Discretization and Model Reduction Error Estimation of Interconnected Dynamical Systems

Dogančić, Bruno; Jokić, Marko

doi:10.1016/j.ifacol.2022.06.029

Cited by 3 publications

(4 citation statements)

References 7 publications

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“…The reliability of numerical models can be improved via probabilistic methods (i.e., Monte Carlo simulations), capacity design, and robust design [55,56]. Methods such as the quad-precision number type, reduced models with fewer degrees of freedoms, discretization, and model order reduction can be employed to minimize the truncation and rounds off errors caused by stored data crossing permissible values, and enhance the scientificity of the shaft wall damage model [57][58][59].…”

Section: Discussionmentioning

confidence: 99%

Shaft Wall Damage to High-Depth Inclined Ore Passes under Impact Wear Behavior

Jiang,

Ji,

Xue

2023

Applied Sciences

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In order to study shaft wall damage resulting from ore drawing in ore passes, a theoretical model for predicting the shaft wall damage to high-depth inclined ore passes is constructed based on field surveys of 25 ore passes in a deep mine in Yunnan, China. The mathematical expression of the total shaft wall damage volume is derived using the contact mechanics theory. Considering the structural characteristics of ore passes, and taking No. 1, 2, 3, and 9 ore passes as examples, combined with numerical simulation and an engineering case, the rationality of the proposed theoretical model is verified with respect to the initial collision position and the damage conditions of the shaft wall. The influence of, and sensitivity to, the ore block size P and the structural parameters of high-depth inclined ore passes on the total shaft wall damage volume Qtol are quantitatively analyzed. The results show that the calculation results of the theoretical model and numerical simulation are in good agreement with the actual engineering situations. Moreover, the ore-pass dip angle θ and the inclined angle of the chute α have a significant impact on the damage to the shaft wall, while the effects of the ore-pass depth H and the shaft diameter D are comparatively minor. With an increase in θ or α, Qtol generally first increases and then decreases. Qtol increases exponentially with P and increases steadily with D. H affects Qtol by influencing the collision frequency between the ore and the shaft wall. Therefore, in the mining design of deep mines, θ and α should be minimized as much as possible or adjusted to approach 90°, thereby reducing damage to the shaft wall. Secondly, ore block size should be strictly controlled to prevent collapses in the shaft wall caused by large ore blocks. This work provides technical support for the long-term safe operation of high-depth inclined ore passes.

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Section: Discussionmentioning

confidence: 99%

Shaft Wall Damage to High-Depth Inclined Ore Passes under Impact Wear Behavior

Jiang,

Ji,

Xue

2023

Applied Sciences

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“…This is common practice, but beyond the scope of this paper. For works on error estimation including both the discretization error and the ROM error, please refer to [45][46][47]. The error estimation reviewed in this work could be combined with the discretization error estimator [37] to realize adaptivity of the mesh size by checking the two estimated errors respectively, during a joint greedy process for both spatial discretization and MOR.…”

Section: Remarkmentioning

confidence: 99%

“…where Ât (μ), Ê(μ), f (•, •), b(μ), ĉ(μ) are defined as in (3) and dk (μ) = V T d k (μ). We make use of both the corrected FOM ( 45) and the corresponding ROM (46) to derive output error estimation for the output error |y k (μ) − ŷk (μ)|, where y k (μ) and ŷk (μ) are the outputs of the FOM in (2) and the ROM in (3) at any time instance t k , respectively. Both systems can be solved using any black-box solver.…”

Section: Error Estimator For Roms Solved With Any Black-box Time-inte...mentioning

confidence: 99%

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A posteriori error estimation for model order reduction of parametric systems

Feng,

Chellappa,

Benner

2024

Adv. Model. and Simul. in Eng. Sci.

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This survey discusses a posteriori error estimation for model order reduction of parametric systems, including linear and nonlinear, time-dependent and steady systems. We focus on introducing the error estimators we have proposed in the past few years and comparing them with the most related error estimators from the literature. For a clearer comparison, we have translated some existing error bounds proposed in function spaces into the vector space $${\mathbb {C}}^n$$ C n and provide the corresponding proofs in $$\mathbb C^n$$ C n . Some new insights into our proposed error estimators are explored. Moreover, we review our newly proposed error estimator for nonlinear time-evolution systems, which is applicable to reduced-order models solved by arbitrary time-integration solvers. Our recent work on multi-fidelity error estimation is also briefly discussed. Finally, we derive a new inf-sup-constant-free output error estimator for nonlinear time-evolution systems. Numerical results for three examples show the robustness of the new error estimator.

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Structure Preserving Uncertainty Modelling and Robustness Analysis for Spatially Distributed Dissipative Dynamical Systems

et al. 2022

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The paper deals with uncertainty modelling, robust stability and performance analysis of multi-input multi-output (MIMO) reduced order spatially distributed dissipative dynamical systems. While researching the topic of modern robust control of such systems, two key findings were discovered: (i) systematic modelling of the uncertainty and model order reduction (MOR) at the level of a subsystem gives both modelling freedom and the ability for obtaining less conservative uncertainties on the level of a subsystem; (ii) for a special class of interconnected dissipative dynamical systems, uncertainty conservatism at the subsystem level can be reduced—a novel, structure preserving algorithm employing subsystem partitioning and subsystem MOR by means of balanced truncation method (BTM) is used to obtain low-order robustly stable interconnected systems. Such systems are suitable for practical decentralized and distributed robust controller synthesis. Built upon a powerful framework of integral quadratic constraints (IQCs), this approach gives uncertainty modelling flexibility to perform robustness analysis of real world interconnected systems that are usually affected by multiple types of uncertainties at once. The proposed uncertainty modelling procedure and its practical application are presented on the numerical example. A spatially discretized vibration dynamical system comprised of a series of simply supported Euler beams mutually interconnected by springs and dampers is examined. Spatial discretization of the mathematical model is carried out using the finite element method (FEM).

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Discretization and Model Reduction Error Estimation of Interconnected Dynamical Systems

Cited by 3 publications

References 7 publications

Shaft Wall Damage to High-Depth Inclined Ore Passes under Impact Wear Behavior

Shaft Wall Damage to High-Depth Inclined Ore Passes under Impact Wear Behavior

A posteriori error estimation for model order reduction of parametric systems

Structure Preserving Uncertainty Modelling and Robustness Analysis for Spatially Distributed Dissipative Dynamical Systems

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