5,595 results on '"model reduction"'
Search Results
2. Multi-scale spatio-temporal transformer: A novel model reduction approach for day-ahead security-constrained unit commitment
- Author
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Liu, Mao, Kong, Xiangyu, Xiong, Kaizhi, Wang, Jimin, and Lin, Qingxiang
- Published
- 2025
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3. Machine learned compact kinetic model for liquid fuel combustion
- Author
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Kelly, Mark, Bourque, G., Hase, M., and Dooley, S.
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- 2025
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4. Knowledge-informed neuro-integrators for aggregation kinetics
- Author
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Lukashevich, D., Tyukin, I., and Brilliantov, N.
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- 2024
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5. A Semi-implicit Stochastic Multiscale Method for Radiative Heat Transfer Problem in Composite Materials.
- Author
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Zhang, Shan, Wang, Yajun, and Guan, Xiaofei
- Abstract
In this paper, we propose and analyze a new semi-implicit stochastic multiscale method for the radiative heat transfer problem with additive noise fluctuation in composite materials. In the proposed method, the strong nonlinearity term induced by heat radiation is first approximated, by a semi-implicit predictor-corrected numerical scheme, for each fixed time step, resulting in a spatially random multiscale heat transfer equation. Then, the infinite-dimensional stochastic processes are modeled and truncated using a complete orthogonal system, facilitating the reduction of the model's dimensionality in the random space. The resulting low-rank random multiscale heat transfer equation is approximated and computed by using efficient spatial basis functions based multiscale method. The main advantage of the proposed method is that it separates the computational difficulty caused by the spatial multiscale properties, the high-dimensional randomness and the strong nonlinearity of the solution, so they can be overcome separately using different strategies. The convergence analysis is carried out, and the optimal rate of convergence is also obtained for the proposed semi-implicit stochastic multiscale method. Numerical experiments on several test problems for composite materials with various microstructures are also presented to gauge the efficiency and accuracy of the proposed semi-implicit stochastic multiscale method. [ABSTRACT FROM AUTHOR]
- Published
- 2025
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- View/download PDF
6. System Identification Based on Experimental Technique Using Stability Boundary Locus Method for Linear Fractional Order Systems.
- Author
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Yüce, Ali
- Subjects
- *
NONLINEAR equations , *FRACTIONAL calculus , *SYSTEM identification , *TRANSFER functions , *TWIN boundaries - Abstract
Fractional calculus is an important mathematical tool that is widely used in control systems. It is established in the literature that fractional order models are more accurate and more effective in system modelling. In this study, an alternative and novel technique is proposed to identify the fractional order time-delayed model of an unknown system. The method is based on obtaining the approximate stability boundary locus (SBL) curve of the unknown system by applying three different experimental tests. Three points on the SBL curve are determined by the experimental tests and then the parameters of the fractional order time-delayed model are computed by solving the nonlinear systems of equation. The system model with double fractional order element plus a time delay is obtained using the proposed method. The proposed method is explained through simulations on a twin rotor system. The proposed method is also used in model order reduction calculation of the higher order transfer functions. [ABSTRACT FROM AUTHOR]
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- 2024
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7. Observer Design for State and Parameter Estimation for Two-Time-Scale Nonlinear Systems.
- Author
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Xiao, Zhenyu and Duan, Zhaoyang
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PARAMETER estimation ,NONLINEAR systems ,INVARIANT manifolds ,ANAEROBIC digestion ,NONLINEAR estimation - Abstract
The design and calculation of nonlinear observers for parameter estimation in multi-time-scale nonlinear systems present significant challenges due to the inherent complexity and stiffness of such systems. This study proposes a framework for designing observers for two-time-scale nonlinear systems, with the objective of overcoming the aforementioned challenges. The design procedure involves reducing the original two-time-scale nonlinear system to a lower-dimensional model that captures only the slow dynamics while approximating the fast states through the use of an algebraic slow motion invariant manifold function. Subsequently, an exponential observer can be devised for this reduced system, which is valid for both state and parameter estimation. By employing the output from the original system, this observer can be adapted for online state and parameter estimation for the detailed two-time-scale system. The challenges associated with estimating parameters in two-time-scale nonlinear systems, the complexities of designing observers for such systems, and the computational burden associated with computing observers for ill-conditioned systems can be effectively addressed through the application of this design framework. A rigorous error analysis validates the convergence of the proposed observer towards the states and parameters of the original system. The viability and necessity of this observer design framework are demonstrated through a numerical example and an anaerobic digestion process. This study presents a practical approach for state and parameter estimation with observers for two-time-scale nonlinear systems. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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8. Accelerate Neural Subspace-Based Reduced-Order Solver of Deformable Simulation by Lipschitz Optimization.
- Author
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Lyu, Aoran, Zhao, Shixian, Xian, Chuhua, Cen, Zhihao, Cai, Hongmin, and Fang, Guoxin
- Subjects
ELASTICITY ,PARAMETERIZATION ,SPEED ,DEFORMATIONS (Mechanics) ,MEMORY - Abstract
Reduced-order simulation is an emerging method for accelerating physical simulations with high DOFs, and recently developed neural-network-based methods with nonlinear subspaces have been proven effective in diverse applications as more concise subspaces can be detected. However, the complexity and landscape of simulation objectives within the subspace have not been optimized, which leaves room for enhancement of the convergence speed. This work focuses on this point by proposing a general method for finding optimized subspace mappings, enabling further acceleration of neural reduced-order simulations while capturing comprehensive representations of the configuration manifolds. We achieve this by optimizing the Lipschitz energy of the elasticity term in the simulation objective, and incorporating the cubature approximation into the training process to manage the high memory and time demands associated with optimizing the newly introduced energy. Our method is versatile and applicable to both supervised and unsupervised settings for optimizing the parameterizations of the configuration manifolds. We demonstrate the effectiveness of our approach through general cases in both quasi-static and dynamics simulations. Our method achieves acceleration factors of up to 6.83 while consistently preserving comparable simulation accuracy in various cases, including large twisting, bending, and rotational deformations with collision handling. This novel approach offers significant potential for accelerating physical simulations, and can be a good add-on to existing neural-network-based solutions in modeling complex deformable objects. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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9. Deconvolution closure for mesoscopic continuum models of particle systems.
- Author
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Panchenko, Alexander, Barannyk, Lyudmyla L., and Cooper, Kevin
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LINEAR momentum , *GRANULAR materials , *OPERATOR equations , *PARTICLE dynamics , *HEAT flux - Abstract
We present a framework for derivation of closed‐form continuum equations governing mesoscale dynamics of large particle systems. Balance equations for spatial averages such as density, linear momentum, and energy were previously derived by a number of authors. These equations are exact, but are not in closed form because the stress and the heat flux cannot be evaluated without the knowledge of particle positions and velocities. Recently, we proposed a method for approximating exact fluxes by true constitutive equations, that is, using nonlocal operators acting only on the average density and velocity. In the paper, constitutive operators are obtained by using filtered regularization methods from the theory of ill‐posed problems. We also formulate conditions on fluctuation statistics which permit approximating these operators by local equations. The performance of the method is tested numerically using Fermi–Pasta–Ulam particle chains with two different potentials: the classical Lennard–Jones and the purely repulsive potential used in granular materials modeling. The initial conditions incorporate velocity fluctuations on scales that are smaller than the size of the averaging window. Simulation results show good agreement between the exact stress and its closed‐form approximation. [ABSTRACT FROM AUTHOR]
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- 2024
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10. Dynamic–quadratic balancing: A computational approach to balancing and model reduction for affine nonlinear systems.
- Author
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Aliyu, Mohammad Dikko S.
- Subjects
NONLINEAR equations ,HANKEL functions ,NONLINEAR systems ,SYSTEM dynamics ,EQUATIONS - Abstract
In this paper, we discuss a new approach to balancing (known as dynamic–quadratic balancing) and model reduction for affine nonlinear system. We give a fresh look to balancing in terms of the dynamics of the system, rather than simply a structural property. With this perspective, we also develop a new approach to obtaining the balancing transformation in one step, instead of a three‐step process as proposed in earlier methods. Further, we explore the relationship between quadratic balancing and input–output stability. In addition, we also develop a computational approach for obtaining the balancing transformation by solving a coupled system of PDEs or inequalities (Lyapunov/Hamilton–Jacobi type). After that, model reduction can be carried out in the conventional way using Hankel singular‐value functions or using a new criterion. Finally, we present some examples to clarify the results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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11. Application and reduction of a nonlinear hyperelastic wall model capturing ex vivo relationships between fluid pressure, area, and wall thickness in normal and hypertensive murine left pulmonary arteries
- Author
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Haider, Mansoor A, Pearce, Katherine J, Chesler, Naomi C, Hill, Nicholas A, and Olufsen, Mette S
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Engineering ,Cardiovascular ,Hypertension ,Lung ,2.1 Biological and endogenous factors ,Aetiology ,arterial wall ,hyperelastic pressure-area relation ,hypoxia ,identifiability ,model reduction ,pulmonary hypertension ,sensitivity analysis ,Mathematical Sciences ,Applied Mathematics ,Mathematical sciences - Abstract
Pulmonary hypertension is a cardiovascular disorder manifested by elevated mean arterial blood pressure (>20 mmHg) together with vessel wall stiffening and thickening due to alterations in collagen, elastin, and smooth muscle cells. Hypoxia-induced (type 3) pulmonary hypertension can be studied in animals exposed to a low oxygen environment for prolonged time periods leading to biomechanical alterations in vessel wall structure. This study introduces a novel approach to formulating a reduced order nonlinear elastic structural wall model for a large pulmonary artery. The model relating blood pressure and area is calibrated using ex vivo measurements of vessel diameter and wall thickness changes, under controlled pressure conditions, in left pulmonary arteries isolated from control and hypertensive mice. A two-layer, hyperelastic, and anisotropic model incorporating residual stresses is formulated using the Holzapfel-Gasser-Ogden model. Complex relations predicting vessel area and wall thickness with increasing blood pressure are derived and calibrated using the data. Sensitivity analysis, parameter estimation, subset selection, and physical plausibility arguments are used to systematically reduce the 16-parameter model to one in which a much smaller subset of identifiable parameters is estimated via solution of an inverse problem. Our final reduced one layer model includes a single set of three elastic moduli. Estimated ranges of these parameters demonstrate that nonlinear stiffening is dominated by elastin in the control animals and by collagen in the hypertensive animals. The pressure-area relation developed in this novel manner has potential impact on one-dimensional fluids network models of vessel wall remodeling in the presence of cardiovascular disease.
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- 2024
12. Enhancing structural analysis efficiency: a comprehensive review and experimental validation of advanced submodeling techniques, introducing the submodeling-density-shape-element removal (S-D-S-ER) method
- Author
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Teke, Ibrahim T. and Ertas, Ahmet H.
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- 2024
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13. Mori-zwanzig approach for belief abstraction with application to belief space planning.
- Author
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Hou, Mengxue, Lin, Tony X., Zhou, Enlu, and Zhang, Fumin
- Subjects
PARTIALLY observable Markov decision processes ,ARTIFICIAL intelligence ,IMAGE processing ,PRODUCTION planning ,PROBLEM solving - Abstract
We propose a learning-based method to extract symbolic representations of the belief state and its dynamics in order to solve planning problems in a continuous-state partially observable Markov decision processes (POMDP) problem. While existing approaches typically parameterize the continuous-state POMDP into a finite-dimensional Markovian model, they are unable to preserve fidelity of the abstracted model. To improve accuracy of the abstracted representation, we introduce a memory-dependent abstraction approach to mitigate the modeling error. The first major contribution of this paper is we propose a Neural Network based method to learn the non-Markovian transition model based on the Mori-Zwanzig (M-Z) formalism. Different from existing work in applying M-Z formalism to autonomous time-invariant systems, our approach is the first work generalizing the M-Z formalism to robotics, by addressing the non-Markovian modeling of the belief dynamics that is dependent on historical observations and actions. The second major contribution is we theoretically show that modeling the non-Markovian memory effect in the abstracted belief dynamics improves the modeling accuracy, which is the key benefit of the proposed algorithm. Simulation experiment of a belief space planning problem is provided to validate the performance of the proposed belief abstraction algorithms. [ABSTRACT FROM AUTHOR]
- Published
- 2025
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14. Kinematics characteristics of unsprung mass in a double wishbone suspension based on velocity transformation.
- Author
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Duan, Yupeng, Wu, Jinglai, and Zhang, Yunqing
- Abstract
The transformation from multibody models to lumped-parameter models is a crucial aspect of vehicle dynamics research. The velocity transformation method is adopted in this research, and the suspension multibody model is described using only one degree of freedom. It is found that the equivalent mass of the system is time-dependent during the simulation process, as observed in numerical simulations. Further symbolic calculations are conducted to derive the analytical form of the equivalent mass, and the results show that once the static parameters are determined, the equivalent mass of the suspension system is determined solely by the vertical position of the suspension upright, which reveals the kinematics characteristic of the equivalent mass of the suspension system. It is found that the equivalent mass experiences smaller changes when the suspension is compressed from the middle position, but larger changes when the suspension is extended. Furthermore, by comparing the multibody model, the lumped-parameter model with static mass, and the proposed lumped-parameter model considering the kinematics characteristic of the equivalent unsprung mass, the proposed model produces simulation results that more closely match the original multibody model than the model with static mass. The improvements in accuracy can be up to 20% under certain evaluation metrics. [ABSTRACT FROM AUTHOR]
- Published
- 2025
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15. Reinforcement learning-based estimation for spatio-temporal systems
- Author
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Saviz Mowlavi and Mouhacine Benosman
- Subjects
Estimation ,Filtering ,Partial differential equations ,Model reduction ,Reinforcement learning ,Medicine ,Science - Abstract
Abstract State estimators such as Kalman filters compute an estimate of the instantaneous state of a dynamical system from sparse sensor measurements. For spatio-temporal systems, whose dynamics are governed by partial differential equations (PDEs), state estimators are typically designed based on a reduced-order model (ROM) that projects the original high-dimensional PDE onto a computationally tractable low-dimensional space. However, ROMs are prone to large errors, which negatively affects the performance of the estimator. Here, we introduce the reinforcement learning reduced-order estimator (RL-ROE), a ROM-based estimator in which the correction term that takes in the measurements is given by a nonlinear policy trained through reinforcement learning. The nonlinearity of the policy enables the RL-ROE to compensate efficiently for errors of the ROM, while still taking advantage of the imperfect knowledge of the dynamics. Using examples involving the Burgers and Navier-Stokes equations with parametric uncertainties, we show that in the limit of very few sensors, the trained RL-ROE outperforms a Kalman filter designed using the same ROM and yields accurate instantaneous estimates of high-dimensional states corresponding to unknown initial conditions and physical parameter values. The RL-ROE opens the door to lightweight real-time sensing of systems governed by parametric PDEs.
- Published
- 2024
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- View/download PDF
16. Modeling of maltodextrin drying kinetics for use in simulations of spray drying.
- Author
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Bürger, Johannes Vincent, Jaskulski, Maciej, and Kharaghani, Abdolreza
- Subjects
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SPRAY drying , *ATMOSPHERIC temperature , *MALTODEXTRIN , *HUMIDITY , *PREDICTION models - Abstract
AbstractThis study investigates the drying kinetics of maltodextrin droplets using experimental and numerical methods. Single droplet drying experiments, conducted under controlled conditions (air velocity 5 cm/s, air humidity 5 g/kg) using the filament method, aim to determine the critical moisture content for surface locking of droplets (initial diameter 1200 − 1600 µm). The experiments examine how this critical moisture content varies with initial solids content of the droplets (20–40% w/w) and air temperature (80–120 °C). A spatially resolved single droplet drying model (complex model) is adapted and validated, showing excellent agreement with experimental drying curves. This model is then employed to simulate conditions more representative of spray drying. A parametric study assesses the influence of air temperature (60–240 °C), initial droplet diameter (30 − 500 µm), and air velocity (0.01–5 m/s) on drying rates, highlighting the interplay among these variables. For these conditions, the complex model is finally reduced to a characteristic drying curve model whose computational simplicity makes it suitable for implementation in computational fluid dynamics simulations of spray drying. To further improve the model predictions and account for the influence of process conditions, an extension modulating the model parameter n (ranging from 0.88 to 1.62, with a median of 1.07) is proposed. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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17. Modeling and Simulation of an Integrated Synchronous Generator Connected to an Infinite Bus through a Transmission Line in Bond Graph.
- Author
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Gonzalez-Avalos, Gilberto, Ayala-Jaimes, Gerardo, Gallegos, Noe Barrera, and Garcia, Aaron Padilla
- Subjects
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BOND graphs , *SYNCHRONOUS generators , *ELECTRIC lines , *ELECTRICAL energy , *ELECTRIC inductance - Abstract
Most electrical energy generation systems are based on synchronous generators; as a result, their analysis always provides interesting findings, especially if an approach different to those traditionally studied is used. Therefore, an approach involving the modeling and simulation of a synchronous generator connected to an infinite bus through a transmission line in a bond graph is proposed. The behavior of the synchronous generator is analyzed in four case studies of the transmission line: (1) a symmetrical transmission line, where the resistance and inductance of the three phases (a , b , c) are equal, which determine resistances and inductances in coordinates (d , q , 0) as individual decoupled elements; (2) a symmetrical transmission line for the resistances and for non-symmetrical inductances in coordinates (a , b , c) that result in resistances that are individual decoupled elements and in a field of inductances in coordinates (d , q , 0) ; (3) a non-symmetrical transmission line for resistances and for symmetrical inductances in coordinates (a , b , c) that produce a field of resistances and inductances as individual elements decoupled in coordinates (d , q , 0) ; and (4) a non-symmetrical transmission line for resistances and inductances in coordinates (a , b , c) that determine resistances and inductance fields in coordinates (d , q , 0) . A junction structure based on a bond graph model that allows for obtaining the mathematical model of this electrical system is proposed. Due to the characteristics of a bond graph, model reduction can be carried out directly and easily. Therefore, reduced bond graph models for the four transmission line case studies are proposed, where the transmission line is seen as if it were inside the synchronous generator. In order to demonstrate that the models obtained are correct, simulation results using the 20-Sim software are shown. The simulation results determine that for a symmetrical transmission line, currents in the generator in the d and q axes are −25.87 A and 0.1168 A, while in the case of a non-symmetrical transmission line, these currents are −26.14 A and 0.0211 A, showing that for these current magnitudes, the generator is little affected due to the parameters of the generator and the line. However, for a high degree of non-symmetry of the resistances in phases a, b and c, it causes the generator to reach an unstable condition, which is shown in the last simulation of the paper. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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18. Graph-based, dynamics-preserving reduction of (bio)chemical systems.
- Author
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Roussel, Marc R. and Soares, Talmon
- Abstract
Complex dynamical systems are often governed by equations containing many unknown parameters whose precise values may or may not be important for the system’s dynamics. In particular, for chemical and biochemical systems, there may be some reactions or subsystems that are inessential to understanding the bifurcation structure and consequent behavior of a model, such as oscillations, multistationarity and patterning. Due to the size, complexity and parametric uncertainties of many (bio)chemical models, a dynamics-preserving reduction scheme that is able to isolate the necessary contributors to particular dynamical behaviors would be useful. In this contribution, we describe model reduction methods for mass-action (bio)chemical models based on the preservation of instability-generating subnetworks known as critical fragments. These methods focus on structural conditions for instabilities and so are parameter-independent. We apply these results to an existing model for the control of the synthesis of the NO-detoxifying enzyme Hmp in Escherichia coli that displays bistability. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
19. Explicit sensitivity analysis of spectral submanifolds of mechanical systems.
- Author
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Li, Mingwu
- Abstract
Model reduction via spectral submanifolds (SSMs) has displayed benefits such as the facilitation of nonlinear analysis and significant speed-up gains. One needs the sensitivity of the SSM-based model reduction to carry over these benefits to the settings of optimal design, modal updating, and uncertainty quantification of high-dimensional nonlinear mechanical systems. Here, we construct explicit third-order, SSM-based model reduction for general mechanical systems. We further derive the explicit sensitivity of the third-order SSM-based reduction using direct and adjoint methods. We demonstrate the effectiveness of the derived explicit sensitivity via a few examples with increasing complexity. We also show that the obtained sensitivity can be used to effectively construct perturbed SSMs, backbone curves, and forced response curves. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
20. Reinforcement learning-based estimation for spatio-temporal systems.
- Author
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Mowlavi, Saviz and Benosman, Mouhacine
- Subjects
- *
REINFORCEMENT learning , *PARTIAL differential equations , *PARAMETRIC equations , *NAVIER-Stokes equations , *BURGERS' equation - Abstract
State estimators such as Kalman filters compute an estimate of the instantaneous state of a dynamical system from sparse sensor measurements. For spatio-temporal systems, whose dynamics are governed by partial differential equations (PDEs), state estimators are typically designed based on a reduced-order model (ROM) that projects the original high-dimensional PDE onto a computationally tractable low-dimensional space. However, ROMs are prone to large errors, which negatively affects the performance of the estimator. Here, we introduce the reinforcement learning reduced-order estimator (RL-ROE), a ROM-based estimator in which the correction term that takes in the measurements is given by a nonlinear policy trained through reinforcement learning. The nonlinearity of the policy enables the RL-ROE to compensate efficiently for errors of the ROM, while still taking advantage of the imperfect knowledge of the dynamics. Using examples involving the Burgers and Navier-Stokes equations with parametric uncertainties, we show that in the limit of very few sensors, the trained RL-ROE outperforms a Kalman filter designed using the same ROM and yields accurate instantaneous estimates of high-dimensional states corresponding to unknown initial conditions and physical parameter values. The RL-ROE opens the door to lightweight real-time sensing of systems governed by parametric PDEs. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
21. A Novel Mayfly Algorithm with Response Surface for Static Damage Identification Based on Multiple Indicators.
- Author
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Wu, Zhifeng, Song, Yanpeng, Chen, Hui, Huang, Bin, and Fan, Jian
- Subjects
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METAHEURISTIC algorithms , *BOX girder bridges , *DEAD loads (Mechanics) , *TIKHONOV regularization , *ALUMINUM alloys , *DIFFERENTIAL evolution , *PARTICLE swarm optimization - Abstract
This paper proposes a novel structural damage identification approach coupling the Mayfly algorithm (MA) with static displacement-based response surface (RS). Firstly, a hybrid optimal objective function is established that simultaneously considers the sensitivity-based residual errors of static damage identification equation and the static displacement residual. In the objective function, the static damage identification equation is addressed by the Tikhonov regularization technique. The MA is subsequently employed to conduct an optimal search and pinpoint the location and intensity of damages at the structural element level. To handle the inconformity of the static loading points and the measurement points of displacements, the model reduction and displacement extension techniques are implemented to reconstruct the static damage identification equation. Meanwhile, the static displacement-based RS is constructed to calculate the displacement residual in the hybrid objective function, thereby circumventing the time-consuming finite element calculations and improving computational efficiency. The identification results of the numerical box girder bridge demonstrate that the proposed method outperforms the particle swarm optimization, differential evolution, Jaya and whale optimization algorithms about both convergence rate in optimal searching and identification accuracy. The proposed method enables more accurate damage identification compared to methods solely based on the indicator of the residual of static damage identification equations or displacement residual. The results of identifying damage in the 21 element-truss structure and the static experiments on identifying damage in an aluminum alloy cantilever beam confirm the high efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
22. NONLINEAR EMBEDDINGS FOR CONSERVING HAMILTONIANS AND OTHER QUANTITIES WITH NEURAL GALERKIN SCHEMES.
- Author
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SCHWERDTNER, PAUL, SCHULZE, PHILIPP, BERMAN, JULES, and PEHERSTORFER, BENJAMIN
- Subjects
- *
TIME integration scheme , *PARTIAL differential equations , *VARIATIONAL principles , *HAMILTONIAN systems - Abstract
This work focuses on the conservation of quantities such as Hamiltonians, mass, and momentum when solution fields of partial differential equations are approximated with nonlinear parametrizations such as deep networks. The proposed approach builds on Neural Galerkin schemes that are based on the Dirac--Frenkel variational principle to train nonlinear parametrizations sequentially in time. We first show that only adding constraints that aim to conserve quantities in continuous time can be insufficient because the nonlinear dependence on the parameters implies that even quantities that are linear in the solution fields become nonlinear in the parameters and thus are challenging to discretize in time. Instead, we propose Neural Galerkin schemes that compute at each time step an explicit embedding onto the manifold of nonlinearly parametrized solution fields to guarantee conservation of quantities. The embeddings can be combined with standard explicit and implicit time integration schemes. Numerical experiments demonstrate that the proposed approach conserves quantities up to machine precision. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
23. A Grouping and Aggregation Modeling Method of Induction Motors for Transient Voltage Stability Analysis.
- Author
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Liang, Zhaowen, Liu, Yongqiang, Mo, Lili, and Zhang, Yan
- Subjects
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POWER distribution networks , *ELECTRIC potential , *DYNAMIC loads , *K-means clustering , *BUSES - Abstract
Induction motors are the most common type of motor in power systems, constituting approximately 70–90% of the dynamic loads, making them significant contributors to system dynamics. In transient voltage stability analysis, dynamic equivalent models are commonly used to simplify the representation of a group of induction motors. This paper presents a method for the grouping and aggregation of induction motors at a common bus. Firstly, grouping rules are provided for clustering induction motors into several subgroups based on the mechanical principles of rotor force and motion, and aggregation rules are provided for aggregating a motor subgroup into a single-unit model based on the relationship between voltage drop and power transmission in distribution networks. Secondly, guided by the grouping rules, high-speed remaining electromagnetic torque and low-speed remaining electromagnetic torque are defined as new clustering indicators, and an adaptive K-means clustering method using silhouette coefficient verification is introduced to obtain the optimal motor subgroups. Thirdly, guided by the aggregation rules, a dynamic equivalent method is further introduced to obtain the equivalent single-unit model from a motor subgroup. Lastly, a transient voltage stability simulation in a typical distribution network is presented to illustrate that the proposed clustering and equivalent methods are more reasonable, accurate, and effective than traditional methods, as the obtained model has better dynamic characteristics and can more accurately reproduce the process of voltage collapse. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
24. Offset-Free Koopman Model Predictive Control of Thermal Comfort Regulation for a Variable Refrigerant Flow-Dedicated Outdoor Air System-Combined System.
- Author
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Chao Pan, Yaoyu Li, and Liujia Dong
- Subjects
- *
LATENT heat , *AIR conditioning , *REDUCED-order models , *COST effectiveness , *PREDICTION models , *THERMAL comfort - Abstract
Variable refrigerant flow (VRF) system has been an appealing solution of air conditioning for residential and commercial buildings, due to its flexibility and cost effectiveness, while lack of ventilation capability is a major drawback. Incorporation of dedicated outdoor air system (DOAS) is a typical practice. However, good coordination between DOAS and VRF is critical for achieving desired thermal comfort is challenging due to the possible complexity of mixed sensible and latent heat exchanges. In this paper, to handle the nonlinear dynamic characteristics of VRF-DOAS system, we propose an offset-free Koopman model predictive control (MPC) strategy for thermal comfort regulation, in which the MPC design is computationally more efficient due to the convex problem formulation and the use of reduced-order Koopman models, and the offset-free MPC structure enhances the robustness to model uncertainties and unmeasured disturbances. A control-oriented model is obtained by hybridizing the first-principle and data-driven modeling approach. The proposed controls strategy is evaluated with a Modelica simulation model of a VRF-DOAS system. A Dymola-Python cosimulation platform is developed via the functional mockup interface (FMI), for which the MPC algorithms are implemented in Python. Simulation results show significantly better performance of the offset-free Koopman MPC in thermal comfort regulation. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
25. Research on Model Reduction of AUV Underwater Support Platform Based on Digital Twin.
- Author
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Lu, Daohua, Ning, Yichen, Wang, Jia, Du, Kaijie, and Song, Cancan
- Subjects
DIGITAL twins ,DIGITAL transformation ,OCEAN waves ,DIGITAL technology ,AUTONOMOUS underwater vehicles ,EIGENVECTORS - Abstract
Digital twin technology, as a data-driven and model-driven innovation means, plays a crucial role in the process of digital transformation and intelligent upgrading of the marine industry, helping the industry to move towards a new stage of more intelligent and efficient development. In order to solve the defects of the Autonomous Underwater Vehicle (AUV) underwater support platform structure deformation field, digital twin technology and model reduction technology are applied to an AUV underwater support platform, and a five-dimensional digital twin model of the AUV underwater support platform is studied, including five dimensions: physical world, digital world, twin data center, service application, and data connection. The digital twin of the subsea support platform is established by using the digital twin modeling technology. The POD method is used to calculate the deformation field matrix of the support structure of the subsea support platform under the 0–5 sea state, and the corresponding eigenvalues and eigenvectors are obtained. By intercepting the eigenvectors corresponding to the eigenvalues of the high energy proportion, the low-order equation is constructed, and the reduced-order model under each sea state can be quickly solved. The experimental results show that the model reduction technology can greatly shorten the model solving time, and the calculated results are highly consistent with the simulation results of the finite element full-order model, which can realize the rapid analysis of the deformation response of the subsea support platform structure, and provide a theoretical basis and technical support for the subsequent simulation, state evaluation, visual monitoring, and predictive maintenance. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
26. A source model simplification method to assist model transformation debugging.
- Author
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Jiang, Junpeng, Jiang, Mingyue, Nie, Liming, and Ding, Zuohua
- Subjects
DEBUGGING ,PROGRAM transformation ,COMPUTER software quality control ,MODELS & modelmaking ,QUALITY assurance ,PRODUCT quality - Abstract
Model transformation, which is a program targeting at transforming an input model to an output model, has been a critical basis for Model-Driven Engineering (MDE). The quality of model transformation programs directly affects the quality of software products built with MDE activities. Therefore, debugging model transformation programs has been crucial from the quality assurance point of view. One of the key impediments to the model transformation debugging is the high complexity and scale of the input models. In order to ameliorate the burden on model transformation debugging, this study proposes an effective approach to systematically reduce input models of model transformation programs. By combining the advantages of input simplification approaches for traditional programs and also the characteristics of model transformation, our approach leverages and adapts the delta debugging technique to model simplification. We conduct experiments to evaluate the proposed approach from two aspects: its effectiveness in model simplification, and its effects on model transformation debugging. Our experimental results confirm the positive contributions of the approach in both aspects. It delivers promising reduction effectiveness, and it can also well support the fault localization in model transformations. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
27. Parameter identification by deep learning of a material model for granular media.
- Author
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Tanyu, Derick Nganyu, Michel, Isabel, Rademacher, Andreas, Kuhnert, Jörg, and Maass, Peter
- Abstract
Classical physical modeling with associated numerical simulation (model-based), and prognostic methods based on the analysis of large amounts of data (data-driven) are the two most common methods used for the mapping of complex physical processes. In recent years, the efficient combination of these approaches has become increasingly important. Continuum mechanics in the core consists of conservation equations that-in addition to the always-necessary specification of the process conditions-can be supplemented by phenomenological material models. The latter are an idealized image of the specific material behavior that can be determined experimentally, empirically, and based on a wealth of expert knowledge. The more complex the material, the more difficult the calibration is. This situation forms the starting point for this work's hybrid data-driven and model-based approach for mapping a complex physical process in continuum mechanics. Specifically, we use data generated from a classical physical model by the MESHFREE software (MESHFREE Team in Fraunhofer ITWM & SCAI: MESHFREE. https://www.meshfree.eu, 2023) to train a Principal Component Analysis-based neural network (PCA-NN) for the task of parameter identification of the material model parameters. The obtained results highlight the potential of deep-learning-based hybrid models for determining parameters, which are the key to characterizing materials occurring naturally such as sand, soil, mud, or snow. The motivation for our research is the simulation of the interaction of vehicles with sand. However, the applicability of the presented methodology is not limited to this industrial use case. In geosciences, when predicting the runout zones of landslides or avalanches and evaluating corresponding protective measures, the parameterization of the respective material model is essential. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
28. Stochastic modeling of stationary scalar Gaussian processes in continuous time from autocorrelation data.
- Author
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Hanke, Martin
- Abstract
We consider the problem of constructing a vector-valued linear Markov process in continuous time, such that its first coordinate is in good agreement with given samples of the scalar autocorrelation function of an otherwise unknown stationary Gaussian process. This problem has intimate connections to the computation of a passive reduced model of a deterministic time-invariant linear system from given output data in the time domain. We construct the stochastic model in two steps. First, we employ the AAA algorithm to determine a rational function which interpolates the z-transform of the discrete data on the unit circle and use this function to assign the poles of the transfer function of the reduced model. Second, we choose the associated residues as the minimizers of a linear inequality constrained least squares problem which ensures the positivity of the transfer function’s real part for large frequencies. We apply this method to compute extended Markov models for stochastic processes obtained from generalized Langevin dynamics in statistical physics. Numerical examples demonstrate that the algorithm succeeds in determining passive reduced models and that the associated Markov processes provide an excellent match of the given data. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
29. Natural model reduction for kinetic equations.
- Author
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Jin, Zeyu and Li, Ruo
- Subjects
LINEAR equations ,TANGENT bundles ,CONSERVATION laws (Physics) ,MACHINE learning ,MODEL theory - Abstract
A promising approach to investigating high-dimensional problems is to identify their intrinsically low-dimensional features, which can be achieved through recently developed techniques for effective low-dimensional representation of functions such as machine learning. Based on available finite-dimensional approximate solution manifolds, this paper proposes a novel model reduction framework for kinetic equations. The method employs projections onto tangent bundles of approximate manifolds, naturally resulting in first-order hyperbolic systems. Under certain conditions on the approximate manifolds, the reduced models preserve several crucial properties, including hyperbolicity, conservation laws, entropy dissipation, finite propagation speed, and linear stability. For the first time, this paper rigorously discusses the relation between the H-theorem of kinetic equations and the linear stability conditions of reduced systems, determining the choice of Riemannian metrics involved in the model reduction. The framework is widely applicable for the model reduction of many models in kinetic theory. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
30. Adaptive Machine Learning Approach for Importance Evaluation of Multimodal Breast Cancer Radiomic Features.
- Author
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Del Corso, Giulio, Germanese, Danila, Caudai, Claudia, Anastasi, Giada, Belli, Paolo, Formica, Alessia, Nicolucci, Alberto, Palma, Simone, Pascali, Maria Antonietta, Pieroni, Stefania, Trombadori, Charlotte, Colantonio, Sara, Franchini, Michela, and Molinaro, Sabrina
- Subjects
SCANNING systems ,BIOPSY ,DIAGNOSTIC imaging ,RECEIVER operating characteristic curves ,RESEARCH funding ,BREAST tumors ,RADIOMICS ,EARLY detection of cancer ,TOMOGRAPHY ,QUANTITATIVE research ,DESCRIPTIVE statistics ,MATHEMATICAL models ,MACHINE learning ,COMPARATIVE studies ,THEORY ,PREDICTIVE validity - Abstract
Breast cancer holds the highest diagnosis rate among female tumors and is the leading cause of death among women. Quantitative analysis of radiological images shows the potential to address several medical challenges, including the early detection and classification of breast tumors. In the P.I.N.K study, 66 women were enrolled. Their paired Automated Breast Volume Scanner (ABVS) and Digital Breast Tomosynthesis (DBT) images, annotated with cancerous lesions, populated the first ABVS+DBT dataset. This enabled not only a radiomic analysis for the malignant vs. benign breast cancer classification, but also the comparison of the two modalities. For this purpose, the models were trained using a leave-one-out nested cross-validation strategy combined with a proper threshold selection approach. This approach provides statistically significant results even with medium-sized data sets. Additionally it provides distributional variables of importance, thus identifying the most informative radiomic features. The analysis proved the predictive capacity of radiomic models even using a reduced number of features. Indeed, from tomography we achieved AUC-ROC 89.9 % using 19 features and 92.1 % using 7 of them; while from ABVS we attained an AUC-ROC of 72.3 % using 22 features and 85.8 % using only 3 features. Although the predictive power of DBT outperforms ABVS, when comparing the predictions at the patient level, only 8.7% of lesions are misclassified by both methods, suggesting a partial complementarity. Notably, promising results (AUC-ROC ABVS-DBT 71.8 % - 74.1 % ) were achieved using non-geometric features, thus opening the way to the integration of virtual biopsy in medical routine. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
31. Research on digital twin modeling method for combustion process based on model reduction
- Author
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Yue Zhang and Jiale Li
- Subjects
Model reduction ,Twin model ,Temperature field prediction ,POD ,Wavelet transform ,Cluster ,Engineering (General). Civil engineering (General) ,TA1-2040 - Abstract
In response to the difficulty in obtaining combustion information within coal-fired boiler furnaces, a method is proposed in this study to improve the reduced-order model using clustering segmentation. This approach aims to rapidly predict the combustion temperature field inside the furnace by establishing a twin model of the combustion temperature field. Initially, the finite volume method is employed to analyze the combustion system of a 600 MW subcritical boiler under various operating conditions. Subsequently, cross-sectional data from burner nozzle positions at each operating condition are extracted. These data are subjected to Proper Orthogonal Decomposition (POD), Spectral Proper Orthogonal Decomposition (SPOD), and Wavelet Transform-POD (WT-POD) for dimensionality reduction to obtain modal data. Comparative analyses are conducted on the modal data obtained from different methods. Furthermore, based on modal data analysis, a Support Vector Machine (SVM) regression model is selected to reconstruct the temperature field. The average absolute error of the reconstructed temperature fields from three methods under different operating conditions is then compared. Finally, the model is refined using clustering segmentation, resulting in an improvement of approximately 0.6 % in reconstruction accuracy. This enhancement demonstrates that the clustered POD-SVR-GA model achieves higher accuracy in reconstructing combustion temperature fields after clustering-based improvements.
- Published
- 2025
- Full Text
- View/download PDF
32. Batch distillation performance improvement through vessel holdup redistribution—Insights from two case studies
- Author
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Surendra Beniwal and Sujit S. Jogwar
- Subjects
Batch distillation ,Ternary separation ,Dynamic optimization ,Model reduction ,Chemical engineering ,TP155-156 ,Information technology ,T58.5-58.64 - Abstract
Middle vessel batch distillation (MVBD) is an energy-efficient configuration for separation of a ternary mixture. This paper focuses on improving the performance of this configuration through dynamic optimization of vessel holdup. Initially, a performance measure accounting for separation and energy efficiency is defined to characterize an operational policy. Subsequently, this measure is maximized by dynamically redistributing holdup in the three (top, middle and bottom) vessels. With the help of two case studies, the impact of various policy decisions and market conditions (such as initial feed distribution and relative cost of products and energy) on the optimal operating policy is analyzed. Specifically, the improvement obtained via holdup redistribution is explained with the help of fundamental concepts of distillation. Lastly, the performance of the proposed approach is compared with some of the existing methods and validated through rigorous simulations.
- Published
- 2024
- Full Text
- View/download PDF
33. Efficiency enhancement techniques in finite element analysis: navigating complexity for agile design exploration
- Author
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Haider, Aun
- Published
- 2024
- Full Text
- View/download PDF
34. Mathematical analysis of the limiting behaviors of a chromatin modification circuit
- Author
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Bruno, Simone, Williams, Ruth J, and Del Vecchio, Domitilla
- Subjects
Genetics ,Singular singularly perturbed system ,Model reduction ,Epigenetic cell memory ,Chromatin modifications ,Synthetic biology ,Applied Mathematics ,Electrical and Electronic Engineering ,Mechanical Engineering ,Industrial Engineering & Automation - Abstract
AbstractIn the last decade, the interactions among histone modifications and DNA methylation and their effect on the DNA structure, i.e., chromatin state, have been identified as key mediators for the maintenance of cell identity, defined as epigenetic cell memory. In this paper, we determine how the positive feedback loops generated by the auto- and cross-catalysis among repressive modifications affect the temporal duration of the cell identity. To this end, we conduct a stochastic analysis of a recently published chromatin modification circuit considering two limiting behaviors: fast erasure rate of repressive histone modifications or fast erasure rate of DNA methylation. In order to perform this mathematical analysis, we first show that the deterministic model of the system is a singular singularly perturbed (SSP) system and use a model reduction approach for SSP systems to obtain a reduced one-dimensional model. We thus analytically evaluate the reduced system’s stationary probability distribution and the mean switching time between active and repressed chromatin states. We then add a computational study of the original reaction model to validate and extend the analytical findings. Our results show that the absence of DNA methylation reduces the bias of the system’s stationary probability distribution toward the repressed chromatin state and the temporal duration of this state’s memory. In the absence of repressive histone modifications, we also observe that the time needed to reactivate a repressed gene with an activating input is less stochastic, suggesting that repressive histone modifications specifically contribute to the highly variable latency of state reactivation.
- Published
- 2023
35. Active vibration control of nonlinear flexible structures via reduction on spectral submanifolds: Active vibration control of nonlinear flexible structures
- Author
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Shen, Cong and Li, Mingwu
- Published
- 2025
- Full Text
- View/download PDF
36. An efficient PGD solver for structural dynamics applications
- Author
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Clément Vella, Pierre Gosselet, and Serge Prudhomme
- Subjects
Model reduction ,Proper Generalized Decomposition ,Hamiltonian formulation ,Symplectic structure ,Ritz Pairs ,Mechanics of engineering. Applied mechanics ,TA349-359 ,Systems engineering ,TA168 - Abstract
Abstract We propose in this paper a Proper Generalized Decomposition (PGD) solver for reduced-order modeling of linear elastodynamic problems. It primarily focuses on enhancing the computational efficiency of a previously introduced PGD solver based on the Hamiltonian formalism. The novelty of this work lies in the implementation of a solver that is halfway between Modal Decomposition and the conventional PGD framework, so as to accelerate the fixed-point iteration algorithm. Additional procedures such that Aitken’s delta-squared process and mode-orthogonalization are incorporated to ensure convergence and stability of the algorithm. Numerical results regarding the ROM accuracy, time complexity, and scalability are provided to demonstrate the performance of the new solver when applied to dynamic simulation of a three-dimensional structure.
- Published
- 2024
- Full Text
- View/download PDF
37. DYNAMIC MODEL REDUCTION USING MODAL TRUNCATION IN THE BUILDING MOTION PROBLEM
- Author
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Vu Thi Nguyet
- Subjects
modal truncation ,model reduction ,dynamic systems ,eigenmode analysis ,duilding motion model ,Technology ,Social sciences (General) ,H1-99 - Abstract
Modal truncation, an advanced algorithm for model reduction in dynamic systems, efficiently simplifies complex models by selectively discarding less influential eigenmodes, maintaining a balance between computational efficiency and model accuracy. This paper explores the algorithm's application to a 48th order building model. Proceed to reduce this model to lower orders, then analyze errors in time and frequency domains. Modal truncation algorithm systematically reduces model dimensions while preserving critical dynamic attributes. Numerical simulations reveal a favorable reduction order range (from order 6th to order 25th) for optimal balance, with sensitivity observed at order 25th. From the results obtained, depending on specific requirements, users can use a lower-order model corresponding to the allowed error to replace the original system. Recommendations include iterative refinement for adaptive reduction orders and in-depth analysis around critical points. This algorithm becomes an effective method for researchers dealing with high-dimensional dynamic systems, offering simpler yet accurate model representations. As technology develops, continued refinements and applications of modal truncation are expected, solidifying its role in the realm of model reduction.
- Published
- 2024
- Full Text
- View/download PDF
38. Research and development needs in combustion modeling
- Author
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Venkateswaran Sankaran
- Subjects
Combustion ,Propulsion ,Chemical kinetics ,Large Eddy simulations ,Data assimilation ,Model reduction ,Fuel ,TP315-360 ,Energy industries. Energy policy. Fuel trade ,HD9502-9502.5 - Abstract
This article provides a perspective on future research and development needs of aerospace propulsion from the vantage point of the Air Force Research Lab (AFRL). Particular applications that inform this perspective include solid and liquid rocket propulsion for booster applications, scramjet propulsion for hypersonic flight and rotating detonation engines for both air and space applications. The R&D needs are expressed in two categories—the first represents foundational research needs informed by specific application challenges, while the second catalogs foundational research needs informed broadly by digital engineering paradigms for future development. The former category concerns traditional research in combustion and energy sciences, while the latter category embraces emerging computational and mathematical research topics. Future progress will be depend upon advancements in both sets of topic areas.
- Published
- 2025
- Full Text
- View/download PDF
39. Models, simulations, and applications of small satellite thermal analysis.
- Author
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Shen, Ming, Zhang, Lei, Sun, Zhaowei, Kong, Lin, Liu, Yuhan, and Xue, Zhipeng
- Subjects
- *
MICROSPACECRAFT , *THERMAL analysis , *SENSITIVITY analysis , *TEST design , *RESEARCH & development - Abstract
Progress in satellite technology places higher expectations on the design period and reliability of thermal control systems, especially for small satellites with high intensification. Here, a thermal analysis is conducted throughout the satellite development process, with thermal modeling serving as the foundation for thermal analysis in the early and formal design and test verification stages. As a result, designers are required to appreciate, penetrate, and properly apply thermal models for the development of satellite thermal systems. Thus, in this article, we reviewed the research and development of thermal model techniques, as well as the preparation of crucial parameters and means of simplification for accurate and fast solutions. In addition, a summary of the relevant application and state-of-the-art technologies such as uncertainty and sensitivity analysis, intelligent optimization design, and parameter correlation, was dedicated to promoting the comprehensive development and innovation of thermal analysis of satellites. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
40. TRANSFORMED MODEL REDUCTION FOR PARTIAL DIFFERENTIAL EQUATIONS WITH SHARP INNER LAYERS.
- Author
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TIANYOU TANG and XIANMIN XU
- Subjects
- *
PARTIAL differential equations , *BURGERS' equation , *TRANSPORT equation , *DECOMPOSITION method , *EMPIRICAL research - Abstract
Small parameters in partial differential equations can give rise to solutions with sharp inner layers that evolve over time. However, the standard model reduction method becomes inefficient when applied to these problems due to the slow decaying Kolmogorov N-width of the solution manifold. To address this issue, a natural approach is to transform the equation in such a way that the transformed solution manifold exhibits a fast decaying Kolmogorov N-width. In this paper, we focus on the Allen--Cahn equation as a model problem. We employ asymptotic analysis to identify slow variables and perform a transformation of the partial differential equations accordingly. Subsequently, we apply the proper orthogonal decomposition method and a QR discrete empirical interpolation method (qDEIM) technique to the transformed equation with the slow variables. Numerical experiments demonstrate that the new model reduction method yields significantly improved results compared to direct model reduction applied to the original equation. Furthermore, this approach can be extended to other equations, such as the convection equation and the Burgers equation. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
41. FEED-FORWARD ARTIFICIAL NEURAL NETWORK AS SURROGATE MODEL TO PREDICT LIFT AND DRAG COEFFICIENT OF NACA AIRFOIL AND SEARCHING OF MAXIMUM LIFT-TO-DRAG RATIO.
- Author
-
KIESZEK, RAFAŁ, MAJCHER, MACIEJ, SYTA, BORYS, and KOZAKIEWICZ, ADAM
- Subjects
ARTIFICIAL neural networks ,FINITE volume method ,NUMERICAL calculations ,GENETIC algorithms ,AEROFOILS - Abstract
The problem of computation time in numerical calculations of aerodynamics has been studied by many research centres. In this work, a feed forward artificial neural network (FF-ANN) was used to determine the dependence of lift and drag coefficients on the angle of attack for NACA four-digit families. A panel method was used to generate the data needed to train the FF-ANNs. Optimisation using a genetic algorithm and a neural metamodel resulted in a non-standard NACA aerofoil for which the optimal angle of attack was determined with a maximum L/D ratio. The optimisation results were validated using the finite volume method. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
42. On the Sample Complexity of Stabilizing Linear Dynamical Systems from Data.
- Author
-
Werner, Steffen W. R. and Peherstorfer, Benjamin
- Subjects
- *
LINEAR dynamical systems , *DYNAMICAL systems , *SCIENCE education , *NUMERICAL solutions for linear algebra - Abstract
Learning controllers from data for stabilizing dynamical systems typically follows a two-step process of first identifying a model and then constructing a controller based on the identified model. However, learning models means identifying generic descriptions of the dynamics of systems, which can require large amounts of data and extracting information that are unnecessary for the specific task of stabilization. The contribution of this work is to show that if a linear dynamical system has dimension (McMillan degree) n , then there always exist n states from which a stabilizing feedback controller can be constructed, independent of the dimension of the representation of the observed states and the number of inputs. By building on previous work, this finding implies that any linear dynamical system can be stabilized from fewer observed states than the minimal number of states required for learning a model of the dynamics. The theoretical findings are demonstrated with numerical experiments that show the stabilization of the flow behind a cylinder from less data than necessary for learning a model. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
43. Salp Swarm Optimization-Based Approximation of Fractional-Order Systems with Guaranteed Stability.
- Author
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Gehlaut, Shekhar and Kumar, Deepak
- Subjects
- *
OPTIMIZATION algorithms , *PARTICLE swarm optimization , *EQUATIONS - Abstract
In this paper, we introduce the salp swarm optimization algorithm (SSOA)-based novel model reduction algorithm for simplifying commensurate and incommensurate fractional-order systems. In the case of commensurate fractional-order systems (CFOSs), the presented method converts it into a non-fractional-order system first. Then, we implement the SSOA with the stability equations to find a non-fractional-order approximant. Finally, the non-fractional-order approximant is transformed to determine the proposed reduced-order CFOS. It is also demonstrated using numerical examples that some existing methods fail to achieve the stability claim. On the other hand, the stability of the proposed fractional-order approximants is ascertained by incorporating stability equations along with SSOA. Further, the proposed method is extended for the model reduction in incommensurate and unstable fractional-order systems. In this case, the Oustaloup approximation is used along with the SSOA and stability equations to obtain the proposed non-fractional-order approximation. The simulation results corroborate the performance of the suggested method in both cases and establish its transcendency. The obtained results showcase the efficacy of optimization in simplification of fractional-order systems. The work also highlights the importance of order reduction in practical engineering and scientific applications of fractional-order systems. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
44. Enhancing load frequency control with plug-in electric vehicle integration in non-reheat thermal power systems.
- Author
-
Shukla, Rakesh Rajan, Garg, Man Mohan, Panda, Anup Kumar, and Das, Debapriya
- Subjects
- *
INTERCONNECTED power systems , *ELECTRIC vehicles , *PARTICLE swarm optimization , *ELECTRICAL load , *RENEWABLE energy sources , *REDUCED-order models - Abstract
As the percentage of renewable energy source within the energy production mix has expanded, it is become gradually difficult to determine the appropriate values for controller gains and model parameters. Controlling system frequency of interconnected power system during sudden load disturbance requires careful consideration of the controller gain values and small signal stability model parameters. This study proposes an innovative methodology for ascertaining controller gain values and model parameters for plug-in electric vehicles (PEVs) in load frequency control (LFC) applications. Proposed method uses the root locus (RL) approach to find the suitable controller gain values and model parameters for PEVs. This paper offers a thorough mathematical description of the proposed RL approach. Routh approximation method is used for reduced-order modelling (ROM), which comprises thermal and PEV systems, to reduce complexity of higher-order system while designing controllers. Fractional-order proportional-integral-derivative controller (FO-PID) is proposed, and its parameters are adjusted using particle swarm optimization (PSO) tool. To validate the efficacy of suggested method, a comprehensive comparison of time response parameters and performance indices (PI) is carefully carried out. Also, the various PEVs state of charge (SOC) levels is investigated, and effects of these levels are studied in LFC with robustness analysis of controller. The proposed method for determining gain value is highly reliable and efficient, outperforming existing methodologies in the literature. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
45. H2 optimal rational approximation on general domains.
- Author
-
Borghi, Alessandro and Breiten, Tobias
- Subjects
- *
LINEAR differential equations , *HARDY spaces , *LINEAR dynamical systems , *PARTIAL differential equations , *WAVE equation , *CONTINUOUS time models , *TRANSFER functions , *INTERPOLATION algorithms - Abstract
Optimal model reduction for large-scale linear dynamical systems is studied. In contrast to most existing works, the systems under consideration are not required to be stable, neither in discrete nor in continuous time. As a consequence, the underlying rational transfer functions are allowed to have poles in general domains in the complex plane. In particular, this covers the case of specific conservative partial differential equations such as the linear Schrödinger and the undamped linear wave equation with spectra on the imaginary axis. By an appropriate modification of the classical continuous time Hardy space H 2 , a new H 2 -like optimal model reduction problem is introduced and first-order optimality conditions are derived. As in the classical H 2 case, these conditions exhibit a rational Hermite interpolation structure for which an iterative model reduction algorithm is proposed. Numerical examples demonstrate the effectiveness of the new method. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
46. Predicting inmate suicidal behavior with an interpretable ensemble machine learning approach in smart prisons.
- Author
-
Akhtar, Khayyam, Yaseen, Muhammad Usman, Imran, Muhammad, Altaf Khattak, Sohaib Bin, and Nasralla, Moustafa M.
- Subjects
SUICIDAL behavior ,SUICIDE risk factors ,SUICIDAL ideation ,EVIDENCE gaps ,PRISONS ,KNOWLEDGE gap theory ,MACHINE learning - Abstract
The convergence of smart technologies and predictive modelling in prisons presents an exciting opportunity to revolutionize the monitoring of inmate behaviour, allowing for the early detection of signs of distress and the effective mitigation of suicide risks. While machine learning algorithms have been extensively employed in predicting suicidal behaviour, a critical aspect that has often been overlooked is the interoperability of these models. Most of the work done on model interpretations for suicide predictions often limits itself to feature reduction and highlighting important contributing features only. To address this research gap, we used Anchor explanations for creating human-readable statements based on simple rules, which, to our knowledge, have never been used before for suicide prediction models. We also overcome the limitation of anchor explanations, which create weak rules on highdimensionality datasets, by first reducing data features with the help of SHapley Additive exPlanations (SHAP). We further reduce data features through anchor interpretations for the final ensemble model of XGBoost and random forest. Our results indicate significant improvement when compared with state-of-the-art models, having an accuracy and precision of 98.6% and 98.9%, respectively. The F1-score for the best suicide ideation model appeared to be 96.7%. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
47. Reconstructing rodent brain signals during euthanasia with eigensystem realization algorithm (ERA)
- Author
-
Aqel, Khitam, Wang, Zhen, Peng, Yuan B., and Maia, Pedro D.
- Abstract
We accurately reconstruct the Local Field Potential time series obtained from anesthetized and awake rats, both before and during CO 2 euthanasia. We apply the Eigensystem Realization Algorithm to identify an underlying linear dynamical system capable of generating the observed data. Time series exhibiting more intricate dynamics typically lead to systems of higher dimensions, offering a means to assess the complexity of the brain throughout various phases of the experiment. Our results indicate that anesthetized brains possess complexity levels similar to awake brains before CO 2 administration. This resemblance undergoes significant changes following euthanization, as signals from the awake brain display a more resilient complexity profile, implying a state of heightened neuronal activity or a last fight response during the euthanasia process. In contrast, anesthetized brains seem to enter a more subdued state early on. Our data-driven techniques can likely be applied to a broader range of electrophysiological recording modalities. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
48. Prediction with data from designed experimentation.
- Author
-
D'Ottaviano, Fabio
- Subjects
- *
FORECASTING , *MODEL validation - Abstract
The intent of this study was to understand via simulation how data from designed experimentation for linear models can succeed in the prediction of individual values despite its relatively small size which renders data splitting for validation purposes nonviable. Another intent was to emphasize why, for a given level of precision, designed experimentation requires far many more runs for the prediction of individual values than it does for its more mundane use of mean prediction, and how this required number of runs can be determined via simulation as a function of the model validation method used. The results showed that prediction with designed data can be successful given its low tendency to overfitting and that model reduction can be detrimental to prediction which contrasts with the pursuit of a bias-variance tradeoff with undesigned data. As designed data increasingly resembles undesigned data, either by containing factors that have zero influence in the response, having high correlation among factors levels, and/or having small n to p ratio, model reduction becomes increasingly necessary for prediction. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
49. External Modeling for State Estimation and Network Applications at BC Hydro
- Author
-
Zhu, Qing, Yao, Michael (Ziwen), Atanackovic, Djordje, Toussaint, Margaret, Chow, Joe H., Series Editor, Stankovic, Alex M., Series Editor, Hill, David J., Series Editor, Vinnakota, Veera Raju, editor, and Nuthalapati, Sarma (NDR), editor
- Published
- 2024
- Full Text
- View/download PDF
50. Performance Enhancement of Car Body Structural Analysis and Optimization with Model Reduction in MSC Nastran
- Author
-
Rakhmatov, R. I., Zharkov, A. V., Chaari, Fakher, Series Editor, Gherardini, Francesco, Series Editor, Ivanov, Vitalii, Series Editor, Haddar, Mohamed, Series Editor, Cavas-Martínez, Francisco, Editorial Board Member, di Mare, Francesca, Editorial Board Member, Kwon, Young W., Editorial Board Member, Tolio, Tullio A. M., Editorial Board Member, Trojanowska, Justyna, Editorial Board Member, Schmitt, Robert, Editorial Board Member, Xu, Jinyang, Editorial Board Member, Radionov, Andrey A., editor, and Gasiyarov, Vadim R., editor
- Published
- 2024
- Full Text
- View/download PDF
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