46 results about "Mathematical equations" patented technology

The invention discloses a hill irrigation area water resource allocation method and application, and the method comprises the steps: firstly, determining an irrigation sheet of water resource supply and demand analysis with the minimum granularity according to the characteristics of a hill irrigation area, combining the water storage, water diversion, water lifting and water transfer projects of the irrigation area, generalizing the topological structure of the hill irrigation area, and obtaining a generalized topological structure diagram of the hill irrigation area; then establishing a hill irrigation area water resource optimization scheduling model according to the hill irrigation area generalization topological structure diagram, and performing optimization solution on the model by using a dual simplex algorithm; respectively carrying out irrigation area social and economic water consumption analysis and irrigation area ecological water consumption analysis, and finally carrying out water balance analysis on the water resource subarea where the irrigation area is located. According to the method, water balance is taken as a basic principle, the natural-social binary water circulation path of the water circulation of the hill irrigation area is coupled in the mathematical equation set, complex simulation sequence coding is avoided, modeling is easy, and the universality is good. The constraint equations are linear, a global optimal solution is easy to seek, and the utilization efficiency of water resources in the hill irrigation area can be effectively improved.

The invention discloses a multi-shaft ultra-long high-ground-temperature railway tunnel fan optimization configuration method which comprises the following steps: acquiring basic calculation parameters of a multi-shaft ultra-long railway tunnel, and further establishing a physical model; based on the physical model, establishing a multi-shaft super-long railway tunnel surrounding rock-lining-airflow-ventilation network heat, humidity and flow coupling mathematical model, and performing rapid solving; on the basis of a mathematical equation solving result of the mathematical model, the feasibility of temperature control and humidity control under the working condition of only natural ventilation is judged, for the working condition that only natural ventilation is not feasible, a ventilation fan decision-making variable is selected, and optimization design is conducted on fan configuration with ventilation energy consumption as the target and the maximum temperature and humidity along the way as the constraint; according to the method, optimization of the fan configuration scheme under the multi-factor working condition is achieved.

The present invention discloses a method for precise modeling of multi-energy and mass flow integration of green hydrogen metallurgical integrated energy system. First, by focusing on the green hydrogen metallurgical integrated energy system, and aiming at the problem that the transmission characteristics of heterogeneous energy flows and material flows are greatly different and difficult to describe in a unified manner, a unified mathematical equation for multi-energy and mass flow transmission based on differential dynamics is proposed. Secondly, in order to simplify complex dynamic problems, the time domain dynamics is converted into a static algebraic problem, and a generalized transmission model based on distributed parameters is constructed. In response to the challenge of heterogeneous distribution parameters of multi-energy and mass flow branches and nodes, an equivalent modeling method for branches and node external ports is further proposed, and the description system of multi-energy and mass flow integrated modeling is improved. Finally, based on the above-mentioned algebraic model, the matrix modeling of the multi-energy and mass flow network is studied, a standardized matrix analysis paradigm is proposed, and by constructing a unified Jacobian matrix, the rapid calculation of the multi-energy and mass flow distribution is realized, providing precise support for the coordinated regulation of multiple links in the system.

The invention provides a method for determining key factors influencing anti-short-circuit capability of a transformer winding, which belongs to the technical field of transformer windings, and comprises the following steps: firstly, obtaining accurate and disturbance data of short-circuit force and tension of a winding wire and compression deformation of an insulating paperboard at different temperatures through a test; then, an adversarial neural network model is established, and an initial data set after augmentation and expansion is generated; and establishing a finite element simulation model of the transformer winding, and inputting the initial data into the finite element simulation model. Meanwhile, a thermal-mechanical coupling and electromagnetic mechanical equation set containing a disturbance term is established and compared with a simulation result for analysis, and an error is determined. And constructing a correction function according to the error, and optimizing the equation set. Then, establishing a three-field coupling iterative calculation model, and establishing a mathematical equation set for describing the influence of the key factors of the anti-short-circuit capability of the transformer winding based on a final calculation result; the technical problems that in the prior art, the data size obtained through experiments is limited, and the influence degree of various factors is difficult to comprehensively reflect are solved.

The application discloses a kind of gas curtain anti-salt three-dimensional numerical simulation method and device and storage medium, it is related to seawater intrusion prevention technical field;The three-dimensional numerical simulation method utilizes the influence of gas curtain system on salinity transfer coefficient in the process of saltwater intrusion, based on the basic equation of mass and energy conservation, multiphase flow seepage field, physicochemical property and driving parameter coupling mathematical equation, establishes ship lock gas phase-fresh water-salt water three-phase numerical model, and through the targeted adjustment of numerical model boundary condition, initial condition and basic parameter, make numerical model can accurately simulate the movement process of saltwater intrusion under the condition of gas curtain in ship lock, to provide theoretical basis for the design and effect verification of ship lock gas curtain anti-salt system.

The disclosed embodiment provides a technology for determining optimized variables in routing based on deterministic cluster. Existing technologies only optimize the number of clusters in stochastic-based routing, so there is a limitation in optimizing variables in routing based on deterministic cluster. In the disclosed embodiment, the amount of energy consumed by the head node and the member nodes may be calculated using a mathematical equation that uses the number of clusters as a variable to derive the optimum number of clusters that minimizes the sum thereof. In addition, in the disclosed embodiment, the most efficient formation of clusters may be determined based on the maximum density packing method. Thus, the disclosed embodiment may maximize the lifespan of a wireless network by maximizing energy efficiency through optimization of variables. Therefore, the present invention has superior competitiveness compared to existing technologies.

The invention discloses a deep carbonate rock transportation conductor dominant seismic genus subdivision three-dimensional modeling method, which comprises the following steps of: optimizing three-dimensional seismic data through multi-scale and multi-direction decomposition and reconstruction so as to establish a dominant three-dimensional seismic data volume capable of optimally representing a deep carbonate rock reservoir; and based on the heterogeneity of the deep carbonate rocks, an isochronous stratigraphic division method is adopted to carry out fine small-layer subdivision on the optimized seismic data. And carrying out seismic horizon calibration by using the underground synthetic record, and calculating the transmission-to-ground ratio of each small layer. By extracting and analyzing the seismic attributes, the optimal seismic attribute capable of effectively predicting the ratio of the output to the ground is screened out. And establishing a mathematical equation by using the indexes to convert the seismic attributes into an output-to-earth ratio data volume. And a three-dimensional transmission-to-earth ratio distribution model is constructed by combining the small-layer transmission-to-earth ratio and the ancient landform depth value of each reservoir forming period, so that a scientific basis is provided for oil and gas transmission and reservoir forming analysis. According to the method, the recognition precision of the reservoir features is remarkably improved, and the method has important application value.

The invention discloses an attraction domain boundary determination method and device of a wind power system and computer equipment. The method comprises the following steps: constructing a mathematical equation set model corresponding to a wind power system; constructing a random disturbance model based on the change factors of the wind power system; adjusting the mathematical equation set model based on a random disturbance model to obtain a target mathematical equation set; solving the target mathematical equation set to obtain a phase trajectory diagram; and determining a target attraction domain boundary of the wind power system based on the phase trajectory diagram. The technical problem that the risk of system chaotic oscillation existing in the attraction domain boundary of the chaotic attractor cannot be determined due to unstable output of a wind power system caused by uncertain factors such as wind speed change is solved.

In some embodiments, an electronic device solves mathematical equations detected in text input into applications other than a calculator application. In some embodiments, an electronic device performs unit conversions in a calculator application. In some embodiments, an electronic device presents graphs of mathematical equations. In some embodiments, an electronic device edits graphs of mathematical equations.

The present invention provides a method for evaluating slope stability under complex conditions, belonging to the fields of engineering disaster prevention and mitigation and computer-aided design. Based on the function relationship between the major principal stress and the minor principal stress of the general non-linear strength criterion in the form of the principal stress, by using the tangent direction of the slip surface at any point on the potential slip surface as its most unfavorable shear direction, the correlation calculation formula of the slip surface stress with its major principal stress and minor principal stress is derived. Then, according to the spatial position relationship between the Mohr stress circle and the shear strength envelope, the mathematical equation of the slip surface shear strength parameter associated with the general non-linear strength criterion in the form of the principal stress is obtained. Subsequently, a cyclic iterative solution strategy is adopted to break the mutual nesting relationship among the slip surface acting force, the slip surface stress and the slip surface shear strength parameter in the evaluation method. The present invention provides a scientific basis for reliably preventing slope collapse and implementing reinforcement measures, and has the advantages of high calculation efficiency, wide application range, strong practicability, etc.

This invention relates to a method for optimizing gradient separation conditions in liquid chromatography, comprising the following steps: 1. Measuring the retention time and peak width of sample components under different isocratic or gradient conditions, and fitting a mathematical equation relating capacity factor, retention time, and gradient. 2. Setting a series of parameters such as minimum retention time, maximum retention time, and minimum resolution. 3. Optimizing the elution gradient program based on objective function evaluation and optimizer algorithms to satisfy the objective function. This invention provides various linear and nonlinear mathematical equations describing the relationship between solvent, capacity factor, and retention time, overcoming the limitations of traditional solvent-retention time prediction models in practice. It can also predict and recommend multi-order isocratic and gradient solvent curves, with fast calculation speed and wide application range.

The application relates to a scribing etching method for controlling the resistance and resistance distribution of a heating film by using a mathematical equation, which comprises the following steps: using an automatic laser etching device to perform laser scribing etching on a non-standard thickness heating film, so that the resistance of the remaining heating film body is the same as that of a standard thickness heating film, the resistance distribution of the remaining heating film body conforms to the line type of the etching line, and the laser scribing etching is controlled by a mathematical equation to control the line type of the etching line. The application has the beneficial effects that the laser scribing etching method replaces the traditional mask etching method, reduces the etching workload, and shortens the etching time; the laser scribing etching method is controlled by a mathematical equation and an automatic laser etching device, can simply and flexibly control the resistance and resistance distribution of the heating film, does not need to adjust a magnetron sputtering device, and does not need to re-produce an etching template, thereby saving production time and cost.

The invention discloses an electromagnetic transient modeling and simulation method for internal faults of a doubly-fed induction generator, and relates to the technical field of power system modeling and simulation. The method comprises the following steps: S1, considering a stator-rotor turn ratio, and reducing the rotor quantity to a stator side to obtain an original mathematical equation; s2, establishing mathematical models of the doubly-fed induction generator under different fault types, correcting a basic equation of the generator according to fault features, and focusing resistance and inductance matrix elements needing to be updated; s3, selecting a flux linkage as a state variable, performing discretization equivalence on the mathematical equation by using a backward Euler integral method, unifying different faults to obtain an equivalent circuit equation, and constructing an equivalent circuit of the generator; s4, the equivalent circuit of the doubly-fed induction generator is connected with an external electrical network, and the equivalent model carries out node admittance matrix iterative solution on the whole circuit based on an EMTDC solver; and updating other concerned electrical information such as the stator current, the rotor current, the electromagnetic torque, the rotating speed, the rotor angle and the like until the simulation is finished.

This invention provides a method, apparatus, and equipment for designing the profile of a forming grinding wheel for a single-flute micro-drill, relating to the technical field of micro-drill bit processing equipment. The profile design method includes steps S1 to S4. S1: Establish the mathematical equation for the end face curve of the single-flute micro-drill. S2: Obtain the mathematical equation for the spiral groove of the single-flute micro-drill by spiraling the end face curve along the axial direction. S3: Based on the meshing relationship between the forming grinding wheel and the spiral groove and the mathematical equation for the spiral groove, obtain the meshing curve formed by the forming grinding wheel and the spiral groove in space. S4: Solve the meshing curve, and perform coordinate operations to reduce the dimension and perform circular arc fitting on the solution to obtain the final profile of the forming grinding wheel. This method can achieve parametric solution of the forming grinding wheel profile, guiding the shaping work of the forming grinding wheel, thereby improving the problems of low efficiency and large error in manual grinding of forming grinding wheels, and improving the development and production efficiency of new products.

The present invention discloses a bridge dynamic interaction analysis method that integrates monitoring data and hybrid substructures. The method first uses hybrid substructure technology to determine the interface constraints of key areas by establishing mathematical equations; then, an expectation-oriented adaptive sparse Gaussian process algorithm is introduced to perform parameter identification of these key areas based on actual monitoring data. Furthermore, the present invention proposes a new theoretical framework to realize the dynamic interaction between substructure nonlinear analysis and main structure linear elastic analysis. The effectiveness of this method is verified by an application example on an actual concrete beam bridge. The present invention not only opens up a new path for the deep integration of monitoring data and finite element models, but also significantly enhances the accuracy of substructure analysis and overall structural performance evaluation.

The invention discloses a method for representing the thickness of a metal film on the surface of a metal substrate through an oscillator, and the method comprises the steps: obtaining the thickness response data of the copper film on the surface of a double-layer metal substrate material through the oscillator based on known metal copper films with different thicknesses and the double-layer metal substrate material; and fitting a mathematical equation between the copper film thickness and the output data of the oscillator through a least square method algorithm. When a copper film with an unknown thickness is measured, firstly, a copper film material with a known thickness is used for calibration, an output value of a current oscillator is recorded, then data of the copper film with the known thickness is substituted into a fitting equation, and an output value of the fitting equation is solved; subtracting the current output value of the oscillator from the output value of the equation to obtain the difference value of the tiny drift; substituting the difference value into the fitting function to generate a new fitting equation after the tiny drift is eliminated; and finally, substituting the oscillator data of the copper film to be detected into the new fitting equation to invert the thickness of the unknown copper film.

The invention discloses a five-component decomposition method based on differential dynamic search whale optimization in the technical field of optimization algorithms and signal processing. The whale optimization five-component decomposition method based on differential dynamic search comprises the following steps: constructing a whale optimization five-component decomposition system, and selecting a specific ship structure local scattering model, specifically, a rotation dihedral angle RD scattering model and a + / -45 degree directional dipole OD scattering model; constructing a mathematical equation; carrying out mathematical constraint on the constructed mathematical equation; and carrying out objective function constraint on the constructed mathematical equation. According to the differential dynamic search whale optimization-based five-component decomposition method, clutter interference is effectively suppressed through simple linear operation, global and local structures of a ship are highlighted, and ship scattering significance is further represented.

The present invention discloses an input device and a design method for a cycloidal gear speed reducer. The device includes: two cycloidal gears arranged diagonally at 180 degrees; and a plurality of pin teeth pins, the arc edges of which are connected to the tooth profile edges of the two cycloidal gears. The present invention simplifies the mathematical equation of the cycloidal gear into a parameter equation set regarding the basic design parameters of the cycloidal gear and the pin teeth pins. By using this parameter equation set, the contour of the cycloidal gear can be designed conveniently and quickly, so that the preparation of the corresponding cycloidal gear is simple, and then the corresponding cycloidal speed reducer can be designed quickly, achieving the effect of reducing production costs.

The invention relates to the technical field of mine rock roadway full-section hard rock tunneling machine construction, in particular to a tunnel arc section TBM track deviation rectification planning and local posture regulation and control method. Comprising the following steps: S1, acquiring an actual track ATA of a TBM shield, and calculating an offset e between the actual track ATA of the TBM and a design track DTA; s2, when the offset e exceeds a preset allowable value, the current actual position serves as a deviation correction track starting point, and position information, including the position, the curvature, the polar angle and the deviation angle, of the deviation correction track CTA starting point is obtained; s3, according to the geometrical relationship, calculating the end point information of the correction track CTA and the position information of the other two control points, and determining a third-order Bezier curve mathematical equation of the final correction track CTA; s4, according to the deviation rectifying track route and the tunneling step length, the deviation rectifying track is separated from the CTA into a plurality of sections; s5, according to the geometric information of each discrete section, the TBM oil cylinder stroke control parameters of the current section are determined; and S6, determining TBM attitude parameters of the current section according to the geometric information of each discrete section.

Disclosed in the embodiments of the present application is a solution process control method. In the method, a cloud management platform may determine a first physics discipline type of a first physical equation to intelligently determine, on the basis of the first physics discipline type, one or more of a first auxiliary equation, a first coupling strategy and a first numerical solution strategy which correspond to the first physical equation, so as to configure mathematical equation sets included in first solution tasks of a current physical-field service and / or a solution mode of each first solution task, thereby solving the first physical equation. It can be seen that in the solution, the cloud management platform may intelligently determine one or more of the first auxiliary equation, the first coupling strategy and the first numerical solution strategy which correspond to the first physical equation, so as to conveniently and efficiently determine, for various physical scenarios, mathematical equation sets included in first solution tasks to be solved and / or a solution mode of each first solution task, thereby solving the first physical equation by means of an appropriate solution process.

The invention belongs to the technical field of bridge structure health monitoring, and discloses a suspension bridge structure system identification method based on observability and state estimation and a high-efficiency algorithm thereof. According to the characteristics of different components of the suspension bridge, an observability state equation of the suspension bridge is established, the identifiability problem of unit parameters is converted into the solvability problem of a mathematical equation, a Jacobian matrix is constructed in combination with a state estimation high-efficiency algorithm (OM-SE), explicit mapping between measurement data and state variables is achieved, and the measurement accuracy of the suspension bridge is improved. And the parameter identification precision and the calculation efficiency are improved. The overall rigidity matrix is established through the parabola main cable unit, the Euler-Bernoulli beam unit and the direct rigidity method, parameter inversion is performed by adopting a double-layer iteration process, the method is suitable for identifying the bending rigidity of the main beam and the axial rigidity of the cable of the large-span suspension bridge, and the method is verified through a reduced scale model test and an actual suspension bridge numerical value case, and the method is suitable for identifying the bending rigidity of the main beam and the axial rigidity of the cable of the large-span suspension bridge. The identification error is controlled within 5%, and the calculation efficiency is improved by more than 70%.

The application relates to a variable-tooth worm and a processing method thereof, and relates to the technical field of worm structure, which comprises a variable-tooth worm composed of a shaft body and a thread tooth arranged on the shaft body, the lead of the thread tooth is constant along the overall length of the worm, the tooth root surface and the tooth top surface can be cylindrical surfaces or circular arc rotary surfaces, the thread tooth is formed by sweeping a linear blade along a space constant-lead variable-diameter helix, a mathematical equation of the helix is given, the related structural parameters of the thread tooth are specifically limited, the processing method of the variable-tooth worm is introduced, and the steps of rough and fine machining of a blank, slotting, heat treatment, gear grinding and the like are included, a five-axis linkage control is adopted for a numerical control machine tool, and the meshing of the worm wheel and the worm can form four to five pairs of continuously meshed contact areas. The application achieves the technical effects of optimizing the structural design of the variable-tooth worm, improving the machining precision and quality, and improving the meshing performance of the worm wheel and the worm.

This invention relates to the field of intelligent manufacturing, specifically to a multidisciplinary motion control modeling method for large component attitude adjustment and alignment systems. It combines the theories of multiple disciplines and fields involved in large component attitude adjustment and alignment systems with the Modelica technology system for the construction and simulation analysis of motion control models for these systems. This invention eliminates the need for pre-defining the input and output variables of components and the order of equation solving during the modeling process. During system solution, it automatically derives the causal relationships between variables based on mathematical equations. It has a wide range of applications, as this invention, based on the Modelica language, achieves integrated modeling and simulation across multiple disciplines and fields, including mechanics and control, overcoming the limitations of cross-platform modeling and simulation across different disciplines.

The invention provides a construction method for fiber orientation of a fiber winding layer, and relates to the technical field of composite material structure simulation analysis, and the construction method comprises the following steps: carrying out geometric discretization and layering pretreatment on a fiber winding layer structure; implementing unit topology reconstruction and spatial positioning; establishing a two-dimensional coordinate equation for representing the outer contour of the fiber winding layer; designing a fiber winding direction based on mechanical conditions of stable fiber winding; constructing a local coordinate system for fiber orientation definition, and completing direction conversion; and integrating an ORIENT subprogram to realize automatic endowing of fiber orientation parameters. According to the method, the limitation of a traditional fiber angle definition method is broken through, the winding stability condition is converted into a computable mathematical equation, and according to a fitted coordinate equation, the construction of a material coordinate system of composite material structure models in different shapes in ABAQUS is achieved.

In the estimation process, the control unit (31) estimates the state of the device (70) on the basis of the specific frequency component (C1) of the physical quantity obtained from the device (70). In the limiting process, when the noise frequency component (Cn) and the specific frequency component (C1) included in the physical quantity satisfy a predetermined relationship, the control unit (31) limits either the estimation process or the operation of the motor (50). The carrier frequency is set to be fc, the frequency for sampling the physical quantity is set to be fs, the electrical angle frequency is set to be f0, and when the physical quantity is a DC signal, the frequency of the noise frequency component (Cn) is represented by any one of formulae 1 to 3; when the physical quantity is an AC signal, the frequency of the noise frequency component (Cn) is represented by any one of formulae 4-6. [Mathematical formula 1] fc + / -6Nfo... (1) Mfs-6Nfo... (2) Mfs-fc + / -6Nfo... (3) fo + / -fc + / -6Nfo... (4) fo + / -Mfs-6Nfo... (5) fo + / -Mfs-fc + / -6Nfo... (6) wherein M and N are natural numbers.

The invention provides a multi-parameter coking process optimization method and system, aiming at a coke oven heating system with mutual influence of multiple parameters, original million-magnitude data are compressed into a simple matrix equation by performing equation compression on data which has physical significance and can be grouped in coke oven thermotechnical data, and the matrix equation is used for optimizing the coke oven heating system. And the function of optimizing the control model of the coking process is realized. According to the method, a grouping progressive regression mode is adopted, multi-dimensional boundary conditions are transmitted and compressed into a group of control equations, and numerical values under any parameters can be found out through step-by-step review to be used for controlling and comparing the furnace conditions of the coke oven; the data query time in the heating control equation is shortened to the time required for calculating several mathematical equations, the operation efficiency of the control equation is improved, and the operation speed of the control equation is effectively improved.

In some embodiments, an electronic device solves mathematical equations detected in text input into applications other than a calculator application. In some embodiments, an electronic device performs unit conversions in a calculator application. In some embodiments, an electronic device presents graphs of mathematical equations. In some embodiments, an electronic device edits graphs of mathematical equations.

The application belongs to the technical field of bridge structure health monitoring, and discloses a suspension bridge structure system identification method based on observability and state estimation and a high-efficiency algorithm thereof; aiming at different component characteristics of the suspension bridge, the identifiable problem of the unit parameters is converted into the solvable problem of the mathematical equation by establishing the observability state equation of the suspension bridge, and the Jacobian matrix is constructed in combination with the high-efficiency algorithm (OM-SE) of state estimation to realize the explicit mapping between the measured data and the state variables, and the precision and the calculation efficiency of the parameter identification are improved. The whole stiffness matrix is established by the parabolic main cable unit, the Euler-Bernoulli beam unit and the direct stiffness method, the parameter inversion is carried out by using the double-layer iteration process, the method is suitable for the identification of the bending stiffness of the main beam and the axial stiffness of the cable of the long-span suspension bridge, and has been verified by the scale model test and the actual suspension bridge numerical case, the identification error is controlled within 5%, and the calculation efficiency is improved by more than 70%.

The invention discloses a multi-station signal time difference positioning system in a complex environment, and relates to the technical field of wireless signal positioning, and the method comprises the steps: S1, building a measurement model based on a TDOA positioning principle; s2, deriving a mathematical relationship between measurement data and an error introduced by measurement noise by using the measurement model; s3, correcting measurement data according to the mathematical relationship so as to reduce an error term introduced by measurement noise; s4, performing iterative correction on the corrected measurement data to enable the measurement data to gradually approach a theoretical value; s5, judging and terminating iteration by utilizing constraint conditions to obtain final corrected measurement data, solving a target position by adopting a least square method to obtain a positioning result with higher precision, and obtaining a solving process of the method; a measurement model between a signal source and each receiving station is established based on a TDOA positioning principle, and a mathematical equation reflecting a relation between a signal propagation path difference and a target position is established through observation data.