Fran Sérgio Lobato

This work presents a novel extension of the Orthogonal Collocation Method (OCM) for the numerical solution of variable-order fractional differential–algebraic equations with prescribed initial conditions. Unlike most existing collocation-based approaches, the proposed formulation is specifically designed for differential–algebraic systems and accommodates time-dependent fractional orders within the Caputo framework. The methodology is validated using two benchmark mathematical problems and subsequently applied to the analysis of a fractional-order Resistor-Inductor-Capacitor (RLC) electrical circuit under free and forced excitation. The numerical results show excellent agreement with analytical solutions and significant improvements over reference solutions reported in the literature. For the benchmark problems, the proposed approach achieved errors several orders of magnitude smaller than those reported in previous studies and substantially lower than those obtained with the Adams-type Predictor–Corrector Method (APCM). In addition, the method required markedly lower computational times while using only a small number of collocation points. For the RLC circuit, the results indicate that the variable fractional order has a pronounced influence on the system dynamics, often comparable to or greater than that of the electrical resistance. Fractional orders close to unity reproduce the classical circuit behavior, whereas lower orders introduce stronger memory effects, leading to reduced current amplitudes, lower energy dissipation, and enhanced energy storage in the reactive components. The proposed framework provides an accurate and computationally efficient tool for simulating variable-order fractional differential–algebraic systems and offers a promising alternative for modeling complex engineering processes characterized by memory and hereditary effects.

Traditionally, reliability analysis neglects the influence of time, leading to inaccurate predictions for systems under progressive degradation and variable loads. However, addressing time dependency is of major significance, as material aging and cumulative damage dynamically alter the system’s condition, increasing the probability of failure throughout its operational lifespan. Time-dependent (or time-variant) reliability analysis addresses this challenge, as time directly affects failure probability. This paper proposes and evaluates two methodologies: Sequential Reliability Analysis (SRA) and Decoupled Reliability Analysis (DRA). SRA transforms the time-dependent problem into an equivalent time-independent one by discretizing time, using a metamodel to approximate the failure probability profile, and performing a one-dimensional search for the optimal value. In this method, reliability analysis is required at each discretized time point. Conversely, DRA also removes time dependency but does so by replacing the time variable with a metamodel dependent on random variables, requiring only one reliability analysis. Both methodologies were validated through mathematical and engineering case studies. The results demonstrate that both provide accurate failure probability estimates, with errors below 2% when compared to reference solutions or Monte Carlo Method (MCM) results. Additionally, the DRA approach achieved a computational cost reduction of up to 99.8% relative to the traditional method. These findings confirm the effectiveness and efficiency of the proposed approaches for time-dependent reliability analysis in engineering applications.

Agricultural drones have been widely used in precision agriculture operations due to their high performance and adaptability to outdoor tasks, such as spraying, mapping, and monitoring. Nevertheless, mission planning remains challenging due to the constraints imposed by operational performance under real field conditions. In this work, a novel multi-objective optimization approach for mission planning of agricultural spraying drones is proposed. This approach contemplated an off-line coverage path planning strategy that simultaneously minimizes total mission time and energy consumption. The parameters that define the coverage path are optimized while considering the operational requirements of the spraying tasks. The framework is applied to a real case study using the DJI AGRAS T10 drone in a crop field. The results obtained from the multi-objective optimization demonstrate significant performance gains in terms of reduction in battery energy consumption of up to 14.2% and a mission time decrease of 9.5% when compared to conventional geometric methods. Thus, the proposed method potentially reduces both the drag energy and the mission time. These findings highlight the potential of multi-objective optimization as a decision-support tool to improve the efficiency and sustainability of drone-based spraying operations in agriculture.

The use of optimization tools in distillation processes can be computationally intensive, due to the scale of the simulation problems associated with the optimization structure. In many situations, it is desirable to obtain a distillation column configuration that is capable of achieving pre-established degrees of purity for the products of interest while simultaneously minimizing operating costs and annualized investments. In this paper, we present the development of an optimization–simulation tool for distillation problems using a low-parameter metaheuristic (the Symbiotic Organisms Search algorithm, SOS) coupled with a simulation tool with sparse Jacobian matrix calculations (using a coloring graph algorithm) and code vectorization. The applicability of the developed framework was demonstrated in a separation train for a non-ideal ternary mixture. The numerical results obtained indicate that the computational tool proved to be viable from a computational time standpoint—with significant gains over the calculation of the Jacobian matrix using finite differences—approaching the vicinity of the optimum region in a small number of iterations. In addition, the possibility of integrating simulation and optimization tools for distillation processes in a single environment was demonstrated, avoiding complex communication structures between the simulator and the optimizer. The results obtained also indicated substantial improvements—in terms of minimizing a metric that involves investments and energy expenditures—in comparison with non-optimized designs for the same separation train.

Establishing precise welding parameters is essential to achieving the desired bead geometry and ensuring consistent quality in manufacturing processes. However, determining the optimal configuration of parameters remains a challenge, particularly when relying on limited experimental data. This study proposes the use of artificial neural networks (ANNs), with their architecture optimized via differential evolution (DE), to predict key MAG welding parameters based on target bead geometry. To address data limitations, cross-validation and data augmentation techniques were employed to enhance model generalization. In addition to the ANN model, machine learning algorithms commonly recommended for small datasets, such as K-nearest neighbors (KNNs) and support vector machines (SVMs), were implemented for comparative evaluation. The results demonstrate that all models achieved good predictive performance, with SVM showing the highest accuracy among the techniques tested, reinforcing the value of integrating traditional ML models for benchmarking purposes in low-data scenarios.

Engineering system design is a highly relevant and dynamic field, with numerous applications reported in the literature. This type of problem generally encompasses several objectives and constraints, including those arising from mass, energy, and momentum balances, material behavior equations, and a range of environmental, physical, and operational restrictions. To address such challenges, a range of evolutionary optimization strategies has been proposed and evaluated. This work presents a Multi-objective Thermal Exchange Optimization (MTEO) algorithm that integrates concepts of Pareto dominance along with crowding distance strategies. To assess its performance, the proposed algorithm is applied to three well-established mechanical design problems. The results demonstrate that the MTEO algorithm provides accurate approximations of the Pareto front in comparison with conventional evolutionary methods. Specifically, average reductions of approximately 36%, 32%, and 68% were observed for the respective design problems. Furthermore, the MTEO parameters were found to be easy to configure across all applications.

The numerical solution of the sedimentation phenomenon presents a significant challenge due to the presence of discontinuities at interfaces, characterized by three distinct regions: (i) clear liquid, (ii) constant solid concentration, and (iii) solid concentration varying from the initial to a maximum value. This problem is particularly relevant in the oil industry, where sedimentation is an essential unit operation in processes such as wastewater treatment, drilling fluid control, and phase separation during production. Discontinuities and abrupt variations in solid concentrations pose significant challenges for traditional numerical methods in solving this model type. In this study, three high-order numerical methods (Tangent of Hyperbola Interface Capturing, Weighted Essentially Non-Oscillatory, and High-Resolution Central Scheme) are employed to solve two classic case studies in the sedimentation process. In general, the results indicate that all three methods were effective in handling the discontinuities at the phase interfaces while maintaining the accuracy and stability of the solution. Moreover, although all methods performed satisfactorily in various aspects, the High-Resolution Central Scheme was found to be the most efficient in terms of computational time.

In recent decades, the study of particulate materials has gained significant attention from the scientific community. This is due to applications that can be developed, among which we can cite the risks to human health and the environment. As a consequence of this concern, classifying nanoparticles is a topic of considerable interest. One of the most used devices to classify nanoparticles in aerosols is the Differential Mobility Analyzer. From a mathematical point of view, particle concentration profiles have been obtained, preferably, considering constitutive relationships. In this contribution, the Poisson–Nernst–Planck equation is used to determine the concentration of monodisperse nanoparticles in aerosols subjected to an electric field. For this purpose, an inverse problem is proposed and solved considering real data and the Differential Evolution algorithm as an optimization tool. The results demonstrate that the proposed methodology was able to obtain good estimates considering the phenomenological model in relation to experimental points, as well as accurate estimates for intermediate profiles considering the Kriging approach. Finally, it is important to mention that the novelty of this contribution lies in predicting the concentration of monodisperse nanoparticles in aerosols subjected to an electric field using the Poisson–Nernst–Planck equation.