extends RNA velocity to multi-lineage systems with cell-specific kinetics

Existing RNA velocity estimation methods strongly rely on predefined dynamics and cell-agnostic constant transcriptional kinetic rates, assumptions often violated in complex and heterogeneous single-cell RNA sequencing (scRNA-seq) data. Using a graph convolution network, DeepVelo overcomes these limitations by generalizing RNA velocity to cell populations containing time-dependent kinetics and multiple lineages. DeepVelo infers time-varying cellular rates of transcription, splicing, and degradation, recovers each cell’s stage in the differentiation process, and detects functionally relevant driver genes regulating these processes. Application to various developmental and pathogenic processes demonstrates DeepVelo’s capacity to study complex differentiation and lineage decision events in heterogeneous scRNA-seq data.

Velocity estimation method for high-spinning vehicle based on a side-mounted single patch antenna

Velocity estimation method for high-spinning vehicle based on a side-mounted single patch antenna

Deduction of the Dimensionless Groups and Type Curves of Temperature Profiles in Two-Layer Soils with Water Flow at Depth

In the common hydrogeologic scenarios of horizontal groundwater flow and a water table below the surface, the steady-state 2D thermal field resulting from the coupling between water flow and heat flow and transport gives rise to a vertical temperature profile that develops progressively over a finite extent of the domain. Beyond this region, the temperature profiles are linear and independent of horizontal position. Such profiles are related to the groundwater velocity so they can be usefully used to estimate this velocity in the form of an inverse problem. By non-dimensionalization of the governing equations and boundary conditions, this manuscript formally derives the precise dimensionless groups governing the main unknowns of the problem, namely, (i) extent of the profile development region, (ii) time required for the steady-state temperature profile solution to be reached and (iii) the temperature–depth profiles themselves at each horizontal position of the development region. After verifying the mathematical dependencies of these unknowns on the deduced dimensionless groups, and by means of a large number of accurate numerical simulations, the type curves related to the horizontal extension of the development of the steady-state profiles, the characteristic time to develop such profiles and the dimensionless vertical temperature profiles inside the characteristic region are derived. These universal graphs can be used for the estimation of groundwater horizontal velocities from temperature–depth measurements.

High-speed multihull anti-pitching control based on heave velocity and pitch angular velocity estimation

This paper proposes a novel anti-pitching control algorithm based on algebraic model predictive control (AMPC) for high-speed multihull, in which the heave velocity and pitch angular velocity cannot be measured directly. Specifically, a multihull vertical control model is established with the employed anti-pitching appendages, and the uncertainty of the model as well as the coupling between heave and pitch motion are investigated. To address unmeasurable of the heave velocity and pitch angular velocity, a novel kinematics-based Kalman filter is designed to estimate these states online, which is substantially different from the existing works. Then, the AMPC strategy for varying receding-horizon optimization is proposed, which significantly reduces the amount of online calculation. To estimate the lumped uncertainty, the second-order filter data of input and output is used to design a disturbance observer with less parameters, which can perform feed-forward compensation to enhance the robustness. The convergence of the disturbance observer and the closed-loop system is analyzed mathematically. Finally, the advantages of the proposed anti-pitching control approach are demonstrated in both theory and simulation.

A MCKF-based cascade vector tracking method designed for ship navigation

In ship navigation, the most widely used technology is global navigation satellite systems (GNSS), which provide the ship’s position and velocity continuously over a period of time. However, when ships are blocked by port buildings or bridges, the quality of signals received from shipborne GNSS receivers may be reduced, resulting in inaccurate ship positioning that poses a risk to navigational safety. In an occluded environment, the measurement process during the signal processing of shipborne GNSS receivers is nonstationary and prone to measurement anomalies, which can contaminate measurement noise with outliers. To address this problem, a cascaded non-coherent vector tracking loop is designed, with the maximum correntropy Kalman filter serving as a cascaded carrier/code pre-filter for shipborne GNSS receivers. The measurement noise covariance matrix of the pre-filter is adaptively calculated and corrected using the carrier-to-noise ratio and the maximum correntropy criterion, respectively. The algorithm proposed is more sensitive to outliers than the traditional tracking methods and can effectively solve the state estimation problem under the condition of measurement anomalies. Specifically, the algorithm offers ships with more precise position and velocity estimations and lower signal tracking errors than traditional tracking methods under both static and dynamic conditions, as demonstrated by shipboard experiments. The horizontal positioning is increased by 88.4% and the horizontal velocity error is reduced by 62.1% in the occluded environment under dynamic conditions.

Estimation of Lateral Velocity and Cornering Stiffness in Vehicle Dynamics Based on Multi-Source Information Fusion

<div>To address the challenge of directly measuring essential dynamic parameters of vehicles, this article introduces a multi-source information fusion estimation method. Using the intelligent front camera (IFC) sensor to analyze lane line polynomial information and a kinematic model, the vehicle’s lateral velocity and sideslip angle can be determined without extra sensor expenses. After evaluating the strengths and weaknesses of the two aforementioned lateral velocity estimation techniques, a fusion estimation approach for lateral velocity is proposed. This approach extracts the vehicle’s lateral dynamic characteristics to calculate the fusion allocation coefficient. Subsequently, the outcomes from the two lateral velocity estimation techniques are merged, ensuring rapid convergence under steady-state conditions and precise tracking in dynamic scenarios. In addition, we introduce a tire parameter online adaptive module (TPOAM) to continually update essential tire parameters such as cornering stiffnesses, with its effectiveness demonstrated through DLC and slalom simulation tests. Using a dual extended Kalman filter (DEKF) observer, the article allows for joint estimation of vehicle states and tire parameters. Ultimately, we offer a cost-effective estimation method of vital dynamic vehicle parameters to support the motion control module in autonomous driving.</div>