Math. Comput. Appl., Volume 29, Issue 2 (April 2024) – 13 articles

This study aims to synthesize and implement a robust fractional order PD (RFOPD) controller to increase the speed at which defects in automated touch panel inspection systems (ATPISs) are detected. A three-dimensional orthogonal stage (TDOS) driven by BLDC servo motors moves the inspection pen (IP) vertically and horizontally. The dynamic equation relating the BLDC servo motor input to the tip motion is established. A touch position identification (TPI) system is used to locate the touch point rapidly. An RFOPD controller is used to actuate the BLDC servo motors and move the TDOS rapidly and accurately in three dimensions. This method displaces the IP to any specified position and shows user-defined inspection trajectories on the touch screens. The gain-phase margin tester (GPMT) and stability equation methods are exploited to schedule the RFOPD controller gain settings and to maintain the specific safety margins for the controlled system. The simulation studies show that the proposed RFOPD controller exhibits better tracking and disturbance rejection responses than a conventional PID controller. The robustness of the RFOPD-controlled ATPIS, considering unmodeled uncertainties and friction-induced disturbances, is verified through simulation and experimental studies. Several user-defined inspection patterns are used to verify performance, and the experimental results show that the proposed RFOPD controller is effective. Full article

In this paper, we derive the well-defined solutions to a $\theta$-dimensional system of difference equations. We show that, the well-defined solutions to that system are represented in terms of Fibonacci and Lucas sequences. Moreover, we study the global stability of the solutions to that system. Finally, we give some numerical examples which confirm our theoretical results. Full article

In this study, the Method of Fundamental Solutions (MFSs) is adopted to model Chemical Vapor Infiltration (CVI) in a fibrous preform. The preparation of dense fiber-reinforced silicon carbide composites is considered. The reaction flux at the solid surface is equal to the diffusion flux towards the surface. The Robin or third-type boundary condition is implemented into the MFS. From the fibers’ surface concentrations obtained by MFS, deposition rates are calculated, and the geometry is updated at each time step, modeling the pore filling over time. The MFS solution is verified by comparing the results to a known analytical solution for a simplified geometry of concentric cylinders with a concentration set at the outer cylinder and a reaction at the inner cylinder. MFS solutions are compared to published experimental data. Porosity transients are obtained by a combination of MFSs with surface deposition to show the relation between the initial and final porosities. Full article

Intraclass correlation in bilateral data has been investigated in recent decades with various statistical methods. In practice, stratifying bilateral data by some control variables will provide more sophisticated statistical results to satisfy different research proposed in randomized clinical trials. In this article, we propose three test statistics (the likelihood ratio test, score test, and Wald-type test statistics) to evaluate the homogeneity of proportion ratios for stratified bilateral correlated data under an equal correlation assumption. Monte Carlo simulations of Type I error and power are performed, and the score test yields a robust outcome based on empirical Type I error and power. Lastly, two real data examples are conducted to illustrate the proposed three tests. Full article

Machine learning and artificial intelligence are growing in popularity thanks to their ability to produce models that exhibit unprecedented performance in domains that include computer vision, natural language processing and code generation. However, such models tend to be very large and complex and impossible to understand using traditional analysis or human scrutiny. Conversely, Symbolic Regression methods attempt to produce models that are relatively small and (potentially) human-readable. In this domain, Genetic Programming (GP) has proven to be a powerful search strategy that achieves state-of-the-art performance. This paper presents a new GP-based feature transformation method called M5GP, which is hybridized with multiple linear regression to produce linear models, implemented to exploit parallel processing on graphical processing units for efficient computation. M5GP is the most recent variant from a family of feature transformation methods (M2GP, M3GP and M4GP) that have proven to be powerful tools for both classification and regression tasks applied to tabular data. The proposed method was evaluated on SRBench v2.0, the current standard benchmarking suite for Symbolic Regression. Results show that M5GP achieves performance that is competitive with the state-of-the-art, achieving a top-three rank on the most difficult subset of black-box problems. Moreover, it achieves the lowest computation time when compared to other GP-based methods that have similar accuracy scores. Full article

This paper introduces an innovative approach to numerically model Structure–Soil-Structure Interaction (SSSI) by integrating the Boundary Element Method (BEM) and the Finite Element Method (FEM) in a coupled manner. To assess the accuracy of the proposed method, a comparative study is undertaken, comparing its outcomes with those generated by the conventional FEM technique. Alongside accuracy, the computational efficiency aspect is crucial for the analysis of large-scale SSSI problems. Hence, the computational performance of the coupled BEM–FEM method undergoes a thorough examination and is compared with that of the standalone FEM method. The results from these comparisons illustrate the superior capabilities of the proposed method in comparison to the FEM method. The novel approach provides more reliable results compared to traditional FEM methods, serving as a valuable tool for engineers and researchers involved in structural analysis and design. Full article

This paper aims to systematically assess the local radial basis function collocation method, structured with multiquadrics (MQs) and polyharmonic splines (PHSs), for solving steady and transient diffusion problems. The boundary value test involves a rectangle with Dirichlet, Neuman, and Robin boundary conditions, and the initial value test is associated with the Dirichlet jump problem on a square. The spectra of the free parameters of the method, i.e., node density, timestep, shape parameter, etc., are analyzed in terms of the average error. It is found that the use of MQs is less stable compared to PHSs for irregular node arrangements. For MQs, the most suitable shape parameter is determined for multiple cases. The relationship of the shape parameter with the total number of nodes, average error, node scattering factor, and the number of nodes in the local subdomain is also provided. For regular node arrangements, MQs produce slightly more accurate results, while for irregular node arrangements, PHSs provide higher accuracy than MQs. PHSs are recommended for use in diffusion problems that require irregular node spacing. Full article

Carbon nanotubes are widely used as material reinforcement in diverse fields of engineering. Being that their contribution is significant to improving the mean properties of the resulting materials, it is important to assess the influence of the variability on carbon nanotubes’ material and geometrical properties to structures’ responses. This work considers functionally graded plates constituted by an aluminum continuous phase reinforced with single-walled or multi-walled carbon. The nanotubes' weight fraction evolution through the thickness is responsible for the plates’ functional gradient. The plates’ samples are simulated considering that only the nanotubes’ material and geometrical characteristics are affected by uncertainty. The results obtained from the multiple regression models developed allow us to conclude that the length of the nanotubes has no impact on the maximum transverse displacement of the plates in opposition to the carbon nanotubes’ weight fraction evolution, their internal and external diameters, and the Young’s modulus. The multiple regression models developed can be used as alternative prediction tools within the domain of the study. Full article

Risk and uncertainty play a vital role in almost every significant economic decision, and an individual’s propensity to make riskier decisions also depends on various circumstances. This article aims to investigate the effects of social and economic covariates on an individual’s willingness to take general risks and extends the scope of existing works by using quantitative measures of risk-taking from the GPS and Gallup datasets (in addition to the qualitative measures used in the literature). Based on the available observed risk-taking data for one year, this article proposes a semi-supervised machine learning-based approach that can efficiently predict the observed risk index for those countries/individuals for years when the observed risk-taking index was not collected. We find that linear models are insufficient to capture certain patterns among risk-taking factors, and non-linear models, such as random forest regression, can obtain better root mean squared values than those reported in past literature. In addition to finding factors that agree with past studies, we also find that subjective well-being influences risk-taking behavior. Full article

This study is centered on examining the static bending behavior of sandwich plates featuring functionally graded materials, specifically addressing distinct representations of porosity distribution across their thickness. The composition of the sandwich plate involves a ceramic core and two face sheets with functionally graded properties. Mechanical loads with a sinusoidal distribution are applied to the sandwich plate, and a four-variable shear deformation theory is employed to establish the displacement field. Notably, this theory involves only four unknowns, distinguishing it from alternative shear deformation theories. Equilibrium equations are derived using the virtual work concept, and Navier’s method is applied to obtain the solution. The study addresses the impact of varying porosities, inhomogeneity parameters, aspect ratios, and side-to-thickness ratios on the static bending behavior of the sandwich plates. The influence of various porosities, inhomogeneity parameter, aspect ratio, and side-to-thickness ratio of the sandwich plates are explored and compared in the context of static bending behavior. The three porosity distributions are compared in terms of their influence on the bending behavior of the sandwich plate. The findings indicate that a higher porosity causes larger deflections and Model A has the highest central deflection. Adopting the four-variable shear deformation theory demonstrated its validity since the results were similar to those obtained in the literature. Several important findings have been found, which could be useful in the construction and application of FG sandwich structures. Examples of comparison will be discussed to support the existing theory’s accuracy. Further findings are presented to serve as benchmarks for comparison. Full article

Accurate forecasting remains a challenge, even with advanced techniques like deep learning (DL), ARIMA, and Holt–Winters (H&W), particularly for chaotic phenomena such as those observed in several areas, such as COVID-19, energy, and financial time series. Addressing this, we introduce a Forecasting Method with Filters and Residual Analysis (FMFRA), a hybrid methodology specifically applied to datasets of COVID-19 time series, which we selected for their complexity and exemplification of current forecasting challenges. FMFFRA consists of the following two approaches: FMFRA-DL, employing deep learning, and FMFRA-SSA, using singular spectrum analysis. This proposed method applies the following three phases: filtering, forecasting, and residual analysis. Initially, each time series is split into filtered and residual components. The second phase involves a simple fine-tuning for the filtered time series, while the third phase refines the forecasts and mitigates noise. FMFRA-DL is adept at forecasting complex series by distinguishing primary trends from insufficient relevant information. FMFRA-SSA is effective in data-scarce scenarios, enhancing forecasts through automated parameter search and residual analysis. Chosen for their geographical and substantial populations and chaotic dynamics, time series for Mexico, the United States, Colombia, and Brazil permitted a comparative perspective. FMFRA demonstrates its efficacy by improving the common forecasting performance measures of MAPE by 22.91%, DA by 13.19%, and RMSE by 25.24% compared to the second-best method, showcasing its potential for providing essential insights into various rapidly evolving domains. Full article

Internet energy consumption has increased rapidly, and energy conservation has become a significant issue that requires focused research efforts. The most promising solution is to identify the minimum power subsets within the network and shut down unnecessary network devices and links to satisfy traffic loads. Due to their distributed network control, implementing a centralized and coordinated strategy in traditional networks is challenging. Software-Defined Networking (SDN) is an emerging technology with dynamic, manageable, cost-effective, and adaptable solutions. SDN decouples network control and forwarding functions, allowing network control to be directly programmable, centralizing control with a global network view to manage power states. Nevertheless, it is crucial to develop efficient algorithms that leverage the centralized control of SDN to achieve maximum energy savings and consider peak traffic times. Traffic demand usually cannot be satisfied, even when all network devices are active. This work jointly addresses the routing of traffic flows and the assignment of SDN devices to these flows, called the Routing and Device Assignment (RDA) problem. It simultaneously seeks to minimize the network’s energy consumption and blocked traffic flows. For this approach, we develop an exact solution based on Mixed-Integer Linear Programming (MILP) as well as a metaheuristic based on a Genetic Algorithm (GA) that seeks to optimize both criteria by routing flows efficiently and suspending devices not used by the flows. Conducted simulations on traffic environment scenarios show up to 34% savings in overall energy consumption for the MILP and 33% savings achieved by the GA. These values are better than those obtained using competitive state-of-the-art strategies. Full article

In this work, we develop a new iterative method for computing the digits of $\pi$ by argument reduction of the tangent function. This method combines a modified version of the iterative formula for $\pi$ with squared convergence that we proposed in a previous work and a leading arctangent term from the Machin-like formula. The computational test we performed shows that algorithmic implementation can provide more than 17 digits of $\pi$ per increment. Mathematica codes, showing the convergence rate for computing the digits of $\pi$, are presented. Full article