17 results about "Mathematical relationship" patented technology

This invention relates to the field of semiconductor manufacturing process monitoring technology, and discloses an online pH monitoring system for polishing slurry based on ultrasonic stirring. The system includes: an ultrasonic stirring module for uniformly stirring the polishing slurry and acquiring acoustic signals, extracting acoustic feature vectors through Fourier transform and wavelet analysis; a multi-sensor data acquisition module for acquiring pH, temperature, turbidity, and redox potential data; an anomaly detection module for constructing an LSTMAutoencoder model, calculating reconstruction errors, and triggering early warnings; a causal analysis module for constructing a causal network of pH changes; a rule generation module for extracting mathematical relationships using symbolic regression and converting them into predictive rules; and an intervention control module for calculating the effectiveness of intervention measures, generating and executing optimal control operations. Through structural causal models and counterfactual reasoning, this invention can accurately identify key factors leading to pH anomalies and their contribution, shortening troubleshooting time.

The application discloses a relative photometry improvement method for an oversaturated detection image, belongs to the technical field of astronomical image photometry, and aims at solving the problem that the nonlinear truncation of the observed light flux is caused by the oversaturation of the gray value of a star in an existing astronomical image, and the systematic deviation exists in a classical relative photometry model in a star apparent magnitude estimation method. The method comprises the following steps: based on a point spread function model of saturation truncation, a mathematical relationship between the total light flux of a star and the observed light flux of the star in an astronomical oversaturated detection image is established; according to the mathematical relationship, a relative photometry improvement model is established; based on the observed light fluxes of a plurality of known stars and corresponding reference apparent magnitudes, an iterative optimization algorithm is adopted to iteratively optimize the relative photometry improvement model, and the optimal model parameter in the model is solved; and based on the optimal model parameter and the observed light flux of a target to be measured, the apparent magnitude estimation value of the target in the astronomical oversaturated detection image is obtained through the relative photometry improvement model.

The present disclosure relates to a method for measuring a sample based on an ellipsometer and an ellipsometric measuring device. The method for measuring a sample based on an ellipsometer comprises: collecting a first measurement Mueller spectrum corresponding to a reference light spot position, and obtaining a first Mueller matrix; moving a cylindrical body along a direction perpendicular to an incident plane by a first preset distance to form a measurement light spot, collecting a second measurement Mueller spectrum corresponding to the measurement light spot position, and obtaining a second Mueller matrix; determining a mathematical relationship between the second Mueller matrix and the first Mueller matrix; representing the second Mueller matrix as a first function of an incident light wavelength, a film thickness, and an included angle based on a Fresnel equation and the mathematical relationship; fitting the second measurement Mueller spectrum based on the first function using a nonlinear regression algorithm to obtain a measured value of the film thickness and the included angle; and calculating a radius of the cylindrical body based on the first preset distance and the measured value of the included angle. The method realizes rapid and non-destructive measurement of the radius of the cylindrical sample.

This invention relates to the field of down-the-hole (DH) drill bit wear measurement technology, specifically a method and system for real-time measurement of DH drill bit wear values. The method involves optimizing and registering an initial three-dimensional model to obtain the overall quantitative wear value of the DH drill bit; analyzing the mapping relationship between drilling parameters and the overall quantitative wear value, and constructing a database of drilling parameters and drill bit wear values; deriving dimensionless variables based on dimensional analysis methods and the database, and combining and filtering these variables with second-order polynomials and cross terms to determine the combination of dimensionless variables affecting drill bit wear; and substituting this combination of dimensionless variables into a multiple linear regression model to establish a mathematical relationship model between drill bit wear and drilling parameters, thereby achieving real-time measurement of the DH drill bit wear value. This invention, based on dimensional analysis to obtain dimensionless variables of drilling parameters and combined with multiple linear regression to construct a model for real-time measurement of DH drill bit wear values, improves construction efficiency and safety.

The invention provides a model and a method for predicting the water-gas ratio and the water yield of formation water of a fracture-vug type water-producing gas well. The model establishment method comprises the following steps: screening out abnormal fluctuation data from gas field production dynamic data to obtain daily output data; calculating the accumulated gas production and formation water-gas ratio of the water-producing gas well according to the daily output data; establishing a formation water-gas ratio calculation model of the water-producing gas well, wherein the model is a mathematical relationship between the formation water-gas ratio and cumulative gas production and contains a plurality of undetermined indexes; the accumulated gas production of the water-producing gas well and the water-gas ratio of the formation water are used for fitting to determine the value of each index, and then a prediction model of the water-gas ratio of the formation water is obtained. The water yield prediction model is established based on the formation water-gas ratio model. According to the prediction method, the future daily water yield can be predicted according to the water yield prediction model. According to the method, the labor cost of a large number of professionals is effectively reduced, the timeliness and convenience are improved, and the method has good applicability and popularization prospects in field practical application.

A multi-time-layer differential scheme for implicit heat transfer calculation using moving particles is presented, with the following specific steps: 1. Before calculation, virtual particles are arranged at the boundary to implement boundary layout, using virtual particles to arrange the first, second, and third types of boundaries for heat transfer calculation, as well as symmetric and periodic geometric boundary conditions; 2. During heat transfer calculation, the physical and mathematical relationships between different particles are given according to the input boundary conditions; 3. The distances between particle i and its neighboring particle j from the boundary surface formed by the boundary particles are calculated, and boundary conditions are applied; 4. The particle properties are given according to the initial input temperature, and the calculation time step length is given according to the stability condition; 5. The coefficient matrix and source terms of the multi-time-layer scheme of the heat diffusion equations are combined to solve the energy equation for temperature; 6. A consistent solution is performed using relevant solving algorithms to solve for the next temperature and determine whether convergence has occurred; 7. After all MPS calculations for a single time step are completed, the next time step is initiated.

The present application belongs to the technical field of oil and gas pipeline internal detection, and particularly relates to a pipeline magnetic flux leakage detection data wall thickness quantification method, aiming at solving the problem that the prior art cannot quantize the pipeline wall thickness with high precision in the pipeline magnetic flux leakage internal detection. The method comprises: obtaining simulation data of oil and gas pipeline magnetic flux leakage detection as a base value; only considering the relationship between the base value and the wall thickness, constructing a univariate model of the pipeline wall thickness and the base value of different diameters, then modeling and fitting the mathematical relationship between the wall thickness and the base value, determining the mathematical model of the wall thickness and the base value based on the fitting result as a first model; introducing a speed influence factor in the first model to establish a wall thickness quantification model with the speed factor, as a second model, that is, the final mathematical model of the wall thickness and the base value; obtaining the base value data, and obtaining the wall thickness quantification result through the final mathematical model of the wall thickness and the base value. The present application realizes high-precision quantification of the pipeline magnetic flux leakage detection wall thickness.

This application discloses a method for solving damage evolution parameters in a damage constitutive model, belonging to structural mechanics and fracture mechanics. The method includes: establishing a mathematical relationship between damage variables and associated variables based on thermodynamic principles, and obtaining an integral expression for the energy dissipation potential per unit volume by combining damage evolution criteria; simplifying the integral expression for the energy dissipation potential per unit volume based on the principle of equivalent strain, obtaining a scalar analytical expression; numerically integrating the scalar analytical expression using the three-point Newton-Cotes integration algorithm, and iteratively solving for the damage evolution parameters using the secant method. This method transforms complex tensor operations into simple scalar analysis, reducing the computational burden. Furthermore, the use of the Newton-Cotes integration method and the secant method iterative solution strategy ensures accurate calculation of damage parameters, enhances computational stability and reliability, and significantly improves the efficiency and accuracy of the solution.

The application discloses a DC system fault location method based on complex domain analysis, comprising the following steps: converting a preliminary fitting exponential function into Z domain for analysis to obtain the converted preliminary fitting exponential function; calculating and solving based on least square method rational approximation to determine the parameters of the preliminary fitting exponential function; calculating the Pearson correlation coefficient to measure the linear relationship between the candidate step length and the minimum fitting error, and optimizing the Pearson correlation coefficient through a particle swarm algorithm to select the best step length; obtaining the final fitting exponential function according to the parameters of the preliminary fitting exponential function and the best step length, solving the mathematical relationship between the distribution characteristics of system poles and the natural oscillation frequency; and calculating the inductance value in the fault line to estimate the fault distance by using the mathematical relationship and combining the inductance value per unit length, so as to realize fault location. The application can realize accurate fault location and meet the speed requirement of fault location.

This invention provides a multi-sensor data processing method, apparatus, and system with the following advantages: Monitoring data is grouped according to data elements to obtain multiple data groups, where each data element includes multiple physical parameters; these data groups are fitted separately, and the data with the smallest fitting error is selected from each group to form a training set; the mathematical relationship between the data elements is calculated using the training set. This invention groups sensor data for processing, uses high-precision sensor data for fitting calculations, shields against data noise interference, and effectively improves the accuracy of sensor data processing.

The embodiment of the present application provides a kind of based on the determination method of induced voltage of split conductor of sub-conductor fracture.The method comprises: obtaining the attribute parameter of transmission line, and according to attribute parameter, construct geometric model;Wherein, attribute parameter includes the structural parameter of tower, the physical parameter of conductor, broken line position parameter, conductor includes ground wire, broken sub-conductor and perfect sub-conductor;According to the geometric model, determine potential coefficient matrix, and according to potential coefficient matrix, construct coupling equation;Wherein, potential coefficient matrix represents the electrostatic coupling strength between each conductor, and coupling equation represents the mathematical relationship between the voltage of conductor and charge amount;Solve coupling equation, obtain the electrostatic induction voltage of broken sub-conductor, and according to the electrostatic induction voltage of broken sub-conductor, determine the induced voltage of split conductor to which it belongs.The method is used to improve the effect of the accuracy of determining the induced voltage of split conductor.

This invention relates to a non-uniform error calibration method for a multi-degree-of-freedom forming robot, comprising the following steps: S1, establishing a kinematic model of the multi-degree-of-freedom forming robot and deriving the mathematical relationship between the displacement of the robot-controlled moving slider and the six-degree-of-freedom coordinates of the end-effector plane; S2, constructing a measurement model using a line laser measuring instrument and fitting the linear equations of the points measured by the line laser measuring instrument using the least squares method; S3, establishing an error model for the multi-degree-of-freedom forming robot; S4, establishing a mapping relationship between the measurement data and the error sources of the multi-degree-of-freedom forming robot. This invention provides a non-uniform error calibration method for a multi-degree-of-freedom forming robot based on a line laser measuring instrument. Compared with traditional point laser trackers, this invention can reduce the complexity of the measurement system, improve calibration efficiency, and enhance calibration accuracy.

The application provides a method for improving the repetition accuracy of a piezoelectric deflection mirror, at least one temperature cycle is performed on the piezoelectric deflection mirror, and the parameter change amount of a parameterized mapping relationship model in adjacent two cycles is used as a criterion to determine whether it is less than or equal to a preset threshold value, so that the stress is fully released and the model parameters are stable; the model describes the mathematical relationship between the deflection angle and the drive code value, and the parameters change with the temperature. The drive code value, the strain gauge acquisition code value and the actual deflection angle at different temperature points are collected, the drive code value-deflection angle relationship curve and the acquisition code value-deflection angle relationship curve are fitted to establish a static temperature mapping. At least one temperature point, the data is collected multiple times at a predetermined time interval, the curve fitting of each parameter in the model with time is performed, the parameter change prediction curve is obtained, and the time-varying law of aging and performance attenuation is revealed. The model parameters are dynamically updated in combination with the above curve, and the errors caused by the temperature change and the time cumulative parameter change are compensated.

The application discloses a method and device for calculating shale content of electro-imaging logging image based on mathematical modeling, and relates to the field of well logging geology. In the same sedimentary environment, the application selects reasonable function simulation to fit the mathematical relationship between the shale content and the conductivity by using the response characteristics of the conductivity to the shale content. Meanwhile, the mathematical relationship between the pixel and the conductivity is fitted by using the calibration relationship between the resistivity and the pixel, the simultaneous relationship is derived, the mathematical model between the pixel and the shale content is derived, and then the mathematical model is used to calculate the shale content of the target layer. The application establishes the mathematical relationship between the pixel value and the shale content, realizes the quantitative calculation of the shale content based on the electro-imaging data for the first time, and expands the geological application depth of the electro-imaging logging. By introducing the conductivity as an intermediate variable, the conversion path of the pixel-conductivity-shale content is established, and a new way for calculating the shale content based on the electro-imaging image itself is provided.

The application belongs to the field of electrochemistry, and discloses an overpotential solving method and device for an electrochemical system, which comprises the following steps: based on the mathematical relationship between the total current of the cathode catalytic layer and the total current of the anode catalytic layer in the target electrochemical system, constructing an inner iteration model with the proton potential bias as the variable to be solved and an outer iteration model with the plate voltage as the variable to be solved; coupling and iteration solving the inner iteration model with the proton potential bias as the variable to be solved and the outer iteration model with the plate voltage as the variable to be solved, obtaining the iteration solving result of the proton potential bias and the iteration solving result of the plate voltage; and calculating the overpotential of the target electrochemical system according to the iteration solving result of the proton potential bias and the iteration solving result of the plate voltage; the application can avoid the defects of long calculation time under low relaxation factor and the risk of voltage and current fluctuation under high relaxation factor, and can significantly improve the calculation efficiency.

The application discloses a dam coarse-grained soil grading design method and system based on a two-parameter grading equation, which comprises the following steps: designing the grading of coarse-grained soil with different grading parameters and maximum particle sizes based on the two-parameter grading equation; performing compaction density tests on each grading to obtain the compaction density of coarse-grained soil under different grading conditions; analyzing the relationship between the grading parameters, the maximum particle size and the compaction density based on the test data, and constructing a corresponding mathematical equation set; solving the equation set to obtain the grading parameters of coarse-grained soil with compaction characteristics under different maximum particle sizes, thereby obtaining the design grading of dam coarse-grained soil. The application establishes a quantitative correlation between the grading of coarse-grained soil and the compaction characteristics by constructing a mathematical relationship model between the grading parameters, the maximum particle size and the compaction density. The quantitative relationship considers the influence of the maximum particle size on the compaction characteristics of coarse-grained soil, and breaks through the limitation that the traditional grading design mainly relies on empirical judgment and specification limit control.