In recent years, my country has completed the transformation of knowledge economy and network economy [1]. Under this circumstance, my country's power grid is also advancing rapidly, and electric energy has become an indispensable tool of life and production for residents and industrial development [2]. Therefore, the stability and high quality of electricity are important factors to ensure that the residents and enterprises lead a happy and productive life [3], and the high efficiency and high accuracy of power grid fault detection are the basic guarantees for maintaining power grid stability and high quality [4]. The existing power grid fault detection methods have professional requirements for manual analysis ability, knowledge, dispatch ability and experience type, which also brings difficulties to the power grid fault detection work [5].

Knowledge graph is an expression form closest to normal cognition, which can represent complex relationships at the semantic level and provide a better ability to manage and understand massive amounts of information. Integrating the knowledge graph into the application of power grid fault diagnosis can fully explore the value of multi-heterogeneous data in power grid fault processing and, to a certain extent, solve the low fault processing accuracy caused by the difference and lack of knowledge reserves of control and operation personnel. It is an effective way to improve the accident handling ability of power grid regulators. Tang

Therefore, this paper integrates the knowledge graph into smart grid fault diagnosis, which not only effectively improves the efficiency of smart grid fault diagnosis but also improves the accuracy of fault diagnosis, laying a foundation for the smooth progress of future grid fault diagnosis.

The knowledge graph can actually be regarded as a knowledge base. This knowledge base can discover the internal connections between entities and attributes and combine these internal connections to form a knowledge network [14]. The constituent factors of the knowledge graph can be regarded as triples, which can be expressed as ‘entity-relationship-entity’ or ‘entity-relationship-attribute.’ When the knowledge graph is displayed in the form of a graph, the entities and attributes in the triplet are represented as nodes, and the relationship between the two is represented as a directed edge connecting the two nodes. They are fused with the same entities and attributes, and the resulting knowledge graph is a network structure.

Knowledge graph includes two forms: one is open domain and the other is closed domain. Open domain knowledge graphs have problems such as entity ambiguity, lack of professionalism and strong noise, while closed domain knowledge graphs have good professionalism, little noise interference and no ambiguity in the relationship between entities and attributes; so, closed domain knowledge graphs are more widely used.

The construction of knowledge map is usually completed through knowledge extraction, knowledge fusion and knowledge processing. Knowledge extraction mainly extracts triples, and the extracted triples are usually non (semi) structured data, which form the knowledge map. The main element is knowledge fusion which performs entity disambiguation and coreference resolution on the extracted entities: entity disambiguation distinguishes entity names that may have multiple meanings; coreference resolution fuses words with the same meaning in the knowledge graph. Then, on the basis of triple adjustment, the extracted structured data are integrated to complete the construction of the knowledge graph [15]. Knowledge processing is to evaluate the quality and effect of the data of the knowledge map during the operation of the knowledge map and update and modify the knowledge map on the basis of the continuous updating of knowledge.

The fault diagnosis of power equipment is special; so, the construction of its knowledge graph requires a series of modifications.

In equipment failure, in addition to fault attributes, equipment components include component defects and the degree of defects. Therefore, in addition to the extraction of the relationship between entities and entities and entities and attributes, attributes and attribute relationships need to be extracted.

The power grid equipment failure knowledge graph belongs to the closed domain knowledge graph. The entity word meaning is only applicable to the power field, and the term specification applicable to itself is compiled in the power grid field; so, the phenomenon of entity ambiguity will not occur. Therefore, in entity disambiguation, time can be saved.

During coreference resolution, attributes will also appear synonymous, and coreference resolution should also be performed. Since the amount of data in the closed domain is small, coreference resolution should be performed on the entity/attribute first, and then, the relationship should be extracted so that the same entity/attribute pair can obtain more relational training samples.

In the process of relation extraction in many related literatures, in order to gain a comprehensive understanding of structured data, tables are used as the basis for summarising triples.

In order to avoid the invalidity of the knowledge graph due to the repetition of relations, the extracted relations need to be further screened [16].

Integrate data integration and data screening into triples to construct a graph-structured power grid equipment fault knowledge map. Therefore, the modified knowledge graph construction process is shown in Figure 1.

When the power grid fails, hundreds of accidents, displacement or abnormal signals will be generated in a short period of time so that the staff cannot comprehensively analyse the fault alarm information, resulting in low efficiency and unsatisfactory information judgement. Therefore, for the knowledge map combined with language processing technology, the knowledge of fault alarm information is automatically parsed to form a structured representation that can be understood and calculated by machines, and then, query matching and judgement analysis are performed based on the device information and business knowledge stored in the knowledge graph. The technical process of fault information analysis is shown in Figure 2.

When the power grid system fails, it is necessary to use the comprehensive intelligent alarm and other information as the trigger signal and use the fault information capture technology to ensure the complete acquisition of remote signalling information when the fault occurs and to eliminate abnormal alarm signals unrelated to the accident; the obtained fault information is analysed one by one through the information extraction technology, and the logical variables required for fault diagnosis are obtained [17]; information matching is to quickly match the fault alarm information after structural analysis from the equipment entity map of the power grid to obtain the corresponding network topology and electrical equipment and meteorological and environmental data in the power loss area; knowledge query It is linked to the relevant knowledge of scheduling procedures, rules and emergency plans for logical analysis of actions and fault diagnosis. The graph data structure of the knowledge graph often has faster query efficiency and can meet the speed requirements of fault diagnosis; according to the compatibility relationship between equipment, circuit breakers and protection, as well as causal relationship, mutual exclusion relationship and control logic, signal error correction is realised And filtering, to determine the authenticity or lack of information, and then complete the action logic judgement and fault information correction, to achieve power grid fault signal analysis and fault mode judgement [18].

After completing the information structuring and logical judgement, the key information flow of the current grid failure can be recorded in the form of triples of the graph, and the important abnormal or fault information can be linked to the relevant analysis or disposal knowledge nodes in the business logic graph so as to realise the complete expression of fault explicit and tacit knowledge [19].

The power grid fault diagnosis system is a system that uses directed arcs to connect the two groups of nodes of the attribute point (circular node) and the transition (bar node). The number of instructions on the attribute point changes when the event occurs [20]. Dependent points, transitions and directed arcs, respectively, construct process states, occurrence events and process evolution laws. As shown in Figure 3, the belonging point p_{1} is not only the input and output belonging point of the transition points 1 but also the input belonging point of the transition s_{2}. When transition s_{2} fires, it removes one instruction from point p_{1} and puts two instructions into point p_{2}, and the instruction at p_{2} can then be used for transitions s_{3} and s_{4}.

Since the model will have different evolutions in each state, the dynamic behaviour of the model should be studied, and the distribution of the instructions on the attribute points is called the model mark, and the current state of the model system is defined by this [21].

A model token is usually represented as follows:

^{−}: ^{+} : ^{−}(_{i}_{j}^{+} (_{j}_{i}

In the formula, ^{±} −^{=} is an order correlation matrix

If and only if the instruction between each input attribute point _{i}_{j}_{i}_{j}_{j}^{=} (:, _{j}^{=} (:, _{j}^{=} column of _{j}^{±} and ^{=} are written as follows:

In the above formula, the columns and rows represent transitions and attribute points, respectively. The correlation matrix can be expressed as follows:

At time k = 0, there are written as follows:

Triggering of transition _{2} results in the following equation:

From the above, the triggering of transition _{2} can indicate the occurrence of an event (such as a circuit breaker tripping), causing the system to transition to another state (such as an open circuit breaker). A fault in the power system can cause the command quantity in the home point to become negative [23].

To identify system failures, construct a redundant pseudocode _{H}_{H}

Suppose formula (4) is introduced into the system and d attribute points are added to the original system, namely:

All _{n}^{*} is a matrix (

Therefore, the evolution of the redundant system can be parameterised as follows:

In formula (10), D is a non-negative integer matrix _{H}

Identify the home point and transition fault in this time interval, assuming that
_{P}

If the diagnosis of power grid fault is to be successfully completed, a concurrent vector needs to be integrated and the evaluation of this quantity should be completed. At time

The above formula (13) also satisfies the following formula:

If no fault occurs,
_{P}

First, the fault at time

When no fault is found at the belonging point or the faults of all the belonging points are acquired, then the concurrent transition fault at time

_{t}_{t}_{t}_{t}^{′} represent the fault state and temporary fault state, respectively, and _{t}_{t}_{t}_{t}

Assuming that the state of the hidden layer of the attribute point at the last moment is _{t−}_{1}, the state of each attribute point of the output value between 0 and 1 is _{t−}_{1}; at this time, the output value determines the number of the attribute point state at the previous moment retained so far; _{f}_{f}

Assuming that the output value between 0 and 1 determines the number of the current state of the input point that has been retained so far, _{i}_{i}

The status of the belonging point can be updated by combining the above conditions of the input gate:

The current state of the belonging point has been retained until now, and the output values are represented by _{t}_{o}_{o}

The current output value can be expressed as follows:

The design and development of the fault diagnosis system should comply with the principles of generality, business orientation and convenience. Versatility means that power grids in different regions need to be systematically developed according to a unified process, and data must be shared; business-oriented means that the performance in the system must conform to the actual operation of the power grid; convenience means that it is necessary to facilitate the daily operation, understanding and management of staff [25].

The fault diagnosis system in this paper uses GUI Tkinter to design the user interface. The system takes user dialogue interaction as the main operation mode [26], uses Python to process MATLAB calculation and displays and searches through Neo4j, which not only improves the efficiency of calculation and search [27] but also strengthens the visualisation effect and the development framework of the power grid fault diagnosis system. There are shown in Figure 4.

In the data processing stage, semi-structured data such as fault cases and processing principles can be converted into structured data through text and web page analysis; the terms are classified according to the scheduling business requirements, and the matching rule text paragraphs are automatically searched based on the terms to achieve entity expansion. Expert experience is added to the data, and finally, various structured data are processed into Neo4j importable schemas through wrappers [28]. There is a coupling relationship between the designed fault scheduling knowledge graph data. For example, the business process contains the terms of accident handling, and the equipment data also include information such as topology and fault [29]. Therefore, in the process of building the knowledge graph, it is necessary to connect and integrate the associated data and reduce data isolation and duplication. In addition, partitioned and hierarchical management of knowledge graphs can improve data convenience and security. On the basis of completing knowledge acquisition, modelling and management, the interaction of computing, database and user platform is realised through the application programme interface, and functional modules are developed according to the knowledge application requirements [30].

Taking the power grid company of a certain city as the experimental data source, the power grid company's power grid site fault quantity, fault location and fault analysis information are obtained, and the data volume reached 5.3TB. In the process of building a graph, structured data are guided by fields, semi-structured data are guided by data indicators extracted from fields and unstructured data are guided by word segmentation.

Based on the internal equipment fault alarm signal of the pilot power grid company, the system proposed in this paper is used to analyse the alarm signal, which helps the monitoring personnel to quickly lock the equipment mechanism or abnormal parameter that may have problems, and obtain the following abnormal signals of the power grid equipment and the signal generating signal. Possible reasons are as in Table 1.

Abnormal alarm signals and possible causes of the signals

Hydraulic mechanism | Low oil pressure opening and locking | Oil pressure circuit leaks; pressure relay is damaged; secondary circuit failure; oil pressure changes with temperature |

Low oil pressure closing lock | ||

Oil pressure low opening and closing total block | ||

Low oil pressure reclosing lock-out | ||

Low oil pressure warning | ||

Oil pressure low opening and closing total block | ||

Low oil pressure reclosing lock-out | ||

N2 leak blocking | N2 pressure circuit leakage; pressure relay damaged; secondary circuit failure | |

N2 leak alert | ||

Arc extinguishing mechanism | SF6 low pressure warning | The circuit breaker has a leak point; the pressure relay is damaged; the secondary circuit is faulty; the air pressure value changes with temperature |

SF7 air pressure low lockout | ||

Pneumatic mechanism | Air pump pressure timed out | The circuit breaker has a leak point; the pressure relay is damaged; the circuit is faulty; the air pressure value changes with temperature |

Air pump high air pressure alarm | The air pump thermal relay is damaged; the secondary circuit is faulty | |

Pneumatic mechanism low air pressure alarm | The circuit breaker has a leak point; the pressure relay is damaged; the circuit is faulty; the air pressure value changes with temperature | |

Pneumatic mechanism low air pressure reclosing lockout | ||

Pneumatic mechanism pneumatic opening and closing total lock | ||

Spring mechanism | Spring is not charged | The energy storage motor is damaged; the motor power disappears or the control circuit is faulty; mechanical failure |

Energy storage motor failure | Motor power air circuit breaker tripped or motor failure | |

Energy storage motor power disappears | Motor power air circuit breaker tripped or power circuit fault | |

The energy storage motor runs overtime | The energy storage motor is damaged; the energy storage state sensor is abnormal; the spring mechanism is abnormal | |

Agency general signal | Heater failure | The heating power supply trips; the auxiliary contact of the power supply is in poor contact; the seasonal heating exits normally |

Structure three-phase inconsistent tripping action | The three phases of the circuit breaker are inconsistent, and one or two phases are tripped; the position relay contact problem | |

Control loop | The first (two) group control loop is disconnected | The secondary circuit wiring is loose; the auxiliary contact of the circuit breaker is in poor contact; the opening and closing coil is damaged |

The first (two) group of control power disappears | Control loop power circuit breaker tripped; control loop upper power supply disappears | |

Institutional local control | Control loop failure; circuit breaker requires field operation |

As it can be seen from Table 1, for the abnormal alarm signals issued by the power grid equipment, the knowledge graph fault diagnosis system proposed in this paper can analyse the causes of these abnormal alarm signals and provide the staff with the reasons for these abnormal alarm signals through the cause analysis and the location of the fault to achieve rapid diagnosis of power grid equipment faults.

In order to analyse the diagnostic efficiency of the fault diagnosis system of the knowledge graph proposed in this paper, the fault diagnosis system of the fuzzy algorithm, the fault diagnosis system of the TF-IDF algorithm and the fault diagnosis system of the knowledge graph proposed in this paper are used to analyse the power grid sites of the pilot power grid companies. The fault quantity, fault location and fault cause are diagnosed and analysed, and it is found that the diagnostic efficiency of the three systems is not the same. The specific diagnostic efficiency is shown in Table 2.

Comparison of diagnostic efficiency of three systems

Amount of failure | 3.2s | 2.8s | 1.1s |

Fault location | 2.9s | 3.0s | 0.9s |

Cause of issue | 3.3s | 3.2s | 1.0s |

Table 2 shows that the fuzzy algorithm fault diagnosis system and the TF-IDF algorithm fault diagnosis system take a long time for the fault quantity, fault location and fault analysis of the pilot power grid, which is basically about 3s; and the knowledge map proposed in this paper is used. The fault diagnosis system spends about 1s on the fault quantity, fault location and fault cause of the pilot power grid, which is much less than another system. Therefore, the knowledge graph fault diagnosis system proposed in this paper has the highest fault diagnosis efficiency for the pilot power grid.

The power grid fault diagnosis efficiency of the three systems is compared above, and it is found that the system in this paper is the most efficient. In order to compare the three systems more comprehensively, the two will compare and analyse the fault diagnosis accuracy of the three systems. The accuracy is shown in Table 3.

Comparison of the diagnostic accuracy of the three systems

Amount of failure | 77.4% | 79.5% | 93.7% |

Fault location | 76.6% | 74.7% | 97.3% |

Cause of issue | 76.1% | 78.3% | 96.5% |

Table 3 shows that the fuzzy algorithm fault diagnosis system and the TF-IDF algorithm's fault diagnosis system have an accuracy rate of 74%–80% for the fault quantity, fault location and fault cause of the pilot power grid, and the knowledge graph proposed in this paper is used. The fault diagnosis system has an accuracy rate between 93% and 98% for the fault quantity, fault location and fault analysis of the pilot power grid, which is much higher than that of other systems. Therefore, the knowledge graph fault diagnosis system proposed in this paper is suitable for the pilot power grid. The accuracy of fault diagnosis is ideal.

In this paper, the knowledge graph is integrated into the power grid fault diagnosis, and a fault diagnosis system is constructed. In the test of the pilot power grid, the system quickly analyses the possible problems of the power grid equipment based on the abnormal alarm signal of the power grid equipment and compares it with the fuzzy algorithm. Compared with the fault diagnosis system of TF-IDF algorithm, the system proposed in this paper is about 2s faster than the other two systems in terms of fault diagnosis efficiency; in terms of fault diagnosis accuracy, the system proposed in this paper is faster than the other two systems. The accuracy rates of the two systems are higher than those of others.

#### Abnormal alarm signals and possible causes of the signals

Hydraulic mechanism | Low oil pressure opening and locking | Oil pressure circuit leaks; pressure relay is damaged; secondary circuit failure; oil pressure changes with temperature |

Low oil pressure closing lock | ||

Oil pressure low opening and closing total block | ||

Low oil pressure reclosing lock-out | ||

Low oil pressure warning | ||

Oil pressure low opening and closing total block | ||

Low oil pressure reclosing lock-out | ||

N2 leak blocking | N2 pressure circuit leakage; pressure relay damaged; secondary circuit failure | |

N2 leak alert | ||

Arc extinguishing mechanism | SF6 low pressure warning | The circuit breaker has a leak point; the pressure relay is damaged; the secondary circuit is faulty; the air pressure value changes with temperature |

SF7 air pressure low lockout | ||

Pneumatic mechanism | Air pump pressure timed out | The circuit breaker has a leak point; the pressure relay is damaged; the circuit is faulty; the air pressure value changes with temperature |

Air pump high air pressure alarm | The air pump thermal relay is damaged; the secondary circuit is faulty | |

Pneumatic mechanism low air pressure alarm | ||

Pneumatic mechanism low air pressure reclosing lockout | ||

Pneumatic mechanism pneumatic opening and closing total lock | ||

Spring mechanism | Spring is not charged | The energy storage motor is damaged; the motor power disappears or the control circuit is faulty; mechanical failure |

Energy storage motor failure | Motor power air circuit breaker tripped or motor failure | |

Energy storage motor power disappears | Motor power air circuit breaker tripped or power circuit fault | |

The energy storage motor runs overtime | The energy storage motor is damaged; the energy storage state sensor is abnormal; the spring mechanism is abnormal | |

Agency general signal | Heater failure | The heating power supply trips; the auxiliary contact of the power supply is in poor contact; the seasonal heating exits normally |

Structure three-phase inconsistent tripping action | The three phases of the circuit breaker are inconsistent, and one or two phases are tripped; the position relay contact problem | |

Control loop | The first (two) group control loop is disconnected | The secondary circuit wiring is loose; the auxiliary contact of the circuit breaker is in poor contact; the opening and closing coil is damaged |

The first (two) group of control power disappears | Control loop power circuit breaker tripped; control loop upper power supply disappears | |

Institutional local control | Control loop failure; circuit breaker requires field operation |

#### Comparison of diagnostic efficiency of three systems

Amount of failure | 3.2s | 2.8s | 1.1s |

Fault location | 2.9s | 3.0s | 0.9s |

Cause of issue | 3.3s | 3.2s | 1.0s |

#### Comparison of the diagnostic accuracy of the three systems

Amount of failure | 77.4% | 79.5% | 93.7% |

Fault location | 76.6% | 74.7% | 97.3% |

Cause of issue | 76.1% | 78.3% | 96.5% |

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 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 Influence of heterogeneity of local officials on the economy of resource-based cities developed with high quality Analysis of influencing factors of SPOC course teaching effect using structural equation modelling Training Model of Basketball Offensive Route Based on Nonlinear Differential Equation Research on the construction of rural interface style based on aesthetic rules 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 Symmetry Analysis and Exact Solutions of Extended Kadomtsev-Petviashvili Equation in Fluids Research on Detection Model of Abnormal Data in Engineering Cost List Research on deformation monitoring of tunnel engineering based on 3D laser scanning Solidification treatment effect of wellsite waste mud based on physical adsorption of a composite curing agent A study of immersive technology for product usability improvement design based on comprehensive value evaluation Intelligent Recommendation System for English Vocabulary Learning – Based on Crowdsensing Application of Nonlinear Fractional Differential Equations in Computer Artificial Intelligence Algorithms Application of calculus function and value chain analysis method in the quantification of financial flexibility management indicators 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 Prediction of surface quality in end milling based on modified convolutional recurrent neural network Analysis of IPO pricing efficiency under the registration system Case application data research of traditional ink art elements in packaging design Research on an early warning model of effectiveness evaluation in ideological and political teaching based on big data Application of intelligent teaching resource organisation model and construction of performance evaluation model Secure transmission of simultaneous wireless information and power transfer system for Internet of things 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 Research on location algorithm of new energy vehicle charging station based on multi-objective decision 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 Research on multi-dimensional optimisation design of user interface under Rhino/GH platform 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 Evaluation of spoken English self-study system considering speech knowledge recognition algorithm Application research on piano teaching in colleges and universities based on remote wireless network communication Construction of Financial Risk Evaluation Index System for Biomass Graphene Fibre Industrialisation Project 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 An online statistical analysis of the hotel management and operation performance model Research on the post-purchase behaviour tendency of the product quality to customers in fast-selling marketing Motion about equilibrium points in the Jupiter-Europa system with oblateness 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 Design of information management system based on wireless communication under the background of Internet of Things The impact of global warming on the small Scottish Fishing Company 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 Research on the relationship between government subsidies, R&D investment and high-quality development of manufacturing industry Research on the protection and inheritance of intangible cultural heritage under the background of rural revitalisation 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 Computer vision recognition and tracking algorithm based on convolutional neural network A review of the treatment techniques of VOC Study on structural parameter design and life analysis of large four-point contact ball bearing channel Some classes of complete permutation polynomials in the form of ( x ^{pm}−x +δ )^{s}+ax ^{pm}+bx overF _{p2m}Digital marketing solutions based on consumer data and homomorphic encryption 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 Application research of bel canto performance based on artificial intelligence technology Fractal structure of magnetic island in tokamak plasma Mechanics of Building Structural Materials Based on Lagrangian Mathematical Model Analysis The Mental Health Education Management of Higher Vocational Students Based on Fractional Differential Equations Application of regression function model based on panel data in financial risk management of bank resource allocation Application of knowledge graph in smart grid fault diagnosis University Ideological and Political Learning Model Based on Statistical Memory Curve Mathematical Equation Research on the optimisation of logistics parcel intelligent sorting and conveying chain combined with variable clustering mathematical method 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 Application of Discriminative Training Algorithm Based on Intelligent Computing in English Translation Evaluation Research on the application of GLE teaching mode in English-medium colleges The application of directional derivative in the design of animation characters and background elements Research on product process design and optimisation model based on IoT intelligent computing Conventional Algorithms in Sports Training Based on Fractional Differential Equations Dynamic Nonlinear System Based on Complex System Theory in the Development of Vocational Education LTE wireless network coverage optimisation based on corrected propagation model The Algorithm Accuracy of Mathematical Model to Improve the Transmission Speed of E-commerce Platform Study on tourism development income index calculation of finite element ordinary differential mathematical equation 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 Impact of ASEAN-China free trade area on fishery value chain based on difference-in-difference method 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 Criminal law imputation path for biometric information Research on composite dynamic disaster prevention and control system of mine earthquake and shock in thick and hard rock mines Research on innovative strategies of college students’ English teaching under the background of artificial intelligence Electromagnetic interference prediction technology of new energy motor drive system Research on the application of PLC technology in electrical automation engineering Research on indoor environment design of comprehensive commercial shopping center based on numerical simulation Application of matrix multiplication in signal sensor image perception Empirical analysis of the economic absolute income hypothesis based on mathematical statistics Analysing the variation of metadiscourse verb patterns in English academic papers from within and between disciplines Impact of COVID-19 policy on stock prices of listed property companies Realization of Book Collaborative Filtering Personalized Recommendation System Based on Linear Regression Equation Research on the experimental principle of deep integration of LETS software and criminal procedure under the background of artificial intelligence 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 VR-based computer maintenance practical training platform development design and application research Research on innovative human capital for China’s economic development based on STI model In-depth analysis of the artistic expression of paper-cut elements in the design of boat space Knowledge graph construction and Internet of Things optimisation for power grid data knowledge extraction Modeling the pathway of breast cancer in the Middle East Construction and intelligent analysis of power grid physical data knowledge graph based on Internet of Things for power system Research on industrial Internet of Things and power grid technology application based on knowledge graph and data asset relationship model Research on the effects of financial literacy on rural household credit constraint Calculus Logic Function in Integrated Manufacturing Automation of Single Chip Microcomputer Football Offense Training Strategy Based on Fractional Differential Mathematical Modeling Research on educational resource recommendation system based on MRLG Rec 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 study on the phenomenon of anaphoric correction in college students’ English conversation 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 Optimal decisions and channel coordination of a green supply chain with marketing effort and fairness concerns Game theoretic model for low carbon supply chain under carbon emissions reduction sensitive random demand Limit cycles of a generalised Mathieu differential system Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Application of data mining in basketball statistics The nonlinear effects of ageing on national savings rate – An Empirical Study based on threshold model Design of fitness walker for the elderly based on ergonomic SAPAD model AtanK-A New SVM Kernel for Classification 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 Analysis and countermeasures of cultivating independent learning ability in colleges teaching English based on OBE theory 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 Projection of Early Warning Identification of Hazardous Sources of Gas Explosion Accidents in Coal Mines Based on NTM Deep Learning Network 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 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 Research on design of customer portrait system for E-commerce Research on rule extraction method based on concept lattice of intuitionistic fuzzy language 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 Design and evaluation of intelligent teaching system on basic movements in PE 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 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 Research on evaluation system of cross-border E-commerce platform based on the combined model 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 Application of hybrid kernel function in economic benefit analysis and evaluation of enterprises Research on classification of e-commerce customers based on BP neural network The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System 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 Study on the influence of adolescent smoking on physical training vital capacity in eastern coastal areas 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 -groupsResearch 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 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 Evaluation and prediction of regional human capital based on optimised BP neural network Study on inefficient land use determination method for cities and towns from a city examination perspective A study of local smoothness-informed convolutional neural network models for image inpainting 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 Computational Algorithm to Solve Two–Body Problem Using Power Series in Geocentric System 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 Nonlinear Channel Estimation for Internet of Vehicles Some Necessary Conditions for Feedback Functions of de Bruijn Sequences 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 An empirical research on economic growth from industrial structure optimisation in the Three Gorges Reservoir area 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 Study of agricultural finance policy information extraction based on ELECTRA-BiLSTM-CRF Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Innovative research of vertical video creation under the background of mobile communication Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model Genetic algorithm-based congestion control optimisation for mobile data network