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A Resonance calculation using energy Spectrum Expansion (RSE) method is newly proposed in this paper. In this method, ultra-fine-group (UFG) spectra appearing in a resonance calculation are expanded by orthogonal bases on energy, which are extracted from the UFG spectra obtained in homogeneous geometry with various background cross sections using singular value decomposition and low-rank approximation. Namely, this method is based on the concept of a reduced order model. A neutron transport equation for flux moments (expansion coefficients) similar to the conventional one is derived and is numerically solved. This method applies to two benchmark problems in which a resonance interference effect and spatial self-shielding effect can appear. The results indicate that this method accurately predicts the reference effective cross sections and reaction rates obtained from direct UFG calculation in heterogeneous geometry. [ABSTRACT FROM AUTHOR]

The reservoir model of the actual oil field usually needs to be divided into hundreds of thousands or millions of grids, so it will be very time-consuming to simulate with traditional reservoir simulators. Moreover, it will also lead to an increase in the computational cost of production optimization and history matching in closed-loop reservoir management. How to greatly increase the speed of reservoir simulation calculation is an urgent problem to be solved. At present, the POD reduced-order model is widely used to increase the speed of numerical simulation, but the accuracy of the method depends on the reasonableness of the model input parameters. When the production system of the training process and the prediction process are quite different, it will produce large errors. In order to overcome this shortcoming, in this paper, a numerical simulation method based on a two-step POD reduced order model is proposed. The full-order simulator is used for data training, and the matrix composed of the state variables of each production system is operated by POD respectively, and the base matrix is obtained. Then, the matrix composed of all the base matrices is subjected to POD operation again, and the final reduced-order base matrix is obtained. Numerical experiment results show that under the condition of ensuring sufficient accuracy, the two-step POD method can reduce the dimensionality of the reservoir model of the example, which will increase the calculation speed of the simulator by nearly 3 times. The two-step POD method has higher accuracy than the conventional POD method. Therefore, the effectiveness of this method has been verified. [ABSTRACT FROM AUTHOR]

This paper integrates nonlinear-manifold reduced order models (NM-ROMs) with domain decomposition (DD). NM-ROMs approximate the full order model (FOM) state in a nonlinear-manifold by training a shallow, sparse autoencoder using FOM snapshot data. These NM-ROMs can be advantageous over linear-subspace ROMs (LS-ROMs) for problems with slowly decaying Kolmogorov n -width. However, the number of NM-ROM parameters that need to be trained scales with the size of the FOM. Moreover, for "extreme-scale" problems, the storage of high-dimensional FOM snapshots alone can make ROM training expensive. To alleviate the training cost, this paper applies DD to the FOM, computes NM-ROMs on each subdomain, and couples them to obtain a global NM-ROM. This approach has several advantages: Subdomain NM-ROMs can be trained in parallel, involve fewer parameters to be trained than global NM-ROMs, require smaller subdomain FOM dimensional training data, and can be tailored to subdomain-specific features of the FOM. The shallow, sparse architecture of the autoencoder used in each subdomain NM-ROM allows application of hyper-reduction (HR), reducing the complexity caused by nonlinearity and yielding computational speedup of the NM-ROM. This paper provides the first application of NM-ROM (with HR) to a DD problem. In particular, this paper details an algebraic DD reformulation of the FOM, training a NM-ROM with HR for each subdomain, and a sequential quadratic programming (SQP) solver to evaluate the coupled global NM-ROM. Theoretical convergence results for the SQP method and a priori and a posteriori error estimates for the DD NM-ROM with HR are provided. The proposed DD NM-ROM with HR approach is numerically compared to a DD LS-ROM with HR on the 2D steady-state Burgers' equation, showing an order of magnitude improvement in accuracy of the proposed DD NM-ROM over the DD LS-ROM. [ABSTRACT FROM AUTHOR]

This paper studies the flutter control of a three-dimensional wing using a nonlinear energy sink (NES), which has a purely cubic stiffness and a linear damper. The structural model is derived by Lagrange's equations and the aerodynamics is modeled using the auto regressive with exogenous input method. Both models are solved in a tightly coupling manner to obtain time domain results. Then, the structural describing function and the aerodynamic continuous-time state space model are used to derive the equivalent linearized aeroelastic system, so that eigenvalue analyses can be used to obtain stable and unstable limit cycle oscillations (LCOs). The LCOs obtained by time domain simulations agree well with the equivalent linearization method, while differences are observed for aperiodic motions which are only predicted in time domain for small damping coefficients. Results show the square of aeroelastic amplitude is inversely proportional to the NES stiffness coefficient for both periodic and aperiodic motions. The NES can induce LCOs below flutter speed for small damping coefficients, indicating a subcritical bifurcation which can change to a supercritical one by increasing the damping coefficient. It is discovered that the upper bound of partial suppression region is quantified by a turning point speed. The regions of complete suppression, partial suppression and no suppression are clarified. • The proposed methodology can obtain periodic solutions of there-dimensional nonlinear aeroelastic systems. • Equivalent linearization method is compared with the time domain method. • The NES can reduce aeroelastic stability boundary for small damping coefficients. • There exists a turning point speed, above which the NES fails to control flutter. • Parameter study is performed and the control strategy is suggested. [ABSTRACT FROM AUTHOR]

Virtual testing and hybrid simulation have become an important trend in airplane design and validation. The traditional Testing Pyramid (or Building Block) approaches that emphasis on uniaxial coupon test and full structure certification test are being challenged. Researchers are trying to use advanced testing and simulation methods to replace the Testing Pyramid approach.

This paper presents an effective procedure for model order reduction of discrete time control system. The exact model derived from complex dynamic systems proves to be very complicated for analysis, control and design. This necessity brings about using a tool known as model order reduction technique or model simplification. A novel mixed method has been implemented in this paper for reducing the order of the large scale dynamic discrete system. Dominant pole based pole clustering method has been used to derive the coefficients of denominator polynomial while Padé approximation has been applied to obtain the coefficients of numerator polynomial of the reduced order model. The proposed method is quite simple and able to generate a stable reduced order model from high order stable discrete systems. The dominancy of poles has been decided by values of the ratio of residue to its pole. The pole is considered dominant which have larger ratio value. An illustrative example has been considered to show the various reduction steps. The result obtained confirms the effectiveness of the approach.

Due to the accelerated growth in the field of power electronics and controller design techniques, the usage of the active magnetic bearing has picked up in industries. Active magnetic bearing helps the rotor to rotate freely without any physical contact. In brief, this paper develops a model of an active magnetic bearing using the finite element method, and its associated reduced order model, followed by the development of a robust control strategy. COMSOL software is used to perform three-dimensional simulation of an active magnetic bearing system. The state space system matrices are extracted from the finite element method, and a linear time-invariant state-space system is generated in MATLAB. Since the original system is large, the reduced order model is constructed. Then, based upon the reduced order model, a sliding mode control is designed to improve the regulation performance of an active magnetic bearing under unmodeled uncertainties. The stability analysis of closed-loop reduced order model with unmodeled uncertainties guarantees the finite time convergence of system states using Lyapunov theory. Further, it is proved that the same control law will also provide satisfactory performance for the original model using the reduced order model as an observer. The numerical simulation is carried out to illustrate the effective performance of the proposed controller for the reduced model as well as the original model with multiple initial conditions. The proposed work offers an alternative approach of using the reduced order model instead of the original model for the controller design of an active magnetic bearing.

In this article, an improved reduced order modelling approach, based on the proper orthogonal decomposition (POD) method, is presented. After projecting the governing equations of flow dynamics along the POD modes, a dynamical system was obtained. Normally, the classical reduced order models do not predict accurate time variations of flow variables due to some reasons. The response of the dynamical system was improved using a calibration method based on a least-square optimization process. The calibration polynomial can be assumed as the pressure correction term which is vanished in projecting the Navier-Stokes equations along the POD modes. The above least- square procedure is a combination of POD method and the solution of an optimization problem. The obtained model can predict accurate time variations of flow field with high speed. For long time periods, the calibration term can be computed using a combined form of POD and Fourier modes. This extension is a totally new extension to this procedure which has recently been proposed by the authors. The results obtained from the calibrated reduced order model show close agreements to the benchmark DNS data, proving high accuracy of our model.

Because the coatings are likely to produce new mistuning which aggravates the vibration failure of coated blades, it is particularly important to study the mistuning identification for coated blades. In this study, the degrees of freedom of the whole disk of the coated blisk is completely constrained, and the orders of the dynamic model of the coated blisk based on component mode mistuning (CMM) method is further reduced. Based on this model, a novel mistuning identification method for the coated blade of the coated blisk by small amount of experimental data is proposed, which can identify the mass, stiffness and damping mistuning of the blade substrates and coatings. The input parameters with high amount of data, such as modal shape matrix, are removed from identification formulas, thus, both the amount of data for identification calculation and the workload of vibration testing are reduced. The mistuning identifications of the numerical case and actual case are carried out respectively, and the identification process of the mistuning identification method in this paper is compared with the one based on the classical CMM model. It is shown that the mistuning identification method is effective and feasible, and the identification efficiency is higher than the classical CMM identification method. [ABSTRACT FROM AUTHOR]

The moduli and loss factors of viscoelastic materials are frequency-dependent, which brings difficulty to solve the eigenvalue problems. In this note, an estimation method for resonance frequencies and loss factors of viscoelastic composite structures from reduced order models is presented. The reduced order model could be constructed from calculated or measured forced vibration data, and there is no need to know the specific structural matrices or to solve the eigenvalue problem of the vibration system directly. Thus, the difficulties caused by frequency-dependent behaviors of moduli and loss factors of viscoelastic materials are avoided. Numerical examples are presented to illustrate and validate the method. [ABSTRACT FROM AUTHOR]

A three-dimensional model of a single-layer lithium-ion pouch cell is presented which couples conventional porous electrode theory describing cell electrochemical behavior with an energy balance describing cell thermal behavior. Asymptotic analysis of the model is carried out by exploiting the small aspect ratio typical of pouch cell designs. The analysis reveals the scaling that results in a distinguished limit and highlights the role played by the electrical conductivities of the current collectors. The resulting model comprises a collection of one-dimensional models for the through-cell electrochemical behavior which are coupled via two-dimensional problems for the Ohmic and thermal behavior in the planar current collectors. A further limit is identified which reduces the problem to a single volume-averaged through-cell model, greatly reducing the computational complexity. Numerical simulations are presented which illustrate and validate the asymptotic results. [ABSTRACT FROM AUTHOR]

The identification of hidden conducting permeable objects from measurements of the perturbed magnetic field taken over a range of low frequencies is important in metal detection. Applications include identifying threat items in security screening at transport hubs, location of unexploded ordnance, and antipersonnel landmines in areas of former conflict, searching for items of archeological significance and recycling of valuable metals. The solution of the inverse problem, or more generally locating and classifying objects, has attracted considerable attention recently using polarizability tensors. The magnetic polarizability tensor (MPT) provides a characterization of a conducting permeable object using a small number of coefficients, has an explicit formula for the calculation of their coefficients, and a well understood frequency behavior, which we call its spectral signature. However, to compute such signatures, and build a library of them for object classification, requires the repeated solution of a transmission problem, which is typically accomplished approximately using a finite element discretization. To reduce the computational cost, we propose an efficient reduced order model (ROM) that further reduces the problem using a proper orthogonal decomposition for the rapid computation of MPT spectral signatures. Our ROM benefits from a posteriori error estimates of the accuracy of the predicted MPT coefficients with respect to those obtained with finite element solutions. These estimates can be computed cheaply during the online stage of the ROM allowing the ROM prediction to be certified. To further increase the efficiency of the computation of the MPT spectral signature, we provide scaling results, which enable an immediate calculation of the signature under changes in the object size or conductivity. We illustrate our approach by application to a range of homogenous and inhomogeneous conducting permeable objects. [ABSTRACT FROM AUTHOR]

In the present work, multiple non existing model order reduction (MOR) techniques for unstable second‐order form systems (SOSs) are proposed. For unstable SOSs, continuous‐time algebraic Lyapunov equations get unsolvable that halt the reduction process. To avoid this problem, unstable SOS is first decomposed into stable and unstable portions and balanced truncation is applied to the stable part. The obtained reduced order model (ROM) for the stable portion is augmented with the unstable portion to obtain the overall reduced system. It is observed that the second‐order structure in ROM for the first technique gets lost as well as augmented unstable dynamics degrade the ROM performance. To cater to these constraints, two structure‐preserving second‐order balanced truncation techniques for unstable SOSs are proposed in second part. System is first stabilized using the Bernoulli feedback stabilization procedure and then gramians are computed for the stabilized system. Further, gramians are partitioned into position and velocity portions to achieve structure preservation in ROM and balanced truncation is applied. As second technique retains second‐order structure as well as involves stabilized system dynamics, this technique far closely approximates original system behavior. Proposed techniques are tested on multiple systems and results certify the correct development of proposed techniques that can be utilized for MOR applications of unstable SOSs. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

The dynamic stall at high angle of attack is an important aerodynamic problem faced by aircraft, and it has always been a hotspot of aerodynamic research. The traditional reduced order model (ROM) methods needs to establish an accurate model, and has a high demand for experience. In this paper, a novel nonlinear aerodynamic identification method based on recurrent neural networks (RNNs) is proposed. The computational fluid dynamics (CFD) method is used to calculate the unsteady aerodynamic parameters of the NACA0012 airfoil. A group of sinusoidal chirp signals with variable amplitude and frequency are adopted as the excitation signals, and the obtained data are used to train the recurrent neural networks, and the ROM of the nonlinear aerodynamic model of high angle of attack dynamic stall is obtained. Finally, the aerodynamic parameters of a group of composite sinusoidal motion signals different from the training signals are predicted by the trained neural networks model and compared with the CFD results. [ABSTRACT FROM AUTHOR]

In this paper, we propose a model for the transverse oscillation of a square-section cylinder under flow. The fluctuating transverse force due to vortex shedding is represented using a coupled nonlinear wake oscillator, while the unsteady force for galloping caused by the varying incidence angle effects is modelled using the quasi-steady approach. First, we analytically investigate the lift behavior and phase angle variation of the square cylinder under forced vibrations. Comparison with experimental data is used to determine the form of the coupling terms and its values. The present model shows advantages in predicting the phase angle, and it successfully captures the change in sign of the phase. Second, the proposed model is directly applied in predicting free oscillation cases without any tuning. The dynamical behaviors predicted by this model are compared with published experiments under different Scruton numbers, and reasonable agreement can be found. The results indicate that the model can not only be applied in simulating the "pure galloping" and "pure VIV," but also is able to capture the interactions of VIV and galloping, including combined and separate VIV-galloping motions. [ABSTRACT FROM AUTHOR]

The paper is concerned with simulation of the periodontal ligament response to force in the initial phase of orthodontic tooth movement. This is based on two previous investigations, a in vitro experiment with specimens of porcine mandibular premolars and a in vivo experiment on human upper first incisors. For the curve fit of the in vitro experiment a model function, assuming viscoelasticity, was introduced. The viscoelastic model function was augmented by a ramp rise time term, to account for observed dependence of the response on actuator velocity, and a previous load history term, to account for the effect of the previous tests on the current test. The correlation coefficient of a curve fit for all tests grouped together was R 2 = 0.98. Next, a curve fit of the in vivo experiment was done. Good correlation was found for a simplified model function, without viscoelastic term ( R 2 = 0.96 ). For both tests, in vitro and in vivo, the ramp rise time term improved correlation. A finite element model of the specimen of the in vitro experiment was created. For the PDL a hyperelastic constitutive model for compressible material was used and model parameters were identified. The present work indicates that the macroscopic response of the periodontal ligament to an external load can be simulated with a poro-visco-hyperelastic model. The simulation showed that poroelastic behaviour will gradually cease when viscoelastic relaxation progresses. This followed also from dimensionless analysis. As a consequence, for slow loading, or if initial response to fast loading is not of interest, a visco-hyperelastic model may suffice. To identify parameters of the finite element model several optimisation problems were solved. A model function, which can be regarded as a reduced order model, allowed a full factorial experiment (analysis) at low cost, to identify initial parameters. The thus found parameters were further refined with an optimum interpolation meta-model. That is, for limited number of parameter combinations the response was simulated with the finite element model and a refined parameter study was conducted by means of optimal interpolation. The thus found optimal parameters were verified by simulation with the finite element model. Optimal interpolation is computationally cheap, which allowed full factorial experiments at low cost. [ABSTRACT FROM AUTHOR]

We present a hybrid, semi-analytical approach to perform an eigenvalue-based flutter analysis of an Unmanned Aerial Vehicle (UAV) wing. The wing has a modern design that integrates metal and composite structures. The stiffness and natural frequency of the wing are calculated using a Finite Element (FE) model. The modal parameters are extracted by applying a recursive technique to the Lanczos method in the FE model. Subsequently, the modal parameters are used to evaluate the flutter boundaries in an analytical model based on the p-method. Two-degree-of-freedom bending and torsional flutter equations derived using Lagrange's principle are transformed into an eigenvalue problem. The eigenvalue framework is used to evaluate the stability characteristics of the wing under various flight conditions. An extension of this eigenvalue framework is applied to determine the stability boundaries and corresponding critical flutter parameters at a range of altitudes. The stability characteristics and critical flutter speeds are also evaluated through computational analysis of a reduced-order model of the wing in NX Nastran using the k- and pk-methods. The results of the analytical and computational methods are found to show good agreement with each other. A parametric study is also carried out to analyse the effects of the structural member thickness on the wing flutter speeds. The results suggest that changing the spar thickness contributes most significantly to the flutter speeds, whereas increasing the rib thickness decreases the flutter speed at high thickness values. [ABSTRACT FROM AUTHOR]

The majority of the most common physical phenomena can be described using partial differential equations (PDEs). However, they are very often characterized by strong nonlinearities. Such features lead to the coexistence of multiple solutions studied by the bifurcation theory. Unfortunately, in practical scenarios, one has to exploit numerical methods to compute the solutions of systems of PDEs, even if the classical techniques are usually able to compute only a single solution for any value of a parameter when more branches exist. In this work, we implemented an elaborated deflated continuation method that relies on the spectral element method (SEM) and on the reduced basis (RB) one to efficiently compute bifurcation diagrams with more parameters and more bifurcation points. The deflated continuation method can be obtained combining the classical continuation method and the deflation one: the former is used to entirely track each known branch of the diagram, while the latter is exploited to discover the new ones. Finally, when more than one parameter is considered, the efficiency of the computation is ensured by the fact that the diagrams can be computed during the online phase while, during the offline one, one only has to compute one-dimensional diagrams. In this work, after a more detailed description of the method, we will show the results that can be obtained using it to compute a bifurcation diagram associated with a problem governed by the Navier-Stokes equations. [ABSTRACT FROM AUTHOR]

Predicting airbag deployment geometries is an important task for airbag and vehicle designers to meet safety standards based on biomechanical injury risk functions. This prediction is also an extraordinarily complex problem given the number of disciplines and their interactions. State-of-the-art airbag deployment geometry simulations (including time history) entail large, computationally expensive numerical methods such as finite element analysis (FEA) and computational fluid dynamics (CFD), among others. This complexity results in exceptionally large simulation times, making thorough exploration of the design space prohibitive. This paper proposes new parametric simulation models which drastically accelerate airbag deployment geometry predictions while maintaining the accuracy of the airbag deployment geometry at reasonable levels; these models, called herein machine learning (ML)-accelerated models, blend physical system modes with data-driven techniques to accomplish fast predictions within a design space defined by airbag and impactor parameters. These ML-accelerated models are evaluated with virtual test cases of increasing complexity: from airbag deployments against a locked deformable obstacle to airbag deployments against free rigid obstacles; the dimension of the tested design spaces is up to six variables. ML training times are documented for completeness; thus, airbag design explorers or optimization engineers can assess the full budget for ML-accelerated approaches including training. In these test cases, the ML-accelerated simulation models run three orders of magnitude faster than the high-fidelity multi-physics methods, while accuracies are kept within reasonable levels within the design space.

This paper investigates the seismic design of fluid viscous dampers connecting adjacent structural systems. A simplified dampers design strategy is proposed, which relies on a linearized reduced order model of the coupled system. A stochastic linearization technique is adopted with the aim of extending the design method to non-linear viscous dampers. The effectiveness of the design method and of the coupling strategy are assessed via numerical analysis of two adjacent buildings with shear-type behavior connected by linear or non-linear viscous dampers and subjected to Gaussian stochastic base acceleration. Different dampers locations are analyzed. The accuracy of the reduced order model is assessed, by comparing the relevant response statistics to those provided by a refined multi degree of freedoms model. Finally, a parametric study is performed to assess the effectiveness of dissipative connection for different values of seismic intensity and dampers parameters (i.e., viscous coefficients and velocity exponents).

Background: Atrial fibrillation is a prevalent cardiac arrhythmia and may reduce cerebral blood perfusion augmenting the risk of dementia. We hypothesize that geometric variations in the cerebral arterial structure called the Circle of Willis (CoW) play an important role in influencing cerebral perfusion. The objective of this work was to develop a novel cardio-cerebral lumped parameter hemodynamic model to investigate the role of CoW variants on cerebral blood flow dynamics under atrial fibrillation conditions. Methods: A computational blood flow model was developed by coupling whole-body and detailed cerebral circulation descriptions, modified to represent six common variations of the CoW. Cerebral blood flow dynamics were simulated in common CoW variants, under control and imposed atrial fibrillation conditions. Risk was assessed based on the frequency of beat-wise hypoperfusion events, and sensitivity analysis was performed with respect to this model output. Results: It was found that the geometry of the CoW influenced the frequency of hypoperfusion events at different heart rates, with the variant missing a P1 segment having the highest risk. Sensitivity analysis revealed that intrinsic heart rate is most associated with the considered outcome. Conclusions: Our results suggest that CoW geometry plays an important role in influencing cerebral hemodynamics during atrial fibrillation. The presented study may assist in guiding our future clinical-imaging research.

The time cost is very high by direct fluid-structure interaction method for mistuned bladed disk structures, so aerodynamic loads generally are ignored or treated as small perturbations in traditional flutter analysis. In order to analyze the flutter characteristics of mistuned blade rapidly and accurately, this paper presents an efficient fluid-structure interaction method based on aerodynamic reduced order model. system identification technology and two basic assumptions are used to build the unsteady aerodynamic reduced order model. Coupled the structural equations and the aerodynamic model in the state space, the flutter stability of mistuned bladed disk can be obtained by changing the structural parameters. For the STCF 4 example, the response calculated by this method agrees well with the results obtained by the direct CFD, but the computational efficiency is improved by nearly two orders of magnitude. This method is used to study the stiffness mistuned cascade system, and the stability characteristics of the system are obtained by calculating the eigenvalues of the aeroelastic matrix. The results show that the stiffness mistuning can significantly improve the flutter stability of the system, and also lead to the localization of the mode. The mistuning mode, mistuning amplitude and fluid structure interaction can influence the flutter stability obviously.

A novel reduced order model (ROM) for unsteady hypersonic aerodynamics is developed, which is applicable for the variations of multi-parameters. The key to the developed ROM lies in the CFD-based model reduction of the steady aerodynamic component, which stems from the quasi-steady nature of aerodynamic forces in the hypersonic regime. Concretely, the proper orthogonal decomposition (POD) method, combined with Kriging interpolation, is used to construct the ROM for the steady aerodynamic component; meanwhile the unsteady part is directly obtained from Donov’s third-order piston theory. The new procedure is applied to a three-dimensional low aspect ratio wing (Lockheed F-104 Starfighter wing). It is shown that the developed ROM is able to accurately predict the unsteady hypersonic aerodynamic loads over a wide range of different flight conditions compared with the direct CFD computation.

This paper revisits oblique wave and streamwise vortex scenarios in a plane Couette flow using restricted nonlinear simulations, where only a single Fourier mode for perturbation is retained. It is shown that this restriction of full dynamics gives a good approximation of the two subcritical paths. In particular, critical energy thresholds and edge states compare favorably with results obtained using direct numerical simulations by Duguet etal. [ABSTRACT FROM AUTHOR]

A study of dynamics of a waveboard is presented. The equations of motion are derived and analysed to understand the intriguing propulsion mechanism. A reduced order model is obtained, and the contributions of different terms are clearly brought out. The geometry of the castor wheels is found to play a key role in the conversion of the twisting oscillatory motion of the rider to the forward translational motion. The process of periodic gain in potential energy and its subsequent conversion to kinetic energy aids the propulsion. Interestingly, the dynamic analysis reveals that the efficacy of this propulsion mechanism tapers off as the speed increases. Rolling resistance in the wheels ultimately limits the speed of the device. The effect of various geometric and dynamic parameters on the motion and forces are studied, and optimality of design is indicated. [ABSTRACT FROM AUTHOR]

This article introduces an equivalent multiple dq-frame model of the modular multilevel converter (MMC) that is derived from a dynamic phasor based small-signal state-space MMC model in the stationary αβ z frame. When compared to a model in the stationary ABC frame, the order of the model in the αβ z frame can be reduced for balanced operation, during which some voltage, and current harmonics are inherently separated in an αβ z representation. The proposed method enables further model order reduction through a generalized transformation towards multiple dq-frames. The development of the model, and the generalized transformation are explained in detail, and the obtained equivalent multiple dq-frame models are verified against a nonlinear averaged model in MATLAB/Simulink. An eigenvalue-based small-signal stability analysis highlights the effect of higher-order harmonics in system-level small-signal stability studies, and two case studies of active harmonic suppression illustrate how the presented model allows an in-depth investigation of the impact of extended control functionalities on the small-signal stability. [ABSTRACT FROM AUTHOR]

Although computational power is increasingly available, high-fidelity simulation based aerodynamic shape optimization is still challenging for industrial applications. To make the simulation based optimization acceptable in the practice of engineering design, a technique combining mesh morphing and reduced order modeling is proposed for efficient aerodynamic optimization based on CFD simulations. The former technique avoids the time-consuming procedure of geometry discretization. And the latter speeds up the procedure of field solution by exploiting pre-computed solution snapshots. To test the efficiency of the proposed method, the windshield of a motorbike is analyzed and optimized. It is shown that even the total number of cells of the mesh is around 0.4 million, the CFD computation and the post-processing of the results can be completed in less than 10 s if the reduced order model is adopted. Running on a personal computer, the generic algorithm is applied to optimize the profile of the windshield. A 8% reduction of the drag coefficient is achieved after 800 queries of the reduced order CFD model and the total CPU time is only around 2 h. [ABSTRACT FROM AUTHOR]

This article deals with damage computation of heterogeneous structures containing locally periodic micro-structures. Such heterogeneous structure is extremely expensive to simulate using classical finite element methods, as the level of discretisation required to capture the micro-structural effects is too fine. The simulation time becomes even higher when dealing with highly non-linear material behaviour, e.g. damage, plasticity and such others. Therefore, a multi-scale strategy is proposed here that facilitates the simulation of non-linear heterogeneous material behaviour in a manner that is computationally feasible. Based on the asymptotic homogenisation theory, this multi-scale technique explores the micro–macro behaviour for elasto-(visco)plasticity coupled with damage. The theory inherently segregates the heterogeneous continua into a macroscopic homogeneous structure and an underlying heterogeneous microscopic periodic unit cell. Several heterogeneous structures have been simulated using the multi-scale method along with a one-dimensional verification with respect to a reference solution. Additionally, a reduced order modelling is used to prevent large memory requirement for storing micro-structural quantities of interest. [ABSTRACT FROM AUTHOR]

This paper presents a Volterra series reduced-order model method to evaluate aerodynamic forces of aircraft engine blade designs, whose shape changes during design and are always excited by upstream wakes. The method uses a superposition of the steady and dynamic Volterra series to reach this aim. The steady series represents the influence of the blade shape changes on the blade aerodynamic forces. The dynamic series represents the impact of the unsteady upstream wakes on the blade aerodynamic forces. A T106LPT blade is used as an example to discuss the proposed method. The accuracy of the ROM method is analyzed by the example at the wake excitation condition with or without shape-change. The example shows that the ROM method can predict the wake induced pressure variation of a shape-change blade without repeated computational fluid dynamics (CFD) analyses. [ABSTRACT FROM AUTHOR]

Summary: The design of a new magnetic resonance imaging (MRI) scanner requires multiple numerical simulations of the same magneto‐mechanical problem for varying model parameters, such as frequency and electric conductivity, in order to ensure that the vibrations, noise, and heat dissipation are minimized. The high computational cost required for these repeated simulations leads to a bottleneck in the design process due to an increased design time and, thus, a higher cost. To alleviate these issues, the application of reduced order modeling techniques, which are able to find a general solution to high‐dimensional parametric problems in a very efficient manner, is considered. Building on the established proper orthogonal decomposition technique available in the literature, the main novelty of this work is an efficient implementation for the solution of 3D magneto‐mechanical problems in the context of challenging MRI configurations. This methodology provides a general solution for varying parameters of interest. The accuracy and efficiency of the method are proven by applying it to challenging MRI configurations and comparing with the full‐order solution. [ABSTRACT FROM AUTHOR]

Summary: Multiquery problems such as uncertainty quantification (UQ), optimization of a dynamical system require solving a differential equation at multiple parameter values. Therefore, for large systems, the computational cost becomes prohibitive. This issue can be addressed by using a cheaper reduced order model (ROM) instead. However, the ROM entails error in the solution due to approximation in a lower dimensional subspace. Moreover, the ROM lacks robustness over a wide range of parameter values. To address these issues, first, an upper bound on the norm of the state transition matrix is derived. This bound, along with the residual in the governing equation, are then used to develop an error estimator for general nonlinear dynamical systems. Furthermore, this error estimator is used in conjunction with the modified greedy search algorithm proposed by Hossain and Ghosh (Int J Numer Methods Eng, 2018;116(12‐13): 741‐758) to adaptively construct a robust proper orthogonal decomposition‐based ROM. This adaptive ROM is subsequently deployed for UQ by invoking it in a statistical simulation. Two numerical studies: (i) viscous Burgers' equation and (ii) beam on nonlinear Winkler foundation, showed an improved accuracy of the error estimator compared to the current literature. A significant computational speed‐up in UQ is achieved. [ABSTRACT FROM AUTHOR]

In this paper, we present a new reduced order model based on radial basis functions (RBFs) and proper orthogonal decomposition (POD) methods for fractional advection-diffusion equations with a Caputo fractional derivative in time. In the proposed scheme, the number of basis functions in the usual RBFs method reduces by the POD technique. Therefore, the computational cost of the RBF-POD method decreases in comparison with usual RBFs method, while the accuracy completely maintains. In the sequel, we provide a complete error analysis in the L 2 norm between the exact solution and the RBFs solution, as well as between the exact solution and the proposed RBF-POD model by using the properties of the native space and projection operators. Also, the obtained error estimation is used to choose the number of POD bases for constructing the RBF-POD model with the required accuracy. Numerical examples are given to confirm the accuracy and efficiency of the proposed scheme. [ABSTRACT FROM AUTHOR]

Summary: A reduced order model designed by means of a variational multiscale stabilized formulation has been applied successfully to fluid‐structure interaction problems in a strongly coupled partitioned solution scheme. Details of the formulation and the implementation both for the interaction problem and for the reduced models, for both the off‐line and on‐line phases, are shown. Results are obtained for cases in which both domains are reduced at the same time. Numerical results are presented for a semistationary and a fully transient case. [ABSTRACT FROM AUTHOR]

A predictor–corrector reduced-order modeling method based on Koiter theory is proposed for nonlinear buckling analysis of thin-walled structures with initial geometric imperfections. The imperfections are implemented into the von Kármán kinematics and are considered using an a priori and a posteriori manners, respectively, in buckling analysis. Since the nonlinear predictor obtained from the reduced order model with imperfections provides a fairly large step size in path-tracing, the a priori account of imperfections still shows advantages in computational efficiency. The advantages are more significant when considering a posteriori the effects of imperfections in the reduced order model of the structure without imperfections, which means building once and for all, by simply adding some independent imperfection terms in the reduced system. The a posteriori accounts of imperfections with the first/second-order accuracies, are developed, respectively, to deal with the linear/nonlinear prebuckling behaviors and small/large imperfection amplitudes. The good performance of the proposed method in terms of reliability, accuracy and computational effort is demonstrated with several examples using the linear buckling modes or measured geometric shapes as whole-field geometric imperfections. • The initial geometric imperfection is applied into reduced-order modeling method. • A priori account of imperfections is also very computationally efficient. • A posteriori account of imperfections with first/second-order accuracy is developed. • The proposed method can be used for small/large imperfection amplitudes. [ABSTRACT FROM AUTHOR]

Summary: Defects such as gas pores can be formed and trapped in the fusion zone during laser welding. These defects can significantly affect the mechanical reliability of the welded joint. Current nondestructive inspection technologies are able to detect micro‐voids in a mass production context. Finite element analysis can therefore be used to assess the lifetime of an observed component via image‐based modeling. Unfortunately, running a simulation per component entails a huge and generally unaffordable computational cost. In addition, voids do not admit a parametric modeling. In this paper, a numerical method is proposed to study the impact of defects on the mechanical response of a welded joint. It is based on model order reduction techniques that decrease the computational cost of each simulation related to an image‐based modeling. To tackle the reduction of nonparametric defects, a multiscale construction of the reduced basis is proposed, although no scale separation is assumed when computing the mechanical response of the structure. Some empirical modes are representing the structure behavior and other empirical modes are related to the defect‐induced local fluctuations. They are then assembled to simulate a defective joint. Assets and limitations of the proposed method are explored through a simplified two‐dimensional (2D) problem. For the sake of reproducibility, this 2D problem is fully parametric. Finally, a realistic three‐dimensional (3D) industrial case is presented, where voids geometries have been measured via computed tomography. This 3D problem being nonparametric, fluctuation modes must be computed on the fly, once the computed tomography has been performed. [ABSTRACT FROM AUTHOR]

Markov chain Monte Carlo (MCMC) methods have become standard in Bayesian inference and multi‐observable inversions in almost every discipline of the Earth sciences. In the case of geodynamic and/or coupled geophysical‐geodynamic inverse problems, however, the computational cost associated with the solution of large‐scale 3‐D Stokes forward problems has rendered probabilistic formulations impractical. Here we present a novel and extremely efficient method to produce ultrafast solutions of the 3‐D Stokes problem for MCMC simulations. Our approach combines the individual benefits of Reduced Basis techniques, goal‐oriented error formulations, and MCMC algorithms to produce an accurate and computationally efficient surrogate for the forward problem. Importantly, the surrogate adapts itself during the MCMC simulation according to the history of the chain and the goals of the inversion. This maximizes the efficiency of the forward problem and removes the need for preinversion off‐line computations to build a surrogate. We demonstrate the benefits and limitations of the method with several numerical examples and show that in all cases the computational cost is of the order of <1% compared to a traditional MCMC approach. The method is general enough to be applied to a range of problems, including uncertainty quantification/propagation, adjoint‐based geodynamic inversions, sensitivity analyses in mantle convection problems, and in the creating surrogate models for complex forward problems (e.g., heat transfer, seismic tomography, and magnetotellurics). Key Points: An efficient method for producing ultrafast solutions of the 3‐D Stokes problem for mantle convection is presentedThis method is particularly well suited for joint geodynamic‐geophysical probabilistic inverse problems and studies of dynamic topographyThe method is suitable to tackle a range of probabilistic inverse problems where fast solutions for a complex forward problem are needed [ABSTRACT FROM AUTHOR]

This paper investigates the recently introduced data-driven correction reduced order model (DDC-ROM) in the numerical simulation of the quasi-geostrophic equations. The DDC-ROM uses available data to model the correction term that is generally used to represent the missing information in low-dimensional ROMs. Physical constraints are added to the DDC-ROM to create the constrained data-driven correction reduced order model (CDDC-ROM) in order to further improve its accuracy and stability. Finally, the DDC-ROM and CDDC-ROM are tested on time intervals that are longer than the time interval over which they were trained. The numerical investigation shows that, for low-dimensional ROMs, both the DDC-ROM and CDDC-ROM perform better than the standard Galerkin ROM (G-ROM) and the CDDC-ROM provides the best results. [ABSTRACT FROM AUTHOR]

In this paper, the application of passive vibrational linear absorber on the indirect reduction of blade vibrations using its mounted on the disk-blade system is studied. The absorber receives the vibration energy of blade through a structural coupling of the disk with blade and losses it by its linear damping. Due to cyclic symmetry, the analysis of the bladed disk is reduced to the number of DOFs in a single sector. A cyclic transformation from physical to modal coordinates is used to perform this reduction. Natural frequencies and forced responses of the system are obtained by solving the characteristic and algebraic equations, respectively. The case study of a steam turbine includes 259 blades in 37 packets of 7 connected blades attached to the perimeter of the disk. Cyclic symmetric finite element analysis at 3000rpm is used to extract the natural modes and frequency diagram of the system. A two DOFs reduced-order model is identified for modeling the frequency-veering region. This region has been formed between the first and second families of natural modes and there is a strong coupling between them in this region. In addition, this region is close to the system excitation line and the possibility of resonance exists. Therefore, some linear energy absorbers are mounted on the disk for the indirect vibration reduction of blades. The initial optimal parameters were determined for the first and second modes using Den Hartog relations. These parameters reduced the system vibrations and they were used in subsequent optimization. The optimization has resulted in the improvement of absorber performance exclusively around the second mode, in compare with the tuned system by Den Hartog relations. [ABSTRACT FROM AUTHOR]

Thin-walled structures are widely used in aeronautical and aerospace engineering. Conical and cylindrical shells structures, under axial compression, are prone to failure by buckling and typically show a snap-back phenomenon in the end-shortening curve. Path-following technologies based on Newton-type methods have difficulties to trace reliably the snap-back response due to the extremely sharp turning angle near the limit point. In this paper, a Koiter's reduction finite element method, termed the Koiter–Newton (KN) method, is presented to trace reliably the post-buckling path of cylinders and cones considering either linear buckling modes or dimples from lateral perturbation loads as geometric imperfection. A robust algorithm based on the bifurcation-detection technique is applied during the solution of the reduced order model to achieve a successful path-tracing. The numerical results presented reveal that the nonlinear prediction obtained from Koiter's perturbation theory at the unloaded state of the structure is numerically accurate up to the buckling load and the initial post-buckling path. [ABSTRACT FROM AUTHOR]

• Model reduction of second-order systems with nonlinear frequency dependent damping proposed. • Proposed method enables fast frequency sweep of such systems. • Ideally suited for systems with large sparse matrices. • More accurate than the popular modal projection based multi-model method. Frequency domain solution of systems with frequency dependent damping is a computationally expensive endeavour especially when dealing with large order three-dimensional systems. A moment-matching based reduced order model is proposed in this work which is capable of handling nonlinear frequency dependent damping in second-order systems. In the proposed approach, local linear systems with frequency independent matrices are derived from the original system, and using the principles of the Rational Krylov approach, orthogonal basis vectors are computed from these local systems through the second-order Arnoldi procedure. The system is then projected on to the basis set to obtain a numerically efficient reduced order model, accurate in the entire frequency domain of interest. The proposed approach is also shown to be more accurate than the popular modal projection based multi-model approach of the same order. The proposed tool is applied to the problem of determining the frequency response of an idealised centrifugal compressor impeller with non-viscous (frequency dependent) damping. [ABSTRACT FROM AUTHOR]

Reduced-order models (ROM) of structurally dominated fluid flows have significant applications in science and engineering, such as design, control, and optimization. Proper-orthogonal decomposition (POD) modes are often computed from the flow field data and is one of the most successful ROM strategies. However, its application to turbulent flows remains a challenging task. For laminar flows, higher modes are often discarded in the development of ROM to obtain the computational advantage over the full-order simulation. Although these higher modes contain relatively lower energy than the first few modes, they are responsible for viscous dissipation. For turbulent flows, the viscous effects are modeled in a ROM framework through linear and nonlinear closure modeling techniques. This study presents a computationally efficient nonlinear closure model which is based on a dynamical system approach. We consider 3D flow field around a cylinder at Reynolds number of 1000 with turbulent wake. We compute the POD modes and develop a conventional ROM. We then add a closure term analogous to the large-eddy simulation approach. The key contribution is the application of proposed closure for turbulent flows. Numerical results demonstrate that the proposed model is computationally efficient as compared to other nonlinear closure models while maintaining the same order of accuracy. [ABSTRACT FROM AUTHOR]