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This paper presents a novel framework combining proper generalized decomposition (PGD) with the shooting method to determine the steady-state response of nonlinear dynamical systems upon a general periodic input. The proposed PGD approximates the response as a low-rank separated representation of the spatial and temporal dimensions. The Galerkin projection is employed to formulate the subproblem for each dimension, then the fixed-point iteration is applied. The subproblem for the spatial vector can be regarded as computing a set of reduced-order basis vectors, and the shooting problem projected onto the subspace spanned by these basis vectors is defined to obtain the temporal coefficients. From this procedure, the proposed framework replaces the complex nonlinear time integration of the full-order model with the series of solving simple iterative subproblems. The proposed framework is validated through two descriptive numerical examples considering the conventional linear normal mode method for comparison. The results show that the proposed shooting method based on PGD can accurately capture nonlinear characteristics within 10 modes, whereas linear modes cannot easily approximate these behaviors. In terms of computational efficiency, the proposed method enables CPU time savings of about one order of magnitude compared with the conventional shooting methods. [ABSTRACT FROM AUTHOR]

This paper proposes a model-based optimization method for the production of automotive seals in an extrusion process. The high production throughput, coupled with quality constraints and the inherent uncertainty of the process, encourages the search for operating conditions that minimize nonconformities. The main uncertainties arise from the process variability and from the raw material itself. The proposed method, which is based on Bayesian optimization, takes these factors into account and obtains a robust set of process parameters. Due to the high computational cost and complexity of performing detailed simulations, a reduced order model is used to address the optimization. The proposal has been evaluated in a virtual environment, where it has been verified that it is able to minimize the impact of process uncertainties. In particular, it would significantly improve the quality of the product without incurring additional costs, achieving a 50% tighter dimensional tolerance compared to a solution obtained by a deterministic optimization algorithm. • Optimizing automotive seal production with a model-based approach. • A reduced order model (ROM) is used for efficient optimization. • Uncertainties in the model and the system itself are taken into account. • Bayesian optimization is applied for robust parameter determination. • A 50% tighter dimensional tolerance is achieved compared to a deterministic solution. [ABSTRACT FROM AUTHOR]

In the early stages of aerospace design, reduced-order models (ROMs) are crucial for minimizing computational costs associated with using physics-rich field information in many-query scenarios requiring multiple evaluations. The intricacy of aerospace design demands the use of high-dimensional design spaces to capture detailed features and design variability accurately. However, these spaces introduce significant challenges, including the curse of dimensionality, which stems from both high-dimensional inputs and outputs necessitating substantial training data and computational effort. To address these complexities, this study introduces a novel multifidelity, parametric, and nonintrusive ROM framework designed for high-dimensional contexts. It integrates machine learning techniques for manifold alignment and dimension reduction--employing proper orthogonal decomposition and model-based active subspace--with multifidelity regression for ROM construction. Our approach is validated through two test cases: the 2D RAE 2822 airfoil and the 3D NASA CRM wing, assessing various fidelity levels, training data ratios, and sample sizes. Compared to the single-fidelity principal component-active subspace (PCAS) method, our multifidelity solution offers improved cost-accuracy benefits and achieves better predictive accuracy with reduced computational demands. Moreover, our methodology outperforms the manifold-aligned ROM method by 50% in handling scenarios with large input dimensions, underscoring its efficacy in addressing the complex challenges of aerospace design. [ABSTRACT FROM AUTHOR]

Copyright of Electric Power is the property of Electric Power Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

ObjectivesWhen assessing the safety of the connectors of a multi-module offshore floating power generation platform, in order to compensate for the inability to carry out the real-time monitoring of the structural stress field across the whole domain due to a limited numbers of sensor, a digital twin method based on a simulation database is proposed that can rapidly predict the platform's stress field. MethodsBy downgrading the three-dimensional physical model of the connectors to a one-dimensional digital model, the stress field data is interpolated and deduced in digital space, thereby achieving the rapid prediction of the structural stress field across the whole domain and its visual display.ResultsThe results show that the simulation model is in good agreement with the test results, with a maximum absolute error of 8.61%; for the interpolation of data under different loading angles, when the interpolation step of the loading angle is 10°, the aver-age absolute error of stress is 1.98%; and for the interpolation of data under different loads, when the interpolation step of the load is 10 t, the average absolute error of stress is 1.28%, achieving the rapid prediction and visualization of the connectors' stress field distribution. Conclusions The digital twin-based model of connectors can provide useful references for the rapid dynamic perception and scientific prediction of the structural strength of offshore floating power generation platforms.

The high-fidelity numerical simulation is the basis for constructing digital twins of reactor cores and other engineering applications. However, the traditional numerical models, such as the finite element model and/or the finite volume model, usually adopt high-resolution grids. The high computation cost makes the traditional high-fidelity models unsuitable for the application of digital twins. Model order reduction is an effective approach to accelerate the simulation whenever a trade-off between computational cost and solution accuracy is a preeminent issue. In this paper, a reduced order model (ROM) which combined both the intrusive and the non-intrusive approaches was constructed for the parameterized thermal-flow problems. The intrusive approach adopted the Galerkin projection method and the non-intrusive approach adopted the radial basis function (RBF) interpolation method. To construct the ROM, some typical numerical solutions were firstly generated by using the finite volume method (also called full-order model, FOM) and then taken as learning samples (also called the snapshots) to generate the reduced bases by the proper orthogonal decomposition (POD) method. After that, the conservation equations of mass, momentum and energy were projected onto the space spanned by the reduced bases. As a result, the number of degrees of freedom is substantially reduced. In terms of the turbulent RANS simulation, the RBF interpolation instead of the Galerkin projection was applied to predict the eddy viscosity in ROM since there exists plenty of turbulent models and projection of those various governing equations would be unfeasible. By this data-driven approach, only the eddy viscosity was treated in the ROM. The parametrization of the Dirichlet boundary conditions was treated by the lift function method, in which a special control function was firstly subtracted from the snapshots of velocity and temperature to yield homogenous field snapshots. After the reduced solution over the inner region was solved by the ROM, the boundary value was patched according to the specified boundary condition. The transient heat transfer behavior of coolant flow in a helical cruciform fuel bundle was tested of which the inlet velocity and temperature were treated as parameters. The results show that this ROM can achieve a speedup of 3-4 orders of magnitude compared to the FOM, and meanwhile the relative errors of the velocity, the pressure and the eddy viscosity field remain less than 10%. However, the prediction of the transient evolution of temperature filed from ROM shows a significant difference with FOM. This may be caused by the modal analysis of transient snapshots, and further investigation would be necessary.

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]

The Koiter-Newton method improves the computational efficiency of nonlinear buckling analysis; however, the construction of reduced-order models using fully nonlinear kinematics is still a tedious and time-consuming work. In this paper, the Koiter-Newton reduced-order method using mixed nonlinear kinematics is presented for the geometrically nonlinear buckling analysis of thin-walled structures. Strain energy variations up to the fourth order were achieved using mixed kinematics for the improved Koiter theory. Corotational kinematics, which is inconvenient for high-order variations, was applied to calculate the first- and second-order variations for the internal force and tangent stiffness, respectively, whereas the third- and fourth-order strain energy variations were facilitated by explicit algebraic formulations using updated von Kármán kinematics. A reduced-order model with 1+m degrees of freedom was established, of which m perturbation loads were considered to make the method applicable for buckling problems. The geometrically nonlinear response was traced using a predictor-corrector strategy by combining the nonlinear prediction solved by the reduced-order model and the correction using Newton iterations. Numerical examples of structures with various buckling behaviors demonstrate that the performance of the proposed method is not obviously affected by using simplified kinematics, and sometimes it even exhibits a superior capability for path-following analysis. [ABSTRACT FROM AUTHOR]

This study discusses a new method for the fractional-order system reduction. It offers an adaptable framework for approximating various fractional-order systems (FOSs), including commensurate and non-commensurate. The fractional-order modeling and control (FOMCON) toolbox in MATLAB and the gaze cues learning-based grey wolf optimizer (GGWO) technique form the basis of the recommended method. The fundamental advantage of the offered method is that it does not need intermediate steps, a mathematical substitution, or an operator-based approximation for the order reduction of a commensurate and non-commensurate FOS. The cost function is set up so that the sum of the integral squared differences in step responses and the root mean squared differences in Bode magnitude plots between the original FOS and the reduced models is as tiny as possible. Two case studies support the suggested method. The simulation results show that the reduced approximations constructed using the methodology under consideration have step and Bode responses more in line with the actual FOS. The effectiveness of the advocated strategy is further shown by contrasting several performance metrics with some of the contemporary approaches disseminated in academic journals. [ABSTRACT FROM AUTHOR]

This paper presents the effect of wing elasticity on the efficiency of a nonintrusive reduced order model using a three-dimensional sweptback wing. For this purpose, a computationally low-cost but highly accurate nonintrusive reduced order method is constructed utilizing proper orthogonal decomposition (POD) coupled with radial basis function (RBF) interpolation. The results are evaluated in terms of order reduction and prediction capability of rigid and aeroelastic ROMs. Our results show that compared to the rigid wing, reduced order modeling is more effectively applied to the aeroelastic sweptback wing due to the postponement of flow separation caused by bending–torsion coupling, when the pressure coefficient (Cp) is considered as the output. We further show that for flexible wings, utilizing rigid nodes is not sufficient for presenting the Cp distribution accurately; hence, separate ROMs must be generated for the deformed positions of the nodes. Moreover, the RBF method is also exploited for prediction of the results with direct interpolation of the data ensemble by generating a surrogate model. Finally, the proposed methods are compared in terms of accuracy, computational cost and practicality. [ABSTRACT FROM AUTHOR]

Copyright of Atomic Energy Science & Technology is the property of Editorial Board of Atomic Energy Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper deals with possibilities of utilizing neural networks in reduced order modelling. First section of the paper contains theory on reduced order models and their implementations. Following this, subsequent chapter contains methodology concept for obtaining sufficient amount of data and creating reduced order models as well as their evaluation process. Next section describes our findings and summarizes them. Conclusion describes further steps we plan to take in this research.

The aim of this work is to explore the effect of the double subdiffusion on the stability in BWRs. A BWR novel reduced order model with double subdiffusion effects: reduced order fractional model (DS-F-ROM) to describe the neutron and heat transfer processes was proposed for this study. The double subdiffusion was developed with a fractional-order two-equation model, and with different fractional-orders and relaxation times. The stability analysis was carried out using the root-locus method and change from the s to the W domain and were confirmed using the time-domain evolution of neutron flux for a unit step change in reactivity. The results obtained using the reduced fractional-order model are presented for different anomalous diffusion coefficient values. Results are compared with normal diffusion and P1 equations, which are obtained straightforwardly with DS-ROM when relaxation time tends to zero, and when the anomalous diffusion coefficient tends to one, respectively.

The balance between accuracy and computational complexity is currently a focal point of research in dynamical system modeling. From the perspective of model reduction, this paper addresses the mode selection strategy in Dynamic Mode Decomposition (DMD) by integrating an embedded fractal theory based on fractal dimension (FD). The existing model selection methods lack interpretability and exhibit arbitrariness in choosing mode dimension truncation levels. To address these issues, this paper analyzes the geometric features of modes for the dimensional characteristics of dynamical systems. By calculating the box counting dimension (BCD) of modes and the correlation dimension (CD) and embedding dimension (ED) of the original dynamical system, it achieves guidance on the importance ranking of modes and the truncation order of modes in DMD. To validate the practicality of this method, it is applied to the reduction applications on the reconstruction of the velocity field of cylinder wake flow and the force field of compressor blades. Theoretical results demonstrate that the proposed selection technique can effectively characterize the primary dynamic features of the original dynamical systems. By employing a loss function to measure the accuracy of the reconstruction models, the computed results show that the overall errors of the reconstruction models are below 5%. These results indicate that this method, based on fractal theory, ensures the model's accuracy and significantly reduces the complexity of subsequent computations, exhibiting strong interpretability and practicality. [ABSTRACT FROM AUTHOR]

This research delves into the numerical predictions of fill-level and residence time distribution (RTD) in starve-fed single-screw extrusion systems. Starve-feeding, predominantly used in ceramic extrusion, introduces challenges which this study seeks to address. Based on a physical industrial system, a comprehensive 3D computational fluid dynamics (CFD) model was developed using a porous media representation of the complex multi-hole plate die. Validations performed using real sensor data, accounting for partial wear on auger screw flights, show an ~11% discrepancy without accounting for screw wear and ~6% when considering it. A 2D convection-diffusion model was introduced as a dimensionality reduced order model (ROM) with the intention of bridging the gap between comprehensive CFD simulations and real-time applications. Central to this model's prediction ability was both the velocity field transfer from the CFD model and calibration of the ROM diffusion coefficient such that a precise agreement of residence time distribution (RTD) curves could be obtained. Some discrepancies between the CFD and the ROM were observed, attributed to the loss of physical information of the system when transitioning from a higher fidelity CFD model to a semi-mechanistic ROM and the inherent complexities of the starved flow in the compression zone of the extruder. This research offers a comprehensive methodology and insights into reduced order modeling of starve-fed extrusion systems, presenting opportunities for real-time optimization and enhanced process understanding. [ABSTRACT FROM AUTHOR]

Model Order Reduction (MOR) techniques have extensive applications across scientific and engineering disciplines, such as neutron field reconstruction of nuclear reactor cores, thermoelastic field reconstruction, fluid, and solid mechanics. In the process of building a Reduced Order Model (ROM), the selection of the basis functions in the offline stage is crucial and directly depends on the parameter space sampling strategy. This problem has always been a challenge in MOR. Research into adaptive sampling algorithms has become a hot topic in recent years. To better understand the application of these algorithms to MOR, this paper focuses on three prevalent adaptive sampling algorithms: pseudo-gradient sampling, adaptive sparse grid sampling, adaptive training set extension. These have been successfully applied in various applications, including nuclear reactor cores, molten salt reactor system, power system for convection problems. We systematically assess and compare their performance, finding that adaptive sampling algorithms excel in sampling divergent and oscillating areas and are generally better than the standard sampling strategy. Specifically, the pseudo-gradient sampling algorithm is effective for small-scale scenarios, while the other two algorithms are designed for large-scale sampling. Their practicality is confirmed through successful applications in nuclear reactor cores.

The boundary conditions in thermal simulation of the spindle system are very complicated and the empirically calculated ones will usually result in a significant discrepancy between experiment and simulation. Thus, the optimal boundary conditions were identified by treating it as an inverse optimization problem in this paper. Moreover, to advance the optimization efficiency, a reduced order model is established to replace the time-consuming thermal simulation of the spindle system. By superposition of truncated eigenmodes and accurately predicted modal coefficients, the reduced order model can reconstruct the field very similar to thermal simulation. Experimental reconstruction of both the temperature field and thermal deformation field by the reduced order model demonstrated its at least 360 times speedup with 99.8 % accuracy compared to the actual thermal simulation. With the accurate reduced order model as a lightweight digital twin and using the differential evolution algorithm, three types of boundary conditions, i.e., the heat generation rates, the convective heat transfer coefficients and the thermal contact resistances, under the shaft rotation speed of 4,000r/min were identified within 11s. The maximum temperature simulation error was reduced from 85.6 % to 6.6 % and the thermal deformation simulation error was reduced from 60.9 % to 10.8 %.

This paper presents a data-driven approach to maximize the power of a wind farm by developing a dynamic mode decomposition with input and output for reduced order model (DMDior)-based reduced order model (ROM) for model predictive control (MPC). The main goal of this research is to efficiently model and manage the complex flow field within a wind farm to enhance power production. We leveraged DMDior to transform extensive high-dimensional flow data into an accurate yet simplified ROM, which successfully represents the essential dynamic features of wind flow, including the critical interactions between turbines and their adaptive response to environmental changes. Based on this ROM, the MPC framework was carefully designed. MPC uses this model to dynamically adjust the yaw angle of a wind turbine to optimally match changing wind patterns to maximize power output. The system also incorporates an adaptive Kalman filter designed for the state estimation in MPC applications. This estimation is critical to the effective execution of the MPC in each iteration. This ensures that the MPC operates based on the most up-to-date and accurate representation of the wind farm’s state, improving the overall reliability and efficiency of the control strategy. This approach demonstrates a practical and effective way to increase the power output of a wind farm, with experimental results indicating a power increase of about 4.72%.

Aerodynamic interference occurs when biplane wings are placed close to each other. Investigating aerodynamic interference on the transonic flutter characteristics of these wings is an important issue. A numerical model is configured with the rigid airfoil positioned above the elastic airfoil at different positions to simulate various levels of aerodynamic interference. The flutter characteristics of the elastic airfoil are analyzed using an efficient aeroelastic analysis method based on the reduced order model. The results suggest that when the rigid airfoil is positioned directly above the elastic airfoil the aerodynamic interference accelerates the airflow on the upper surface of the elastic airfoil. This leads to a subsonic dip phenomenon, and the instability mode after the subsonic dip gradually transitions from first order to second order. Furthermore, aerodynamic interference leads to an earlier occurrence of a shock wave on the upper surface of the elastic airfoil, which causes earlier appearances of transonic dip and S-shape flutter boundary. Moreover, the S-shape flutter boundary is widened as a consequence of the interference. Remarkably, the part of the S-shape flutter boundary is solely induced by the first-order mode instability, which is different from the typical alternating instability of the first-order and second-order modes together. When the rigid airfoil is positioned diagonally above the elastic airfoil, aerodynamic interference causes a later occurrence of a shock wave on the upper surface of the elastic airfoil, which leads to later appearances of the transonic dip and S-shape flutter boundary. Additionally, the S-shape flutter boundary is widened. [ABSTRACT FROM AUTHOR]

A digital twin is a virtual model of a real-world structure (such as a device or equipment) which supports various problems or operations that occur throughout the life cycle of the structure through linkage with the actual structure. Digital twins have limitations as a general simulation method because the characteristic changes (motion, stress, vibration, etc.) that occur in the actual structure must be acquired through installed sensors. Additionally, it takes a huge computing cost to output changes in the structure's characteristics in real time. In particular, in the case of ships and offshore structures, simulation requires a lot of time and resources due to the size of the analysis model and environmental conditions where the wave load acts irregularly, so the application of a different simulation methodology from existing ones is required. The order reduction method, which accurately represents the system's characteristics and expresses them in a smaller model, can significantly reduce analysis time and is an effective option. In this study, to analyze the applicability of the order reduction method to the development of digital twins for offshore structures, the structural responses of a multi-connected floating offshore structure were estimated by applying the order reduction method based on distortion base mode. The order reduction method based on the distortion base mode predicts the responses by constructing an order-reduced conversion matrix consisting of the selected distortion base mode, based on the mode vector's orthogonality and autocorrelation coefficients. The predicted structural responses with the reduced order model (ROM) were compared with numerical analysis results derived using the higher order boundary element method and finite element method with in-house code owned by the Korea Research Institute of Ship & Ocean Engineering and measured responses with a model test. When compared with the numerical analysis results, the structural responses were predicted with high accuracy in the wave direction and wave frequency band of the selected distortion base mode, but there are differences due to changed characteristics of the structure when compared with the results of the model test. In addition, differences were also seen in reduced order model evaluation with different sensor locations, and it was confirmed that the more similar the extracted distortion base modes of input sensor location set is to the distortion base modes of predicted location set, the higher accuracy is in predicting the structural responses. As a result, the performance of the reduced order model is determined by the distortion base mode selection method, the locations of the sensor, and the prediction for the structural response. [ABSTRACT FROM AUTHOR]

The Craig–Bampton (CB) method is a well-known substructuring technique that reduces the size of a finite element model (FEM) using a set of vibration modes. For large FEA models, the reduction process could be computationally expensive since it requires algebra operations on FEM mode shapes and FEM system sparse matrices. In this paper, we investigate the potential of usage of GPU parallel processing to speed up solving the system of linear equations that results from the CB reduction process made for a model of cyclic structures. A Python based high-level approach, employing the CuPy, GinkGo and STRUMPACK libraries on the GPU, is compared with an optimized Fortran code. In side-to-side comparisons, employing the same inputs, the Python-GPU code is run on a single GPU device and the Fortran code is run on a multi-core compute node. The CB reduction process was split into several parts, each dealing with different kind of algebraic formulation of the problem. Performance comparisons were focused on the sparse system linear solver, since it turned out to be the most time-consuming part. The results suggest that the current GPU-based linear sparse solvers do not surpass the state-of-the-art CPU-based MKL PARDISO solver (at least up to 1M DOFs). [ABSTRACT FROM AUTHOR]

To enhance the computation efficiency and accuracy of three-dimensional steady temperature field of transformer windings, we propose a new non-invasive Reduced Order Model (ROM) based on a mechanism-embedded cascade network. Initially, a snapshot matrix is formed from the Full Order Model (FOM) and then combined with Proper Orthogonal Decomposition (POD) to extract key modal features that characterize the temperature field. Subsequently, a cascade network architecture, integrating Multilayer Perceptron (MLP) and Radial Basis Function Neural Network (RBFNN), is devised to swiftly map working condition parameters to modal coefficients. Additionally, the cascade network is embedded with condition sensitivity and modal contribution mechanisms to further enhance prediction accuracy. Finally, by linearly weighting the modes with predicted modal coefficients, a rapid reconstruction of the steady temperature field in transformer windings is achieved. Validation against Fluent software simulations and experimental measurements demonstrate a close agreement, with computational errors of less than 4K and an impressive single solution time of only 0.0087 s, which is 48760 times faster compared to Fluent software.

A computationally efficient two-surface plasticity model is assessed against crystal plasticity. Focus is laid on the mechanical behavior of magnesium alloys in the presence of ductility-limiting defects, such as voids. The two surfaces separately account for slip and twinning such that the constitutive formulation captures the evolving plastic anisotropy and evolving tension-compression asymmetry. For model identification, a procedure is proposed whereby the initial guess is based on a combination of experimental data and computationally intensive polycrystal calculations from the literature. In drawing direct comparisons with crystal plasticity, of which the proposed model constitutes a heuristically derived reduced-order model, the available crystal plasticity simulations are grouped in two datasets. A calibration set contains minimal data for both pristine and porous material subjected to one loading path. Then the two-surface model is assessed against a broader set of crystal plasticity simulations for voided unit cells under various stress states and two loading orientations. The assessment also includes microstructure evolution (rate of growth of porosity and void distortion). The ability of the two-surface model to capture essential features of crystal plasticity is analyzed along with an evaluation of computational cost. The prospects of using the model in guiding the development of physically sound damage models in Mg alloys are put forth in the context of high-throughput simulations.

In fast reactors, restructuring of the fuel micro-structure driven by high temperature and high temperature gradient can cause the formation of columnar grains. The non-spheroidal shape and the non-uniform temperature field in such columnar grains implies that standard models for fission gas diffusion can not be applied. To tackle this issue, we present a reduced order model for the fission gas diffusion process which is applicable in different geometries and with non-uniform temperature fields, maintaining a computational requirement in line with its application in fuel performance codes. This innovative application of reduced order models as meso-scale tools within fuel performance codes represents a first-of-a-kind achievement that can be extended beyond fission gas behaviour.

This study discusses a new method for the fractional-order system reduction. It offers an adaptable framework for approximating various fractional-order systems (FOSs), including commensurate and non-commensurate. The fractional-order modeling and control (FOMCON) toolbox in MATLAB and the gaze cues learning-based grey wolf optimizer (GGWO) technique form the basis of the recommended method. The fundamental advantage of the offered method is that it does not need intermediate steps, a mathematical substitution, or an operator-based approximation for the order reduction of a commensurate and non-commensurate FOS. The cost function is set up so that the sum of the integral squared differences in step responses and the root mean squared differences in Bode magnitude plots between the original FOS and the reduced models is as tiny as possible. Two case studies support the suggested method. The simulation results show that the reduced approximations constructed using the methodology under consideration have step and Bode responses more in line with the actual FOS. The effectiveness of the advocated strategy is further shown by contrasting several performance metrics with some of the contemporary approaches disseminated in academic journals.

This paper presents the effect of wing elasticity on the efficiency of a nonintrusive reduced order model using a three-dimensional sweptback wing. For this purpose, a computationally low-cost but highly accurate nonintrusive reduced order method is constructed utilizing proper orthogonal decomposition (POD) coupled with radial basis function (RBF) interpolation. The results are evaluated in terms of order reduction and prediction capability of rigid and aeroelastic ROMs. Our results show that compared to the rigid wing, reduced order modeling is more effectively applied to the aeroelastic sweptback wing due to the postponement of flow separation caused by bending–torsion coupling, when the pressure coefficient (Cp) is considered as the output. We further show that for flexible wings, utilizing rigid nodes is not sufficient for presenting the Cp distribution accurately; hence, separate ROMs must be generated for the deformed positions of the nodes. Moreover, the RBF method is also exploited for prediction of the results with direct interpolation of the data ensemble by generating a surrogate model. Finally, the proposed methods are compared in terms of accuracy, computational cost and practicality.

Mechanical metamaterials (MMs) are micro-structured systems that have long attracted research as well as application interests due to their exotic dynamic functionalities and properties not seen in ordinary materials. Graded MM arrays further enrich the scope of achievable dynamic behavior by employing non-periodic media. Designing such systems is particularly challenging due to the unclear design-performance relationship as well as the heavy computational burden. In this work, we aim to control the time domain response patterns of finite MM arrays and introduce a data-driven design approach that addresses the current challenges. A high-fidelity reduced order modeling (ROM) method is incorporated with statistical learning approaches to realize data generation and physics validation with minimal effort. A variational autoencoder (VAE) is trained to learn the design-performance relation and is used to retrieve classes of design configurations associated with a desired performance. An example application for impact mitigation is shown, and the designed MM arrays exhibit superior protection performance. The combined ROM-VAE approach presents a systematic toolset for designing graded MM arrays with modulated responses, capable of a broad spectrum of tasks such as fast prototyping, inverse generation, and design principle identification.

A computationally efficient two-surface plasticity model is assessed against crystal plasticity. Focus is laid on the mechanical behavior of magnesium alloys in the presence of ductility-limiting defects, such as voids. The two surfaces separately account for slip and twinning such that the constitutive formulation captures the evolving plastic anisotropy and evolving tension-compression asymmetry. For model identification, a procedure is proposed whereby the initial guess is based on a combination of experimental data and computationally intensive polycrystal calculations from the literature. In drawing direct comparisons with crystal plasticity, of which the proposed model constitutes a heuristically derived reduced-order model, the available crystal plasticity simulations are grouped in two datasets. A calibration set contains minimal data for both pristine and porous material subjected to one loading path. Then the two-surface model is assessed against a broader set of crystal plasticity simulations for voided unit cells under various stress states and two loading orientations. The assessment also includes microstructure evolution (rate of growth of porosity and void distortion). The ability of the two-surface model to capture essential features of crystal plasticity is analyzed along with an evaluation of computational cost. The prospects of using the model in guiding the development of physically sound damage models in Mg alloys are put forth in the context of high-throughput simulations. [ABSTRACT FROM AUTHOR]

There has been an extensive amount of work developing reduced-order models (ROMs) for bladed disks using single-sector models and a cyclic analysis. Several ROMs currently exist to accurately model a bladed disk with under-platform dampers. To better predict the complex nonlinear response of a system with under-platform dampers, this work demonstrates how two linear models can determine bounds for the nonlinear response. The two cases explored are where the under-platform damper is completely stuck and also where the damper slides without friction. This work utilizes the component mode mistuning method to model small mistuning and a parametric ROM method to capture changes in properties due to rotational speed effects. Previously, these ROM methodologies have modeled freestanding bladed disk systems. To evaluate the ROM in predicting the bounds, blade tip amplitudes from the models are compared with high-speed rotating experiments conducted in a large, evacuated vacuum tank. The experimental data were collected during testing using strain gauges and laser blade tip timing probes. The blade amplitudes of the tip timing data, strain gauge data, and computational simulations are compared to determine the effectiveness of the simplified linear analysis in bounding the nonlinear response of the physical system. [ABSTRACT FROM AUTHOR]

For the calculation of transient fluid–solid coupling temperature field of transformer, the traditional Galerkin finite element full order model has the defect that the calculation time is up to hours-level, which is difficult to meet the timeliness requirements of the digital twin model. Firstly, the implementation architecture of transformer digital twin based on IoT is established, and the necessity of multiphysical field simulation and model reduction technology for building the digital twin model is introduced. Then, based on the method of transformer digital twin implementation,it is proposed to combine the proper orthogonal decomposition (POD) with the finite element (FE) to establish the Galerkin FE full order model for the governing equation of the transient temperature field, the reduced order mode composed of the first several bases is intercepted to build the reduced order model of transient fluid–solid coupling temperature field. Finally, the POD reduced order model is applied to calculate the temperature rise of a transformer. According to the actual transformer temperature rise test, the temperature values of different measuring points are selected to compare the calculation error and time of the reduced order model and the full order model. The results show that the error between the third order model and full order model meets the criterion of POD truncation error, and the calculation time is shortened by 192 times, which can meet the seconds-level calculation requirements.

The balance between accuracy and computational complexity is currently a focal point of research in dynamical system modeling. From the perspective of model reduction, this paper addresses the mode selection strategy in Dynamic Mode Decomposition (DMD) by integrating an embedded fractal theory based on fractal dimension (FD). The existing model selection methods lack interpretability and exhibit arbitrariness in choosing mode dimension truncation levels. To address these issues, this paper analyzes the geometric features of modes for the dimensional characteristics of dynamical systems. By calculating the box counting dimension (BCD) of modes and the correlation dimension (CD) and embedding dimension (ED) of the original dynamical system, it achieves guidance on the importance ranking of modes and the truncation order of modes in DMD. To validate the practicality of this method, it is applied to the reduction applications on the reconstruction of the velocity field of cylinder wake flow and the force field of compressor blades. Theoretical results demonstrate that the proposed selection technique can effectively characterize the primary dynamic features of the original dynamical systems. By employing a loss function to measure the accuracy of the reconstruction models, the computed results show that the overall errors of the reconstruction models are below 5%. These results indicate that this method, based on fractal theory, ensures the model’s accuracy and significantly reduces the complexity of subsequent computations, exhibiting strong interpretability and practicality.

We present a Reduced Order Method approach to the heat exchange and loses in a simulated 3D cavity of CSP tower receivers. We validate the method in a 2D Boussinesq model problem for natural convection monitoring temperature, pressure and velocity for different values of the Rayleigh number. For the 3D problem of heat loses estimation we compute the snapshots with Ansys Fluent in a realistic model of a cavity with wind velocity and wall temperatures as varying parameters. The reduction in computational time can be up to four orders of magnitude with relative errors of 10^-5.

The estimation of fluid flows inside a centrifugal pump in realtime is a challenging task that cannot be achieved with long-established methods like CFD due to their computational demands. We use a projection-based reduced order model (ROM) instead. Based on this ROM, a realtime observer can be devised that estimates the temporally and spatially resolved velocity and pressure fields inside the pump. The entire fluid-solid domain is treated as a fluid in order to be able to consider moving rigid bodies in the reduction method. A greedy algorithm is introduced for finding suitable and as few measurement locations as possible. Robust observability is ensured with an extended Kalman filter, which is based on a time-variant observability matrix obtained from the nonlinear velocity ROM. We present the results of the velocity and pressure ROMs based on a unsteady Reynolds-averaged Navier-Stokes CFD simulation of a 2D centrifugal pump, as well as the results for the extended Kalman filter.

Graphene nanocomposites have attracted much attention in materials science due to their superior mechanical properties. It is difficult for conventional multiscale methods to provide substantial assistance to the research of such materials due to their huge computational costs. Nonuniform transformation field analysis is a very effective reduced order homogenization method for elastoplastic multiscale analysis. However, the reduced order model derived from this method has the shortcoming of low universality and high application threshold. As suggested in [19], an improved reduced order model is proposed by combining the nonuniform transformation field analysis with the k-means clustering algorithm. One can embed the required microscopic constitutive model into the reduced order homogenization framework without the need to derive a new reduced order model. Based on the cluster-based nonuniform transformation field analysis, the influence of the microscopic plastic strain field evolution on the macroscopic response of the material under consideration is revealed, while the mechanical properties of graphene nanocomposites are predicted. The numerical results show that the new reduced order model can accurately predict the macroscopic mechanical properties of composite materials, and its acceleration rate compared to the traditional finite element computations reaches103-104. [ABSTRACT FROM AUTHOR]

To analyze the complex spatiotemporal evolution law of the high-speed jet flow field in a liquid-ring pump ejector, both the classic and spectral proper orthogonal decomposition (SPOD) methods were introduced to decompose the transient flow field based on the numerical large eddy simulation. The proper orthogonal decomposition (POD) reduced order model (ROM) of the complex flow in the ejector was established to analyze the transient characteristics and reconstruct the flow field. The spatial mode characteristics of density, pressure and vorticity field, and the frequency domain characteristics of mode coefficients were analyzed. The results show that the spatiotemporal decoupling analysis of a high-speed jet flow field can be accomplished by the POD and SPOD methods. A large-scale symmetric coherent structure is formed in the shear layer of the first two modes of vorticity, and a small-scale antisymmetric structure is formed at the trailing edge of the jet flow for the third and fourth modes. This reflects the evolutionary characteristics of the jet shear vortex. There is a significant spatial correlation between the density and pressure modes, reflecting that the evolution of the two structures has important correlation characteristics. The spectral analysis of the mode coefficients shows that the dominant frequencies of 1250 Hz and 18 kHz correspond to the self-excited oscillation frequency of shock waves and the vortex shedding frequency. The POD-ROM can reconstruct the high-speed flow field of the ejector with enough accuracy using the first 30-order modes, and the root mean square error and mean absolute percentage error for the velocity prediction are 0.48% and 0.24%, respectively.

The cost of obtaining a large amount of flow field information by traditional experiment or CFD is unacceptable,so it is of significance to develop faster forecasting calculation methods.Proper orthogonal decomposition(POD)is used to extract the dominant mode of the tandem flow field.Radial basis function network(RBFN)is used to respond to the coefficients of the POD basis functions to realize the construction of the reduced-order prediction model of the flow field.Then the adaptive sampling method is developed for the reduced order model.The prediction model is verified by the unsteady flow field data of a cascade.It is concluded that the hybrid method can be utilized to accurately predict the aerodynamics parameters and flow field of tandem cascade.Compared with static sampling,the number of samples required for adaptive sampling to achieve the same reconstruction accuracy is reduced by about 25%.

The incompressible Navier-Stokes equation can be used for modeling and simulation of fluid flow. One of the important mathematical models for simulating the pollution in the urban street canyons is the pollutant transition equation (PTE) which it is obtained from the incompressible Navier-Stokes equation. The current paper is devoted to propose a new meshless numerical procedure e.g. gradient smoothing method (GSM). First, the time derivative is approximated by the finite difference scheme. Then, the space derivative is discretized by the gradient smoothing method. Also, the proper orthogonal decomposition (POD) approach is utilized to reduce the used CPU time. Several examples with real world application are solved to verify the efficiency of the developed numerical procedure. [ABSTRACT FROM AUTHOR]

The present study is devoted to the computational homogenization of woven composites by using a reduced order model, called the cluster-based nonuniform transformation field analysis (CNTFA). The CNTFA is newly reformulated by taking into account anisotropic properties of phases. The nonlinear effective behavior of woven composite is directly derived from the given constitutive relation of each phases in the local material coordinates. The number of required integration points in representative volume element (RVE) is reasonably reduced by using data compression technology based on clustering of RVE. Also, the numerical procedure to perform the proposed method within ABAQUS framework is described in detail. Numerical examples show that the proposed method is very useful to predict not only the macroscopic behavior of woven composites, but also microscopic stress/strain distribution in RVE. The proposed method would be applied to any composite with nonlinear anisotropic phases. [ABSTRACT FROM AUTHOR]

Major concerns of carbon dioxide (CO2) sequestration in subsurface formations are knowledge of the well injectivity and gas storage capacity of the formation, the CO2 pressure and saturation plume extensions during and after injection, and the risks associated with CO2 leakage and fault reactivation. Saline reservoirs are considered as one of the target formations for CO2 sequestration through structural, residual, dissolution, and mineral trapping mechanisms. The boundary condition of the saline reservoir dictates the pressure and saturation plume extension of the injected supercritical CO2 that could expand over large distances. This can lead to sources of risk, e.g., leakage and/or fault reactivation due to presence of wells, thief zones, and geological discontinuities. Therefore, there is a critical need to develop a model that describes how risk-related performance metrics (i.e., the CO2 saturation plume size, the pressure differential plume area, and the pressure differential at specific locations) vary as a function of the size of injection, time following injection, injection operations, and geologic environment. In this study, a systematic reservoir modeling studies of anthropogenic CO2 sequestration in Citronelle dome, Alabama, was performed where all relevant scenarios and conditions to address the questions of the saturation and pressure plume size in the area of review (AoR) and post-injection site care (PISC) are considered. The objective for this study was firstly to systematically simulate CO2 sequestration, i.e., saturation dynamics, and pressure behavior over a range of operational and geological conditions and to derive conclusions about the factors influencing saturation and pressure plume size, post-injection behavior, and the risk associated with them, by developing third-generation reduced order models (ROMs) for reservoir behavior. Finally, to assess the uncertainty associated with our studies, Latin Hypercube Sampling (LHS) together with an experimental design technique, i.e., Plackett–Burman design, was used. Application of Pareto charts and respond surfaces enabled us to determine the most important parameters impacting saturation and pressure plume sizes and to quantify the auto- and cross-correlation among different parameters in both history-matched and upscaled models. [ABSTRACT FROM AUTHOR]

A digital twin is a virtual model of a real-world structure (such as a device or equipment) which supports various problems or operations that occur throughout the life cycle of the structure through linkage with the actual structure. Digital twins have limitations as a general simulation method because the characteristic changes (motion, stress, vibration, etc.) that occur in the actual structure must be acquired through installed sensors. Additionally, it takes a huge computing cost to output changes in the structure’s characteristics in real time. In particular, in the case of ships and offshore structures, simulation requires a lot of time and resources due to the size of the analysis model and environmental conditions where the wave load acts irregularly, so the application of a different simulation methodology from existing ones is required. The order reduction method, which accurately represents the system’s characteristics and expresses them in a smaller model, can significantly reduce analysis time and is an effective option. In this study, to analyze the applicability of the order reduction method to the development of digital twins for offshore structures, the structural responses of a multi-connected floating offshore structure were estimated by applying the order reduction method based on distortion base mode. The order reduction method based on the distortion base mode predicts the responses by constructing an order-reduced conversion matrix consisting of the selected distortion base mode, based on the mode vector’s orthogonality and autocorrelation coefficients. The predicted structural responses with the reduced order model (ROM) were compared with numerical analysis results derived using the higher order boundary element method and finite element method with in-house code owned by the Korea Research Institute of Ship & Ocean Engineering and measured responses with a model test. When compared with the numerical analysis results, the structural responses were predicted with high accuracy in the wave direction and wave frequency band of the selected distortion base mode, but there are differences due to changed characteristics of the structure when compared with the results of the model test. In addition, differences were also seen in reduced order model evaluation with different sensor locations, and it was confirmed that the more similar the extracted distortion base modes of input sensor location set is to the distortion base modes of predicted location set, the higher accuracy is in predicting the structural responses. As a result, the performance of the reduced order model is determined by the distortion base mode selection method, the locations of the sensor, and the prediction for the structural response.

Induction machines are a crucial type of electrical equipment utilized as motors in various industries and single-phase forms in household applications. They make up more than 80% of the industrial motors used today. This paper presents a dynamic simulation of three-phase induction machines based on the (d-q) model, providing a clear and easy-to-understand explanation of the behavior of the induction motor in the synchronous reference frame. The simulation is implemented using SIMULINK/MATLAB software, and full-order model analysis is conducted for transient analysis. However, modeling induction machines as part of power system analysis can be done with a less detailed model than the full-order one. In this paper, a reduced-order model is employed to simulate the induction motor using MATLAB/SIMULINK. The results of the reduced-order system and the full-order framework are compared to investigate the model's limits, and the computational benefits of saving time during large power system simulations justify the relative decrease in accuracy. The use of a reduced-order model results in a significant reduction in computation time when simulating large and very large-scale power systems, with a much higher accuracy in transient analysis than the conventional steady-state model.

Application of machine learning is currently one of the hottest topics in the fluid mechanics field. While machine learning seems to have a great possibility, its limitations should also be clarified. In our research group, we have started a research project to construct a nonlinear feature extraction method by applying machine learning techniques to big data of fluid flow, i.e., extracting the low-dimensional nonlinear modes essential to the unsteady flow phenomena and deriving the governing equations for such low-dimensionalized dynamics. This self-review article is a focused but extended version of the keynote lecture given by the author at the 7th International Conference on Jets, Wakes and Separated Flows (ICJWSF2022). We will first introduce the use of a convolutional neural network (CNN) to learn the temporal evolution of cross-sectional velocity field in a turbulent channel flow. Subsequently, we also consider an application of CNN for extraction of low-dimensional dynamics for flow around a bluff body accompanying vortex shedding and our preliminary attempt to use the extracted low-dimensional dynamics for an advanced design of flow control.

• The flutter of drag reduction spike is dominated by a single bending mode. • The parameterized reduced structural equation contains structural parameters explicitly. • Effects of structural mass, damping and stiffness are investigated by eigenvalue analyses. • Better understanding of effects of structural parameters by the energy method. Attaching a spike to the blunt nose of a vehicle is one of the simplest ways to reduce drag in supersonic and hypersonic conditions. However, the spike can encounter aeroelastic instability which remains a challenging topic and limits applications in practical engineering. Computational fluid dynamics/computational structural dynamics coupling method is used and the results show the spike can experience flutter at low structural stiffness ratios and the flutter is dominated by a single mode. To evaluate the effects of structural parameters efficiently, this paper proposes a parameterized eigenvalue method by deriving the parameterized reduced structural equation which is coupled with an aerodynamic reduced order model. Results show both the critical flutter frequency and the critical natural frequency decrease with the increase of structural damping ratio and the flutter frequency is close to the natural frequency only for large mass ratios. It is found that the critical flutter frequency does not change with the mass ratio for zero structural damping, but this is not true for non-zero structural damping. This paper also proposes an energy method based on the work-energy principle and the aerodynamic frequency response function. The energy method can also obtain the critical flutter frequency and can explain how the structural parameters influence the flutter characteristics. [ABSTRACT FROM AUTHOR]

• The flutter mechanism of the "diamond-back" folding wing under supersonic inflow is investigated. • The characteristics of the flutter boundary of the "diamond-back" folding wing with Mach number and swept-back angle are studied. • The flutter evolution mechanism is analyzed by using the characteristics of aerodynamic and flow field, instability characteristics of system dynamics, and characteristics of structural natural mode. • The "jump" phenomenon on the flutter boundary is found and analyzed in detail. Folding wings with adjustable geometry offer a viable solution for vehicles to adapt to complex and variable flight environments, while enhancing aerodynamic performance. This paper investigates the flutter mechanism and characteristics of the "diamond-back" folding wing under supersonic inflow by a ROM-based aeroelastic method. The evolution mechanism is analyzed by the characteristics of aerodynamic and flow field, system dynamics, and structural natural mode. The findings reveal that, firstly, as the Mach number increases, the flutter critical speed monotonically increases, while the flutter critical frequency exhibits fluctuations within a specific range. Secondly, the study reveals a pivotal transformation in the modal shapes at a 35° swept-back angle that reshapes the system dynamics, transitioning from second and third-order coupled instability to first and second-order coupled instability. Consequently, this nonlinear change significantly amplifies the flutter critical speed and reduces the flutter critical frequency. Lastly, the combined effect of Mach number and swept-back angle significantly influences the local flutter boundary. Under low supersonic speeds and large swept-back angles, a bow shock forms in the local flow field region, resulting in notable changes in pressure distribution. As the Mach number increases, the local flutter boundary exhibits a nonlinear trend of first increasing, then decreasing, and then increasing again. Conversely, as the swept-back angle increases, it demonstrates a nonlinear trend of first decreasing, then increasing. These insights provide valuable guidance for the aerodynamic and structural refinement of "diamond-back" folding wings, catering to sophisticated flight dynamics and environmental adaptability. [ABSTRACT FROM AUTHOR]

Fast simulation for stratified indoor airflow distributions is desired for various applications, such as design of advanced indoor environments, emergency management, and coupled annual energy simulation for buildings with stratified air distributions. Reduced order models trained by pre-computed computational fluid dynamics results are fast, but their prediction may be inaccurate when applied for conditions outside the training domain. To overcome this limitation, we propose a fast and self-learning model based on an in situ adaptive tabulation (ISAT) algorithm, which is trained by a fast fluid dynamics (FFD) model as an example. The idea is that the ISAT will retrieve the solutions from an existing data set if the estimated prediction error is within a pre-defined tolerance. Otherwise, the ISAT will execute the FFD simulation, which is accelerated by running in parallel on a graphics processing unit, for a full-scale simulation. This paper systematically investigates the feasibility of the ISAT for indoor airflow simulations by presenting the ISAT-FFD implementation alongside results related to its overall performance. Using a stratified indoor airflow as an example, we evaluated how the training time of ISAT was impacted by four factors (training methods, error tolerances, number of inputs, and number of outputs). Then we demonstrated that a trained ISAT model can predict the key information for inputs both inside and outside the training domain. The ISAT was able to answer query points both inside and close to training domain using retrieve actions within a time less than 0.001 s for each query. Finally, we provided suggestions for using the ISAT for building applications.