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Motivated by recent developments in batch Reinforcement Learning (RL), this paper contributes to the application of batch RL in energy management in microgrids. We tackle the challenge of finding a closed-loop control policy to optimally schedule the operation of a storage device, in order to maximize self-consumption of local photovoltaic production in a microgrid. In this work, the fitted Q-iteration algorithm, a standard batch RL technique, is used by an RL agent to construct a control policy. The proposed method is data-driven and uses a state-action value function to find an optimal scheduling plan for a battery. The battery’s charge and discharge efficiencies, and the nonlinearity in the microgrid due to the inverter’s efficiency are taken into account. The proposed approach has been tested by simulation in a residential setting using data from Belgian residential consumers. The developed framework is benchmarked with a model-based technique, and the simulation results show a performance gap of 19%. The simulation results provide insight for developing optimal policies in more realistically-scaled and interconnected microgrids and for including uncertainties in generation and consumption for which white-box models become inaccurate and/or infeasible.

This article presents two numerical methods of the order of three for singular perturbation problems, with a small positive parameter using finite differences. It is a problem with an initial layer in the neighborhood of the initial nodal point whose width is of the order of the small parameter ϵ . Explicit order three classical methods are modified, and a new scheme is designed for singular perturbation problems. It is a fitted operator method and it is explicit with a variable fitting factor (VFF) evaluated at all nodal points. To reduce the calculation time of the scheme with VFF, the VFF is replaced by a fixed constant fitting factor (CFF). It is implicit with a CFF which is evaluated only one time at the initial nodal point. These two schemes are both optimal concerning the small parameter ϵ and uniform of order three. The three order methods presented in this article are superior to the three order methods available in the literature. To view the initial layer when the mesh size is larger than the parameter in the problem, these two fitted operator methods are extended to fitted mesh methods since fitted mesh methods are layer rescaling. The construction of the fitted mesh method is also provided. That is, the uniform mesh is extended to non-uniform mesh. Experimental results are presented to show the optimal and higher-order performance of the two numerical methods using three test problems.

The large integration of variable energy resources is expected to shift a large part of the energy exchanges closer to real-time, where more accurate forecasts are available. In this context, the short-term electricity markets and in particular the intraday market are considered a suitable trading floor for these exchanges to occur. A key component for the successful renewable energy sources integration is the usage of energy storage. In this paper, we propose a novel modelling framework for the strategic participation of energy storage in the European continuous intraday market where exchanges occur through a centralized order book. The goal of the storage device operator is the maximization of the profits received over the entire trading horizon, while taking into account the operational constraints of the unit. The sequential decision-making problem of trading in the intraday market is modelled as a Markov Decision Process. An asynchronous version of the fitted Q iteration algorithm is chosen for solving this problem due to its sample efficiency. The large and variable number of the existing orders in the order book motivates the use of high-level actions and an alternative state representation. Historical data are used for the generation of a large number of artificial trajectories in order to address exploration issues during the learning process. The resulting policy is back-tested and compared against a number of benchmark strategies. Finally, the impact of the storage characteristics on the total revenues collected in the intraday market is evaluated.

This paper highlights the role that reinforcement learning can play in the optimization of treatment policies for chronic illnesses. Before applying any off-the-shelf reinforcement learning methods in this setting, we must first tackle a number of challenges. We outline some of these challenges and present methods for overcoming them. First, we describe a multiple imputation approach to overcome the problem of missing data. Second, we discuss the use of function approximation in the context of a highly variable observation set. Finally, we discuss approaches to summarizing the evidence in the data for recommending a particular action and quantifying the uncertainty around the Q-function of the recommended policy. We present the results of applying these methods to real clinical trial data of patients with schizophrenia.

In the last few decades, numerical simulation for nonlinear oscillators has received a great deal of attention, and manyresearchers have been concerned with the design and analysis ofnumerical methods for solving oscillatory problems. In this paper, from the perspective of the continuous finite element method, we propose and analyze new energy-preserving functionally fitted methods, in particular trigonometrically fitted methods of an arbitrarily high order for solving oscillatory nonlinear Hamiltonian systems with a fixed frequency. To implement these new methods in a widespread way, they are transformed into a class of continuous-stage Runge–Kutta methods. This paper is accompanied by numerical experiments on oscillatory Hamiltonian systems such as the FPU problem and nonlinear Schrödinger equation. The numerical results demonstrate the remarkable accuracy and efficiency of our new methods compared with the existing high-order energy-preserving methods in the literature.

High‐performance flexible strain sensors are gaining more and more attention with their bespoken detection range, excellent sensing performance, and good stability, which are highly desired in wearable electronics. Herein, a thermoplastic polyurethane elastomer (TPU) fibrous membrane is prepared as a flexible substrate by electrostatic spinning technology, then a coating of polydopamine is formed through fast synthesizing the dopamine on TPU fibrous membrane surface and loaded with carbon nanotubes (CNTs) to develop an extremely sensitive flexible strain sensor. The flexible sensor prepared by TPU fibrous membrane coated with polydopamine layer has an outstanding sensibility under the pulling force (Gauge Factor of 10 528.53 with 200% strain), rapid reaction time (188–221 ms), wide sensing range (up to 200%), good stability, and durability. The theoretical studies reveal the underlying cause for the high sensitivity and the inherent relationship between the amount of conducting routes and the length between adjacent conducting fillers in the sensor. The demonstration of the device shows a promising application to sense human motion at various locations of the body, with the accurate and stable electrical signal output generated at corresponding motion. A thermoplastic polyurethane elastomer (TPU) fibrous membrane is prepared as a flexible substrate by electrostatic spinning technology, and a coating of polydopamine is formed through fast polymerizing the dopamine on the TPU fiber membrane surface and loaded with CNTs to develop a flexible strain sensor with extremely high sensitivity (Gauge Factor of 10528.53 with 200% strain).

An optimized embedded 5(3) pair of explicit Runge–Kutta–Nyström methods with four stages using phase-fitted and amplification-fitted techniques is developed in this paper. The new adapted pair can exactly integrate (except round-off errors) the common test: y″=−w2y. The local truncation error of the new method is derived, and we show that the order of convergence is maintained. The stability analysis is addressed, and we demonstrate that the developed method is absolutely stable, and thus appropriate for solving stiff problems. The numerical experiments show a better performance of the new embedded pair in comparison with other existing RKN pairs of similar characteristics.

The present study evaluated the ratcheting response of notched and press-fitted Al 7075-T6 specimens under stress-controlled asymmetric cycles. The degree of the interference fit (DIF) directly influenced the magnitude and the rate of progressive plastic strain at the notch edge region. Local ratcheting at the hole–pin interference region was analyzed by means of two kinematic-hardening rules—the Ahmadzadeh–Varvani (A–V) rule and the Chaboche rule—coupled with the Neuber rule. Ratcheting strains at the notch root of aluminum samples with DIF = 0 (non-press-fitting samples) were measured and found to be the highest in magnitude. For the press-fitted samples, however, ratcheting strains dropped noticeably as the DIF increased from 1% to 2%. The press-fitting process plastically deformed the perimeter edges of the notches and improved the materials strength locally at the notch edges, resulting in better resistance against ratcheting progress. Local ratcheting strains at distances of 0.5, 1.3, and 3.0 mm from the notch roots were predicted for both pinned and unpinned samples via the hardening rules and were compared with those of measured ratcheting values. The ratcheting curves predicted by means of the A-V and Chaboche hardening rules closely agreed with the experimental data. The predicted ratcheting curves were positioned, respectively, above and below the measured ratcheting data.

Topology optimization has the potential to be widely applied to produce innovative and efficient structures, allowing engineers to optimize their aesthetics and performance. This article adopted a 172-line Matlab code TriTOP172 to implement topology optimization in the unstructured triangular mesh using the bi-directional evolutionary structural optimization method. Its most significant feature is the elimination of zig-zag boundaries essentially existing in the commonly used rectangular mesh. The code uses 40 lines for preliminary setup and optimization iterations and a 78-line function to obtain the body-fitted mesh by solving the balance of a truss network. It also has a 20-line function of nonlinear diffusion to further smooth boundaries and control structure complexity and a 34-line function of finite element analysis. Numerical examples of compliance minimization are provided to assist readers in understanding the algorithm and its implementation. This code can be employed with further extensions to solve complicated conceptual design problems efficiently in several engineering fields. The educational Matlab program is accessible on the website and displayed in the Appendix.

In the present paper, the regularity and finite difference methods for Caputo-Hadamard fractional differential equations with initial value singularity are taken into consideration. To overcome the weak singularity and enhance convergence precision, a fitted scheme on nonuniform meshes is applied to such problems. Firstly, based on L log , 2 - 1 σ approximation, the temporal convergence accuracy of fitted scheme for the sub-diffusion equations is O ( N - min { 2 r α , 2 } ) , where N denotes the number of time steps, α is the fractional order and r is the mesh grading parameter. It is indicated that the performance of the fitted scheme is better than that of the standard L log , 2 - 1 σ scheme on (i) exponent meshes (i.e., r = 1 ) and (ii) graded meshes with the optimal choice of the mesh grading. Secondly, a second-order fitted scheme on exponent meshes for the diffusion-wave equations is obtained. Furthermore, for the sake of improving the computational efficiency and demonstrating the effectiveness of the decomposition of the solution, the fast algorithm and further decomposition of the solution for the sub-diffusion equations are investigated. Ultimately, some examples are presented to verify the availability of our theoretical results.