Generally speaking, there are three dynamic modeling methods for flexible multi-body systems: The first is Newton-Euler method, which requires the momentum theorem to clarify the corresponding dynamic equations of all separated bodies, and then use constraints to remove the corresponding constraints. This method meets the requirement that there is a rigid body in the system. Secondly, it refers to the virtual displacement method, which should combine the virtual displacement principle to obtain the first Lagrangian equation, or combine the variational principle to construct the second Lagrangian equation, so as to obtain the dynamic model. Finally, it refers to other typical methods such as IGC, AIGC, NSD, etc.^{[1]}

^{nq}^{nq×nq} The generalized mass matrix representing positive definite symmetry of the system, ^{nq}^{nq}^{n}^{×q} Stands for Lagrange times subvector,

Is the constraint matrix, ^{nq}^{nq}^{nq}^{[2]}

In the above formula, P represents relative or absolute coordinates in the floating coordinate system, and A represents deformation coordinates.

Modeling and numerical simulation are the core content of the study of dynamics of flexible multi-body system. It is very difficult to quickly construct the corresponding motion equations of the system, especially to form the numerical solution equations required by computer operation. Due to the large scale of solving the coefficients and variables of the dynamics equation of flexible multi-body system, the actual derivation process is complicated, so the symbolic calculus method is used to deal with the modeling of the system by using finite element method.^{[3]}

^{[4]}:

^{[5]}

There are many methods to transform algebraic mixed equations into numerical models, such as augmented method, reduced method and mixed method. Based on the analysis of the algebraic equations obtained in the above research, it can be seen that:

Taking the derivative of t using the second expression of the algebraic equations, we can get:

Among them:

The compatible conditions are as follows:

According to an antenna in the flexible multi-body system dynamics model, the control equation of characteristic analysis, comparison on the relatively mature after the numerical simulation method, the constraint default direct correction method, the precise integration method, the nonlinear programming method acquired two, on the basis of continue to analyze the solving process, actual problems and computational cost, In the end, the direct default correction method of the augmented method is selected for solving analysis. The specific process is as follows:^{[6]}

The above formula conforms to

This condition. For nq+nλ unknown variables q and λ, the above equations belong to closed algebraic equations, and the actual solvability will be affected by the non-singularity of the coefficient matrix. In order to better analyze the application principle of direct default correction method, we can first define the method of constraint stability. In Baumgarte (Baumgarte) constrained default stability method, the following equations can be obtained because of the large error accumulation:

The above formula conforms to

Generally speaking, α, β=5 ~ 50 should be set as the critical error resistance state under the condition of α=β, and the actual response stability is faster. The Lagrange multiplier can be obtained by combining the number of dynamic equations of flexible multi-body system and the actual derivative results:

After sorting, it can be obtained:

The above formula conforms to ^{*} = ^{T}^{−1}^{T}^{−1} (^{−1}

On the one hand, coordinate default should be corrected. The numerical solution of the coordinate at time t=t (I) is assumed to be

Taylor expansion of the position constraint equation can obtain:

Among them:

After sorting, it can be obtained:

In general, because the number of generalized coordinates exceeds the number of constraint equations in the system, in other words ^{nq × nq} Is full row rank. Combined with the generalized force theory analysis of the matrix, because the constraint equation is not independent, so there is (GCT) −1, then the generalized inverse G+ (q, t) equation of the Jacobi matrix G (q, t) is: ^{+} (^{T}^{T}^{−1}

At this point, the minimal norm solution is obtained, as follows:

Minimal norm solution ^{(i)} As the least influential correction during the study of the dynamics equation, the generalized coordinates can be obtained which are closest to the real motion of the system, which is very important for numerical simulation research.

On the other hand, speed default is corrected. Combined with the above analysis, the hypothesis is consistent

For this condition, the modified item is ^{(i)}, Then we can get:

The constraint equation of the corresponding velocity is:

By simplifying the conditions, we can get:

Thus, the equation of velocity correction value can be obtained as follows:

The minimal norm solution of the above equation is studied by using the computational method of nonlinear programming method, and the specific results are shown as follows:

In the study of the basic numerical methods of dynamic equations, the following points are specific: First, Treanor method. Assume that the unknown function value at tj is yij (I = 0,1... N-1), then calculate the unknown function value yi of tj+1=t+h, j+1, the formula is:

Where, when PI ≤0 is met, the following equation can be obtained:

In accord with pi> When the condition is 0, we can get:

In the above formula:

Among them, qi should be defined in combination with the following formula:

^{[8]}

Second, Gill's law. Kiel's formula for integrating from t to t+h is:

Among them:

In the above formula:

Where, yi (o) represents the position function value yi (t) at point T, yi (4) represents the unknown function value yi (t+ H) at point T + H after one step of integration, qi (O) represents that the initial value is 0, and qi (4) is regarded as the next qi (O) at each step of integration. In practice, this method can offset the rounding error accumulated in each step, effectively improve the accuracy of integration application, and has strong numerical stability for ill-posed dynamic equations. At the same time, the equation calculation has a lower stage error, compared with other methods can improve the integration speed, the actual calculation is also effectively controlled, the overall program has been improved. Third, the Gear method. The general expression formula is:

Using Taylor expansion, the order is p=k, and the coefficient αj (j= 0,1 …) can be calculated under the condition that k= 1–6. K-1), βk, and the corresponding formula can be obtained:

When K= 1,2, the method is a-stable, and when K= 3 ~ 6, the method is A (α) -stable and rigid stable. The results of A (α) -stable α Max and rigid stable parameters Dmin and θ Max are shown in the table 1 below:

Stability parameter analysis

K | 1,2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|

_{max} |
A - stable, 90° | 86°54′ | 73°14′ | 51°50′ | 18°47′ |

_{min} |
0 | 0.1 | 0.7 | 2.4 | 6.1 |

_{max} |
0.75 | 0.75 | 0.75 | 0.5 |

There are many countermeasures to improve this method, as shown below:

In the above formula, assuming βk is not equal to 0, and meets βk+β K-1 =1 condition, then we still need to calculate the order P =k in the formula, and βk=β is regarded as a free parameter, using Taylor expansion and k order compatible conditions, accurately calculate the corresponding expression formula.

Assuming β=20, the following formula can be obtained:

Compared with the Gear method of the same order, the actual stability region of these formulas is larger, and the corresponding results are shown in the following table:

Stability region comparison results

K | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|

Improve gill method | A - stable | 89°55′ | 85°32′ | 73°2′ | 51°23′ | 18°32′ |

Jill method | A - stable | 86°54′ | 73°13′ | 51°50′ | 18°47′ | unstable |

It can be seen that the disadvantage of this method is that the order of the equation keeps rising, the initial value is difficult to judge, and the multi-step time discrete has a comprehensive influence on the constraint equation, resulting in the drift of the solution. In other words, the rigidity should not be too high, and the Gear method will lose effect when the integral variable appears high-frequency oscillation, because the Gear method does not have A stability region.

The whole software system design includes the finite element analysis, structural design, the content such as geometry modeling, optimization design module, the deployment dynamics analysis module is the process in control, and to exchange data information of an operation, the corresponding numerical simulation module is master data information during the process control need to know. It can be seen that numerical simulation module is the basic requirement to ensure that the process control module can play an effective role. Flow chart 1 of the system platform constructed for deployable antenna in this paper is shown as follows:

The corresponding design system flow chart 2 is:

Flow chart 3 of the numerical calculation module is:

First, we have to deal with differential equations. In order to calculate the differential equation more quickly, it is necessary to deal with the equation obtained in the above research effectively. Because the equations are nQ-dimensional second order ordinary differential equations, so _{1} = _{2} =

Among them,

Assuming t=0, the initial formula of the system is:

Then the above equation of dynamics can be numerically integrated.

Secondly, we need to deal with numerical simulation methods. In this paper, a numerical integration method library is constructed, which contains a variety of different methods for effective selection during simulation. At present, in addition to several methods proposed in this paper, runge-Kutta method with fixed or variable step size and Gear method with variable step size and variable order are also involved. In addition, input more parameters, such as simulation start time, end time, etc.

Finally, the kinetic equation must be calculated and analyzed. On the one hand, for the multi-body system with closed loop, its dynamics equation is differential mixed equation, which needs to be contracted to obtain the pure differential form of the system dynamics equation, which is consistent with the dynamics equation of the tree multi-body system in form, and can be treated and solved in the same way. On the other hand, when the joints in the system have active drive, the simulation should focus on the justice mixing problem.^{[9,10]}

On the one hand, the study of the dynamics of rigid crank is mainly to verify the accuracy of the numerical simulation model. The Gill method of fixed step length is used to study the movement of rigid crank under the action of constant driving torque. The cross section of homogeneous crank is rectangular and shows a trend of horizontal rotation. At this point, the model parameters of the rigid crank involve the arm length L reached 0.75 meters, the cross-sectional area A was 60×15×10 square meters, and the mass M reached 1.4 kg. The driving torque is 62N•m, the crank is in horizontal position at the initial moment, and the initial conditions are as follows:

Among them, the left figure is based on the results obtained from the theoretical research of traditional fixed-axis rotation mechanics, and the right figure is the results obtained from the theoretical simulation analysis of multi-body system dynamics in this paper. Combined with the model parameters, the actual angular acceleration of the crank is 236.19rad/s2. Therefore, it can be found that, on the one hand, the rigid model obtained according to the dynamic model is valid; on the other hand, the dynamic response obtained by the program is consistent with the traditional calculation, which further indicates the correctness of the design model studied in this paper.

On the other hand, the dynamics of two - link flexible manipulator is simulated. The corresponding model is shown in Figure 6 below:

Assuming that both links are in horizontal position at the initial moment and the actual deformation is 0, the initial conditions are as follows:

Gill method with variable step size was used for analysis. The integral step size was H = LE-4, the simulation accuracy was EPS = le-L2, the simulation time was tend=1.2sec, and the calculation time was 2min56sec. The left and right graphs in FIG. 7 show the relation curves between angular velocity and time of two connecting rods at angles θ1 and θ2 respectively.

The Treanor method with fixed step length is used for analysis. Except that the calculation time is 47sec, other conditions are consistent. The relation between the actual angular velocity and time of the two connecting rods is shown in Figure 8 as follows:

Meanwhile, the above two methods are used to calculate the simulation results of h= LE-5 and H = LE-6 integral step sizes respectively. The actual calculation speed is shown in Table 3 below:

Speed comparison

The integral step | Le-4 | Le-5 | Le-6 |
---|---|---|---|

Variable step size Gill | 2min56sec | 48min6sec | 2h43min53sec |

Fixed step length Treanor | 47sec | 8min21sec | 11min20sec |

Combined with the analysis in Table 3 above, it can be seen that Gill method takes a long time to calculate a small integral step. However, Treanor method has no clear requirements on the integral step length, and the actual settlement time is very close. Compared with the corresponding dynamic change graphs, Gill's method has stronger stability for numerical solutions than Treanor's method, with higher actual accuracy. With the increase of calculation time, the angular velocity of the two links will continue to rise, which may cause dynamic hardening and increase the probability of data simulation failure.^{[11,12]}

To sum up, the flexible multi-lift system dynamics studied in this paper integrates multiple disciplines. The actual development not only supplements and summarizes the original discipline, but also expands the thinking space of researchers and scholars, and promotes the construction of practical numerical simulation models to be more diversified. At present, the research work of flexible multibody system dynamics has obtained many research results from modeling scheme, symbolic calculus, tempering effect, numerical simulation and so on. Although related research is still a new subject, with the continuous exploration and data accumulation of domestic and foreign researchers, it is inevitable to start from this in the future development of deployable antenna application optimization. In addition, the future research direction of flexible multi-body dynamics will also change. For example, because the current high-precision integration algorithm cannot meet the requirements of implementation simulation, researchers should continue to discuss the appropriate simulation algorithm. In the calculation strategy, we can choose a new modeling method and computing system, such as recursive model, so as to make use of the parallel processing and vector processing capabilities of multi-processing computing, and conduct in-depth research on the simulation of relevant models.

#### Speed comparison

The integral step | Le-4 | Le-5 | Le-6 |
---|---|---|---|

Variable step size Gill | 2min56sec | 48min6sec | 2h43min53sec |

Fixed step length Treanor | 47sec | 8min21sec | 11min20sec |

#### Stability parameter analysis

K | 1,2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|

_{max} |
A - stable, 90° | 86°54′ | 73°14′ | 51°50′ | 18°47′ |

_{min} |
0 | 0.1 | 0.7 | 2.4 | 6.1 |

_{max} |
0.75 | 0.75 | 0.75 | 0.5 |

#### Stability region comparison results

K | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|

Improve gill method | A - stable | 89°55′ | 85°32′ | 73°2′ | 51°23′ | 18°32′ |

Jill method | A - stable | 86°54′ | 73°13′ | 51°50′ | 18°47′ | unstable |

Law of interest rate changes in financial markets based on the differential equation model of liquidity Research and implementation of smart city public information mining analysis system based on mobile edge model of game theory Basalt fibre continuous reinforcement composite pavement reinforcement design based on finite element model Design of college education evaluation based on accompanying data acquisition and mathematical analysis Industrial transfer and regional economy coordination based on multiple regression model Enterprise financial strategy and performance management analysis based on principal component analysis Study on the Dynamic Change of Regional Water Level and Climate Based on Forecast Equation Satisfactory consistency judgement and inconsistency adjustment of linguistic judgement matrix Municipal Civil Engineering Construction Based on Finite Element Differential Equations Financial Risk Prevention Model of Financial Institutions Based on Linear Partial Differential Equation Analysis of the relationship between industrial agglomeration and regional economic growth based on the multi-objective optimisation model Constraint effect of enterprise productivity based on constrained form variational computing The impact of urban expansion in Beijing and Metropolitan Area urban heat Island from 1999 to 2019 Ultrasonic wave promoting ice melt in ice storage tank based on polynomial fitting calculation model Training Model of Basketball Offensive Route Based on Nonlinear Differential Equation Optimization Algorithm of New Media Hot Event Push Based on Nonlinear Differential Equation Mathematical Differential Equation in Calculating the Strength of Building Beam Structure Impact Resistance Stability of Building Structural Engineering Based on Fractional Differential Equations The Technical Research on the Assessment of Network Security Situation Based on D-S Evidence Theory Computer big data modeling system based on finite element mathematical equation simulation Uniqueness of system integration scheme of artificial intelligence technology in fractional differential mathematical equation Uniqueness of system integration scheme of artificial intelligence technology in fractional differential mathematical equation The Composition System of Pop Music Movement Based on Finite Element Differential Equations The Structure and Influencing Factors of Innovation and Entrepreneurship Ability of Higher Vocational Students Based on Structural Equation Model Model System Study of Accordion Score Based on Fractional Differential Equations Data mining of Chain convenience stores location Parameter Id of Metal Hi-pressure State Equation P-Matrix Reasoning and Information Intelligent Mining Research on Detection Model of Abnormal Data in Engineering Cost List Research on deformation monitoring of tunnel engineering based on 3D laser scanning Intelligent Recommendation System for English Vocabulary Learning – Based on Crowdsensing Application of Nonlinear Fractional Differential Equations in Computer Artificial Intelligence Algorithms Preservation and utilisation of historic buildings in old district of Guangzhou from the perspective of space syntax Application of calculus function and value chain analysis method in the quantification of financial flexibility management indicators Copyright protection of original online music products based on applied statistical mathematics – take music trade network as an example Optimal Research in Piano Shape Sound and Sound Propagation Model Based on Nonlinear Differential Equations Regarding new wave distributions of the non-linear integro-partial Ito differential and fifth-order integrable equations Badminton players’ trajectory under numerical calculation method Research on the influencing factors of agricultural product purchase willingness in social e-commerce situation Research on mathematical quantitative model of the incremental cost and income of green small towns based on the whole life cycle Mathematical methodology in the seismic resilience evaluation of the water supply system Prediction of surface quality in end milling based on modified convolutional recurrent neural network Research on sustainable design of sports centre based on algorithm verification Research on an early warning model of effectiveness evaluation in ideological and political teaching based on big data Innovations to Attribute Reduction of Covering Decision System Based on Conditional Information Entropy Numerical simulation of vortex vibration in main girder of cable-stayed bridge based on bidirectional fluid–structure coupling Optimisation of construction mode of residential houses based on the genetic algorithm under BIM technology A study on the reform of college English education inspired by the cultural differences between China and the United States Research on innovative strategies of college students’ English teaching under the blessing of big data Institutional investor company social responsibility report and company performance Research on multi-dimensional optimisation design of user interface under Rhino/GH platform Mathematical analysis of China's birth rate and research on the urgency of deepening the reform of art education First-principles calculations of magnetic and mechanical properties of Fe-based nanocrystalline alloy Fe _{80}Si_{10}Nb_{6}B_{2}Cu_{2}Has the belt and road initiative boosted the resident consumption in cities along the domestic route? – evidence from credit card consumption Attitude control for the rigid spacecraft with the improved extended state observer A long command subsequence algorithm for manufacturing industry recommendation systems with similarity connection technology Application of Higher-Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Informatisation of educational reform based on fractional differential equations Application research on piano teaching in colleges and universities based on remote wireless network communication Research on the control of quantitative economic management variables under the numerical method based on stochastic ordinary differential equations Network monitoring and processing accuracy of big data acquisition based on mathematical model of fractional differential equation System dynamics model of output of ball mill Sensitivity Analysis of the Waterproof Performance of Elastic Rubber Gasket in Shield Tunnel Design of Morlet wavelet neural network to solve the non-linear influenza disease system Motion about equilibrium points in the Jupiter-Europa system with oblateness Badminton players’ trajectory under numerical calculation method Ultra-short-term power forecast of photovoltaic power station based on VMD–LSTM model optimised by SSA Optimal preview repetitive control for impulse-free continuous-time descriptor systems Development of main functional modules for MVB and its application in rail transit Analysis of agricultural economic development and optimisation measures under the strategy of rural revitalisation Study on the impact of forest fire prevention policy on the health of forest resources Value Creation of Real Estate Company Spin-off Property Service Company Listing Selection by differential mortality rates Digital model creation and image meticulous processing based on variational partial differential equation The modelling and implementation of the virtual 3D animation scene based on the geometric centre-of-mass algorithm The policy efficiency evaluation of the Beijing–Tianjin–Hebei regional government guidance fund based on the entropy method The transfer of stylised artistic images in eye movement experiments based on fuzzy differential equations Research on behavioural differences in the processing of tenant listing information: An eye-movement experiment Innovation of Economic Management Risk Control in Retailer Supply Chain Based on Differential Equation Model A review of the treatment techniques of VOC Some classes of complete permutation polynomials in the form of ( x ^{pm}−x +δ )^{s}+ax ^{pm}+bx overF _{p2m}The consistency method of linguistic information and other four preference information in group decision-making Statistical Model of College Ideological and Political Learning Based on Fractional Differential Equations Research on the driving principle and guiding strategy of the public's collaborative supervision of the sharing economy in my country Research on the willingness of Forest Land’s Management Rights transfer under the Beijing Forestry Development Nonlinear Differential Equation in Anti-aging Test of Polymer Nanomaterials A mathematical model of the fractional differential method for structural design dynamics simulation of lower limb force movement step structure based on Sanda movement Fractal structure of magnetic island in tokamak plasma Mechanics of Building Structural Materials Based on Lagrangian Mathematical Model Analysis Numerical calculation and study of differential equations of muscle movement velocity based on martial articulation body ligament tension Study on the maximum value of flight distance based on the fractional differential equation for calculating the best path of shot put The Mental Health Education Management of Higher Vocational Students Based on Fractional Differential Equations Sports intensity and energy consumption based on fractional linear regression equation Application of regression function model based on panel data in financial risk management of bank resource allocation University Ideological and Political Learning Model Based on Statistical Memory Curve Mathematical Equation Analysis of the properties of matrix rank and the relationship between matrix rank and matrix operations Research on Resonance Properties of Semantic Wave Fractal Fractals Based on Quantitative Analysis of English Corpus Research on urban landscape big data information processing system based on ordinary differential equations Modeling of fractional differential equation in cloud computing image fusion algorithm Study on Establishment and Improvement Strategy of Aviation Equipment Research on Financial Risk Early Warning of Listed Companies Based on Stochastic Effect Mode Nonlinear strategic human resource management based on organisational mathematical model Conventional Algorithms in Sports Training Based on Fractional Differential Equations Dynamic Nonlinear System Based on Complex System Theory in the Development of Vocational Education The Algorithm Accuracy of Mathematical Model to Improve the Transmission Speed of E-commerce Platform The Security of Database Network Model Based on Fractional Differential Equations Electric Vehicle Mechanical Transmission System Based on Fractional Differential Equations The Practice System of Physics and Electronics Courses in Higher Vocational Colleges Based on Fractional Differential Equations The Economic Model of Rural Supply and Demand Under the Data Analysis Function Based on Ordered Probit 3D Modeling System of Indoor Environment Art Landscape Design under Statistical Equation Electronic Information Security Model of Nonlinear Differential Equations The Optimization Model of College Students' Physical Exercise Motivation and Self-control Ability Based on the Mathematical Model of Probability Theory A new variety from Sichuan, China— Paris polyphylla var.nullopetalina (Trilliaceae)Impact of ASEAN-China free trade area on fishery value chain based on difference-in-difference method Spatial–temporal graph neural network based on node attention A contrastive study on the production of double vowels in Mandarin Mathematical analysis of civil litigation and empirical research of corporate governance Health monitoring of Bridges based on multifractal theory Health status diagnosis of the bridges based on multi-fractal de-trend fluctuation analysis Application and risk assessment of the energy performance contracting model in energy conservation of public buildings Sensitivity analysis of design parameters of envelope enclosure performance in the dry-hot and dry-cold areas TOPSIS missile target selection method supported by the posterior probability of target recognition The incentive contract of subject librarians in university library under the non-linear task importance Research on indoor environment design of comprehensive commercial shopping center based on numerical simulation Empirical analysis of the economic absolute income hypothesis based on mathematical statistics Realization of Book Collaborative Filtering Personalized Recommendation System Based on Linear Regression Equation Study on Interactive Relations between Enterprise Social Media and Decision Style Based on a vector Autoregressive Model Research on Dynamics of Flexible Multibody System with Deployable Antenna Based on Static Lagrangian Function The Optimization of Mathematics Teaching Models in Colleges and Universities Based on Nonlinear Differential Equations Study on spatial planning and design of learning commons in university libraries based on fuzzy matrix model The Stability Model of Piano Tone Tuning Based on Ordinary Differential Equations Construction and application of automobile user portrait based on k-mean clustering model The Homework Model of Screening English Teaching Courses Based on Fractional Differential Equations Research on a method of completeness index based on complex model Fake online review recognition algorithm and optimisation research based on deep learning Research on the sustainable development and renewal of Macao inner harbour under the background of digitisation Support design of main retracement passage in fully mechanised coal mining face based on numerical simulation Study on the crushing mechanism and parameters of the two-flow crusher Interaction design of financial insurance products under the Era of AIoT Modeling the pathway of breast cancer in the Middle East ARMA analysis of the green innovation technology of core enterprises under the ecosystem – Time series data Image design and interaction technology based on Fourier inverse transform Calculus Logic Function in Integrated Manufacturing Automation of Single Chip Microcomputer Football Offense Training Strategy Based on Fractional Differential Mathematical Modeling Research on China interregional industrial transformation slowdown and influencing factors of industrial transformation based on numerical simulation The medical health venture capital network community structure, information dissemination and the cognitive proximity The Mathematical Analysis Model of Educational System in Music Courses in Colleges and Universities Continuing Education Network Data Center Model Based on Fractional Differential Mathematical Equations A generative design method of building layout generated by path Analysis of the causes of the influence of the industrial economy on the social economy based on multiple linear regression equation Research of neural network for weld penetration control Computer Art Design Model Based on Nonlinear Fractional Differential Equations The Optimization Model of Public Space Design Teaching Reform Based on Fractional Differential Equations The Approximate Solution of Nonlinear Vibration of Tennis Based on Nonlinear Vibration Differential Equation Graphical Modular Power Technology of Distribution Network Based on Machine Learning Statistical Mathematical Equation Employment and Professional Education Training System of College Graduates Based on the Law of Large Numbers Economic Research on Multiple Linear Regression in Fruit Market inspection and Management Nonlinear Differential Equations in Preventing Financial Risks Lagrange’s Mathematical Equations in the Sports Training of College Students Simulation Research of Electrostatic Precipitator Power Supply Voltage Control System Based on Finite Element Differential Equation Research on the effect of generative adversarial network based on wavelet transform hidden Markov model on face creation and classification Research on Lightweight Injection Molding (CAE) and Numerical Simulation Calculate of New Energy Vehicle Power Flow Calculation in Smart Distribution Network Based on Power Machine Learning Based on Fractional Differential Equations Demonstration of application program of logistics public information management platform based on fuzzy constrained programming mathematical model Basketball Shooting Rate Based on Multiple Regression Logical-Mathematical Algorithm The Optimal Application of Lagrangian Mathematical Equations in Computer Data Analysis Similarity Solutions of the Surface Waves Equation in (2+1) Dimensions and Bifurcation Research on predictive control of students’ performance in PE classes based on the mathematical model of multiple linear regression equation Beam control method for multi-array antennas based on improved genetic algorithm The influence of X fuzzy mathematical method on basketball tactics scoring Optimal decisions and channel coordination of a green supply chain with marketing effort and fairness concerns Application of regression function model based on panel data in bank resource allocation financial risk management Game theoretic model for low carbon supply chain under carbon emissions reduction sensitive random demand Research on aerobics training posture motion capture based on mathematical similarity matching statistical analysis Limit cycles of a generalised Mathieu differential system Application of Sobolev-Volterra projection and finite element numerical analysis of integral differential equations in modern art design Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Research on motion capture of dance training pose based on statistical analysis of mathematical similarity matching Application of data mining in basketball statistics Application of B-theory for numerical method of functional differential equations in the analysis of fair value in financial accounting Research on the influence of fuzzy mathematics simulation model in the development of Wushu market Study on audio-visual family restoration of children with mental disorders based on the mathematical model of fuzzy comprehensive evaluation of differential equation Difference-in-differences test for micro effect of technological finance cooperation pilot in China Application of multi-attribute decision-making methods based on normal random variables in supply chain risk management Exploration on the collaborative relationship between government, industry, and university from the perspective of collaborative innovation The impact of financial repression on manufacturing upgrade based on fractional Fourier transform and probability AtanK-A New SVM Kernel for Classification Validity and reliability analysis of the Chinese version of planned happenstance career inventory based on mathematical statistics Visual positioning system for marine industrial robot assembly based on complex variable function Mechanical behaviour of continuous girder bridge with corrugated steel webs constructed by RW Study of a linear-physical-programming-based approach for web service selection under uncertain service quality The Relationship Between College Students’ Taekwondo Courses and College Health Based on Mathematical Statistics Equations A mathematical model of plasmid-carried antibiotic resistance transmission in two types of cells Fractional Differential Equations in the Exploration of Geological and Mineral Construction AdaBoost Algorithm in Trustworthy Network for Anomaly Intrusion Detection Burnout of front-line city administrative law-enforcing personnel in new urban development areas: An empirical research in China Enterprise Financial Risk Early Warning System Based on Structural Equation Model A Study on the Application of Quantile Regression Equation in Forecasting Financial Value at Risk in Financial Markets Fractional Differential Equations in the Model of Vocational Education and Teaching Practice Environment Information transmission simulation of Internet of things communication nodes under collision free probability equation Image denoising model based on improved fractional calculus mathematical equation Random Fourier Approximation of the Kernel Function in Programmable Networks The Complexity of Virtual Reality Technology in the Simulation and Modeling of Civil Mathematical Models University Library Lending System Model Based on Fractional Differential Equations Calculation and Performance Evaluation of Text Similarity Based on Strong Classification Features Intelligent Matching System of Clauses in International Investment Arbitration Cases Based on Big Data Statistical Model Evaluation and Verification of Patent Value Based on Combination Forecasting Model Financial Institution Prevention Financial Risk Monitoring System Under the Fusion of Partial Differential Equations Prediction and Analysis of ChiNext Stock Price Based on Linear and Non-linear Composite Model Calculus Logic Function in Tax Risk Avoidance in Different Stages of Enterprises The Psychological Memory Forgetting Model Based on the Analysis of Linear Differential Equations Optimization Simulation System of University Science Education Based on Finite Differential Equations The Law of Large Numbers in Children's Education Optimization System of Strength and Flexibility Training in Aerobics Course Based on Lagrangian Mathematical Equation Data structure simulation for the reform of the teaching process of university computer courses Calculating university education model based on finite element fractional differential equations and macro-control analysis Educational research on mathematics differential equation to simulate the model of children's mental health prevention and control system Analysis of enterprise management technology and innovation based on multilinear regression model Verifying the validity of the whole person model of mental health education activities in colleges based on differential equation RETRACTION NOTE Research on the mining of ideological and political knowledge elements in college courses based on the combination of LDA model and Apriori algorithm Research on non-linear visual matching model under inherent constraints of images Good congruences on weakly U-abundant semigroups Can policy coordination facilitate unimpeded trade? An empirical study on factors influencing smooth trade along the Belt and Road Research on the processing method of multi-source heterogeneous data in the intelligent agriculture cloud platform Internal control index and enterprise growth: An empirical study of Chinese listed-companies in the automobile manufacturing industry Determination of the minimum distance between vibration source and fibre under existing optical vibration signals: a study Nonlinear differential equations based on the B-S-M model in the pricing of derivatives in financial markets Fed-UserPro: A user profile construction method based on federated learning A multi-factor Regression Equation-based Test of Fitness Maximal Aerobic Capacity in Athletes Garment Image Retrieval based on Grab Cut Auto Segmentation and Dominate Color Method Financial Risk Prediction and Analysis Based on Nonlinear Differential Equations Constructivist Learning Method of Ordinary Differential Equations in College Mathematics Teaching Multiple Effects Analysis of Hangzhou Issuing Digital Consumer Coupons Based on Simultaneous Equations of CDM Model Response Model of Teachers’ Psychological Education in Colleges and Universities Based on Nonlinear Finite Element Equations A Hybrid Computational Intelligence Method of Newton's Method and Genetic Algorithm for Solving Compatible Nonlinear Equations Pressure Image Recognition of Lying Positions Based on Multi-feature value Regularized Extreme Learning Algorithm English Intelligent Question Answering System Based on elliptic fitting equation Precision Machining Technology of Jewelry on CNC Machine Tool Based on Mathematical Modeling Application Research of Mathematica Software in Calculus Teaching Computer Vision Communication Technology in Mathematical Modeling Skills of Music Creation Based on Homogeneous First-Order Linear Partial Differential Equations Mathematical Statistics Technology in the Educational Grading System of Preschool Students Music Recommendation Index Evaluation Based on Logistic Distribution Fitting Transition Probability Function Children's Educational Curriculum Evaluation Management System in Mathematical Equation Model Query Translation Optimization and Mathematical Modeling for English-Chinese Cross-Language Information Retrieval The Effect of Children’s Innovative Education Courses Based on Fractional Differential Equations Fractional Differential Equations in the Standard Construction Model of the Educational Application of the Internet of Things Optimization research on prefabricated concrete frame buildings based on the dynamic equation of eccentric structure and horizontal-torsional coupling Optimization in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics Green building considering image processing technology combined with CFD numerical simulation MCM of Student’s Physical Health Based on Mathematical Cone Sports health quantification method and system implementation based on multiple thermal physiology simulation Research on visual optimization design of machine–machine interface for mechanical industrial equipment based on nonlinear partial equations Research on identifying psychological health problems of college students by logistic regression model based on data mining Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching A mathematical model of PCNN for image fusion with non-sampled contourlet transform Nonlinear Differential Equations in Computer-Aided Modeling of Big Data Technology The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Financial customer classification by combined model Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Recognition of Electrical Control System of Flexible Manipulator Based on Transfer Function Estimation Method Automatic Knowledge Integration Method of English Translation Corpus Based on Kmeans Algorithm Real Estate Economic Development Based on Logarithmic Growth Function Model Design of Tennis Mobile Teaching Assistant System Based on Ordinary Differential Equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis High Simulation Reconstruction of Crowd Animation Based on Optical Flow Constraint Equation Construction of Intelligent Search Engine for Big Data Multimedia Resource Subjects Based on Partial Least Squares Structural Equation 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm Analysis of the Teaching Quality of Physical Education Class by Using the Method of Gradient Difference The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching Optimal Solution of the Fractional Differential Equation to Solve the Bending Performance Test of Corroded Reinforced Concrete Beams under Prestressed Fatigue Load Animation VR scene mosaic modeling based on generalized Laplacian equation Radial Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Cross-border E-commerce Platform Operation Based on Fractional Differential Equations The influence of accounting computer information processing technology on enterprise internal control under panel data simultaneous equation Research on Stability of Time-delay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Construction of comprehensive evaluation index system of water-saving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the win-lose regression function equation Automatic extraction and discrimination of vocal main melody based on quadratic wave equation Analysis of wireless English multimedia communication based on spatial state model equation Optimization of Linear Algebra Core Function Framework on Multicore Processors Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory Mathematical function data model analysis and synthesis system based on short-term human movement Human gait modelling and tracking based on motion functionalisation The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Financial Accounting Measurement Model Based on Numerical Analysis of Rigid Normal Differential Equation and Rigid Functional Equation Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate Differential equation model of financial market stability based on Internet big data 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Children’s cognitive function and mental health based on finite element nonlinear mathematical model Fractional Differential Equations in Electronic Information Models BIM Engineering Management Oriented to Curve Equation Model Leakage control of urban water supply network and mathematical analysis and location of leakage points based on machine learning Analysis of higher education management strategy based on entropy and dissipative structure theory Prediction of corporate financial distress based on digital signal processing and multiple regression analysis Mathematical Method to Construct the Linear Programming of Football Training Multimedia sensor image detection based on constrained underdetermined equation The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Application of Numerical Computation of Partial Differential Equations in Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic management rate based on parameter analysis of estimation model of ordinary differential equation Influence analysis of piano music immersion virtual reality cooperation based on mapping equation Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation Label big data compression in Internet of things based on piecewise linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Design of language assisted learning model and online learning system under the background of artificial intelligence Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups ofp -groupsThe internal mechanism of corporate social responsibility fulfillment affecting debt risk in China: analysis of intermediary transmission effect based on degree of debt concentration and product market competitive advantage Study on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Asymptotic stability problem of predator–prey system with linear diffusion Research on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Research on threat assessment problems of island air defence system based on the leader-follower model Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Study on inefficient land use determination method for cities and towns from a city examination perspective A sentiment analysis method based on bidirectional long short-term memory networks Evaluation of ecosystem health in Futian mangrove wetland based on the PSR-AHP model A study of local smoothness-informed convolutional neural network models for image inpainting Towards more efficient control of the ironmaking blast furnace: modelling gaseous reduction of iron ores in H _{2}-N_{2}atmosphereAlgorithm of overfitting avoidance in CNN based on maximum pooled and weight decay Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model