177 results about "Finite difference method" patented technology

The invention discloses a multi-scale wave-flow-sediment coupling beach evolution prediction model method, and relates to the technical field of tidal flat landform morphology evolution simulation, comprising the steps of integrating a tidal current power module, a wave motion module and a sediment power module, solving, and predicting landform morphology evolution of a tidal flat area; establishing a coordinate system according to actually measured tidal flat topographic data, obtaining tidal current, wave and sediment data based on a hydrometric station, taking the data as boundary conditions, and importing the boundary conditions into the model; constructing a beach evolution prediction model based on integration of tidal current power, wave motion and sediment power modules, and setting parameters required by each module; a finite difference method is adopted to solve a fluid continuity equation, a wave energy conservation equation, a one-dimensional vertical average suspended sediment convection and diffusion equation and a bottom bed updating equation, and tidal flat section terrains at different stages are obtained, so that the tidal flat section form evolution process under the action of waves and flow is accurately simulated, and compared with a traditional tidal current sediment model, the simulation precision is higher, and the simulation efficiency is higher. And the calculation efficiency can be obviously improved.

A central air-conditioning system energy consumption simulation method based on a multi-region coupling model comprises the steps that basic data and initial parameters of a cold-chain logistics center site are obtained, and the basic data and the initial parameters are preprocessed; and constructing a multi-region coupling physical mechanism model based on a heat and mass transfer equation, and outputting a physical model state through a finite difference method by taking the basic data and the initial parameters as boundary conditions. And taking the physical model state as the input of a convolutional neural network, extracting short-period penetration load characteristics through time sequence convolution, and outputting a short-period penetration load prediction result. And combining the short-term penetration load prediction result with the cargo thermal parameters and the partition state as the input of a Transform model, and outputting multi-region energy consumption distribution prediction data. And performing strategy optimization processing on the multi-region energy consumption distribution prediction data through MPC, and calculating a preliminary control strategy. And searching a global optimal solution in the high-dimensional nonlinear parameter space through a myxomycete optimization algorithm, and outputting an optimal control strategy.

The invention relates to the technical field of underground engineering safety monitoring and disaster simulation, in particular to a digital twinborn deduction platform for underground engineering disaster chain evolution simulation, which comprises a multi-disaster coupling numerical simulation module used for acquiring multi-source data including design drawing data, geological data and engineering monitoring data, and based on the multi-source data, establishing an initial stress field model by using a numerical calculation method combining a finite element and a finite difference, and carrying out leakage-settlement-structure failure multi-disaster coupling numerical simulation. According to the method, the partial differential equation for describing the evolution law of the underground engineering is used as a constraint term to be embedded into the deduction model, and online identification and dynamic extrapolation of parameters are executed by fusing real-time monitoring data, so that the accuracy of disaster evolution simulation under complex working conditions is remarkably improved; and the problem that the traditional numerical calculation method is difficult to meet the real-time requirement of digital twinning is solved.

The invention provides a railway track damage detection method based on a doliolaria algorithm and a temperature inversion theory, and the method comprises the steps: S1, building a track inversion model, and carrying out the analysis of a discrete track model through a finite difference method; s2, performing simulation calculation on the track model, and obtaining temperature distribution of the track two-dimensional I-shaped flat plate by using a finite difference method; s3, introducing a doliolaria algorithm, taking the orbit internal temperature data obtained by solving the forward problem as the input of an inverse problem, and performing inversion identification on the orbit internal temperature information; and S4, accurately detecting the damage condition of the track by using the internal temperature data obtained by inversion. The railway track damage detection method based on the dogvessel squirt algorithm and the temperature inversion theory has the beneficial effects that nondestructive detection of the internal temperature of the track is achieved based on the temperature inversion theory, and then the purpose of accurately evaluating the track damage is achieved.

The invention discloses a sparse Bayesian learning shallow sea target depth and horizontal distance passive estimation method, and the method comprises the steps: calculating a modulus depth function hypothesis space through employing a finite difference method based on a prior sound velocity profile and a horizontal wavenumber hypothesis interval; preprocessing the vertical array data to a frequency domain, constructing a linear underdetermined equation set about the frequency domain vertical array data and a modulus depth function of a hypothesis space under sparse constraint, and solving by using a sparse Bayesian learning algorithm to obtain estimation of a horizontal wave number spectrum; performing spectrum peak search on the horizontal wave number spectrum, estimating the order and the horizontal wave number of an actual excitation mode, and estimating a mode depth function of each order of mode by using a finite difference method; vertical array copy sound fields under different depths and horizontal distances are calculated according to a normal wave sound field formula; and respectively performing conjugate transpose multiplication on the vertical array copy sound field and actual data to obtain a depth-horizontal distance ambiguity surface, and searching the position of the maximum surface value as the estimation of the depth and horizontal distance of the source.

The invention discloses an ultra-deep well drilling wellbore pressure inversion correction method, and aims to improve pressure prediction precision and well control safety in an ultra-deep well drilling process. The method mainly comprises the following two parts: firstly, establishing a wellbore pressure calculation model, fully considering the change of drilling fluid density along with temperature and pressure based on a mass and momentum conservation equation in a drill rod and an annulus, performing discrete solution on the established control equation by adopting a finite difference method, and performing iterative calculation from a well bottom to a well mouth and from the well mouth to the well bottom, so as to obtain a well pressure calculation model; and acquiring pressure and physical property parameters of each node. Secondly, on the basis of model output, a friction correction factor is introduced, a nonlinear state space model is constructed, an unscented Kalman filter (UKF) algorithm is used for conducting dynamic estimation on the friction correction factor, and online self-adaptive correction on the wellbore pressure model is achieved; according to the method, the accuracy of wellbore pressure calculation is effectively improved, and reliable technical support is provided for ultra-deep well operation.

The invention belongs to the technical field of nuclear reactor physical numerical calculation, and particularly relates to a method for improving precision and convergence of solving a diffusion equation based on a PINN, and the method comprises the following steps: S1, building a neural network algorithm model combining a physical information neural network PINN and source iteration; s2, aiming at a multi-region smooth transition neutron diffusion problem with small cross section difference between materials, optimizing the neural network algorithm model by adopting an optimization strategy of a training level; and S3, aiming at the multi-region neutron diffusion problem of large neutron flux gradient at the boundary due to large cross section difference between materials, improving the neural network algorithm model by adopting a domain-divided neural network architecture. According to the method, the problem that the calculation cost is exponentially increased in a high-dimensional or complex geometric scene due to the fact that a traditional finite difference method and a finite element method depend on grid division is avoided.

The invention discloses a parallel modeling method for simulating propagation of electric waves in irregular terrains, and relates to the field of radio. The method comprises the following steps: constructing a terrain-related first parabolic equation about radio wave propagation; introducing an auxiliary function, and determining a second parabolic equation; writing the second parabolic equation into a solution in an exponential function form, performing approximate transformation on an exponential term containing a topographic factor, and performing high-order fractional approximation on an exponential term containing a pseudo differential factor; based on a finite difference method, solving an intermediate variable of a high-order fraction in parallel, and further solving a field function subjected to terrain translation; and restoring the field function in combination with the auxiliary function and the terrain profile. Compared with the prior art, the method has the advantages of high calculation precision and high calculation efficiency, and is particularly suitable for predicting radio wave propagation loss on irregular terrains.

The invention provides an integrated energy system integrated dynamic simulation method, system and device and a medium, and relates to the technical field of energy utilization, and the method comprises the steps: configuring a transfer matrix and a state equation based on an energy network dynamic two-port model, and representing a dynamic transmission process corresponding to a gas network pipeline parameter characteristic and a heat network pipeline parameter characteristic; constructing an equipment dynamic simulation model; a comprehensive energy system model with a dynamic transmission process and an equipment dynamic simulation model is built based on a nonlinear finite difference method, dynamic simulation is conducted on the built comprehensive energy system model, transient behaviors of gas net turbulence and heat pump working medium phase change are captured through a nonlinear partial differential equation, dynamic simulation is achieved, and a simulation result is stored. According to the invention, the transient process can be captured, and dynamic interactive simulation of gas-heat-power grid is supported; the dynamic coupling equipment is abundant, the expansibility and the adaptability are excellent, a novel equipment model or an external control strategy can be accessed, and the method is suitable for various application scenes.

The invention provides a linear equation set of a diffusion equation diagram neural network model for water quality prediction, an F-GNN method and a system, and the F-GNN method comprises the steps: S1, collecting the monitoring historical data of each station, and constructing a space-time diagram; s2, on the basis of the space-time diagram, calculating a diffusion equation calculation formula by adopting a finite difference method, constructing an overdetermined linear equation set according to the diffusion equation calculation formula, and estimating parameters of the diffusion equation of each river reach by applying a least square method; and S3, if the parameters of the diffusion equation of each river reach are positive numbers, performing F-GNN prediction to obtain feature prediction of each station. According to the method, the defect that a water quality prediction model lacks space-time joint modeling is overcome, the problem that a traditional data driving model is prone to overfitting under the small sample condition is solved, diffusion equation constraints are introduced, the defect is effectively overcome, meanwhile, physical constraints are introduced, prediction precision and reliability are improved, and the method is suitable for large-scale popularization and application. The method is suitable for various environment monitoring scenes.

The invention relates to the technical field of multi-physics coupling, in particular to a multi-physics field coupling parameterized model establishment method, which comprises the following steps of: establishing a basic equation of each physics field through a physical law and a mathematical principle, and embedding coupling parameters in the equation to describe an interaction relationship among the multiple physics fields to form a coupling equation set; further adopting a finite element method or a finite difference method to solve the model, improving the calculation precision of an interface area through an adaptive grid encryption technology, and combining sensitivity analysis, a gradient descent method or a genetic algorithm to carry out iterative optimization on key parameters; the accuracy of the model is verified through comparison of an experiment and a simulation result, and if a significant difference exists, nonlinear coupling parameters are dynamically adjusted, so that calibration and reliability improvement of the model are realized. Through the reasonable method and steps, an accurate and reliable parameterized model with practical application value is established, so that the complex multi-physics field coupling problem is better understood and solved, and the calculation efficiency is improved.

The invention discloses an internal wave electromagnetic response numerical simulation method based on a layered ocean model. The method comprises the following steps: acquiring geomagnetic field parameters; calculating distribution characteristics of seawater conductivity along with depth, and dispersing the distribution characteristics into a layered ocean conductivity model; an internal wave mechanical model is constructed, internal wave velocity field distribution is established through characteristic parameters of internal waves, and dynamic input is provided for electromagnetic field response calculation; substituting the internal wave velocity field and the geomagnetic field into a Maxwell equation set, and constructing an internal wave induction electromagnetic field control equation; and applying tangential electric field continuity and normal current continuity conditions on a layered interface, and performing discrete and iterative solution on an equation by adopting a finite difference method to obtain distribution characteristics of the electric field and the magnetic field at different depths and frequencies. According to the method, the problem of insufficient precision caused by a uniform conductivity hypothesis is solved, and application limitation caused by an ideal geomagnetic field hypothesis is avoided, so that accurate simulation of internal wave induction electromagnetic response under a complex ocean condition can be realized.

The invention provides a blast furnace temperature anomaly prediction method based on digital twinning, and relates to the technical field of digital twinning, an adaptive diffusion coefficient is determined according to a tuyere convolute area image acquired in real time, an error caused by an unfixed value of the adaptive diffusion coefficient in the prior art can be avoided, and then the temperature anomaly of a blast furnace can be predicted based on the determined adaptive diffusion coefficient. According to the method, an energy conservation equation can be determined, a velocity field is solved according to real-time observation data corresponding to the tuyere convolution area image, a mass conservation equation and a momentum conservation equation, the velocity of the velocity field is input into the energy conservation equation corresponding to the tuyere convolution area image, the equation is solved by adopting a finite difference method, and a temperature field is obtained. According to the method, the temperature field characteristics of the temperature field are extracted, the temperature field characteristics are processed through the abnormal condition prediction model, the temperature label of the temperature field is obtained, and experimental results show that blast furnace temperature anomaly prediction is improved, and the real-time performance is remarkably improved.

The invention discloses a simulation forecasting method suitable for urban rainstorm waterlogging in areas lacking pipe network data, which is characterized in that for areas without pipe network data, rainwater inspection well information is acquired by calling a Baidu map, pipeline drainage flow is generalized based on a rainwater well equivalent drainage method, and for areas with pipe network data, pipeline drainage flow is generalized by calling a Baidu map. Constructing a drainage pipe network model based on a one-dimensional Saint-View equation by adopting a finite difference method; then, constructing a hydrodynamic model, coupling a rainwater well equivalent drainage method and a drainage pipe network model with an FVCOM model, simulating an earth surface ponding evolution process, and obtaining a rainstorm waterlogging data set; and training and establishing a water depth prediction model based on the obtained data, then predicting the water depth of each prediction point after a specific time in an actual rainfall event, and giving an alarm in advance when a waterlogging early warning range is reached. According to the method, the submerged water depth of a waterlogging-prone point can be predicted in advance, waterlogging forecasting of a city lacking pipe network data can be achieved, and rainstorm disaster loss is greatly reduced.

The invention relates to a theoretical research method of an ultrafast laser ablation mechanism, which comprises the following steps of: creating a double-temperature model for solving the change of electron and lattice temperatures along with time by adopting a finite difference method; in order to further explain a removal mechanism of a macroscopic material, a fluid mechanics model is established, a solid-liquid interface is tracked by a thermal enthalpy-pore method, a liquid-gas interface is tracked by a level set method, and the influence of backflushing pressure, surface tension, gravity and a Margoney effect on a molten pool is considered; and solving a Navier-Stokes equation set and a level set equation to obtain a solid-liquid-gas three-phase fluid mechanics model. The lattice temperature obtained by the double-temperature model is used as a heat source to be input into the fluid dynamic model, and the process of molten pool flowing and metal steam eruption is obtained. According to the method, the whole femtosecond laser ablation process is simulated by using a simulation method. Compared with an experimental method, on one hand, the time and the cost are greatly saved, and on the other hand, the problem that the temperature change of the femtosecond scale cannot be accurately measured by the current characterization means is also avoided.

This invention provides a virtual-real fusion-based force feedback simulation control method for ship rudder control sticks, comprising: constructing a set of fluid control equations for the flow field on the rudder surface; discretizing the set of fluid control equations using a standard structured mesh to obtain a discretized set of fluid control equations; solving the discretized set of fluid control equations based on the finite difference method and boundary conditions to obtain the drag torque value of the fluid acting on the rudder plate; converting the drag torque value into a damping torque value; the control unit outputting a motor drive command based on the magnitude of the damping torque value; and the motor driver, based on the motor drive command output by the control unit, driving the force feedback simulation motor to generate a corresponding simulated damping torque value, which acts on the control stick to produce force feedback. This invention provides real-time control stick force feedback for the helmsman, allowing for direct perception of the ship's navigation status and enhancing steering stability.

The invention provides a physical field data fusion method, which belongs to the technical field of multi-source data fusion, and comprises the following steps: multiplying low-fidelity physical field data by a sensor mask matrix to obtain low-fidelity sensor data; constructing a multi-order difference format based on a finite difference method and a Taylor expansion theory, and processing the low-fidelity physical field data to obtain low-fidelity multi-order partial differential physical field data; training the pre-trained data fusion model through the low-fidelity multi-order partial differential physical field data and the low-fidelity sensor data to obtain a data fusion model; the data fusion model is finely adjusted and optimized by updating sensor data and updating multi-order partial differential physical field data, and an optimized data fusion model is obtained and used for fusion processing of multi-source heterogeneous multi-physical field data; the optimized data fusion model obtained by the method can perform feature extraction and fusion on the multi-source heterogeneous multi-physics field data to obtain high-fidelity data with consistent representation and high confidence.

The invention discloses a forward and inverse kinematics calculation method for a 2-RSS-1U parallel mechanism of a humanoid robot, and relates to the technical field of humanoid robots, and the inverse kinematics calculation method comprises the following steps: establishing an ankle shaft seat point coordinate system, and obtaining a pitch angle and a roll angle of a sole; calculating coordinates of the bottom coordinate points of the ankle connecting rods relative to the initial coordinate system based on a spatial triangular relation; converting to a driving motor coordinate system by combining the known position relation of the coordinate system; and calculating the angle of the driving motor according to the connecting rod length and vertex coordinates. The forward kinematics resolving method comprises the following steps: determining a fixed translation relationship between a mechanism constant parameter and a coordinate system; constructing a nonlinear equation set by taking the roll angle and the pitch angle as unknown quantities; and solving by combining a two-dimensional residual vector with a Newton iteration method, estimating a Jacobian matrix by using a finite difference method in iteration, judging convergence according to a residual threshold, and outputting an attitude angle. According to the forward and inverse kinematics calculation method, the calculation stability and adaptability can be improved.

The invention discloses a plate structure defect Lamb wave full waveform inversion method based on U-Net neural network regularization, and belongs to the field of nondestructive testing. Firstly, a two-dimensional sound wave equation is solved through a frequency domain finite difference method, and analog signals of all receiving points are obtained; the method comprises the following steps: constructing a target function to represent a relative deviation between an analog signal and a sensor actual measurement signal, and converting an inversion problem of defects in a metal plate into an optimization problem of the target function; performing derivation on the target function by using an adjoint state method to obtain a gradient, updating the velocity field along the negative direction of the gradient, and performing regularization processing on the velocity field through a specific coding-decoding structure of the U-Net neural network to suppress noise and artifacts; a frequency serial inversion strategy is adopted, and inversion is carried out step by step from low frequency to high frequency. According to the method, artifacts in the inversion process are suppressed by using the U-Net neural network, dependence of inversion on initial model precision is reduced by using a frequency domain serial inversion strategy, and high-precision inversion of plate structure defects is realized.

The invention relates to a catenary riser slug flow-induced vibration forecasting method and system. The method comprises the following steps: constructing a catenary riser vibration equation under the action of a slug flow based on specific geometric parameters, material parameters and fluid parameters of a catenary riser and considering the influence of the internal flow force of the slug flow; acquiring slug flow main parameters such as liquid holdup of a liquid slug area, slug flow unit length and liquid slug area length, constructing a slug flow space-time distribution model in a pulse wave form, and calculating slug flow space-time distribution; performing spatial discretization on a catenary riser vibration equation, and converting a partial differential equation into an ordinary differential equation set by using a second-order precision finite difference method; according to the method, the calculated space-time distribution of the slug flow is substituted into the ordinary differential equation set, then the fourth-order Runge-Kutta method is adopted to carry out time integration on the ordinary differential equation set, the slug flow-induced vibration response of the flexible catenary riser can be rapidly and efficiently solved, the calculation efficiency is high, the engineering applicability is high, and the safety and reliability of deep sea oil and gas development can be improved.

The application belongs to the field of gear transmission system squeeze film damper damping, especially relates to a kind of gear squeeze film damper damping quick calculation method and system, obtains the structural parameter of squeeze film damper, carries out velocity calculation and constructs the Reynolds equation of squeeze film damper oil film pressure;Based on half-step center finite difference method, the Reynolds equation is solved, and the oil film distribution pressure of oil film damper is obtained;Based on oil film distribution pressure, the oil film counterforce of oil film damper is calculated using double integral algorithm.Compared with the classical short bearing approximate solution and long bearing approximate solution, its use range is wide, and compared with super relaxation iteration method, its calculation efficiency is high.Make it can be used in gear dynamics model to carry out damping analysis.When solving fluid Reynolds equation by finite difference method, only the working condition with regular boundary condition can be processed.Based on variational principle and Galerkin method, a new more general finite element method is proposed to calculate the oil film counterforce of SFD.

This invention discloses a simulation method for determining different snow storage material cover options. The method includes: a simulation method for snow storage experiments, including mathematical methods for calculating the total amount of solar radiation on any slope and mathematical methods for unsteady-state heat transfer; and a numerical method for simulating the performance of snow storage cover options, including finite difference methods and economic analysis methods. This method solves the existing problem of selecting snow storage cover material options for different regions and climate conditions.

The invention discloses a triangular mesh-based high-order electromagnetic field simulation method, and belongs to the field of computational electromagnetism. In order to solve the problems of significant numerical dispersion and phase error accumulation when an existing triangular mesh time domain finite difference method is used for processing a complex geometric structure, the method comprises the following steps: firstly, introducing a first additional loop on a basic triangular mesh, and combining with a first optimization coefficient to construct a high-order model; and a second additional loop is further introduced, and an optimization model is constructed in combination with a second optimization coefficient, so that the phase error is effectively inhibited under the coarse mesh, and high-precision electromagnetic simulation of a large-scale polygon structure is realized.

The invention provides a comprehensive pipe gallery safety state evaluation method and system, and relates to the technical field of comprehensive pipe gallery safety state evaluation methods, and the method comprises the steps: employing a steady-state heat release method to calculate the simulation temperature of each three-dimensional grid node; a finite difference method is adopted to calculate a temperature field distribution coefficient of each three-dimensional grid node, and a temperature distribution coefficient of a three-dimensional grid center point is obtained through an arithmetic average method; a coupling damage method is adopted to construct a coupling coefficient matrix of any grid position, equivalent damage energy of any grid position is calculated through an inner product method, and the equivalent damage energy is mapped into a safety coefficient of any grid center point through normalization. By adopting three-dimensional grid discretization, complex geometric characteristics of the pipe gallery structure can be more accurately captured, the position of a potential fire source is clearly marked, the hidden danger recognition efficiency is improved through targeted monitoring, high-precision calculation of a simulated temperature field under the complex boundary condition is achieved, equivalent damage energy is mapped into a dimensionless safety coefficient, and cross-regional risk comparability is achieved.

The calculation method of the uplift displacement of a lower tunnel caused by a layered foundation pit excavation comprises the following steps: (1) according to the relative position relationship between the foundation pit and the lower tunnel, relevant parameters are determined, and a calculation analysis model is established; (2) according to the load acting on the inside of the soil, a stress-strain solution below the load acting surface is derived, the tunnel and the foundation are respectively equivalent to an Euler-Bernoulli long beam and a Lifshin foundation model, the change of the additional stress of the soil caused by the unloading of the foundation pit excavation is calculated by using the Mindlin solution of the elastic layered foundation, and thus a corresponding mechanical model is obtained, and a longitudinal deformation control differential equation of the tunnel under the unloading of the foundation pit excavation is derived; and (3) finally, the finite difference method is used to calculate the uplift deformation of the lower existing tunnel caused by the foundation pit excavation. The calculation method can more reasonably simulate the mechanical model of the layered foundation tunnel, and makes the calculation of the uplift amount of the lower tunnel caused by the foundation pit excavation more accurate and reliable.

The application discloses a numerical simulation method for tsunamis and lake surges based on Boussinesq type equations, and comprises the following steps: obtaining digital elevation and initial disturbance data of a target area; constructing a high-order Boussinesq type control equation containing adjustable dispersion parameters and a frequency dispersion term to adjust the dispersion approximation precision; under a unified explicit time advancing system, discretizing the conservation term and the frequency dispersion term by using a finite volume method and a finite difference method respectively, and loading data to a calculation grid; judging the dry and wet states based on a preset water depth threshold, and truncating the frequency dispersion term for solving in the dry grid area to obtain simulation results of a flow field and a water level field. By constructing the control equation containing the adjustable dispersion parameters and the mixed numerical discrete framework, combining the explicit time advancing and the dry and wet grid truncation processing, the method does not need iteration and is simple to calculate; the dispersion description precision is improved, and the numerical stability problem of the dry and wet boundary is solved.

The application discloses a boundary plasma simulation method under a unit magnetic surface coordinate system and belongs to the technical field of magnetic confinement tokamak boundary plasma simulation. Firstly, a physical model is expressed by using a unit magnetic surface coordinate system, physical quantity and geometric effect are separated by using unitized base vectors, and singularity near an X point is avoided; secondly, a toroidal Fourier series representation is combined with difference along a magnetic field line, problem dimension is reduced, and numerical dissipation is reduced; thirdly, a generalized finite difference method and a transformed coordinate system are adopted to process the X point and adjacent points, and the X point can be directly contained in a grid; finally, a grid screening method is used to pre-calculate geometric quantities and difference coefficients under high-density grids, and the calculation precision of geometric effect is improved. The application can accurately simulate the influence of the X point on the stability of the boundary plasma, significantly reduces the consumption of computing resources, and improves the simulation efficiency and accuracy.

This embodiment discloses a dynamic evaluation method for the reliability of railway tunnels along the time axis. By considering the time-effect control equations for the initial lining of railway tunnels, as well as initial and boundary conditions, a loss function for a physical driving model is established using the finite difference method to train the model. This solves the problem that the solutions of traditional AD sampling points are independent and it is difficult to effectively utilize information from adjacent areas. After training the physical driving model, the initial lining displacement values ​​of the railway tunnel are predicted, and a system limit state function is established based on the predicted initial lining displacement values ​​to obtain the time-varying failure probability of the railway tunnel. By establishing a time-effect control equation for the initial lining of railway tunnels, this invention can fully consider the spatial and temporal variation characteristics of surrounding rock parameters, improve the efficient fusion capability of real-time monitoring data, and make the evaluation results close to the actual state of the tunnel, greatly reducing potential railway traffic hazards.

The present invention provides a linear equation system, F‑GNN method and system for a diffusion equation graph neural network model for water quality prediction. The F‑GNN method includes: step S1, collecting historical data monitored at each site and constructing a spatiotemporal graph; step S2, based on the spatiotemporal graph, using the finite difference method to calculate the diffusion equation formula, constructing an overdetermined linear equation system based on the diffusion equation formula, and then using the least squares method to estimate the parameters of the diffusion equation for each river section; step S3, if the parameters of the diffusion equation for each river section are all positive numbers, then performing F‑GNN prediction to obtain a characteristic prediction for each site. The present invention solves the problem of lack of spatiotemporal joint modeling in water quality prediction models. Traditional data-driven models are prone to overfitting problems in small sample conditions. The present invention effectively compensates for this deficiency by introducing diffusion equation constraints. At the same time, the introduction of physical constraints improves prediction accuracy and reliability, making it suitable for a variety of environmental monitoring scenarios.

The invention provides a crossed ball guide rail workbench five-degree-of-freedom motion error analysis method, which comprises the steps of establishing a skin surface model based on part tolerance information and plane feature information, obtaining displacement spinor through constraint registration simulation, establishing a Jacobian matrix based on an assembly structure, and constructing a Jacobian skin surface model in combination with spinor information, calculating to obtain pose offset information of left and right guide rails and a slide rail in the guide rail pair, determining a space pose of a guide rail system in a global coordinate system by combining an actually measured raceway shape error, substituting the space pose into a crossed ball guide rail error model established based on a Hertz contact theory and static balance, and obtaining a five-degree-of-freedom motion error of the slide table through iterative solution. And finally, carrying out key error sensitivity analysis by adopting Monte Carlo simulation and a difference method. According to the method, the error transmission relation from the base to the working table function point can be accurately analyzed, the influence degree of the part tolerance on the motion precision is revealed, and an important reference basis is provided for design and assembly of the precise working table.