Numerical Equations Research Articles

Residual analysis for the identification of potential MIR-derived biomarkers of heat stress in dairy cattle.

Numerous prediction equations have been developed based on mid-infrared (MIR) spectra and some could be potentially used as biomarkers of heat stress. However, practical experience shows that confusion between the effect of heat stress and other effects like lactation stage or feeding variation over the year can easily occur. On this basis, the objective of this study was to identify potential milk components predicted by MIR as biomarkers of heat stress based on a 2-step approach allowing to correct for those effects. The first step consisted in the estimation of residuals from test-day random regression models on days in milk (DIM) to remove systematic lactation stage effects. These models contained also, among other, general (i.e., month of production) or specific (i.e., herd × test-day (HTD)) fixed effects related to feeding and management. During the second step, means and variances of residuals by temperature and humidity index (THI) classes were studied. The models were applied to 611,063 records from 97,042 primiparous Holstein cows from 2015 to 2022 in the south of Belgium. The MIR-predicted milk components with the highest deviations from the mean with increasing THI were protein percentage, casein concentration, magnesium (Mg) concentration and, to a lesser extent, polyunsaturated fatty acid (PUFA) concentration. Concerning residual variances, the highest heteroscedasticity with THI was obtained for milk MIR monounsaturated fatty acid (MUFA), C18:1 cis-9 and citrate concentrations. Conversely, a relative homoscedasticity of variance with increasing THI was observed for several milk MIR components including protein percentage and casein concentration. Based on the criteria of the "good biomarkers" guidelines, milk protein percentage seems to be the most promising trait of this study, followed by Mg concentration. However, in the context of genetic evaluation which requires variability, milk MIR MUFA, C18:1 cis-9 or citrate concentration variations, if they are heritable, could be of great interest. Finally, an increase in milk MIR citrate concentration variance could be an early warning for the detection of heat stress in the frame of dairy herd improvement (DHI).

The probabilistic dependence of ship-induced waves is preserved spatially and temporally in the Savannah River (USA)

The rapid changes in the shipping fleet during the last decades has increased the ship-induced loads and, thus, their impact on infrastructures, margin protections and ecosystems. Primary waves have been pointed out as the cause of those impacts, with heights that can exceed 2 m and periods around 2 minutes. Consequently, extensive literature can be found on their estimation mainly from a deterministic perspective with methods based on datasets limited to one location, making difficult their generalization. These studies propose either computationally expensive numerical models or empirical equations which often underestimate the extreme primary waves, hindering their use for design purposes. Moreover, a framework to allow the design of infrastructure under ship-wave attack based on probabilistic concepts such as return periods is still missing. In this study, a probabilistic model based on bivariate copulas is proposed to model the joint distribution of the primary wave height, the peak of the total energy flux, the ship length, the ship width, the relative velocity of the ship and the blockage factor. This model, a vine-copula, is developed and validated for four different deployments along the Savannah river (USA), with different locations and times. To do so, the model is quantified using part of the data in one deployment and validated using the rest of the data from this deployment and data of the other three. The vine-copula is validated from both a predictive performance point of view and with respect to the statistical properties. We prove that the probabilistic dependence of the data is preserved spatially and temporally in the Savannah river.

Development of an Optimized Non-Linear Model for Precise Dew Point Estimation in Variable Environmental Conditions

Accurate dew point estimation is crucial for measuring water condensation in various fields such as environmental studies, agronomy, or water harvesting, among others. Despite the numerous models and equations developed over time, including empirical and machine learning approaches, they often involve trade-offs between accuracy, simplicity, and computational cost. A major limitation of the current approaches is the lack of balance among these three factors, limiting their practical applications under diverse conditions. This research addresses these key challenges by developing a new, streamlined equation for dew point estimation. Using the Magnus–Tetens equation, deemed as the most reliable equation, as a benchmark, and by applying a process of non-linear regression fitting and parametric optimization, a new equation was derived. The results demonstrate high accuracy with a streamlined implementation, validated through extensive data and computational simulations. This study highlights the importance of accurate dew point modeling, especially under variable environmental conditions, provides a reliable solution to existing limitations, paving the way for enhanced efficiency in related processes and research endeavors, and offers researchers and practitioners a practical tool for more effective modeling of water condensation phenomena.

On Solutions of Some Functional Equations of Radical Type

Many authors have studied various functional equations of forms patterned on the equation expressed as ga2+b2=g(a)+g(b), which can be considered, e.g., for real functions. Such equations are usually referred to as radical functional equations or of the radical type. Authors mainly study the so-called Ulam stability of such equations, i.e., they investigate how much the mappings satisfying the equations approximately (in a sense) differ from the exact solutions of these equations. Quite often, information about the solutions of these equations is also provided, but unfortunately, sometimes, such information is given in a misleading or incomplete way. It seems, therefore, that there is a need for a publication containing simple descriptions of such solutions (with appropriate examples), which would help in easy correction of such information and avoidance of similar problems for future authors. This is the main motivation for this expository paper. We present a general approach to the topic and consider two general forms of such equations. Moreover, the results presented in this paper show significant symmetry between the solutions of numerous functional equations and the solutions of equations of the radical type that correspond to them. To make this publication accessible to a wider audience, we omit various related information, avoid advanced generalizations, and present several simple examples.

THE EXTERNAL DRAFT TUBE GASLIFT BIOREACTOR: HYDRODYNAMIC CHARACTERISTICS AND PARAMETRIC OPTIMIZATION

Gaslift reactors are employed in several bioapplications due to their characteristics of cost-effectiveness and high efficiency. However, the nutrient and thermal gradient is one of the obstacles that stand in the way of its widespread use in biological applications. The diagnosis, analysis, and tracking of fluid paths in external draft tube gaslift bioreactor-type are the main topics of the current study. Several parameters were considered to assess the mixing efficiency such as downcomer-to-rizer diameter ratio (Ded/Dr), the position of the diffuser to the height of bioreactor ratio (Pd/Lr), and gas bubble size (Db). The multiple regression of liquid velocity indicates the optimal setting: Ded/Dr is (0.5), Pd/Lr is (0.02), and Db is (400) um. However, for technical and operational reasons, it was necessary to make some changes in the optimal values obtained from the numerical equations. The study also revealed that the size of gas bubbles is the characteristic that has the greatest influence on the dynamic efficiency of the fluid inside the bioreactor, since, reducing the bubble size by half can enhance the improvement rate in the circulation of the liquid up to 35%.

On the Atomic Structure

In recent years, it has been recognized that treatment of the spectral problem should be associated with closed orbits. This paper proves that the closed orbit obtained by Bohr using numerical algebraic equation is reasonable both mathematically and physically and that the de Broglie wavelength of the electron in the hydrogen atom is equal to the circumference of its orbit. By Bohr model and de Broglie’s matter-wave thought, some quantization conditions, electronic transition formulae, a mechanism and details of emitting photon wave train, a filling order of electrons in the periodic table, and Madelung rule have been deduced theoretically. We solve the Löwdin’s challenge problem.

NUMA-aware parallel sparse LU factorization for SPICE-based circuit simulators on ARM multi-core processors

In circuit simulators that resemble the Simulation Program with Integrated Circuit Emphasis (SPICE), one of the most crucial steps is the solution of numerous sparse linear equations generated by frequency domain analysis or time domain analysis. The sparse direct solvers based on lower-upper (LU) factorization are extremely time-consuming, so their performance has become a significant bottleneck. Despite the existence of some parallel sparse direct solvers for circuit simulation problems, they remain challenging to adapt in terms of performance and scalability in the face of rapidly evolving parallel computers with multiple NUMA hardware based on ARM architecture. In this paper, we introduce a parallel sparse direct solver named HLU, which re-examines the performance of the parallel algorithm from the viewpoint of parallelism in pipeline mode and the computing efficiency of each task. To maximize task-level parallelism and further minimize the thread waiting time, HLU devises a fine-grained scheduling method based on an elimination tree in pipeline mode, which employs depth-first search (DFS-like) to iteratively search for parent tasks and then place dependent tasks in the same task queue. HLU also suggests two NUMA node affinity strategies: thread affinity optimization based on NUMA nodes topology to guarantee computational load balancing and data affinity optimization to enable effective memory placement when threads access data. The rationality and effectiveness of the sparse solver HLU are validated by the SuiteSparse Matrix Collection. In comparison with KLU and NICSLU, the experimental results and analysis show that HLU attains a speedup of up to 9.14× and 1.26x (geometric mean) on a Huawei Kunpeng 920 Server, respectively.

Forecast of electric transport property via two models

Temperature and synthesis condition-dependent resistivity are critical parameters for determining the electrical properties of materials. Modeling serves as a powerful tool for predicting the electrical transport characteristics of materials. The first objective of this work was to conduct a quantitative analysis of the reported metallic and insulating resistivity behaviors in double-phase materials. Using non-linear regression, both a phenomenological model and an Asym2sig asymmetric peak model were employed to quantitatively analyze the temperature-dependent resistivity. The fitting results align closely with the observed resistivity-temperature curves. The second objective of this work was to establish a method linking chemical composition (synthesis conditions) to the parameters derived from the two models, calculation on the principle of non-linear curve fitting, two numerical equations are highlighted for quantitatively analyzing chemical composition-dependent parameters. The observed effects of chemical composition on the shift in the temperature-resistive curve, which are fundamental to understanding resistivity behavior, are discussed quantitatively for the first time to our knowledge for resistive-temperature behavior. Hence, the resistivity of both crystalline and non-crystalline materials can be forecasted across various compositions and temperatures using the methods presented, even without experimental data.

Computationally efficient and error aware surrogate construction for numerical solutions of subsurface flow through porous media

Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by the solution of Darcy’s partial differential equation for a given permeability field. The subsurface permeability is modeled as a random field since it is known only up to statistical properties. This induces uncertainty in the computed pressure. Solving the partial differential equation for an ensemble of random permeability simulations enables estimating a probability distribution for the pressure at the critical location. These simulations are computationally expensive, and practitioners often need rapid online guidance for real-time pressure management. An ensemble of numerical partial differential equation solutions is used to construct a Gaussian process regression model that can quickly predict the pressure at the critical location as a function of the extraction rate and permeability realization. The Gaussian process surrogate analyzes the ensemble of numerical pressure solutions at the critical location as noisy observations of the true pressure solution, enabling robust inference using the conditional Gaussian process distribution.Our first novel contribution is to identify a sampling methodology for the random environment and matching kernel technology for which fitting the Gaussian process regression model scales as O(nlogn) instead of the typical O(n3) rate in the number of samples n used to fit the surrogate. The surrogate model allows almost instantaneous predictions for the pressure at the critical location as a function of the extraction rate and permeability realization. Our second contribution is a novel algorithm to calibrate the uncertainty in the surrogate model to the discrepancy between the true pressure solution of Darcy’s equation and the numerical solution. Although our method is derived for building a surrogate for the solution of Darcy’s equation with a random permeability field, the framework broadly applies to solutions of other partial differential equations with random coefficients.

The MOOSE fluid properties module

The Fluid Properties module within the Multiphysics Object-Oriented Simulation Environment (MOOSE) is used to compute fluid properties for numerous applications, ranging from nuclear reactor thermal hydraulics to geothermal energy. Those applications drove the development of the module to enable numerous different fluid equations of states, property lookups with primitive and conserved flow variable to cater to pressure and density-driven solvers, and an object-oriented design facilitating expansion and maintenance. Each fluid property is implemented in its own class but inherits capabilities such as automatic differentiation, automated out-of-bounds handling or variable conversion capabilities. This paper presents the module, its design, its user and developer interface, its content in terms of fluids and properties, and several of its applications showing its major role in the MOOSE simulation ecosystem. Program summaryProgram title: MOOSE Fluid Properties moduleCPC Library link to program files:https://doi.org/10.17632/cwzhsyp6pd.1Developer's repository link:https://github.com/idaholab/moose/tree/next/modules/fluid_propertiesLicensing provisions: LGPLProgramming language: C++, PythonNature of problem: The simulation of thermal hydraulics of advanced nuclear reactor systems, such as heat pipe micro-reactors or molten-salt cooled pebble bed reactors, requires a wide variety of discretizations of the fluid flow equations, from 1D thermal hydraulics to computational fluid dynamics at various levels of fidelity, with a wide variety of coolants. Applications are developed within the MOOSE C++ framework by Argonne and Idaho National Laboratories to simulate these reactors for research and design purposes. These applications (Sockeye, SAM, others) rely on MOOSE for the computation of fluid properties. The fluid properties module contains properties for most advanced nuclear reactor coolants, including an interface to the Molten Salt Thermodynamics Database (MSTDB) developed by Oak Ridge National Laboratory. Single phase, two phase, and gas mixtures fluid properties are computed by the module.Solution method: The fluid properties module includes numerous numerical methods to support the wide range of applications, notably forward automatic differentiation, conversion methods between pressure and density-driven variable sets, spline-based table lookups which are the current state of the art for the fast computation of fluid properties. The integration with MOOSE facilitates uncertainty quantification with regards to the fluid properties and optimization studies with regards to the fluid composition.

A non-localized spatial–temporal constitutive relation in rarefied gas dynamics

Although the Boltzmann equation is instrumental in capturing the dynamics of rarefied gases, finding its solutions in engineering problems is challenging. Therefore, over the past century and a half, numerous partial differential equations based on a few macroscopic variables have been introduced. However, they not only have complicated forms but also cannot make satisfactory prediction when the Knudsen number is large. Here, we propose a non-localized spatial–temporal (NiST) constitutive relation for rarefied gas dynamics, where the stress/heat flux at time t and position x is determined by the velocity/temperature gradient in the nearby spatial–temporal coordinates, via convolution operators. Utilizing solutions of the Boltzmann equation for the Couette/Fourier/Poiseuille flow and the spontaneous Rayleigh–Brillouin scattering, we extract the universal parameters of non-locality as functions of the spatial and temporal Knudsen numbers. Subsequent validation through sound propagation and backward-facing step flow demonstrates that the NiST constitutive relation is capable of accurately forecasting rarefied gas flows across a broad spectrum of Knudsen numbers.

Investigating forced convection in porous media-filled cavities for designing supplementary passive cooling systems

This study aims to propose innovative passive cooling methods within the reservoir section of a closed-loop liquid cooling system. The techniques employed in this study include using a cold wall, a porous medium, varying inlet positions, and nozzles of different sizes and shapes. The effects of parameters associated with these techniques on outlet temperature reduction, pressure drop, and average Nusselt number (Nu¯) have been analyzed in detail. The reservoir section has been numerically modeled as a two-dimensional (2D) and a three-dimensional (3D) cavity. The numerical model implements mass, momentum, energy, and conservation equations for the Darcy model in the porous region. A fluid flow with Re=50 with a laminar generalized porous media modeling approach employing Brinkman’s and Forchheimer’s terms has been used. The optimized inlet position with respect to maximum cooling (55.60 K) and moderate pressure drop (2.30kPa) for the 2D cavity has been identified in this work for a given Darcy number and porosity. Results show that decreasing porosity improves convective heat transfer efficiency and increases pressure drop. Similarly, varying Darcy’s number affects heat transfer, with lower Da values resulting in reduced outlet temperature reduction and lower Nu¯, with higher pressure drop. A similar analysis was conducted for the 3D reservoir. The use of a converging nozzle can lead to an increase in cooling by 61.61% and 3.44% for the 2D and 3D reservoirs, respectively.

Entropy formation in second grade nanofluid flow across a curved surface with the impact of activation energy and chemical reaction

The heat and mass transfer through the second-grade nanofluid across a curved surface is investigated in the present article with the consequences of chemical reaction, activation energy and Ohmic heating. The Buongiorno model is employed to simulate the thermophoretic and Brownian diffusions effect. The flow phenomena for second-grade fluid (SGF) have been modelled in the form of system of partial differential equations (PDEs) which are converted into a system of ordinary differential equations (ODEs) by substituting the similarity variables. The model equations are converted into a system of ODEs by inserting a suitable variable. The set of dimensionless equations along with boundary conditions are evaluated computationally through the numerical differential equation solver (ND Solve) technique. The entropy optimization, energy curve, Nusselt number, mass transfer, Sherwood number, velocity and skin friction are computed and examined versus distinct physical parameters. The finding reveals that the concentration and velocity profile exhibits enhancement as the curvature parameter increases, whereas an opposite trend has been found in relation to the energy outline. Furthermore, the concentration profile raises as the activation energy increased, while diminishes with the augmentation of chemical reaction.

Mathematical Analysis of Neural Networks for Signal Processing

In flag preparing, neural systems have gotten to be exceptionally valuable since they give adaptable ways to see at and get it complicated information patterns. A full scientific ponder of neural systems utilized for flag preparing errands is given in this paper. The most objective of the consider is to figure out the fundamental thoughts, structures, and numerical equations that make neural networks work well in preparing information from distinctive regions. The fundamental thoughts of neural systems are looked at, beginning with neurons, layers, and actuation capacities, which are the network's building squares. Scientific models appear how these parts work together within the arrange and how they offer assistance turn input signals into valuable yields through rehashed learning forms. The numerical modeling of feedforward and repetitive neural systems is emphasized, appearing how well they work with both consecutive and time-series information. The think about moreover talks approximately more progressed points, such as optimization strategies like slope plummet and its varieties, which are exceptionally critical for educating neural systems to create forecasts with less botch. The science system incorporates looking into regularization strategies such as L1 and L2 regularization, which are vital for maintaining a strategic distance from overfitting and making generalization way better. Neural systems are utilized in flag handling in a wide run of real-world circumstances, counting discourse and voice acknowledgment, picture handling, organic flag examination, and broadcast communications. Case considers appear how neural systems offer assistance illuminate issues within the genuine world by finding highlights, lowering noise, and making strides flag acknowledgment in situations that alter.

POSE: POSition Encoding for accelerated quantitative MRI

Quantitative MRI utilizes multiple acquisitions with varying sequence parameters to sufficiently characterize a biophysical model of interest, resulting in undesirable scan times. Here we propose, validate and demonstrate a new general strategy for accelerating MRI using subvoxel shifting as a source of encoding called POSition Encoding (POSE). The POSE framework applies unique subvoxel shifts along the acquisition parameter dimension, thereby creating an extra source of encoding. Combining with a biophysical signal model of interest, accelerated and enhanced resolution maps of biophysical parameters are obtained. This has been validated and demonstrated through numerical Bloch equation simulations, phantom experiments and in vivo experiments using the variable flip angle signal model in 3D acquisitions as an application example. Monte Carlo simulations were performed using in vivo data to investigate our method's noise performance. POSE quantification results from numerical Bloch equation simulations of both a numerical phantom and realistic digital brain phantom concur well with the reference method, validating our method both theoretically and for realistic situations. NIST phantom experiment results show excellent overall agreement with the reference method, confirming our method's applicability for a wide range of T1 values. In vivo results not only exhibit good agreement with the reference method, but also show g-factors that significantly outperforms conventional parallel imaging methods with identical acceleration. Furthermore, our results show that POSE can be combined with parallel imaging to further accelerate while maintaining superior noise performance over parallel imaging that uses lower acceleration factors.

Thermal network for breeding blanket analysis and design in fusion reactor

Achieving carbon neutrality in energy production has become crucial and fusion energy is a promising way to a sustainable energy future. Breeding blanket is a critical component of a fusion reactor, ensuring tritium self-sufficiency and heat recovery for power generation. Breeding blanket needs an effective thermal management system as it operates under the high plasma in fusion reactors and the heat generated by the breeding reaction, which should be collected for power conversion. In this study, a thermal circuit model is used to analyze the design of a breeding blanket cooling system; in this model, each component is regarded as a thermal resistance element. Numerical simulations, empirical correlations, and equations are used to compute each resistance element. The thermal circuit results are then integrated into power conversion system using GateCycle for a basic analysis of power generation efficiency of a breeding blanket. Furthermore, we investigated the modified jet impingement design by changing thermal circuit elements to enhance cooling performance. The use of protrusions enhances the thermal performance of the impinging jet by 11 %, contributing to an overall enhancement in system efficiency. These findings could offer valuable insights for advancing the development of efficient, sustainable fusion energy systems.

Study on non-uniform circumferential temperature distribution of annular fuel in the tight lattice configuration of a lead-bismuth cooled fast reactor

To guarantee the safe operation of nuclear reactors and protect fuel elements from being damaged under long-term thermal stress, analyzing the circumferential temperature distribution of the outer cladding of nuclear fuel rods in reactors with tight lattice structures is crucial. In this work, a mathematical and physical model was established through theoretical analysis to calculate the circumferential temperature distribution of the outer cladding of an annular fuel rod. The proposed model provides an analytical expression for the circumferential temperature distribution, and the key factors influencing this distribution are determined. The results of the mathematical-physical model and numerical simulation are then combined through numerical fitting. Consequently, a numerical fitting equation is obtained under the steady-state condition of the lead-bismuth reactor using annular fuel and compared with the numerical simulation data acquired via computational fluid dynamics. The results demonstrate that the proposed numerical fitting equation has high accuracy and can serve as a valuable computational tool for analyzing the circumferential temperature of fuel claddings during the operation of lead-bismuth reactors with annular fuels.

Understanding Cyclotron Motion: A Visual Approach to Electron Dynamics in Electric and Magnetic Fields

Physics material is often material that is difficult for students to understand because of its abstract concepts, one of which is in the material of electric and magnetic fields that discuss the motion of cyclotrons in connecting theoretical concepts and practical applications. Cyclotron motion is accelerated by an electric field that is influenced by the Lorentz force on the combination of electric and magnetic fields. This paper is made with the aim to analyze and visualize the electric field and magnetic field around the cyclotron motion particles using Python animation. In this study, a helix-shaped trajectory is used to represent the movement of electron particles. The animation developed depicts the electric and magnetic field vectors moving around the helix trajectory. In running the particle trajectory animation, numerical equations are involved. The involved numerical equations are second-order ordinary differential equations. This research not only provides theoretical insights into the electrostatic and magnetostatic properties of electron particles but also provides effective visualizations for further education and research. The resulting animation facilitates to enhance the understanding of the concept of how electric and magnetic fields interact and move in the context of electron particles moving in a helix trajectory, opening up opportunities for further exploration in the development of knowledge related to cyclotron motion that is often difficult to understand only through theoretical approaches.

Computational intelligent techniques for predicting optical behavior of different materials

The current research introduces a comparison study of the utilization of artificial neural networks (ANN) and genetic programming (GP) for predicting the optical behavior of different materials. The experimental data for a variety of materials, including semiconductors, insulators, oxides, and halides are extracted and utilized in ANN and GP as inputs. Simulation and prediction processes are carried out based on ANN and GP techniques. The most important aim presented in the current research is to obtain two equations of n as a function of Eg by the two based on ANN and GP models. The first numerical equation is obtained based on the ANN model exhibiting mean squared error (MSE) does not exceed 10−1. The second nonlinear equation is obtained based on the GP model with an acceptable fitness value. The estimated results based on the proposed approaches ANN and GP presented a great match with their targets. It demonstrated that the trained results including simulated and predicted results based on ANN and GP introduce excellent fitting compared with alike results obtained based on the conventional theoretical techniques. The mean absolute percentage error values prove that the ANN model is significantly more accurate than the GP model. Since lower error values suggest better prediction, hence it is clear that ANN performed better than GP. The equation derived by the ANN model is utilized to predict the refractive index for binary and ternary compounds. The values of the refractive index have been predicted for materials for which measurements have been made practically as a test step to ensure the accuracy of the results obtained through the deduced mathematical equations. Then, the application of these equations was generalized to materials that were not measured experimentally. A detailed discussion of the modeling results is introduced and proved that ANN and GP models are effective and successful tools for predicting the refractive index for different types of materials.

Strain Behavior of Short Concrete Columns Reinforced with GFRP Spirals

This paper presents a comprehensive study focused on evaluating the strain generated within short concrete columns reinforced with glass-fiber-reinforced polymer (GFRP) bars and spirals under concentric compressive axial loads. This research was motivated by the lack of sufficient data in the literature regarding strain in such columns. Five full-scale RC columns were cast and tested, comprising four strengthened with GFRP reinforcement and one reference column reinforced with steel bars and spirals. This study thoroughly examined the influence of various test parameters, such as the reinforcement type, longitudinal reinforcement ratio, and spacing of spiral reinforcement, on the strain in concrete, GFRP bars, and spirals. The experimental results showed that GFRP–RC columns exhibited similar strain behavior to steel–RC columns up to 85% of their peak loads. The study also highlighted that the bearing capacity of the columns increased by up to 25% with optimized reinforcement ratios and spiral spacing, while the failure mode transitioned from a ductile to a more brittle nature as the reinforcement ratio increased. Additionally, it is preferable to limit the compressive strain in GFRP bars to less than 20% of their ultimate tensile strain and the strain in GFRP spirals to less than 12% of their ultimate strain to ensure the safe and reliable use of these materials in RC columns. This research also considers the prediction of the axial load capacities using established design standards permitting the use of FRP bars in compressive members, namely ACI 440.11-22, CSA-S806-12, and JSCE-97, and underscores their limitations in accurately predicting GFRP–RC columns’ failure capacities. This study proposes an equation to enhance the prediction accuracy for GFRP–RC columns, considering the contributions of concrete, spiral confinement, and the axial stiffness of longitudinal GFRP bars. This equation addresses the shortcomings of existing design standards and provides a more accurate assessment of the axial load capacities for GFRP–RC columns. The proposed equation outperformed numerous other equations suggested by various researchers when employed to estimate the strength of 42 columns gathered from the literature.