Maximum Operating Research Articles

The elliptic maximal function

We study the elliptic maximal functions defined by averages over ellipses and rotated ellipses which are multi-parametric variants of the circular maximal function. We prove that those maximal functions are bounded on Lp for some p≠∞. For this purpose, we obtain some sharp multi-parameter local smoothing estimates.

$$A_p$$ weights on nonhomogeneous trees equipped with measures of exponential growth

AbstractThis paper aims to study $$A_p$$ A p weights in the context of a class of metric measure spaces with exponential volume growth, namely infinite trees with root at infinity equipped with the geodesic distance and flow measures. Our main result is a Muckenhoupt Theorem, which is a characterization of the weights for which a suitable Hardy–Littlewood maximal operator is bounded on the corresponding weighted $$L^p$$ L p spaces. We emphasise that this result does not require any geometric assumption on the tree or any condition on the flow measure. We also prove a reverse Hölder inequality in the case when the flow measure is locally doubling. We finally show that the logarithm of an $$A_p$$ A p weight is in BMO and discuss the connection between $$A_p$$ A p weights and quasisymmetric mappings.

On the local existence and blow-up solutions to a quasi-linear bi-hyperbolic equation with dynamic boundary conditions

This note aims to study the existence of the local solutions and derive a blow-up result for a quasi-linear bi-hyperbolic equation with dynamic boundary conditions. We use the maximal monotone operator theory to demonstrate the solution’s local well-posedness, and a concavity method to establish the blow-up result.

Prediction of outflow temperature of reservoir based on theory-guided machine learning models and optimization of operation for improving outflow temperature

The proportion of hydropower within the energy-resource structure is gradually increasing. However, the construction of reservoirs inevitably leads to ecological and environmental issues, especially the release of low-temperature water in summer and its detrimental effects on fish spawning and reproduction. These issues can be alleviated by optimizing the reservoir operation scheme, but the large amount of time required for predicting the reservoir outflow temperature emerges as the primary constraint. In this study, we considered Pubugou (PBG) Reservoir and proposed an efficient and high-precision prediction method for reservoir outflow temperature based on theory-guided machine learning (TGML) algorithms. This method was applied to the multi-objective optimization of the reservoir operations, and an optimization operation plan was proposed to improve the outflow temperature. The research results indicate that the LightGBM machine learning model shows good predictive performance, with a maximum deviation of no more than 1 °C in predicting the outflow temperature. There is a significant competitive relationship between reservoir power generation and the outflow temperature. Compared with the current operational scheme, the maximum power operation plan results in a 4.4% increase in total power generation but causes the average outflow temperature during the fish spawning period to decrease by 0.1 °C. The total power generation of the improved outflow temperature operation scheme was 0.8% lower than that of the actual scheme, but the average outflow temperature during fish spawning increased by 0.2 °C. Properly increasing the discharge flow from the reservoir and lowering the water level can thus help alleviate the issue of outflow temperature.

Fuzzy machine learning predictions of settling velocity based on fractal aggregate physical features in water treatment

The dynamics of gravitational sedimentation in water treatment are crucial for optimising particulate matter removal. This study addresses the effect of fractal aggregate features on settling velocity and explores fuzzy machine learning (ML) for predicting this phenomenon. Particle image velocimetry determined aggregate velocities within a sedimentation column, with features identified concurrently. Using a comprehensive methodological framework, significant predictors were selected through various statistical analyses. The fuzzy ML model, developed with the ‘FisPro’ package in R, incorporated a hierarchical partitioning scheme using Lukasiewicz and Sum operators for conjunction and disjunction processes, respectively. The Wang-Mendel method extracted fuzzy rules, with defuzzification achieved using the maximum crisp operator. Hyperparameter optimization was conducted through grid search techniques, and model performance was evaluated using 3-fold cross-validation. The findings reveal that Margination, Radius, and Clumpiness significantly impact settling velocity. The model demonstrates exceptional predictive accuracy (R2 = 0.923) across both training and validation datasets, highlighting its potential for forecasting terminal velocity in water treatment. This research suggests that precise predictions of sedimentation dynamics can improve particulate matter removal efficiency and encourages further investigations into diverse aggregate types and environmental scenarios, advocating for integrating physics-informed ML approaches to enhance the model.

New Kantorovich-type Szász–Mirakjan Operators

In this paper, we present a Kantorovich-type Szász–Mirakjan operators. Initially, we establish the recurrence relationship for the moments of these operators and provide the central moments up to the fourth degree. Subsequently, we analyze the local approximation properties of these operators using Peetre’s K-function. We investigate the rate of convergence, by utilizing the ordinary modulus of continuity and Lipschitz-type maximal functions. Additionally, we prove weighted approximation theorems and Voronoskaja-type theorems specific to these new operators. Following this, we introduce bivariate extension of these operators and investigate some approximation properties. Lastly, we include several numerical illustrative examples.

A Unified Version of Weighted Weak-Type Inequalities for the One-Sided Hardy–Littlewood Maximal Function in Orlicz Classes

A Unified Version of Weighted Weak-Type Inequalities for the One-Sided Hardy–Littlewood Maximal Function in Orlicz Classes

Intrinsic square function and wavelet characterizations of variable Hardy–Lorentz spaces

Let p(⋅):Rn→(0,∞] be a variable exponent function satisfying the globally log-Hölder continuous condition and q∈(0,1]. The goal of this article is to characterize the variable Hardy–Lorentz space Hp(⋅),q(Rn) in terms of various intrinsic square functions including the intrinsic g-function, the intrinsic Lusin area integral and the intrinsic gλ⁎-function. Using the intrinsic square function and the known atomic characterizations of Hp(⋅),q(Rn), and establishing some estimates on a discrete Littlewood–Paley g-function and a Peetre-type maximal function, the authors further give several equivalent characterizations of Hp(⋅),q(Rn) via wavelets. What is different from the existing works is that we merely assume p+=ess supx∈Rnp(x)∈(0,∞). One of the important tools that make it possible is to find a new dual space of Hp(⋅),q(Rn).

Effects of cushion gas pressure and operating parameters on the capacity of hydrogen storage in lined rock caverns (LRC)

Hydrogen storage in lined rock cavern (LRC) provides versatile site selection, safety, and stability, making it a crucial option. In this study, a thermodynamic mathematical model was established to describe hydrogen storage in LRC. This model is based on the principles of mass, momentum, and energy conservation while accounting for the authentic compressibility of hydrogen. The thermodynamic fluctuations throughout the seasonal cycle in LRC were computed using the COMSOL Multiphysics software. The results indicate that when the hydrogen storage reaches the operating pressure, the lower the cushion gas pressure, the greater the hydrogen injection amount, and the higher the utilization rate of storage capacity. With a cushion gas pressure of 3 MPa, the storage capacity utilization rate exceeds that at 15 MPa by 41 %. The injection rate of 0.5 kg/s results in a temperature increase of 12 °C compared to 0.27 kg/s, indicating twice the temperature rise at the 0.27 kg/s injection rate. An increase in injection temperature corresponds to higher temperature within the hydrogen storage cavern upon completion of gas injection, thereby reducing the time needed for gas injection to reach maximum operating pressure. A lower initial cavern temperature results in a longer time for hydrogen storage to reach maximum operating pressure.

A new representation learning based maximum power operation towards improved energy management integration with DG controllers for photovoltaic generators using online deep exponentially expanded RVFLN algorithm

To incorporate Local Energy Management System (LEMS) based Tertiary Controller (TC) operation with multiple Photovoltaic based Distributed Generations (PV-DGs) level Primary Controller/ PC: Independent DG Controllers (IDGC) more adequately, a new representation learning (Symmetrical Input-Output weight Encoded Data Compression/ SIODC, with Exponential Expansion based Random Vector Functional Link Network towards Softmax layer’s Control Reference Estimation/ ExRVFLN-SoCRE) based MPPT controller is proposed in this paper in terms of Secondary Controllers (SCs). A new Hybrid LEMS (HyLEMS) is presented towards the proposed Deep Neural Network based SCs (i.e. DNN-SCs) in a distributed (SCdist), as well as centralized (SCcent) manner, to ease the computational, and communication requirements. To investigate that multiple PV-DGs based duty cycle (kth instant Control References/CRs estimation) controllers are considered here with auxiliary Battery Energy Storage Systems (BESS), and AC utility, integrated to Common DC feeder in terms of DC-DC converter dynamics. To avoid Control Reference Estimation Error (CREE) due to initial randomization, optimization subroutines are incorporated for SIODC by generalized semi-supervised learning, and for ExRVFLN-SoCRE by Lagrange multiplier weighted, rms based cost function. The proposed control performance is verified in MATLAB Simulink® based average modeling, and validated through dSPACE DS1104 based RTI with multi-PV (emulators) test-bench as well.

Sharp maximal function estimates for linear and multilinear pseudo-differential operators

In this paper, we study pointwise estimates for linear and multilinear pseudo-differential operators with exotic symbols in terms of the Fefferman-Stein sharp maximal function and Hardy-Littlewood type maximal function. Especially in the multilinear case, we use a multi-sublinear variant of the classical Hardy-Littlewood maximal function introduced by Lerner, Ombrosi, Pérez, Torres, and Trujillo-González [16], which provides more elaborate and natural weighted estimates in the multilinear setting.

Localized operators on weighted Herz spaces

AbstractWe introduce the notion of localized operators. We extend the boundedness of the localized operators from the weighted Lebesgue spaces to the weighted Herz spaces. The localized operators include the Hardy operator, the Riemann–Liouville fractional integrals, the general Hardy‐type operators, the geometric mean operator, and the one‐sided maximal function. Therefore, this paper extends the mapping properties of the the Hardy operator, the Riemann–Liouville fractional integrals, the general Hardy‐type operators, the geometric mean operator, and the one‐sided maximal function to the weighted Herz spaces.

Evaluating the thermal stability of an interior permanent magnet synchronous machine through iterative multi‐physics simulation

AbstractThis paper investigates the thermal operating capability of an interior permanent magnet synchronous machine. An iterative workflow is presented, combining electromagnetic modeling, control, power‐loss modeling, and thermal modeling to identify maximum thermal stable operating points. Special attention is given to the critical temperatures of winding and permanent magnets. A nonlinear reduced order model based on finite element method model was used to simulate the system, including an inverter model with space vector pulse width modulation in combination with field‐oriented control. Furthermore, an advanced iron core loss model and thermal lumped parameter model were employed. The presented approach allows for evaluating losses and their impact on steady‐state temperatures. The obtained results highlight the significant influence of space vector pulse width modulation on iron core losses and the importance of considering both advanced power‐loss models and adequate thermal models when analyzing the machine's thermal state. This research emphasizes the concept of a thermally stable envelope, providing a comprehensive understanding of the thermal boundaries under various operating conditions.

A cost-effective linear propulsion system featuring PMEDW for HTS maglev vehicle: design, implementation, and dynamic test

Since 2021, the first high-speed, high-temperature superconducting maglev engineering prototype has proven its practical feasibility. However, the pressing need to mitigate the high costs of the current linear synchronous motor (LSM) technology remains paramount. This study aims to tackle this issue by introducing a novel, cost-effective propulsion way featuring the PMEDWs, optimizing its specifications, studying electromagnetic characteristics, fabricating a physical prototype, and conducting line tests to confirm application feasibility. Firstly, the conceptual prototype is introduced, outlining its functionality and principles. Subsequently, employing dynamic simulation models, structural specifications are optimized, and electromagnetic characteristics are evaluated. Afterwards, a comprehensive HTS maglev prototype weighting 1200 kg equipped with four PMEDWs and measurement system is designed and fabricated. Finally, validation of the simulation model effectiveness is conducted using a dedicated test rig. Dynamic line tests along a 165-meter line measure the performance metrics of the speed, levitation and propulsion gap, lateral and vertical accelerations, and propulsion and guidance forces, and maximum operation speed of 3. 03 m/s at n = 500 rpm. This study implements the physical prototype and dynamic testing of the PMEDW propulsion system, and confirms its feasibility for the first time, and the estimated cost is approximately one-tenth of the existing LSM motors in the 165-m test line. This technology promises significant innovation in linear propulsion methods, offering an economical alternative for Maglev vehicles.

Hardy–Littlewood fractional maximal operators on homogeneous trees

We study the mapping properties of the Hardy–Littlewood fractional maximal operator between Lorentz spaces of the homogeneous tree and discuss the optimality of all the results.

Calcium Manganite Based Materials for Thermochemical Energy Storage in High Temperature Solar Thermal Plants: Materials Screening

The urgent need for sustainable energy supply requires maximum exploitation of renewable energy sources. The latter, being of intermittent nature, need to be coupled with efficient energy storage. Solar-thermal power-plants are inherently compatible with thermal storage, which is a cost-efficient method of storing energy for later use but the field is currently dominated by sensible heat molten salts used as heat storage media but with a maximum operating temperature of about 560oC. Certain ceramic materials, able to induce reversible reduction-oxidation reactions under air flow, are promising alternatives to molten salts because they can withstand much higher temperatures (>1000oC) and thus can be integrated with high-efficiency air-Brayton thermodynamic cycles. At the same time the chemical energy stored/released during such reduction-oxidation reactions can boost energy storage density by up to 10 times cf. sensible only concepts. In this framework, Ca-Mn-based perovskite compositions were demonstrated to function effectively as energy storage materials. The current work offers insights on material synthesis parameters to achieve relatively high purity Ca-Mn-based compositions and subsequently optimize their redox performance in the course of a preliminary 5-cycle campaign. Moreover, the occurring structural transitions and their corresponding heat effects are also discussed and elaborated upon. This study is the first step towards the, currently in progress, process of synthesising – at multi kg scale – and shaping these compositions into extruded honeycomb-like monolithic structures for subsequent future application in lab- and pilot-scale high temperature thermochemical energy storage systems.

Airtightness evaluation of lined caverns for compressed air energy storage under thermo-hydro-mechanical (THM) coupling

Large-scale compressed air energy storage (CAES) technology can effectively facilitate the integration of renewable energy sources into the power grid. The airtightness of caverns is crucial for the economic viability and efficiency of CAES systems. This paper presents a new thermo-hydro-mechanical (THM) model for investigating the effects of complex thermodynamic changes on air leakage in concrete-lined rock caverns. The model is validated using field measurement data, numerical simulations, and analytical solutions. Subsequent simulations were conducted to analyze air leakage, pore pressure, and leakage range under various operating conditions. Finally, the impacts of different parameters on air tightness were assessed. The results indicate that the daily air leakage mass percentage (TDALMP) in the concrete-lined CAES cavern is 0.60 % under the operating pressure of 4.5–10 MPa, which meets the tightness requirement. The permeability of the lining is a key parameter for airtightness, in this case, the permeability of the concrete lining cannot exceed 1 × 10−19 m2. The daily air leakage rate can be reduced by modestly increasing the cavern radius, lowering the temperature of the injected air, and decreasing the maximum operating pressure. These results can provide a reference for the study and construction of CAES caverns in similar projects.

Numerical investigation of ionic transport and overpotential effects in the electrolyte of the lithium-ion battery

ABSTRACT In this study, we numerically investigated the electrochemical performance of a CGR 17,600 lithium-ion battery (LIB), focusing on lithium-ion transport dynamics within the electrolyte. Using a one-dimensional Nernst-Planck model and finite difference method, we simulated ion diffusion and migration during galvanostatic charge-discharge cycles. Our model predicts concentration profiles, overpotentials, and resistances, identifying a maximum safe operating current of 0.8271 A. The analysis reveals that diffusion dominates during discharge, while migration prevails during charging. The study also characterises ohmic resistance of 0.0497 Ω and steady-state resistance of 0.1904 Ω, underscoring their importance in battery efficiency. Additionally, a transference coefficient of 0.4 highlights effective ion transport, critical for optimising LIB design and performance.

Target localization algorithm based on improved short-time Fourier transform

The properties of Doppler through-wall radar (TWR) in target localization applications mainly depend on the accuracy of instantaneous frequency (IF) estimations obtained from the time-frequency distribution (TFD) of target echo. However, when the time-frequency aliasing occurs in TFD, it is difficult to accurately estimate the target IF curves. To solve this problem, an improved short-Time Fourier transform is proposed in this paper. Firstly, a series of rough estimation time-frequency information (IF and chirp rate) of target echoes are obtained by fractional Fourier transform. Secondly, we update the time-frequency window according to the rough time-frequency information of the target signal. Meanwhile, we define a new distribution estimator based on the local maximum. Finally, the target IF curve is obtained by the local maximum operator as well as the updated window function. The experimental results show that the method significantly improves the target IF estimation and localization accuracy by 76.5 % and 74.6 %, respectively, compared with STFT.

A hierarchical energy management strategy for DC microgrid hybrid energy storage systems based on fractional-order sliding mode controller

A hierarchical energy management strategy (EMS) for a fuel cell (FC)-supercapacitor (SC)‑lithium battery hybrid energy storage system (HESS), based on a fractional-order sliding mode controller (FOSMC), is proposed to address the nonlinear behavior of low-voltage direct current (DC) microgrid HESS. To fully exploit the energy of the SC, the system management layer divides the EMS into maximum power operation mode and state machine control algorithm operation mode. For the first time in equipment control layer, a FOSMC, more suitable for handling nonlinear characteristics, is employed, and its stability is evaluated using the Lyapunov method. Finally, a 48 V HESS experimental platform is constructed for validation, demonstrating that the proposed EMS enhances the stability, response speed, and robustness of the HESS. Compared to conventional sliding mode controller (SMC) and integral sliding mode controller (ISMC), the adoption of a FOSMC reduces the steady-state error of the bus voltage by at least 9.1 % and increases the response speed by at least 11.1 %, while exhibiting good robustness to external disturbances and uncertainties in controller parameters. This fills the current research gap in parameter robustness validation.