有限时空观测下流场重建的可观测性、时间信息增益与可信边界调研

No abstract available

No abstract available

Sensing and reconstruction for supersonic flow field based on wall-pressure is promising. A new method for three-dimensional (3D) spatial flow-field reconstruction for the isolator of a scramjet is proposed, and a potential mapping between wall pressure and the spatial flow field has been established for the supersonic isolator. Combining theoretical methods and practical engineering applications, improved particle swarm optimization was used to optimize the sensor arrangements on the wall for the 3D flow field. The model successfully reconstructs the Mach-number field with high accuracy and learns the spatial mapping between the wall pressure in the flow channel and the supersonic Mach-number field. Hence, the 3D reconstruction model can capture the nonlinear physics and learn the spatial position effect and gradient effect in the supersonic isolator. This method can fully consider adding various restrictions and constraints while also taking into account the effectiveness of flow-field reconstruction and the guiding significance for practical engineering. A novel research approach is provided for predicting the 3D Mach-number field in the supersonic isolator, and the technical and methodological reference is provided for the exploration of the spatial supersonic flow field.

No abstract available

No abstract available

Acquiring high-resolution flow field data in reacting flow systems is essential for understanding their underlying mechanisms. However, it still remains challenging due to experimental limitations in capturing full-dimensional high-resolution measurements. This study introduces a novel observation-guided generative diffusion model and takes the rotating detonation combustor as a case study to reconstruct detailed flow fields from sparse or incomplete observations. Compared to discriminative models, the generative model demonstrates robust generalization across different observation configurations without the need for retraining. Results also indicate that the proposed observation-gradient-guided strategy surpasses existing flow field reconstruction studies in accuracy and consistency. The model operates effectively in scenarios including incomplete velocity fields and sparse pressure fields. Furthermore, the model can generate higher-resolution flow fields through a cascaded adaptive refinement reconstruction. This study provides a model with strong generative performance and generalization capability for flow field reconstruction research. As a surrogate model, it has the potential for flow field visualization and analysis in scientific research and engineering applications.

In the realm of experimental fluid mechanics, accurately reconstructing high-resolution flow fields is notably challenging due to often sparse and incomplete data across time and space domains. This is exacerbated by the limitations of current experimental tools and methods, which leave critical areas without measurable data. This research suggests a feasible solution to this problem by employing an inverse physics-informed neural network (PINN) to merge available sparse data with physical laws. The method's efficacy is demonstrated using flow around a cylinder as a case study, with three distinct training sets. One was the sparse velocity data from a domain, and the other two datasets were limited velocity data obtained from the domain boundaries and sensors around the cylinder wall. The coefficient of determination (R2) coefficient and mean squared error (RMSE) metrics, indicative of model performance, have been determined for the velocity components of all models. For the 28 sensors model, the R2 value stands at 0.996 with an associated RMSE of 0.0251 for the u component, while for the v component, the R2 value registers at 0.969, accompanied by an RMSE of 0.0169. The outcomes indicate that the method can successfully recreate the actual velocity field with considerable precision with more than 28 sensors around the cylinder, highlighting PINN's potential as an effective data assimilation technique for experimental fluid mechanics.

Detection of flow fields constitutes a critical role in the advancement and innovation of hypersonic aircraft. Under hypersonic conditions, aircraft aerodynamics manifest a multitude of complex phenomena, including intense turbulence and fluctuations, transitions within the boundary layer, interactions between shock waves and boundary layers, as well as the effects of high-temperature gas. Thus, the surveillance of hypersonic aircraft flow fields is imperative not only for flight safety but also for the progression of hypersonic technologies. Given the practical limitations that restrict sensors installed to only key areas for detection, we propose a GNN-based method for hypersonic aircraft flow field reconstruction from limited sensors. Moreover, we have introduced a novel graph modeling technique for enhancing the reconstruction motivated by that solely the most significant edges within the graph are efficacious for field reconstruction. The methodology encompasses the following steps, modeling graphs from diverse perspectives, and transforming them into minimum spanning trees. These sparse graphs are then integrated with learnable weights optimized by automatic differentiation. Our method has been tested on an open-source turbulence dataset, the two components of graph pruning and weight optimization bring about 34% and 10% improvements on average. Furthermore, our approach has been validated in the reconstruction of hypersonic aircraft flow fields for at least 10% error reduction among all the situations.

No abstract available

No abstract available

No abstract available

The super-resolution reconstruction based on sparse measurement information is an important issue in the field of experimental fluid dynamics, and using a small amount of information for high-precision turbulent flow field reconstruction has high research value. Traditionally, interpolation and reconstruction methods are used to reconstruct the flow field. In recent years, artificial intelligence technologies represented by deep neural networks have been increasingly applied to flow field reconstruction problems due to their advantages in handling high-dimensional and nonlinear function fitting problems. However, these methods do not fully consider the physical mechanisms followed by flow field evolution and require a large amount of high-precision data, which may result in high experimental costs. Physical Information Neural Network (PINN) is an unsupervised learning method that utilizes neural networks to fit solutions to partial differential equations of flow field evolution, thereby overcoming the strict requirements of traditional methods on data attributes. However, due to the complexity of the Navier-Stokes equations, the accuracy of traditional PINN methods cannot meet the modeling requirements. This article proposes a PINN based method that effectively combines test data and physical information, and applies this method to the problem of super-resolution turbulent flow field reconstruction. Using high-precision measurement data of turbulence in a square channel as the experimental dataset, the method was used to reconstruct a high-resolution velocity field based on downsampling information of turbulent flow field, and compared with traditional bicubic interpolation methods and flow field reconstruction methods based on Convolutional Neural Networks(CNN). The experimental results show that the PINN method proposed in this paper can quickly complete super-resolution flow field reconstruction using sparse flow field measurement information, and is insensitive to noise in the data. It has significant advantages in accuracy and robustness when the sampling ratio is large.

The rapid reconstruction of the internal flow field within pressure vessel equipment based on features from limited detection points was of significant value for online monitoring and the construction of a digital twin. This paper proposed a surrogate model that combined Proper Orthogonal Decomposition (POD) with deep learning to capture the dynamic mapping relationship between sensor monitoring point information and the global flow field state during equipment operation, enabling rapid reconstruction of the temperature field and velocity field. Using POD, the order of the tested temperature field was reduced by 99.75%, and the order of the velocity field was reduced by 99.13%, effectively decreasing the dimensionality of the flow field. Our analysis revealed that the first modal coefficient of the temperature field snapshot data, after modal decomposition, had a higher energy proportion compared to that of the velocity field snapshot data, along with a more pronounced marginal effect. This indicates that more modes need to be retained for the velocity field to achieve a higher total energy proportion. By constructing a CSSA-BP model to represent the mapping relationship between the modal coefficients of the temperature and velocity fields and the data collected from the detection points, a comparison was made with the BP method in reconstructing the temperature field of a shell-and-tube heat exchanger. The CSSA-BP method yielded a maximum mean squared error (MSE) of 9.84 for the reconstructed temperature field, with a maximum mean absolute error (MAE) of 1.85. For the velocity field, the maximum MSE was 0.0135 and the maximum MAE was 0.0728. The global maximum errors for the reconstructed temperature field were 4.85%, 3.65%, and 4.29%, respectively. The global maximum errors for the reconstructed velocity field were 17.72%, 11.30%, and 16.79%, indicating that the model established in this study has high accuracy. Conventional CFD simulation methods require several hours, whereas the reconstruction model proposed here can rapidly reconstruct the flow field within 1 min after training is completed, significantly reducing reconstruction time. This work provides a new method for quickly obtaining the internal flow field state of pressure vessel equipment under limited detection points, offering a reference for online monitoring and the development of digital twins for pressure vessel equipment.

In this paper, we present an innovative approach using physics-informed neural networks to reconstruct high-frequency, full-field flows, including the pressure field, by integrating sparse, noisy, low-temporal-resolution particle image velocimetry (PIV) data with high-temporal-resolution pressure probe data. This method effectively leverages the spatial richness of PIV data and the temporal abundance of pressure probe data, offering a complementary spatial and temporal data fusion. The incorporation of physical laws via equation constraints enables the neural network to accurately learn and predict complex fluid dynamics, achieving comprehensive flow field reconstructions. Rigorous testing across various flow types—periodic, non-periodic, and complex—against critical parameters like sampling interval (SI), number of grid points per snapshot (NGPIS), and number of pressure probes (NPP) has demonstrated remarkable accuracy. The results show reconstruction errors for velocity components (u, v) and pressure (p) below 5% with sufficient data, and around 10% for v and p, and below 5% for u in data-limited scenarios. A case study with SI = 30, NGPIS = 2000, NPP = 5 underscores the enhanced robustness and accuracy of random sampling, especially under various noisy conditions. Thus, this approach shows significant potential for temporal and spatial reconstruction of flow fields.

The flow-field reconstruction of a rotating detonation combustor (RDC) is essential to understand the stability mechanism and performance of rotating detonation engines. This study embeds a reduced-order model of an RDC into a neural network (NN) to construct a physics-informed neural network (PINN) to achieve the full-dimensional high-resolution reconstruction of the combustor flow field based on partially observed data. Additionally, the unobserved physical fields are extrapolated through the NN-embedded physical model. The influence of the residual point sampling strategy and observation point spatial-temporal sampling resolution on the reconstruction results are studied. As a surrogate model of the RDC, the PINN fills the gap that traditional computational fluid dynamics methods have difficulty solving, such as inverse problems, and has engineering value for the flow-field reconstruction of RDCs.

We propose a spatiotemporal coupling deep neural network approach for time-resolved reconstruction of the velocity field around a circular cylinder. The neural network leverages two distinct data types: (1) non-time-resolved velocity field around the cylinder, consisting of fixed frequency sampling and variable frequency sampling velocity field, and (2) the time-resolved surface pressure sequence around the cylinder. The deep neural network comprises two sub-networks: a convolutional autoencoder (CAE) for nonlinear mode extraction and a Transformer for sequence-to-sequence learning. We refer to this architecture as CTNet (CAE-Transformer Network). The encoder in the CAE maps non-time-resolved velocity field to a latent vector, enabling the extraction of nonlinear modal coefficients. An appropriate time window length for the surface pressure sequence is then selected to establish a Transformer sequence learning model, using the chosen sequence as input to predict the corresponding nonlinear modal coefficients. Once the Transformer is well trained, the time-resolved nonlinear modal coefficients of velocity field can be achieved. Along with the well-trained decoder in the CAE, the time-resolved velocity field can be reconstructed from the output of the Transformer. We verify the performance of CTNet by a simulated dataset at a representative Reynolds number of 3900. The results show a relative reconstruction error of just 6.3% for the time-resolved velocity field, demonstrating high reliability in the reconstruction. We further compare the reconstructed velocity field obtained with and without the utilization of variable frequency sampling velocity field. Notably, the inclusion of variable frequency sampling velocity field significantly improves the reconstruction quality.

Fluid dynamics is governed by partial differential equations (PDEs) which are solved numerically. The limitations of traditional methods in data assimilation hinder their effective engagement with experiments. Physics-informed neural network (PINN) has emerged as a hybrid data-physics-driven model for convective problems. However, the approach suffers from low accuracy and poor efficiency due to the way of incorporating PDEs. In this work, a novel convolutional neural network framework integrating finite volume method (FVM) is developed to address the challenge. The interface variables of the grid are predicted by the neural network for the first time, rather than a complex procedure in FVM. The physical law is then learned by minimizing the residual of the discretized conservative form of PDEs. A comparison between this model and the original PINN regarding prediction accuracy demonstrates the superiority of embedding PDEs through FVM. The effects of sampling strategies and quantities are studied. The result confirms the model’s capability to utilize sparsely available internal measurement data. Furthermore, the model performs well even in scenarios where partial initial and boundary conditions are absent.

Flow field reconstruction from sparse and noisy data remains a challenging task in fluid mechanics due to low efficiency and high hardware demands. This study introduces the finite volume method into the physics-informed neural network (PINN) method, proposing a finite volume physics-informed neural network (FVPINN) method under weak-form constraints. The method transforms volume integrals to surface integrals via the divergence theorem and employs control volume discretization, thereby reducing reliance on automatic differentiation for high-order derivatives. The experimental results show that FVPINNs achieve comparable prediction accuracy to Vanilla PINNs in the two-dimensional (2D) steady Cavity flow and Kovasznay flow problems, under both noiseless and noisy conditions, with average training time reduced by 44.91% and 43.94%, respectively. In the unsteady 2D cylinder flow scenarios, FVPINNs exhibit slightly higher sensitivity to noise, particularly in velocity field reconstruction, yet still maintain predictive performance comparable to Vanilla PINNs across all noise levels. Notably, FVPINNs achieve a significant reduction of 45.46% in average training time, highlighting their superior computational efficiency in transient flow modeling. Overall, FVPINNs significantly improve computational efficiency while maintaining prediction accuracy, showing strong robustness and potential for broader application.

No abstract available

No abstract available

No abstract available

No abstract available

No abstract available

Abstract Measurements of distributed surface pressure fluctuations over trailing-edge serrations at a Reynolds number $${\text{Re}}_{\theta }$$ Re θ  = 4900 are performed with time-resolved 3D particle imaging velocimetry using helium filled soap bubbles as flow tracers. The sparse velocity vector field obtained with Lagrangian particle tracking is densely reconstructed using VIC+, a data assimilation technique based on the vortex-in-cell method. The instantaneous pressure distribution is inferred by invoking the momentum equation. Experiments are performed first over a flat plate, as assessment of the technique, where the properties of the convecting turbulent boundary layer are assessed and surface pressure fluctuations are validated against synchronous surface microphone measurements. The analysis of the flow over the trailing-edge serration focuses on the characterization of the spatial distribution and spectral coherence of surface pressure fluctuations, i.e. the flow features responsible for the acoustic scattering. Present results indicate that the measurement technique is suited to describe the spatio-temporal development of the pressure fluctuations over the serration surface at the proposed scale of the experiments. Graphic abstract

No abstract available

This study presents the application of time-resolved particle image velocimetry (TR-PIV) to measure the mean and fluctuating velocity components in a turbulent boundary layer (TBL) over an axisymmetric body of revolution. A narrow wall-normal strip of the flow was captured using a synchronised high-speed laser and camera at a recording frequency of up to 80 kHz. The resulting streamwise and wall-normal velocity TR-PIV data were validated against hot-wire anemometry measurements and direct numerical simulations (DNS) of a flat plate under matched flow conditions. The mean flow results showed good agreement between all methods, while the expected attenuation due to the spatial averaging was found in the TR-PIV turbulence statistics closer to the wall. A key outcome of this study is the establishment of an effective laser sheet thickness for the TR-PIV using DNS as a reference. This study fills a gap in understanding the spectral response and limitations of TR-PIV in such complex flows, particularly how spatial resolution and noise influence the accuracy of turbulence measurements. The TR-PIV streamwise velocity energy spectra were compared with DNS data that were spatially filtered to match the resolution of the TR-PIV and hot-wire. A transfer function was derived to determine cut-off wavelengths as a function of wall-normal distance. The cut-off wavelengths enabled the quantification of the resolvable turbulence scales within the TBL, revealing that the spatial resolution is a limiting factor for TR-PIV. The methodology was applied to locations with zero and favourable pressure gradients, providing insights into how pressure gradients influence spectral content and the limitations of TR-PIV in capturing the full range of turbulence scales. The outlined methodology is applicable more broadly and can be used to enhance the accuracy of experimental techniques in future boundary layer investigations.

No abstract available

No abstract available

In the first part of this 3-paper-series time-resolved PIV is performed in the transonic cascade to elucidate the shock-boundary layer interaction process and to provide comparative data for numerical studies and analysis in part 2 and 3. The application of modern high-speed camera technology combined with a dual-pulse high-speed laser system enabled TR-PIV in the cascade for image areas covering ∼ 30% of the chord and ∼ 6% of the blade pitch, at fs = 20 kHz or 0.18tc for the acquisition of multiple time sequences with duration of ∼ 2000 tc. The sampling rate is sufficient to capture fluctuations of the separating region and accompanying movements of the shock system. To enable correlations of density variations of the shock system and velocity data, shadowgraphs are acquired synchronously with TR-PIV recordings at the same sampling rate. The TR-PIV and shadowgraph measurement setups, the image processing and the resulting spatial resolutions are described in this part. A analysis of power spectral densities along near-wall rows in PIV data reveals the chord-wise spatial distribution of specific peaks and bands, which are also visible in the shock buffet spectrum. A SPOD of TR-PIV data is conducted to enable inspection of spatio-temporal modes of velocity fluctuations at specific broad peaks and tones in the buffet frequency range. Results indicate, that upstream of the main shock oblique shock waves occur at higher order harmonics of the fundamental buffet frequency and at specific high-frequency tones. To locate possible sources of distinct tones at the entrance of the center passage, a SPOD of high-speed schlieren recordings is performed, capturing the shock systems in three passages. The results show that with these high-frequency tones opposing vibrations of bow and lip shocks occur for neighboring blades.

The tracking characteristics and light scattering properties of tracer particles are the crucial issues of time-resolved Particle Image Velocimetry (PIV) experiment technology for the accurate measurement of the unsteady velocity field in the wake of a cylinder. A Laskin-40 particle generator was chosen with 1-μm-diameter DEHS as the tracer particle, and a hot-wire anemometer was employed to assess its frequency response property. The high frequency PIV device featured a sampling rate of 1000 Hz, for which the test area is the rectangular wake flow region of 7.5 times the diameter of a 20 mm-diameter metal cylinder from its trailing edge and 3.3 times the diameter from both sides. The study focused on the unsteady flow fields at 20 m/s wind speed and the Reynolds number (Re) of 2.67 × 10 4 for the cylinder. By the flow field and frequency spectrum analysis based on the velocity field data acquired by PIV, the research gained insights into the transient characteristics of flow field and frequency property of vortex shedding in the wake of the cylinder. As the time-resolved PIV technology provides abundant flow field information that allows accurate identification of the vortex shedding and its spatial temporal development in the wake, it is worth spreading in unsteady flow field measurement.

No abstract available

Data assimilation using particle image velocimetry (PIV) and Reynolds-averaged Navier–Stokes (RANS) simulation was performed for an ideally expanded supersonic jet flying at a Mach number of 2.0. The present study aims to efficiently reconstruct all the physical quantities in the aeroacoustic fields that match well with a realistic, experimentally obtained flow field. The two-dimensional, two-component PIV measurement was applied to the jet axis plane, and the time-averaged velocity field was obtained using single-pixel ensemble correlation. Two-dimensional axisymmetric RANS simulation using the Menter shear stress transport (SST) model was also performed, and the parameters of the SST model were optimized via data assimilation using the ensemble Kalman filter. The standard deviation of the observation noise σ, which is a parameter of the ensemble Kalman filter, is estimated by the previously proposed method (Nakamura et al., Low-Grid-Resolution-RANS-Based Data Assimilation of Time-Averaged Separated Flow Obtained by LES. Int. J. Comp. Fluid. Dyn., 2022), and its effectiveness was investigated for the first time. This method effectively estimated the magnitude of σ at each generation without tuning the hyperparameters. The assimilated flow fields exhibited similar flow structures observed in PIV such as the potential core length or shear layer. Therefore, the present framework can be used to estimate time-averaged full flow fields that match well with experimentally observed flow fields, and has the potential to construct a database for the Navier-Stokes-based stability analysis that requires a full flow field.

State observer techniques are investigated for the assimilation of three-dimensional velocity measurements into computational fluid dynamics simulations based on Reynolds-averaged Navier–Stokes (RANS) equations. The method relies on a forcing term, or observer, in the momentum equation, stemming from the difference between the computed velocity and the reference value, obtained by measurements or high-fidelity simulations. Two different approaches for the forcing term are considered: proportional and integral-proportional. This technique is demonstrated considering an experimental database that describes the time-average three-dimensional flow behind a generic car-mirror model. The velocity field is obtained by means of Robotic Volumetric PIV measurements. The effects of the different forcing terms and the spatial density of the measurement input to the numerical simulation are studied. The state observer approach forces locally the solution to comply with the reference value and the extent of the region modified by the forcing input is discussed. The velocity distribution and flow topology obtained with data assimilation are compared with attention to the object wake and the reattachment point where the largest discrepancy is observed between the different approaches. The results show that the integral term is more effective than the proportional one in reducing the mismatch between simulation and the reference data, with increasing benefits when the density of forced points, or forcing density, is increased.

We use image plane filtering technique to filter out the focused light field in digital holographic reconstruction, which can reduce the defocusing effect of this part of the light field on reconstruction at other distances.

Abstract A new combination of materials with matched indices of refraction was used in average and statistical PIV analysis of a 5 × 5 rod bundle with prototypical pressurized water reactor (PWR) mixing vane spacer grids. The new combination of materials shows improved matching of refractive index which enabled detailed PIV measurement of subchannel flow, even when viewed through a relatively large number of material interfaces. Convergence of average full field PIV measurements at ∼ 27 , 000 Reynolds number was demonstrated as independent of measurement plane depth relative to camera view window. A method for average vector post-processing elimination is proposed using validation statistics from PIV. The proposed method shows potential for eliminating vectors in areas of poor-convergence for planes with little interfering geometry. A full uncertainty quantification was performed on the full field of each PIV measurement planes. Similar to convergence rates, uncertainty demonstrated independence from measurement plane depth. Additional material interface between camera and measurement plane does not appear to have affected instantaneous velocity measurements’ contribution to average vector fields. Symmetric measurement planes were compared between 2 rod pitch intervals of the spacer grid. Velocity and statistically derived quantities show good coherence between symmetric planes. Measurements near and even below the tips of the mixing vanes were collected and analyzed.

Currently, computational fluid dynamics (CFD) is widely used in the nuclear thermal hydraulics field for design and safety analyses. To validate CFD codes, high quality multi dimensional flow field data are essential. The Matched Index of Refraction (MIR) Flow Facility at Idaho National Laboratory has a unique capability to contribute to the development of validated CFD codes through the use of Particle Image Velocimetry (PIV). The significance of the MIR facility is that it permits non intrusive velocity measurement techniques, such as PIV, through complex models without requiring probes and other instrumentation that disturb the flow. At the heart of any PIV calculation is the cross-correlation, which is used to estimate the displacement of particles in some small part of the image over the time span between two images. This image displacement is indicated by the location of the largest peak. In the MIR facility, uncertainty quantification is a challenging task due to the use of optical measurement techniques. Currently, this study is developing a reliable method to analyze uncertainty and sensitivity of the measured data and develop a computer code to automatically analyze the uncertainty/sensitivity of the measured data. The main objective of this study is to develop a well established uncertainty quantification method for the MIR Flow Facility, which consists of many complicated uncertainty factors. In this study, the uncertainty sources are resolved in depth by categorizing them into uncertainties from the MIR flow loop and PIV system (including particle motion, image distortion, and data processing). Then, each uncertainty source is mathematically modeled or adequately defined. Finally, this study will provide a method and procedure to quantify the experimental uncertainty in the MIR Flow Facility with sample test results.

No abstract available

Particle image velocimetry (PIV) has become the chief experimental technique for velocity field measurements in fluid flows. The technique yields quantitative visualizations of the instantaneous flow patterns, which are typically used to support the development of phenomenological models for complex flows or for validation of numerical simulations. However, due to the complex relationship between measurement errors and experimental parameters, the quantification of the PIV uncertainty is far from being a trivial task and has often relied upon subjective considerations. Recognizing the importance of methodologies for the objective and reliable uncertainty quantification (UQ) of experimental data, several PIV-UQ approaches have been proposed in recent years that aim at the determination of objective uncertainty bounds in PIV measurements. This topical review on PIV uncertainty quantification aims to provide the reader with an overview of error sources in PIV measurements and to inform them of the most up-to-date approaches for PIV uncertainty quantification and propagation. The paper first introduces the general definitions and classifications of measurement errors and uncertainties, following the guidelines of the International Organization for Standards (ISO) and of renowned books on the topic. Details on the main PIV error sources are given, considering the entire measurement chain from timing and synchronization of the data acquisition system, to illumination, mechanical properties of the tracer particles, imaging of those, analysis of the particle motion, data validation and reduction. The focus is on planar PIV experiments for the measurement of two- or three-component velocity fields. Approaches for the quantification of the uncertainty of PIV data are discussed. Those are divided into a-priori UQ approaches, which provide a general figure for the uncertainty of PIV measurements, and a-posteriori UQ approaches, which are data-based and aim at quantifying the uncertainty of specific sets of data. The findings of a-priori PIV-UQ based on theoretical modelling of the measurement chain as well as on numerical or experimental assessments are discussed. The most up-to-date approaches for a-posteriori PIV-UQ are introduced, highlighting their capabilities and limitations. As many PIV experiments aim at determining flow properties derived from the velocity fields (e.g. vorticity, time-average velocity, Reynolds stresses, pressure), the topic of PIV uncertainty propagation is tackled considering the recent investigations based on Taylor series and Monte Carlo methods. Finally, the uncertainty quantification of 3D velocity measurements by volumetric approaches (tomographic PIV and Lagrangian particle tracking) is discussed.

Andrea Sciacchitano1,∗ and Stefano Discetti 1 Faculty of Aerospace Engineering, TU Delft, Delft, The Netherlands 2 Aerospace Engineering Research Group, Universidad Carlos III de Madrid, Leganés, Spain E-mail: A.Sciacchitano@tudelft.nl The determination of a confidence interval is a key requirement for any measurement. In particle image velocimetry (PIV), the quantification of the measurement uncertainty strengthens the suitability of the technique for the discovery of new physics of fluid flows, as well as for the validation of numerical simulations by computational fluid dynamics. The present special issue on uncertainty quantification (UQ) in PIV and Lagrangian particle tracking (LPT) follows the successful one published in 2015 [1], which focused on the a-posteriori UQ of instantaneous two-component PIV measurements. Since then, the PIV technique has greatly advanced, further extending its range of applicability from micrometric scales to metre-scale three-dimensional flow measurements. In this special issue, the uncertainty associated with different aspects of the PIV and LPT techniques is addressed, including seeding particles, system calibration and imaging, the evaluation of derived flow properties, and novel processing algorithms based on neural networks. Bias errors in PIV statistics caused by the temporal and spatial inhomogeneity of seeding particles (intermittent particle seeding or conditional particle sampling) as well as by the particle lag are investigated by Martins et al [2]. By making use of a synthetic PIV experiment based on large eddy simulations, the authors show that particle lag and intermittent seeding yield bias errors on the local average velocities. The errors are even larger for derived flow quantities, such as Reynolds stresses, turbulent fluxes and velocity gradients. Paolillo and Astarita [3] analyse the contribution to the measurement uncertainty of different calibration models applied to optical systems that include refractive surfaces, i.e. interfaces separating two media with different refractive indexes. Models based on physical laws (refractive camera model, relying on the pinhole camera model and on a ray-tracing procedure) as well as analytical models (based on polynomials, multi-plane polynomials and rational functions) are comparatively assessed. The results show that the refractive camera model outperforms the analytical models, and that the latter require high-order polynomials to minimise the calibration errors. Qureshi et al [4] investigate the measurement errors of PIV and PTV in presence of particle image streaks, often caused by the relatively long exposure times in supersonic or hypersonic flows or bio-medical applications. The results based on the analysis of synthetic and experimental images show that the PTV

Abstract We present an experimental benchmark database for the transitional cavity flow. The database is obtained by planar Particle Image Velocimetry measurements at the median plane of the cavity model, for Reynolds numbers between 6300 and 19,000 based on the cavity height. A detailed uncertainty analysis of the experimental results is performed via the correlation statistics method for PIV uncertainty quantification and linear error propagation. The experimental results are compared to two-dimensional Reynolds-Averaged Navier Stokes (RANS) numerical simulations with different turbulence models. It is shown that, when the standard k-ω turbulence model is employed, the discrepancy between numerical simulations and experimental results exceeds the uncertainty of the latter. Conversely, RANS simulations with the SST k-ω turbulence model agree well with the experimental data in terms of time-averaged flow properties; however, the turbulent kinetic energy results present significant discrepancies at all considered Reynolds numbers. The data presented in this paper is made available for open-access download via the 4TU.ResearchData repository with DOI: https://do i.org//10.4121/14061233 .

No abstract available

No abstract available

The uncertainty of a PIV displacement field is estimated using a generic post-processing method based on statistical analysis of the correlation process using differences in the intensity pattern in the two images. First the second image is dewarped back onto the first one using the computed displacement field which provides two almost perfectly matching images. Differences are analyzed regarding the effect of shifting the peak of the correlation function. A relationship is derived between the standard deviation of intensity differences in each interrogation window and the expected asymmetry of the correlation peak, which is then converted to the uncertainty of a displacement vector. This procedure is tested with synthetic data for various types of noise and experimental conditions (pixel noise, out-of-plane motion, seeding density, particle image size, etc) and is shown to provide an accurate estimate of the true error.

A statistical tool called design of experiments (DOEs) is introduced for uncertainty quantification in particle image velocimetry (PIV). DOE allows to quantify the total uncertainty as well as the systematic uncertainties arising from various experimental factors. The approach is based on measuring a quantity (e.g. time-averaged velocity or Reynolds stresses) several times by varying the levels of the experimental factors which are known to affect the value of the measured quantity. Then, using Analysis of Variances, the total variance in the measured quantity is computed and hence the total uncertainty. Moreover, the analysis provides the individual variances for each of the experimental factors, leading to the estimation of the systematic uncertainties from each factor and their contributions to the total uncertainty. The methodology is assessed for planar PIV measurements of the flow over a NACA0012 airfoil at 15 degrees angle of attack considering five experimental factors, namely camera aperture, inter-frame time separation, interrogation window size, laser sheet thickness and seeding density. Additionally, the methodology is applied to the investigation by stereoscopic PIV of the flow at the outlet of a ducted Boundary Layer Ingesting propulsor. The total uncertainty in the time-averaged velocity as well as the constituent systematic uncertainties due to the experimental factors, namely camera aperture, inter-frame time separation, interrogation window size and stereoscopic camera angle, are quantified.

Ultrasound Particle image velocimetry (UPIV) is a non-invasive flow measurement technique where acousticopaque flow tracers are injected into a working fluid and ensonified to create ultrasound images. These images are processed using PIV cross-correlation based algorithms to measure the velocity field (Kim et al., 2004). UPIV is useful for opaque flows, primarily where complex flows exist, accordingly, it is used in many industrial and clinical research applications such as studying intracardiac flow (Crase et al., 2007). Furthermore, the measurement provides suitable temporal and spatial resolutions for improved diagnostic metrics. Mentioned applications and the sensitive diagnostic industrial and clinical decisions made based on these measurements intensifies the importance of characterizing the UPIV measurement accuracy and associated uncertainty. However, quantifying UPIV measurement uncertainty is non-trivial due to the complexity of possible uncertainty sources, their combination, and propagation through the measurement chain. The formation of a particle image by ultrasound significantly differs from optical imaging, introducing unique aspects to image quality that must be considered. Particle images are formed across several ultrasound scan lines, yielding an elliptical particle image shape. Furthermore, the particle’s reflected pressure wave is converted to a digital signal that undergoes signal modulation, and this process forms a non-Gaussian point spread function (PSF) along the scan line direction. Additionally, clusters of tracers produce a single, bright image intensity and speckle image pattern. Compared to conventional PIV images, UPIV incurs significantly higher image noise due to lack of filtration for the ultrasound reflection of the non-tracer obstacles.

No abstract available

No abstract available

Can you trust results from modeling and simulation? This text provides a framework for assessing the reliability of and uncertainty included in the results used by decision makers and policy makers in industry and government. The emphasis is on models described by PDEs and their numerical solution. Procedures and results from all aspects of verification and validation are integrated with modern methods in uncertainty quantification and stochastic simulation. Methods for combining numerical approximation errors, uncertainty in model input parameters, and model form uncertainty are presented in order to estimate the uncertain response of a system in the presence of stochastic inputs and lack of knowledge uncertainty. This new edition has been extensively updated, including a fresh look at model accuracy assessment and the responsibilities of management for modeling and simulation activities. Extra homework problems and worked examples have been added to each chapter, suitable for course use or self-study.

No abstract available

No abstract available

No abstract available

No abstract available

The spatially varying geographic-parameters introduce significant uncertainty into the ocean model. Due to the impracticality of manually tuning spatial varying parameters, data assimilation methods are widely used for geographic-parameter optimization (GPO). Practically, the limited observations do not contain enough information to perform GPO directly on the entire grid. Therefore, techniques are required to reduce the complexity of the parameters. A full-grid GPO scheme based on the ensemble adjustment Kalman filter (EAKF) is developed. Via smoothing the spatial distribution of posterior parameter members, the EAKF-smoothing (EAKF-S) introduces additional spatial correlations among parameters. Meanwhile, the small-scale correlation between the state and the parameters, which exhibit strong pseudo-correlations, is filtered out. A tide model of the Bohai Sea and Yellow Sea, considering 8 principal tidal constituents. is constructed using the Princeton Ocean Model with the generalized coordinate system (POMgcs). The EAKF-S is employed for optimizing the full-grid bathymetry. In twin experiment, based on idealized water level observations, EAKF-S effectively reduced model errors and approximately inverted the “true” bathymetry. After GPO, the lowest mean absolute error of the parameter ensemble is 0.83 m. A series of practical GPO experiments based on synthetic water level observations calculated from NAO.99Jb data are performed. First, the improvement of EAKF-S in accuracy and efficiency over standard EAKF is proven using an M2 tide model. After that, a practical experiment on an 8 constituents tide model is performed. The results show that the forecasting performance of all 8 constituents is improved after GPO, indicating the efficacy of EAKF-S.

No abstract available

<p>Ocean biogeochemical (BGC) models utilize a large number of poorly-constrained global parameters to mimic unresolved processes and reproduce the observed complex spatio-temporal patterns. Large model errors stem primarily from inaccuracies in these parameters whose optimal values can vary both in space and time. This study aims to demonstrate the ability of ensemble data assimilation (DA) methods to provide high-quality and improved BGC parameters within an Earth system model in idealized twin experiment framework. &#160;We use the Norwegian Climate Prediction Model (NorCPM), which combines the Norwegian Earth System Model with the Dual-One-Step ahead smoothing-based Ensemble Kalman Filter (DOSA-EnKF). The work follows on Gharamti et al. (2017) that successfully demonstrates the approach for one-dimensional idealized ocean BGC models. We aim to estimate five spatially varying BGC parameters by assimilating Salinity and Temperature hydrographic profiles and surface BGC (Phytoplankton, Nitrate, Phosphorous, Silicate, and Oxygen) observations in a strongly coupled DA framework &#8211; i.e., jointly updating ocean and BGC state-parameters during the assimilation. The method converges quickly (less than a year), largely reducing the errors in the BGC parameters and eventually it is shown to perform nearly as well as that of the system with true parameter values. Optimal parameter values can also be recovered by assimilating climatological BGC observations and challenging sparse observational networks. The findings of this study demonstrate the applicability of the approach for tuning the system in a real framework.</p><p>&#160;</p><p><strong>References</strong>:</p><p>Gharamti, M. E., Tjiputra, J., Bethke, I., Samuelsen, A., Skjelvan, I., Bentsen, M., & Bertino, L. (2017). Ensemble data assimilation for ocean biogeochemical state and parameter estimation at different sites.&#160;Ocean Modelling,&#160;112, 65-89.</p>

We propose the ensemble Kalman smoother multiple distribution estimation filter (EnKS-MDEF) for nonlinear state estimation problems. The EnKS-MDEF is an example of the multiple distribution estimation filter (MDEF), which is a particle filter (PF) that estimates the filtered state probability density function (pdf) using multiple conditional state pdfs. The one step behind (OSB) smoothed state pdf used for calculating the filtered state pdf of the MDEF is approximated by the ensemble Kalman smoother (EnKS). Then, the particle weights for the EnKS-MDEF remain equal during the filter execution, which indicates that the EnKS-MDEF is a degeneracy-free PF. Since, the MDEF and the EnKS-MDEF, both estimate the OSB smoothed state pdf prior to calculating the filtered state pdf, these filters provide a simultaneous estimation of filtered and OSB smoothed states. The examples of the EnKS-MDEF are the EnKS-extended and unscented Kalman multiple distribution estimation filters, and their filtering and OSB smoothing performances are evaluated and compared with those for the representative filters and smoothers using a benchmark simulation problems.

No abstract available

No abstract available

No abstract available

No abstract available

Assessment of the state of the environment with observational data is one of the most urgent modern issues. Such an assessment can be made using forecast models based on data assimilation systems. One of the most popular algorithms for data assimilation is the ensemble Kalman filter, in which the forecast error covariance is estimated using an ensemble of forecasts for perturbed initial fields. Parameter estimation is an important part of atmospheric chemistry modelling. In particular, pollutant emission may be a parameter to be estimated. A single-time estimation based on observations may not give the required accuracy. In this context, the method of ensemble smoothing (EnKS), which uses data from the entire time interval to estimate the parameter at a given time, is becoming increasingly popular. In this paper, we consider a generalization of a previously proposed method called the ensemble π-algorithm, which is a variant of stochastic ensemble Kalman filter. The generalized algorithm is an ensemble smoothing algorithm in which ensemble smoothing is performed for the sample average value and then the ensemble of perturbations is transformed. The proposed algorithm is stochastic. Numerical experiments with a 1-dimensional advection-diffusion model are carried out with the smoothing algorithm proposed in the article.

No abstract available

No abstract available

We examine the application of ensemble Kalman filter algorithms to the smoothing problem in high-dimensional geophysical prediction systems. The goal of smoothing is to make optimal estimates of the geophysical system state making best use of observations taken before, at, and after the analysis time. We begin by reviewing the underlying probabilistic theory, along with a discussion how to implement a smoother using an ensemble Kalman filter algorithm. The novel contribution of this paper is the investigation of various key issues regarding the application of ensemble Kalman filters to smoothing using a series of Observing System Simulation Experiments in both a Lorenz 1996 model and an Atmospheric General Circulation Model. The results demonstrate the impacts of non-linearities, ensemble size, observational network configuration and covariance localization. The Atmospheric General Circulation model results demonstrate that the ensemble Kalman smoother (EnKS) can be successfully applied to high-dimensional estimation problems and that covariance localization plays a critical role in its success. The results of this paper provide a foundation of understanding which will be useful in future applications of EnKS algorithms.

No abstract available

No abstract available

Reconstructing physical fields from sensor measurements is a challenging task in scientific and engineering applications, especially when sensors are sparse and unevenly distributed. Existing generative models directly incorporate point observations into the generation process to guide the generation of the full field. However, they did not provide equitable guidance for relatively sparsely observed regions, resulting in an imbalanced reconstruction error. To mitigate this imbalance, we propose proper orthogonal decomposition conditioned flow matching (POD-FM), a framework that synergistically integrates gappy POD's global physical consistency propagation to provide reconstruction guidance for poorly observed regions. Specifically, we take the POD modal coefficients inverted from observations as physically interpretable global feature guidance, then jointly encode them with the point observations to guide the generative model to reconstruct the full field. These coefficients provide a low-dimensional global prior that anchors the probability flow to the dominant modes of the field, which supplements implicit physical consistency for sparsely observed areas, and thus alleviates the accuracy imbalance caused by uneven sensor distribution. The efficacy of POD-FM has been verified on three progressive POD modal complexity datasets. Experiments have shown that POD-FM achieved higher accuracy and could effectively suppress the influence of sensor noise. The code will be available at https://github.com/XinWang199/POD-FM.

No abstract available

Full-state estimation with a limited number of sen-sors is a valuable and challenging task in monitoring and con-trolling complex physical systems. Supervised learning methods based on deep neural networks have shown excellent performance by learning the nonlinear mapping from sparse observations to global field. However, The neural network is a black box with weak explanation for physical processes, and the reconstruction performance is limited to the architecture and optimization of neural network. This paper aims to leverage the structure and laws inherent in data to reconstruct the global field by solving optimization problems instead of single network learning. We propose a unified global field reconstruction framework consisting of neural network prediction, proper orthogonal de-composition (POD), and linear optimization problem solving. The deep neural network is first trained to provide referenced global fields, which are combined with exact observations and the reference modes extracted by POD to establish a linear optimization problem. The objective of optimization problem is to superpose POD modes to satisfy the values of observations and referenced fields. The experiments conducted on fluid and thermal field reconstruction problems show that the proposed unified framework can significantly improve the reconstruction accuracy of neural networks and boost the performance of directly solving optimization problems without referenced fields.

To meet the real-time requirements of digital twin and enhance computational efficiency, this paper explores the application of modal decomposition techniques, proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD), in the field of pump fluid dynamics instead of traditional numerical simulation, which is limited by the complexity of the Navier–Stokes equations. Before decomposition, transient flow field of pump impeller and volute needs to be calculated under 0.6Q and 1.0Q, with significant differences. The results show that the first five modes capture most of the flow field's energy, with errors remaining below 10−2 even at 30 modes. However, the flow at off-design conditions is more unstable, with higher reconstruction errors using POD and more fragmented flow features in the DMD analysis. More importantly, to address potential incomplete data, gappy-POD was used to reconstruct data from single and multiple snapshots with varying levels of data loss. For single snapshots, reconstruction error is minimally affected by data sparsity, with errors below 0.0005 at 20 modes. For multiple snapshots, reconstruction accuracy is more sensitive to the iteration count and sparsity level, with a negative correlation between the sparsity level and the number of modes. Especially, when the sparsity level is less than or equal to 50%, the error does not significantly decrease after 10 iterations. At an 80% sparsity level, the iteration count significantly impacts the data repairing, with the first ten modes being more beneficial for repairing in missing data after 15 iterations.

As full-scale detailed hemodynamic simulations of the entire vasculature are not feasible, numerical analysis should be focused on specific regions of the cardiovascular system, which requires the identification of lumped parameters to represent the patient behavior outside the simulated computational domain. We present a novel technique for estimating cardiovascular model parameters using gappy Proper Orthogonal Decomposition (g-POD). A POD basis is constructed with FSI simulations for different values of the lumped model parameters, and a linear operator is applied to retain information that can be compared to the available patient measurements. Then, the POD coefficients of the reconstructed solution are computed either by projecting patient measurements or by solving a minimization problem with constraints. The POD reconstruction is then used to estimate the model parameters. In the first test case, the parameter values of a 3-element Windkessel model are approximated using artificial patient measurements, obtaining a relative error of less than 4.2%. In the second case, 4 sets of 3-element Windkessel are approximated in a patient’s aorta geometry, resulting in an error of less than 8% for the flow and less than 5% for the pressure. The method shows accurate results even with noisy patient data. It automatically calculates the delay between measurements and simulations and has flexibility in the types of patient measurements that can handle (at specific points, spatial or time averaged). The method is easy to implement and can be used in simulations performed in general-purpose FSI software.

A trajectory planning algorithm based on the traditional A* formulation is designed to determine the minimum-energy path from a start to a final location taking into account the prevailing wind conditions. To obtain average wind conditions in an urban environment, full-scale Reynolds-averaged Navier–Stokes simulations are first performed using OpenFoam® for various inlet wind directions on a computational model representing complex buildings on the campus of the Technical University of Berlin. The proper orthogonal decomposition (POD) modes of the full database are then calculated in an offline stage with the wind direction as a parameter. Next, the online reconstruction of the complete urban wind field is performed by Gappy POD using simulated pointwise measurements obtained by sparse sensors. Finally, the trajectory planning algorithm is applied to the reconstructed wind field and validated by comparison with the trajectory computed on the full-order computational fluid dynamics (CFD) model. The main conclusion is that the error made by calculating the energy requirements for a specific trajectory based on an inexpensive reduced-order model of the wind field instead of an expensive full-order CFD database is only a few percent in all investigated cases. Therefore, a reliable and trustworthy trajectory can be calculated from the inexpensive reduced-order model obtained with only a few velocity sensors. Furthermore, it is shown that the energy consumption along a trajectory could be reduced by up to 20% by taking the prevailing wind field into consideration instead of considering the shortest path.

Preview measurements of the inflow by turbine-mounted lidar systems can be used to optimise wind turbine performance or alleviate structural loads. However, nacelle-mounted lidars suffer data losses due to unfavourable environmental conditions and laser beam obstruction by the rotating blades. Here, we apply proper orthogonal decomposition (POD) to the simulated line-of-sight wind speed measurements of a turbine-mounted scanning lidar obtained from two large eddy simulations. This work aimed at identifying the dominant POD modes that can be used to subsequently derive a reduced-order representation of the turbine inflow. Secondly, we reconstructed the data points lost due to blade passage by using Gappy-POD. We found that only a few modes are required to capture the dynamics of the wind field parameters commonly used for lidar-assisted wind turbine control, such as the effective wind speed, vertical shear and directional misalignment. By evaluating turbine-relevant metrics in the time and frequency domain, we found that a ten-mode reconstruction could accurately describe most spatio-temporal variations in the inflow. Furthermore, a modal interpretation is presented by direct comparison with these wind field parameters. We found that the Gappy-POD method performs substantially better than spatial interpolation techniques, accurately reconstructing up to even 50% of missing data. A POD-based wind field reconstruction offers a trade-off between wind field reconstruction techniques requiring flow assumptions and more complex physics-based representations, offers dimensional reduction and can overcome the blade passage limitation of nacelle-mounted lidar systems.

Abstract The proper orthogonal decomposition (POD) method has been applied in nuclear reactor physics to extract features of dominant flux or power. In particular, the gappy POD method is used to handle field reconstruction problems based on incomplete data due to limited observations. However, one important question is that the observation data is never noise-free in practice, which might result in blurred property of the gappy POD method, for example, the estimation error might no longer converge or even diverge as the data size increases. To address this issue, a stabilized gappy POD method is proposed within the data assimilation framework, which involves the preknowledge of the manifold structure of the physical states and the L-curve for setting regularization parameter. This method is applied to simulate the power distribution during the control rods movement process for the HPR1000 reactor core. In the numerical experiments, the stabilized gappy POD approach uses some dominant POD basis vectors and a small number of sensor signals, to obtain accurate reconstructed field with low computational cost. In addition, the stabilized gappy POD method has been integrated into the CORCA-3D code package to assimilate the observation data of nuclear reactors, which shows more stable result than the 3D-Var and CC methods used at present.

No abstract available

No abstract available

Abstract The proper orthogonal decomposition (POD) has been widely used in fluid dynamic applications for extracting dominant flow features. The “gappy” POD is an extension to this method that allows the consideration of incomplete data sets. In this paper, the gappy POD is extended to handle unsteady flow reconstruction problems, such as those encountered when limited flow measurement data is available. In addition, a systematic approach for effective sensor placement is formulated within the gappy framework using a condition number criterion. This criterion allows for accurate flow reconstruction results and yields sensor configurations that are robust to sensor noise. Two applications are considered. The first aims to reconstruct the unsteady flow field using a small number of surface pressure measurements for a subsonic airfoil undergoing plunging motion. The second considers estimation of POD modal content of a cylinder wake flow for active control purposes. In both cases, using the dominant POD basis vectors and a small number of sensor signals, the gappy approach is found to yield accurate flow reconstruction results.

No abstract available

No abstract available

Nacelle-mounted lidar systems suffer data loss due to unfavourable atmospheric conditions such as rain or fog and most importantly the rotation of the blades that obstruct the laser beam from measuring upstream of the turbine. In this paper, we apply Gappy Proper Orthogonal Decomposition (Gappy-POD) to reconstruct incomplete flow fields from nacelle-mounted lidar measurements. For this purpose, two scanning nacelle-based SpinnerLidar simulations are performed inside a Large Eddy Simulation, one measuring the undisturbed wind inflow and the other in the wake of a reference turbine. Data loss of up to 90 % is simulated by artificially removing measurement points. The performance of Gappy-POD in reconstructing the wind fields is evaluated by comparing metrics such as effective wind speeds, vertical shear, yaw misalignment, wake deficit, wake meandering and the turbulent spectra in fixed and rotating frames of reference. We see that Gappy-POD is capable of accurately reconstructing missing data in comparison to normally used spatial interpolation techniques even in cases where 90 % of the data was missing. As a result, the dynamics of the reconstructed wind fields can be investigated based on highly accurate lidar-based wind field retrievals. The methodology can be used as a tool to develop effective wind field reconstruction techniques from sparse data.

No abstract available

Real-time estimation of three-dimensional field data for enclosed spaces is critical to HVAC control. This task is challenging, especially for large enclosed spaces with complex geometry, due to the nonuniform distribution and nonlinear variations of many environmental variables. Moreover, constructing and maintaining a network of sensors to fully cover the entire space is very costly, and insufficient sensor data might deteriorate system performance. Facing such a dilemma, gappy proper orthogonal decomposition (POD) offers a solution to provide three-dimensional field data with a limited number of sensor measurements. In this study, a gappy POD method for real-time reconstruction of contaminant distribution in an enclosed space is proposed by combining the POD method with a limited number of sensor measurements. To evaluate the gappy POD method, a computational fluid dynamics (CFD) model is utilized to perform a numerical simulation to validate the effectiveness of the gappy POD method in reconstructing contaminant distributions. In addition, the optimal sensor placement is given based on a quantitative metric to maximize the reconstruction accuracy, and the sensor placement constraints are also considered during the sensor design process. The gappy POD method is found to yield accurate reconstruction results. Further works will include the implementation of real-time control based on the POD method.

No abstract available

No abstract available

No abstract available

No abstract available

No abstract available

Abstract. Observations of turbulence in the planetary boundary layer are critical for developing and evaluating boundary layer parameterizations in mesoscale numerical weather prediction models. These observations, however, are expensive and rarely profile the entire boundary layer. Using optimized configurations for 449 and 915 MHz wind profiling radars during the eXperimental Planetary boundary layer Instrumentation Assessment (XPIA), improvements have been made to the historical methods of measuring vertical velocity variance through the time series of vertical velocity, as well as the Doppler spectral width. Using six heights of sonic anemometers mounted on a 300 m tower, correlations of up to R2 = 0. 74 are seen in measurements of the large-scale variances from the radar time series and R2 = 0. 79 in measurements of small-scale variance from radar spectral widths. The total variance, measured as the sum of the small and large scales, agrees well with sonic anemometers, with R2 = 0. 79. Correlation is higher in daytime convective boundary layers than nighttime stable conditions when turbulence levels are smaller. With the good agreement with the in situ measurements, highly resolved profiles up to 2 km can be accurately observed from the 449 MHz radar and 1 km from the 915 MHz radar. This optimized configuration will provide unique observations for the verification and improvement to boundary layer parameterizations in mesoscale models.

No abstract available

Observations of turbulence in the planetary boundary layer are critical for developing and evaluating boundary layer parameterizations in mesoscale numerical weather prediction models. These observations, however, are expensive, and rarely profile the entire boundary layer. Using optimized configurations for 449 MHz and 915 MHz wind profiling radars during the eXperimental Planetary boundary layer Instrumentation Assessment, improvements have been made to the histor5 ical methods of measuring vertical velocity variance through the time series of vertical velocity, as well as the Doppler spectral width. Using six heights of sonic anemometers mounted on a 300-m tower, correlations of up to R = 0.74 are seen in measurements of the large-scale variances from the radar time series, and R = 0.79 in measurements of small-scale variance from radar spectral widths. The total variance, measured as the sum of the smalland large-scales agrees well with sonic 10 anemometers, with R = 0.79. Correlation is higher in daytime, convective boundary layers than nighttime, stable conditions when turbulence levels are smaller. With the good agreement with the in situ measurements, highly-resolved profiles up to 2 km can be accurately observed from the 449 MHz radar, and 1 km from the 915 MHz radar. This optimized configuration will provide unique observations for the verification and improvement to boundary layer parameterizations in mesoscale 15

No abstract available

Simple processes (SPs) are a class of spectrally correlated (SC) processes that their Loeve bi-frequency spectrum is supported by a countable collection of special curves. While spectral coherence is a well-established tool for analyzing relationships between stationary processes, its extension to SC processes like discrete time harmonizable simple processes (DTHSPs) remains underexplored. This gap limits the ability to study the coherencies among many real-world signals. In this work, the spectral coherence for two DTHSPs is defined and robust estimator of the introduced spectral coherence for both known and unknown spectral structures is proposed. For known SP’s structures, we employ the periodogram covariances to establish the estimator and characterize its asymptotic properties. For unknown SP’s structures, a spectral ciphering-based approach is employed to estimate the coherence. Then, multiple testing procedures are developed to determine whether two DTHSPs are coherent or incoherent. Theoretical results are validated through simulations under two scenarios: (1) a time-lagged linear relationship between two DTHSPs and (2) independent DTHSPs. According to the numerical simulations, the proposed approach demonstrates superior performance compared to existing approaches in terms of key metrics such as precision, recall, F1-score and specificity. Finally, the proposed framework is applied to a real-world dataset, showcasing its practical utility in identifying spectral dependencies.

The cross-power spectral density (CPSD) acoustic analogy is a generalization of Lighthill’s analogy that directly predicts near-field statistics at multiple spatial points. The methodology was previously applied and validated to predict noise from isotropic turbulence and off-design supersonic jet flows. We present a simplification of the CPSD model for near-field predictions of acoustic coherence from jet fine-scale mixing noise. Validation predictions are presented with a NASA Glenn Research Center experimental jet database. The simplified mathematical model is presented along with the physical significance of each term. The application of the model can be applied to predict loading and coherence on the fuselage of aircraft, rockets, and associated structures. This approach can help designers minimize sonic fatigue or failure in flight-vehicles and support structures.

Reconstructing spatiotemporal fields from partial observations is fundamental to scientific inference, from inferring atmospheric states from satellite data to recovering fluid states from imaging. When observations are incomplete, the inverse problem is fundamentally ill-posed: even when the underlying PDE dynamics are Markovian in the full state, partial observation operators induce a non-Markovian posterior that cannot be resolved from a single timestep. We propose a history-bootstrapped autoregressive flow matching (HB-ARFM) for spatiotemporal inverse reconstruction under partial observability. Observation history bootstraps the initial reconstruction via conditional flow matching, reducing ambiguities. The same conditional transport model is then applied autoregressively, conditioning on both new observations and past predictions to propagate the reconstruction forward in time. We evaluate the method on boiling dynamics reconstruction, recovering full velocity and temperature fields from interface geometry and motion. Across two inverse tasks with varying observation sparsity, HB-ARFM produces physically and temporally valid reconstructions where other models fail.

Magnetohydrodynamic (MHD) phenomena play a pivotal role in the design and operation of nuclear fusion systems, where electrically conducting fluids (such as liquid metals or molten salts employed in reactor blankets) interact with magnetic fields of varying intensity and orientation, influencing the resulting flow dynamics. The numerical solution of MHD models entails the resolution of highly nonlinear, multiphysics systems of equations, which can become computationally demanding, particularly in multi-query, parametric, or real-time contexts. This study investigates a fully data-driven framework for MHD state reconstruction that integrates dimensionality reduction through Singular Value Decomposition (SVD) with the SHallow REcurrent Decoder (SHRED), a neural network architecture designed to reconstruct the full spatio-temporal state from sparse time-series measurements of selected observables, including previously unseen parametric configurations. The SHRED methodology is applied to a three-dimensional geometry representative of a portion of a WCLL blanket cell, in which lead-lithium flows around a water-cooled tube. Multiple magnetic field configurations are examined, including constant toroidal fields, combined toroidal-poloidal fields, and time-dependent magnetic fields. Across all considered scenarios, SHRED achieves high reconstruction accuracy, robustness, and generalization to magnetic field intensities, orientations, and temporal evolutions not seen during training. Notably, in the presence of time-varying magnetic fields, the model accurately infers the temporal evolution of the magnetic field itself using temperature measurements alone. Overall, the findings identify SHRED as a computationally efficient, data-driven, and flexible approach for MHD state reconstruction, with significant potential for real-time monitoring, diagnostics and control in fusion reactor systems.

Magnetohydrodynamic (MHD) effects play a key role in the design and operation of nuclear fusion systems, where electrically conducting fluids (such as liquid metals or molten salts in reactor blankets) interact with magnetic fields of varying intensity and orientation, which affect the resulting flow. The numerical resolution of MHD models involves highly nonlinear multiphysics systems of equations and can become computationally expensive, particularly in multi-query, parametric, or real-time contexts. This work investigates a fully data-driven framework for MHD state reconstruction that combines dimensionality reduction via Singular Value Decomposition (SVD) with the SHallow REcurrent Decoder (SHRED), a neural network architecture designed to recover the full spatio-temporal state from sparse time-series measurements of a limited number of observables. The methodology is applied to a parametric MHD test case involving compressible lead-lithium flow in a stepped channel subjected to thermal gradients and magnetic fields spanning a broad range of intensities. To improve efficiency, the full-order dataset is first compressed using SVD, yielding a reduced representation used as reference truth for training. Only temperature measurements from three sensors are provided as input, while the network reconstructs the full fields of velocity, pressure, and temperature. To assess robustness with respect to sensor placement, thirty randomly generated sensor configurations are tested in ensemble mode. Results show that SHRED accurately reconstructs the full MHD state even for magnetic field intensities not included in the training set. These findings demonstrate the potential of SHRED as a computationally efficient surrogate modeling strategy for fusion-relevant multiphysics problems, enabling low-cost state estimation with possible applications in real-time monitoring and control.

We introduce FLEX (FLow EXpert), a backbone architecture for generative modeling of spatio-temporal physical systems using diffusion models. FLEX operates in the residual space rather than on raw data, a modeling choice that we motivate theoretically, showing that it reduces the variance of the velocity field in the diffusion model, which helps stabilize training. FLEX integrates a latent Transformer into a U-Net with standard convolutional ResNet layers and incorporates a redesigned skip connection scheme. This hybrid design enables the model to capture both local spatial detail and long-range dependencies in latent space. To improve spatio-temporal conditioning, FLEX uses a task-specific encoder that processes auxiliary inputs such as coarse or past snapshots. Weak conditioning is applied to the shared encoder via skip connections to promote generalization, while strong conditioning is applied to the decoder through both skip and bottleneck features to ensure reconstruction fidelity. FLEX achieves accurate predictions for super-resolution and forecasting tasks using as few as two reverse diffusion steps. It also produces calibrated uncertainty estimates through sampling. Evaluations on high-resolution 2D turbulence data show that FLEX outperforms strong baselines and generalizes to out-of-distribution settings, including unseen Reynolds numbers, physical observables (e.g., fluid flow velocity fields), and boundary conditions.

Real-time monitoring of safety-critical interior states is an open problem across energy, environmental and industrial systems where direct instrumentation is infeasible. Approaches based on governing equations, discrete state vectors or fixed sensor locations cannot deliver mesh-independent, field-level reconstruction at arbitrary interior coordinates in real time. Here we introduce neural operator-based virtual sensing, a framework for recovering inaccessible interior fields from sparse boundary measurements, instantiated with MIMONet, a multi-input, multi-output neural operator that fuses heterogeneous inputs and decodes coupled fields through a shared latent representation. Across three engineering-grade evaluations of escalating complexity - confined recirculating flow, pressurized water reactor subchannels and compact power-system heat exchangers - MIMONet attains relative reconstruction error below 5% with sub-millisecond inference, with calibrated uncertainty and noise resilience. We validate the framework on three independent real-world datasets spanning electrochemical energy, atmospheric science and physical oceanography: current-density mapping in a hydrogen fuel cell, wind-speed profiling on meteorological towers, and North Atlantic ocean state from a global reanalysis. MIMONet improves on classical virtual-sensing baselines by 72-84%, including 84% for fuel-cell internal fields recovered from 10% sensor coverage and 83% for hub-height wind speed recovered from lower-level tower sensors. Most notably, it recovers sea-surface height, a field with no direct sensors, from its learned coupling to observed temperature and salinity at 4.1x lower error than the best classical predictor. These results establish operator-based virtual sensing as a practical route to real-time field observability in systems where the states that matter most cannot be measured directly.

Data assimilation (DA) integrates observational information with model predictions to improve state estimation in complex systems. While filtering provides the basis for online forecasts by using only past and present observations, it can exhibit delays and biases when the underlying dynamics evolve rapidly or undergo regime transitions. Smoothing, which additionally incorporates future observations, provides a natural pipeline for hindcasting and reanalysis that yields an uncertainty reduction beyond the filter. This paper introduces an ensemble Kalman--Bucy smoother (EnKBS) for continuous-time DA of nonlinear dynamical systems, where the smoother's conditional distributions are reconstructed using ensemble moments. The result is a derivative-free framework that does not require explicit computation of tangent-linear or adjoint models, which recovers the exact smoothing mean and covariance equations in the infinite-ensemble limit for linear--Gaussian systems. Incorporating standard regularization techniques for high-dimensional systems, such as covariance localization and inflation, the skill of the EnKBS is demonstrated in various important scientific problems. By integrating future observations, which reveal the underlying causal mechanisms for retrospective state updates, the EnKBS is used for Bayesian-based inference of causal relationships and their temporal influence range in a dyadic trigger-feedback model and the development of a causality-driven iterative learning algorithm that identifies the structure and recovers the hidden parameters of a nonlinear reduced-order model mimicking midlatitude atmospheric circulation. Notably, both tasks remain effective with an ensemble size of $O(10)$ under partial observations, suggesting that EnKBS can support the instantaneous discovery of high-dimensional complex systems over time.