Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system

With the development and popular application of Building Internet of Things (BIoT) systems, numerous types of equipment are connected, and a large volume of equipment data is collected. For convenient equipment management, the equipment should be identified and labeled. Traditionally, this process is performed manually, which not only is time consuming but also causes unavoidable omissions. In this paper, we propose a k-means clustering-based electrical equipment identification toward smart building application that can automatically identify the unknown equipment connected to BIoT systems. First, load characteristics are analyzed and electrical features for equipment identification are extracted from the collected data. Second, k-means clustering is used twice to construct the identification model. Preliminary clustering adopts traditional k-means algorithm to the total harmonic current distortion data and separates equipment data into two to three clusters on the basis of their electrical characteristics. Later clustering uses an improved k-means algorithm, which weighs Euclidean distance and uses the elbow method to determine the number of clusters and analyze the results of preliminary clustering. Then, the equipment identification model is constructed by selecting the cluster centroid vector and distance threshold. Finally, identification results are obtained online on the basis of the model outputs by using the newly collected data. Successful applications to BIoT system verify the validity of the proposed identification method.

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A Cahn-Hilliard-Biot system and its generalized gradient flow structure

Applied Mathematics Letters ◽

10.1016/j.aml.2021.107799 ◽

2021 ◽

pp. 107799

Author(s):

Erlend Storvik ◽

Jakub Wiktor Both ◽

Jan Martin Nordbotten ◽

Florin Adrian Radu

Keyword(s):

Flow Structure ◽

Gradient Flow ◽

Generalized Gradient ◽

Biot System

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A staggered finite element procedure for the coupled Stokes-Biot system with fluid entry resistance

Computational Geosciences ◽

10.1007/s10596-019-09931-7 ◽

2020 ◽

Vol 24 (4) ◽

pp. 1497-1522 ◽

Cited By ~ 1

Author(s):

E. A. Bergkamp ◽

C. V. Verhoosel ◽

J. J. C. Remmers ◽

D. M. J. Smeulders

Keyword(s):

Finite Element ◽

Finite Element Procedure ◽

Biot System

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Physics informed deep learning for coupled flow and poromechanics. Mandel’s problem

10.31224/osf.io/4yvnu ◽

2021 ◽

Author(s):

Saumik Dana ◽

Teeratorn Kadeethum

Keyword(s):

Deep Learning ◽

System Modeling ◽

Activation Function ◽

Learning Paradigm ◽

Coupled Flow ◽

Steep Gradient ◽

Learning Framework ◽

Temporal Domain ◽

Biot System ◽

Spatio Temporal

We evaluate the performance of the physics informed deep learning paradigm for solving the Biot system modeling coupled flow and poromechanics using Mandel’s problem analytical solution. The solution presents a unique set of challenges to the deep learning paradigm, such as the disparity in expected orders of magnitude of the output variables as well as the non-monotonicity and steep gradient in one of the output variables in a certain spatio-temporal domain. We tackle those challenges in this work and comment on the effect of activation function and minimization algorithm on the deep learning framework.

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Error Estimation of Euler Method for the Instationary Stokes–Biot Coupled Problem

Journal of Mathematics ◽

10.1155/2021/5982948 ◽

2021 ◽

Vol 2021 ◽

pp. 1-14

Author(s):

Koffi Wilfrid Houédanou ◽

Jamal Adetola

Keyword(s):

Finite Element ◽

Computational Model ◽

Error Estimation ◽

Stokes Equations ◽

Euler Method ◽

Error Estimators ◽

Fully Discrete ◽

Coupled Problem ◽

System Equilibrium ◽

Biot System

In this paper, we study a finite element computational model for solving the interaction between a fluid and a poroelastic structure that couples the Stokes equations with the Biot system. Equilibrium and kinematic conditions are imposed on the interface. A mixed Darcy formulation is employed, resulting in continuity of flux condition of essential type. A Lagrange multiplier method is used to impose weakly this condition. With the obtained finite element solutions, the error estimators are performed for the fully discrete formulations.

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ON NUMERICAL SOLUTION OF 1D POROELASTICITY EQUATIONS IN A MULTILAYERED DOMAIN

Mathematical Modelling and Analysis ◽

10.3846/13926292.2005.9637288 ◽

2005 ◽

Vol 10 (3) ◽

pp. 287-304 ◽

Cited By ~ 5

Author(s):

A. Naumovich ◽

O. Iliev ◽

F. Gaspar ◽

F. Lisbona ◽

P. Vabishchevich

Keyword(s):

Finite Difference ◽

Difference Scheme ◽

Numerical Solution ◽

Analytical Solutions ◽

Numerical Experiments ◽

Order Of Convergence ◽

Staggered Grid ◽

Finite Volume Discretization ◽

Collocated Grid ◽

Biot System

Finite volume discretization of Biot system of poroelasticity in a multilayered domain is presented. Staggered grid is used in order to avoid non‐physical oscillations of the numerical solution, appearing when a collocated grid is used. Various numerical experiments are presented in order to illustrate the accuracy of the finite difference scheme. In the first group of experiments, problems having analytical solutions are solved, and the order of convergence for the velocity, the pressure, the displacements, and the stresses is analyzed. In the second group of experiments numerical solution of real problems is presented. Straipsnyje pateikta Bioto sistemos poringai elastiškai terpei daugiasluosneje srityje diskretizacija baigtiniu tūriu metodu. Norint išvengti skaitinio sprendinio ne fiziniu osciliaciju atsirandančiu naudojant kolokacini tinkla, naudojamas judantis tinklas. Straipsnyje pateikti ivairūs skaitiniai eksperimentai iliustruoja baigtiniu skirtumu schemos tiksluma. Pirmoje tokio eksperimento dalyje sprendžiami uždaviniai, turintys analizinius sprendinius, ir analizuojama greičio, slegio, išstūmimo, itempiu artutiniu sprendiniu konvergavimo eile. Antroje eksperimento dalyje pateikta skaitinis realiu procesu modeliavimas.

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