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Design of next-generation membranes requires a nanoscopic understanding of the effect of biologically inspired heterogeneous surface chemistries and topologies (roughness) on local water and solute behavior. In particular, the rejection of small, neutral solutes, such as boric acid, poses a heretofore unsolved challenge. In prior work, a computational inverse design technique using an evolutionary optimization successfully uncovered new surface design strategies for optimized transport of water over solutes in smooth, model pores consisting of two surface chemistries. However, extending such an approach to more complex (and realistic) scenarios involving many surface chemistries as well as surface roughness is challenging due to the expanded design space. In this work, we develop a new approach that uses active learning to optimize in a reduced feature space of surface group interactions, finding parameters that lead to their assembly into ordered, optimal patterns. This approach rapidly identifies novel surface functionalizations that maximize the difference in water and boric acid transport through the nanopore. Moreover, we find that the roughness of the nanopore wall, independent of its chemistry, can be leveraged to enhance transport selectivity: oscillations in the pore wall diameter optimally inhibit boric acid transport by creating energetic wells from which the solute must escape to transport down the pore. This proof-of-concept demonstrates the potential for active learning strategies, in concert with molecular simulations, to rapidly navigate complex design spaces of aqueous interfaces and is promising as a tool for engineering water-mediated surface interactions for a broad range of applications. [ABSTRACT FROM AUTHOR]

Directional fluid flow in perivascular spaces surrounding cerebral arteries is hypothesized to play a key role in brain solute transport and clearance. While various drivers for a pulsatile flow, such as cardiac or respiratory pulsations, are well quantified, the question remains as to which mechanisms could induce a directional flow within physiological regimes. To address this question, we develop theoretical and numerical reduced-order models to quantify the directional (net) flow induceable by peristaltic pumping in periarterial networks. Each periarterial element is modeled as a slender annular space bounded internally by a circular tube supporting a periodic traveling (peristaltic) wave. Under reasonable assumptions of a small Reynolds number flow, small radii, and small-amplitude peristaltic waves, we use lubrication theory and regular perturbation methods to derive theoretical expressions for the directional net flow and pressure distribution in the perivascular network. The reduced model is used to derive closed-form analytical expressions for the net flow for simple network configurations of interest, including single elements, two elements in tandem, and a three element bifurcation, with results compared with numerical predictions. In particular, we provide a computable theoretical estimate of the net flow induced by peristaltic motion in perivascular networks as a function of physiological parameters, notably, wave length, frequency, amplitude, and perivascular dimensions. Quantifying the maximal net flow for specific physiological regimes, we find that vasomotion may induce net pial periarterial flow velocities on the order of a few to tens of μ m/s and that sleep-related changes in vasomotion pulsatility may drive a threefold flow increase. [ABSTRACT FROM AUTHOR]

In this paper, a formulation of reduced-order finite element (FE) model is presented for geometrically nonlinear dynamic analysis of viscoelastic structures based on the fractional-order derivative constitutive relation and harmonic balance method. The main focus is to formulate the nonlinear reduced-order models (ROMs) in the time and frequency domain without involving the corresponding full-order FE models, and it is carried out by means of a special factorization of the nonlinear strain–displacement matrix. Furthermore, a methodology for the enrichment of reduction basis (RB) over that obtained from conventional approaches is presented where the proper orthogonal decomposition method is utilized by comprising the correlation matrix as the union of stiffness-normalized reduction basis vectors and the corresponding static derivatives. The results reveal a significantly reduced computational time due to the formulation of the nonlinear ROMs without involving the full-order FE model. A good accuracy of the nonlinear ROMs of viscoelastic structures is also achieved through the present method of enrichment of RB. [ABSTRACT FROM AUTHOR]

This study proposes a high computationally efficient data-driven predictive entry guidance method for hypersonic vehicles under multiple no-fly zones. The method uses a reduced-order motion-model-based semianalytic guidance framework to obtain a trained neural network that only requires two-dimensional input. First, the sixth-order entry dynamic motion model is simplified to a third-order model by considering height as the independent variable. Second, based on the reduced-order motion model, a novel exponential function is introduced to yield a semianalytic range-to-go expression in longitudinal guidance. Third, to generate sample trajectory data for training the neural network, the semianalytic guidance framework is supported by the reduced-order motion model with the semianalytic range-to-go expression. Then, a new dynamic lateral guidance reversal logic based on a chain mode strategy is employed to avoid no-fly zones with different configurations and numbers. Finally, to obtain real-time trajectory online, a data-driven online predictive guidance method is proposed based on a back propagation neural network trained by sample trajectory data generated by the semianalytic guidance framework. The proposed method overcomes the drawbacks of most predictor–corrector guidance methods; i.e., the corrected guidance parameters are heavily dependent on the initial values of each iteration in each guidance cycle. Advantageously, the proposed method greatly reduces the online command calculation time in one guidance cycle and only requires two input data to train the neural network, i.e., height and range-to-go, thus yielding results that are close to the engineering reality. The effectiveness of the proposed method is verified through simulations. [ABSTRACT FROM AUTHOR]

Accurate and efficient modeling and simulation of spacecraft electrical systems are crucial because of their complexity. However, existing models often struggle to balance simulation efficiency and accuracy. This paper introduces a model reduction method based on singular perturbation theory to simplify the full-order model of spacecraft electrical systems. The experimental results show that the reduced-order simplified model saves 50% of the simulation time with almost no degradation in the simulation accuracy and can be applied to real-world scenarios, such as digital twins. This method offers a new approach for rapid simulation of spacecraft electrical systems and has broad application prospects. [ABSTRACT FROM AUTHOR]

This study presents a physics-based reduced-order model (ROM) to assess the mixing behavior of hydrogen and natural gas in pipelines, facilitating the integration of hydrogen into natural gas networks—a key strategy for reducing carbon emissions. The methodology consists of dimensional analysis to identify crucial dimensionless parameters, CFD simulations for data collection, and statistical analysis for effective data modeling. This approach enables rapid evaluation of injection strategies and operational conditions, reducing the computational demands of traditional CFD simulations. The model correlates reduced-order parameters with key dimensionless numbers like Reynolds number, and diameter and velocity ratios, to develop a predictive tool for assessing mixture quality. Validated through extensive simulations, the model accurately predicts gas mixing, using beta distributions for statistical representation to enhance data interpretability and applicability. • Developed a reduced-order model based on CFD data for hydrogen-natural gas mixing. • Used dimensional analysis to simplify the model and reduce computational demand. • Applied beta distributions to analyze mass fractions and improve mixture prediction. [ABSTRACT FROM AUTHOR]

Snap-through is a nonlinear jump phenomenon that is increasingly being designed into engineering structures. The rich and varied dynamics of snap-through present a significant bottleneck in the design process as costly dynamic simulations are required to ensure predictable behaviour. The purpose of this research is to investigate the use of a recent projection-based, reduced-order modelling technique, namely, implicit condensation and expansion with inertial compensation, to reproduce the snap-through behaviours found in bistable finite element systems in analogous models with minimal degrees of freedom. In this work, the free response of a simple mass-spring oscillator is used to differentiate different types of snap-through. This provides a framework for discussing the dynamics of a family of buckled beams. The ability of the reduced-order models to faithfully reproduce these dynamics is investigated by testing the existence and stability of predicted periodic orbits. It is shown that the minimum projection basis required to capture snap-through accurately can be found through considering the minimum energy required for different types of snap-through. For bistable beams, this can be further simplified to just requiring an eigenvalue analysis at the most unstable equilibrium. [ABSTRACT FROM AUTHOR]

Paper presents an effective technique for developing reduced-order models to predict the dynamic responses of systems using the receptance coupling and frequency-based substructuring (RCFBS) method. The proposed approach is particularly suited for reconfigurable dynamic systems across various applications, like cars, robots, mechanical machineries, and aerospace structures. The methodology focuses on determining the overall system receptance matrix by coupling the receptance matrices (FRFs) of individual subsystems in a disassembled configuration. Two case studies, one with distributed parameters and the other with lumped parameters, are used to illustrate the application of this approach. The first case involves coupling three substructures with flexible components under fixed–fixed boundary conditions, while the second case examines the coupling of subsystems characterized by multiple masses, springs, and dampers, with various internal and connection degrees of freedom. The accuracy of the proposed method is validated against a numerical finite element analysis (FEA), direct methods, and a modal analysis. The results demonstrate the reliability of RCFBS in predicting dynamic responses for reconfigurable systems, offering an efficient framework for reduced-order modeling by focusing on critical points of interest without the need to account for detailed modeling with numerous degrees of freedom. [ABSTRACT FROM AUTHOR]

The safe and stable operation of a hydrogen Knudsen compressor is essential for transporting hydrogen in microfluidic systems. This study uses proper orthogonal decomposition to identify the coherent structures within the hydrogen flow field during non-equilibrium evolution. A long short-term memory neural network is then used to create a multi-fidelity reduced-order model, connecting two-dimensional and three-dimensional data to uncover transient flow mechanisms and enable rapid flow field prediction. The results show that the coherent structures of hydrogen flow, representing the most energetic modes, retain 99% of the flow energy and significantly influence the evolution of Poiseuille and thermal transpiration flows during non-equilibrium processes. The multi-fidelity reduced-order model effectively captures hydrogen transient flow and instabilities at various stages, achieving a 99.4% reduction in computational time while maintaining a maximum relative error of 0.53%. This approach facilitates the rapid prediction and control of flow states during hydrogen transport. [Display omitted] • The coherent structures of hydrogen flow within microchannels are revealed. • The gradient distribution of coherent structures dominate hydrogen flow. • The coherent structures are consistent across different temperature rises. • A multi-fidelity reduced-order model for the Knudsen compressor is developed. • The prediction time for hydrogen flow within microchannels is reduced by 99.4%. [ABSTRACT FROM AUTHOR]

Isentropic processes are crucial in engineering as they represent idealized processes and serve as reference conditions for thermodynamic analyses. Existing methods for calculating isentropic processes in non-ideal fluids are either too slow for practical engineering applications [equation of state (EOS) approach] or inaccurate (classic modified polytropic isentrope equation: P v κ = Const. where exponent κ is the isentropic expansion coefficient). This paper proposes a novel isentrope equation, P v λ = Const. , with a path-specific exponent λ correcting for κ variation in generic non-ideal fluid isentropic processes. The benefit of this approach is that it maintains the isentrope equation's polytropic form, so that the explicit isentropic relations can be derived, enabling straightforward and rapid calculations and a better physical understanding. Using supercritical carbon dioxide as the fluid to test the hypothesis, the proposed isentropic relations accurately calculate the stagnation state within 2% of the exact EOS calculation, whereas the classic isentropic relations have errors up to 50%. Additionally, the fitted λ function is explicit and can calculate the stagnation state approximately 15–20 times faster than the EOS approach. Moreover, the results of two other non-ideal fluids, hexamethyldisiloxane and R-143a, are included to prove the robustness and general applicability of the proposed equations. This method strikes a balance between accuracy, simplicity, and computational speed for calculating isentropic processes in non-ideal fluids, offering greatly simplified expressions for thermodynamics modeling in engineering applications such as turbomachinery reduced-order models and design optimizations. [ABSTRACT FROM AUTHOR]

We investigate ocean circulation changes through the lens of data assimilation using a reduced-order model. Our primary interest lies in the Stommel box model, which reveals itself to be one of the most practicable models that has the ability of reproducing the meridional overturning circulation. The Stommel box model has at most two regimes: TH (temperature driven circulation with sinking near the north pole) and SA (salinity driven with sinking near the equator). Currently, the meridional overturning is in the TH regime. Using box-averaged Met Office EN4 ocean temperature and salinity data, our goal is to provide a probability that a future regime change occurs and establish how this probability depends on the uncertainties in initial conditions, parameters, and forcings. We will achieve this using data assimilation tools and DAPPER within the Stommel box model with fast oscillatory regimes. [ABSTRACT FROM AUTHOR]

Matrix (including interface) failure is a typical form of failure in the composite laminates for cryogenic storage tanks causing functionally useless of the structure. In this work, a low-cost multiscale model based on the Self-consistent Clustering Analysis (SCA) method is developed to predict the matrix failure process of the composite storage tanks. First, a reduced order model modeling method with fiber/matrix interfaces is proposed. Then, in conjunction with Progressive Failure Analysis (PFA), a reduced-order model is used to predict matrix failure and interface failure of the composites, mesh sensitivity analyses were carried out, and strength damage envelopes were obtained for unidirectional composites subjected to a combination of transverse stresses and in-plane shear. Compared with the prediction results of the Puck criterion, the errors in predicting damage strength for compressive-shear load and tensile-shear load do not exceed 10% and 30%, respectively. And finally, the thermal-mechanical load analysis of the composite storage tanks is carried out and the effect of homogenous temperature field and heterogenous temperature field on the load-bearing performance of the composite structure is analyzed. The method is proved to have good accuracy and to be very efficient. Its main feature is the ability to rapidly predict the stiffness and strength properties of composite structures under different environmental conditions, in agreement with experimental results, showing the potential to reduce the time and cost required for structural design. [ABSTRACT FROM AUTHOR]

Pulmonary artery stenosis (PAS) often presents in children with congenital heart disease, altering blood flow and pressure during critical periods of growth and development. Variability in stenosis onset, duration, and severity result in variable growth and remodeling of the pulmonary vasculature. Computational fluid dynamics (CFD) models enable investigation into the hemodynamic impact and altered mechanics associated with PAS. In this study, a one-dimensional (1D) fluid dynamics model was used to simulate hemodynamics throughout the pulmonary arteries of individual animals. The geometry of the large pulmonary arteries was prescribed by animal-specific imaging, whereas the distal vasculature was simulated by a three-element Windkessel model at each terminal vessel outlet. Remodeling of the pulmonary vasculature, which cannot be measured in vivo, was estimated via model-fitted parameters. The large artery stiffness was significantly higher on the left side of the vasculature in the left pulmonary artery (LPA) stenosis group, but neither side differed from the sham group. The sham group exhibited a balanced distribution of total distal vascular resistance, whereas the left side was generally larger in the LPA stenosis group, with no significant differences between groups. In contrast, the peripheral compliance on the right side of the LPA stenosis group was significantly greater than the corresponding side of the sham group. Further analysis indicated the underperfused distal vasculature likely moderately decreased in radius with little change in stiffness given the increase in thickness observed with histology. Ultimately, our model enables greater understanding of pulmonary arterial adaptation due to LPA stenosis and has potential for use as a tool to noninvasively estimate remodeling of the pulmonary vasculature. [ABSTRACT FROM AUTHOR]

A reduced-order model (ROM) of the global oceans is developed by projecting the hydrostatic Boussinesq equations of motion onto a proper orthogonal decomposition (POD) basis. Three-dimensional POD modes are calculated from the ocean fields of an ensemble climate reanalysis dataset. The coefficients in the POD ROM are calculated using a regression approach. The performance of various POD ROM configurations are assessed. Each configuration is derived from an alternate sea-water equation of state, linking the density and temperature fields. POD ROM variants incorporating an equation of state in which density is a quadratic function of temperature, are able to reproduce the statistics of the large-scale structures at a fraction of the computational cost required to numerically simulate this flow. Due to the speed and efficiency of calculation, such reduced-order models of the global geophysical system will enable researchers and policy makers to assess the physical risk for a broader range of potential future climate scenarios. [ABSTRACT FROM AUTHOR]

With the large-scale integration of renewable energy into off-grid DC systems, the stability issues caused by their fluctuations have become increasingly prominent. The dual active bridge (DAB) converter, as a DC-DC converter suitable for high power and high voltage level off-grid DC systems, plays a crucial role in maintaining and regulating grid stability through its control methods. However, the existing control methods for DAB are inadequate: linear control fails to meet dynamic response requirements, while nonlinear control relies on detailed model structures and parameters, making the control design complex and less accurate. To address this issue, this paper proposes a feedforward control strategy for a DC-DC converter in an off-grid hydrogen production system based on a linear extended state observer (LESO) and super-twisting sliding mode control (STSMC). Firstly, a reduced-order simplified model of the DAB was constructed through the structure of DAB. Then, based on the reduced-order simplified model, a feedforward control based on LESO and STSMC was designed, and its stability was analyzed. Finally, a simulation comparison of PI, LESO + terminal sliding mode control (TSMC), and LESO + STSMC control methods was conducted in a DC off-grid hydrogen production system. The results verified the proposed control method's enhancement of the DAB's rapid dynamic response capability and the system's transient stability. [ABSTRACT FROM AUTHOR]

The estimation of space-varying geological parameters is often not computationally affordable for high-dimensional subsurface reservoir modeling systems. The adjoint method is generally regarded as an efficient approach for obtaining analytical gradient and, thus, proceeding with the gradient-based iteration algorithm; however, the infeasible memory requirement and computational demands strictly prohibit its generic implementation, especially for high-dimensional problems. The autoregressive neural network (aNN) model, as a nonlinear surrogate approximation, has gradually received increasing popularity due to significant reduction of computational cost, but one prominent limitation is that the generic application of aNN to large-scale reservoir models inevitably poses challenges in the training procedure, which remains unresolved. To address this issue, model-order reduction could be a promising strategy, which enables us to train the neural network in a very efficient manner. A very popular projection-based linear reduction method, i.e., propel orthogonal decomposition (POD), is adopted to achieve dimensionality reduction. This paper presents an architecture of a projection-based autoregressive neural network that efficiently derives an easy-to-use adjoint model by the use of an auto-differentiation module inside the popular deep learning frameworks. This hybrid neural network proxy, referred to as POD-aNN, is capable of speeding up derivation of reduced-order adjoint models. The performance of POD-aNN is validated through a synthetic 2D subsurface transport model. The use of POD-aNN significantly reduces the computation cost while the accuracy remains. In addition, our proposed POD-aNN can easily obtain multiple posterior realizations for uncertainty evaluation. The developed POD-aNN emulator is a data-driven approach for reduced-order modeling of nonlinear dynamic systems and, thus, should be a very efficient modeling tool to address many engineering applications related to intensive simulation-based optimization. [ABSTRACT FROM AUTHOR]

This paper proposes a design framework to create individualised finger actuators that can be expanded to a generic hand. An actuator design is evaluated to help a finger achieve tendon-gliding exercises (TGEs). We consider musculoskeletal analysis for different finger sizes to determine joint forces while considering safety. The simulated Finite Element Analysis (FEA) response of a bi-directional Pneumatic Network Actuator (PNA) is mapped to a reduced-order model, creating a robust design tool to determine the bending angle and moment generated for actuator units. A reduced-order model is considered for both the 2D plane-strain formulation of the actuator and a full 3D model, providing a means to map between the results for a more accurate 3D model and the less computationally expensive 2D model. A setup considering a cascade of reduced-order actuator units interacting with a finger model determined to be able to achieve TGE was validated, and three exercises were successfully achieved. The FEA simulations were validated using the bending response of a manufactured actuator interacting with a dummy finger. The quality of the results shows that the simulated models can be used to predict the behaviour of the physical actuator in achieving TGE. [ABSTRACT FROM AUTHOR]

Advanced Aerial Mobility (AAM) platforms are poised to begin high-density operations in urban areas nationwide. This new category of aviation platforms spans a broad range of sizes, from small package delivery drones to passenger-carrying vehicles. Unlike traditional aircraft, AAM vehicles operate within the urban boundary layer, where large structures, such as buildings, interrupt the flow. This study examines the response of a package delivery drone, a general aviation aircraft, and a passenger-carrying urban air mobility aircraft through an urban wind field generated using Large Eddy Simulations (LES). Since it is burdensome to simulate flight dynamics in real-time using the full-order solution, reduced-order wind models are created. Comparing trajectories for each aircraft platform using full-order or reduced-order solutions reveals little difference; reduced-order wind representations appear sufficient to replicate trajectories as long as the spatiotemporal wind field is represented. However, examining control usage statistics and time histories creates a stark difference between the wind fields, especially for the lower wing-loading package delivery drone where control saturation was encountered. The control saturation occurrences were inconsistent across the full-order and reduced-order winds, advising caution when using reduced-order models for lightly wing-loaded aircraft. The results presented demonstrate the effectiveness of using a simulation environment to evaluate reduced-order models by directly comparing their trajectories and control activity metrics with the full-order model. This evaluation provides designers valuable insights for making informed decisions for disturbance rejection systems. Additionally, the results indicate that using Reynolds-averaged Navier–Stokes (RANS) solutions to represent urban wind fields is inappropriate. It was observed that the mean wind field trajectories fall outside the 95% confidence intervals, a finding consistent with the authors' previous research. [ABSTRACT FROM AUTHOR]

Reduced order models (ROMs) are often coupled with concurrent multiscale simulations to mitigate the computational cost of nonlinear computational homogenization methods. Construction (or training) of ROMs typically requires evaluation of a series of linear or nonlinear equilibrium problems, which itself could be a computationally very expensive process. In the eigenstrain‐based reduced order homogenization method (EHM), a series of linear elastic microscale equilibrium problems are solved to compute the localization and interaction tensors that are in turn used in the evaluation of the reduced order multiscale system. These microscale equilibrium problems are typically solved using either the finite element method or semi‐analytical methods. In the present study, a reduced order variational spectral method is developed for efficient computation of the localization and interaction tensors. The proposed method leads to a small stiffness matrix that scales with the order of the reduced basis rather than the number of degrees of freedom in the finite element mesh. The reduced order variational spectral method maintains high accuracy in the computed response fields. A speedup higher than an order of magnitude can be achieved compared to the finite element method in polycrystalline microstructures. The accuracy and scalability of the method for large polycrystals and increasing phase property contrast are investigated. [ABSTRACT FROM AUTHOR]

Modular Multilevel Converter Virtual Synchronous Generator (MMC-VSG) technology is gaining widespread attention for its ability to enhance the inertia and frequency stability of the power grid integrated with converter-interfaced renewable energy sources. However, the excitation voltage regulation in the MMC-VSG can generate equivalent negative damping torque and cause low-frequency oscillation problems similar to those in synchronous machines. This article aims to improve the system's damping torque and minimize low-frequency oscillations by introducing a Virtual Power System Stabilizer (VPSS) into the power control loop. Building on the study of dynamic interactions between various control links of the MMC, this research establishes a reduced-order model (ROM) and a Phillips–Heffron state equation for the MMC-VSG single machine infinite bus system, using a hybrid modeling approach and a zero-pole truncation method. It also analyzes the mechanism of low-frequency oscillations in the MMC-VSG system through the damping torque method. The analysis reveals that the negative damping torque produced during the excitation voltage regulation process causes changes in the virtual power angle, which in turn increases the risk of low-frequency oscillation in the MMC-VSG. To address this issue, the article proposes an optimized control method for the MMC-VSG dual power loop architecture (power-angle/excitation) VPSS. This strategy compensates for the inadequate damping torque of a single loop VPSS and effectively suppresses low-frequency oscillations in the system. [ABSTRACT FROM AUTHOR]

The dual three-phase permanent magnet synchronous motor (DTP-PMSM) under a V/f control framework is widely applied in belts, fans, pumps, etc. However, the oscillation in power and rotor speed is difficult to quantify and suppress, due to the higher-order model of the DTP-PMSM. Thus, a power-revolutions per minute (RPM) reduced-order model and power control strategy of the DTP–PMSM are proposed for oscillation description and suppression. Firstly, according to the structure and V/f control framework, the reduced-order model is proposed under a power-RPM scale with coupled performances between sub-PMSMs, and then the decoupled method is employed. Moreover, the oscillated performances of power and rotor speed are detailed in small signals. Secondly, a power control strategy is proposed, including active power feedforward for active damping and reactive power droop control for high power quality and approaching optimal torque per ampere. Compared with the traditional strategies, the proposed method can achieve a stable and efficient operation, with a higher power factor of the DTP–PMSM, less stator current, and lower electromechanical power loss. Finally, an experimental platform of the DTP–PMSM is set up for the correctness and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

The development of reduced-order models has been a pivotal advancement in the computational analysis of fluid dynamics, substantially simplifying the complexity and boosting the efficiency of simulations. The accuracy and practicality of these models largely depend on the reduction techniques applied and the inherent characteristics of the fluid dynamics systems they represent. In this paper, we introduce an innovative machine-learning framework for assessing model uncertainty in computationally intensive reduced-order models. By combining subspace construction methods with advanced Bayesian inference techniques, our approach effectively captures the posterior distribution of model parameters, thereby providing an accurate representation of uncertainty in aerodynamic performance predictions. We employ the NACA0012 airfoil as a case study to validate our method's ability to enhance the efficiency of reduced-order models and precisely measure the uncertainty inherent in predictions made by recurrent neural networks. It is important to note that our approach is influenced by specific constraints and variables that significantly impact the mean and variability of the predicted final lift coefficient distribution. Our findings indicate that setting the goodness of fit (R2) threshold above 0.985 markedly improves the correlation between Computational Fluid Dynamics (CFD) outcomes and model predictions, increasing from 72.2% to 97.9% as the interval amplification factor adjusts from 1.5 to 3. However, this adjustment causes a considerable expansion of the confidence interval, from 0.0737 to 0.1282, an increase of over 70%. Despite these challenges, our machine learning-based methodology provides essential insights into the further development of reduced-order modeling and uncertainty quantification in fluid dynamics. This highlights the need for ongoing research into the model parameters, especially in applications concerning aircraft control systems, to meet design specifications and ensure system reliability. [ABSTRACT FROM AUTHOR]

Thin-walled structures, i.e. the wing-upper-skin panels, are prone to buckling accompanied by a significantly large out-of-plane deflection. The computational efficiency of the conventional finite element based full-order method is not satisfactory for nonlinear buckling problems of the structure. In this work, the skin panels on the upper surface of the wing butt box are selected using a sub-modeling technique based on the nonlinear structural analysis. A reduced-order method is proposed to trace the geometrically nonlinear response of the single and double-curved skin panels in a stepwise manner. A predictor-corrector strategy is developed using the Koiter-perturbation-theory based reduced-order model and Newton iterations. The high-efficiency of the proposed method is validated by comparing the number of path-following steps and iterations with the full-order method. A fairly large step size is achieved to significantly reduce the computational cost in a nonlinear buckling analysis. The influence of the number of closely-spaced modes on the numerical accuracy and efficiency of the proposed reduced-order method is also studied. Different boundary condition, location, and thickness of the wing-upper-skin panel, are considered to further demonstrate the favorable performance of the proposed method. • Nonlinear buckling analysis is applied to skin panels with single and double-curved shapes on the wing upper surface. • A reduced-order method is adopted to trace geometrically nonlinear responses in predictor-corrector based stepwise manner. • Influence of the number of closely-spaced modes on numerical accuracy and efficiency of the proposed method is investigated. • Numerical accuracy and high-efficiency of the proposed method are validated for skin panels con- sidering various parameters. [ABSTRACT FROM AUTHOR]

It is widely acknowledged that the effects of soil-structure interaction (SSI) can have substantial implications during periods of intense seismic activity; therefore, accurate quantification of these effects is of paramount importance in the design of earthquake-resistant structures. The analysis of SSI is typically conducted using either direct or substructure methods. Both of these approaches involve the use of numerical models with truncated or reduced-order computational domains. To ensure effective truncation, it is crucial to employ boundary representations that are capable of perfectly absorbing outgoing waves and allowing for the consistent application of input motions. At present, such capabilities are not widely available to researchers and practicing engineers. In order to address this issue, this study implemented the Domain Reduction Method (DRM) and Perfectly Matched Discrete Layers (PMDLs) in OpenSees. The accuracy and stability of these implementations were verified through the use of vertical and inclined incident SV waves in a two-dimensional problem. In terms of computational efficiency, PMDLs require a shorter analysis time (e.g., with PMDLs, the analysis concluded in 35 min as compared to 250 min with extended domain method) and less computational power (one processor for PMDLs against 20 processors for the extended domain method) thus offering a balance between accuracy and efficiency. Furthermore, illustrative examples of the aforementioned implemented features are presented, namely the response analysis of single-cell and double-cell tunnels exposed to plane waves inclined at an angle. [ABSTRACT FROM AUTHOR]

The dynamic characteristics of the track and bridge system change continuously with the mileage and operating environment, exhibiting highly significant nonlinear and nonuniform spatial distribution features. Based on the Generalized Rayleigh–Ritz Method (GRRM) and Component Mode Synthesis (CMS), this work presents a novel method to establish a three-dimensional model of train–track–bridge interaction that considers the nonuniform distribution of track–bridge system parameters and the nonlinear contact between track and bridge layers. Unlike traditional Finite Element Method (FEM) models, the GRRM-based structure employs generalized displacements without nodal degrees of freedom, thus avoiding the complex processes of element discretization and assembly when constructing tracks/bridges with nonuniform physical and geometric parameters. Additionally, when dealing with the nonlinear contact relationship between track and bridge layers, this model does not require incremental or iterative methods. By introducing CMS to truncate the modes of each substructure in the track–bridge system and establishing the reduced-order model of the entire system based on boundary conditions at the coupling interface, the matrix dimensions can be effectively reduced, thereby improving computational efficiency. The accuracy and efficiency of this newly developed train–track–bridge dynamic model have been validated through comparisons with FEM-based models and measured results. Finally, several numerical examples demonstrate the engineering practicality of this model. [ABSTRACT FROM AUTHOR]

Wind tunnel experiments were performed to quantify the coupling mechanisms between incoming wind flows, power output fluctuations, and unsteady tower aerodynamic loads of a model wind turbine under periodically oscillating wind environments across various yaw misalignment angles. A high-resolution load cell and a data logger at high temporal resolution were applied to quantify the aerodynamic loads and power output, and time-resolved particle image velocimetry system was used to characterize incoming and wake flow statistics. Results showed that due to the inertia of the turbine rotor, the time series of power output exhibits a distinctive phase lag compared to the incoming periodically oscillating wind flow, whereas the phase lag between unsteady aerodynamic loads and incoming winds was negligible. Reduced-order models based on the coupling between turbine properties and incoming periodic flow characteristics were derived to predict the fluctuation intensity of turbine power output and the associated phase lag, which exhibited reasonable agreement with experiments. Flow statistics demonstrated that under periodically oscillating wind environments, the growth of yaw misalignment could effectively mitigate the overall flow fluctuation in the wake region and significantly enhance the stream-wise wake velocity cross correlation intensities downstream of the turbine hub location. [ABSTRACT FROM AUTHOR]

This paper investigates the thermal operating capability of an interior permanent magnet synchronous machine. An iterative workflow is presented, combining electromagnetic modeling, control, power‐loss modeling, and thermal modeling to identify maximum thermal stable operating points. Special attention is given to the critical temperatures of winding and permanent magnets. A nonlinear reduced order model based on finite element method model was used to simulate the system, including an inverter model with space vector pulse width modulation in combination with field‐oriented control. Furthermore, an advanced iron core loss model and thermal lumped parameter model were employed. The presented approach allows for evaluating losses and their impact on steady‐state temperatures. The obtained results highlight the significant influence of space vector pulse width modulation on iron core losses and the importance of considering both advanced power‐loss models and adequate thermal models when analyzing the machine's thermal state. This research emphasizes the concept of a thermally stable envelope, providing a comprehensive understanding of the thermal boundaries under various operating conditions. [ABSTRACT FROM AUTHOR]

Rotor–stator interaction is an inherently unsteady phenomenon in turbomachinery that significantly influences the performance of turbomachinery. Accurate prediction of the unsteady turbomachinery rotor–stator interaction flow remains a great challenge considering computational cost. In the Reynolds-averaged Navier–Stokes framework, the harmonic balance (HB) method emerges as a potential reduced-order modeling technique, offering significant computational savings over traditional unsteady methods, and revealing unsteady flow characteristics that are elusive to the steady mixing-plane method. In this study, a graphical processing unit (GPU)-based solver utilizing the finite volume method is developed to accelerate the computation of the HB method compared to the traditional central processing unit (CPU)-based solver. An implicit data-parallel block-Jacobi lower-upper relaxation (DP-BJ-LUR) method is first proposed to better fit the distinct parallel architecture of GPU. The HB method with different harmonics, as well as unsteady time marching method, is conducted to evaluate the accuracy and acceleration for convergence of the proposed method by a quasi-three-dimensional radial slice case and a full three-dimensional case for National Aeronautics and Space Administration (NASA) Stage 35 compressor. Acceleration performance of GPU-based solver, impact of relaxation steps on the DP-BJ-LUR method, and numerical accuracy are compared in detail. A maximum speedup of 102 times with 1 harmonic and 90 times with 12 harmonics is achieved by the GPU-based solver on a single NVIDIA Ray Tracing Texel eXtreme 3080Ti GPU compared with the CPU-based solver on a single CPU core of Intel® Xeon® Platinum 9242. [ABSTRACT FROM AUTHOR]

Crossflow filtration is a separation technique where fluid flows tangentially across a membrane or porous media, reducing clogging by sweeping away retained particles and allowing continuous filtration. Dispersion of solute matter in crossflow filtration plays an essential role in the separation performance of many industrial processes. The current work aims to generalize the Taylor dispersion theory and study the solute transport in a slit–porous medium system with a crossflow. The solute is depleted by the porous medium at the slit top porous wall or the interface between the slit and the porous medium, where the continuity of the solute concentration and mass flux is applied. The solute is simultaneously transported axially by the main flow along the slit and vertically by the crossflow perpendicular to the slit. Using the Reynolds decomposition and cross-sectional averaging techniques, the generalized reduced-order model for the advection-dispersion solute transport in the slit–porous medium system with the presence of a crossflow is established, where the effective velocity of the main flow and the effective dispersion coefficient are obtained. The analysis of the results reveals that the nondimensional Taylor dispersion coefficient scales with the Peclet numbers for the crossflow and the main flow, respectively, as D T ∼ Pe v − 5 / 3 (when Pe v ≥ 20) and D T ∼ Pe u 2 . The proposed theoretical model, along with the findings of this study, paves the way for the fundamental study of dispersion in more complex systems. [ABSTRACT FROM AUTHOR]

The National Transportation Noise Map predicts time-averaged road traffic noise across the continental United States (CONUS) based on annual average daily traffic counts. However, traffic noise can vary greatly with time. This paper outlines a method for predicting nationwide hourly varying source traffic sound emissions called the Vehicular Reduced-Order Observation-based Model (VROOM). The method incorporates three models that predict temporal variability of traffic volume, predict temporal variability of different traffic classes, and use Traffic Noise Model (TNM) 3.0 equations to give traffic noise emission levels based on vehicle numbers and class mix. Location-specific features are used to predict average class mix across CONUS. VROOM then incorporates dynamic traffic class mix data to obtain dynamic traffic class mix. TNM 3.0 equations then give estimated equivalent sound level emission spectra near roads with up to hourly resolution. Important temporal traffic noise characteristics are modeled, including diurnal traffic patterns, rush hours in urban locations, and weekly and yearly variation. Examples of the temporal variability are depicted and possible types of uncertainties are identified. Altogether, VROOM can be used to map national transportation noise with temporal and spectral variability. [ABSTRACT FROM AUTHOR]

We present a systematic and automatic approach for integrating tableting reduced-order models with upstream unit operations. The approach not only identifies the upstream critical material attributes and process parameters that describe the coupling to the first order and, possibly, the second order, but it also selects the mathematical form of such coupling and estimates its parameters. Specifically, we propose that the coupling can be generally described by normalized bivariate rational functions. We demonstrate this approach for dry granulation, a unit operation commonly used to enhance the flowability of pharmaceutical powders by increasing granule size distribution, which, inevitably, negatively impacts tabletability by reducing the particle porosity and imparting plastic work. Granules of different densities and size distributions are made with a 10% w/w acetaminophen and 90% w/w microcrystalline cellulose formulation, and tablets with a wide range of relative densities are fabricated. This approach is based on product and process understanding, and, in turn, it is not only essential to enabling the end-to-end integration, control, and optimization of dry granulation and tableting processes, but it also offers insight into the granule properties that have a dominant effect on each of the four stages of powder compaction, namely die filling, compaction, unloading, and ejection. [ABSTRACT FROM AUTHOR]

This paper presents reduced-order modeling of thermal power dispatch (TPD) from a pressurized water reactor (PWR) for providing heat to nearby heat consuming industrial processes that seek to take advantage of nuclear heat to reduce carbon emissions. The reactor model includes the neutronics of the reactor core, thermal–hydraulics of the primary coolant cycle, and a three-lump model of the steam generator (SG). The secondary coolant cycle is represented with quasi-steady state mass and energy balance equations. The secondary cycle consists of a steam extraction system, high-pressure and low-pressure turbines, moisture separator and reheater, high-pressure and low-pressure feedwater heaters, deaerator, feedwater and condensate pumps, and a condenser. The steam produced by the SG is distributed between the turbines and the extraction steam line (XSL) that delivers steam to nearby industrial processes, such as production of clean hydrogen. The reduced-order simulator is verified by comparing predictions with results from separate validated steady-state and transient full-scope PWR simulators for TPD levels between 0% and 70% of the rated reactor power. All simulators indicate that the flow rate of steam in the main steam line and turbine systems decrease with increasing TPD, which causes a reduction in PWR electric power generation. The results are analyzed to assess the impact of TPD on system efficiency and feedwater flow control. Due to the simplicity of the proposed reduced-order model, it can be scaled to represent a PWR of any size with a few parametric changes. In the future, the proposed reduced-order model will be integrated into a power system model in a digital real-time simulator (DRTS) and physical hardware-in-the-loop simulations. [ABSTRACT FROM AUTHOR]

This paper reviews the recent advances on the combination of component mode synthesis and model order reduction for geometrically nonlinear analysis, focusing on fixed-interface substructures and non-intrusive reduced-order models. These approaches offer significant potential for engineering applications by enabling accurate mechanical behavior prediction without detailed geometric and material information. Additionally, they facilitate safe sharing and collaboration between companies, reducing design times and production costs while also offering computational efficiency. However, challenges remain, indicating the need for future improvements in this area. [ABSTRACT FROM AUTHOR]

Variable refrigerant flow (VRF) system has been an appealing solution of air conditioning for residential and commercial buildings, due to its flexibility and cost effectiveness, while lack of ventilation capability is a major drawback. Incorporation of dedicated outdoor air system (DOAS) is a typical practice. However, good coordination between DOAS and VRF is critical for achieving desired thermal comfort is challenging due to the possible complexity of mixed sensible and latent heat exchanges. In this paper, to handle the nonlinear dynamic characteristics of VRF-DOAS system, we propose an offset-free Koopman model predictive control (MPC) strategy for thermal comfort regulation, in which the MPC design is computationally more efficient due to the convex problem formulation and the use of reduced-order Koopman models, and the offset-free MPC structure enhances the robustness to model uncertainties and unmeasured disturbances. A control-oriented model is obtained by hybridizing the first-principle and data-driven modeling approach. The proposed controls strategy is evaluated with a Modelica simulation model of a VRF-DOAS system. A Dymola-Python cosimulation platform is developed via the functional mockup interface (FMI), for which the MPC algorithms are implemented in Python. Simulation results show significantly better performance of the offset-free Koopman MPC in thermal comfort regulation. [ABSTRACT FROM AUTHOR]

Complex practical system designs pose significant challenges from a research perspective, often resulting in high computational requirements for analysis. Model order reduction (MOR) is a valuable technique to address this issue. This study provides a comprehensive review of the literature on MOR, focusing specifically on high-dimensional complex systems. It examines the fundamental theories and limitations of established MOR methods, including the Factor division method, Pade approximation (PA) method, Stability equation (SE) method, Differentiation method, and Routh approximation (RA) method. The study also investigates the frequency domain approach for obtaining a reduced-order model (ROM). Among the MOR methods, the PA method is a widely studied and practical approach that aims to retain the crucial dynamics of a high-dimensional complex system. This survey presents a detailed discussion of the PA method for obtaining the ROM. Additionally, six test systems are analyzed to compare the step and frequency responses generated by various MOR strategies. The integral square error criterion is used to assess the effectiveness of the reduction procedures. Finally, the study proposes a new system abatement method based on Atomic Orbital Search (AOS) optimization for obtaining the ROM of large-scale linear time-invariant (LTI) systems and designing controllers based on the reduced order model. [ABSTRACT FROM AUTHOR]

The use of Lamb waves within a guided wave (GW)–based scheme holds promise toward monitoring and nondestructive evaluation (NDE) of plate structures. Their short wavelength enables interaction with small defects and they can travel long distances, thus offering extensive spatial coverage. In boosting the performance of these schemes for more advanced damage identification tasks, such as precise damage localization and quantification, the fusion of measurement data with models is advantageous. Such a hybrid scheme, which relies on the inclusion of engineering models, is hampered by the short wavelengths of GW-based schemes. Short wavelengths require a fine discretization of numerical models in space and in time, which results in high computational costs. In alleviating this issue, we propose a reduced-order model (ROM) relying on exploitation of the frequency response function (FRF) principle, which is parameterized with respect to the positioning of local defects. Through appropriate coordinate transformations, the surrogate, constructed based on the matching pursuit (MP) algorithm, can exploit the mechanical properties of the wave so that only a small amount of training simulations are needed. The efficacy of the proposed surrogate is demonstrated in a synthetic inverse setting, using a particle swarm optimization (PSO) strategy. [ABSTRACT FROM AUTHOR]

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The design of the high-speed on/off valve is challenging due to the interrelated structural parameters of its driving actuator. Hence, this study proposes a multi-objective optimization approach that integrates a backpropagation neural network and artificial fish swarm algorithm optimization techniques to accurately model the electromagnetic solenoid structure. The backpropagation neural network is fitted and trained using simulation data to obtain a reduced-order model of the system, enabling the precise prediction of the system's output based on the input structural parameters. By employing the artificial fish swarm algorithms, with optimization objectives focusing on the valve's opening and closing times, a Pareto optimal solution set comprising 30 solutions is generated. Utilizing the optimized structural parameters, a prototype is manufactured and an experimental setup is constructed to verify the dynamic characteristics and flow pressure drop. The high-speed on/off valve achieves an approximate opening and closing time of 3 ms. Notably, the system output predicted using the backpropagation neural network (BPNN) exhibits consistency with the experimental findings, providing a reliable alternative to mathematical modeling. [ABSTRACT FROM AUTHOR]

The Stochastic Reduced-Order Models (SROMs) are a non-embedded uncertainty analysis method that has the advantages of high computational efficiency, easy implementation, and no dimensional disasters. Recently, it has been widely used in the field of EMC simulation. In the process of optimizing electromagnetic protection design, the worst-case estimation value is an extremely important uncertainty quantification simulation result. However, the SROMs have a large error in providing this result, which limits its application in the field of EMC simulation prediction. An improved SROM based on the Radial Basis Function (RBF) neural network algorithm is proposed in this paper, which improves the fitness function in the genetic algorithm center clustering process and constructs an RBF neural network model to obtain accurate worst-case estimation results. The accuracy improvement effect of the algorithm proposed in this paper in worst-case estimation is quantitatively verified by using a parallel cable crosstalk prediction example from published literature. [ABSTRACT FROM AUTHOR]

We present a new balancing-based structure-preserving model reduction technique for linear port-Hamiltonian descriptor systems. The proposed method relies on a modification of a set of two dual generalized algebraic Riccati equations that arise in the context of linear quadratic Gaussian balanced truncation for differential algebraic systems. We derive an a priori error bound with respect to a right coprime factorization of the underlying transfer function thereby allowing for an estimate with respect to the gap metric. We further theoretically and numerically analyze the influence of the Hamiltonian and a change thereof, respectively. With regard to this change of the Hamiltonian, we provide a novel procedure that is based on a recently introduced Kalman–Yakubovich–Popov inequality for descriptor systems. Numerical examples demonstrate how the quality of reduced-order models can significantly be improved by first computing an extremal solution to this inequality. [ABSTRACT FROM AUTHOR]

Coupled Monte Carlo (MC) and thermal-hydraulic analysis is valuable as a design or reference tool but can be slow, especially when implemented in a Picard iteration. Previous work has developed a novel prediction block to achieve convergence with fewer MC simulations. The prediction works in two stages: (1) a surrogate-like model predicts macroscopic cross sections on the fly and (2) a reduced-order neutronic model predicts the flux response to the updated cross sections. The main challenge with the prediction block is that the reduced-order neutronic model cannot reproduce the spatial flux distribution with high fidelity. This paper investigates the well-established Jacobian-free Newton Krylov (JFNK) method to preserve equivalency between a homogeneous (nodal diffusion) solution and a high-fidelity transport (MC) solution. Instead of performing multiple computationally consuming MC simulations, the nonlinear iterative approach iterates on correction parameters, e.g., assembly discontinuity factors (ADFs) or super homogenization (SPH) factors, using unexpensive nodal solutions. The JFNK approach does not require additional overhead from the MC solver to generate flux tallies. Further, the approach iterates on diffusion solutions produced directly from a desired code, thus ensuring that the parameters are compatible with that code. The approach is applied to correct a nodal diffusion solution for a realistic three-dimensional pressurized water reactor core. The results obtained in the paper show that the method is very successful in reproducing the heterogeneous solution (up to 2.5% difference in assembly flux for SPH and 0.3% for ADFs) without needing to modify the source code of the nodal diffusion solver. In addition, the results show that ADFs yield the best agreement and are also stable (i.e., weakly varying) when thermal-hydraulic fields are perturbed. [ABSTRACT FROM AUTHOR]

We propose a technique for performing spectral (in time) analysis of spatially-resolved flowfield data, without needing any temporal resolution or information. This is achieved by combining projection-based reduced-order modeling with spectral proper orthogonal decomposition. In this method, space-only proper orthogonal decomposition is first performed on velocity data to identify a subspace onto which the known equations of motion are projected, following standard Galerkin projection techniques. The resulting reduced-order model is then utilized to generate time-resolved trajectories of data. Spectral proper orthogonal decomposition (SPOD) is then applied to this model-generated data to obtain a prediction of the spectral content of the system, while predicted SPOD modes can be obtained by lifting back to the original velocity field domain. This method is first demonstrated on a forced, randomly generated linear system, before being applied to study and reconstruct the spectral content of two-dimensional flow over two collinear flat plates perpendicular to an oncoming flow. At the range of Reynolds numbers considered, this configuration features an unsteady wake characterized by the formation and interaction of vortical structures in the wake. Depending on the Reynolds number, the wake can be periodic or feature broadband behavior, making it an insightful test case to assess the performance of the proposed method. In particular, we show that this method can accurately recover the spectral content of periodic, quasi-periodic, and broadband flows without utilizing any temporal information in the original data. To emphasize that temporal resolution is not required, we show that the predictive accuracy of the proposed method is robust to using temporally-subsampled data. [ABSTRACT FROM AUTHOR]

Enhanced transformation field analysis (E‐TFA), recently proposed for reduced‐order modeling, is here formulated for and applied to multiscale analysis. The approach is able to reproduce a highly complex nonlinear macroscale behavior, resulting from a microstructure with cohesive interfaces embedded in an elasto‐plastic bulk. E‐TFA features a consistent tangent matrix in its solution procedure, which enables a straightforward definition of the upscaled tangent stiffness tensor. Numerical tests show that, compared to FE 2$$ {}^2 $$, the proposed approach yields accurate solutions at a lower computational cost. [ABSTRACT FROM AUTHOR]

AbstractNoise signals obtained from local power range monitors and average power range monitors are routinely used for extracting stability information for boiling water reactors. The stability parameters of decay ratio (DR) and natural frequency are produced by signal processing algorithms. While theoretically a dynamical system like a reactor core composed of coherently coupled components possesses a unique DR, noise measurements from different detectors have been reported in several published works to produce different DRs, creating the impression that a DR is not unique at a given operating state but rather is space dependent. This paper is an attempt to reconcile theory with measurements and resolve the space-dependent DR paradox that was encountered afresh in the course of designing a new high-fidelity online stability monitor. As such, the issue of space dependence could not be overlooked as attributable to variability within the uncertainty of noise analysis algorithms. [ABSTRACT FROM AUTHOR]

A reduced-order model was generated from aerodynamic simulation data for the optimal design and operation management of an air-jet ejector to remove contaminated materials in manufacturing plants. Three significant design parameters of the nozzle structure after studying the computational fluid dynamics (CFD) of the preliminary design cases were determined. Polynomial type and deep neural feedforward network-based meta-models were established based on parametric CFD simulations considering three design variables, which were used to predict the suction performance; the models were successfully validated by comparing the results with those of the complete CFD. Finally, a proper orthogonal decomposition was adopted to reconstruct an internal flow field within a few seconds to facilitate real-time monitoring of the air flow without complete CFD simulations, which was realized as a digital twin for the air-jet ejector system. [ABSTRACT FROM AUTHOR]

In order to save the time and material costs associated with refrigeration system performance evaluations, a reduced-order model (ROM) using highly accurate numerical analysis results and some experimental values was developed. To solve the shortcomings of these traditional methods in monitoring complex systems, a simplified reduced-order system model was developed. To evaluate the performance of the refrigeration system compressor, the temperature of several points in the system where the compressor actually operates was measured, and the measured values were used as input values for ROM development. A lot of raw data to develop a highly accurate ROM were acquired from a VRF system installed in a building for one year, and in this study, specific operating conditions were selected and used as input values. In this study, the ROM development process can predict the performance of compressors used in air conditioning systems, and the research results on optimizing input data required for ROM generation were observed. The input data are arranged according to the design of experiments (DOE), and the accuracy of ROM according to data arrangement is compared through the experiment results. [ABSTRACT FROM AUTHOR]

We present a reduced-order model to calculate response matrices rapidly for filter stack spectrometers (FSSs). The reduced-order model allows response matrices to be built modularly from a set of pre-computed photon and electron transport and scattering calculations through various filter and detector materials. While these modular response matrices are not appropriate for high-fidelity analysis of experimental data, they encode sufficient physics to be used as a forward model in design optimization studies of FSSs, particularly for machine learning approaches that require sampling and testing a large number of FSS designs. [ABSTRACT FROM AUTHOR]

To solve the problem of slow simulation calculation of magnetic field in oil-immersed transformers, this paper proposes a fast calculation method based on the proper orthogonal decomposition (POD) and Kriging response surface method. First, based on the POD reduction method, the discrete equation of the magnetic field is reduced to obtain the modal coefficient matrix. Then, taking the transformer load rate as an important parameter, the sample space is determined, and the corresponding snapshot matrix of the sample space is obtained through COMSOL software. Based on the Kriging function, a response function for the load rate and modal coefficients is constructed, and combined with the reduced mode, the winding magnetic field is quickly reconstructed. Finally, to verify the effectiveness of the method, four additional load conditions were selected to analyze the deviation between the reduced-order model and the full-order model from the perspective of computational accuracy and efficiency. The results show that, in terms of computational accuracy, the maximum relative error between the reduced-order model and the simulation model in the verification points is only 1.045%, while the rest of the points are below 1%. In terms of computational efficiency, the method proposed in this article improves the computational efficiency to 4743 times that of the full-order model. It only takes 0.9 s to calculate the results corresponding to a certain operating condition, which can achieve fast calculation. [ABSTRACT FROM AUTHOR]