28 results about "Mathematical theory" patented technology

The invention discloses a Laplace transformation-based steady-state boundary driven solute transport model solution and parameter calculation method, which comprises the following steps of: establishing a one-dimensional finite-scale underground water solute transport mathematical model on the basis of an underground water solute transport system; solving the mathematical model by combining groundwater dynamics, a convection-dispersion equation and a Laplacian transformation method, deducing a convection-dispersion test theoretical model under the condition of different Peclet numbers, and obtaining a standard curve for determining a medium permeability coefficient and a hydrodynamic dispersion parameter under the condition of different Peclet numbers; and carrying out a convection-dispersion test, and determining permeability coefficients and hydrodynamic dispersion parameters of the medium under different Peclet numbers by adopting a wiring method. The method has a rigorous mathematical model and strict mathematical theory derivation, perfects related theories and methods for determining the medium permeability coefficient and the hydrodynamic dispersion parameter in the convection-dispersion test under different Peclet numbers, and solves the technical problems existing in application of the convection-dispersion test in a one-dimensional finite scale model.

The invention aims to provide a virtual simulation method of a diesel engine movement mechanism considering rotation speed fluctuation. The method comprises the following steps: acquiring structure and material parameters of a valve mechanism, acquiring contact parameters of the valve mechanism, acquiring cam lift data, acquiring rigidity damping parameters and structure parameters of a gear transmission system, and acquiring cylinder pressure data. The output torque of a gas distribution unit, the angular acceleration of a cam shaft and the angular acceleration and torque of each gear are predicted respectively, the load torque state is judged, the crankshaft rotation angular acceleration is predicted, and the crankshaft dynamic angular velocity and the angular velocity fluctuation quantity are calculated. All motion mechanisms of the diesel engine are included, all kinetic parameters of the motion mechanisms of the diesel engine can be predicted, and the prediction result is complete. The influence of crankshaft rotating speed fluctuation caused by the load on the kinetic parameters of the diesel engine movement mechanism is considered, and the prediction result better conforms to engineering practice. Complex mathematical theories are not needed, a common numerical method can be adopted for solving, the calculation scale is small, and the calculation speed is high.

The invention discloses a depth operator network ocean flow velocity prediction method based on a Green function, and belongs to the technical field of ocean current prediction, and the method comprises the steps: constructing a depth operator network model based on the Green function; the depth operator network model is trained, the fitting process of an incompressible two-dimensional Navier-Stokes equation solution operator is converted into the fitting process of an integral kernel, a pre-training model is obtained, and a Green function and convergence parameters thereof are learned; collecting sea area surface time sequence ocean flow velocity data as training data; and initializing the pre-training model by using the Green function and the convergence parameter thereof, and carrying out transfer learning on the initialized pre-training model by using the training data to obtain an ocean flow velocity prediction model, thereby predicting the ocean flow velocity distribution of the target sea area at the future moment. According to the method, the mathematical theory and deep learning are combined, the modeling ability for non-local dynamics is effectively enhanced by using the Green function, the calculation efficiency and generalization performance are improved, and an efficient and stable calculation method is provided for ocean flow velocity prediction.

The application relates to the technical field of circuits, and discloses a neural network optimization circuit, which can simultaneously train multiple target training data and simultaneously optimize errors of the multiple target training data, has high parallelism, fast calculation speed, on-chip learning ability, no non-continuous signals such as switch signals and clock signals in the training process, realizes fast convergence under the guarantee of strict mathematical theory, uses analog circuits, and has low expansion cost. Furthermore, the second differentiator is placed from the disturbance source to the position of the output of the adder, the original convergence direction of the circuit can be maintained, the requirement for disturbance power is reduced, and the stability of the network is improved.

The invention discloses a winter bamboo shoot three-dimensional space distribution detection system and method based on artificial intelligence, and belongs to the technical field of intelligent agricultural detection.The winter bamboo shoot three-dimensional space distribution detection method based on artificial intelligence comprises the steps that a high-frequency continuous wave signal with the center frequency of 900 MHz is transmitted to soil through software defined radio equipment; echo signals reflected by a target object in soil are received, signal preprocessing including filtering, noise reduction and digital processing is carried out, through detailed mathematical formula and multi-algorithm fusion, the winter bamboo shoot identification accuracy exceeds 95% and is far better than that of a traditional method, and the identification accuracy of the winter bamboo shoots is improved from the electromagnetic wave propagation theory and the signal processing algorithm to a deep learning model. Complete mathematical theory support is provided, scientificity and reliability of technology implementation are ensured, the software defined radio technology is adopted, compared with traditional ground penetrating radar equipment, the cost is reduced, and the equipment is more suitable for agricultural application and popularization.

This invention discloses a method for constructing QC-LDPC codes that minimizes the number of short loops, comprising the following steps: Step 1: Randomly generate the initial QC-LDPC code base matrix according to the construction requirements; Step 2: Count the number of short loops passing through each element in the base matrix; Step 3: Sort all elements in the base matrix according to the number of short loops; Step 4: Iterate through each element sequentially, calculate the number of short loops corresponding to all values ​​of the element, select the value with the fewest short loops as the new value of the element, if the element value changes, return to Step 2 for the next round of optimization, otherwise continue to traverse the next element; Step 5: Replace each element in the base matrix with a CPM (Current Minimum Quantity). This invention performs global optimization on all elements in the entire matrix, which can approach the global optimum solution, and does not rely on mathematical theories such as finite fields, has no restrictions on parameters, and has great flexibility.

The present invention discloses a public opinion evolution analysis model that integrates network game theory and opinion dynamics, as well as its establishment method and application, belonging to the field of social network analysis technology. The public opinion evolution analysis model in the present invention combines social network game theory and opinion dynamics theory, and constructs a mathematical model of public opinion evolution (POEM) based on relevant theories in social science while considering more comprehensive factors. It realizes the scientific simulation of the psychological activities of individuals in the process of public opinion dissemination, breaking through the two major limitations of single behavior statistics in traditional network game models and the lack of behavioral characterization in opinion dynamics models; and uses uncertainty mathematical theory to characterize the psychological trends and decision-making behaviors of social individuals in the process of public opinion evolution, more accurately depicting the impact of individual dissemination behavior on the evolution of social public opinion.

The application discloses an aero-engine key part dangerous position temperature rapid evaluation method and device, electronic equipment and storage medium, the method comprises the steps that S1, the temperature value, pressure value and rotating speed value in the flow channel are calculated by using the proportional conversion method, the steady-state temperature of the key part dangerous position is calculated, the transition state temperature calculation reduction model is established, and the model parameters are obtained; S2, the material parameters of the aero-engine key part, the temperature value, pressure value and rotating speed value corresponding to the main flow channel at the life calculation point are substituted into the transition state temperature calculation reduction model to rapidly calculate the transient temperature of the aero-engine key part dangerous position under any state. The application directly calculates the rapid temperature of the key part dangerous position by substituting the mathematical theoretical model established by the flight parameters, avoids the consumption of hardware resources and solving time caused by large-scale simulation solving, improves the calculation speed to the order of millisecond, shortens the design cycle, and reduces the calculation cost.

The invention provides a mathematical knowledge reasoning verification method and system based on mathematical text formalization, and belongs to the field of mathematical knowledge reasoning check, and the method comprises the steps: S1, converting an input English text describing mathematical knowledge into a formalized formula list which can be recognized and processed by a computer; and S2, performing logical reasoning verification and algebraic calculation verification on the formalized formula, and judging correctness of a reasoning process and a conclusion. According to the method, an English text describing mathematical knowledge is automatically converted into a formalized language with complete semantic information, and automatic reasoning verification of the mathematical knowledge is realized on the basis of the formalized language; the method does not depend on a data set, does not need model training, and has wide application scenes and remarkable values in the fields of mathematical theory research, computer-aided proof, mathematical software development and the like.

The invention relates to the technical field of image processing, in particular to a binary full-order polynomial image interpolator and a binary full-order polynomial image interpolator method, the binary full-order polynomial image interpolator is composed of an ROM chip, an RAM chip and a matrix multiplier of a storage matrix, and the input end of an interpolator module is connected with the output end of a low-resolution image sensor; the output end of the interpolated high-resolution image signal is connected with an image display screen or a memory; according to the method, a binary total-order polynomial is used as an image interpolation function, and the term number of the binary total-order polynomial must be the square of a positive integer; according to strict proving, a powerful mathematical theory is used as a support, a reasonable image interpolation method is designed by adopting a binary full-order polynomial, low-resolution images and videos can be converted into high-resolution images and videos to be stored, the images obtained after interpolation are best in effect, clear in image and high in resolution, and the method is suitable for large-scale popularization and application. Distortion cannot be caused, and the requirement for high-quality image processing is met.

The application is based on the unmanned ship formation encounter risk space-time analytic method of quantum field theory, including the following steps: constructing the initial quantum state of the ship, accurately characterizing the uncertainty distribution of the ship position through the Gaussian wave packet model; calculating the probability density of the ship at a certain state at a certain time; superposition calculation of the sum of the probabilities of all position pairs of two ships satisfying the geometric collision condition; based on the sum of the probabilities of all position pairs of two ships satisfying the geometric collision condition, the total value of the risk potential field of the encounter risk of two ships is calculated; the total value of the risk potential field of the encounter risk of two ships is compared with the risk threshold value, and whether the two ships exist the risk of collision is judged, the method of the application realizes the fundamental paradigm conversion from the classical trajectory description to the quantum field operator description by establishing the multi-level calculation framework under the quantum mechanics form system, and provides a new mathematical theoretical basis for the ship navigation risk analysis.

A fractal model method for researching mineral impact energy and particle size distribution characteristics comprises the following steps: firstly, establishing a fractal model of particle size distribution of crushed magnetite according to a fractal mathematical theory, representing the particle size condition after crushing by using a fractal dimension D, and then repeatedly performing crushing experiments under different impact crushing energies through a falling weight impact testing machine to obtain the fractal model of the particle size distribution of the crushed magnetite. The method comprises the following steps of: crushing ore, collecting crushed ore particles, realizing size grading through screening, weighing and recording the weight of the particles of each size grade, and establishing an ln (M (x) / M) and ln (x / xmax) functional equation under different impact energies according to an established fractal model; further establishing a functional equation of the fractal dimension D and different impact crushing energies; by means of the method, the function relation between the magnetic iron ore crushing particle size condition and the impact crushing energy can be constructed, the function relation obtained through the method can further guide and adjust the crushing energy of crushing equipment, and therefore the particle size condition of the crushed magnetic iron ore is controlled.

The invention provides a method and a device for determining a main field operation direction of an agricultural machine, and the method comprises the steps: fitting a fitting polygonal region of a field plot through employing the mathematical theories of concave points, edges and included angles, and then determining an allowable edge through employing the mathematical theories of edges, slopes and the like on the basis of the fitting polygonal region, thereby planning the main operation direction of the agricultural machine. According to the method, the real field plot area can be restored with high precision, the method can be suitable for various field plots which do not need to be segmented and can be completed in one time in different shapes, the generalization ability is high, it can be ensured that the optimal path is planned, and the operation efficiency is improved.

This invention discloses a relative acoustic impedance prediction method for composite microperforated plate structures based on a surrogate model, belonging to the field of vibration and noise control technology. This invention considers the structural parameters of variable cross-section series-parallel composite microperforated plate structures and uses Latin hypercube sampling to generate parameter samples. Relative acoustic impedance data for different structures are obtained through numerical simulation. Fourier series functions are constructed using the relative acoustic impedance data to solve for the fitting coefficients, thus achieving a fit to the relative acoustic impedance. A multi-input / output multilayer perceptron neural network is built to predict the fitting coefficients based on the structural parameters, forming a relative acoustic impedance prediction surrogate model with the fitting coefficients as an intermediate bridge. The relative acoustic impedance prediction method of this invention effectively solves the contradictory problems of high accuracy but long time consumption in numerical simulation of acoustic superstructures, and high requirements for mathematical theory and low accuracy in analytical solution derivation, thus balancing the accuracy and efficiency of acoustic superstructure design.

The invention discloses a method for predicting the paleo-water flow direction of a braided river based on a linear fractal theory. The method comprises the following steps: S1, collecting well drilling data of a known unit, and drawing a plane layout diagram of the paleo-water flow direction of the known unit braided river; s2, coarsening the known unit plaid river paleocurrent direction plane distribution diagram to obtain a known unit coarsening model; s3, coarsening the model of a known unit, and solving linear fractal parameters according to known paleocurrent nodes; s4, utilizing a linear calculation formula to predict the palaeowater flow direction of the unknown unit to distinguish the river, and drawing a distribution diagram; and S5, according to actual geology, perfecting the plane distribution map of the paleocurrent direction of the unknown unit, and completing prediction of the paleocurrent direction of the braided river. According to the method for predicting the paleo-water flow direction of the braided river based on the linear fractal theory, the paleo-water flow direction is predicted through the mathematical theory, the accuracy of predicting the paleo-water flow direction of the braided river in a non-exploration mature area is improved, and the problem that prediction cannot be conducted due to lack of data in the non-mature exploration area is solved.

The application discloses a CAD large model method and system based on AI and vector bundle, and belongs to the field of computer-aided design. The method comprises the following steps: S1, constructing a mathematical model of manifold space, and mapping three-dimensional information of an object to a linear space through a vector bundle; S2, collecting drawing data of multiple industries, and constructing a drawing data set of multiple industries; S3, pre-training the drawing data set of multiple industries through the mathematical model of manifold space, and extracting feature template tensors corresponding to drawings of each industry; S4, based on the feature template tensors, using a large model with an embedded M-MoE architecture to encode, decode and cyclically optimize and update parameters; and S5, mapping the manifold tensor output in the previous step to a three-dimensional space, generating CAD drawings and reports, and cyclically optimizing and outputting results through a loss function. The application constructs a CAD large model based on artificial intelligence and vector bundle mathematical theory, and realizes intelligent drawing generation, automatic auditing, language interactive editing and full life cycle management.

The invention provides a vibro-replacement gravel pile composite foundation equivalent permeability coefficient calculation method which comprises the steps that a three-dimensional finite element seepage calculation model of a pile-soil composite foundation is established, theoretical analysis is combined, the seepage law of the composite foundation is explored, and the equivalent permeability coefficient calculation method suitable for horizontal and vertical seepage of the composite foundation is given. The influence factors such as the permeability coefficient of the gravel pile, the permeability coefficient of soil around the pile and the gravel pile replacement rate m are comprehensively considered, the influence factors are comprehensively considered, and the calculation result precision is high; the calculation method is simple and convenient, the formula is simple and clear, complex mathematical theories and numerical models are not adopted, and the calculation process is greatly simplified; the three physical quantities including the gravel pile permeability coefficient, the pile periphery soil permeability coefficient and the gravel pile replacement rate m required by the calculation method are very convenient to obtain in engineering practice, and the calculation method has high practicability and wide applicability.

This invention discloses a method, system, device, and medium for characterizing the intrinsic features of spatial field strength distribution. It verifies the existence of intrinsic features by constructing characteristic basis functions of the field strength distribution, then establishes an eigenvalue set through eigenmode decomposition, and iteratively solves the corresponding constraint functions. The final eigenvalue dataset is used to characterize the intrinsic features of the spatial field strength distribution, improving the feature analysis capability of electromagnetic information in the spatial domain. Based on a reasonable characterization of the intrinsic features of the field strength distribution, it uses sparse space construction as a breakthrough to reduce the sampling rate and the non-correlation of the sampling matrix and sparse basis as constraints to construct sparse basis and sampling methods. This combines basic electromagnetic field theory, signal processing methods, and mathematical theory, filling the gap in the theoretical research on the construction of characteristic functions in the spatial domain for electromagnetic signal time-frequency analysis.

A fractal model method for studying the impact energy of minerals and the particle size distribution characteristics, first, according to the mathematical theory of fractal, the fractal model of the particle size distribution of magnetite crushing is established, the fractal dimension D is used to represent the particle size after crushing, then the crushing experiment under different impact crushing energy is repeatedly carried out through the falling weight impact testing machine, and the crushed ore particles are collected, the particle size grading is realized through screening, then the weight of each particle size level is weighed and recorded, then according to the established fractal model, the function equation of ln(M(x) / M) and ln(x / xmax) under different impact energy is established; Further, the function equation of fractal dimension D and different impact crushing energy is established; Through this method, the function relationship between the particle size of magnetite crushing and the impact crushing energy can be constructed, and the function relationship obtained by this method can guide the adjustment of the crushing energy of the crushing equipment, so as to control the particle size of the crushed magnetite.

The invention provides an MCMC-based dam foundation engineering rock mass displacement prediction method, which is realized on the basis of cross application of numerical analysis software and mathematical calculation software, is used for parameter inversion and model state estimation during dam foundation excavation, and specifically comprises the following steps of: establishing a high arch dam foundation three-dimensional numerical calculation model; a constitutive equation of a dam foundation columnar jointed rock mass is combined to carry out three-dimensional numerical calculation analysis, the deformation and stress distribution change rule of the dam foundation rock mass in the step-by-step excavation process is studied, a Markov Monte Carlo method (MCMC) is utilized to carry out dynamic estimation and parameter correction on a model in the step-by-step excavation process, and therefore the dam foundation columnar jointed rock mass deformation and stress distribution change rule is obtained. According to the method, the uncertainty of rheological mechanical parameters can be qualitatively and quantitatively analyzed, understanding of engineering on the dam foundation excavation unloading state is deepened, a better dam foundation state prediction effect is achieved, the mechanical mechanism and the mathematical theory are combined, and displacement prediction of high arch dam foundation excavation with the data driving method combined with the mechanical mechanism is achieved.

The invention discloses a gold bonding wire motion trail modeling and electrical parameter extraction method, which comprises the following steps of: simulating gold bonding wire parameters of a full-automatic bonding machine through software programming, and outputting an image containing a gold wire motion trail; establishing a mathematical function expression for the motion trail of the gold wire in the image through a mathematical theory analysis method, and determining numerical values of fitting parameters in the mathematical function expression; importing the mathematical function expression into three-dimensional electromagnetic software to construct a gold wire three-dimensional physical model, simulating the gold wire three-dimensional physical model, and extracting simulation physical parameters and simulation electrical performance parameters of the gold bonding wire; accurately testing the gold bonding wire by using a TRL calibration test fixture to obtain actually measured physical parameters and actually measured electrical parameters of the gold bonding wire; and comparing the simulated physical parameters and the actually measured physical parameters of the gold bonding wire, and comparing the simulated electrical parameters and the actually measured electrical parameters of the gold bonding wire. According to the method, the motion trail and the electrical parameters of the gold wire can be accurately described, and accurate design of the hybrid integrated circuit is facilitated.

The invention discloses an image noise reduction method based on multi-parameter Hardy function space analysis, and relates to the field of image noise reduction, and the method is based on the unique mathematical theory of a multi-parameter Hardy space in the harmonic analysis field, and carries out the deep analysis of an image pixel matrix through constructing a model adaptive to an image signal. In the transformation process, high-frequency and low-frequency components and noise components of the image can be accurately separated through the method. By analyzing the transformation coefficient of the image in the multi-parameter Hardy space, noise and image real signals can be effectively identified and separated. The method has the advantages that parameters can be flexibly adjusted according to different image features and noise types, and self-adaptive noise reduction is achieved. Experimental results show that the method retains key detail information such as image edges and textures to the greatest extent while effectively removing various noises, remarkably improves image quality, and has wide application prospects in the fields of medical images, satellite remote sensing images, security monitoring and the like.

A method for constructing an integrated energy system optimal scheduling model considering virtual heat storage, relating to the technical field of power systems. The method comprises: establishing operational models of working equipment of an integrated energy system, establishing an integrated demand response model for integrated energy loads and an orderly charging model for electric vehicles, and establishing a heating network energy flow calculation model considering virtual heat storage; on the basis of a mathematical theory, processing a direct current power flow model of a power distribution network, and by using a second-order cone relaxation method, converting general power flow constraints into mixed integer quadratically constrained programming constraints; and according to power flow constraints of the power distribution network, a heating network and a gas network of the integrated energy system, by taking minimization of the total operating cost of an integrated energy operator as an objective function, constructing an integrated energy system optimal scheduling model considering virtual heat storage. The method achieves accurate description of operating characteristics of integrated energy systems, so as to implement coordinated optimal scheduling of multiple energy sources and improve the economy, environmental protection property and reliability of the systems, thus providing support for efficient operation of the integrated energy systems.

The present invention discloses an interpretable small target detection method based on Gaussian curvature, which mainly solves the problem of low detection accuracy of existing methods. The implementation steps are as follows: obtaining a training sample set and a test sample set; constructing an interpretable small target detection model based on Gaussian curvature: including a backbone network and a structural feature enhancement network arranged in parallel with it; initializing parameters; training the small target detection model; updating the parameters of the small target detection model; and obtaining small target detection results. In the present invention, the backbone network is used to extract features of different scales. In the structural feature enhancement network, a Gaussian curvature-guided structure extraction block is constructed in combination with mathematical theory, making the model highly interpretable. It effectively extracts texture structure information through Gaussian curvature calculation. The feature fusion block then fuses the texture structure information with multi-scale feature information to compensate for target features lost in the downsampling operation of the backbone network, thereby improving the accuracy of small target detection.

The invention discloses an aero-engine key part dangerous part temperature rapid evaluation method and device, electronic equipment and a storage medium, and the method comprises the steps: S1, carrying out the calculation of a temperature value, a pressure value and a rotating speed value in a flow channel and the steady-state temperature of a key part dangerous part through employing a proportional conversion method, establishing a temperature calculation order reduction model in a transition state and acquiring model parameters; and S2, substituting the material parameters of the aero-engine key component, and the temperature value, the pressure value and the rotating speed value corresponding to the main runner under the life calculation point into the temperature calculation reduced-order model in the transition state to quickly calculate the transient temperature of the dangerous part of the aero-engine key component in any state. According to the method, the temperature of the dangerous part of the key part is directly and quickly calculated by substituting the flight parameters into the established mathematical theoretical model, so that the consumption of hardware resources and solving time in large-scale simulation solving is avoided, the calculation speed is improved to millisecond magnitude, the design period is shortened, and the calculation cost is reduced.

A wave field control method in an elastic thin plate based on potential theory, comprising: based on wave propagation principle and partial differential equation mathematical theory in an elastic medium, describing the wave field in the elastic thin plate generated by a source term with compact support property, combining partial known data on the boundary of a given region and radiation conditions at infinity, establishing an external problem of wave field control; based on the basic solution and potential theory, formulating an integral representation of the wave field satisfying the external problem, obtaining the corresponding relationship between the boundary data and the wave field; according to the corresponding relationship, converting the wave field control problem in the elastic thin plate into a single-dipole distribution problem on the boundary of the given region, the goal of the single-dipole distribution problem is to generate a control field with zero inside the given region and non-zero outside, using the method combining finite difference and numerical integration, discretizing the control field of the wave field, establishing the corresponding relationship between the approximate control field of the wave field and the single-dipole, based on the corresponding relationship between the approximate control field and the single-dipole, using the method combining finite difference and moment method to establish a boundary element model, and solving the boundary element model to obtain the calculated values of the single-dipole position and amplitude, then bringing them into the discretization expression of the control field of the wave field to obtain the calculated value of the approximate control field of the wave field, finally realizing the control of the wave field in the elastic thin plate.

The invention discloses a vehicle-pile-network interaction data fusion method based on a fuzzy mathematical theory, and belongs to the field of intelligent traffic systems and electric vehicle charging infrastructures, and the method comprises the steps: firstly collecting vehicle, pile and network original data, and carrying out the time-space alignment, standardization and abnormal value processing, thereby providing a high-quality basis for subsequent fusion; fuzzifying the key data by using a fuzzy membership function to improve a federated weighted average method to realize data-level fusion to obtain a unified fuzzy data set; on the basis, constructing a five-dimensional feature matrix, extracting key principal components through principal component analysis, completing feature-level fusion, and extracting core features; and finally, constructing a fuzzy rule base, calculating a rule weight by using a Dasarathy model, screening significant and important rules to realize decision-level fusion, and integrating multi-stage results to output final fusion data. According to the method, the data fusion precision and reliability are improved, and city-level vehicle-pile-network regulation potential quantification and efficient cooperative operation are assisted.

The application discloses an automatic formal fault analysis method for block ciphers, which comprises three stages of formal fault propagation model establishment, fault attribute mining and formal fault analysis. The formal fault propagation model of the cipher core measures the propagation process of faults in the cipher iteration. The method can automatically establish a formal fault propagation model for the cipher core design and is suitable for describing the propagation process of different types of faults in the cipher iteration. In the fault attribute mining stage, inherent behavior patterns are extracted from the fault trajectory simulated by the formal fault propagation model as fault attributes, thereby providing mathematical theory support for the formal analysis. In the formal fault analysis stage, the formal verification tool is used to automatically search for correct keys based on the extracted fault attributes. The method has better scalability and universality, does not require complex formula derivation, supports ciphertext-only analysis, and can recover the keys only by using a small amount of ciphertext, and is more effective than the existing method.