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This paper develops a line-search algorithm that uses objective function models with tunable accuracy to solve smooth optimization problems with convex constraints. The evaluation of objective function and its gradient is potentially computationally expensive, but it is assumed that one can construct effective, computationally inexpensive models. This paper specifies how these models can be used to generate new iterates. At each iteration, the model has to satisfy function error and relative gradient error tolerances determined by the algorithm based on its progress. Moreover, a bound for the model error is used to explore regions where the model is sufficiently accurate. The algorithm has the same first-order global convergence properties as standard line-search methods, but only uses the models and the model error bounds. The algorithm is applied to problems where the evaluation of the objective requires the solution of a large-scale system of nonlinear equations. The models are constructed from reduced order models of this system. Numerical results for partial differential equation constrained optimization problems show the benefits of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Highlights During the manufacturing of thermoset‐based carbon fiber‐reinforced polymer (CFRP) structures, a curing process involving thermal, chemical, and mechanical interactions occurs. This process gives rise to micro‐scale residual stresses due to differences in fiber and resin properties, leading to decreased mechanical properties compared to nominal values. A trans‐scale analysis method utilizing the reduced order model (ROM) is applied in this study to establish a connection between the manufacturing and in‐service processes for unidirectional CFRP (UD‐CFRP). By employing this method, the evolution of residual stresses at the micro‐scale during UD‐CFRP manufacturing is predicted, and the impact of these residual stresses on structural performance during service is assessed. Specifically, the manufacturing‐induced residual stresses reduce the material strength by a minimum of 19.31%, while also exploring the correlation between macro‐scale and micro‐scale failures. Notably, the computational cost of this method is significantly lower, with a reduction factor of 103 compared to the finite element method. Empirical evidence supports the effectiveness of this method in accurately predicting outcomes throughout both the manufacturing and in‐service processes. Trans‐scale analysis method links composites manufacturing simulation to in‐service performance. Highly efficient trans‐scale method excels in cost, accuracy, consistency, and convergence. Residual stresses from the curing process significantly impact matrix safety. [ABSTRACT FROM AUTHOR]

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.)

Due to the inherent unpredictability of marine trial conditions, safety issues in the launching and recovery process are commonplace. For these issues, digital twin (DT) maintenance offers a novel idea. In this paper, a blended-wing-body underwater glider skeleton is selected as a research object. And a simple demo is created to investigate the major technologies that may be involved in DT maintenance. According to this specimen, the necessary development environments are developed to obtain physical information and produce a DT model in cyberspace respectively. An attitude sensor is used as the physical data collector, while real-time structural field prediction and virtual reality visualisation are employed. By using the attitude angles and structural data, it is possible to achieve real-time monitoring of the skeleton strength. Through the means of this straightforward case study, the key technologies are supported and can be applied to far more complex inquiries. [ABSTRACT FROM AUTHOR]

The parameterization method has demonstrated remarkable efficacy in the construction of reduced order models for nonlinear dynamical systems, which are mostly applied to depict the dynamics near a fixed point or a forced periodic solution perturbed from it. In this paper, we develop a method based on direct linear algebra to construct reduced order models around the limit cycles of high dimensional autonomous self-excited nonlinear systems. In particular, Taylor–Fourier series is adopted to parameterize the invariant manifold around a periodic solution of the self-excited systems. The basic theory and derivation of equations are presented in terms of matrices and Kronecker product, which benefits computer implementation and enhances computational efficiency. Two approaches to solve co-homological equations based on Floquet normal form and direct linear algebra are introduced and compared. The method based on Floquet normal form proves to be impossible to be applied in the high dimensional cases due to the extensive computing consumption. To facilitating the implementation, an iterative formula for the series expansion of generic nonlinear functions by composition of elementary function is also proposed. The reduced order models of a self-excited wing model, a rotor-stator rubbing model and a FEM rotor model are constructed. It is shown that the proposed approaches are valuable in predicting responses of high-dimensional self-excited nonlinear systems and can greatly reduce the computational costs. [ABSTRACT FROM AUTHOR]

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 paper introduces a tunable design for an electrically actuated vibrating ring micro-gyroscope. This mechanism contains eight piezoelectric micro-beams attached to the vibrating ring in each drive and sense directions. Employing a full geometric non-linear model for the vibrating ring and accounting for the micro-beam's mid-plane stretching; the mathematical model associated with the present system is obtained. Afterward, utilizing the Hamilton principle together with the Ritz method, the reduced equations of motion are derived. The present results are validated by those available in the literature for simpler systems. A three-dimensional (3D) finite element (FE) simulation was carried out in COMSOL Multiphysics commercial software for the case of static deformation since dynamic simulation imposes great computational costs. Next, in-depth parametric studies emphasizing the effect of piezoelectric actuation are conducted. Finally, reporting guidelines for tuning the present vibrating ring micro-gyroscope, the advantages of the proposed design are addressed. [ABSTRACT FROM AUTHOR]

In this paper we carry out an error analysis for a reduced order method for the Allen-Cahn equation. First, an ensemble of snapshots is formed from the numerical solutions at some time instances of the full order model, which is a time-space discretisation of the Allen-Cahn equation. The reduced order model is essentially a new spatial discretisation method by using low dimensional approximations to the original approximation space. The low dimensional approximation space is generated from the ensemble of snapshots by applying a proper orthogonal decomposition method. To determine the error between the exact solution and the solution of the reduced order model. We consider a time-space discretisation for which an error estimate of the full model solution is available. Specifically, the full discretisation is based on a stabilized auxiliary variable approach for the time stepping and a spectral Galerkin method for the spatial discretisation. The advantages of this full discretisation are its unconditional stability, the availability of error estimates and its ease of implementation. An estimate of the errors in the H 1 seminorm is rigorously derived for both the full order model and the reduced order model, which is then verified by some numerical examples. [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]

Electrostatically actuated MEMS plate devices have many potential applications as micro-actuators and highly sensitive sensors. Bistability may occur in microplate devices and it refers to two stable configurations for a single value of actuating load. In this work, bistable behaviour of initially curved rectangular microplates, under the electrostatic and mechanical load actuation, has been investigated. In which detail investigation of bistability in load-deflection equilibrium paths and their associated characteristics, and later, resonance frequency behaviour in bistable regions have been carried out. For this, the governing differential equations of an initially curved rectangular plate have been developed using Kirchhoff's plate theory, including von Karman nonlinearity. Then, Galerkin's principle has been used to develop reduced order model of the governing partial differential equation of motion. To validate the results of reduced order model, we have carried out finite element analysis using a software COMSOL Multiphysics. We have observed qualitatively distinct behaviour in bistability characteristics of electrostatically and mechanically actuated microplates. We have also observed high sensitivity near bistability points and these points can be tuned by varying device parameters. This investigation could potentially help design bistable MEMS devices. [ABSTRACT FROM AUTHOR]

A data-driven reduced order model (ROM) based on a proper orthogonal decomposition-radial basis function (POD-RBF) approach is adopted in this paper for the analysis of blood flow dynamics in a patient-specific case of atrial fibrillation (AF). The full order model (FOM) is represented by incompressible Navier–Stokes equations, discretized with a finite volume (FV) approach. Both the Newtonian and the Casson's constitutive laws are employed. The aim is to build a computational tool able to efficiently and accurately reconstruct the patterns of relevant hemodynamics indices related to the stasis of the blood in a physical parametrization framework including the cardiac output in the Newtonian case and also the plasma viscosity and the hematocrit in the non-Newtonian one. Many FOM-ROM comparisons are shown to analyze the performance of our approach as regards errors and computational speed-up. [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]

Combining the accurate physical description of high‐fidelity mechanical formulations with the practical versatility of low‐order discrete models is a fundamental and open‐ended topic in structural dynamics. Finding a well‐balanced compromise between the opposite requirements of representativeness and synthesis is a delicate and challenging task. The paper systematizes a consistent methodological strategy to identify a physics‐based reduced‐order model (ROM) preserving the physical accuracy of large‐sized models with distributed parameters (REM), without resorting to classical techniques of dimensionality reduction. The leading idea is, first, to select a limited configurational set of representative degrees of freedom contributing significantly to the dynamic response (model reduction) and, second, to address an inverse indeterminate eigenproblem to identify the matrices governing the linear equations of undamped motion (structural identification). The physical representativeness of the identified model is guaranteed by imposing the exact coincidence of a selectable subset of natural frequencies and modes (partial isospectrality). The inverse eigenproblem is solved analytically and parametrically, since its indeterminacy can be circumvented by selecting the lumped mass matrix as the primary unknown and the stiffness matrix as a parameter (or vice versa). Therefore, explicit formulas are provided for the mass matrix of the ROM having the desired low dimension and possessing the selected partial isospectrality with the REM. Minor adjustments are also outlined to remove a posteriori unphysical effects, such as defects in the matrix symmetry, which are intrinsic consequences of the algebraic identification procedure. The direct and inverse eigenproblem solutions are explored through parametric analyses concerning a multistory frame, by adopting a high‐fidelity Finite Element model as REM and an Equivalent Frame model as ROM. Before mass matrix identification, modal analysis results indicate a general tendency of ROM to underestimate natural frequencies, with the underestimation strongly depending on the actual mass distribution of the structure. After the identification of the mass matrix and the elimination of unphysical defects, isospectrality is successfully achieved. Finally, extensions to prototypical highly massive masonry buildings are presented. The qualitative and quantitative discussion of the results under variation of the significant mechanical parameters provides useful insights to recognize the validity limits of the approximations affecting low‐order models with lumped parameters. [ABSTRACT FROM AUTHOR]

The research introduces an innovative method for creating a digital twin (DT) of heat energy storage and retrieval system (HESRS) for real-time monitoring and performance analysis. The HESRS, type of HVAC system, is evaluated based on parameters like stored heat energy, heat extraction via heat transfer fluid (HTF), and Phase Change Material (PCM) temperatures. Data from temperature sensors is sent to the cloud in real-time. A reduced-order model (ROM) analyses it on the cloud and sends results to an Android app. The DT is then simulated in augmented reality through our app, Twin-X, marking distinctive approach to digital twin development. [ABSTRACT FROM AUTHOR]

This article proposes a novel hybrid technique of order abatement for large-scale models that combines the Mihailov stability method (MSM) and the stability equation method (SEM). In this approach, the denominator coefficients of the higher-order system (HOS) are estimated using the MSM, while the numerator coefficients are computed using the SEM. The suggested approach is based on the MSM, which guarantees the stability of the estimated model if the actual model is stable. The MSM also makes sure that important factors of the original plant, such as dominant poles and stability, are retained in the reduced order system (ROS). The suggested approach is compared to several current conventional reduction methods using error indicators, and the smallest performance error indices values reflect the supremacy of the method. The transfer function (TF) of the ROS is then used to design controllers by employing the moment matching technique. When the controller designed with the approximated model is applied to the real HOS, it indicates that the response of the closed-loop system of the real model entirely overlaps with the response of the reference plant. To further demonstrate the efficiency of the proposed schemes, time-domain specifications are produced and time responses are plotted. [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.)

Copyright of Electric Machines & Control / Dianji Yu Kongzhi Xuebao is the property of Electric Machines & Control 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]

AbstractConcurrent multiscale damage analysis is still a challenge in woven composite structural level due to its extremely high computational cost. In this paper, a novel efficient concurrent multiscale framework for woven composite structures is proposed based on data-driven reduced order model, and the multiscale damage behavior of 4-H satin weave carbon/carbon composites is investigated using this framework. The elastic properties of yarn are predicted using the information from fibers and matrix. The mesoscale anisotropic damage behaviors of the open hole plate under uniaxial tension are simulated using this framework. The simulation results have good agreement with the experiment. [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]

The electronic wedge brake (EWB) uses self-reinforcement principles to optimise stopping power, but its mathematical model has various actuation angles and system dynamics making controller design complex and computationally burdensome. Therefore, the model order reduction (MOR) is made based on three factors that may have a negligible influence on the EWB system: the motor inductance, lead screw axial damping, and wedge mass. Six reduced order model (ROM) types were proposed when one, two, or all factors were ignored. The ROM accuracy was analysed using the frequency and time domain. The percentage of root means square error (RMSE) response value between the EWB benchmark model, and the predicted response based on the ROM was found to be less than 2%, with ROM size reduced from 5 to 2 orders. It guarantees that the new ROM series will be useful for simpler EWB controller design. The proposed ROM simplifies the original model drastically while retaining accuracy at an adequate level. Even though the simplest EWB model is a 2nd order linear system, the best ROM vary depending on EWB design parameters. [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]

Gas bearings use pressurized gas as a lubricant to support and guide rotating machinery. These bearings have a number of advantages over traditional lubricated bearings, including higher efficiency in a variety of applications and reduced maintenance requirements. However, they are more complex to operate and exhibit nonlinear behaviors. This paper presents a parametric hyper reduced order model (h-ROM) of a gas bearings supported rotor enabling to speed up the computations up to a factor 100 while preserving satisfactory accuracy. A Galerkin projection setting is employed to reduce the dimension of the governing equations and the nonlinear terms are efficiently tackled with a sparse sampling technique. The performances of the h-ROM are compared to a high fidelity model both in terms of accuracy and computation time, demonstrating the potential for future anomaly detection applications. [ABSTRACT FROM AUTHOR]

This work investigates linear and non-linear parametric reduced order models (ROM) capable of replacing computationally expensive high-fidelity simulations of human body models (HBM) through a non-intrusive approach. Conventional crash simulation methods pose a computational barrier that restricts profound analyses such as uncertainty quantification, sensitivity analysis, or optimization studies. The non-intrusive framework couples dimensionality reduction techniques with machine learning-based surrogate models that yield a fast responding data-driven black-box model. A comparative study is made between linear and non-linear dimensionality reduction techniques. Both techniques report speed-ups of a few orders of magnitude with an accurate generalization of the design space. These accelerations make ROMs a valuable tool for engineers. [ABSTRACT FROM AUTHOR]

Kinetic transport equations are notoriously difficult to simulate because of their complex multiscale behaviors and the need to numerically resolve a high-dimensional probability density function. Past literature has focused on building reduced order models (ROM) by analytical methods. In recent years, there has been a surge of interest in developing ROM using data-driven or computational tools that offer more applicability and flexibility. This paper is a work toward that direction. Motivated by our previous work of designing ROM for the stationary radiative transfer equation in [Z. Peng, Y. Chen, Y. Cheng, and F. Li, J. Sci. Comput., 91 (2022), pp. 1--27] by leveraging the low-rank structure of the solution manifold induced by the angular variable, we here further advance the methodology to the time-dependent model. Particularly, we take the celebrated reduced basis method (RBM) approach and propose a novel micro-macro decomposed RBM (MMD-RBM). The MMD-RBM is constructed by exploiting, in a greedy fashion, the low-rank structures of both the micro- and macro-solution manifolds with respect to the angular and temporal variables. Our reduced order surrogate consists of reduced bases for reduced order subspaces and a reduced quadrature rule in the angular space. The proposed MMD-RBM features several structure-preserving components: (1) an equilibrium-respecting strategy to construct reduced order subspaces which better utilize the structure of the decomposed system, and (2) a recipe for preserving positivity of the quadrature weights thus to maintain the stability of the underlying reduced solver. The resulting ROM can be used to achieve a fast online solve for the angular flux in angular directions outside the training set and for arbitrary order moment of the angular flux. We perform benchmark test problems in 2D2V, and the numerical tests show that the MMD-RBM can capture the low-rank structure effectively when it exists. A careful study in the computational cost shows that the offline stage of the MMD-RBM is more efficient than the proper orthogonal decomposition method, and in the low-rank case, it even outperforms a standard full-order solve. Therefore, the proposed MMD-RBM can be seen both as a surrogate builder and a low-rank solver at the same time. Furthermore, it can be readily incorporated into multiquery scenarios to accelerate problems arising from uncertainty quantification, control, inverse problems, and optimization. [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]

Miniaturized microelectromechanical system (MEMS) microspeakers are currently trending in the development of acoustic transducers. When a transducer is scaled down to fit on a microelectronic chip, its physics differ from the macroscopic world, and some common modeling assumptions become invalid. One of the effects observed in MEMS microspeakers is nonlinear squeeze film damping. Understanding this effect is crucial, as non-linearities in the speaker can result in perceptible harmonic distortions, which are undesirable in audio applications. In this study, we analyze the influence of squeeze film damping on harmonic distortions using a lumped parameter model of a MEMS microspeaker. This leads to a nonlinear ordinary differential equation, and an approximate analytical solution for moderate non-linearities is obtained using homotopy. We present our solution strategy, including the resulting closed-form expression, and verify our findings against numerical solutions. [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.