Convergence Criteria Research Articles

Well-Posedness and Convergence Results for History-Dependent Inclusions

We consider an inclusion in a real Hilbert space governed by a time-dependent set of constraints and a history-dependent operator. We introduce the concept of T - well-posedness for this inclusion, associated to a given Tykhonov triple T . Next, we provide a T -well-posedness result that we use in order to deduce the continuous dependence of the solution with respect to the data. Then, we state and prove a convergence criterion to the solution of the inclusion that we use to prove a convergence result for an associate penalty problem. Moreover, we show that this criterion allows us to construct a Tykhonov triple T -which give rise to an optimal well-posedness concept for the corresponding inclusion. Finally, we use these abstract results in the study of a nonlinear viscoelastic constitutive law with long memory term and unilateral constraints.

Physics statistical analysis of crystal violet adsorption onto activated bamboo fiber powder: Insights from thermodynamic functions

This current research scrutinizes the adsorption behavior of Crystal Violeton Activated Bamboo Fiber Powder (ABFP)for water purification. By leveraging four advanced statistical physics scenarios (Hill framework with single energy, Hill framework with dual-energy, Double-layer framework with single energy and Double-layer framework with dual energy), experimental data is meticulously fitted to elucidate the surface adhesion phenomenon by uncovering its decisive influencing metrics.Four convergence criteria (R2, RMSE, AIC and RSS) have been employed to identify the most accurate model while steriographic along with energetic-thermodynamic metrics have been inspected in response to combined effects of temperature and concentration. Major outcomes revealed that the fourth scenario exhibits the most favorable agreement with the measured points. The spatial arrangement factor n varied from 0.58 to 0.75 indicating that the dye retention can occur via two different orientations (parallel and non-parallel) with different percentages. In addition, the adsorption amounts at temperatures of 298, 308 and 318 K were 1403.13, 1365.75 and 1270.79 mg/g, respectively, revealing the exothermicity of crystal violet adsorption onto the pores of Activated Bamboo Fiber Powder. The estimated docking energies were below 40 kJ/mol, suggesting that physical forces primarily govern the surface attachment. Assessment of enthalpy and Gibbs free energy demonstrated that the adsorption process occursfeasibly, spontaneously and is accompanied by heat release. The pore size distribution (PSD) of (ABFP) are determined. Since, the Activated Bamboo Fiber Powder (ABFP) showed promising results for competitive adsorption, thus being of relevance to the industrial sector.

Real-time flood forecasting and uncertainty analysis: a case study of the Krong H’nang hydropower reservoir

ABSTRACT Early and reliable flood forecasting is crucial for mitigating the impacts of floods and ensuring the safe operation of irrigation and hydroelectric facilities. Traditional methods often use a calibrated event-based rainfall-runoff model with a limited number of simulations, making it difficult to measure parameter uncertainties accurately. This paper introduces a new method for estimating the parameters of the HEC-HMS model and evaluating the uncertainties in real-time flood forecasting. First, the Latin Hypercube Sampling (LHS) procedure is used to efficiently sample the parameter values throughout the feasible parameter space. Next, thousands of parameter sets are simulated using a deterministic rainfall-runoff model, generating numerous initial solutions for the Shuffled Complex Evolution (SCE-UA) algorithm to search and evolve. Additional parameter sets are then generated as the search evolves, leading to new simulations until the algorithm reaches the convergence criteria. The optimal solutions are selected based on predefined multiple objective functions. Uncertainty of the forecast results is also computed using the Generalized Likelihood Uncertainty Estimation (GLUE) method and represented as confidence intervals. The method was applied to forecast flood hydrographs at the Krong H’nang hydropower reservoir in Vietnam, using data from 33 flood events from 2016 to 2021. The results demonstrate that the program can effectively forecast the flood hydrograph up to 4 hours in advance (the Kling-Gupta efficiency KGE > 0.8 and the absolute relative volume error |VE| < 10%). The observed values fall within the uncertainty range of Q5%-Q95%. Compared to the conventional method, which uses a fixed parameter set value, this approach is superior and therefore can assist policymakers and operators in more effectively managing reservoir operations.

Energies of an Electron in a One-Dimensional Lattice Using the Dirac Equation: The Coulomb Potential

The energies of an electron in a one-dimensional crystal are studied with both the Schrödinger and Dirac equations using the plane wave expansion method. The crystalline potential sensed by the electron in a cell was calculated by accounting for the Coulombic (electrostatic) interaction between the electron and the surrounding cores (immobile positive ions at the center of the crystal cells). The energies and wave functions of the electron were calculated as a function of four parameters: the period ap of the lattice, the dimension ndim of the matrix in the momentum space, the partition number lpa in which the unit cell is divided to calculate the potential and the number of cores nco that affect the electron. It was found that 8000 cores (surrounding the electron) were needed to reach our convergence criterion. An analytical equation that accurately describes the behavior of the energies in function of the cores that affect the electron was also found. As case studies, the energies for pseudo-lithium and pseudo-graphene were obtained as a first approximation for one-dimensional lattices. Subsequently, the energies of an isolated dimer nanoparticle were also calculated using the supercell method.

Distributed adaptive moving horizon estimation for multi-sensor networks subject to quantization effects

This paper investigates the distributed state estimation problem for multi-sensor networks with quantized measurements. Within the Bayesian framework, a distributed adaptive moving horizon estimation algorithm is developed. Unlike the existing methods regarding quantized errors roughly as bounded uncertainties, the posterior distributions of the errors are demanded to be derived. To overcome the difficulty of evaluating the posterior distributions for series of the states and quantized errors jointly, the variational Bayesian methodology is adopted to approximate the true distributions. Based on the fixed-point iteration method, the update rules are analytically derived, with the convergence criterion provided. Furthermore, by incorporating the average consensus algorithm into the prediction process, all sensors can achieve consensus on their estimates in a distributed manner. Finally, a numerical example of target tracking under logarithmic and uniform quantization effects is given to illustrate the validity of the proposed algorithm.

Research on the convergence of some types of functional branched continued fractions

An analysis of research on the problem of convergence of various types of functional branched continued fractions has been carried out. Branched continued fractions with $N$ branching branches and branched continued fractions with independent variables are considered. The definition and, in our opinion, characteristic criteria of convergence of multidimensional generalizations of C-, S-, g-, J-fractions are given, both for branched continued fractions of the general form with $N$ branching branches and branched continued fractions with independent variables. Such multidimensional generalizations of continued fractions arise, in particular, in the development of various classes of hypergeometric functions of several variables, in particular, the functions of Appel, Lauricella, Horn, etc.

Radiative MHD Casson Non-Newtonian Nanofluid Slip Flow Induced by Stretching Cylinder: A Numerical Approach

Objectives: This article investigates the continuous magnetohydrodynamics slip flow across an extending cylinder, including heat radiation and free stream velocity. The proposed model incorporated the Brownian motion parameter and thermophoresis. Methods: Applying the similarity transformation to a system of partial differential equations yields an ordinary differential equation of first order. Since, there is the nonlinear nature of the modified equations, these ordinary differential equations are addressed by employing mathematical modeling. The shooting process has been embraced to solve changed equations by implementing the following Runge-Kutta Fehlberg method. Findings: Graphical representations are used to show how several fluid factors, such as Casson fluid parameter, free stream velocity, thermophoresis, magnetic parameter, Brownian motion parameter, heat generation parameter, Lewis number, radiation parameter, chemical reaction and curvature parameter affect concentration, temperature and velocity. Results for physical quantity of interest are also computed and reported in tabular form. The study's main findings showed that nanoparticle temperatures rise with greater Brownian motion parameter values, whereas nanoparticle concentration falls with higher heat radiation parameter values. Additionally, it is found that with rise in Lewis number rises as 0.1, 0.4, 0.7, 1.0, 1.3, heat transfer rate falls down by 21.19%. The outcomes are calculated using the MATLAB software. Novelty: This technique's validity is defended by comparing its most recent findings to previously published results and successfully meeting the convergence criteria. The present work emphasizes the analysis of free stream flow in the cylindrical area, specifically in the existence of partial slip and heat radiation, under convective circumstances. This study has significant implications for electronic devices such as processors as well as many businesses and the field of biological and medical sciences. The present investigation aims to support production businesses in achieving the desired level of quality of their products by effectively managing the transport phenomena. Keywords: Stretching cylinder, Heat radiation, Brownian motion, Thermophoresis, Non-Newtonian nanofluid, Shooting technique

Multiplayer hierarchical decision‐making for discrete‐time nonlinear networks of service via value iteration adaptive dynamic programming

AbstractIn this article, the multiplayer hierarchical decision‐making problem for discrete‐time nonlinear networks of service is studied from the perspective of Nash–Stackelberg–Nash games. A novel two‐level value iteration adaptive dynamic programming algorithm is developed to solve the coupled nonlinear Hamilton–Jacobi–Bellman equations associated with the game problem, which neither requires the system drift dynamics to be known as a priori nor requests the initial strategies to be admissible. Moreover, both the value function sequences and the strategy sequences generated by the algorithm converge to their theoretical optimality. An implementation framework for the algorithm is constructed by leveraging the regularized least‐squares method, and a convergence criterion that guarantees the admissibility of the approximated strategies is also proposed. The effectiveness of the proposed algorithm and implementation framework are finally demonstrated through two numerical simulation examples.

On the Significance of Hydrate Formation/Dissociation during CO2 Injection in Depleted Gas Reservoirs

Summary The study aims to quantitatively assess the risk of hydrate formation within the porous formation and its consequences on injectivity during storage of CO2 in depleted gas reservoirs considering low temperatures caused by the Joule-Thomson (JT) effect and hydrate kinetics. Hydrates formed during CO2 storage operation can occupy porous spaces in the reservoir rock, reducing the rock’s permeability and thus becoming a hindrance to the storage project. The aim was to understand which mechanisms can mitigate or prevent the formation of hydrates. The key mechanisms we studied included water dry-out, heat exchange with surrounding rock formation, and capillary pressure. A semicompositional thermal reservoir simulator is used to model the fluid and heat flow of CO2 through a reservoir initially composed of brine and methane. The simulator can model the formation and dissociation of both methane and CO2 hydrates using kinetic reactions. This approach has the advantage of computing the amount of hydrate deposited and estimating its effects on the porosity and permeability alteration. Sensitivity analyses are also carried out to investigate the impact of different parameters and mechanisms on the deposition of hydrates and the injectivity of CO2. Simulation results for a simplified model were verified with results from the literature. The key results of this work are as follows: (1) The JT effect strongly depends on the reservoir permeability and initial pressure and could lead to the formation of hydrates within the porous media even when the injected CO2 temperature was higher than the hydrate equilibrium temperature; (2) the heat gain from underburden and overburden rock formations could prevent hydrates formed at late time; (3) permeability reduction increased the formation of hydrates due to an increased JT cooling; and (4) water dry-out near the wellbore did not prevent hydrate formation. Finally, the role of capillary pressure was quite complex, as it reduced the formation of hydrates in certain cases and increased in other cases. Simulating this process with heat flow and hydrate reactions was also shown to present severe numerical issues. It was critical to select convergence criteria and linear system tolerances to avoid large material balance and numerical errors.

Quantum-Enhanced Generalized Pattern Search Optimization

While the development of quantum computers promises a myriad of advantages over their classical counterparts, care must be taken when designing algorithms that substitute a classical technique with a potentially advantageous quantum method. The probabilistic nature of many quantum algorithms may result in new behavior that could negatively impact the performance of the larger algorithm. The purpose of this work is to preserve the advantages of applying quantum search methods for generalized pattern search algorithms (GPSs) without violating the convergence criteria. It is well known that quantum search methods are able to reduce the expected number of oracle calls needed for finding the solution to a search problem from O(N) to O(N) However, the number of oracle calls needed to determine that no solution exists with certainty is exceedingly high and potentially infinite. In the case of GPS, this is a significant problem since overlooking a solution during an iteration will violate a needed assumption for convergence. Here, we overcome this problem by introducing the quantum improved point search (QIPS), a classical–quantum hybrid variant of the quantum search algorithm QSearch. QIPS retains the O(N) oracle query complexity of QSearch when a solution exists. However, it is able to determine when no solution exists, with certainty, using only O(N) oracle calls.

Distributed fusion-based algorithms for learning high-dimensional Bayesian Networks: Testing ring and star topologies

Learning Bayesian Networks (BNs) from high-dimensional data is a complex and time-consuming task. Although there are approaches based on horizontal (instances) or vertical (variables) partitioning in the literature, none can guarantee the same theoretical properties as the Greedy Equivalence Search (GES) algorithm, except those based on the GES algorithm itself. This paper proposes a parallel distributed framework that uses GES as its local learning algorithm, obtaining results similar to those of GES and guaranteeing its theoretical properties but requiring less execution time. The framework involves splitting the set of all possible edges into clusters and constraining each framework node to only work with the received subset of edges. The global learning process is an iterative algorithm that carries out rounds until a convergence criterion is met. We have designed a ring and a star topology to distribute node connections. Regardless of the topology, each node receives a BN as input; it then fuses it with its own BN model and uses the result as the starting point for a local learning process, limited to its own subset of edges. Once finished, the result is then sent to another node as input. Experiments were carried out on a large repertory of domains, including large BNs up to more than 1000 variables. Our results demonstrate our proposal's effectiveness compared to GES and its fast version (fGES), generating high-quality BNs in less execution time.

Simulation study of heat transfer behaviour of turbulent two-phase flow in a 3D cubic shell and tube heat exchanger using water and different nanofluids

This research utilizes a two-phase flow model to replicate the thermal exchange in a counter flow shell and tube heat exchanger, comparing the efficacy of different nanofluids against pure water. The shell space is represented as a closed cubic area filled with diverse fluids, while the tube functions as the thermal exchange component. It investigates parameters like nanofluid variations, nanoparticle dimensions, and volume ratios to enhance the efficiency of temperature exchange between the shell and tube fluids. The Reynolds-averaged Navier-Stokes (RANS) technique is employed to analyze turbulence within the heat exchanger, utilizing ANSYS@FLUENT (Version 2022 R1) for simulations, which were considered reliable when convergence criteria reached 10−5. The outcomes are assessed based on velocity, thermal conductivity, Nusselt number, temperature dispersion, and turbulent kinetic energy. Notably, the results underscore that integrating nanoparticles into the fluid amplifies its thermal conductivity, with higher concentrations yielding more significant enhancements. Nanofluids, particularly those comprising SiO2-H2O with small nanoparticles and high volume fractions, exhibit notable improvements in heat transfer compared to pure water. TiO2-H2O follows in second place, trailed by CuO-H2O and Al2O3-H2O. The application of the RANS method effectively elucidates turbulence patterns and their impact on heat transfer dynamics between the shell and tube. An increase in Reynolds number has shown an adverse effect on heat transfer. Overall, this study furnishes valuable insights for optimizing heat transfer performance in such systems.

Modification of Adomian decomposition technique in multiplicative calculus and application for nonlinear equations

Multiplicative calculus is a mathematical system that offers an alternative to traditional calculus. Instead of using addition and subtraction to measure change, as in traditional calculus, it uses multiplication and division. The framework of nonlinear equations is an incredibly powerful tool that has proven invaluable in advancing our understanding of various phenomena across a wide range of applied sciences. This framework has enabled researchers to gain deeper insights into a vast array of scientific problems. The physical interpretation of iterative methods for nonlinear equations using multiplicative calculus offers a unique perspective on solving such equations and opens up potential applications across various scientific disciplines. Multiplicative calculus naturally aligns with processes characterized by exponential growth or decay. In many physical, biological, and economic systems, quantities change in a manner proportional to their current state. Multiplicative calculus models these processes more accurately than traditional additive approaches. For example, population growth, radioactive decay, and compound interest are all better described multiplicatively. The primary objective of this work is to modify and implement the Adomian decomposition method within the multiplicative calculus framework and to develop an effective class of multiplicative numerical algorithms for obtaining the best approximation of the solution of nonlinear equations. We build up the convergence criteria of the multiplicative iterative methods. To demonstrate the application and effectiveness of these new recurrence relations, we consider some numerical examples. Comparison of the multiplicative iterative methods with the similar ordinary existing methods is presented. Graphical comparison is also provided by plotting log of residuals. The purpose in constructing new algorithms is to show the implementation and effectiveness of multiplicative calculus.

Adaptive Kriging-based method with learning function allocation scheme and hybrid convergence criterion for efficient structural reliability analysis

Adaptive Kriging-based method with learning function allocation scheme and hybrid convergence criterion for efficient structural reliability analysis

Mosco Convergence of Gradient Forms with Non-Convex Interaction Potential

This article provides a new approach to address Mosco convergence of gradient-type Dirichlet forms, EN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {E}}^N$$\\end{document} on L2(E,μN)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^2(E,\\mu _N)$$\\end{document} for N∈N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N\\in {\\mathbb {N}}$$\\end{document}, in the framework of converging Hilbert spaces by K. Kuwae and T. Shioya. The basic assumption is weak measure convergence of the family (μN)N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${(\\mu _N)}_{N}$$\\end{document} on the state space E—either a separable Hilbert space or a locally convex topological vector space. Apart from that, the conditions on (μN)N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${(\\mu _N)}_{N}$$\\end{document} try to impose as little restrictions as possible. The problem has fully been solved if the family (μN)N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${(\\mu _N)}_{N}$$\\end{document} contain only log-concave measures, due to Ambrosio et al. (Probab Theory Relat. Fields 145:517–564, 2009). However, for a large class of convergence problems the assumption of log-concavity fails. The article suggests a way to overcome this hindrance, as it presents a new approach. Combining the theory of Dirichlet forms with methods from numerical analysis we find abstract criteria for Mosco convergence of standard gradient forms with varying reference measures. These include cases in which the measures are not log-concave. To demonstrate the accessibility of our abstract theory we discuss a first application, generalizing an approximation result by Bounebache and Zambotti (J Theor Probab 27:168–201, 2014).

Using Entropy as the Convergence Criteria of Ant Colony Optimization and the Application at Gene Chip Data Analysis.

When Ant Colony Optimization algorithm (ACO) is adept at identifying the shortest path, the temporary solution is uncertain during the iterative process. All temporary solutions form a solution set. Where each solution is random. That is, the solution set has entropy. When the solution tends to be stable, the entropy also converges to a fixed value. Therefore, it was proposed in this paper that apply entropy as a convergence criterion of ACO. The advantage of the proposed criterion is that it approximates the optimal convergence time of the algorithm. In order to prove the superiority of the entropy convergence criterion, it was used to cluster gene chip data, which were sampled from patients of Alzheimer's Disease (AD). The clustering algorithm is compared with six typical clustering algorithms. The comparison shows that the ACO using entropy as a convergence criterion is of good quality. At the same time, applying the presented algorithm, we analyzed the clustering characteristics of genes related to energy metabolism and found that as AD occurs, the entropy of the energy metabolism system decreases; that is, the system disorder decreases significantly.

Universal Ensemble-Embedding Graph Neural Network for Direct Prediction of Optical Spectra from Crystal Structures.

Optical properties in solids, such as refractive index and absorption, hold vast applications ranging from solar panels to sensors, photodetectors, and transparent displays. However, first-principles computation of optical properties from crystal structures is a complex task due to the high convergence criteria and computational cost. Recent progress in machine learning shows promise in predicting material properties, yet predicting optical properties from crystal structures remains challenging due to the lack of efficient atomic embeddings. Here, Graph Neural Network for Optical spectra prediction (GNNOpt) is introduced, an equivariant graph-neural-network architecture featuring universal embedding with automatic optimization. This enables high-quality optical predictions with a dataset of only 944 materials. GNNOpt predicts all optical properties based on the Kramers-Krönig relations, including absorption coefficient, complex dielectric function, complex refractive index, and reflectance. The trained model is applied to screen photovoltaic materials based on spectroscopic limited maximum efficiency and search for quantum materials based on quantum weight. First-principles calculations validate the efficacy of the GNNOpt model, demonstrating excellent agreement in predicting the optical spectra of unseen materials. The discovery of new quantum materials with high predicted quantum weight, such as SiOs, which host exotic quasiparticles with multifold nontrivial topology, demonstrates the potential of GNNOpt in predicting optical properties across a broad range of materials andapplications.

Exponential Boundary Control for 2-D Spatial Distributed Parameter Systems Under Boundary Collocated and Planar Linear Measurements.

For a class of 2-D spatial distributed parameter systems (DPSs) with space-dependent diffusivity, this article aims to achieve exponential realization of their desired profiles. To reduce the number of required sensors and actuators, a planar output feedback boundary control strategy is proposed with combining two nonfull-domain measurement methods, boundary collocated measurement and planar linear measurement, in which only two boundaries of the considered 2-D spatial DPSs are controlled and a little output information is measured. Moreover, by employing the Poincaré-Wirtinger inequality and variable substitution dexterously, the final exponential convergence criteria of the error system can be obtained with method of "Diverse treatment for same term." Finally, we provide a general numerical example and an application example in 2-D heat conduction systems to illustrate the effectiveness and practicability of the proposed measurement and control schemes.

Comprehensive numerical modeling analysis and experimental validation of a multi-turn pulsating heat pipe

The aim of this paper is to present the results of the experimentally validated numerical code designed for thermal-fluid computations in pulsating heat pipes using CFD techniques. The analysis was carried out using the OpenFOAM software, where an algorithm was developed to simulate multiphase flow with phase change and coupled heat transfer between the fluid and solid domains. The article meticulously delineates the steps involved in implementing and validating the model, commencing from basic comparative tests like the Stefan problem, progressing through Scriven’'s bubble growth, and culminating in an experiment with single- and multi-turn pulsating heat pipes. The algorithm has been refined by including a convergence criterion based on the Galusinski-Vigneaux number, which allows faster results and reduces the likelihood of numerical anomalies. Finally, an experiment was carried out to evaluate the thermal efficiency of a two-loop heat pipe on a specially designed experimental set-up constructed by the authors. In the experiment, ethanol was utilized as the working fluid, operating within a temperature range of 20 to 90 °C. The experiment was carried out with three distinct filling ratios: 50 %, 62.5 %, and 75 %. The validated parameters included pressure and temperature at the measurement points and the experimentally derived thermal efficiency results were compared with the numerical results. The model showed an error of 7.06 ± 3.73 %.

Analytical model for flexural-torsional coupling behavior of prestressed corrugated steel-concrete composite girders

Prestressed corrugated steel-concrete (PCSC) composite girders are often subjected to combined bending and torsion in practice, but the existing theoretical models have mainly focused on pure torsional behavior. Thus, this paper proposed a modified combined action softened truss model (MCA-STM) to predict the flexural-torsional coupling behavior and failure modes of PCSC composite girders. The equivalent loading and nonlinear equations were modified, and the convergence criteria of flexural and torsional failure were established, considering the structural characteristics of PCSC composite girders. A new optimized algorithm was employed to solve the MCA-STM, providing a more efficient and numerically stable solution procedure. A 3D finite element analysis (FEA) model of the PCSC composite girder was established, which was verified by comparing the available test results. A parametric study was carried out based on the verified FEA model to get more datasets with various parameters, and the results were compared to the proposed analytical model. The curves obtained by the FEA and MCA-STM are in good agreement, indicating that the proposed analytical model can predict the full flexural-torsional coupling behavior and failure modes of the PCSC composite girders.