18 results about "Mathematical equations" patented technology

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.

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 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.

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.

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.

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.

The application provides an intelligent ship maneuvering motion prediction method based on mathematical equation-data driving fusion, and comprises the following steps: on the basis of an MMG model, a four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives is established based on the Taylor series expansion thought; based on the four-degree-of-freedom ship maneuvering motion prediction model with variable high-order hydrodynamic derivatives, an extended Kalman filtering algorithm is used to perform parameter identification on hydrodynamic derivatives of different orders; on the basis of the optimal order prediction model, real ship motion data are combined to construct a ship motion prediction residual; a least squares support vector machine algorithm is used for black box modeling to approximate the motion prediction residual; a BP neural network is built, the prediction residual of the least squares support vector machine black box model and the prediction result of the optimal model are used as input, and real ship navigation data are used as output to learn and train the neural network, so that the estimation of the ship motion state is realized.

The invention provides a profile design method, device and equipment for a formed grinding wheel of a single-blade micro drill, and relates to the technical field of micro drill bit machining equipment. The profile design method comprises steps S1 to S4. S1, establishing an end face curve mathematical equation of the single-edge micro drill; and S2, the end face curve spirally moves in the axial direction to obtain a spiral groove mathematical equation of the single-edge micro drill. And S3, according to the meshing relation between the formed grinding wheel and the spiral groove and the spiral groove mathematical equation, a meshing curve formed by the formed grinding wheel and the spiral groove in the space is obtained. And S4, the meshing curve is solved, coordinate operation dimensionality reduction and arc fitting are carried out on a solving result, and the final profile of the formed grinding wheel is obtained. According to the method, parameterization solution of the profile shape of the formed grinding wheel can be achieved, shape correction work of the formed grinding wheel is guided, and therefore the problems that manual grinding of the formed grinding wheel is low in efficiency, large in error and the like are solved, and the development and production efficiency of new products is improved.

The invention relates to a mathematical application question intelligent solving method and device, equipment and a medium. The method comprises the steps of performing semantic analysis on an input application question text to generate an entity relation graph; performing dimension consistency verification on the entity relation graph based on a pre-constructed dimension knowledge base to obtain a dimension verification result; performing dynamic unit conversion processing according to the dimension verification result and the problem target unit to generate a standardized data set; solving a mathematical equation based on the entity relation graph and the standardized data set to obtain an initial answer; and performing composite verification processing on the initial answer, generating a verification result, performing output decision processing, and generating a final answer. By adopting the method, the problem of dimension errors caused by inconsistent units in the prior art can be effectively solved, and the accuracy and reliability of a mathematical application problem solving system are improved.

The invention provides a vibration and noise reduction blade design method based on quadric function airfoil thickness distribution, an impeller and a blade. The vibration and noise reduction blade design method comprises the steps that a performance target is determined; determining physical boundary conditions of the blade; a thickness distribution control law of reverse solving is determined, a mathematical equation set with a quartic polynomial function of the blade thickness changing along the blade height as a solving target is constructed, and coefficients are undetermined unknown numbers; a two-dimensional airfoil section is determined, a parameterized stacking line is defined in a three-dimensional space, and a two-dimensional airfoil coordinate point set is generated in combination with the thickness distribution control rate; and determining a three-dimensional blade entity. According to the method, blade load distribution serves as a direct control target for suppressing flow noise and a vibration excitation source, and a blade thickness distribution reverse solution method with blade top load distribution as a target and geometric requirements and blade top leakage suppression as constraints is adopted. And establishing a set of analytic forward design system for directly generating the three-dimensional blade geometry from a preset performance target.

This application discloses a solution process control method. In this method, a cloud management platform can determine the first physics discipline type of the first physical equation, and then intelligently determine one or more of the first auxiliary equation, first coupling strategy, and first numerical solution strategy corresponding to the first physical equation based on the first physics discipline type. This allows for the configuration of the mathematical equation set and / or the solution method for each first solution task in the current physics field service, thereby solving the first physical equation. As can be seen, in this solution, the cloud management platform can intelligently determine one or more of the first auxiliary equation, first coupling strategy, and first numerical solution strategy corresponding to the first physical equation, thus conveniently and efficiently determining the mathematical equation set and / or the solution method for each first solution task for various physical scenarios, and solving the first physical equation with a suitable solution process.

The invention discloses a single-line bidirectional railway cycle train timetable generation method and system based on an optimization model, the system collects and processes railway basic data through a specified data interface, then the system constructs a mathematical optimization model, the model takes one or more preset performance indexes as an optimization target, and the time table of a single-line bidirectional railway cycle train is generated. Meanwhile, various physical constraints, safety constraints and operation constraints of train operation are expressed as a series of mathematical equations or inequations. And then, solving the mathematical model by utilizing an integrated or externally called optimization solver so as to determine the accurate arrival and departure time of each train at each station. And finally, the system generates a human-readable train timetable and / or a visual train working diagram according to an optimization result returned by the solver. According to the method and the system provided by the invention, by constructing a comprehensive mathematical optimization model and utilizing an advanced solving technology, high automation and optimization of a single-line two-way railway (cycle) train timetable generation process are realized.

A method of modelling system behaviour of a physical system, the method including, in one or more electronic processing devices obtaining quantified system data measured for the physical system, the quantified system data being at least partially indicative of the system behaviour for at least a time period, forming at least one population of model units, each model unit including model parameters and at least part of a model, the model parameters being at least partially based on the quantified system data, each model including one or more mathematical equations for modelling system behaviour, for each model unit calculating at least one solution trajectory for at least part of the at least one time period; determining a fitness value based at least in part on the at least one solution trajectory; and, selecting a combination of model units using the fitness values of each model unit, the combination of model units representing a collective model that models the system behaviour.