In order to determine the importance of influencing factors of energy consumption in oilfield water injection systems, the distribution of energy loss in the water injection system was analyzed, the factors affecting the energy consumption of the water injection system were determined, and an evaluation index system for the energy consumption of the water injection system was established. This indicator system covers all links and all energy loss nodes of the energy loss of the water injection system, thereby an evaluation model for influencing factors of energy consumption in water injection system based on entropy weight - grey correlation method was built. Use the entropy weight method to get the ranking of the importance of energy consumption indicators; use the gray correlation method to determine the correlation between each water injection system and energy consumption factors. The application results show that the entropy weight-grey correlation method proposed in this paper can effectively obtain the importance of the energy consumption factors of the oilfield water injection system, and provide scientific guidance for the daily management and targeted optimization of the water injection system.
Oilfield water injection is an important means to replenish energy into strata in oilfield development process so as to improve oilfield recovery ratio [1]. At present, the power consumption of the water injection system accounts for about 33% ~ 56% of the total power consumption of the oil field [2]. Therefore, it is essential to evaluate the energy consumption of water injection system and find out the influencing factors resulting in high system energy consumption, so that the operating efficiency of water injection system can be improved [3].
In recent years, researches on the influencing factors and evaluation of water injection system energy consumption including: Peng et al. studied methods to improve the operation efficiency of water injection systems, and the influencing factors of energy consumption, and established an oilfield water injection system optimization control mathematical model [4]; Lei et al. established a comprehensive evaluation model for ground systems and digital dynamic statistics [5]; Zhou et al. established a reasonable index system and evaluation method that reflect the energy efficiency of the water injection system according to the characteristics of Xinjiang oilfields[6]; Tan et al. established an energy consumption model using association rules and chaotic time series, and studied the relationship between energy consumption factors in the water injection system [7] and so on. However, the above scholars did not give a clear statement on the importance of the factors affecting the energy consumption of the water injection system.
When determining the importance of energy consumption influencing factors, the entropy weight-grey correlation method can be used, which can solve the sorting problem of influencing factors. Wang et al. applied the gray correlation analysis method to the analysis and research of pipeline corrosion influencing factors in the oilfield water injection system [8]; Nan et al. used the improved entropy weight-grey correlation method to determine the key factors that have a significant impact on the reliability of power supply in the power supply area [9]; Zhang et al. reasonably evaluated the workshop's manufacturing capacity in combination with entropy weight method and grey relational analysis method [10]; Jia et al. analyzed the island earthquake emergency response capacity of different island counties based on the entropy weight method-grey correlation analysis method [11]; Liu et al. used entropy weight-improved grey correlation method to study the influence of 12 risk factors on tunnel collapse, and determine the risk assessment of highway tunnel collapse [12]. Therefore, the entropy weight-grey correlation analysis method has been applied in many fields, and has achieved good analysis and evaluation results, but it has not been applied in the analysis of the importance of the energy consumption factors of the oilfield water injection system. For this reason, this paper establishes a water injection system energy consumption evaluation index system, and uses the entropy weight-grey correlation method to determine the importance of the factors affecting the water injection system energy consumption.
To analyze the composition of the energy consumption of the water injection system, the starting point is to analyze the process flow of the water injection system, and then to clarify the energy flow direction of the system, to find out the nodes of energy loss in the system, and to finally classify the influencing factors of the energy loss nodes [13].
Oilfield water injection system is a continuous closed hydraulic system which consists of water source, water injection station, water distributing station and water injection pipe network [14]. Its structure is shown in Fig.1.
It can be seen from Figure 1 that when the water injection system is operating, the incoming water from the water source is pressurized by the water injection station and then enters the water distribution room through the water injection main line and the water injection branch line. After the pressure is adjusted by the valve in the water distribution room, it finally flows into the water injection well [15]. Therefore, the water injection system is that supplies water to each water distribution station, and each water distributing station is connected to multiple wellheads, to form a complex water injection system with large area [16].
In the entire water injection process, the power input to the water injection system is recorded as the total input energy of the system, and the water energy output to the water injection well is recorded as the output energy of the system, that is, the effective energy [17]. During the energy transfer process of the water injection system from input to output, the loss of system energy is mainly distributed in the seven nodes of the two components, and the energy flow of the water injection system is shown in Figure 2 [18].
It can be seen from Figure 2 that the energy loss link of the water injection system is divided into two parts, namely the water injection pump station part and the water injection pipe network part. Among them, the water injection pump station part contains 3 loss nodes: engine loss, water injection pump loss, and differential pressure loss at pump line; The water injection pipe network part contains 4 loss nodes: trunk loss, throttling loss at water distributing station, single-well line loss, and wellhead loss. From the above analysis, it can be seen that the influencing factors that affect the energy consumption of the water injection system are more complicated. In order to facilitate further analysis, they are classified into three categories: equipment factors, pipe network factors and stratigraphic factors [19,20,21,22], as shown in Figure 3.
Among them, device and pipe network are subjective factors, including the operating efficiency of water injection pump, engine and pipe network and the water injection pipe network techniques, they can improve operating efficiency through optimization and modification; strata is an objective factor, It reflects the energy that the entire water injection system must provide to meet the objective requirements of injection-production balance, such as the required water injection pressure and water injection volume [23]. As a result, we could only analyze the reason of energy consumption in water injection system and its improvement direction from subjective factors, namely device factors and pipe network factors.
On the basis of clarifying the distribution of energy loss in the water injection system and the factors affecting the energy consumption of the water injection system, the energy consumption evaluation index of the water injection system will be determined.
The determined energy consumption evaluation index of the water injection system should cover all links of the energy loss of the water injection system, and it should be a comprehensive set of system indicators that reflect not only the equipment factors of the system, but also the pipe network factors of the system. The energy consumption evaluation index system of the oilfield water injection system is shown in Table 1.
Energy consumption index system for water injection system.
System link | Energy loss node | Energy consumption index | Test parameter |
---|---|---|---|
Pump A_{1} | Engine loss B_{1} | Power factor C_{1} | Active power D_{1}, reactive power D_{2}, power factor D_{3} |
Water injection pump loss B_{2} | Unit efficiency C_{2} | Pump inlet pressure D_{4}, outlet pressure D_{5}, outlet flow D_{6} | |
Differential pressure loss of pump line B_{3} | Differential pressure of pump line C_{3} | Station outlet pressure D_{6} | |
Pipe network A_{2} | Trunk loss B_{4} | Trunk pressure loss C_{4} | Truck pressure D_{8} |
Throttling loss of water distributing station B_{5} | Valve control of water distributing station C_{5} | Oil pressure of water distributing station D_{9} | |
Single-well pipeline loss B_{6} | Single-well pipeline pressure loss C_{6} | Wellhead pressure D_{10} | |
Wellhead loss B_{7} | Wellhead valve control C_{7} | Wellhead flow D_{11} |
Table 1 presents four parts of content, namely system link, energy loss node, energy consumption index, and test parameter.
System link: Two components of energy loss, namely pump A_{1} and pipe network A_{2}.
Energy loss node: it is the 7 loss nodes of the two components in the system link, there are 3 items in the pump A_{1}: engine loss B_{1}, water injection pump loss B_{2}, differential pressure loss of pump line B_{3}. Pipe network A_{2} are 4 items: trunk loss B_{4}, throttling loss of water distributing station B_{5}, single-well pipeline loss B_{6}, wellhead loss B_{7}.
Energy consumption index: According to the energy loss node of pump A_{1}, the corresponding energy consumption index is determined to be 3 items: power factor C_{1}, unit efficiency C_{2}, differential pressure of pump line C_{3}. Determined by the energy loss node of pipe network A_{2} The corresponding energy consumption indicators are 4 items: trunk pressure loss C_{4}, Valve control of water distributing station C_{5}, single-well pipeline pressure loss C_{6}, wellhead valve control C_{7}, a total of 7 energy consumption indicators.
Test parameters: 11 parameters need to be tested in order to obtain energy consumption indicators, as shown in Table 1.
Based on the evaluation index system of water injection system energy consumption factors established in Table 1, this paper will use the entropy weight-grey correlation method to determine the comprehensive evaluation model of water injection system energy consumption factors. Entropy can reflect the disorder degree of a system, and the index entropy value can indicate the information quantity contained in the system, that is to say, the smaller is entropy value is, the larger its weight will be [24]. Established on basis of objectively measured data, the grey correlation method figures out how proximate the evaluation indexes of each energy consumption influencing factor of each water injection system is to the optimal ideal system energy consumption level [25]. For this reason, the entropy weight-grey correlation method can be used to study the importance of factors affecting energy consumption of water injection systems.
The implementation steps of the entropy weight-grey correlation method of the water injection system are as follows:
Select several water injection systems, and obtain the test parameters in Table 1 according to GB/T 33653-2017 Energy Consumption Test and Calculation Method for Oilfield Production System [26], and calculate their energy consumption indicators.
Construct the energy consumption index of each system as an evaluation index matrix
Calculate the entropy value
According to the gray correlation method, taking the evaluation index matrix
By calculating the gray correlation coefficient of the water injection system, and further combining with the entropy weight
The value of energy consumption index corresponding to the energy consumption influencing factors of each water injection system in the oil field is different, and the degree of influence on the water injection system is also different, and their proportions are also different. Hence, it is crucial to determine the weight of each evaluation index scientifically and reasonably. The calculation steps are as below:
First, collect the test parameters of each water injection system in an oil field over the years, and calculate its energy consumption index, and then construct the energy consumption index of each system as an evaluation index, and list them as matrix
Where:
As the selected energy consumption indexes from each water injection system are in different units, so this index matrix is handled by dimensionless method.
Where:
To normalize the standardized index matrix, figure out the proportion
Figure out the entropy value
Where: in case that
Figure out the entropy weight
Where, it satisfies
Select a water injection system with the optimal value of energy consumption in the oilfield water injection system as the reference sequence, and use the data in formula (1) as the comparison sequence to form a matrix, and then normalize the data sequence to index values to obtain the water injection system The correlation with energy consumption indicators, The larger the correlation is, the higher they are correlated to each other. Thereby, the evaluation condition of energy consumption influencing indexes for water injection system can be distinguished. The calculation steps of grey correlation analysis method are as below:
According to the index system with determined data, the data of water injection system with optimal energy consumption is taken as the reference series {
In order to simplify the calculation of evaluation indexes, the evaluation index values of each water injection system are normalized.
The correlation coefficient is a dispersal measure to reflect how proximate the comparison series of selected water injection systems is to the reference series (i.e. target value) of water injection system with the optimal energy consumption, which is expressed as
Where:
The information of correlation coefficient is dispersed and not easy to analyze. In order to make the obtained evaluation results to fit the actual situation, the weight obtained by using entropy weight method is integrated with the correlation coefficient, then the entropy weight - grey correlation is:
According to the rank of correlation degree, the ranking results of evaluation indexes of influencing factors for selected water injection systems are obtained.
Using the above-established evaluation index system for energy consumption influencing factors of the water injection system, and based on the entropy weight-grey correlation method analysis method given, taking five water injection systems in an oil field as an example to, determine the importance of the energy consumption influencing factors of each system.
For example, to determine the importance of the energy consumption factors of five water injection systems in an oil field, first collect basic information about the operation of each system as shown in Table 2.
Basic information of an oilfield water injection system.
Research system | Water injection qty/m^{3}/d | System efficiency/% | Water injection well/head | Pump unit/set |
---|---|---|---|---|
System(Optimal) | 8925.36 | 67.01 | 61 | 4 |
System I | 19247.76 | 49.44 | 108 | 7 |
System II | 3924.00 | 63.01 | 47 | 3 |
System III | 7995.26 | 67.48 | 55 | 4 |
System IV | 15826.08 | 42.85 | 83 | 6 |
System V | 5216.40 | 46.92 | 36 | 5 |
In Table 2, System (Optimum) is the current optimal water injection system selected, which is taken as the optimal energy consumption reference system, and System I to System V are the systems that need to be analyzed.
Then obtain the test parameters of five water injection systems, such as: active power D_{1}, outlet pressure D_{5}, outlet flow D_{6}, truck pressure D_{8}, etc., and calculate the energy consumption indicators of each water injection system. See Table 3 for statistics.
Energy consumption index of an oilfield water injection system.
Energy consumption index | System (Optimal) | System I | System II | System III | System IV | System V |
---|---|---|---|---|---|---|
Power factor C_{1} | 0.93 | 0.83 | 0.95 | 0.75 | 0.91 | 0.70 |
Pump unit loss C_{2}/% | 20.18 | 15.26 | 14.59 | 34.92 | 20.91 | 16.96 |
Differential pressure of pump line C_{3}/% | 4.14 | 4.15 | 1.95 | 2.01 | 1.83 | 6.11 |
Trunk pressure loss C_{4}/MPa | 0.39 | 1.57 | 2.18 | 0.51 | 0.15 | 0.57 |
Valve control pressure loss C_{5}/MPa | 3.42 | 3.39 | 7.73 | 2.00 | 2.93 | 2.33 |
Single-well pipeline pressure loss C_{6}/MPa | 0.22 | 0.43 | 0.67 | 0.51 | 0.81 | 0.21 |
Wellhead valve control C_{7}/% | 0.00 | 0.01 | 0.22 | 0.02 | 0.07 | 0.13 |
The energy consumption index of the five systems in Table 3 is constructed as an evaluation index matrixby formula (1):
According to the evaluation index matrix in formula (10), the index values are standardized and normalized by formulas (2)~(6), and the entropy value of each energy consumption index is calculated, and the entropy weight is obtained, thereby determining the weight of the energy consumption index Sort, as shown in Table 4.
Weight of energy consumption index of an oilfield water injection system.
Energy consumption index | Entropy weight | Weight rank |
---|---|---|
C_{1} | 0.0000160 | 6 |
C_{2} | 0.9831032 | 1 |
C_{3} | 0.0060623 | 3 |
C_{4} | 0.0010549 | 4 |
C_{5} | 0.0096778 | 2 |
C_{6} | 0.0000752 | 5 |
C_{7} | 0.0000105 | 7 |
For this reason, the importance of energy consumption indicators is ranked by the entropy weight method: unit efficiency C_{2} > valve control of water distributing station C_{5} > differential pressure of pump line C_{3} > trunk pressure loss C_{4} > single-well pipeline pressure loss C_{6} > power factor C_{1} > wellhead valve control C_{7}.
According to the energy consumption index parameters in Table 3, the evaluation index matrix [
The gray correlation coefficients of the energy consumption indicators of the system are calculated by formula (8), as shown in Table 5.
Grey correlation coefficient of an oilfield water injection system.
Energy consumption index | System I | System II | System III | System IV | System V |
---|---|---|---|---|---|
C_{1} | 0.9621 | 0.9922 | 0.9337 | 0.9922 | 0.9168 |
C_{2} | 0.9258 | 0.9166 | 0.8064 | 0.9883 | 0.9502 |
C_{3} | 0.9997 | 0.4669 | 0.9244 | 0.9186 | 0.9297 |
C_{4} | 0.9848 | 0.3385 | 0.9985 | 0.9969 | 0.9977 |
C_{5} | 0.9996 | 0.3615 | 0.9813 | 0.9935 | 0.9856 |
C_{6} | 0.9914 | 0.3447 | 0.9881 | 0.9761 | 0.9996 |
C_{7} | 1.0000 | 0.3334 | 0.9999 | 0.9997 | 0.9994 |
The gray correlation degree of the water injection system calculated by formula (9) is shown in Table 6:
Grey correlation degree of water injection system in an oil field.
System I | System II | System III | System IV | System V | |
---|---|---|---|---|---|
Relevancy |
0.9271 | 0.9078 | 0.8090 | 0.9879 | 0.9505 |
Rank | 3 | 4 | 5 | 1 | 2 |
It is known from above calculation that, the order of the energy consumption influence degree of the five water injection systems obtained by the gray correlation method is as follows: system IV > system V > system I > system II > system III.
From the above analysis results, it can be seen that there are 7 influencing factors in the energy consumption of the water injection system. The order of their importance is as follows: pump unit loss > valve control pressure loss > differential pressure loss of pump line > trunk pressure loss > single-well pipeline pressure loss > power factor loss > wellhead loss.
After clarifying the importance of the influencing factors of the water injection system, it provides scientific guidance for the daily management and optimization of the water injection system. In particular, the pump unit loss and pipe network pressure loss have a greater impact on the system energy consumption. Through targeted system optimization, the energy consumption caused by the pump unit and pipe network pressure can be minimized; and the wellhead valve control loss importance is the lowest, therefore, its impact on the water injection system can be ignored.
The distribution of energy loss in the water injection system was analyzed, the factors affecting the energy consumption of the water injection system were determined, and the energy consumption evaluation index system of the water injection system was established. This indicator system covers all links and all energy loss nodes of the water injection system. It has determined 7 energy consumption indicators and 11 test parameters, so that it fully reflects the energy consumption of each link of the water injection system and the operating status of the system.
Established an evaluation model of energy consumption influencing factors of water injection system based on entropy weight-grey correlation analysis method, and determined the main influencing factors of energy consumption of oilfield water injection system. Using the entropy method to get the ranking of the importance of energy consumption indicators: unit efficiency C_{2} > valve control of water distributing station C_{5} > differential pressure of pump line C_{3} > trunk pressure loss C_{4} > single-well pipeline pressure loss C_{6} > power factor C_{1} > wellhead valve control C_{7}. The gray correlation method can be used to determine the correlation between each water injection system and energy consumption factors.
Through application examples, the results show that the entropy weight-grey correlation method proposed in this paper can effectively obtain the importance of the energy consumption factors of the oilfield water injection system, and provide scientific guidance for the daily management and targeted optimization of the water injection system.
Weight of energy consumption index of an oilfield water injection system.
Energy consumption index | Entropy weight | Weight rank |
---|---|---|
C_{1} | 0.0000160 | 6 |
C_{2} | 0.9831032 | 1 |
C_{3} | 0.0060623 | 3 |
C_{4} | 0.0010549 | 4 |
C_{5} | 0.0096778 | 2 |
C_{6} | 0.0000752 | 5 |
C_{7} | 0.0000105 | 7 |
Grey correlation coefficient of an oilfield water injection system.
Energy consumption index | System I | System II | System III | System IV | System V |
---|---|---|---|---|---|
C_{1} | 0.9621 | 0.9922 | 0.9337 | 0.9922 | 0.9168 |
C_{2} | 0.9258 | 0.9166 | 0.8064 | 0.9883 | 0.9502 |
C_{3} | 0.9997 | 0.4669 | 0.9244 | 0.9186 | 0.9297 |
C_{4} | 0.9848 | 0.3385 | 0.9985 | 0.9969 | 0.9977 |
C_{5} | 0.9996 | 0.3615 | 0.9813 | 0.9935 | 0.9856 |
C_{6} | 0.9914 | 0.3447 | 0.9881 | 0.9761 | 0.9996 |
C_{7} | 1.0000 | 0.3334 | 0.9999 | 0.9997 | 0.9994 |
Energy consumption index system for water injection system.
System link | Energy loss node | Energy consumption index | Test parameter |
---|---|---|---|
Pump A_{1} | Engine loss B_{1} | Power factor C_{1} | Active power D_{1}, reactive power D_{2}, power factor D_{3} |
Water injection pump loss B_{2} | Unit efficiency C_{2} | Pump inlet pressure D_{4}, outlet pressure D_{5}, outlet flow D_{6} | |
Differential pressure loss of pump line B_{3} | Differential pressure of pump line C_{3} | Station outlet pressure D_{6} | |
Pipe network A_{2} | Trunk loss B_{4} | Trunk pressure loss C_{4} | Truck pressure D_{8} |
Throttling loss of water distributing station B_{5} | Valve control of water distributing station C_{5} | Oil pressure of water distributing station D_{9} | |
Single-well pipeline loss B_{6} | Single-well pipeline pressure loss C_{6} | Wellhead pressure D_{10} | |
Wellhead loss B_{7} | Wellhead valve control C_{7} | Wellhead flow D_{11} |
Basic information of an oilfield water injection system.
Research system | Water injection qty/m^{3}/d | System efficiency/% | Water injection well/head | Pump unit/set |
---|---|---|---|---|
System(Optimal) | 8925.36 | 67.01 | 61 | 4 |
System I | 19247.76 | 49.44 | 108 | 7 |
System II | 3924.00 | 63.01 | 47 | 3 |
System III | 7995.26 | 67.48 | 55 | 4 |
System IV | 15826.08 | 42.85 | 83 | 6 |
System V | 5216.40 | 46.92 | 36 | 5 |
Energy consumption index of an oilfield water injection system.
Energy consumption index | System (Optimal) | System I | System II | System III | System IV | System V |
---|---|---|---|---|---|---|
Power factor C_{1} | 0.93 | 0.83 | 0.95 | 0.75 | 0.91 | 0.70 |
Pump unit loss C_{2}/% | 20.18 | 15.26 | 14.59 | 34.92 | 20.91 | 16.96 |
Differential pressure of pump line C_{3}/% | 4.14 | 4.15 | 1.95 | 2.01 | 1.83 | 6.11 |
Trunk pressure loss C_{4}/MPa | 0.39 | 1.57 | 2.18 | 0.51 | 0.15 | 0.57 |
Valve control pressure loss C_{5}/MPa | 3.42 | 3.39 | 7.73 | 2.00 | 2.93 | 2.33 |
Single-well pipeline pressure loss C_{6}/MPa | 0.22 | 0.43 | 0.67 | 0.51 | 0.81 | 0.21 |
Wellhead valve control C_{7}/% | 0.00 | 0.01 | 0.22 | 0.02 | 0.07 | 0.13 |
Grey correlation degree of water injection system in an oil field.
System I | System II | System III | System IV | System V | |
---|---|---|---|---|---|
Relevancy |
0.9271 | 0.9078 | 0.8090 | 0.9879 | 0.9505 |
Rank | 3 | 4 | 5 | 1 | 2 |
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 Response model for the psychological education of college students based on non-linear finite element equations 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 Regarding new wave distributions of the non-linear integro-partial Ito differential and fifth-order integrable equations Badminton players’ trajectory under numerical calculation method Innovations to Attribute Reduction of Covering Decision System Based on Conditional Information Entropy Nonlinear Differential Equations in the Teaching Model of Educational Informatisation The evaluation of college students’ innovation and entrepreneurship ability based on nonlinear model Smart Communities to Reduce Earthquake Damage: A Case Study in Xinheyuan, China 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 Cognitive Computational Model Using Machine Learning Algorithm in Artificial Intelligence Environment Research on tourism income index based on ordinary differential mathematical equation Application of Higher-Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Sports Science Teaching of Athletics Based on Nonlinear Mathematical Equation 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 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}Deformation and stress theory of surrounding rock of shallow circular tunnel based on complex variable function method The consistency method of linguistic information and other four preference information in group decision-making Research on the willingness of Forest Land’s Management Rights transfer under the Beijing Forestry Development A mathematical model of the fractional differential method for structural design dynamics simulation of lower limb force movement step structure based on Sanda movement 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 Sports intensity and energy consumption based on fractional linear regression equation Translog function in government development of low-carbon economy Analysis of the properties of matrix rank and the relationship between matrix rank and matrix operations Research on the Psychological Distribution Delay of Artificial Neural Network Based on the Analysis of Differential Equation by Inequality Expansion and Contraction Method Study on Establishment and Improvement Strategy of Aviation Equipment Research on Financial Risk Early Warning of Listed Companies Based on Stochastic Effect Mode The Model of Sugar Metabolism and Exercise Energy Expenditure Based on Fractional Linear Regression Equation Constructing Artistic Surface Modeling Design Based on Nonlinear Over-limit Interpolation Equation Numerical Simulation Analysis Mathematics of Fluid Mechanics for Semiconductor Circuit Breaker Characteristics of Mathematical Statistics Model of Student Emotion in College Physical Education Human Body Movement Coupling Model in Physical Education Class in the Educational Mathematical Equation of Reasonable Exercise Course The contribution of structural equation model analysis to higher education agglomeration and innovation and entrepreneurship Study on the evolutionary game theory of the psychological choice for online purchase of fresh produce under replicator dynamics formula The influence of X fuzzy mathematics method in basketball tactics scoring Mathematical statistics algorithm in the bending performance test of corroded reinforced concrete beams under fatigue load Nonlinear strategic human resource management based on organisational mathematical model Back propagation mathematical model for stock price prediction Evolutionary game research on the psychological choice of online shopping of fresh agricultural products based on dynamic simulation model Differential equation model of financial market stability based on big data Multi-attribute decision-making methods based on normal random variables in supply chain risk management Linear fractional differential equations in bank resource allocation and financial risk management model Construction and reform of art design teaching mode under the background of the integration of non-linear equations and the internet Spatial–temporal graph neural network based on node attention A contrastive study on the production of double vowels in Mandarin Financial accounting measurement model based on numerical analysis of rigid normal differential equation and rigid generalised functional equation Research of cascade averaging control in hydraulic equilibrium regulation of heating pipe network Mathematical analysis of civil litigation and empirical research of corporate governance Health monitoring of Bridges based on multifractal theory College students’ innovation and entrepreneurship ability based on nonlinear model Health status diagnosis of the bridges based on multi-fractal de-trend fluctuation analysis Mathematical simulation analysis of optimal testing of shot puter's throwing path Performance evaluation of college laboratories based on fusion of decision tree and BP neural network Application and risk assessment of the energy performance contracting model in energy conservation of public buildings The term structure of economic management rate under the parameter analysis of the estimation model based on common differential equation Sensitivity analysis of design parameters of envelope enclosure performance in the dry-hot and dry-cold areas The Spatial Form of Digital Nonlinear Landscape Architecture Design Based on Computer Big Data The improvement of museum information flow based on paste functional mapping method The art design of industrialised manufacturing furniture products based on the simulation of mathematical curves TOPSIS missile target selection method supported by the posterior probability of target recognition Research on Evaluation of Intercultural Competence of Civil Aviation College Students Based on Language Operator The incentive contract of subject librarians in university library under the non-linear task importance Modelling and Simulation of Collaborative Innovation System in Colleges and Universities Based on Interpreted Structural Equation Model Small amplitude periodic solution of Hopf Bifurcation Theorem for fractional differential equations of balance point in group competitive martial arts The Optimal Solution of Feature Decomposition Based on the Mathematical Model of Nonlinear Landscape Garden Features Composite mechanical performance of prefabricated concrete based on hysteresis curve equation Higher education innovation and reform model based on hierarchical probit Application of Fuzzy Mathematics Calculation in Quantitative Evaluation of Students’ Performance of Basketball Jump Shot The teaching of sports science of track and field-based on nonlinear mathematical equations Visual error correction of continuous aerobics action images based on graph difference function Ecological balance model of effective utilization of agricultural water resources based on fractional differential equations Application of Higher Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Precision algorithms in second-order fractional differential equations Application of Forced Modulation Function Mathematical Model in the Characteristic Research of Reflective Intensity Fibre Sensors Fractional differential equations in National Sports Training in Colleges and Universities Radioactive source search problem and optimisation model based on meta-heuristic algorithm Visualized calculation of regional power grid power data based on multiple linear regression equation Application of mathematical probabilistic statistical model of base – FFCA financial data processing Least-squares method and deep learning in the identification and analysis of name-plates of power equipment Research on a method of completeness index based on complex model Distribution network monitoring and management system based on intelligent recognition and judgement 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 Topological optimisation technology of gravity dam section structure based on ANSYS partial differential equation operation Interaction design of financial insurance products under the Era of AIoT Modeling the pathway of breast cancer in the Middle East Corporate social responsibility fulfilment, product-market competition and debt risk: Evidence from China ARMA analysis of the green innovation technology of core enterprises under the ecosystem – Time series data Reconstruction of multimodal aesthetic critical discourse analysis framework Image design and interaction technology based on Fourier inverse transform What does students’ experience of e-portfolios suggest 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 optimal model of employment and entrepreneurship models in colleges and universities based on probability theory and statistics 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 Analysing the action techniques of basketball players’ shooting training using calculus method Engineering project management based on multiple regression equation and building information modelling technology 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 Mathematical model of back propagation for stock price forecasting Application of regression function model based on panel data in bank resource allocation financial risk management Application of Logical Regression Function Model in Credit Business of Commercial Banks Research on aerobics training posture motion capture based on mathematical similarity matching statistical analysis Application of Sobolev-Volterra projection and finite element numerical analysis of integral differential equations in modern art design Research on motion capture of dance training pose based on statistical analysis of mathematical similarity matching 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 Application of Lane-Emden differential equation numerical method in fair value analysis of financial accounting Regression function model in risk management of bank resource allocation Application of numerical method of functional differential equations in fair value of financial accounting Optimal solution of fractional differential equations in solving the relief of college students’ mental obstacles Risk contagion in financial markets based on copula model Calculating university education model based on finite element fractional differential equations and macro-control analysis Automatic parameter selection ZVD shaping algorithm for crane vibration suppression based on particle swarm optimisation 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 Calculation of tourism development income index based on finite element ordinary differential mathematical equation Adoption of deep learning Markov model combined with copula function in portfolio risk measurement Radar system simulation and non-Gaussian mathematical model under virtual reality technology Comparison of compression estimations under the penalty functions of different violent crimes on campus through deep learning and linear spatial autoregressive models Research and application of constructing football training linear programming based on multiple linear regression equation Research on management evaluation of enterprise sales cash flow percentage method based on the application of quadratic linear regression equations Mathematical simulation analysis of optimal detection of shot-putters’ best path Determination of the minimum distance between vibration source and fibre under existing optical vibration signals: a study Mathematical modelling of enterprise financial risk assessment based on risk conduction model Nonlinear differential equations based on the B-S-M model in the pricing of derivatives in financial markets Mathematical simulation experiment based on optimisation of heat treatment process of aluminium alloy materials Mathematical model of transforming image elements to structured data based on BP neural network Educational reform informatisation based on fractional differential equation 3D Mathematical Modelling Technology in Visual Rehearsal System of Sports Dance 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 Informationisation of teaching model for track and field education based on finite element higher-order fractional differential equation Information technology of preschool education reform of fine arts based on fractional differential equation Information Teaching Model of Preschool Art Education in Colleges and Universities Based on Finite Element Higher-Order Fractional Differential Equation Application of artificial intelligence algorithm in mathematical modelling and solving College Students’ Mental Health Climbing Consumption Model Based on Nonlinear Differential Equations Communication architecture of power monitoring system based on incidence matrix model Differential equation to verify the validity of the model of the whole-person mental health education activity in Universities Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory Analysis and Prediction of College Students’ Mental Health Based on K-means Clustering Algorithm Mathematical function data model analysis and synthesis system based on short-term human movement Human gait modelling and tracking based on motion functionalisation Analysis and synthesis of function data of human movement Energy-saving technology of BIM green buildings using fractional differential equation Study on the training model of football movement trajectory drop point based on fractional differential equation Financial Accounting Measurement Model Based on Numerical Analysis of Rigid Normal Differential Equation and Rigid Functional Equation User online consumption behaviour based on fractional differential equation Differential equation model of financial market stability based on Internet big data Multi-attribute Decision Method Based on Normal Random Variable in Economic Management Risk Control Children’s cognitive function and mental health based on finite element nonlinear mathematical model Dichotomy model based on the finite element differential equation in the educational informatisation teaching reform model Nonlinear Dissipative System Mathematical Equations in the Multi-regression Model of Information-based Teaching Stock price analysis based on the research of multiple linear regression macroeconomic variables Fractional Linear Regression Equation in Agricultural Disaster Assessment Model Based on Geographic Information System Analysis Technology