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This paper proposed a user-friendly and adaptive home intelligent agent with self-learning capability for optimal scheduling of smart home energy systems. The intelligent agent autonomously identifies model parameters based on system operation data, eliminating the need for manual input and making it more user-friendly and practical to implement. It can also self-learn the latest energy consumption information from an updated dataset and adaptively adjust model parameters to accommodate changing conditions. Utilizing these determined models as input, the intelligent agent performs day-ahead optimal scheduling using the proposed many-objective integer nonlinear optimization model and automatically controls system operation. Experimental studies were conducted on a laboratory-based smart home energy system to verify the effectiveness of the developed intelligent agent in different scenarios. The results consistently demonstrate Mean Absolute Percentage Errors below -12.7 % across all three scenarios, indicating the accuracy of the intelligent agent. Furthermore, the optimal scheduling significantly enhances system performances. After optimization, daily operational costs, peak-valley differences, and CO2 emissions were reduced by 34.1 % to 81.6 %, 29.2 % to 36.7 %, and 19.6 % to 43.2 %, respectively. Moreover, the PV generation self-consumption rate and self-sufficiency rate improved by 29.6 % to 38.0 % and 40.5 % to 49.4 %, respectively. The proposed intelligent agent provides invaluable guidance for optimal dispatch of smart home energy systems in real-world settings.

This paper proposes the notion of model adaptivity for fluid flow modelling, where the underlying model (the governing equations) is adaptively changed in space and time. Specifically, this work introduces a hybrid and adaptive coupling of a 3D bulk fluid flow model with a 2D thin film flow model. As a result, this work extends the applicability of existing thin film flow models to complex scenarios where, for example, bulk flow develops into thin films after striking a surface. At each location in space and time, the proposed framework automatically decides whether a 3D model or a 2D model must be applied. Using a meshless approach for both 3D and 2D models, at each particle, the decision to apply a 2D or 3D model is based on the user-prescribed resolution and a local principal component analysis. When a particle needs to be changed from a 3D model to 2D, or vice versa, the discretization is changed, and all relevant data mapping is done on-the-fly. Appropriate two-way coupling conditions and mass conservation considerations between the 3D and 2D models are also developed. Numerical results show that this model adaptive framework shows higher flexibility and compares well against finely resolved 3D simulations. In an actual application scenario, a 3 factor speed up is obtained, while maintaining the accuracy of the solution. • Novel notion of model adaptivity: governing equations are adaptively changed. • Coupling 3D Navier–Stokes and 2D thin film flow. • No a-priori information describing where to use which model. • Model and discretization changed on-the-fly. [ABSTRACT FROM AUTHOR]

Summary: Homogenization methods are drawing increasing attention for simulation of heterogeneous materials like composites. For balancing the accuracy and the numerical efficiency of such strategies, we deal with both model and discretization errors of the finite element method (FEM) on a macroscale. Within a framework of goal‐oriented adaptivity, we consider linear elastic heterogeneous materials, for which first‐order homogenization schemes apply. A novel model hierarchy is proposed based on mean‐field and full‐field homogenization methods. For the former, we consider several well‐established schemes like Mori‐Tanaka or self‐consistent as basic models, and for the latter, as superior models, unit cell problems are solved via the FEM under an a priori chosen boundary condition. For a further stage of the model hierarchy, we consider hierarchical unit cells within the frame of the FEM toward an adaptive selection of the unit cell size. By means of several numerical examples, we illustrate the effectiveness of the proposed adaptive approach. [ABSTRACT FROM AUTHOR]

We consider model adaptivity for gas flow in pipeline networks. For each instant in time and for each pipe in the network a model for the gas flow is to be selected from a hierarchy of models in order to maximize a performance index that balances model accuracy and computational cost for a simulation of the entire network. This combinatorial problem involving partial differential equations is posed as an optimal switching control problem for abstract semilinear evolutions. We provide a theoretical and numerical framework for solving this problem using a two stage gradient descent approach based on switching time and mode insertion gradients. A numerical study demonstrates the practicability of the approach. [ABSTRACT FROM AUTHOR]

In engineering practice, models are typically kept as simple as possible for ease of setup and use, computational efficiency, maintenance, and overall reduced complexity to achieve robustness. In solid mechanics, a simple and efficient constitutive model may be favored over one that is more predictive, but is difficult to parameterize, is computationally expensive, or is simply not available within a simulation tool. In order to quantify the modeling error due to the choice of a relatively simple and less predictive constitutive model, we adopt the use of a posteriori model-form error-estimation techniques. Based on local error indicators in the energy norm, an algorithm is developed for reducing the modeling error by spatially adapting the material parameters in the simpler constitutive model. The resulting material parameters are not material properties per se , but depend on the given boundary-value problem. As a first step to the more general nonlinear case, we focus here on linear elasticity in which the “complex” constitutive model is general anisotropic elasticity and the chosen simpler model is isotropic elasticity. The algorithm for adaptive error reduction is demonstrated using two examples: (1) A transversely-isotropic plate with hole subjected to tension, and (2) a transversely-isotropic tube with two side holes subjected to torsion. [ABSTRACT FROM AUTHOR]

The research field of model adaptivity is well established, aiming at adaptive selection of mathematical models from a well defined class of models (model hierarchy) to achieve a preset level of accuracy. The present work addresses its application to a class of linear elastic composite problems. We will show that the classical bounding theories can provide a model hierarchy in a natural and theoretically consistent manner, without combination of different methods using a priori knowledge. To arrive at computable higher order bounds, the classical singular approximation is made. As a new finding, this may, under certain circumstances, give rise to an overlap effect. To overcome this, a correction is proposed. Additionally, the model adaptivity is coupled to the well established adaptive finite element method (FEM), such that both macro model and macro discretization errors are controlled. The proposed adaptive procedure is driven by a goal-oriented a posteriori error estimator based on duality techniques. For efficient computation of the dual solution, a patch-based recovery technique is proposed and compared to existing methods. For illustration, numerical examples are presented. [ABSTRACT FROM AUTHOR]

A new adaptive modeling method for aircraft engine by using equilibrium manifold (EM) and its expansion (EME) model is presented, following research undertaken by the authors at School of Transportation Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing, China. The property of the expansion model and the effect of mapping design to the form are systematically studied. The model adaptivity analysis is discussed, and this paper also gives the identification procedure of modeling the aircraft engine approximate nonlinear model; the deterioration modification of compressor and the comparison with linear parameter-varying model and Kalman estimator are discussed. Simulations illustrate that modeling accuracy is high and the structure is simpler. [ABSTRACT FROM AUTHOR]

We propose a duality based a posteriori error estimator for the computation of functionals averaged in time for nonlinear time dependent problems. Such functionals are typically relevant for (quasi-)periodic solutions in time. Applications arise, e.g. in chemical reaction models. In order to reduce the numerical complexity, we use simultaneously locally refined meshes and adaptive (chemical) models. Hence, considerations of adjoint problems measuring the sensitivity of the functional output are needed. In contrast to the classical dual-weighted residual (DWR) method, we favor a fixed mesh and model strategy in time. Taking advantage of the (quasi-)periodic behaviour, only stationary dual problems have to be solved. [ABSTRACT FROM AUTHOR]

Abstract: A computational methodology for goal-oriented combined discretization and expansive (refined) model adaptivity by overall implicit error control of quantities of interest is presented, requiring estimators of primal and dual discretization and model errors. In the case of dimensional within model adaptivity, prolongations of coarse model solutions into the solution space of a fine model for defining a consistent model error are necessary, which can be achieved at the element level by two strategies. The first one is an orthogonalized kinematic prolongation of nodal displacements, whereas the second one uses prolongations of the external loads which are then used to solve additional local variational problems thus yielding prolongated solutions which a priori fulfill the required orthogonality relations at the element level. Finally, a numerical example of an elastic continuous T-beam is presented with comparative results where goal-oriented error estimation is applied to linear elasticity with a discrete Reissner–Mindlin plate model as the coarse model and the 3D theory as the fine model. [Copyright &y& Elsevier]

Abstract: We introduce an a posteriori modeling error estimator for the effective computation of electric potential propagation in the heart. Starting from the Bidomain problem and an extended formulation of the simplified Monodomain system, we build a hybrid model, called Hybridomain, which is dynamically adapted to be either Bi- or Monodomain ones in different regions of the computational domain according to the error estimator. We show that accurate results can be obtained with the adaptive Hybridomain model with a reduced computational cost compared to the full Bidomain model. We discuss the effectivity of the estimator and the reliability of the results on simulations performed on real human left ventricle geometries retrieved from healthy subjects. [Copyright &y& Elsevier]

Abstract: In finite element simulation of sheet metal forming, shell elements are widely used. The limits of applicability of the shell elements are sometimes disregarded, which leads to an error in predictions of important values such as springback geometry. The underlying kinematic assumptions of the shell elements do not hold where the thickness of the metal sheet approaches the value of the radius of curvature. Complex three-dimensional material behavior effects cannot be represented precisely as the result of the simplified kinematics. Here we present a model adaptivity scheme based on a model error indicator. The model-adaptive technique presented in this paper aides to resolve only the critical areas of the structure with a three-dimensional discretization while keeping reasonable computational cost by utilizing shell elements for the rest of the structure. The model error indicator serves as a guide for subsequent automatic adaptive re-meshing of the work-piece followed by a model-adaptive finite element analysis. The accuracy of the approximation obtained by the model-adaptive technique coincides well with that of a more expensive solution obtained with solid elements only. [Copyright &y& Elsevier]

Abstract: We are interested in the simulation and optimization of gas transport in networks. Those networks consist of pipes and various other components like compressor stations and valves. The gas flow through the pipes can be modelled by different equations based on the Euler equations. For the other components, purely algebraic equations are used. Depending on the data, different models for the gas flow can be used in different regions of the network. We use adjoint techniques to specify model and discretization error estimators and present a strategy that adaptively applies the different models while maintaining the accuracy of the solution. [ABSTRACT FROM AUTHOR]

A modification of the hp–d method is presented, which allows to locally enhance a dimensionally reduced finite element approximation with an Ansatz based on a more accurate, i.e. dimensionally higher, model. The procedure is based on a hierarchical domain decomposition which is applied to couple discretizations of different types of mechanical models, like beams, plates and solids. Thereby, the error of the underlying mathematical model can be reduced in critical regions by introducing locally a physically more sophisticated model. Two examples are given to demonstrate the basic properties of the proposed method. In the first example the solution of a one-dimensional beam model is improved locally by a two-dimensional finite element computation. In the second example the local enhancement of a Reissner–Mindlin plate by a fully three-dimensional continuum approach is considered, yielding a significant reduction of the model error. [Copyright &y& Elsevier]

We investigate the concept of dual-weighted residuals for measuring model errors in the numerical solution of nonlinear partial differential equations. The method is first derived in the case where only model errors arise and then extended to handle simultaneously model and discretization errors. We next present an adaptive model/mesh refinement procedure where both sources of error are equilibrated. Various test cases involving Poisson equations and convection diffusion-reaction equations with complex diffusion models (oscillating diffusion coefficient, nonlinear diffusion, multicomponent diffusion matrix) confirm the reliability of the analysis and the efficiency of the proposed methodology. [ABSTRACT FROM AUTHOR]