175 results about "Analytical expressions" patented technology

The invention relates to the field of heat supply network analogue simulation, and particularly discloses a regional heat supply network dynamic simulation method and system, a terminal and a medium, the method comprises the following steps: constructing a hydraulic model semi-analytical expression and a thermal model semi-analytical expression of a pipeline in a regional heat supply network, and according to the pipeline momentum conservation and the node mass conservation, calculating the thermal model semi-analytical expression of the pipeline in the regional heat supply network; constructing semi-analytic coefficient recursive relation linear equations, and respectively calculating semi-analytic coefficients of a hydraulic model semi-analytic expression and a thermal model semi-analytic expression through the two semi-analytic coefficient recursive relation linear equations according to initial conditions and boundary conditions of the pipe section; the calculated semi-analytic coefficient meets the condition that the truncation error is not greater than a truncation error threshold value; and substituting the semi-analytic coefficient into the semi-analytic expression to obtain a semi-analytic calculation result of each pipe section of each pipeline under all time steps. According to the method, non-iterative calculation of the PDAEs is realized, the calculation complexity is reduced, the simulation efficiency is improved, and the solution continuity can be ensured.

A design method of a trust region satellite-borne dual-base interference SAR system is provided, relating to the field of radar measurement. Firstly, error sources of the interference SAR system are classified and analyzed, phase errors caused by image decoherence are calculated according to wave positions, and an analytical expression of baseline-related errors is reserved; a maximum phase error caused by imaging processing and an electronic device are estimated; and a baseline error is estimated. Then, the phase errors and the baseline errors are converted into elevation errors through an elevation fuzzy number, thereby obtaining an analytical expression of the elevation errors and the baseline parameters (length and dip angle). With a relative height measurement accuracy index of the system as an optimization object, a feasible solution interval between the baseline length and the baseline dip angle of the system is solved through a trust region algorithm. A minimum value of the baseline length is corrected according to a flying-around safety distance of a dual-satellite formation. According to the method of the present disclosure, the design of the satellite-borne dual-base interference SAR system can be guided, so that the satellite-borne dual-base interference SAR system is ensured to carry out terrain elevation surveying and mapping tasks with high accuracy and high reliability.

The invention provides a logarithmic terminal sliding mode control method for a nonlinear system, and belongs to the technical field of sliding mode control. According to the invention, a first-order logarithmic terminal sliding mode control strategy and a super-torsion logarithmic terminal sliding mode control strategy are obtained based on a designed logarithmic terminal sliding mode surface, a logarithmic terminal sliding mode cooperative control architecture oriented to a nonlinear system is obtained, multi-objective optimization of buffeting suppression, global rapid convergence and sliding time explicit is realized, and the method is suitable for large-scale popularization and application. The global convergence speed of the system state on the sliding mode surface can be improved while sliding mode control buffeting is weakened, the sliding time of the system state on the sliding mode surface is explicitly given, the strict mathematical correspondence between the controller gain coefficient and the system dynamic performance is determined through the explicit analytical expression of the sliding time parameter, and the system dynamic performance is improved. A quantitative theoretical basis is provided for parameter setting of an industrial field, and the system robustness under a complex working condition is remarkably enhanced.

The ELM-based frequency safety constraint linearization optimization scheduling method comprises the following steps: establishing a fire-wind-light multi-energy complementary frequency dynamic response model, and deducing a time domain analytical expression of a frequency safety index by taking a frequency maximum change rate and a frequency maximum deviation as the frequency safety index of a system; considering a frequency lowest point security constraint and a frequency maximum change rate security constraint, and establishing a frequency security constraint-containing optimization scheduling model; a maximum bearable disturbance power linearization mapping method based on ELM is provided, nonlinear frequency security constraints are converted into a series of linear constraint sets, and linearization processing of the frequency security constraints is achieved; and piecewise linearization is carried out on quadratic terms in the established objective function containing the frequency security constraint optimization scheduling model, the overall model is converted into a mixed integer linear model, and a Gurobi solver is used to solve the linearly processed model. The scheduling method can ensure that the system frequency is safe and stable, so that the established optimal scheduling model gives consideration to both economy and frequency safety.

The invention discloses a three-dimensional contour reconstruction method based on phase smoothing preprocessing in a phase shift profilometry, a storage medium and equipment. The method comprises the following steps: establishing a mathematical model between a phase shift fringe image and a phase in the phase shift profilometry to obtain an analytic expression for calculating the phase, a fringe background component and a fringe modulation amplitude; separating a modulation component from the phase shift fringe image, calculating a modulation degree of the phase shift fringe image, normalizing the modulation component according to the modulation degree, and performing low-pass filtering on the normalized modulation component; and finally, synthesizing the original background component and the modulation component subjected to low-pass filtering into a new phase shift fringe image, completing preprocessing, and calculating a phase by using the preprocessed image. According to the method, the influence of background component noise, the surface reflectivity of the object to be measured and other factors on the phase smoothing effect is avoided, the high-frequency characteristics in the phase can be reserved, the good phase smoothing effect is achieved, and the precision of the reconstructed three-dimensional contour is improved.

The invention discloses a human body posture intelligent identification method based on a multi-modal micro-motion feature and a Transform network, and the method comprises the steps: deducing micro-Doppler signal mathematical analysis expressions corresponding to different parts of a human body from human body target radar echo modeling; the method comprises the following steps: performing data preprocessing on target echo data acquired by a millimeter wave radar by adopting two-dimensional fast Fourier transform to obtain a one-dimensional spectrum sequence and a two-dimensional Doppler image corresponding to different postures, and respectively sending the one-dimensional spectrum sequence and the two-dimensional Doppler image into a one-dimensional Transform network and a two-dimensional Transform network for feature extraction; and carrying out feature splicing by adopting a multi-modal feature fusion model and outputting a classification result. According to the method, the problems of low recognition rate, poor robustness and the like in the existing human body posture intelligent recognition means can be solved.

The invention discloses a steady-state boundary convection-dispersion model parameter acquisition method based on a variable separation method, and the method comprises the steps: constructing a convection-dispersion mathematical model under a one-dimensional finite-scale steady-state boundary condition, and carrying out the dimensionless processing of an original mathematical model through a dimensionless factor; secondly, analyzing and solving the new mathematical model after nondimensionalization by adopting a separation variable method, systematically deriving an analytical solution expression of a one-dimensional steady-state boundary convection-dispersion model in combination with a groundwater dynamic theory and a solute transport mechanism, and constructing a standard curve capable of reflecting different permeability parameters and solute transport related parameters; an indoor one-dimensional convection-dispersion test is carried out, water level and solute concentration measured data at different observation points are obtained, and permeability parameters and solute transport related parameters of a test medium are efficiently obtained through wiring. According to the method, the accuracy and adaptability of the convection-dispersion model in the aspect of parameter identification under the limited scale condition are enhanced; and operation is simple, parameter identification quantity is large, and precision is high.

The invention discloses a fault transient current analysis method of a network-forming converter considering a power angle swing process. The method belongs to the technical field of power system fault analysis, is used for realizing accurate solution of transient current of a network-forming converter under a three-phase symmetric drop fault of power grid voltage, and comprises the following steps: firstly, constructing a power angle swing equation based on a virtual synchronous machine control strategy; taylor series expansion is carried out on an equation nonlinear term at a steady-state equilibrium point after the fault, a linear oscillation component and a nonlinear disturbance component are separated, and a power angle approximate analytical solution is derived; secondly, establishing a grid-connected current first-order differential equation containing power grid impedance based on circuit topology, and substituting the simplified power angle expression to obtain a time domain analytical expression of voltage on the power grid impedance under a three-phase static coordinate system; and finally, in combination with a solving method of a first-order differential equation and a current steady-state initial value condition, establishing a current analytical expression of the whole fault transient process.

The invention belongs to the technical field of aircraft structure design, and particularly relates to an aircraft arbitrary space four-bar mechanism parameter optimization method, which comprises the following steps: firstly, determining input conditions or preposed requirements of a four-bar mechanism, secondly, establishing a mathematical model of a four-bar mechanism optimization problem, and then, carrying out derivation and analysis to obtain a four-bar mechanism parameter optimization result. The method comprises the following steps: establishing an analytic expression of parameter variables of the four-bar mechanism and compiling a corresponding calculation program, then carrying out iterative optimization on the parameters of the four-bar mechanism by utilizing an optimization algorithm, and finally outputting an optimization result to obtain an optimal design parameter.

Disclosed are techniques for an AI system with a large language mode (LLM) with improved accuracy and reliability in solving mathematical problems. An initial query is transformed into a template query by replacing the original input values with variables. Multiple prompts are sent to the LLM, each being different from one another, and contextually related to the template query. Multiple results are responsively received from the LLM, each result including an analytical expression to solve the mathematical problem. Each of the expressions is evaluated using a numerical evaluation tool with variables of the expression being assigned a common set of randomly sampled values. A consensus is achieved when the evaluated expressions satisfy a consensus condition, such as when all outputs match consistently over N experiments or trials. After the consensus condition is reached, the original inputs are evaluated with one or more of the expressions, and the solution is output.

The invention belongs to the technical field of resource planning, and particularly relates to a power distribution network distributed resource robust planning method and device based on cluster division, and the method comprises the steps: building a source-storage robust locating and sizing model as an upper model based on cluster division, and setting a target function and constraint conditions thereof; based on cluster planning, constructing an intra-cluster reliability index calculation model as a lower-layer model, and setting a target function; combining the upper-layer model and the lower-layer model to obtain a double-layer joint planning model; aiming at an island operation scene under a cluster division condition, designing a reliability merging optimization method integrated with island operation characteristics, and optimizing the double-layer joint planning model to obtain an analytical expression of a reliability index; and obtaining a joint planning scheme of the distributed resources of the power distribution network by solving the optimized double-layer joint planning model. According to the method, the source load uncertainty and the reliability index are effectively considered, and the economical efficiency, the flexibility and the reliability of power distribution network planning are remarkably improved.

The application discloses a kind of analytic expression probabilistic power flow calculation method, device and storage medium.The application is determined after the mapping relationship between the injection power of node and the operating state of power system by linear power flow model, using first-order polynomial fitting correction method to revise the operating state of power system, make the operating state of the power system after revision be closer to real operating state, according to the mapping relationship between the injection power of node and the operating state of power system after revision, update linear power flow model, carry out analytic expression probabilistic power flow calculation using updated linear power flow model, to effectively improve the accuracy of probabilistic power flow calculation.

The invention provides a flexible DC converter station short-circuit current calculation method, system and device and a storage medium, and the method carries out the calculation based on a segmented voltage reduction scene, and the method comprises the steps: monitoring a local electrical quantity, and comparing the local electrical quantity with a rated value of a multiple; when the voltage exceeds the threshold value, carrying out segmented voltage reduction control, and obtaining a final voltage instruction value; and according to the final voltage instruction value, reverse pull type transformation is carried out by using a transfer function of the fault current of the flexible DC converter station to obtain a time domain expression, and an analytical expression of each phase of current is obtained through Park inverse transformation of the time domain expression, so that the short-circuit current is obtained. According to the method, a proper final voltage instruction value is sought by adopting segmented voltage reduction during the fault period of the flexible DC converter station, so that a power electronic device is prevented from being damaged by overcurrent of the converter; a fault transient model is constructed by combining a pull-type domain model in the calculation process, the fault current of the flexible DC side is analyzed and calculated, and accurate calculation of the fault current of the flexible DC converter station can be realized according to a unified current expression.

The invention relates to the technical field of broadband radar signals, and provides a radar target robust intelligent detection and interference adaptive suppression method and system, and the method comprises the steps: carrying out the decorrelation transformation of received data and a parameter matrix through employing the skew symmetry characteristic of a clutter covariance matrix, and completing the preprocessing of initial data; carrying out correlation calculation estimation under the condition of no target hypothesis and under the condition of target hypothesis, and constructing distance extension target Gradient detection statistics under the condition of a known clutter skew symmetry covariance matrix; constructing a detection statistic lambda of the radar target robust intelligent detection and interference adaptive suppression method; and determining a detection threshold T through theoretical calculation or Monte Carlo simulation according to a preset false alarm probability, comparing the detection statistic lambda with the detection threshold T, and judging whether a distance expansion target exists in the current distance unit to be detected or not according to a comparison result. According to the method, an analytical expression design is adopted, a complex iterative calculation process is avoided, and the operation efficiency is improved.

The invention discloses a doubly-fed wind turbine generator fault current analysis and controller parameter identification method, a storage medium and equipment, and belongs to the technical field of electric power. The method aims at solving the problems that an existing identification method for the double-fed fan in the fault state is low in identification precision, depends on optimization algorithm performance and is not suitable for practical engineering due to the fact that an identification scene is too ideal. According to the method, firstly, an accurate and detailed doubly-fed fan topology, an RSC controller and an LVRT control strategy are established, and then a detailed doubly-fed fan fault current analytic expression is obtained through derivation of a mathematical model; a reactive support coefficient, a reactive voltage threshold and a maximum current are determined through a voltage drop fault test, then a rotor reactive current reference value is obtained according to a voltage drop value corresponding to a new fault, the reactive support coefficient and the reactive voltage threshold, and a power current reference value is obtained by combining the maximum current. And controller parameters in the RSC controller are identified based on the fault current analytical expression.

The invention relates to a robot ball joint singularity avoidance method based on damping factor analytic expression. The method comprises the following operation steps that a pose difference calculation module calculates the rotation matrix variable quantity of an end effector of a robot in real time; the self-adaptive Jacobian matrix construction module is used for a damping factor dynamic adjustment mechanism based on SVD (Singular Value Decomposition) analysis; the joint space updating module is used for realizing smooth updating of a joint angle through optimized inverse kinematics solution; through a theoretically guided damping adjustment mechanism, precision-continuity-efficiency triple optimization of singularity avoidance of the ball joint of the robot is realized for the first time, and a universal solution is provided for high-precision robot control.

The invention discloses a single-epoch GNSS ambiguity precision factor determination method with constraints, and relates to the field of GNSS ambiguity estimation. The method comprises the steps of constructing a single-epoch multi-frequency multi-system GNSS double-difference mathematical model with additional constraints, obtaining an ambiguity vector floating point solution variance-covariance matrix analytic expression after the constraints are added, and establishing a single-epoch multi-frequency multi-system C-ADOP approximation formula with constraint conditions and an ADOP scaling factor non-difference non-inverse transformation analytic expression. A C-ADOP approximation formula and an ADOP scaling factor non-difference non-inverse transformation analysis formula are combined, a single-epoch multi-frequency multi-system C-ADOP non-difference non-inverse transformation approximation formula with constraint conditions is obtained, and then a single-epoch multi-frequency multi-system GNSS ambiguity precision factor C-ADOP with the constraint conditions is calculated; according to the method, the single-epoch GNSS ambiguity estimation precision with constraint conditions added and the ambiguity fixing success rate estimation precision are improved.

The invention discloses a vehicle model nonlinear characteristic analysis and quantification method based on Volterra series, and the method comprises the following steps: building a vehicle dynamics model, and describing the basic motion characteristics of a vehicle; the transformation model is a polynomial nonlinear expression mode suitable for Volterra series analysis; calculating a kernel function of the kinetic model by adopting a harmonic detection method; a frequency multiplication signal transfer function is extracted, and the nonlinear degree is quantized; and the analytic expression of the signal transmission characteristic and the nonlinear degree of the vehicle under different driving states and environment information is obtained. Different driving parameters and environment information are introduced into the calculated kernel function, the signal transmission characteristic and the non-linear degree under the corresponding working condition can be calculated, and the calculation result can be used for effectively guiding controller design.

The invention relates to a rapid calculation method and system for a space magnetic field of a circular coil. The method comprises the following steps: converting an integral expression of a Biot-Savart law into a closed analytical solution containing first and second types of complete elliptic integrals; on the basis of an analytical expression of elliptic integration, the magnetic field intensity and direction generated by the coil at any point in the space can be efficiently and precisely calculated, and the defects that traditional finite element simulation calculation is complex, consumed time is too long, and efficiency and precision of a direct numerical integration method are difficult to consider at the same time are overcome. The method is particularly suitable for application scenes such as WPT system design, multi-transmitting-coil amplitude-phase control optimization and real-time simulation which need to carry out rapid and frequent calculation on the magnetic field. According to the method, full-automatic rapid calculation from physical parameter input to magnetic field result output is achieved, the core advantage of the method is that an analytical formula is utilized, the tedious process of numerical simulation and integration is avoided, and the calculation efficiency is remarkably improved while high precision is guaranteed.

The application relates to the technical field of estimation of maximum frequency deviation of power grid nodes and is used for solving the problem that the existing estimation method of maximum frequency deviation of power grid nodes cannot reflect the time-space difference characteristics of frequency response of an interconnected power system. First, a two-region frequency response model TAFR considering the time-space difference characteristics of frequency of power grid nodes is established, a time-domain analytical expression describing the node frequency difference mechanism is obtained by adopting the mode analysis and average system frequency model aggregation idea, and a maximum frequency deviation estimation method reflecting the time-space difference is proposed on the basis of the analytical expression. The established TAFR model considers the distribution of tie-line parameters, system inertia and damping, and equivalently processes the new energy frequency modulation parameters, compared with the existing frequency dynamic response model, the model has improved accuracy and applicability while ensuring the time-space difference.

The invention discloses a programmable switch power consumption estimation method and device based on component decomposition, and a medium, and the method comprises the steps: firstly, decomposing a data packet processing flow into three operation components, namely a parser, a matching component and an action component; secondly, constructing a power consumption estimation model: total power consumption = operation power consumption + basic power consumption; wherein the basic power consumption = idle power consumption + port configuration power consumption + basic forwarding power consumption; operation power consumption = parser power consumption + matching power consumption + action power consumption (respectively corresponding to three operation components). Then, utilizing a control variable method to respectively generate multiple groups of test cases for the resolver, the matching and the action operation, deploying the test cases on a target programmable switch, and collecting power consumption data; and on the basis, fitting to obtain a mathematical expression of the power consumption of each operation component. And finally, the analytic expressions are substituted into a total power consumption model to obtain a materialized power consumption estimation model for the target switch, and the materialized power consumption estimation model is used for estimating the power consumption of the target switch.

The invention discloses a turbulence model construction method for aerodynamic simulation of a hybrid three-compartment vehicle, and relates to the field of model simulation, and the method comprises the steps: S1, employing a flow field inversion method, and obtaining the dense space distribution of a turbulence model correction term; s2, screening local flow field characteristics related to the correction distribution characteristics; s3, training by adopting a symbol regression method to obtain an analytical expression of a turbulence model correction term; s4, through mathematical derivation, an analytical expression of a correction term is migrated into the standard model, so that the correction term is added in front of a damage term of a transport equation of the dissipation rate of the standard model; s5, selecting an initial value of a to-be-calibrated coefficient in the correction item according to the smoothness degree of the chassis of the hybrid three-compartment vehicle; and S6, calibrating the to-be-calibrated coefficient in the expression in the step S4 on the basis of real vehicle experimental data of the hybrid three-compartment vehicle to obtain the turbulence model for aerodynamic simulation of the hybrid three-compartment vehicle.

The invention discloses a level set field reconstruction method and system based on a three-dimensional finite element grid and a medium. Relates to the technical field of geometric reconstruction. Positioning a space Cartesian grid area intersected with the boundary surface grid based on a separation axis theory; calculating a geometric space point-surface position relation, calculating a directed projection distance from a space Cartesian grid center to a two-dimensional boundary surface grid, and correcting the positive and negative characteristics of a Cartesian grid level set value based on a three-dimensional eight-direction rapid scanning method, so that the grid level set value is consistent with a region boundary value; according to the method, the geometric reconstruction problem of the deformable body which is complex in appearance and free of explicit analytic expression can be efficiently and accurately solved, a coupling approach between a finite element grid and a Cartesian grid is established under a non-conformal grid system, and the flexibility and universality of explicit calculation of a level set function under the Cartesian grid are improved.

The application provides a kind of multi-data stream security analysis method and device with dynamic index.The method comprises: obtaining corresponding dynamic indexable expression chain based on the correlation analysis expression of multi-data stream;Dynamic indexable expression graph is obtained based on the dynamic indexable expression chain;Determine the dynamic expression path in the dynamic indexable expression graph based on the graph node in the dynamic indexable expression graph and the edge between graph nodes;Determine the index corresponding to the flow table based on the dynamic expression path, and perform network security analysis on the multi-data stream based on the index of the flow table.The multi-data stream security analysis method with dynamic index provided by the application can perform dynamic index analysis on multi-data stream correlation analysis expression, improve real-time multi-data stream correlation analysis performance, and improve the efficiency of multi-data stream security analysis and detection.

The invention belongs to the technical field of ship intelligent digital optimization design, and particularly relates to a ship global deformation and optimization method, program and equipment considering drainage volume precision control and deformation rationality and a storage medium. The analytical expression of the drainage volume variation about the global deformation parameter is obtained based on the numerical integration and the recursion formula, the reasonable deformation parameter range of the ship body is determined based on the global deformation modification function and the regular design space, the ship body does not need to be actually deformed, the corresponding volume variation can be directly predicted according to the design parameter, and the calculation accuracy is improved. Accurate feedforward control of volume constraint and direct judgment of rationality of the deformed ship are realized. On the basis, rapid optimization of any ship type structure under the constraint of reasonable deformation and accurate volume control is realized in combination with an agent model. According to the method, a traditional'design-verification-adjustment 'experience iteration process is converted into deterministic one-step calculation, and subsequent optimization can be directly carried out in a pre-verified reasonable design space.

The invention discloses a rapid calculation method and device for the sensitivity of a linear periodic time-varying system based on a matrix sparse technology, and belongs to the technical field of modeling analysis of the linear periodic time-varying system.The rapid calculation method comprises the steps that an LTP system is converted into an equivalent LTI system, and the eigenvalue, the left eigenvector and the right eigenvector of the LTP system are obtained; based on a functional derivative method, obtaining a sensitivity analytical expression of the LTP system characteristic value to the parameter; according to the influence mechanism of the parameters on the system matrix, obtaining an analysis form of the influence of the parameters on the LTP system matrix in the sensitivity analysis expression; and converting a partial derivative of a system matrix to a steady-state trajectory into sparse calculation of a vector field Hessian matrix by using a matrix sparse technology, thereby obtaining a calculation result of the characteristic value sensitivity of the LTP system. According to the method, the sparse characteristic of the system matrix in the PEPS is utilized, the calculated amount and the storage requirement of the system matrix on trajectory partial derivative solving are reduced, and therefore calculation of the LTP characteristic value sensitivity is accelerated.

The invention discloses a single-stage bidirectional DC-AC converter minimum current stress optimization method, system and device and a medium, and belongs to the technical field of power electronic converter control, and the method comprises the steps: building an operation mechanism comprising four effective working modes based on the single-stage bidirectional DC-AC converter through a frequency conversion phase shift control strategy and aiming at bidirectional energy transmission demands, the inverter and the rectifier respectively correspond to inversion and rectification modes under different relations of input and output voltages. Taking the minimum current stress as a target function, solving the optimal shift ratio by combining the transmission power constraint and the soft switching condition, and calculating the real-time switching frequency by adopting equal power modulation. Frequency conversion control is introduced on the basis of phase shift control, power factor correction and soft switching constraint can be achieved at the same time, the optimal phase shift ratio and the switching frequency are directly solved through an analytical expression, and the calculation complexity of a traditional iterative algorithm is avoided.

The invention discloses an approximate iteration analytic calculation method for a flight trajectory of a hypersonic flight vehicle, which comprises the following steps of: firstly, establishing a gliding flight dynamics mode of the hypersonic flight vehicle, and ignoring lateral motion to obtain a longitudinal plane dynamics model in a linear matrix differential equation form; secondly, according to the characteristics of different types of flight trajectories, performing targeted simplification on a linear matrix differential equation, and analyzing the characteristics of a jump gliding trajectory and a balanced gliding trajectory through matrix eigenvalues; then, on the basis of the quasi-equilibrium gliding condition, lift-drag ratio characteristics of the equilibrium gliding track are analyzed; then, an approximate dynamic model in a short-time period is established, and a flight path analytical expression in the short-time period is obtained; and finally, based on the flight path analytical calculation expression in the short-time period, proposing a flight path approximate iteration analytical calculation process in the long-time period. The method is simple in structure and easy for engineering realization, and has a relatively large popularization and application space.

The invention discloses an integral transformation fracture phase field model implementation method of a random-order polynomial cohesion law, and belongs to the technical field of phase field model finite element analysis. The method comprises the following steps: inputting a parameter equation of a polynomial cohesion law of any order and a target order into a subprogram; deducing a cohesion eigenfunction of a random-order polynomial cohesion law by using a subprogram to determine an analytical expression of a random-order polynomial energy density eigenfunction, solving a target-order polynomial energy density eigenfunction expression and first two-order derivatives thereof, and determining an expansion expression at a zero point by using Maclaurin series; and inputting the target-order polynomial energy density eigenfunction expression, the first two-order derivatives thereof and the expansion expression at the zero point into a phase field model solver to obtain a calculation result of the target-order polynomial integral transformation fracture phase field model. According to the method, the simulation calculation of the integral transformation fracture phase field model of the target-order polynomial cohesion law can be realized under a universal finite element framework, and the accuracy and the efficiency are improved.

The invention provides a fault rate calculation method for a transformer cooling system considering a leakage fault, which comprises the following steps of: firstly, analyzing a dynamic transfer process among a normal operation state, a fracture fault state and a leakage fault state of a cooler pipeline, and constructing a three-state Markov transfer model of the cooler pipeline; then, sensor information such as main transformer oil temperature, winding temperature, cooler outlet oil pressure, water pressure, oil temperature and water temperature is collected, and a knowledge and data driving-based fracture fault related transfer rate calculation method is provided; thirdly, based on the frequency and the transfer rate which are easy to count or calculate, an analytical expression of the transfer rate and the frequency is established by combining a Markov model and a frequency duration method, and the transfer rate related to the leakage fault in the model is calculated; and finally, integrating the transfer rate, constructing a fault rate calculation model of the transformer cooling system, and proposing to predict the future fault rate of the cooling system based on a time convolutional network and a Transform hybrid model. According to the method provided by the invention, fault rate monitoring, analysis and early warning of the transformer cooling system can be realized.