Search Results (12)

Accurate electricity price forecasting (EPF) is essential for market participants to optimize trading strategies and for power systems to accommodate the increasing penetration of volatile renewable energy sources. However, electricity price series are characterized by strong nonlinearity, high volatility, and significant structural breaks, which pose substantial challenges to conventional forecasting models. Although numerous hybrid deep learning models have been proposed for EPF, most existing approaches either overlook structural breaks or treat them as outliers rather than as signals of regime shifts, often resulting in systematic forecasting degradation when market conditions change abruptly. To address this issue, this study proposes COCAL-TTL, a novel multi-stage structural break-aware forecasting framework that integrates regime-adaptive data partitioning with a functionally differentiated hybrid deep learning architecture. First, a joint detection scheme combining the Iterated Cumulative Sum of Squares (ICSS) algorithm and the Chow test is employed to partition Spanish electricity market data from 2014 to 2023 into distinct regimes. Within each regime, CEEMDAN is applied to extract multi-scale features, which are subsequently reconstructed into trend, periodic, and random components based on an independent sample t-test and Fast Fourier Transform (FFT). The CNN-SE Attention-LSTM (CAL) model, with hyperparameters optimized by the Osprey Optimization Algorithm (OOA), serves as the primary forecasting engine. In addition, a dedicated heterogeneous error correction module, namely TTL, is introduced, in which Temporal Convolutional Network, Transformer, and LSTM are designed to capture local transients, long-range dependencies, and transitional dynamics in the residual series, respectively. Empirical results demonstrate that compared with the Naive benchmark, COCAL-TTL achieves percentage MAPE improvements of 58.48% and 48.97% in low- and high-volatility regimes, respectively. These findings indicate that the proposed structural break-aware framework provides a robust data-driven solution for EPF under heterogeneous market conditions and offers technical support for stable electricity market operation in the context of renewable energy integration. Full article

The Kuramoto–Sivashinsky (KS) equation and its fractional generalizations (FKSs) arise as canonical models for a wide class of nonlinear dissipative–dispersive systems, including thin-film flows, combustion fronts, drift–wave turbulence in plasmas, and chemically reacting media, where shock-like and strongly localized structures play a central role in the dynamics. Despite their apparent simplicity, KS-type models become analytically intractable once higher-order dissipation, geometric effects, and memory (fractional) operators are incorporated, and standard perturbative or transform-based schemes often lead to cumbersome recursive structures, slow convergence, or severe restrictions on the initial data. In this work, a novel direct approximation procedure, referred to as the Tantawy Technique (TT), is developed and implemented to solve and analyze planar fractional KS-type equations and their Burgers-type reductions in a systematic manner. The central difficulty is to construct, for a given physically motivated initial profile, a rapidly convergent series in fractional time that remains stable for a broad range of the fractional order and transport coefficients, while still retaining a clear link to the underlying shock-wave physics. To overcome this, the TT combines (i) a Tanh-based exact shock solution of the planar integer-order KS equation, obtained first as a reference via the standard Tanh method, with (ii) a carefully designed fractional-time ansatz in powers of $t^{\rho }$, where the spatial coefficients are determined recursively from the governing equation in the Caputo sense. This construction yields closed-form expressions for the first few terms in the approximation hierarchy and allows one to monitor convergence through residual and absolute error measures. Full article

As the popularity of smartphones, wearable devices, intelligent vehicles, and countless other devices continues to rise, the surging demand for mobile data traffic has resulted in an increasingly crowded electromagnetic spectrum. Spectrum sharing serves as a solution to optimize the utilization of wireless communication channels, allowing various types of users to share the same frequency band securely. This paper investigates spectrum allocation and power control problems in overlay spectrum sharing, with a focus on promoting green communication. Maximizing weighted sum energy efficiency (WSEE) requires solving complex multiple-ratio fractional programming (FP) problems. In contrast, weighted sum power (WSP) minimization offers a more straightforward approach. Moreover, because WSP is directly related to users’ power consumption, we can dynamically adjust their weights to balance their residual energy. We prioritize WSP minimization over the more common WSEE maximization. This choice not only simplifies computation but also maintains users’ quality of service (QoS) requirements. The joint optimization for multiple primary users (PUs) and secondary users (SUs) can be decomposed into two components: a weighted bipartite matching problem and a series of convex resource allocation problems. Utilizing Newton’s method, our system-level simulation results show that the proposed scheme achieves optimal performance with minimal computational time. We explore strategies to accelerate the proposed scheme by refining the selection of initial values for Newton’s method. Full article

The development of numerical or analytical solutions for fractional mathematical models describing specific phenomena is an important subject in physics, mathematics, and engineering. This paper’s main objective is to investigate the approximation of the fractional order Caudrey–Dodd–Gibbon ($CDG$) nonlinear equation, which appears in the fields of laser optics and plasma physics. The physical issue is modeled using the Caputo derivative. Adomian and homotopy polynomials facilitate the handling of the nonlinear term. The main innovation in this paper is how the recurrence relation, which generates the series solutions after just a few iterations, is handled. We examined the assumed model in fractional form in order to demonstrate and verify the efficacy of the new methods. Moreover, the numerical simulation is used to show how the physical behavior of the suggested method’s solution has been represented in plots and tables for various fractional orders. We provide three problems of each equation to check the validity of the offered schemes. It is discovered that the outcomes derived are close to the accurate result of the problems illustrated. Additionally, we compare our results with the Laplace residual power series method (LRPSM), the natural transform decomposition method (NTDM), and the homotopy analysis shehu transform method (HASTM). From the comparison, our methods have been demonstrated to be more accurate than alternative approaches. The results demonstrate the significant benefit of the established methodologies in achieving both approximate and accurate solutions to the problems. The results show that the technique is extremely methodical, accurate, and very effective for examining the nature of nonlinear differential equations of arbitrary order that have arisen in related scientific fields. Full article

This study provides an innovative and attractive analytical strategy to examine the numerical solution for the time-fractional Schrödinger equation (SE) in the sense of Caputo fractional operator. In this research, we present the Elzaki transform residual power series method (ET-RPSM), which combines the Elzaki transform (ET) with the residual power series method (RPSM). This strategy has the advantage of requiring only the premise of limiting at zero for determining the coefficients of the series, and it uses symbolic computation software to perform the least number of calculations. The results obtained through the considered method are in the form of a series solution and converge rapidly. These outcomes closely match the precise results and are discussed through graphical structures to express the physical representation of the considered equation. The results showed that the suggested strategy is a straightforward, suitable, and practical tool for solving and comprehending a wide range of nonlinear physical models. Full article

In this paper, we suggest a modification for the residual power series method that is used to solve fractional-order Helmholtz equations, which is called the Shehu-transform residual power series method ($\mathbb{S}$T-RPSM). This scheme uses a combination of the Shehu transform ($\mathbb{S}$T) and the residual power series method (RPSM). The fractional derivatives are taken with respect to Caputo order. The novelty of this approach is that it does not restrict the fractional order and reduces the need for heavy computational work. The results were obtained using an iterative series that led to an exact solution. The 3D graphical plots for different values of fractional orders are shown to compare $\mathbb{S}$T-RPSM results with exact solutions. Full article

In this article, a new analytical scheme of the ARA transform is introduced to solve systems of fractional partial differential equations. The principle of the proposed technique is based on combining the ARA transform with the residual power series method to create an approximate series solution for a system of partial differential equations of fractional order on the form of a rapid convergent series. To illustrate the effectiveness, accuracy, and validity of the suggested technique, an Attractive physical system, the fractional neutron diffusion equation with one delayed neutrons group, is discussed and solved. Two different neutron flux initial conditions are presented numerically to clarify various cases in order to ensure the theoretical results. The necessary Mathematica codes are run using vital nuclear reactor cross-section data, and the results for various values of time are tabulated and graphically represented. Full article

High-speed EMUs (electric multiple-units) frequently pass through the phase-separation zone during operation. Overvoltage generated during the operation of the vehicle-mounted circuit breaker has a long duration and high waveform steepness, which accelerates the service life of the vehicle-mounted equipment and is likely to cause insulation failures. For the above-mentioned problems, the operating overvoltage characteristics of high-speed EMU were obtained by traction substation-catenary-EMUs system (SCES) analysis and experiments, thus deriving the influences of the closed phase angle and the residual magnetism of the vehicle-mounted transformer on operating overvoltage. The results showed that the voltage phase of the catenary significantly affected the operating overvoltage, and the closed switching overvoltage was small at 0–40°, 140–210° and 320–350°. The voltage on the primary side of the vehicle-mounted transformer was 60.78 kV, with the transient impact of high-frequency oscillation overvoltage of 22.71 kV, and an initial period of oscillation of 0.01 ms. Then, the period became longer, and it took 0.5 ms for the high-frequency oscillation from attenuation to disappearance. Finally, a scheme of series reactance suppression devices was proposed to protect vehicle-mounted voltage transformers. This work is to provide data support for the insulation design and system protection of a traction power supply system. Full article

Power consumption forecasting is a crucial need for power management to achieve sustainable energy. The power demand is increasing over time, while the forecasting of power consumption possesses challenges with nonlinearity patterns and various noise in the datasets. To this end, this paper proposes the RobustSTL and temporal convolutional network (TCN) model to forecast hourly power consumption. Through the RobustSTL, instead of standard STL, this decomposition method can extract time series data despite containing dynamic patterns, various noise, and burstiness. The trend, seasonality, and remainder components obtained from the decomposition operation can enhance prediction accuracy by providing significant information from the dataset. These components are then used as input for the TCN model applying deep learning for forecasting. TCN employing dilated causal convolutions and residual blocks to extract long-term data patterns outperforms recurrent networks in time series forecasting studies. To assess the proposed model, this paper conducts a comparison experiment between the proposed model and counterpart models. The result shows that the proposed model can grasp the rules of historical time series data related to hourly power consumption. Our proposed model overcomes the counterpart schemes in MAPE, MAE, and RMSE metrics. Additionally, the proposed model obtains the best results in precision, recall, and F1-score values. The result also indicates that the predicted data can fit the pattern of the actual data. Full article

Nowadays, marine propulsion systems based on thermal machines that operate under the diesel cycle have positioned themselves as one of the main options for this type of applications. The main comparative advantages of diesel engines, compared to other propulsion systems based on thermal cycle engines, are the low specific fuel consumption of residual fuels, and their higher thermal efficiency. However, its main disadvantage lies in the emissions produced by the combustion of the residual fuels, such as carbon dioxide (CO₂), sulfur oxide (SO_x), and nitrogen oxide (NO_x). These emissions are directly related to the operating conditions of the propulsion system. Over the last decade, the International Maritime Organization (IMO) has adopted a series of regulations to reduce CO₂ emissions based on the introduction of an Energy Efficiency Design Index (EEDI) and an Energy Efficiency Operational Indicator (EEOI). In this context, adding a Shaft Generator (SG) to the propulsion system favoring lower EEDI and EEOI values. The present work proposes a selective control system and optimization scheme that allows operating the shaft generator in Power Take Off (PTO) or Power Take In (PTI) mode, ensuring that the main engine operates, always, at the optimum fuel efficiency point, thus ensuring minimum CO₂ emissions. Full article

In this paper, the general state of quantum mechanics equations that can be typically expressed by nonlinear fractional Schrödinger models will be solved based on an attractive efficient analytical technique, namely the conformable residual power series (CRPS). The fractional derivative is considered in a conformable sense. The desired analytical solution is obtained using conformable Taylor series expansion through substituting a truncated conformable fractional series and minimizing its residual errors to extract a supportive approximate solution in a rapidly convergent fractional series. This adaptation can be implemented as a novel alternative technique to deal with many nonlinear issues occurring in quantum physics. The effectiveness and feasibility of the CRPS procedures are illustrated by verifying three realistic applications. The obtained numerical results and graphical consequences indicate that the suggested method is a convenient and remarkably powerful tool in solving different types of fractional partial differential models. Full article

The modeling of fuzzy fractional integro-differential equations is a very significant matter in engineering and applied sciences. This paper presents a novel treatment algorithm based on utilizing the fractional residual power series (FRPS) method to study and interpret the approximated solutions for a class of fuzzy fractional Volterra integro-differential equations of order $0<\beta \le 1$ which are subject to appropriate symmetric triangular fuzzy conditions under strongly generalized differentiability. The proposed algorithm relies upon the residual error concept and on the formula of generalized Taylor. The FRPS algorithm provides approximated solutions in parametric form with rapidly convergent fractional power series without linearization, limitation on the problem’s nature, and sort of classification or perturbation. The fuzzy fractional derivatives are described via the Caputo fuzzy $\mathrm{H}$ -differentiable. The ability, effectiveness, and simplicity of the proposed technique are demonstrated by testing two applications. Graphical and numerical results reveal the symmetry between the lower and upper $r$ -cut representations of the fuzzy solution and satisfy the convex symmetric triangular fuzzy number. Notably, the symmetric fuzzy solutions on a focus of their core and support refer to a sense of proportion, harmony, and balance. The obtained results reveal that the FRPS scheme is simple, straightforward, accurate and convenient to solve different forms of fuzzy fractional differential equations. Full article