Search Results (140)

Compressive sensing (CS) is capable of resolving high frequencies from subsampled data. However, it is challenging to apply CS in non-periodic flow fields with multiple frequencies. This study introduces a novel data fusion CS approach aimed at reconstructing temporally resolved flow fields from subsampled particle image velocimetry (PIV) data, integrating constraints derived from a limited number of high-frequency pointwise measurements. The approach combines measurements from particle image velocimetry (PIV), which have high spatial resolution but low temporal resolution, and a few pointwise probes, which have high temporal resolution but low spatial resolution. In the proposed method, proper orthogonal decomposition (POD) is conducted first to the PIV data, thus acquiring spatial modes and low-temporally resolved coefficients. To reconstruct the non-periodic and multiple-frequency coefficients from the PIV data, the traditional CS yields strong high-frequency noise. In this regard, the coefficients obtained from the pointwise measurements using least square (LS) regression can serve as a reciprocal space to suppress the high-frequency noise in the CS reconstruction. Using relaxation factors, the results from LS regression apply the upper and lower boundaries for the CS. By fusing the pointwise measurement and PIV data, the reconstruction performance can be significantly improved. To verify the performance, non-periodic and multiple frequency flow fields in the wake of two cylinders with different diameters are used. Compared to the ground truth, CS and LS reconstruction give an error of about 7% and 13%, respectively. On the other hand, the data fusion CS only has an error of about 2%. The dependency of this method on the number of pointwise probes is also examined. Full article

An innovative high-order dimensionality reduction approach, which integrates a condensed finite-difference scheme with proper orthogonal decomposition techniques, has been explored for solving diffusion equations. The difference scheme with forth order accurate in both space and time is introduced through the idea of interpolation approximation. The quartic spline function and $(2,2)$ Padé approximation were utilized in space and time discretization, respectively. The stability and convergence were proven. Moreover, the dimensionality reduction formulas were derived using the proper orthogonal decomposition (POD) method, which is based on the matrix representation of the compact finite-difference scheme. The bases of the POD method were established by cumulative contribution rate of the eigenvalues of snapshot matrix that is different from the traditional ways in which the bases were established by the first eigenvalues. The method of cumulative contribution rate can optimize the degree of freedom. The error analysis of the reduced bases high-order POD finite-difference scheme was provided. Numerical experiments are conducted to validate the soundness and dependability of the reduced-order algorithm. The comparisons between the $(2,2)$ finite-difference method, the traditional POD method, and reduced dimensional method with cumulative contribution rate were discussed. Full article

Proper orthogonal decomposition (POD) is a widely used linear dimensionality reduction technique, but it often fails to capture critical features in complex nonlinear flows. In contrast, clustering methods are effective for nonlinear feature extraction, yet their application in dimensionality reduction methods is hindered by unstable cluster initialization and inefficient mode sorting. To address these issues, we propose a clustering-based dimensionality reduction method guided by POD structures (C-POD), which uses POD preprocessing to stabilize the selection of cluster centers. Additionally, we introduce an entropy-controlled Euclidean-to-probability mapping (ECEPM) method to improve modal sorting and assess mode importance. The C-POD approach is evaluated using the one-dimensional Burgers’ equation and a two-dimensional cylinder wake flow. Results show that C-POD achieves higher accuracy in dimensionality reduction than POD. Its dominant modes capture more temporal dynamics, while higher-order modes offer better physical interpretability. When solving an inverse problem using sparse sensor data, the Gappy C-POD method improves reconstruction accuracy by 19.75% and enhances the lower bound of reconstruction capability by 13.4% compared to Gappy POD. Overall, C-POD demonstrates strong potential for modeling and reconstructing complex nonlinear flow fields, providing a valuable tool for dimensionality reduction methods in fluid dynamics. Full article

To address the challenge of low computational efficiency in nonlinear Economic Model Predictive Control (EMPC) for large-scale systems such as wastewater treatment plants (WWTPs), this paper proposes a Trajectory Piecewise Linearization (TPWL)-based EMPC framework integrated with global maximum error control (GMEC) and Proper Orthogonal Decomposition (POD). The TPWL method constructs a reduced-order model framework, while GMEC iteratively refines the linearization point selection process. A two-stage strategy is employed: first, coarse selection of candidate linearization points along the original nonlinear model’s state trajectory based on Euclidean distance, followed by refinement to determine optimal points that minimize global approximation errors. Simulation results demonstrate that the proposed method reduces computational time by at least 65% under identical weather conditions while maintaining effluent quality and total cost indices within acceptable thresholds. Compared with conventional TPWL-POD approaches, this framework achieves higher model accuracy and superior EMPC control performance. These advancements underscore the method’s potential for real-time implementation in complex industrial systems, balancing computational efficiency with control precision. Additionally, the framework’s modular design enables integration with existing optimization techniques to further reduce computational complexity without compromising effluent quality compliance. Full article

The periodic unsteady flow induced by rotor–stator interaction (RSI) is the primary cause of blade forced vibration and fatigue failure. Therefore, analyzing the excitation characteristics of RSI flow fields under multi-parameter conditions is essential for vibration analysis and optimization in fluid–structure interaction. This study derives the Toeplitz structure of the correlation matrix in proper orthogonal decomposition (POD) for strictly periodic flow fields and reveals that the POD spatial modes appear in pairs with a 90° spatial phase difference, which originates from the cosine and sine form of the eigenvectors of the Toeplitz matrix. Taking a 1.5-stage compressor cascade as an example, the POD method is employed to effectively extract the main spatiotemporal characteristics of the RSI flow field, and the spatial symmetry and phase difference of the POD modes are further interpreted from a physical perspective. To address the high computational cost and resource demands arising from large-scale similar cases in multi-parameter excitation optimization and analysis, a reduced-order modeling (ROM) method based on time–space and parameter decoupling is proposed using multi-parameter POD. Spatial bases are extracted through the first-level POD, and a second-level POD is applied to the first-level coefficients to obtain temporal bases and coefficients that are solely parameter-dependent. A radial basis function (RBF) interpolation is used to establish the mapping between parameters and the second-level coefficients, enabling efficient multi-parameter ROM construction. The resulting ROM achieves a relative prediction error of less than 1.4% under typical operating conditions and less than 2.9% near the choke boundary, improving computational efficiency by four orders of magnitude while maintaining accuracy, thereby providing an effective approach for aerodynamic excitation acquisition. Full article

The high-dimensional integral–differential nature of the neutron transport equation and the complexity of nuclear reactors result in high computational costs. A set of reduced-order modeling frameworks based on Proper Orthogonal Decomposition (POD) is developed to improve the computational efficiency for neutron diffusion calculations while maintaining accuracy, especially for small samples. For modal coefficient calculations, three methods—Galerkin, radial basis function (RBF), and Deep Neural Network (DNN)—are introduced and analyzed for molten salt reactors. The results show that all three reduced-order models achieve sufficient accuracy, with neutron flux L₂ errors below 1% and delayed neutron precursor (DNP) L₂ errors below 2.4%, while the acceleration ratios exceed 800. Among these, the POD–Galerkin model demonstrates superior performance, achieving average L₂ errors of less than 0.00658% for neutron flux and 1.01% for DNP concentration, with an acceleration ratio of approximately 1800 and excellent extrapolation ability. The POD–Galerkin reduced-order model significantly enhances the computational efficiency for solving neutron multi-group diffusion equations and DNP conservation equations in molten salt reactors while preserving the solution accuracy, making it ideal for a liquid fuel molten salt reactor in the case of small samples. Full article

The construction and operation of reservoirs have significantly altered the downstream flow regime, and the flood regional composition (FRC) method has been widely used to estimate design flood considering the regulation impact of upstream cascade reservoirs. This paper proposes a novel flood regional composition based on the proper orthogonal decomposition (FRC-POD) method that comprehensively takes into account typical-year flood differences and the multi-site flood source characteristics. The proposed method is applied at Cuntan hydrologic station in the upper Yangtze River and compared with the typical-year flood composition (TYFC) method and the most likely flood regional composition (MLFRC) method. The results show the following: (1) The proposed FRC-POD method can identify main flood sources in the design section and pay more attention to floods from the mainstream and the uncontrolled interval basin. (2) Compared with the originally designed values, the 1000-year design peak discharge and 3 d, 7 d, and 15 d flood volumes estimated by the FRC-POD method are decreased by 41.3%, 40.2%, 36.6%, and 34.7%, respectively. (3) Current FRC methods depend on the selected typical-year flood events and have several solutions, while the proposed method has only one final solution, which is more reasonable in practical application. (4) A comparative study proves that the FRC-POD method could obtain rational design flood estimation and is worth further study. Full article

The rapid and accurate prediction of temperature fields in complex structures remains a significant challenge in thermal engineering. Experimental approaches often struggle to provide comprehensive data, while traditional full-order numerical methods are hindered by their excessive computational demands. This study addresses these limitations by developing a novel reduced-order extrapolation method that integrates proper orthogonal decomposition (POD) with the finite volume method (FVM). We demonstrate the efficacy of our approach through its application to multilayered thermally unstable structures under non-periodic boundary conditions. The results reveal exceptional performance in both prediction accuracy and computational efficiency. When validated against experimental data and conventional FVM results, our method achieves a maximum relative error of less than 5% while delivering a remarkable computational speed-up of more than 1400 times when running complex explosive structure simulations. Notably, our analysis uncovers a critical limitation of POD: increasing the number of modes does not proportionally enhance the prediction accuracy, due to inherent methodological constraints. This innovative strategy offers promising potential for real-time temperature monitoring and thermal protection in advanced engineering systems, particularly for complex devices requiring precise thermal management. Full article

To quantify the uncertainties in multi-dimensional flow field correlated responses caused by uncertain model parameters, this paper presents an adaptive multi-fidelity model based on gappy proper orthogonal decomposition (Gappy-POD), which integrates the two conventional approaches for enhancing the efficiency of surrogate modeling, namely, multi-fidelity modeling and adaptive sampling algorithms. The challenges surrounding the selection of initial high-fidelity samples and the subsequent incremental augmentation of these samples are addressed. The k-means clustering algorithm is employed to identify locations within the parameter space for conducting high-fidelity simulations, leveraging insights gained from low-fidelity responses. An adaptive sampling criterion, leveraging the low-fidelity projection error derived from the Gappy-POD method, is implemented to progressively augment high-fidelity samples. The results demonstrate that the adaptive model consistently outperforms random sampling methods, highlighting its superiority in terms of accuracy and reliability, providing an efficient and reliable prediction model for uncertainty quantification. Full article

The valve-side bushing of a converter transformer is a critical component in ultra-high-voltage direct current (UHVDC) systems, making its monitoring through digital twin technology highly significant. However, the complex structure and spatio-temporal nonlinearity of the bushing result in a large computational demand for its digital twin model, which requires an effective order reduction algorithm. This paper proposes a Spatio-temporal Non-uniformity Proper Orthogonal Decomposition (SN-POD) algorithm considering the inhomogeneity of space and time consumption to meet the reduced-order computational requirements of UHV valve-side bushings. This proposed method reduces the calculation time to 10% of the full-order simulation model while controlling the error range of the key research area less than 0.1%. The test results show that this method has good robustness, calculation speed, and accuracy. This research can significantly enhance the computational efficiency of digital twin modeling for valve-side bushings and provide a technical foundation for constructing digital twin models for UHV valve-side bushings. Full article

Dynamical processes during the different stages of evolution of tropical cyclones play crucial roles in their development and intensification, making them one of the most powerful natural forces on Earth. Given their classification as extreme atmospheric events resulting from multiple interacting factors, it is significant to study their dynamical behavior and the nonlinear effects generated by emerging structures during scales and intensity transitions, correlating them with the surrounding environment. This study investigates the extraordinary and record-breaking case of Tropical Cyclone Freddy (2023 Indian Ocean tropical season) from a purely dynamical perspective, examining the superposition of energetic structures at different spatio-temporal scales, by mainly considering thermal fluctuations over 12 days of its evolution. The tool used for this investigation is the Proper Orthogonal Decomposition (POD), in which a set of empirical basis functions is built up, retaining the maximum energetic content of the turbulent flow. The method is applied on a satellite imagery dataset acquired from the SEVIRI radiometer onboard the Meteosat Second Generation-8 (MSG-8) geostationary platform, from which the cloud-top temperature scalar field is remote sensed looking at the cloud’s associated system. For this application, considering Freddy’s very long life period and exceptionally wide path of evolution, reanalysis and tracking data archives are taken into account in order to create an appropriately dynamic spatial grid. Freddy’s eye is followed after its first shape formation with very high temporal resolution snapshots of the temperature field. The energy content in three different characteristic scale ranges is analyzed through the associated spatial and temporal component spectra, focusing both on the total period and on the transitions between different categories. The results of the analysis outline several interesting aspects of the dynamics of Freddy related to both its transitions stages and total period. The reconstructions of the temperature field point out that the most consistent vortexes are found in the outermost cyclonic regions and in proximity of the eyewall. Additionally, we find a significant consistency of the results of the investigation of the maximum intensity phase of Freddy’s life cycle, in the spatio-temporal characteristics of its dynamics, and in comparison with one analogous case study of the Faraji tropical cyclone. Full article

The cavitation phenomenon significantly impacts the performance of pump turbines, necessitating in-depth research on their cavitation characteristics. This study investigates the performance characteristics of a pump turbine through experimental and numerical simulation methods, with consistent results verifying the accuracy of the numerical simulations. The cavitation flow field is numerically analyzed to compare the cavitation distribution and velocity streamlines at different stages of cavitation development. The Q criterion and entropy production method are employed to identify vortex structures and energy loss regions, respectively, exploring the correlation between vortices and energy losses in the cavitation flow field under low-flow pump conditions. The results demonstrate that intensified cavitation generates more multi-scale vortices in the flow field, leading to increased entropy production and reduced energy efficiency. Proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) methods were subsequently applied to extract vorticity characteristics from transient cavitation flow fields, revealing primary energy loss regions and elucidating the evolution and distribution patterns of vortices. The POD analysis shows that low-order modes represent dominant vortex structures, while intensified cavitation increases both the quantity of vortices and their complexity in scale, distribution, and evolutionary frequency. The DMD results further indicate distinct evolutionary patterns for vortices of different scales. This research provides insights into the instability characteristics of cavitation flow fields in pump turbines under low-flow pump conditions and offers theoretical support for optimizing the design of pump turbines to expand their high-efficiency operational range. Full article

This research proposes a method for reducing the dimension of the coefficient vector for Crank–Nicolson mixed finite element (CNMFE) solutions to solve the fourth-order variable coefficient parabolic equation. Initially, the CNMFE schemes and corresponding matrix schemes for the equation are established, followed by a thorough discussion of the uniqueness, stability, and error estimates for the CNMFE solutions. Next, a matrix-form reduced-dimension CNMFE (RDCNMFE) method is developed utilizing proper orthogonal decomposition (POD) technology, with an in-depth discussion of the uniqueness, stability, and error estimates of the RDCNMFE solutions. The reduced-dimension method employs identical basis functions, unlike standard CNMFE methods. It significantly reduces the number of unknowns in the computations, thereby effectively decreasing computational time, while there is no loss of accuracy. Finally, numerical experiments are performed for both fourth-order and time-fractional fourth-order parabolic equations. The proposed method demonstrates its effectiveness not only for the fourth-order parabolic equations but also for time-fractional fourth-order parabolic equations, which further validate the universal applicability of the POD-based RDCNMFE method. Under a spatial discretization grid $40\times 40$, the traditional CNMFE method requires $2\times {41}^2$ degrees of freedom at each time step, while the RDCNMFE method reduces the degrees of freedom to $2\times 6$ through POD technology. The numerical results show that the RDCNMFE method is nearly 10 times faster than the traditional method. This clearly demonstrates the significant advantage of the RDCNMFE method in saving computational resources. Full article

Well placement optimization refers to the identification of optimal locations for wells (producers and injectors) to maximize net present value (NPV) and oil recovery. It is a complex challenge in all phases of production (primary, secondary and tertiary) of a reservoir. Reservoir simulation is primarily used to solve this intricate task by analyzing numerous scenarios with varied well locations to determine the optimum location that maximizes the targeted objective functions (e.g., NPV and oil recovery). Proxy models are a computationally less expensive alternative to traditional reservoir simulation techniques since they approximate complex simulations with simpler models. Previous review papers have focused on analyzing various optimization algorithms and techniques for well placement. This article explores various types of proxy models that are the most suitable for well placement optimization due their discrete and nonlinear natures and focuses on recent advances in the area. Proxy models in this article are sub-divided into two primary classes, namely data-driven models and reduced order models (ROMs). The data-driven models include statistical- and machine learning (ML)-based approximations of nonlinear problems. The second class, i.e., a ROM, uses proper orthogonal decomposition (POD) methods to reduce the dimensionality of the problem. This paper introduces various subcategories within these two proxy model classes and presents the successful applications from the well placement optimization literature. Finally, the potential of integrating a data-driven approach with ROM techniques to develop more computationally efficient proxy models for well placement optimization is also discussed. This article is intended to serve as a comprehensive review of the latest proxy model techniques for the well placement optimization problem. In conclusion, while proxy models have their own challenges, their ability to significantly reduce the complexity of the well placement optimization process for huge reservoir simulation areas makes them extremely appealing. With active research and development occurring in this area, proxy models are poised to play an increasingly central role in oil and gas well placement optimization. Full article

There has been extensive research on the partial differential equations governing the theory of gas flow in coal mines. However, the traditional Proper Orthogonal Decomposition–Radial Basis Function (POD-RBF) reduced-order algorithm requires significant computational resources and is inefficient when calculating high-dimensional data for coal mine gas pressure fields. To achieve the rapid computation of gas extraction pressure fields, this paper proposes a model reduction method based on deep neural networks (DNNs) and convolutional autoencoders (CAEs). The CAE is used to compress and reconstruct full-order numerical solutions for coal mine gas extraction, while the DNN is employed to establish the nonlinear mapping between the physical parameters of gas extraction and the latent space parameters of the reduced-order model. The DNN-CAE model is applied to the reduced-order modeling of gas extraction flow–solid coupling mathematical models in coal mines. A full-order model pressure field numerical dataset for gas extraction was constructed, and optimal hyperparameters for the pressure field reconstruction model and latent space parameter prediction model were determined through hyperparameter testing. The performance of the DNN-CAE model order reduction algorithm was compared to the POD-RBF model order reduction algorithm. The results indicate that the DNN-CAE method has certain advantages over the traditional POD-RBF method in terms of pressure field reconstruction accuracy, overall structure retention, extremum capture, and computational efficiency. Full article