Order Reduction Method Research Articles

Model Order Reduction for Delayed PEEC Models With Guaranteed Accuracy and Observed Stability

In this work, a stable and accurate model order reduction method for large-scale partial element equivalent circuit (PEEC) models with many delays is proposed. The method reduces the dimension of the original model by interpolating the original transfer function. The interpolation points are iteratively selected using a greedy algorithm. An efficient error estimator for the reduced transfer function makes the greedy algorithm very successful in both, properly selecting the interpolation points and tightly measuring the error of the reduced transfer function. The resulting reduced-order model is accurate both in the frequency and in the time domain. Numerical tests have shown that the reduced-order model successfully filters the instability behavior of the original model and exhibits stability over a large time interval.

A physics and data co-driven surrogate modeling approach for temperature field prediction on irregular geometric domain

In the whole aircraft structural optimization loop, thermal analysis plays a very important role. But it faces a severe computational burden when directly applying traditional numerical analysis tools, especially when each optimization involves repetitive parameter modification and thermal analysis. Recently, with the fast development of deep learning, several Convolutional Neural Network (CNN) surrogate models have been introduced to overcome this obstacle. However, for temperature field prediction on irregular geometric domains (TFP-IGD), CNN can hardly be competent since most of them stem from processing for regular images. To alleviate this difficulty, we propose a novel physics and data co-driven surrogate modeling method. First, after adapting the Bezier curve in geometric parameterization, a body-fitted coordinate mapping is introduced to generate coordinate transforms between the irregular physical plane and regular computational plane. Second, a physics-driven CNN surrogate with partial differential equation (PDE) residuals as a loss function is utilized for fast meshing (meshing surrogate); then, we present a data-driven surrogate model based on the multi-level reduced-order method, aiming to learn solutions of temperature field in the above regular computational plane (thermal surrogate). Finally, combining the grid position information provided by the meshing surrogate with the scalar temperature field information provided by the thermal surrogate (combined model), we reach an end-to-end surrogate model from geometric parameters to temperature field prediction on an irregular geometric domain. Numerical results demonstrate that our method can significantly improve accuracy prediction on a smaller dataset while reducing the training time when compared with other CNN methods.

A fast two-phase non-isothermal reduced-order model for accelerating PEM fuel cell design development

A reduced-order model (ROM) is developed for proton exchange membrane fuel cells (PEMFCs) considering the non-isothermal two-phase effects, with the goal of enhancing computational efficiency and thus accelerating fuel cell design development. Using analytical order reduction and approximation methods, the fluxes and source terms in conventional 1D conservation equations are reduced to six computing nodes at the interfaces between each cell component. The errors associated with order reduction are minimized by introducing new approximation methods for the potential distribution, the transport properties, and the membrane hydration status. The trade-off between model accuracy and computational efficiency is studied by comparing the simulation results and computational times of the new model with a full 1D model. The new model is nearly two orders of magnitude faster without sacrificing too much accuracy (<4% difference) compared to the 1D model. The new model is then used to analyze the influence of the membrane electrode assembly (MEA) design on cell performance and internal state distributions, offering insights into MEA structural optimization. The model can be readily extended to account for more detailed physico-chemical processes, such as Knudsen diffusion or the influence of micro-porous layers, and it can be an effective tool for understanding and designing PEMFCs.

Design and Application of Silicon on Insulator Based SiGe VTFET in IIR Filter by Balanced Truncation (BT) Method of Model Order Reduction

Design and Application of Silicon on Insulator Based SiGe VTFET in IIR Filter by Balanced Truncation (BT) Method of Model Order Reduction

Radial basis function partition of unity procedure combined with the reduced-order method for solving Zakharov–Rubenchik equations

A meshless radial basis function based on partition of unity (RBF-PU) method is proposed to solve Zakharov–Rubenchik equations. In this local method, the domain is split into overlapping patches forming a covering of it and also, it provides accurate results for PDEs. Time discretization is performed using a second-order implicit explicit backward difference method (IMEX-BDF2). Although the proper orthogonal decomposition (POD) is applied to reduce the dimension of the governing model, the computational complexity of the reduced model for nonlinear terms still depends on the number of variables of the full model. To overcome this subject, we employ the discrete empirical interpolation method (DEIM). Two problems with different situations are solved by the proposed method and the comparison of numerical findings with the conservative compact difference scheme and RBF-FD method shows that the presented method provides accurate results at a low computing cost.

A Symmetric Fractional-order Reduction Method for Direct Nonuniform Approximations of Semilinear Diffusion-wave Equations

We introduce a symmetric fractional-order reduction (SFOR) method to construct numerical algorithms on general nonuniform temporal meshes for semilinear fractional diffusion-wave equations. By using the novel order reduction method, the governing problem is transformed to an equivalent coupled system, where the explicit orders of time-fractional derivatives involved are all \(\alpha /2\) \((1<\alpha <2)\). The linearized L1 scheme and Alikhanov scheme are then proposed on general time meshes. Under some reasonable regularity assumptions and weak restrictions on meshes, the optimal convergence is derived for the two kinds of difference schemes by \(H^2\) energy method. An adaptive time stepping strategy which based on the (fast linearized) L1 and Alikhanov algorithms is designed for the semilinear diffusion-wave equations. Numerical examples are provided to confirm the accuracy and efficiency of proposed algorithms.

A physics‐based model reduction approach for node‐to‐segment contact problems in linear elasticity

AbstractThe article presents a novel model order reduction method for mechanical problems in linear elasticity with nonlinear contact conditions. Recently, we have proposed an efficient reduction scheme for the node‐to‐node formulation [Manvelyan et al., Comput Mech 68, 1283–1295 (2021)] that leads to linear complementarity problems (LCPs). Here, we enhance the underlying contact problem to a node‐to‐segment formulation, which leads to quadratic inequalities as constraints. The adjoint system corresponds to a nonlinear complementarity problem that describes the Lagrange multiplier. The latter is solved by a Newton‐type iteration based on a LCP solver in each time step. Since the maximal set of potential contact nodes is predefined, an additional substructuring by Craig–Bampton can be performed. This contact treatment turns out to be necessary and allows exclusion of the Lagrange multipliers and the nodal displacements at contact from reduction. The numerical solutions of the reduced contact problem achieve high accuracy and the dynamic contact carries over the behavior of the full order model. Moreover, if the contact area is small compared to the overall structure, the reduction scheme performs very efficiently. The performance of the resulting reduction method is assessed on two 2D computational examples from linear elasticity.

Estimating wind velocity and direction using sparse sensors on a cylinder

Using finite pressure measurements on a cylinder, we are able to estimate both the oncoming wind speed and direction of uniform flow over a cylinder at Reynolds numbers 20 000&amp;lt;Re&amp;lt;120 000. While reduced-order methods, such as proper orthogonal decomposition with QR factorization, require at least nine sensors to estimate the oncoming wind speed and direction with &amp;lt;10% error, other methods, such as probabilistic approaches or curve-fitting, can achieve similar results with as few as five sensors. A utility function, based on the Kullback–Leibler divergence, is used to determine the locally optimal location of the sensors to accurately estimate inlet conditions. It was found that sensor arrangement also plays a significant role, with unevenly distributed sensors being preferable than evenly distributed sensors. These techniques, when paired with existing flow field estimation approaches, allow the user to predict the surrounding flow field from any oncoming direction.

Frequency-Domain Model Order Reduction of Electromagnetic Field in Induction Motor

A model order reduction (MOR) method for an induction motor using a Cauer ladder network (CLN) is developed in the frequency domain. A multiport frequency transformation between the stator and mover domains is derived by neglecting the spatial harmonic interactions. Even after neglecting the harmonic interactions, the reduced model provides a reasonably accurate frequency response, which is more accurate than that of the conventional approximated equivalent circuit.

Investigation on model order reduction methods for flexible bodies with contact-impact based on partition modeling

The finite element method is widely used to solve the problem of flexible bodies with contact-impact. To express the high-frequency and high-transient characteristics of the impact process and the high stress distribution of the local contact region, the amount of the node coordinates will be very large, which brings great burden to the dynamic simulation. It is particularly important to reduce the degrees of freedom of the system in the contact-impact problem. However, as the impact itself is a strong nonlinear problem, the linear model reduction techniques cannot be used directly. The partition method is presented to solve this problem, in which the deformation of the contact region is described by finite element node coordinates to preserve the local nonlinear characteristic while the deformation of the non-contact region is described by the reduced elastic coordinates. Different model reduction techniques including modal truncation method and Krylov subspace method are used to reduce the degrees of freedom of the non-contact region of an experimental rod-plate impact case, and the results are compared with that of the finite element method and the experiment. The simulation results show that the partition method can effectively reduce the degrees of freedom of the system and maintain good accuracy. Moreover, the Krylov subspace method has an advantage over the modal method in the model reduction of contact-impact problem.

Model predictive control of portable electronic devices under skin temperature constraints

Thermal management is becoming a major challenge for electronics, and a better temperature control algorithm that could maximize the system performance will play a greater role in fully utilizing the existing cooling capacity. Unfortunately, the simplest look-up table method is still widely used as the temperature control algorithm in current portable electronic devices, especially laptops, resulting in a significant performance loss of devices. In this paper, a general temperature control framework for a commercial laptop that considers the skin temperature constraints is proposed based on the model predictive control algorithm. In specific, a high-accuracy compact thermal model is first generated through the model order reduction method and validated by abundant experimental data. Then the proposed MPC is numerically evaluated in three test scenarios, covering different workloads and performance indexes. The results show that the proposed MPC outperforms the baseline look-up table method by achieving about 10–20% higher performance index in different test scenarios. The open-loop optimal control method is also considered to estimate the optimality of the proposed MPC. Moreover, a parametric study is conducted to analyze the influence of different control parameters, indicating broad prospects for the future application of the proposed MPC algorithm.

Bayesian inference for random field parameters with a goal-oriented quality control of the PGD forward model’s accuracy

Numerical models built as virtual-twins of a real structure (digital-twins) are considered the future of monitoring systems. Their setup requires the estimation of unknown parameters, which are not directly measurable. Stochastic model identification is then essential, which can be computationally costly and even unfeasible when it comes to real applications. Efficient surrogate models, such as reduced-order method, can be used to overcome this limitation and provide real time model identification. Since their numerical accuracy influences the identification process, the optimal surrogate not only has to be computationally efficient, but also accurate with respect to the identified parameters. This work aims at automatically controlling the Proper Generalized Decomposition (PGD) surrogate’s numerical accuracy for parameter identification. For this purpose, a sequence of Bayesian model identification problems, in which the surrogate’s accuracy is iteratively increased, is solved with a variational Bayesian inference procedure. The effect of the numerical accuracy on the resulting posteriors probability density functions is analyzed through two metrics, the Bayes Factor (BF) and a criterion based on the Kullback-Leibler (KL) divergence. The approach is demonstrated by a simple test example and by two structural problems. The latter aims to identify spatially distributed damage, modeled with a PGD surrogate extended for log-normal random fields, in two different structures: a truss with synthetic data and a small, reinforced bridge with real measurement data. For all examples, the evolution of the KL-based and BF criteria for increased accuracy is shown and their convergence indicates when model refinement no longer affects the identification results.

Reduced-order modelling for approximated analytical calculation of linear permanent magnet machines

In this paper, we propose an order reduction method which can be applied in the approximated analytical model for linear permanent magnet machines (LPMMs). The proposed model takes the periodic boundary condition into account the Poisson and Laplace equations, hence, the analytical solution requires low harmonic orders in each subdomain. The magnetic results show that the proposed model can maintain high accuracy while taking low computational time. 2D finite element computations, as well as measurements, validate the proposed model. The proposed model in this paper can also be further applied in permanent magnet machines with high pole and slot combination, to reduce the computational time.

A novel hybrid of Nonlinear Sine Cosine Algorithm and Safe Experimentation Dynamics for model order reduction

ABSTRACT The current study introduces the hybridization of the Nonlinear Sine Cosine Algorithm (NSCA) and Safe Experimentation Dynamics (SED) as a novel optimization method for model order reduction of high-order single-input single-output (SISO) systems. Reciprocated synergism between both meta-heuristic algorithms is achieved by appropriating the nonlinear position-updated mechanism of NSCA for enhanced exploration/exploitation competencies and proficiency of SED in maximizing stagnation avoidance within the local optima. Named the NSCA-SED algorithm, the applicability of the proposed method is assessed by scholastic adoption of a sixth-order numerical transfer function towards two independent high-order systems enclosing Double-Pendulum Overhead Crane and Flexible Manipulator. Experimentation results further suggested NSCA-SED as the superior alternative in terms of execution robustness and consistency excellence against other available optimization-based methods for tackling model order reduction. Exemplified simulations sequentially demonstrated considerable improvements by the employment of NSCA-SED over conventional SCA following respective enhanced proportions of 97.17%, 13.17% and 29.03% for Example 1, Example 2 and Example 3.

A reduced-order method with PGD for the analysis of dynamically loaded journal bearing

A reduced-order method with PGD for the analysis of dynamically loaded journal bearing

Robust Reduced-Order Active Disturbance Rejection Control Method: A Case Study on Speed Control of a One-Dimensional Gimbal

Usually, the order of active disturbance rejection control (ADRC) is equal to the relative order of the plant. To improve the control performance, a robust reduced-order method for ADRC is investigated in this paper. Firstly, frequency domain analysis shows that the lower-order extended state observer (ESO) has a smaller disturbance estimation error, so disturbance attenuation capability can be improved by reducing the order of ADRC. However, using only reduced-order ADRC will worsen the robustness of closed-loop systems. Therefore, a robust ADRC method based on a modified noise reduction disturbance observer (MNRDOB) is proposed. The main role of the MNRDOB is to improve the control performance of the closed-loop system by modifying the structure of the controlled object. In addition, the robust stability of the closed-loop control system based on the MNRDOB is discussed. Moreover, some simulations are used to demonstrate the robustness and noise suppression effects of the compound control method reduced-order ADRC with MNRDOB, and the parameter tuning method for the MNRDOB to improve the robustness of the system is given. Finally, some experiments on speed control of a one-dimensional gimbal are performed, and the results show that the proposed method is excellent in overshoot, tracking accuracy, and disturbance attenuation.

Advances in CFD Modeling of Urban Wind Applied to Aerial Mobility

The feasibility, safety, and efficiency of a drone mission in an urban environment are heavily influenced by atmospheric conditions. However, numerical meteorological models cannot cope with fine-grained grids capturing urban geometries; they are typically tuned for best resolutions ranging from 1 to 10 km. To enable urban air mobility, new now-casting techniques are being developed based on different techniques, such as data assimilation, variational analysis, machine-learning algorithms, and time series analysis. Most of these methods require generating an urban wind field database using CFD codes coupled with the mesoscale models. The quality and accuracy of that database determines the accuracy of the now-casting techniques. This review describes the latest advances in CFD simulations applied to urban wind and the alternatives that exist for the coupling with the mesoscale model. First, the distinct turbulence models are introduced, analyzing their advantages and limitations. Secondly, a study of the meshing is introduced, exploring how it has to be adapted to the characteristics of the urban environment. Then, the several alternatives for the definition of the boundary conditions and the interpolation methods for the initial conditions are described. As a key step, the available order reduction methods applicable to the models are presented, so the size and operability of the wind database can be reduced as much as possible. Finally, the data assimilation techniques and the model validation are presented.

A learning-based projection method for model order reduction of transport problems

The Kolmogorov n-width of the solution manifolds of transport-dominated problems can decay slowly. As a result, it can be challenging to design efficient and accurate reduced order models (ROMs) for such problems. To address this issue, we propose a new learning-based projection method to construct nonlinear adaptive ROMs for transport problems. The construction follows the offline–online decomposition. In the offline stage, we train a neural network to construct adaptive reduced basis dependent on time and model parameters. In the online stage, we project the solution to the learned reduced manifold. Inheriting the merits from both deep learning and the projection method, the proposed method is more efficient than the conventional linear projection-based methods, and may reduce the generalization error of a solely learning-based ROM. Unlike some learning-based projection methods, the proposed method does not need to take derivatives of the neural network in the online stage.

Proper Orthogonal Decomposition Analysis Reveals Cell Migration Directionality During Wound Healing.

A proper orthogonal decomposition (POD) order reduction method was implemented to reduce the full high dimensional dynamical system associated with a wound healing cell migration assay to a low-dimensional approximation that identified the prevailing cell trajectories. The POD analysis generated POD modes that were representative of the prevalent cell trajectories. The shapes of the POD modes depended on the location of the cells with respect to the wound and exposure to disturbed (DF) or undisturbed (UF) fluid flow where the net flow was in the antegrade direction with a retrograde component or fully antegrade, respectively. For DF and UF, the POD modes of the downstream cells identified trajectories that moved upstream against the flow, while upstream POD modes exhibited sideways cell migrations. In the absence of flow, no major shape differences were observed in the POD modes on either side of the wound. The POD modes also served to reconstruct the cell migration of individual cells. With as few as three modes, the predominant cell migration trajectories were reconstructed, while the level of accuracy increased with the inclusion of more POD modes. The POD order reduction method successfully identified the predominant cell migratory trajectories under static and varying pulsatile fluid flow conditions serving as a first step in the development of artificial intelligence models of cell migration in disease and development.

A deep learning based reduced order modeling for stochastic underground flow problems

In this paper, we propose a deep learning based reduced order modeling method for stochastic underground flow problems in highly heterogeneous media. We aim to utilize supervised learning to build a reduced surrogate mapping from the stochastic parameter space that characterizes the possible highly heterogeneous media to the solution space of a stochastic flow problem. Offline preparation includes collecting a set of full-order solutions to form a global snapshot space and extracting dominating POD modes using a particular well-designed spectral problem to represent full-order solutions. Due to the small dimension of reduced-order solutions, the complexity of neural network is significantly lightened, which effectively relieves the burden of training. We adopt the generalized multiscale finite element method (GMsFEM), where a set of local multiscale basis functions that can capture the heterogeneity of the media and source information are constructed to efficiently generate globally defined snapshot space. In an online stage, one can rapidly obtain the reduced-order pressure and then corresponding full-order solution is recovered using a linear transformation. Due to the decoupling of offline and online procedures, the proposed reduced order method serves as a non-intrusive tool that can achieve fast simulations independent of input parameters. Rigorous theoretical analyses are provided and extensive numerical experiments for linear and nonlinear stochastic flows are provided to verify the superior performance of the proposed method.