With the fast advancement of China's economy, the engineering construction has also achieved great-leap-forward development, which accounts for an increasing proportion in China's social economy. However, in the process of expanding the scale of the industry, the engineering construction has exposed a series of problems such as out-of-control cost, disconnection between technology and cost management, etc. At the same time, more and more foreign enterprises have entered China, which forms a fierce competitive relationship with domestic construction enterprises. Therefore, it forces the level of China's engineering cost management to be further improved in order to meet the increasingly competitive international and domestic circumstances.

The process of China's engineering cost management can be divided into three stages. The first is the planned economy era before the early 1980s. At this stage, China's engineering cost management is mainly based on the quota pricing model of budget where the government implements long-term price control and follows the rule of combining quantity and price. The government is the sole investor of projects and the price is highly uniform. The second stage is the transition from planned economy to market economy from 1985 to 2003. At this stage, China's constructing expense the board is in the underlying time of change, which breaks the traditional pricing model and puts forward the idea of “control quantity, open price and introduce competition”. The government protection is gradually weakened, and the subject of investment begins to diversify and the amount of which is increasing. Limited market competition has been achieved under the guidance of national macro-control. The third stage is the era of socialist market economy after 2003. According to the demand of market, China's engineering cost management has been adjusted and improved. With the condition that market price is the main factor, the construction market is gradually opening up and moving towards full market competition under the national macro-guidance. In short, after a series of evolution, China's engineering cost management is gradually transforming from the traditional quota pricing model to a new model of “macro-control of government, independent quotation of enterprises, market-determined price and comprehensive social supervision”, while the price mechanism of the construction market is gradually taking shape. In market economy, the level of construction market price is very sensitive to economic risk factors such as exchange rate change, loan interest rate and inflation, which makes the fluctuation of market price become the key to the cost control. In addition, with the continuous expansion of the scale of China's construction market, the participants of projects have increasingly demand for engineering cost data.

However, the industry of China's constructing expense is still in the early stage of informatisation, and the analysis of big data in engineering cost list is lagging behind. Many documents, especially about the extensive unit cost of each project, have countless data anomalies. The list data are seriously deviated from historical data, and the complete unit cost of the rundown is conflicting with the depiction of the rundown, which brings great difficulties to the subsequent utilisation. Therefore, it is urgent to explore another location technique for strange information in engineering cost list. Based on this, this paper studies the detection model of engineering cost list, which aims to effectively promote the standardised management of engineering cost data.

China's construction industry often adopts a bill of quantities for bidding. First, the tenderer compiles the bill of quantities for entities and non-entities of a project. Then the bidder applies the company's enterprise quota to bid for the quantity bill according to the standard of them. It is an important method in the field of engineering valuation in China. Comprehensive unit cost is the form of bill of quantities valuation, that is, direct costs, management fees, taxes and profits are calculated for each project in the process of quotation, among which direct costs include the calculation of labour costs, materials costs and machinery usage fees [1]. The valuation process of quantity bill is shown in Figure 1.

There is a lot of useful data information in the engineering cost list, and the thorough unit cost of the rundown is the information firmly connected with the designing expense. As of now, the conventional location strategy for strange information at the exhaustive unit cost of the rundown fundamentally recognises the unusual information of which the contrast between the far reaching unit value information of the rundown and the chronicled information is excessively enormous, but there is another kind of abnormal data in the actual situation. In other words, albeit the exhaustive unit cost of the rundown has little contrast with the verifiable information in general, there are irregularities that are genuinely conflicting with the portrayal of the rundown that can’t be recognised well by the conventional recognition. The model of engineering cost list studied in this paper is mainly used to detect the abnormal data of extensive unit cost in the list with complete description of information [2].

In this project, the data set used for detection of abnormal data in engineering cost list is normal list data of more than 5,000 list items named “cast-in-place reinforcement component” and abnormal list data of more than 400 [3]. The extensive unit cost distribution of more than 5,000 pieces of normal list data is shown in Figure 2.

By analysing the acquired data set, it can be found that the data set used for detection of abnormal data in comprehensive unit cost has the following characteristics besides those of inventory data:

It can be seen from the distribution chart of the comprehensive unit cost of the list that the boundary of the list is obvious on the whole, the normal list data fluctuate in a small range in several intervals and the clustering trend of the extensive unit cost is obvious, which is convenient for the subsequent clustering work [4].

By analysing the attributes of the list data, it can be found that the list materials of the same name “cast-in-place reinforcement component” are basically identical, and the main differences are concentrated in the description, including the used technology, operation methods, specific material models and so on.

The comprehensive unit cost of some abnormal data is within the reasonable floating range of normal data, and the difference with normal data is only reflected in the description of list. This detection method is difficult to implement, which is also a kind of anomaly [5] that this paper focuses on.

To take care of the issue of strange information location, which has a major hole between the exhaustive unit value information and authentic information, this paper has followed the traditional detection method based on distribution statistics of historical data that is relatively mature at present. While this kind of abnormal data were found before, the exhaustive unit cost is conflicting with the rundown. After analysing the characteristics of normal data and abnormal data of “cast-in-place component reinforcement”, it is observed that the connection between extensive unit cost of rundown and description of list can be compared with the relationship between list information and category labels. That is, the far-reaching unit cost of the rundown can be utilised as the name of the rundown depiction, and the connection between rundown portrayal and extensive unit cost can be investigated. When a normal list is entered, the correlation between its list portrayal and comprehensive unit cost is bound to be strong, while when an abnormal list is entered, the past hypothesis shows that the connection between its rundown portrayal and thorough unit cost will undoubtedly be frail [6].

According to this, this paper proposes a strategy for recognising unusual information of extensive unit cost of rundown, which takes extensive unit cost of the list as the label. Firstly, the descriptions of the normal list are clustered according to extensive unit cost, and the cluster centre is taken as the label of each type. Then, a list classifier is trained according to the training data to analyse the connection between the list data and the label. For the test data, the degree of association between the list data and the category label is analysed. If the degree is lower than the threshold value, the extensive unit cost of the data is judged abnormal [7]. The flowchart is shown in Figure 3.

Simply choosing the extensive unit cost of each rundown as the name will cause too many categories, which results in poor information in every classification. Moreover, the extensive unit cost of the normal list under the same process and material model fluctuates within a reasonable range, which will cause serious problem of over-fitting [8]. Through the distribution of the normal data obtained in this subject, it can be seen that it has obvious trend of clustering, which promotes to the idea of clustering the extensive unit cost of the list and taking the bunching focus as the name of every sort.

In this paper, K-means is used to cluster the list according to the extensive unit cost. The K-means algorithm finally tends to select the clustering centres with large gaps, and at the same time, all points are attributed to the clustering centres with close distances, which is obviously different from the overall boundary of the extensive unit cost but similar to the list portrayal that the extensive unit cost of the list fluctuates within a reasonable range [9].

K-means clustering algorithm has the benefits of quick running velocity and large amount of data processing, but K-means clustering can only deal with continuous variables and only get local optimal solutions. Meanwhile, it is necessary to determine the clustering category for that the results of clustering are easily influenced by the initial clustering [10].

The flow is as follows: First and foremost, decide the quantity of bunching classifications k and at the first group the informational collection. The bunching results are communicated by k clustering centres. Then, at that point, the calculation embraces the iterative refreshing strategy, in light of the given grouping objective capacity (or rule of bunching impact), and every emphasis cycle is done towards diminishing the genuine capacity esteem. At last, the grouping result causes the genuine worth to get the base to accomplish a superior bunching impact [11].

Enter:

K: Number of clusters

D: Data set containing n objects

Output: The set of k clusters and the criterion is to minimise the sum of squares error.

Steps:

Choose k initial clustering centres:

Assuming that the R-th iteration has been carried out, if a sample x

Calculate each cluster centre after reclassification:

If
^{[12]}.

It is called the mean K algorithm for that the sample mean of k clusters is to be calculated in step (3). The characteristic of this algorithm is as follows: after determining the initial cluster centre, the distance from all samples to the cluster centre is calculated, all samples according to the principle of minimum distance are classified from the initial classification and then each cluster centre is recalculated, which is a batch processing method. Another method is one by one processing. When a sample is read in, it is classified into the nearest class, then a new classification is formed and a new cluster centre is calculated; after that, the next classified sample is read in, that is, the classification of each sample changes the cluster centre [13] once.

The normal lists are grouped into 5 categories according to the extensive unit cost. Its results are as shown in Figure 4, and the clustering centres are 3846, 4043, 4196, 4608 and 5002. The clustering centres of each category are used as their classification labels to facilitate subsequent processing [14]. It can be seen that the distribution of extensive unit cost of list indicates strong regularity. The extensive unit cost data of normal list are obviously clustered into several clusters in the data distribution map, and the simple K-means clustering algorithm can fully meet the requirements of simple clustering in this paper.

The description in the engineering cost list involves many proper nouns and special symbols, as well as the scattered distribution of characteristic words. As a result, Bayesian list classification method is used to classify the list data in the detection of abnormal data in engineering cost list.

In this paper, Laplace smoothing parameter in Bayesian list classification method is used to classify the list in detection of abnormal data. Laplace smoothing is a method to deal with the problem of zero-probability event. The core idea of which is to increase the numerator count of estimation by 1 and uniformly increase the denominator by the corresponding value. In this way, the influence on the overall probability estimation can be neglected, and the probability of zero can be avoided. Therefore, Laplacian smoothing is also called additive smoothing [15].

_{j}

Assume _{j}_{j}, j_{1},_{2}, ⋯,_{m}^{T} represents the obedience for Dirichlet distribution, whose parameter is _{C1}, _{C2}, ⋯, _{Cm}

Consequently, the posterior distribution of

The posterior probability _{C1}, _{C2}, ⋯, _{Cm}_{Cj}

_{i}|C

_{j}

If _{j}_{jl}t_{i}_{k}_{l}_{i}_{j}_{1},_{2}, ⋯,_{Sj}^{T} obeys Dirichlet distribution with parameter,

If _{j}_{1},_{j}_{2}, ⋯,_{j}_{Sj}_{jl}

Consequently, the posterior distribution of

Posterior probability _{C1}, _{C2}, ⋯,_{Sj}_{jl}

Then, the estimation of conditional probability is written as follows:

In the above equations (

In this paper, K is set as an integer between 5 and 15 in K-means to cluster, and then, the influence of Laplace smoothing parameter in Bayesian list classification method is test. Here, only two typical cases are listed.

In the test, more than 5,000 pieces of normal list data were selected for K-means clustering, and the cluster centre of each piece was used as its category label, 4,500 pieces of them were regarded as training data and the remaining 500 were used as test sets [18].

When K=9, the results of Laplacian smoothing parameters’ influence on accuracy are shown in Table 1 and Figure 5. It can be seen that Laplacian smoothing parameters have no influence on classification accuracy when there are few categories of clustering.

Experimental results of K=9 Laplacian smoothing parameters

_{laplace} |
0.0001 | 0.001 | 0.01 | 0.1 |
---|---|---|---|---|

Accuracy | 0.998 | 0.998 | 0.998 | 0.998 |

Meanwhile, when K=13, the results are shown in Table 2 and Figure 6 that when there are many categories of list clustering, Laplacian smoothing parameters have certain influence on classification accuracy, and the smaller Laplacian parameters, the higher the accuracy of list classification [19].

Results of K=13 Laplacian smoothing parameters

_{laplace} |
0.0001 | 0.001 | 0.01 | 0.1 |
---|---|---|---|---|

Accuracy | 0.9552 | 0.9561 | 0.9443 | 0.9242 |

The characterisation of typical rundown information in the location isn’t clear, and really, there is an association between the cycle and material model in the portrayal of comparative records. Assuming the rundowns in a similar classification are coercively assembled into two distinct classifications, the last impact can’t be ensured, and on the off chance that there are too couple of classes of bunching, it can’t accomplish the impact of recognising typical information from unusual information as indicated by group marks and rundown depictions. So, it is important to decide the K with the most elevated exactness based on outcomes [20].

From Table 3 and Figure 7, it can be seen that when the K of clustering is less than 10, the two Bayesian list classification methods are very effective, while when K is greater than 10, the classification accuracy of the two list classification methods begins to decline, which shows that the limit of the number of clusters of data in this batch is 10. When the value of K continues to increase, it is forcing the lists that belong to one category to be grouped into different categories. Furthermore, it can be seen that the effect of the polynomial Bayesian list classification method is better than the effect of the Bernoulli Bayesian list classification method. Therefore, the polynomial Bayesian list classification method is finally selected to classify the list data in the detection of abnormal data [21].

Accuracy results of K value in K-means and the two Bayesian classification methods

K | 5 | 7 | 9 | 10 | 11 | 13 | 15 |
---|---|---|---|---|---|---|---|

Polynomial | 0.998 | 0.998 | 0.998 | 0.998 | 0.967 | 0.935 | 0.891 |

Bernoulli | 0.998 | 0.998 | 0.998 | 0.998 | 0.961 | 0.913 | 0.873 |

By utilising the previous classifier and utilising the clustering centre obtained by K-means, the abnormal data of engineering cost list which is inconsistent with the list portrayal can be detected. Just the ordinary rundown information is utilised in preparing the rundown classifier. Hence, the rundown classifier will just become familiar with the relationship between the typical broad unit cost of the rundown and the portrayal [22].

In the ensuing contribution of ordinary information, the classifier can characterise the rundown into the classification addressed by the right bunch community as per the learned information and rundown depiction. Right now, it is viewed as that the broad unit cost of the rundown matches the rundown depiction and is ordinary information [23]. Since the classifier has not taken in the comparing connection between the broad unit cost and the rundown depiction, in this way, assuming the strange information is input, the classifier is more disposed to arrange the rundown depiction into the name that it ought to definitely relate to. In the meantime, the connection between the result list depiction and its own broad unit cost mark is frail. It is viewed as that the rundown depiction would not match the broad unit be able to cost, which is abnormal information [24].

The process of abnormal data detection is as follows: Firstly, the traditional method is used to judge whether the data are abnormal; if the data are normal, the attribute of list portrayal is extracted as the classification basis; afterwards, the two grouping places A and B which are nearest to the broad unit cost of the rundown are gotten. After preprocessing and other work, it is input into the trained list classifier, and the probabilities P_{A} and P_{B} that belong to A and B in the list portrayal are calculated; next, the smaller value of 1-P_{A} and 1-P_{B} is taken as the anomaly index. If the anomaly index exceeds the threshold, it is regarded as abnormal data; otherwise, it is normal data. The flow chart is shown in Figure 8.

The impact of the quantity of clusters K in K-means on the detection method is studied mainly in the test, and the indexes of evaluation mainly include the accuracy and recall rate of abnormal data.

According to Table 4, the formulas are as follows:

Abnormal data recognition pointers

Actually abnormal data | Actually normal data | |
---|---|---|

Identify as abnormal data | TP | FP |

Identify as normal data | FN | TN |

In the test, K is selected as 5, 7 and 9 [26], which has higher classification accuracy and is relatively stable in the previous test.

The results in Table 5 and Figure 9 can be seen that the recall rate of the abnormal data detection method is very high as a whole. When the worth of K is bigger, that is, there are more categories of training data clustering, the recall of abnormal data will be improved, which means that the finer the category granularity of test data, the more abnormal data can be detected. However, the corresponding accuracy rate decreases, mainly because some normal data will be regarded as abnormal data, when the categories increase. In pragmatic application, the review rate ought to be inside the adequate reach, and simultaneously, to diminish the manual survey of unusual information in the later period, the K-means grouping technique [27] is selected with K=5 in the actual detection after considering the two indicators comprehensively.

Table of detection on abnormal data

K of K-means | 5 | 7 | 9 |
---|---|---|---|

Recall rate | 0.8579 | 0.8874 | 0.9094 |

Accuracy | 0.9112 | 0.9013 | 0.8969 |

In this test, a strategy is proposed to tackle the issue that the conventional technique for strange information recognition can’t identify the unusual information connected with the rundown depiction. Thus, the strategy is contrasted and the conventional technique that in light of distance, where K=5 [28].

The traditional idea of distance-based method is basically to compute the contrast between test information and preparing information. In the event that the quantity of preparing information (whose distinction esteem is under a specific worth) is more noteworthy than the edge, the test information is considered as expected information and in any case unusual information [29].

From the results in Table 6 and Figure 10, it tends to be seen that utilising the rundown characterisation technique to distinguish the strange information of the broad unit cost in the designing expense list proposed has higher exactness than the customary strategy, and it has better acknowledgement of unusual information. The fundamental explanation is that the conventional strategy just considers the circulation law of broad unit cost in ordinary information. Without considering the connection between the broad unit cost and the rundown depiction, the customary technique is hard to identify the unusual information and has helpless impact [30].

Experimental table of comparison between traditional methods and methods of this subject

Evaluation index | Accuracy | Recall rate |
---|---|---|

Distance-based approach | 0.8298 | 0.6202 |

List classification method | 0.9112 | 0.8579 |

In this paper, the detection model of abnormal data in engineering cost list is studied. Combined with the selected data, a means to detect abnormal data of list extensive unit cost based on list classification is proposed. K-means clustering method is introduced to cluster the list in light of the extensive unit cost. Bayesian list classification method is used to classify the list data in detection, and the classification accuracy of polynomial Bayesian method is high. On this basis, the K-means with K=5 is selected. By comparing the detection method of abnormal data in designing expense list with the conventional identification strategy in light of distance, it is known that the detection proposed in this paper has higher accuracy and higher recall rate than the traditional method, which has excellent effect and certain application value.

#### Experimental table of comparison between traditional methods and methods of this subject

Evaluation index | Accuracy | Recall rate |
---|---|---|

Distance-based approach | 0.8298 | 0.6202 |

List classification method | 0.9112 | 0.8579 |

#### Abnormal data recognition pointers

Actually abnormal data | Actually normal data | |
---|---|---|

Identify as abnormal data | TP | FP |

Identify as normal data | FN | TN |

#### Table of detection on abnormal data

K of K-means | 5 | 7 | 9 |
---|---|---|---|

Recall rate | 0.8579 | 0.8874 | 0.9094 |

Accuracy | 0.9112 | 0.9013 | 0.8969 |

#### Results of K=13 Laplacian smoothing parameters

_{laplace} |
0.0001 | 0.001 | 0.01 | 0.1 |
---|---|---|---|---|

Accuracy | 0.9552 | 0.9561 | 0.9443 | 0.9242 |

#### Experimental results of K=9 Laplacian smoothing parameters

_{laplace} |
0.0001 | 0.001 | 0.01 | 0.1 |
---|---|---|---|---|

Accuracy | 0.998 | 0.998 | 0.998 | 0.998 |

#### Accuracy results of K value in K-means and the two Bayesian classification methods

K | 5 | 7 | 9 | 10 | 11 | 13 | 15 |
---|---|---|---|---|---|---|---|

Polynomial | 0.998 | 0.998 | 0.998 | 0.998 | 0.967 | 0.935 | 0.891 |

Bernoulli | 0.998 | 0.998 | 0.998 | 0.998 | 0.961 | 0.913 | 0.873 |

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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 -groupsThe internal mechanism of corporate social responsibility fulfillment affecting debt risk in China: analysis of intermediary transmission effect based on degree of debt concentration and product market competitive advantage Study on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Asymptotic stability problem of predator–prey system with linear diffusion Research on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations 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 sentiment analysis method based on bidirectional long short-term memory networks 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