Method For Numerical Solution Research Articles

Large Deflection Analysis of Functionally Graded Beam by Using Combining Method

In this study, the large deflection behavior of a circular cross-section beam is examined using the Combining Method (CM). The CM is a numerical solution method that uses block diagrams in the Matlab-Simulink program and weighting coefficients in the Differential Quadrature Method (DQM). The beam material considered is Functionally Graded Material (FGM). Boundary conditions of the beam are taken as clamped-free (C-F) and a singular load is assumed to be applied from the free end of the beam. Geometric nonlinear analysis is performed while calculating the large deflection equations of the beam and performing numerical analysis. The effects of increasing the force applied to the beam, changing the beam cross-section in the longitudinal direction, and changing the material index of the FGM on the extreme deflection behavior of the beam were examined. For comparison purposes, the results obtained from CM are compared with the results obtained from both SolidWorks-Simulation and Ansys-Workbench programs. As a result of the analysis, increasing the applied force causes the x and y coordinates of the end point of the beam to decrease. The change in geometry and material index greatly affects the large deflection occurring in the beam.

Research on the prediction model of energy separation effect of vortex tube based on trajectory deflection characteristics and its numerical solution method

In this paper, in order to establish the energy separation mechanism of the vortex tube, the hydrodynamic behavior of the compressible fluid in the asymmetric cavity space is investigated, and a numerical model of the trajectory deflection behavior is deduced and established; in order to form the optimal design method of the structural parameters of the vortex tube, the force situation of the fluid microelements entering different regions of the vortex chamber of the vortex tube is analyzed, and the trajectory deflection equations are corrected by combining with the expansion behavior of the fluid and the characterizing equations of vortex strength, transportability, and vortex initiation characteristics are given. The characterization equations of vortex strength, transportability and vortex initiation characteristics are given, and the numerical simulation of their influence parameters is carried out; in order to realize the prediction of the vortex tube performance of a given structure, the multifactor Pearson thermodynamic map is used to correlate and analyze the experimental data of vortex tubes reported publicly in the past years, and the polynomial regression equations are designed and established for the prediction of the vortex tube's energy separation effect and the confidence level and the degree of coincidence of the prediction results are examined. The confidence level and degree of agreement of the prediction results were examined. It is found that: the trajectory deflection motion of the compressible fluid in the asymmetric cavity space is the result of the combined effect of structural air pressure bias and the expansion behavior of the incident fluid; in order to improve the vortex strength in the vortex tube, the vortex initiation chamber space should be as small as possible; the increase of the diameters of the hot-end pipe and the cold-end pipe is conducive to the enhancement of vortex strength, but at the same time, it weakens the vortex transport in the heat pipe; the vortex initiation chamber size has a negative correlation with the hot-end temperature rise, and the inlet fluid pressure has a The negative correlation between the size of the vortex chamber and the temperature rise at the hot end, the positive correlation between the increase of inlet fluid pressure and the resulting temperature rise, and the strong correlation between the inlet fluid pressure and the friction coefficient on the effect of energy separation; the predictive equations for the effect of energy separation obtained by the fitting are in good agreement with the real situation.

Fourier–Gegenbauer pseudospectral method for solving periodic fractional optimal control problems

This paper introduces a new, highly accurate model for periodic fractional optimal control problems (PFOCPs) based on Riemann–Liouville and Caputo fractional derivatives (FDs) with sliding fixed memory lengths. This new model enables periodic solutions in fractional-order control models by preserving the periodicity of the fractional derivatives. Additionally, we develop a novel numerical solution method based on Fourier and Gegenbauer pseudospectral approaches. Our method simplifies PFOCPs into constrained nonlinear programming problems (NLPs), readily solvable by standard NLP solvers. Some key innovations of this study include: (i) The derivation of a simplified FD calculation formula to transform periodic FD calculations into evaluations of trigonometric Lagrange interpolating polynomial integrals, efficiently computed using Gegenbauer quadratures. (ii) The introduction of the αth-order fractional integration matrix based on Fourier and Gegenbauer pseudospectral approximations, which proves to be highly effective for computing periodic FDs. A priori error analysis is provided to predict the accuracy of the Fourier–Gegenbauer-based FD approximations. Benchmark PFOCP results validate the performance of the proposed pseudospectral method.

Разработка и исследование подхода к обработке сигналов цифровых измерительных трансформаторов тока и напряжения

During the development of secondary systems of stations and substations, including relay protection, automation, control, electricity metering, etc., qualitative changes have recently occurred due to the introduction of digital technologies. The introduction of digital technologies is supported by innovative development programs such as “Digital Transformation 2030”. The introduction of digital technologies is associated with the use of digital data transmission channels according to uniform standards. Projects of “digital substations” are being actively implemented with the transmission of digital information at all levels, including the primary equipment, the transmission of information both from current and voltage measuring transformers, and from switching devices. Currently, digital instrument transformers are actively being developed and implemented, in which information about measured currents and voltages is presented in digital code. New approaches to measure primary currents and voltages, and transmit information pose new challenges, and open prospects for improving signal processing methods used for relay protection purposes. Thus, the relevant aim of the study is the development and research of approaches to digital processing of signals of digital instrument current and voltage transformers. To solve the problems posed within the framework of this study, analytical and numerical solution methods have been used. Numerical methods are applied using software products such as MathCAD and the Python programming language to generate signals and display them on graphs. To substantiate the reliability, verification of the results obtained by different methods is carried out. The authors have formulated an approach to digital processing of signals obtained using current sensors of a digital instrument transformer. The authors have studied the approach to determine synchronized current vector values by processing information received from primary current converters. The characteristics of the algorithm for obtaining a vector have been analyzed and the dependences of errors on the influence of distorting factors have been plotted. The proposed approach is a development of the existing approach to obtain a vector by getting information from current sensors operating on different physical principles. The results show the advantages of the proposed method. The proposed digital signal processing algorithm is more technically expensive since it contains at least two metrologically calibrated measuring channels instead of one. However, all other things being equal, it allows to increase the accuracy and speed of the digital processing algorithms taken as a prototype. The results obtained can be used to formulate algorithms for measuring relay protection devices.

Fractional-order brucellosis transmission model between interspecies with a saturated incidence rate

In this study, brucellosis dynamics between interspecies are discussed with the Atangana-Baleanu fractional derivative to examine the transmission of brucellosis by its behavior. The recovered compartment, recruitment, and natural death rate for humans are considered for the fractional order model to analyze the transmission dynamics in more detail from an epidemiological point of view. Additionally, the saturated incidence rate is suggested for brucellosis as indirectly transmitted to individuals from the environment. By fixed point theory, it is verified that developed fractional transmission dynamics have a unique solution. The model under consideration employs the Adams-type predictor-corrector method for numerical solution. All comparative results are plotted by MATLAB.

Review of Adams-Bashforth method for numerical solution of first order ordinary differential equations

This project work presents a comprehensive review of the Adams-Bashforth method for the numerical solution of explicit first-order ordinary differential equations (ODEs). The study begins with a historical overview of the development of ordinary differential equations (ODEs), tracing back to the seminal works of Newton, Leibniz, and their contemporaries. The evolution of differential equations as a distinct mathematical discipline and their wide-ranging applications across various fields are discussed. Furthermore, the paper provides an in-depth analysis of the Adams-Bashforth method, a prominent numerical technique for solving ODEs. The method is derived and analyzed using Mathematica Software, demonstrating its efficacy and accuracy in approximating solutions to ODEs. A comparison with existing methods such as the Euler method and the Runge-Kutta method highlights the advantages of the Adams-Bashforth method, particularly in terms of computational efficiency and accuracy. Moreover, fundamental concepts related to ODEs, including the initial value problem, existence, and uniqueness of solutions, are explored in the context of numerical solution methods. The properties of linear multistep methods and their relevance to solving ODEs efficiently are also discussed. In conclusion, this project work provides valuable insights into the Adams-Bashforth method as a powerful tool for the numerical solution of first-order ODEs. By leveraging modern computational tools such as Mathematica Software, the method offers a practical and efficient approach to solving complex differential equations encountered in various scientific and engineering applications.

A computational- experimental model of reactor kinetic for investigating the linearity response of in-core neutron detectors of a low power research reactor

In this study, the linear response of fission chamber (FC) neutron detectors in Isfahan miniature neutron source reactor (MNSR) is investigated through experiments and calculations at different powers of the reactor. The linearity of the response of the main neutron detector in the MNSR is important due to its safety functions in reactor power control. Additionally, determining the linear response region of this detector presents a linear neutron dosimetry field even outside of the reactor core, i.e. at the outlet of external beam tubes. Moreover, it is very difficult to remove and calibrate this neutron detector that has been installed in the reactor core for a long time. For this purpose, an alternative method for measuring the linearity of the response of a neutron detector is extended by investigating the kinetic behavior of reactor. The aim of this method is to calculate the delayed neutrons population in the reactor core and compare with the FC detector response. In this method, the numerical solution method is used to solve the point kinetic equation with 15 delayed neutron groups (6 delayed neutron groups and 9 photo-neutron groups) after inserting a large negative reactivity into the MNSR core by considering temperature and xenon reactivity feedbacks during a coupling procedure. To obtain the xenon reactivity feedback, xenon concentration is calculated by coupling the 135Xe and 135I production equations and the εpPFnlPTnl parameter is obtained by an experimental method. Furthermore, the value of fission cross section (Σf) is calculated using a validated model in the Dragon code. The large reactivities are inserted at two initial power of 150 W and 30 kW to investigate the response of the main FC neutron detector in a cold xenon-free condition and by considering temperature and xenon reactivity feedbacks, respectively. The results demonstrate that the response of the MNSR FC detector is linear in the neutron flux range between 5 × 107 to 1 × 1012 n.cm−2.s−1, which is equivalent to reactor power of 1.5 W to 30 kW. This innovative method can be applied to calibrate the neutron detectors in other research and power reactors.

Multiple-arc optimization of low-thrust Earth–Moon orbit transfers leveraging implicit costate transformation

This work focuses on minimum-time low-thrust orbit transfers from a prescribed low Earth orbit to a specified low lunar orbit. The well-established indirect formulation of minimum-time orbit transfers is extended to a multibody dynamical framework, with initial and final orbits around two distinct primaries. To do this, different representations, useful for describing orbit dynamics, are introduced, i.e., modified equinoctial elements (MEE) and Cartesian coordinates (CC). Use of two sets of MEE, relative to either Earth or Moon, allows simple writing of the boundary conditions about the two celestial bodies, but requires the formulation of a multiple-arc trajectory optimization problem, including two legs: (a) geocentric leg and (b) selenocentric leg. In the numerical solution process, the transition between the two MEE representations uses CC, which play the role of convenient intermediate, matching variables. The multiple-arc formulation at hand leads to identifying a set of intermediate necessary conditions for optimality, at the transition between the two legs. This research proves that a closed-form solution to these intermediate conditions exists, leveraging implicit costate transformation. As a result, the parameter set for an indirect algorithm retains the reduced size of the typical set associated with a single-arc optimization problem. The indirect heuristic technique, based on the joint use of the necessary conditions and a heuristic algorithm (i.e., differential evolution in this study) is proposed as the numerical solution method, together with the definition of a layered fitness function, aimed at facilitating convergence. The minimum-time trajectory of interest is sought in a high-fidelity dynamical framework, with the use of planetary ephemeris and the inclusion of the simultaneous gravitational action of Sun, Earth, and Moon, along the entire transfer path. The numerical results unequivocally prove that the approach developed in this research is effective for determining minimum-time low-thrust Earth–Moon orbit transfers.

Comparative study and validation of a new analytical method for hydraulic modelling of bidirectional low temperature networks

Bidirectional Low Temperature Networks (BLTNs) are an innovative technology of district heating and cooling systems. Because of their intrinsic feature of supplying simultaneous heating and cooling either directly from an energy source/sink or through distributed heat pumps and chillers, circulation pumps installed at each building extract water from the network and a distinct pressure cone is subsequently created. Variations in the amount (and direction) of the extracted water call for accurate hydraulic design and analysis to ensure safe and adequate network operation. This paper proposes a new analytical solution method for fast hydraulic modelling of BLTNs. The analytical method was compared against three numerical solution methods and validated using different current and future operating scenarios of a real-world bidirectional network. In all modelled cases, the calculated mass flows and pressure drops using the new analytical method yielded very small Normalised Mean Bias Error (NMBE) and Coefficient of Variation of the Root Mean Square Error (CV(RMSE)), suggesting excellent agreement between the analytical and numerical solution methods. The new analytical method offers better performance over its numerical counterparts due to its explicit nature, ease of implementation, and quick modelling time.

Analysis of Underlapped Symmetrically Ported Valve-Controlled Asymmetric Cylinder Drive

The valve-controlled cylinder drive system is the most common type among hydraulic applications. Nonlinear behaviour in such systems is inevitable when the valve spool is around its null position. We utilised the component linking method to investigate the nonlinearities in a Moog valve-controlled asymmetric cylinder drive system by simulation in Fortran, in which a generalised concept is introduced and validated by comparing to the experimental results. An X factor is proposed in the generalised concept to describe the asymmetric cylinder state, which is a constant when the cylinder is extending or retracting, but numerically calculated when the valve spool is in the underlap region. This analytical solution is approximately 200 times more computationally efficient than the numerical solution method. This paper utilises the component linking method to simulate the Moog valve-controlled asymmetric cylinder drive system in Matlab Simulink, and proposes an analytical solution for the X factor when the valve spool is in the underlap region. This analytical solution is approximately 200 times more computationally efficient than the numerical solution method.

A Stable Finite Volume Method for Numerical Solution of Time-Tempered Fractional Sine–Gordon Equations

A Stable Finite Volume Method for Numerical Solution of Time-Tempered Fractional Sine–Gordon Equations

Tensor networks for solving the time-independent Boltzmann neutron transport equation

Tensor network techniques, known for their low-rank approximation ability that breaks the curse of dimensionality, are emerging as a foundation of new mathematical methods for ultra-fast numerical solutions of high-dimensional Partial Differential Equations (PDEs). Here, we present a mixed Tensor Train (TT)/Quantized Tensor Train (QTT) approach for the numerical solution of time-independent Boltzmann Neutron Transport equations (BNTEs) in Cartesian geometry. Discretizing a realistic three-dimensional (3D) BNTE by (i) diamond differencing in space, (ii) multigroup-in-energy, and (iii) discrete ordinates collocation in angle leads to large generalized eigenvalue problems that generally require a matrix-free approach and large computer clusters. Starting from this discretization, we construct a TT representation of the PDE fields and discrete operators, followed by a QTT representation of the TT cores. We then solve the tensorized generalized eigenvalue problem using a fixed-point scheme with tensor network optimization techniques. We validate our approach by applying the method to two examples of 3D neutron transport problems, currently solved by the Los Alamos National Laboratory PARallel TIme-dependent SN (PARTISN) solver.1 We demonstrate that our TT/QTT method, executed on a standard desktop computer, leads to large compression. This allows for the storage of terrabyte-sized neutron angular flux eigenvectors in megabytes. Additionally, we create megabyte-sized full access TT representations of yottabyte-sized transport matrix operators. By leveraging the TT operators and solution methods, we obtain a 7500 times speedup when compared to the PARTISN solution time with an error of less than 10−5.

Modeling and Numerical Computation of the Longitudinal Non-Linear Dynamics of High-Speed Elevators

High-speed elevator systems comprise numerous components, and vibration issues are prevalent. The evident non-linear behavior resulting from changes in the wire rope length adds complexity to the investigation of elevator dynamics issues. This paper investigates dynamics modeling and numerical solution methods for longitudinal vibrations in a typical high-speed elevator system. The primary contributions of this paper include constructing a dynamics model for high-speed elevators using a substructure dynamics modeling approach. This model incorporates Newton’s law and the Lagrange equation to comprehensively represent the dynamics of the elevator car, car frame, traction system, and tension system. Additionally, a non-linear dynamics model of the steel wire rope is developed using the centralized mass method. This paper also presents an algorithm to solve the time-domain dynamics based on the variable-step-length Runge–Kutta method. Furthermore, it investigates the non-linear dynamics of elevators considering variations in the elevator’s intrinsic frequency and different elevator control strategies, focusing on the response characteristics of high-speed elevator dynamics. The findings of this thesis hold significant importance in the field of high-speed elevator dynamics. They aid in the design and debugging of high-speed elevator systems and serve as a foundation for future research into the non-linear aspects of elevators.

Thermal Characteristics of Spindle System Based on the Comprehensive Effect of Multiple Nonlinear Time-Varying Factors

The thermal characteristics of the spindle system for CNC machine tools are influenced by multiple factors which are nonlinear and time-varying. In this paper, a nonlinear time-varying thermal characteristics solving model for the spindle system was established based on the numerical solution method. Through theoretical deduction and data fitting, mathematical models of nonlinear time-varying factors including the friction torque generated by lubricants, convective heat transfer coefficient, and coolant and ambient temperature are constructed. The temperature and displacement of the spindle system at each time step are solved by considering the comprehensive effect of multiple nonlinear time-varying factors. And the actual temperature and axial deformation data of the spindle system are obtained through thermal characteristics detection experiments. By comparing solution results affected by multiple nonlinear time-varying factors and by non time-varying factors with experimental data, it can be concluded that the nonlinear time-varying thermal characteristics model has advantages in reflecting the trend of numerical changes and the accuracy of result solving over a method considering non time-varying factors and the solution values of temperature affected by multiple nonlinear time-varying factors are almost consistent with detection values and the relative errors are all within ±3%. The relative error of axial deformation between the value solved by the model and the detection value is close to −1%. This conclusion demonstrates the rationality and accuracy of the thermal characteristics solving model and the construction of nonlinear time-varying factors. This study is of great significance for exploring the thermal characteristics of the spindle system and improving CNC machine tool performance in depth.

Numerical and analytical solution of temperature distribution in foamed soy suspension during vacuum microwave drying

Objective. Technologies of vacuum dehydration of solutions in the microwave field are constantly developing in the direction of increasing the energy efficiency of the drying process and reducing the cost of target products. This scientific direction fully applies to vacuum microwave drying of soy suspension in a foamed state. In this regard, the most important task is to improve mathematical modeling, which provides significant assistance in the study of heat and mass transfer processes occurring in vacuum dryers with microwave power supply; in the design of new installations and the development of effective modes of their operation; the development of optimal modes of vacuum drying foamed soy suspension, taking into account thermophysical and electrophysical characteristics. Method. The research is based on computer simulation methods. Result. Using the results of previous studies, a mathematical apparatus was obtained for finding the temperature in a foamy product during vacuum microwave drying. Its difference from existing mathematical models lies in the possibility of using simple methods for analyzing differential equations with fewer unknown variables. A method of numerical and analytical solution of a mathematical model of the process of vacuum microwave drying of foamed suspension is proposed. Experimental verification showed quite satisfactory convergence of the simulation results with an error of 10-12%. Conclusion. The study of numerical methods for solving the formulated problem makes it possible to determine the temperature at any point of the soybean suspension, taking into account the thermophysical and electrical characteristics of the suspension in a wide range of operating parameters.

Investigation of Magneto Hydrodynamics Properties of Reiner–Philippoff Nanofluid with Gyrotactic Microorganism in a Porous Medium

Investigation of Magneto Hydrodynamics Properties of Reiner–Philippoff Nanofluid with Gyrotactic Microorganism in a Porous Medium Nanofluids have many potential applications in engineering, medicine, and biotechnology due to their enhanced thermal, electrical, and optical properties. However, the flow and heat transfer characteristics of nanofluids are influenced by various factors, such as the type and size of nanoparticles, the base fluid, the magnetic field, the radiation, the chemical reaction, and the presence of microorganisms. Therefore, it is important to study the effects of these factors on the nanofluid flow and heat transfer using mathematical models and numerical methods. One of the mathematical models that can describe the nanofluid flow is the Reiner-Philippoff model, which is a classical non-Newtonian fluid model that accounts for the shear-thinning behaviour of some fluids. The Reiner-Philippoff model has been used to study the nanofluid flow over a stretching sheet, which is a simplified model of many industrial processes involving stretching or shrinking surfaces. However, most of the previous studies have neglected the effects of the Arrhenius reaction, thermal radiation, viscous dissipation, and bio-convection on the nanofluid flow over a stretching sheet. The objective of this paper is to fill this gap by conducting a numerical investigation of the effects of the Arrhenius reaction, thermal radiation, viscous dissipation, and bio-convection on a Reiner-Philippoff nanofluid of MHD flow through a stretching sheet. This also considers the effects of thermophoresis and Brownian motion, which are two mechanisms that govern the transport of nanoparticles in nanofluids. The article utilized a similarity transformation to reduce the governing partial differential equations into ordinary differential equations, which are then solved by using the MATLAB computational tool bvp4c technique. The paper also employs a hybrid numerical solution method using Runge-Kutta fourth order with a shooting technique and an optimization technique using the Bayesian regularization method for Runge-Kutta to improve the accuracy of the prediction outcomes. The main finding of this paper is that the Arrhenius reaction, thermal radiation, viscous dissipation, and bio-convection have significant effects on the velocity, temperature, concentration, and motile microorganism profiles of the nanofluid flow over a stretching sheet. The paper also discusses how these effects can be controlled by varying the relevant parameters. This provides graphical results for the profiles of velocity, temperature, concentration, and motile microorganisms for different values of these parameters. The study also compares its results with some existing results in the literature and finds good agreement.

Numerical analysis of the SIS infectious disease model with spatial heterogeneity

PurposeThe susceptible-infectious-susceptible (SIS) infectious disease models without spatial heterogeneity have limited applications, and the numerical simulation without considering models’ global existence and uniqueness of classical solutions might converge to an impractical solution. This paper aims to develop a robust and reliable numerical approach to the SIS epidemic model with spatial heterogeneity, which characterizes the horizontal and vertical transmission of the disease.Design/methodology/approachThis study used stability analysis methods from nonlinear dynamics to evaluate the stability of SIS epidemic models. Additionally, the authors applied numerical solution methods from diffusion equations and heat conduction equations in fluid mechanics to infectious disease transmission models with spatial heterogeneity, which can guarantee a robustly stable and highly reliable numerical process. The findings revealed that this interdisciplinary approach not only provides a more comprehensive understanding of the propagation patterns of infectious diseases across various spatial environments but also offers new application directions in the fields of fluid mechanics and heat flow. The results of this study are highly significant for developing effective control strategies against infectious diseases while offering new ideas and methods for related fields of research.FindingsThrough theoretical analysis and numerical simulation, the distribution of infected persons in heterogeneous environments is closely related to the location parameters. The finding is suitable for clinical use.Originality/valueThe theoretical analysis of the stability theorem and the threshold dynamics guarantee robust stability and fast convergence of the numerical solution. It opens up a new window for a robust and reliable numerical study.

A numerical method for solutions of tempered fractional differential equations

The main objective of this paper is to develop a technique for approximating the numerical solution of certain class of tempered fractional differential equations. The proposed technique is based on the Newton–Cotes quadrature formula, and it is established by using generalized Lagrange interpolation polynomials. The product integration technique is used to develop a formula for the left and right-sided tempered fractional integrals. Next, by using these formulas, a method is developed for solving a general class of tempered fractional differential equations. Furthermore, three distinct classes of initial value problems and one of the terminal value problems for tempered fractional differential equations are taken into consideration and each class is illustrated by a numerical experiment to demonstrate the validity and effectiveness of the proposed methodology. Moreover, upper bound of error in the numerical approximations have been provided.

Численное моделирование пьезопроводных процессов в двумерной постановке для коллектора трещиновато-порового типа

The process of two-phase filtration in a carbonate formation of fractured-pore type is considered. A mathematical model in a spatially two-dimensional formulation is proposed, a numerical method for solution and a parallel algorithm for its implementation are developed. The mathematical model is based on the Buckley-Leverett approach. The reservoir takes into account the exchange of fluids between low-permeability pores and natural fracturing, specified within the framework of the dual porosity model. The numerical algorithm is based on the use of the finite difference method and the splitting scheme by physical processes. To speed up calculations, a parallel algorithm based on two-dimensional domain decomposition is used. Numerical experiments were carried out, which showed that the developed algorithm is highly efficient and allows one to calculate the necessary characteristics of the modeled physical process.

Analysis of sensitivity to hydrate blockage risk in natural gas gathering pipeline

During the operational process of natural gas gathering and transmission pipelines, the formation of hydrates is highly probable, leading to uncontrolled movement and aggregation of hydrates. The continuous migration and accumulation of hydrates further contribute to the obstruction of natural gas pipelines, resulting in production reduction, shutdowns, and pressure build-ups. Consequently, a cascade of risks is prone to occur. To address this issue, this study focuses on the operational process of natural gas gathering and transmission pipelines, where a comprehensive framework is established. This framework includes theoretical models for pipeline temperature distribution, pipeline pressure distribution, multiphase flow within the pipeline, hydrate blockage, and numerical solution methods. By analyzing the influence of inlet temperature, inlet pressure, and terminal pressure on hydrate formation within the pipeline, the sensitivity patterns of hydrate blockage risks are derived. The research indicates that reducing inlet pressure and terminal pressure could lead to a decreased maximum hydrate formation rate, potentially mitigating pipeline blockage during natural gas transportation. Furthermore, an increase in inlet temperature and terminal pressure, and a decrease in inlet pressure, results in a displacement of the most probable location for hydrate blockage towards the terminal station. However, it is crucial to note that operating under low-pressure conditions significantly elevates energy consumption within the gathering system, contradicting the operational goal of energy efficiency and reduction of energy consumption. Consequently, for high-pressure gathering pipelines, measures such as raising the inlet temperature or employing inhibitors, electrical heat tracing, and thermal insulation should be adopted to prevent hydrate formation during natural gas transportation. Moreover, considering abnormal conditions such as gas well production and pipeline network shutdowns, which could potentially trigger hydrate formation, the installation of methanol injection connectors remains necessary to ensure production safety.