Kutta Algorithm Research Articles

A Comparative Numerical Study of Heat and Mass Transfer Individualities in Casson Stagnation Point Fluid Flow Past a Flat and Cylindrical Surfaces

There is a consensus among researchers that the simultaneous involvement of heat and mass transfer in fluid flow owns numerous daily life applications like energy systems, automobiles, cooling of electronic devices, power generation by the stream, electric power, and diagnosing and characterizing diseases, to mention just a few. Owing to such motivation, we considered both heat and mass transfer aspects in non-Newtonian fluid flow regimes. The Casson fluid is considered as a non-Newtonian fluid. For better novelty the flow is considered at both flat and cylindrical surfaces along with stagnation point, magnetic field, mixed convection, heat generation, viscous dissipation, thermal radiations, and temperature-dependent thermal conductivity. The ultimate differential equations are nonlinear, and hence difficult to solve analytically. Therefore, a numerical scheme, namely the shooting method with the Runge–Kutta algorithm, is adopted to report an acceptable solution for flow field description. The outcomes are shared comparatively for flat and cylindrical surfaces. We have seen that compared to a flat surface, the cylindrical surface has a larger Nusselt number magnitude.

Computation of Sakiadis flow of an Eyring-Powell rheological fluid from a moving porous surface with a non-Fourier heat flux model

This article examines theoretically and numerically the effect of non-Fourier heat flux on non-Newtonian (Eyring-Powell) Sakiadis convective flow from a moving permeable surface accompanied by a parallel free-stream velocity, as a simulation of polymeric coating processes. The Cattaneo-Christov model is deployed which features thermal relaxation effects as these are important in thermal polymer processing. The physical flow problem is modeled in a Cartesian coordinate system and the governing conservation differential equations and associated boundary conditions are rendered dimensionless by applying suitable transformations. Liquid velocity and thermal distributions are computed considering numerical procedure namely, a shooting method in conjunction with the 5th order Runge–Kutta algorithm (R-K5) executed in a symbolic software. Validation with the three-stage Lobatto IIIA algorithm in MATLAB is included. The impact of key parameters on streamline distributions is also computed. Velocity is increased with increment in Eyring-Powell first parameter for the Sakiadis case whereas it is reduced with Eyring-Powell second parameter for the case where sheet and liquid are inspiring in the similar direction. The special case of Blasius flow is also examined (stationary sheet). For higher injection, there is a solid dampening in the boundary-layer flow for both Sakiadis and Blasius scenarios.

Modified SEIQHRDP and Machine Learning Prediction for the Epidemics

This paper is dedicated to investigating the transmission and prediction of viruses within human society. In the first phase, we augment the classical Susceptible-Exposed-Infectious-Recovered (SEIR) model by incorporating four novel states: protected status (P), quarantine status (Q), self-home status (H), and death status (D). The numerical solution of this extended model is obtained using the well-established fourth-order Runge- Kutta algorithm. Subsequently, we employ the next matrix method to calculate the basic reproduction number (R0) of the infectious disease model. We substantiate the stability of the basic reproductive number through an analysis grounded in Routh-Hurwitz theory. Lastly, we turn to the application and comparison of statistical models, specifically the Autoregressive Integrated Moving Average (ARIMA) and Bidirectional Long Short-Term Memory (Bi-LSTM) models, for time series prediction.

A Chaotic Multi‐Objective Runge–Kutta Optimization Algorithm for Optimized Circuit Design

Circuit design plays a pivotal role in engineering, ensuring the creation of efficient, reliable, and cost‐effective electronic devices. The complexity of modern circuit design problems has led to the exploration of multi‐objective optimization techniques for circuit design optimization, as traditional optimization tools fall short in handling such problems. While metaheuristic algorithms, especially genetic algorithms, have demonstrated promise, their susceptibility to premature convergence poses challenges. This paper proposes a pioneering approach, the chaotic multi‐objective Runge–Kutta algorithm (CMRUN), for circuit design optimization, building upon the Runge–Kutta optimization algorithm. By infusing chaos into the core RUN structure, a refined balance between exploration and exploitation is obtained, critical for addressing complex optimization landscapes, enabling the algorithm to navigate nonlinear and nonconvex optimization challenges effectively. This approach is extended to accommodate multiple objectives, ultimately generating Pareto Fronts for the multiple circuit design goals. The performance of CMRUN is rigorously evaluated against 11 multiobjective algorithms, encompassing 15 benchmark test functions and practical circuit design scenarios. The findings of this study underscore the efficiency and real‐world applicability of CMRUN, offering valuable insights for tailoring optimization algorithms to the real‐world circuit design challenges.

Runge Kutta Optimization for Fixed Size Multimodal Test Functions

In this study, it is aimed to increase the success of the Runge Kutta (RUN) algorithm, which is used in the solution of many optimization problems in the literature, on fixed-size test functions by changing the parameter values. Optimization can be defined as making a system most efficient at the least possible cost under certain constraints. For this process, many optimization algorithms have been designed in the literature and used to obtain the best solutions for certain problems. The most important parts in solving these problems are modeling the problem correctly, determining the parameters and constraints of the problem, and finally choosing a suitable meta-heuristic algorithm for the solution of the objective function. Not every algorithm is suitable for every problem structure. Therefore, in this study, the suitability of the RUN algorithm for the solution of fixed-size functions will be evaluated. Theoretically, Runge-Kutta methods used in numerical analysis are an important type of the family of closed and open iterative methods for solution approximations of ordinary differential equations. The RUN algorithm is also designed with inspiration from these methods. In order to evaluate the performance of the RUN algorithm on fixed-size functions in the study, 10 fixed-size multimodal test functions (Shekel's Foxholes, Kowalik, Six-Hump Camel-Back, Branin, Goldstein-Price, Hartman3, Hartman6, Shekel5, Shekel7, Shekel10) have been found in the literature before was selected. Solutions for each of the selected functions are obtained by changing the parameter values of the RUN algorithm. The obtained solution values were evaluated by comparing the solutions obtained with Slime Mold Algorithm (SMA) and Hunger Games Search (HGS) algorithms.

Dynamical Stability of a 3-DOF Auto-Parametric Vibrating System

PurposeThis article concentrates on the oscillating movement of an auto-parametric dynamical system comprising of a damped Duffing oscillator and an associated simple pendulum in addition to a rigid body as main and secondary systems, respectively.MethodsAccording to the system generalized coordinates, the controlling equations of motion are derived utilizing Lagrange's approach. These equations are solved applying the perturbation methodology of multiple scales up to higher orders of approximation to achieve further precise unique outcomes. The fourth-order Runge–Kutta algorithm is employed to obtain numerical outcomes of the governing system.ResultsThe comparison between both solutions demonstrates their high level of consistency and highlights the great accuracy of the adopted analytical strategy. Despite the conventional nature of the applied methodology, the obtained results for the studied dynamical system are considered new.ConclusionsIn light of the solvability criteria, all resonance scenarios are classified, in which two of the fundamental exterior resonances are examined simultaneously with one of the interior resonances. Therefore, the modulation equations are achieved. The conditions of Routh–Hurwitz are employed to inspect the stability/instability regions and to analyze them in accordance with the solutions in the steady-state case. For various factors of the examined structure, the temporary history solutions, the curves of resonance in terms of the adjusted amplitudes and phases, and the stability zones are graphically presented and discussed.ApplicationsThe results of the current study will be of interest to wide range experts in the fields of mechanical and aerospace technology, as well as those working to reduce rotors dynamical vibrations and attenuate vibration caused by swinging structures.

Modeling and Characteristic Analysis of Combined Beam Tri-Stable Piezoelectric Energy Harvesting System Considering Gravity

The emergence of the vibration energy harvesting system makes it possible for wireless monitoring nodes in coal mines to realize self-power supply. In order to reveal the influence of gravity effect on the response characteristics of the combined beam tri-stable piezoelectric energy harvesting system (CTEHS), the system’s nonlinear magnetism is calculated according to the principle of point magnetic charge dipole, and the system’s nonlinear resilience is obtained through experimental measurements and nonlinear fitting methods. Based on the Lagrange equation, the system’s electromechanical coupling motion model considering gravity is established. The system’s motion equation is solved numerically based on the Runge–Kutta algorithm, and the effects of the end magnet mass and the initial vibration point on the bifurcation behavior, potential energy, and system output performance are investigated by emulation and experiment. The research shows that the magnet’s gravity effect causes a change in the stable equilibrium position and the system’s motion state and also causes the system to generate additional gravitational potential energy, which leads to a potential asymmetric well of the system. Under the consideration of magnet gravity, the appropriate end magnet mass and initial vibration point can not only reduce the system’s requirements for external excitation strength but also effectively improve the system’s response and output. This research provides a new theoretical basis for the optimal design of the tri-stable piezoelectric energy harvesting system.

Rolling bearing fault feature extraction method based on GWO-optimized adaptive stochastic resonance signal processing

The failure of rolling bearings affects the function and precision of rotating machinery significantly, which has drawn lots of attention in this field. Dealing with the failure of rolling bearings, fault feature extraction is the first and most important problem. In this work, we convert the bearing fault signal into stochastic resonance dynamics equivalently. And, adaptive stochastic resonance is adopted to extract the fault signal feature. In addition, for industrial application of fault signal processing with large amplitude and noise intensity greater than 1, normalized scale transformation is introduced into adaptive stochastic resonance and then solved by fifth-order Runge–Kutta algorithm. Then, to further optimize the solving precision of stochastic resonance model, the scaling coefficient and step size of Runge–Kutta algorithm are chosen with the help of Grey Wolf Optimizer (GWO). Thus, we can obtain a fast convergence speed, high calculation accuracy and effective improvement of signal-to-noise ratio fault feature extraction method for rolling bearing fault signal processing. Finally, a comparation simulation was carried out to demonstrate the efficiency of the proposed method. Compared with Cuckoo Search Optimizer-based stochastic resonance signal processing method, the proposed method achieved a higher signal-to-noise ratio (SNR) to benefit the fault feature extraction. In summary, this work gives out a more practical and effective solution for rolling bearing fault feature extraction in rotating machinery fault diagnosis field.

Research on Maneuverability Prediction of Double Waterjet Propulsion High Speed Planing Craft

A mathematical model for predicting the maneuvering motion of a ship is constructed, using a planing craft with dual waterjet propulsion as the object of study. This model is based on the standard approach of the MMG (Maneuvering Modeling Group) and uses the Runge–Kutta algorithm to solve the differential equations. For the simulation of the turning and Z-shape maneuvering motion, the RANS equation is first solved using the program STAR-CCM + and then the PMM motion of the hull is simulated using the overlapping grid approach to derive the hydrodynamic derivative. The established method for predicting the ship’s maneuverability is feasible, as shown by the calculated results, which agree well with those obtained using data from the sea trials. This method was used to simulate the rudder rotation and Z-shape motion of the planing craft at medium and high speeds to predict the maneuverability index.

Nonlinear approximation for buoyancy-driven mixed convection heat and mass transfer flow over an inclined porous plate with Joule heating, nonlinear thermal radiation, viscous dissipation and thermophoresis effects

This study considered a classical magnetohydrodynamics (MHD) mixed convection heat and mass transfer flow over an inclined porous plate with thermophoresis, Joule heating, viscous dissipation, and nonlinear thermal radiation. The impact of nonlinear density variation with temperature and concentration (NDTC) in the buoyancy term is also taken into consideration. The mathematical model is first transformed into ordinary differential equations (ODEs) by similarity variables. The reduced ODEs are solved through the classical Runge–Kutta algorithm after utilizing the shooting technique. Some major findings of the analysis include; the heat transfer rate increases with the fluid injection but it decreases the rate of particle deposition and skin friction. Regarding the fluid suction, the heat transfer rate is observed to decrease as the fluid suction intensifies whereas increases the particle deposition and shear stress at the plate surface. As (a classical horizontal flat plate), the rate of heat transfer enhances but decreases the particle deposition rate and plate shear stress. With blowing/suction and in the presence of the magnetic parameter, the plate shear stress and heat transfer increase with nonlinear thermal radiation propagation whereas decreases the particle deposition. The species concentration near the porous plate, velocity, and temperature curves is enhanced by escalating the dissipation parameter. The radiative heat flux boosts the fluid temperature that consequently enhanced the velocity and the species concentration near the porous plate. The fluid velocity past the porous plate is higher in the case of a vertical plate () compared to the classical flow over a horizontal porous plate ().

Application of compact local integrated RBF (CLI-RBF) for solving transient forward and backward heat conduction problems with continuous and discontinuous sources

It is well-known that the inverse heat problems (IHP) are ill-posed such that we encounter to some difficulties in the numerical techniques. In the current article, a numerical technique based on the compact local integrated radial basis function (CLI-RBF) method is developed for solving IHP with continuous/discontinuous heat source. For this aim, the derivative of space variable is discretized by the CLIRBF procedure that in this manner yields a system of ODEs related to the time variable. Then, the final system of ODEs is solved by adaptive fourth-order Runge–Kutta algorithm. Finally, several challenging examples are solved by the new numerical method. The computer implementations confirm that the present method has enough accuracy for solving IHP with continuous/discontinuous heat source in one- and two-dimensional cases.

Combined Underdamped Bistatic Stochastic Resonance for Weak Signal Detection and Fault Diagnosis under Wavelet Transform

A novel combined underdamped bistable stochastic resonance (CUBSR) is proposed in this paper. Under the noise-free condition, the output amplitude is used as a measurement index of classical bistable stochastic resonance (CBSR) and CUBSR, which demonstrate CUBSR does not have output saturation characteristics and has a more prominent signal enhancement capability. Then, the expressions of mean first-pass time (MFPT), steady-state probability density (SPD) and signal-to-noise ratio (SNR) are derived. Combined with the fourth-order Runge–Kutta algorithm and genetic algorithm (GA) for numerical simulations, the comparison of the theoretical derivation and numerical simulation of CUBSR can be verified. Then, the two systems are applied to the engineering application of bearing fault diagnosis. Finally, the multi-scale noise-modulated SR method based on wavelet packet transform is studied to overcome the limitation of traditional parameter modulation and to achieve SR detection at multiple frequencies. Simulation analysis and bearing fault diagnosis show that the method can effectively detect the multi-frequency weak signal submerged in noise, resulting in a significant enhancement in signal amplitude.

A novel hybrid model based on Laguerre polynomial and multi-objective Runge–Kutta algorithm for wind power forecasting

In recent years, the application of wind power forecasting in power systems has gained widespread recognition. However, most studies have only focused on improving forecasting accuracy and few have considered the stability of forecasting results. To solve these two issues simultaneously, this study proposed a novel hybrid wind power forecasting model. First, two types of Laguerre polynomials are used to construct the hybrid Laguerre neural network. Then, a multi-objective Runge–Kutta algorithm is proposed to optimize the weights of the neural network while enhancing the accuracy and stability of the forecasting. Finally, ensemble learning is introduced to further improve the forecasting capability of the model. To verify the effectiveness of the proposed hybrid forecasting model, a large number of comprehensive experiments are carried out using the wind power data of a wind farm in Xinjiang, China. The experimental results show that the proposed hybrid forecasting model had higher forecasting accuracy and better stability than other forecasting models.

An alternative numerical method to study spin transfer-induced magnetic reversals in nanopillar devices with non-zero damping

In this paper, we present an alternative method to investigate spin transfer-induced magnetization changes in nano-pillars made of Heusler alloys by numerically solving the Landau-Lifshitz-Gilbert-Slonczewski (LLGS) with non-zero damping using the Runge-Kutta Method (RKM). We first developed the LLGS equation, including the spin-transfer torque term as well as the interface anisotropy field, and then numerically integrated the LLGS components using the Runge–Kutta algorithm. Asa result, stable processes of magnetization reversal were performed and analyzed according to the main parameters of the LLGS equation with/without interface anisotropy. Furthermore, the changes of switching time and threshold current density were also examined in the presence of interface anisotropy. The obtained results were compared with a systematic study of magnetization reversal using micromagnetic simulations. Accordingly, we found a very good agreement between the micromagnetic simulation and the RKM, both in terms of magnetization state and switching time.

A novel two-dimensional exponential potential bi-stable stochastic resonance system and its application in bearing fault diagnosis

It is difficult for classical stochastic resonance systems to extract weak signals under strong noise environment, therefore a novel two-dimensional exponential potential bi-stable stochastic resonance system (NTBSR) is proposed. First, the equivalent potential function, the mean first-pass time (MFPT) and the output signal-to-noise ratio (SNR) of NTBSR are derived under the adiabatic approximation theory. At the same time, the influence of different system parameters on them is explored. Then, NTBSR, the one-dimensional bi-stable stochastic resonance system (OBSR) and the two-dimensional classical bi-stable stochastic resonance system (TCBSR) are respectively simulated numerically, based on the fourth-order Runge–Kutta algorithm. It is found that the output SNR of NTBSR is the best. Finally, the NTBSR is applied to the fault signal diagnosis of different types of bearings, and the parameters are optimized through the adaptive genetic algorithm (AGA). The test results are compared with wavelet transform method, and TCBSR. The detection results on two sets of bearing fault data show that the NTBSR system has better effects on the enhancement and detection of bearing fault signals, and it is verified that the stochastic resonance method is superior to the traditional wavelet transform method in terms of signal detection and noise utilization. This provides good theoretical support and application value for practical engineering application.

Nonlinear and chaotic vibrations of rotating functionally graded GPL reinforced composite pre-twisted blade subjected to aerodynamic force

The nonlinear and chaotic vibrations of the rotating functionally graded graphene platelet reinforced composite (FG-GPLRC) pre-twisted blade subjected to the aerodynamic force are investigated by taking into account the cantilever boundary condition. The rotating FG-GPLRC pre-twisted blade is simplified to a rotating FG-GPLRC pre-twisted cylindrical panel. The graphene platelets (GPLs) are dispersed uniformly and oriented randomly in every layer while the GPL volume fractions vary from the layer to layer, which leads to four different GPL distribution patterns. Based on the strain–displacement relationship of the pre-twisted cylindrical panel derived by Green strain tensor, the natural frequencies of the rotating FG-GPLRC pre-twisted cylindrical panel are obtained by using the first-order shear deformation theory and Chebyshev–Ritz method. Lagrange’s formulation is used to derive the nonlinear ordinary differential equations of motion. The complex chaotic vibrations of the rotating FG-GPLRC pre-twisted cylindrical panel are investigated by performing numerical simulations on the basis of Runge–Kutta algorithm. The bifurcation diagrams, Lyapunov exponents, time histories, phase portraits and Poincare maps are depicted to detect the periodic and chaotic vibrations of the rotating FG-GPLRC pre-twisted cylindrical panel with different parameters, such as Coriolis force, GPL distribution pattern, steady-state rotating speed, perturbation rotating speed and aerodynamic force. The double-parameter maximum Lyapunov exponent is regarded as an effective method to detect the chaotic regions of the rotating FG-GPLRC pre-twisted cylindrical panel.

Modeling and Feature Analysis of Air Traffic Complexity Propagation

Air traffic complexity, an essential attribute of air traffic situation, is the main driving force of workload for air-traffic controllers and is the key to achieving refined air traffic control. The existing air traffic complexity studies are based on static network, ignoring the dynamic evolution of between-aircraft proximity relations. Research on such evolution course and propagation characteristics will help to comprehensively explore the mechanisms of complexity formation. Herein, an air traffic complexity propagation research method based on temporal networking and disease propagation modeling is proposed. First, a temporal network is built with aircraft as nodes and between-aircraft proximity relations as edges. Second, the disease propagation model is introduced to simulate the evolution course of between-aircraft proximity relations, and the propagation model is solved using Runge–Kutta algorithm and particle swarm optimization. Third, based on the solved results of the propagation model, the aircraft are divided into three groups with high, medium, and low propagation capability, respectively. Finally, the effects of different factors on the propagation course are analyzed using multivariate linear regression. Real data validation shows the propagation of high-propagation capability aircraft is significantly affected by duration, and the temporal-correlation coefficient. The propagation of medium-propagation capability aircraft is significantly affected by duration and the clustering degree. By adjusting the influencing factors, the air traffic complexity propagation process can be effectively controlled.

Applicability of two-dimensional numerical simulation associated with vortex-induced vibration response of the circular cylinder

ABSTRACT The VIV responses of the circular cylinder at low and moderate Reynolds numbers are calculated according to two-dimensional numerical simulation and the fourth-order Runge–Kutta algorithm. The first part of the study is focused on the applicability of 2D numerical simulation between the response of 2D numerical simulation and the actual response, which can guide the preliminary engineering studies by vortex shedding. The reasonable vortex shedding mode of each branch, and the change process of the trajectory from the ‘8’ type to the ‘droplet’ type, are discussed in the second part of the study. And independent calculations under different speed reduction conditions are employed to suit practical application scenarios. The comparison shows the applicability of the 2D numerical simulations at low Reynolds numbers. Although the amplitude calculation results at moderate Reynolds numbers are inconsistent with the experimental results, the two-dimensional numerical simulation has good reliability in the trailing vortex capture.

The Combined Impact of Thermal Radiation and Thermophoresis on Buoyancy-Driven Flow Near an Inclined Porous Plate

Abstract This report presents a similarity solution for the buoyancy-driven flow of viscous incompressible fluid past an inclined porous plate influenced by nonlinear thermal radiation and thermophoresis. The boundary layer equations are reduced to some set of ODEs through similarity variables. Furthermore, the ODEs are converted to IVP through the shooting technique. The numerical solution is obtained through the Runge–Kutta algorithm in Maple software. The impact of the emergence parameters present in the mathematical model is explained through graphs and tables. Results obtained showed that with combined effects of suction/injection and nonlinear thermal radiation, the heat transfer rate is directly proportional to the angle of inclination but inversely proportional to plate shear stress and mass transfer rate. Furthermore, it was observed that the heat transfer rate declines with higher buoyancy force but enhances the plate shear stress. Also, the mass transfer rate could be enhanced with a higher thermophoresis effect. Suction propagates the velocity and temperature profiles whereas it decreases the rate of particle concentration, while the contrast is true for injection. In addition, nonlinear thermal radiation complements the fluid temperature, particle concentration, and fluid transport.

Theoretical and Numerical Analyses and Application of Novel Underdamped Tri-Stable Stochastic Resonances under Symmetric Trichotomous Noise

In this paper, a novel underdamped tri-stable stochastic resonance (NUTSR) is presented in order to overcome the low out-performance of weak signal reinforcement in the classical tri-stable stochastic resonance (CTSR). The two systems are compared using the input and output amplitude as a measure when noiseless. NUTSR improves the output saturation characteristics and has more outstanding signal enhancement capability. In the background of Gaussian noise, the expressions of mean first-pass time (MFPT), steady-state probability density (SPD) and signal-to-noise ratio (SNR) are derived. The fourth-order Runge–Kutta algorithm and genetic algorithm (GA) is used for numerical simulations. Then the numerical simulation results of the two systems are compared comprehensively, and the theoretical deduction and numerical simulation results of NUTSR are also compared. Moreover, the two systems are applied in two bearing fault types of 6205-2RS JEM SKF and HRB 6205-2Z. Finally, the feasibility of NUTSR is verified under different noise, which is simulated numerically under symmetric trichotomous that NUTSR has better noise immunity and the increase in signal amplitude is more pronounced.