This article proposes a fault component location method based on graph theory and analyzes the properties of the elements in the fault judgment matrix. We can use the exclusive OR algorithm to determine the faulty section. On this basis, the realization model and algorithm essence of the optimal test set is given. At the same time, we propose an optimal test set design for circuit fault diagnosis based on graph theory. Finally, the realization of the article verified that the method adapts to the flexible operation mode of the active distribution network structure and can accurately determine the fault section.

#### Keywords

- Graph analysis
- Electrical equipment
- Mechanical equipment
- Failure analysis
- Electrical control

#### MSC 2010

- 05C10

A process enterprise is a relatively fixed production line established according to process conditions and requirements. The type of equipment structure is complex, and the investment is relatively large. Once the production line of a process enterprise is built, its production capacity largely depends on the operation and use of the equipment. Compared with discrete enterprises, equipment failures and shutdowns cause greater losses to enterprises [1]. This puts forward higher requirements for troubleshooting hidden troubles, finding fault causes, and troubleshooting.

Process companies often rely on various power sources and chemical reactions to perform production operations under high temperature and high-pressure conditions. Among its equipment, electrical energy equipment has an important position. This type of equipment is mostly distributed in two places: one is at the front end of the production line. It plays a role in providing energy, such as substation equipment connected to the high-voltage power grid. The second is interspersed between production equipment. It plays a role in driving and controlling single or multiple production equipment, such as various motors, control cabinets, etc. Due to the distribution and role of electrical equipment in the enterprise, we found that electrical equipment failures have the following characteristics.

1) The scope of influence is large. Once a failure occurs, the entire equipment chain under its control may be shut down, or cascading failures occur. 2) The discovery is difficult. The electrical equipment does not directly perform production operations. Most of them are left unattended, and failures are not easy to detect and manifest in production equipment failure. Equipment management personnel, often only after a lot of investigation work, can eliminate the source of the fault in the production equipment and then turn to the inspection of electrical equipment. 3) Rely on many experiences. The number of electrical equipment is huge, the control relationship is complicated, and it is difficult to locate the fault source. In the past, fault location mostly relied on the experience of managers and familiarity with equipment systems.

These characteristics of electrical equipment make it difficult to quickly locate the source of the fault and delineate the area that may be affected for emergency repair [2]. Quickly finding the equipment and its control equipment to determine the possible impact of the fault has become a difficult problem for process companies in equipment management.

The simple equipment control network in the process enterprise comprises substation equipment, control equipment, production equipment, etc. The substation equipment is located at the front end of the enterprise's production system, and the electric energy enters the production system through multi-stage voltage reduction [3]. One control device can control multiple lower-level devices, and the lower-level devices can be either control devices or production equipment. This one-way control and the controlled relationship between substation equipment, control equipment, and production equipment can form an equipment network without a closed loop.

The equipment can be decomposed according to its structure to form the equipment BOM, and each part can control a piece of lower-level equipment. For large equipment, different parts of a device are controlled by different control devices [4]. If the equipment BOM is decomposed and added to the control chain, the control chain is more complicated. Since the equipment part can be abstracted into a single piece of equipment, it is not necessary to consider adding parts to the control chain for the time being.

We abstract the device as a node while abstracting the control relationship as a directed edge. The controlling device points to the controlled device, and there is no connected directed edge if there is no control relationship between the devices. In this way, the control network can be abstracted into a directed graph represented by nodes and directed edges, which we also call a control graph. There are two main mathematical representation methods for control charts: arrays and matrices. Array notation builds nodes and processes on a multi-dimensional array to make full use of the adjacency relationship between nodes and edges. The disadvantage is that it occupies a lot of resources, and the operation is complicated. Matrix representation uses the relationship between nodes or between nodes and paths. This way of representation is convenient for the realization of computer algorithms and, at the same time, occupies fewer computer resources. The direction of the arrow along the control edge in the control diagram is called the forward direction, and vice versa. We take any device in the control diagram as a starting point, which is called a reference device [5]. Downward you can find a chain of equipment controlled by it, called the forward control chain. You can find a chain of equipment that controls it upwards, which we call the reverse control chain. The start device has only the forward control chain, and the end has only the reverse control chain.

We use points ω_{i}(^{0} (ω_{1}, ω_{2}, ⋯, ω_{n}). Since the control relationship between devices is one-way, the correct control chart is a directed chart without loops [6]. To avoid the formation of loops during the formation of computer algorithms, we sort the equipment according to the control relationship to form an ordered equipment set _{1}, ω_{2}, ⋯, ω_{n}).

The adjacency matrix is based on the control relationship between devices. The row vector _{i}_{i}_{i} in the control chart. We use _{ij}_{i}(_{j}(_{ji}_{j} to device ω_{i}. The formation of the control relationship matrix

From the one-way nature of the device control relationship, it can be seen that there is no mutual control relationship between devices, that is:

At the same time, the equipment set is ordered, and it can be seen that:

From the above characteristics of the control relation matrix, it can be known that the matrix A is an upper triangular sparse matrix. That is, there is no loop in the matrix A. In addition, the matrix A has the following characteristics:

There are _{i} controls the device of _{i} is called the controlled equipment set _{i}

The existence of _{i} is controlled by _{i} is called control equipment set _{i}

There must be at least one start device node and end device node in the device control relationship diagram [7]. We can use the control relationship matrix in this article to quickly determine whether a device is controlled or control other devices. If the column vector _{i}_{i}_{i}, ω_{i} is the starting device of the control chart. Row vector _{i}_{i}_{i} does not control any device, and device F is the end device of the control chart.

Informing the control network diagram, we denote the set of devices that have been incorporated into the control network as ^{B}_{i} | _{i}_{i} is called the next-neighbor device node. The controlled device set of all the device nodes in ^{B}^{E}_{i}_{i}_{+1} | ω_{i} ∈ ^{B}_{i+1} ∈ ^{B}_{ij}

Step1: Determine the starting device node of the control chart. Determine the starting device node-set ^{B}^{B}_{i} ∈ ^{B}

Combined with Figure 1, the pseudo-code is implemented as follows:

Function1 finds the starting device node for drawing

Search Begin Equipment (_{1}, ω_{2}, ⋯, ω_{n}))

For (ω_{i} ∩

Begin

If (_{i}

We will include ω_{i} into ^{B}

Draw the starting device node;

End

Step2: Find the next-neighbor device node from the starting device node. Starting from the starting device node ω_{i} of the control network diagram, use the control relationship matrix to determine ω_{i} the next-neighbor device node-set (^{E}

Step3: draw points and draw edges. If the next neighbor device node ω_{j} ∈ _{j} ∩ _{j} ∈

Step4: Iterative drawing. After drawing points and drawing edges of all the next neighbor nodes of the starting device node in Step3 ends, all terminal device nodes in Step2 will be used as the starting device node. Cycle Setp2 and Step3 process. After several loop iterations, the device nodes and control edges are continuously extended to form a control graph. The specific process is shown in Figure 2.

Combined with Figure 2 to achieve pseudo-code as follows:

Function 2 iteratively draw the network diagram

Init Chat (^{B}_{i} | _{i}

For (ω_{i} ∈ ^{B}

Begin

If (_{i}

For (ω_{i} ∈ _{i}

If (ω_{j} ∩ ^{E}_{j} into ^{E}

Begin

If (ω_{j} ∩ _{j} ∈

Increase the control edge;

Else increases the control edge;

End

Init Chat (^{E}

The control diagram can comprehensively reflect the control relationship between the enterprise's electrical equipment and production equipment. It can express the complex control relationship through simple graphics [9]. This is convenient for equipment managers to grasp the overall situation of the enterprise's electrical equipment control network.

In troubleshooting, searching, and controlling the scope of the fault, the control chart has a large range, and the complicated control relationship is displayed on one chart, which also brings certain difficulties to the search. Therefore, we propose two concepts of reverse control chain and forward control chain. The reverse control chain is based on a certain device as the starting point, looking upwards for the superior device that controls it and the superior device of the superior device until a control chain is formed by one or several starting devices in the control chart [10]. The forward control chain is based on a certain device as a starting point to find the lower-level equipment it controls and the lower-level equipment. A controlled chain is formed by equipment until the end of the control chart.

The reverse control chain has only one starting point as the reference device. The formation of the reverse control chain is to find the equipment set that controls the reference equipment after the reference equipment fails. Since the failure of electrical equipment is often manifested as a certain failure phenomenon of the production equipment, after the failure phenomenon occurs, the cause is often not found on the equipment exhibited by the failure phenomenon. We need to quickly show the reverse control chain of the equipment and its control relationship. This is of great help to quickly find the cause of the fault.

The formation of the reverse control chain is similar to the formation of the control chart, but the scope of equipment involved is smaller [11]. The judgment condition of the adjacent device node is the row vector _{i}

The forward control chain is to find the set of devices controlled by it after finding the source of the faulty device. Due to the complex situation of equipment failure, there are multiple possible causes. After finding the control device set, these devices can be included in the fault source. After removing the influence of the source of the fault, look for other causes of the fault. This is useful for analyzing complex faults. If the equipment set under its control has not failed, this equipment can also be used as the key preventive object when the equipment failure does not affect the function of the production line at the initial stage. The forward control chain is a special case when the starting device node number of the logical reasoning diagram of the equipment control relationship is “1”. The algorithm and implementation process are the same as drawing the logical reasoning diagram of the equipment control relationship.

To test the validity and correctness of the algorithm proposed in this paper, we select some electrical and mechanical production equipment in a certain cement production line, such as verification. The selected equipment forms ordered equipment set as: _{1}, ω_{2}, ω_{3}, ω_{4}, ω_{5}, ω_{6}, ω_{7}, ω_{8}, ω_{9}, ω_{10},). It satisfies that the equipment in the equipment concentration has no independent equipment, and the serial number of the control device is less than the serial number of the controlled device. The relationship between them can be shown in Table 1.

Control relationship table

Equipment wi | Set of controlled equipment Li | Control equipment set Fi |
---|---|---|

w1 | w3 | |

w2 | w3, w4 | |

w3 | w5, w6, w7 | w1, w2 |

w4 | w5 | w2 |

w5 | w7 | w3 |

w6 | w9, w10 | w3 |

w7 | w10 | w3, w5 |

w8 | w9 | w4 |

w9 | ∅ | w6, w8 |

w10 | ∅ | w6, w7 |

According to the control relationship between the devices described in Table 1, it can be concluded that the device nodes are taken in order. For ω_{1}, _{1} ≠ 0 is _{1} = {ω_{3}} = ∅ and ω_{3} ∈ _{3} to the control chart and add the control edges from ω_{1} to ω_{3}. Repeat the above process and finally get the control chart shown in Figure 3. The equipment control relationship matrix

Take the device ω_{7} as an example to search the device set of the reverse control chain. The first judge knowing _{7} ≠ 0. We put ω_{7} into _{7}). Judge knowing _{7} ≠ ∅ = {ω_{3}, ω_{5}}, judge knowing ω_{3}, ω_{5} all ∈ _{3} and ω_{5} into _{1}, ω_{3}, ω_{5}, ω_{7}}. After reverse addition, the reverse control chain starting from ω_{7} is obtained as shown in Figure 4. Take the device ω_{3} as the starting point and follow the control chart formation method to find the forward control chain (Figure 5).

This article considers the control relationship between electrical and mechanical equipment in process enterprises as the research object. Based on analyzing the characteristics of electrical equipment faults and control relations, the relevant theories of graph theory are used to construct the electrical equipment control relations matrix of process enterprises. At the same time, the article proposes an algorithm for forming a control relationship control chart and a search algorithm for forward and reverse control chains. It has been verified that the method proposed in this paper can quickly and accurately form the equipment diagram and control chain. This algorithm is of great significance to the dynamic management of the control chain of electrical equipment in process enterprises. This laid the foundation for subsequent computer implementation.

#### Control relationship table

Equipment wi | Set of controlled equipment Li | Control equipment set Fi |
---|---|---|

w1 | w3 | |

w2 | w3, w4 | |

w3 | w5, w6, w7 | w1, w2 |

w4 | w5 | w2 |

w5 | w7 | w3 |

w6 | w9, w10 | w3 |

w7 | w10 | w3, w5 |

w8 | w9 | w4 |

w9 | ∅ | w6, w8 |

w10 | ∅ | w6, w7 |

Law of interest rate changes in financial markets based on the differential equation model of liquidity Basalt fibre continuous reinforcement composite pavement reinforcement design based on finite element model 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 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 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 deformation monitoring of tunnel engineering based on 3D laser scanning Intelligent Recommendation System for English Vocabulary Learning – Based on Crowdsensing 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 Innovations to Attribute Reduction of Covering Decision System Based on Conditional Information Entropy Institutional investor company social responsibility report and company performance 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 Application of Higher-Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Informatisation of educational reform based on fractional differential equations 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 Optimal preview repetitive control for impulse-free continuous-time descriptor systems Development of main functional modules for MVB and its application in rail transit 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 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 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 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 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 The Optimization Model of Public Space Design Teaching Reform Based on Fractional Differential Equations Employment and Professional Education Training System of College Graduates Based on the Law of Large Numbers Nonlinear Differential Equations in Preventing Financial Risks 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 Demonstration of application program of logistics public information management platform based on fuzzy constrained programming mathematical model The Optimal Application of Lagrangian Mathematical Equations in Computer Data Analysis 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 Application of regression function model based on panel data in bank resource allocation financial risk management 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 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 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 Fractional Differential Equations in the Model of Vocational Education and Teaching Practice Environment Image denoising model based on improved fractional calculus mathematical equation The Complexity of Virtual Reality Technology in the Simulation and Modeling of Civil Mathematical Models Calculation and Performance Evaluation of Text Similarity Based on Strong Classification Features Evaluation and Verification of Patent Value Based on Combination Forecasting Model Prediction and Analysis of ChiNext Stock Price Based on Linear and Non-linear Composite Model The Psychological Memory Forgetting Model Based on the Analysis of Linear Differential Equations The Law of Large Numbers in Children's Education 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 Good congruences on weakly U-abundant semigroups 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 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 Computer Vision Communication Technology in Mathematical Modeling 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 in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics 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 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 Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm 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 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 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 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 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 Mathematical Method to Construct the Linear Programming of Football Training The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method 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 Video adaptive watermark embedding and detection algorithm based on phase function equation Evaluation of ecosystem health in Futian mangrove wetland based on the PSR-AHP model 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 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 The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Fractional Differential Equations in Sports Training in Universities Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model