Sparse Measurements Research Articles

Decomposition of power number in a stirred tank and real time reconstruction of 3D large-scale flow structures from sparse pressure measurements

We consider the flow inside an unbaffled stirred tank at Re = 600 and decompose the pressure field into components that are constant, linear and quadratic with respect to the temporal coefficients of velocity POD (proper orthogonal decomposition) modes. The pressure components are used to analyse the power number of individual blades and blade combinations. We also employ an identification algorithm to derive a linear dynamic estimator that allows the reconstruction (in real time) of the instantaneous 3D velocity field from sparse pressure measurements at the impeller blades. The first pair of POD modes are reconstructed with reasonable accuracy using the pressure signal from a single sensor. The results improve with 6 or 12 sensors. Application of the estimator to Re=500 and 700 shows that it is robust to changes in operating conditions. The work opens the possibility for real time control of mixing with targeted feeding location and rate.

Bayesian-Based Hyperparameter Optimization of 1D-CNN for Structural Anomaly Detection.

With the rapid development of sensor technology, structural health monitoring data have tended to become more massive. Deep learning has advantages when handling big data, and has therefore been widely researched for diagnosing structural anomalies. However, for the diagnosis of different structural abnormalities, the model hyperparameters need to be adjusted according to different application scenarios, which is a complicated process. In this paper, a new strategy for building and optimizing 1D-CNN models is proposed that is suitable for diagnosing damage to different types of structure. This strategy involves optimizing hyperparameters with the Bayesian algorithm and improving model recognition accuracy using data fusion technology. Under the condition of sparse sensor measurement points, the entire structure is monitored, and the high-precision diagnosis of structural damage is performed. This method improves the applicability of the model to different structure detection scenarios, and avoids the shortcomings of traditional hyperparameter adjustment methods based on experience and subjectivity. In preliminary research on the simply supported beam test case, the efficient and accurate identification of parameter changes in small local elements was achieved. Furthermore, publicly available structural datasets were utilized to verify the robustness of the method, and a high identification accuracy rate of 99.85% was achieved. Compared with other methods described in the literature, this strategy shows significant advantages in terms of sensor occupancy rate, computational cost, and identification accuracy.

Real-time calculation method of transformer winding temperature field based on sparse sensor placement

The Real-time obtain of the transformer winding temperature field is of great significance for understanding the operation status of the transformer. Limited by the spatial sampling rate of the sensor measurement method and the computational efficiency of the Computational Fluid Dynamics (CFD) method, the existing techniques cannot complete the real-time obtain of the transformer winding temperature field well. In this study, an estimator is designed, and used as a bridge to establish the relationship between the sparse measurement data of the winding temperature and the winding temperature field, and the real-time obtain of the winding temperature field is realized. Firstly, the proper orthogonal decomposition (POD) modes are obtained based on the prior information on the winding temperature field. Then, a sparse placement strategy of sensors is designed based on the QR factorization with column pivoting (QR-pivot) method, the measurement matrix is formed, and the sparse measurement data of the winding temperature are obtained. Finally, an estimator is designed to complete the winding temperature field's real-time calculation using the winding temperature's sparse measurement data. The transformer temperature rise test proves the effectiveness of the method. This study can provide a new approach for the real-time obtain of transformer winding temperature field.

Reconstructing 3D human pose and shape from a single image and sparse IMUs.

This article presents an approach to improve 3D human pose estimation by fusing a single image with sparse inertial measurement units (IMUs). Based on a dual-stream feature extract network, we design a model-attention network with a residual module to closely couple the dual-modal feature from a static image and sparse inertial measurement units. The final 3D pose and shape parameters are directly obtained by a regression strategy. Extensive experiments are conducted on two benchmark datasets for 3D human pose estimation. Compared to state-of-the-art methods, the per vertex error (PVE) of human mesh reduces by 9.4 mm on Total Capture dataset and the mean per joint position error (MPJPE) reduces by 7.8 mm on the Human3.6M dataset. The quantitative comparison demonstrates that the proposed method could effectively fuse sparse IMU data and images and improve pose accuracy.

Isotopic evidence for an intensified hydrological cycle in the Indian sector of the Southern Ocean

The hydrological cycle is expected to intensify in a warming climate. However, observational evidence of such changes in the Southern Ocean is difficult to obtain due to sparse measurements and a complex superposition of changes in precipitation, sea ice, and glacial meltwater. Here we disentangle these signals using a dataset of salinity and seawater oxygen isotope observations collected in the Indian sector of the Southern Ocean. Our results show that the atmospheric water cycle has intensified in this region between 1993 and 2021, increasing the salinity in subtropical surface waters by 0.06 ± 0.07 g kg−1 per decade, and decreasing the salinity in subpolar surface waters by -0.02 ± 0.01 g kg−1 per decade. The oxygen isotope data allow to discriminate the different freshwater processes showing that in the subpolar region, the freshening is largely driven by the increase in net precipitation (by a factor two) while the decrease in sea ice melt is largely balanced by the contribution of glacial meltwater at these latitudes. These changes extend the growing evidence for an acceleration of the hydrological cycle and a melting cryosphere that can be expected from global warming.

Joint parameter-input estimation for digital twinning of the Block Island wind turbine using output-only measurements

This paper presents a recursive Bayesian inference framework for digital twinning of an offshore wind turbine (OWT) in the Block Island Wind Farm (BIWF), the first commercial offshore wind farm in the U.S. with jacket substructure. The framework employs a window-based extended Kalman filter (EKF) to jointly estimate the dynamic input loads and unknown model parameters of the finite element (FE) model of the turbine using sparse output-only measurements. The estimation of input loads on the OWT is critical for fatigue life estimation, foundation monitoring and control strategy. In the proposed joint estimation algorithm, unknown input time histories are divided into overlapping windows and the current window of inputs is concatenated with uncertain model parameters to form an augmented state vector. To account for the uncertainty about wind direction and misalignment between wind direction and the turbine yaw angle, two independent horizontal wind load time histories in X and Y directions are estimated at the nacelle level. A numerical validation study is first performed in which wind loads of the OWT are simulated using the multi-physics platform FAST, and structural vibration responses are generated using the FE model in OpenSees. The window-based EKF is implemented using the simulated measurements, and the estimations of structural stiffness as the updating model parameter and input loads are observed to have high accuracy. The proposed algorithm is then validated using in-situ measurements on one of the OWT in BIWF. To investigate the effectiveness and robustness of the method under different environmental and operational conditions, four cases are considered in which the turbine is operating at the rated rotor speed (region 3 of power generation), below the rated rotor speed (region 2), idling rotor state (region 1 or no power), and region 4 beyond cut-out wind speed. Accurate predictions of acceleration and strain data are obtained using the proposed algorithm, and the estimations of model parameter are consistent and close to their nominal value under different conditions. These results from numerical and experimental studies validate the proposed window-based EKF for joint parameter-input estimation and digital twinning for long-term structural health monitoring of the OWT.

Multispectral Satellite-Derived Bathymetry Based on Sparse Prior Measured Data

Satellite-derived bathymetry is an economic and effective method of obtaining large-scale, high-resolution bathymetric information. At present, bathymetric inversion models require existing bathymetric data as a necessary condition, but these may be difficult to obtain around many small islands. Under the condition of sparse measurement data, many common methods have low levels of accuracy. This paper proposes a method of transferring a bathymetric model for an island that has in situ data to an island that has little in situ data. First, in situ data are used to establish a high-precision satellite bathymetry model for a given island. Second, this model is transplanted to other islands. The addition of just 2–3 data points to correct the model results can reduce the mean relative error to 6.62% in the range of 0–20 m. This is close to the accuracy of establishing the model using a large number of measurement data (mean relative error of 5.25%).

Quantification of data‐related uncertainty of spatially dense soil moisture patterns on the small catchment scale estimated using unsupervised multiple regression

AbstractMultiple regression analysis is a valuable method to reduce information gaps in a sparse soil moisture data set by fusing its information content with those of densely mapped data sets. Regression analysis utilizing uncertain data results in an indeterminate regression model and indeterminate soil moisture predictions when applying the regression model. We employ an unsupervised multiple regression approaches, taking optimally located sparse soil moisture measurements directly as coefficients in a linear regression model. We propagate data uncertainties into our probabilistic soil moisture estimation results by embedding the regression in a Monte Carlo approach. The computed uncertainty defines the quantitative limit for information retrieval from the resultant ensemble of soil moisture maps. This raises doubts on the true presence of some prominent channel‐like features of increased soil moisture that are clearly visible in a previously and deterministically derived soil moisture map ignoring the presence of data uncertainty. The approach followed in this work is computationally simple and could be applied routinely to databases of similar size. Insufficient uncertainty communication by the data provider became the biggest obstacle in our efforts and led us to the insight that the geoscientific community may need to revise their standards with regard to uncertainty communication related to measured and processed data.

An Efficient Compressive Sensing Event-Detection Scheme for Internet of Things System Based on Sparse-Graph Codes

This work studied the event-detection problem in an Internet of Things (IoT) system, where a group of sensor nodes are placed in the region of interest to capture sparse active event sources. Using compressive sensing (CS), the event-detection problem is modeled as recovering the high-dimensional integer-valued sparse signal from incomplete linear measurements. We show that the sensing process in IoT system produces an equivalent integer CS using sparse graph codes at the sink node, for which one can devise a simple deterministic construction of a sparse measurement matrix and an efficient integer-valued signal recovery algorithm. We validated the determined measurement matrix, uniquely determined the signal coefficients, and performed an asymptotic analysis to examine the performance of the proposed approach, namely event detection with integer sum peeling (ISP), with the density evolution method. Simulation results show that the proposed ISP approach achieves a significantly higher performance compared to existing literature at various simulation scenario and match that of the theoretical results.

Tensor-based flow reconstruction from optimally located sensor measurements

Reconstructing high-resolution flow fields from sparse measurements is a major challenge in fluid dynamics. Existing methods often vectorize the flow by stacking different spatial directions on top of each other, hence confounding the information encoded in different dimensions. Here, we introduce a tensor-based sensor placement and flow reconstruction method which retains and exploits the inherent multidimensionality of the flow. We derive estimates for the flow reconstruction error, storage requirements and computational cost of our method. We show, with examples, that our tensor-based method is significantly more accurate than similar vectorized methods. Furthermore, the variance of the error is smaller when using our tensor-based method. While the computational cost of our method is comparable to similar vectorized methods, it reduces the storage cost by several orders of magnitude. The reduced storage cost becomes even more pronounced as the dimension of the flow increases. We demonstrate the efficacy of our method on three examples: a chaotic Kolmogorov flow, in situ and satellite measurements of the global sea surface temperature and three-dimensional unsteady simulated flow around a marine research vessel.

A Graph Neural Network Based Radio Map Construction Method for Urban Environment

Radio maps can enhance the capability of wireless sensor networks and improve the efficiency of spectrum utilization. However, the construction of an accurate radio map in the urban environment is a challenging task, since the dense buildings lead to a non-line-of-sight (NLOS) transmission environment. With this focus, we first transform the spatial sparse measurement points into a graph structure and extract the connected relation through the building map. Then, we propose a graph neural network (GNN) scheme to recover the complete radio map from sparse measurements. Numerical results show that our algorithm outperforms the benchmark methods in accuracy and is robust to noise.

Flow Reconstruction Around a Surface-Mounted Prism from Sparse Velocity and/or Scalar Measurements Using a Combination of POD and a Data-Driven Estimator

A data-driven algorithm is proposed for flow reconstruction from sparse velocity and/or scalar measurements. The algorithm is applied to the flow around a two-dimensional, wall-mounted, square prism. To reduce the problem dimensionality, snapshots of flow and scalar fields are processed to derive POD modes and their time coefficients. Then a system identification algorithm is employed to build a reduced order, linear, dynamical system for the flow and scalar dynamics. Optimal estimation theory is subsequently applied to derive a Kalman estimator to predict the time coefficients of the POD modes from sparse measurements. Analysis of the flow and scalar spectra demonstrate that the flow field leaves its footprint on the scalar, thus extracting velocity from scalar concentration measurements is meaningful. The results show that remarkably good reconstruction of the flow statistics (Reynolds stresses) and instantaneous flow patterns can be obtained using a very small number of sensors (even a single scalar sensor yields very satisfactory results for the case considered). The Kalman estimator derived at one condition is able to reconstruct with acceptable accuracy the flow fields at two nearby off-design conditions. Further work is needed to assess the performance of the algorithm in more complex, three-dimensional, flows.

On the use of Fourier Features-Physics Informed Neural Networks (FF-PINN) for forward and inverse fluid mechanics problems

Physics Informed Neural Networks (PINN), a deep learning tool, has recently become an effective method for solving inverse Partial Differential Equations (PDEs) where the boundary/initial conditions are not well defined and only noisy sparse measurements sampled in the domain exist. PINN, and other Neural Networks, tends to converge to the low frequency solution in a field that has multiple frequency scales, this is known as spectral bias. For PINN this happens when solving PDEs that exhibit periodic behavior spatially and temporally with multi frequency scales. Previous studies suggested that Fourier Features-Neural Networks (FF-NN) can be used to overcome the spectral bias problem. They proposed the Multi Scale-Spatio Temporal-Fourier Features-Physics Informed Neural Networks (MS-ST-FF-PINN) to overcome the spectral bias problem in PDEs solved by PINN. This has been evaluated on basic PDEs such as Poisson, wave and Gray-Scott equations. In this paper we take MS-ST-FF-PINN a step further by applying it to the incompressible Navier-Stokes equations. Furthermore, a comparative analysis between the PINN and the MS-ST-FF-PINN architectures solution accuracy, the learnt frequency components and the rate of convergence to the correct solution is included. To show this three test cases are shown (a)-Forward time independent double-lid-driven cavity, (b)-Inverse time independent free surface estimation of Kelvin wave pattern, and (c)-Inverse 2D time-dependent turbulent Von Karman vortex shedding interaction downstream of multiple cylinders. The results show that MS-ST-FF-PINN is better at learning low and high frequency components synchronously at early training iterations compared to the PINN architecture that does not learn the high frequency components even after multiple iteration numbers such as the Kelvin wave pattern and the Karman vortex shedding cases. However, for the third test case, the MS-ST-FF-PINN architecture showed a discontinuity for the temporal prediction of the pressure field due to over-fitting.

Extended Smoothing Methods for Sparse Test Data Based on Zero-Padding

Aiming at the problem of sparse measurement points due to test conditions in engineering, a smoothing method based on zero-padding in the wavenumber domain is proposed to increase data density. Firstly, the principle of data extension and smoothing is introduced. The core idea of this principle is to extend the discrete data series by zero-padding in the wavenumber domain. The conversion between the spatial and wavenumber domains is achieved using the Discrete Fourier Transform (DFT) and the Inverse Discrete Fourier Transform (IDFT). Then, two sets of two-dimensional discrete random data are extended and smoothed, respectively, and the results verify the effectiveness and feasibility of the algorithm. The method can effectively increase the density of test data in engineering tests, achieve smoothing and extend the application to areas related to data processing.

BICePs v2.0: Software for Ensemble Reweighting Using Bayesian Inference of Conformational Populations.

Bayesian Inference of Conformational Populations (BICePs) version 2.0 (v2.0) is a free, open-source Python package that reweights theoretical predictions of conformational state populations using sparse and/or noisy experimental measurements. In this article, we describe the implementation and usage of the latest version of BICePs (v2.0), a powerful, user-friendly and extensible package which makes several improvements upon the previous version. The algorithm now supports many experimental NMR observables (NOE distances, chemical shifts, J-coupling constants, and hydrogen-deuterium exchange protection factors), and enables convenient data preparation and processing. BICePs v2.0 can perform automatic analysis of the sampled posterior, including visualization, and evaluation of statistical significance and sampling convergence. We provide specific coding examples for these topics, and present a detailed example illustrating how to use BICePs v2.0 to reweight a theoretical ensemble using experimental measurements.

Real-Time Topology Estimation for Active Distribution System Using Graph-Bank Tracking Bayesian Networks

Real-time topology estimation in distribution grid with high penetration of distributed energy resources remains a challenging task due to the insufficient high-precision measurements and frequent topology variations. This article proposes a real-time distribution system topology estimation approach building on the graph theory and Bayesian networks with sparse measurements. The graph theory develops the topology graph bank to effectively leverage the prior knowledge of topology models, including the topology structure and the switching relationship between different topologies. This allows the development of the Bayesian networks for topology tracking using real-time voltage and power injection measurements. A novel discrete method considering the similarity of data correlation information is proposed for the optimal placement of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μ</i> PMUs to ensure the performance of topology estimation. Numerical results on the IEEE 33-node and 123-node systems show that the BN-based topology estimation model has better performance against incomplete information, i.e., missing data, than other alternatives.

Sparse sensor reconstruction of vortex-impinged airfoil wake with machine learning

Reconstruction of unsteady vortical flow fields from limited sensor measurements is challenging. We develop machine learning methods to reconstruct flow features from sparse sensor measurements during transient vortex–airfoil wake interaction using only a limited amount of training data. The present machine learning models accurately reconstruct the aerodynamic force coefficients, pressure distributions over airfoil surface, and two-dimensional vorticity field for a variety of untrained cases. Multi-layer perceptron is used for estimating aerodynamic forces and pressure profiles over the surface, establishing a nonlinear model between the pressure sensor measurements and the output variables. A combination of multi-layer perceptron with convolutional neural network is utilized to reconstruct the vortical wake. Furthermore, the use of transfer learning and long short-term memory algorithm combined in the training models greatly improves the reconstruction of transient wakes by embedding the dynamics. The present machine-learning methods are able to estimate the transient flow features while exhibiting robustness against noisy sensor measurements. Finally, appropriate sensor locations over different time periods are assessed for accurately estimating the wakes. The present study offers insights into the dynamics of vortex–airfoil interaction and the development of data-driven flow estimation.Graphic abstract

Identify Best Learning Method for Heart Diseases Prediction Under impact of Different Datasets Characteristics

This paper introduces an experimental study of the heart disease datasets characteristics impact on the performance of classification algorithms in the aim of identifying the best algorithm for each dataset under its characteristics. The performance of five machine learning algorithms (logistic regression (LR), K-Nearest Neighbor (KNN), Decision tree (DT), Random Forest (RF), and support vector machine (SVM)), single layer neural network (ANN), and deep neural network (DNN), has been evaluated using five heart disease datasets under four data complexity measurement: number of samples (dataset size), number of features (dimension of dataset), Data sparsity measures, and correlation of features. All datasets have been processed and normalized then the mutual information-based feature selection method was used to solve the overfitting problem. The results show that in general, the machine learning especially the Random Forest algorithm achieves high classification accuracy than deep learning network. In other hand, the high sparsity and less mutual information of dataset has large impact on degradation of the performance of classification algorithms than other characteristics of data.

Artificial intelligence velocimetry reveals in vivo flow rates, pressure gradients, and shear stresses in murine perivascular flows

Quantifying the flow of cerebrospinal fluid (CSF) is crucial for understanding brain waste clearance and nutrient delivery, as well as edema in pathological conditions such as stroke. However, existing in vivo techniques are limited to sparse velocity measurements in pial perivascular spaces (PVSs) or low-resolution measurements from brain-wide imaging. Additionally, volume flow rate, pressure, and shear stress variation in PVSs are essentially impossible to measure in vivo. Here, we show that artificial intelligence velocimetry (AIV) can integrate sparse velocity measurements with physics-informed neural networks to quantify CSF flow in PVSs. With AIV, we infer three-dimensional (3D), high-resolution velocity, pressure, and shear stress. Validation comes from training with 70% of PTV measurements and demonstrating close agreement with the remaining 30%. A sensitivity analysis on the AIV inputs shows that the uncertainty in AIV inferred quantities due to uncertainties in the PVS boundary locations inherent to in vivo imaging is less than 30%, and the uncertainty from the neural net initialization is less than 1%. In PVSs of N = 4 wild-type mice we find mean flow speed 16.33 ± 11.09 µm/s, volume flow rate 2.22 ± 1.983 × 103 µm3/s, axial pressure gradient ( - 2.75 ± 2.01)×10-4 Pa/µm (-2.07 ± 1.51 mmHg/m), and wall shear stress (3.00 ± 1.45)×10-3 Pa (all mean ± SE). Pressure gradients, flow rates, and resistances agree with prior predictions. AIV infers in vivo PVS flows in remarkable detail, which will improve fluid dynamic models and potentially clarify how CSF flow changes with aging, Alzheimer's disease, and small vessel disease.

Vibration-Based Structural Damage Identification Using P-CNN and Time-Frequency Hybrid Index under the Conditions of Uncertainties and Incomplete Measurements

The accuracy of vibration-based structural damage identification is affected by uncertainties in vibration measurements and finite element modeling. Moreover, a sufficient number of sensor measurements are not practical in large-scale structures. In this regard, the frequency domain [frequencies and mode shapes (FMS)] and time domain [acceleration cross-correlation function (ACCF)] indexes are put into a parallel convolutional neural network (P-CNN, a new convolutional neural network architecture with dual-channel) to locate and quantify structural damage. First, this approach is verified by a numerical model of a simply-supported beam, and the performance is evaluated by comparing it with methods using FMS and ACCF indexes input to the conventional 2D-CNN, respectively. The comparative results demonstrate that the proposed method can identify the damage with the lowest error, and the errors are less than 5%. In addition, three sparse measurement conditions are adopted to investigate the effect of the number of measuring points on damage identification. It is found that under the influence of uncertainties, even if only four sensors are used, this approach can identify damage accurately. Second, an engineering example of a continuous rigid frame bridge is adopted to validate the feasibility of the proposed method. The results show that when the number of sensors accounts for 65% and 47% of test sensors, respectively, it performs well in locating and quantifying structural damage. Therefore, this method can not only reduce the number of sensors and eliminate uncertainties effects, but also improve the performance of the 2D-CNN through information fusion and complementarity, which is also beneficial to minimize the cost of sensor layout in actual structures.