Waterproofing is one of the cruxes for underground projections, which should be paid especial attention to in shield tunnels. Segment joints are the main leakage points and rubber gaskets are generally used for joints waterproofing. Therefore, waterproof properties of the rubber gasket should be strictly controlled.

There are many researches focusing on the impermeability performance of waterproof materials. Shalabi et al. [1,2] investigated the waterproof performance of gasket-in-groove under different contact stress states and studied the differences of waterproof ability between circular and longitudinal seams under the action of cyclic loading. Based on the variation law of mechanical properties of materials, Shi et al. [3] proposed a time-dependent constitutive model of rubber gaskets, and the relevant parameters were obtained by the material ageing test. Gong et al. [4] studied the water resistance characteristics of rubber gaskets for river crossing tunnels by using the new high-water pressure and automatic loading device.

In addition to the impermeability of waterproof materials, the optimization design method of rubber gaskets has also attracted considerable attention. Xiang and Shi [5] analyzed the deforming characteristics of elastic gaskets under different levels of compression, the distribution of contact stress and the compressive force needed during installation through Finite Element Method (FEM). Then the section that satisfied all design requirements was found based on the FEM analysis results by repeated adjustments and trials. Novak et al. [6] developed a probabilistic technique to evaluate gasket designs under different assembly conditions. Jones [7] outlined the procedures about optimizing gasket geometries and presented a comparison which showed the benefits of using such techniques. Krishnan [8] proposed a Computer Aided Engineering (CAE) approach to design, evaluate and optimize automotive powertrain gaskets, seals and gasket/seal assemblies.

Due to the elasticity of rubber materials, the gasket deforms easily when it is squeezed. Some sections of elastic gaskets, provided by different manufacturers, were measured by researchers which were used in the shield tunnel of a city subway, as shown in Figure 1. It can be seen from Figure 1, all of the geometry sizes, locations and shapes of the internal holes are wrong. Based on the optimization design experience, those incorrect parts have significant influences on the waterproof performance of rubber gaskets.

In addition, mechanical parameters, such as hardness of synthetic rubber materials, are largely influenced by places of production, compositions and temperatures. Generally, it is required that the hardness should change in a range of ±5 degrees by considering the randomness of mechanical properties.

Although many studies have been conducted to analysis the waterproof performance of EPDM (Ethylene Propylene Diene Monomer) rubber materials and the gasket optimization design method, the effect on the waterproof performance of rubber gaskets due to the continuous change of the structural parameter still remains unknown. In addition, the effects of the uncertainties of geometry sizes, machining errors and material parameters on the waterproof performance of rubber gaskets are not considered in previous optimization processes.

Based on the aforementioned, it is known that traditional design methods for the elastic rubber gasket have many defects. Therefore, aiming at dealing with the problems involved in the traditional methods, an innovative sensitivity analysis method is proposed, where the material hardness, coordinates of the hole center, apertures are regarded as random input variables instead of deterministic ones. Monte Carlo method and FEM are combined to acquire the sensitivity values of the waterproof performance with regard to the uncertain structural parameters.

The rest of the paper is organized as follows. After the introduction, we briefly explain the background theory of stochastic FEM based on the Monte Carlo method and ANSYS PDS module in section 2. Section 3 discusses a new method for the sensitivity analysis of elastic rubber gaskets in shield tunnel lining joints. Finally, we close the paper with some conclusions and remarks.

Since the geometry sizes, machining errors, materials, actual working loads are all random for the same batch of products in practical engineering, we need to use stochastic FEM to carry out the detailed analysis. The stochastic FEM [9] used in this paper is a combination of the Monte Carlo method and the FEM.

Monte Carlo method [10], also known as statistical test method or random simulation method, is based on the theory of statistical sampling. The structural stochastic analysis process carried out by using Monte Carlo method can be summarized as following three basic steps.

Sampling random variables. Random sampling based on the known probability distribution of the basic random variables.

Solving structural response. For each sample, the finite element method is used to calculate the response of the structure.

Statistical analysis of the response. According to the calculation results of all samples, the mean value, variance and even probability distribution function of the response are obtained.

A major drawback of the Monte Carlo method is the need of large sampling space. In order to overcome this shortcoming, this paper uses the Latin Hypercube Sampling (LHS) method [11] which reduces the sampling number by improving the convergence rate. LHS [12] method does not change the mean and variance of sampling space, and can greatly improve the computing efficiency. Therefore, it is more suitable for solving the stochastic response of engineering structures.

The PDS module of ANSYS combines the finite element method with the probability design technology. Based on the probability design of FEM, it can be used to study the uncertain effect on waterproof properties of rubber gaskets. The parametric modeling in ANSYS-PDS is often employed to carry out probability design analysis and the APDL (ANSYS Parametric Design Language) command flow is generally used to build the parametric model for probability design analysis. Based on the parametric model, the new model can be built by just changing some parameters, so it is more efficient and less costly to repeatedly analyze the effects of parameters on the waterproof performance, such as hardness, size, etc. The probability design analysis process based on ANSYS-PDS is shown in Figure 2.

In order to tackle the problems produced in the traditional design methods, a new sensitivity analysis method of the waterproof performance with regard to the uncertain structural parameters has been presented in this section.

The geometry sizes of the rubber gasket and segment groove studied in this paper are shown in Figure 3. The selected random parameters are as follows.

Material parameters of rubber _{10}, _{01}. The constitutive model used in this paper is the Mooney-Rivlin two-parameter model [13]. The model can describe the deformation characteristics of rubber materials in 150%.

The center coordinates of all the holes in the cross section _{i}_{i}

Radius of each round hole _{i}

The elastic rubber gasket in shield tunnel lining joints is EPDM synthetic rubber. In general, the hardness of rubber materials is clearly defined and the hardness of IRHD (International Rubber Hardness Standard) is often adopted, and the hardness tolerance required is ±5 degrees [14]. The relationship between hardness _{r}_{01}, _{10} are:
_{10}=0.700MPa, _{01}=0.035MPa, _{01} and _{10} of the equations (1) and (2) can be obtained as follows:

The center coordinates of the holes are _{1}=_{3}=2.75mm, _{2}=3.5mm, _{4}=9.5mm, _{1}=3.5mm, _{2}=8.3mm, _{3}=13mm, _{4}=11.5mm, respectively. The apertures are _{1}=_{3}=1.75mm, _{2}=_{4}=2mm. The _{01}, _{10}, center coordinates _{i}_{i}_{i}

Statistical characteristics of random input variables

Variable name | Distribution pattern | Mean value | Standard deviation | Min limit value | Max limit value |
---|---|---|---|---|---|

_{01}/MPa | truncated normal | 0.035 | 0.05_{01} | 0.0279 | 0.044 |

_{10}/MPa | truncated normal | 0.700 | 0.05_{10} | 0.5578 | 0.88 |

_{i} | truncated normal | _{i} | 0.15 | _{i} | _{i} |

_{i} | truncated normal | _{i} | 0.15 | _{i} | _{i} |

_{i} | truncated normal | _{i} | 0.03 | _{i} | _{i} |

In this paper, the unilateral compression model is employed to simulate the compression process of the rubber gasket, as in Figure 4. The rubber gasket can be considered as the flexible body and the concrete groove can be regarded as the rigid body. There are rigid-flexible contacts between the groove and the rubber and flexible-flexible contacts between the rubber and the rubber.

Due to the hyper elasticity characteristic of rubber materials, the model is established with the PLANE182 element. The contact elements use TARGE169 and CONTA172 elements with friction coefficient of 0.25 for rubber materials.

According to the maximum allowable opening amount in engineering, the unilateral compression can be set as 5 mm. All the degrees of the nodes of the groove are constrained and the X-direction degrees as well as the rotational degrees of the nodes of the upper pressure plate are constrained. All nodes of the upper pressure plate are specified to have a Y-direction displacement of 5 mm (compression direction).

Sensitivity analysis (SA) [16,17,18,19,20] is an important step in the process of model establishment and result discussion. In this section, the sensitivity analysis method based on the Spearman rank correlation coefficient is adopted [21].

The sequence of random structure parameters of the sealing gasket is _{10}, _{01}, _{i}_{i}_{i}

Let
_{j}_{1}, _{j}_{2}, . . . , _{jn}

For each data pair, the Spearman rank correlation coefficient _{sj}

Let _{k j}_{j}_{1}, _{2}, . . . ,_{14}; _{k j}

The Spearman rank correlation coefficient is an important parameter used to test the correlation between variables in nonparametric statistics. If the coefficient is close to 1 or −1, it indicates that the input variables significantly affect the output variables. If the coefficient is close to 0, it illustrates that the effect is weak. Besides, if the coefficient is positive, the output variables increase with the increase of the input variables. If the coefficient is negative, the output variables decrease with the increase of the input variables [23].

In the ANSYS-PDS module, the Monte Carlo method and Latin Hypercube Sampling method are chosen as the probability analysis methods and the cycle times is set to be 500 times for performing probability design analysis. Then, the trends of

The specific sensitivity values of the random input variables based on the Spearman rank correlation coefficient are listed in Table 2.

The sensitivity values of the input variables

Var. | _{01} | _{10} | _{1} | _{2} | _{3} | _{4} | _{1} | _{2} | _{3} | _{4} | _{1} | _{2} | _{3} | _{4} |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

0.049 | 0.971 | 0.126 | −0.102 | 0.094 | 0.011 | 0.010 | −0.019 | 0.010 | 0.032 | −0.072 | −0.040 | −0.138 | −0.102 | |

0.036 | 0.918 | 0.080 | −0.107 | 0.074 | −0.277 | −0.027 | 0.031 | −0.002 | 0.035 | −0.069 | 0.031 | −0.062 | −0.065 |

As can be seen from Table 2, the _{10} is the most effective factor for the average contact stress of the bottom surface, followed by _{3}, _{1}, _{4}, _{2}, and the influence of _{10} is greater than that of the other four variables. The _{10} is also the most significant factor for the average contact stress of the upper surface, followed by _{4}, _{2}, and the influence of _{10} is greater than that of the other two variables. Furthermore, in the random input variable space, it will make the average contact stresses of both the upper and bottom surfaces increase by increasing the rubber hardness _{10}. Besides, it will make the average contact stress of the bottom surface increase by increasing _{1}. The average contact stresses on both the upper and bottom surfaces will decrease with the increase of _{2}. The average contact stress on the upper surface will decrease with the increase of _{4}. The average contact stress on the bottom surface will decrease with the increase of _{3} or _{4}.

The maximum and minimum limit values of random input variables are calculated by the mean values and tolerances. In this section, the tolerances of random input variables are changed in order to analyze their influence on the sensitivity.

(1) Rubber hardness tolerance

The rubber hardness tolerances are chosen as ±5 degrees, ±4 degrees, ±3 degrees, ±2 degrees, ±1 degrees, respectively. The maximum and minimum limit values of _{01} and _{10} can be calculated using the equations (2), (4) and (5). The statistical characteristics of the other input variables are the same as those in Table 1. The same analysis method and sampling times as the above are used to get the sensitivity values of average contact stresses on upper and bottom surfaces, as shown in Figure 6. From Figure 6, it can be found that the rubber hardness tolerance has little effect on the contact stress sensitivity when the rubber hardness tolerance is in the ranges of ±5∼±3 degrees. When the rubber hardness tolerance is restricted within the range of ±2 degrees by taking stricter production standards, the effect of the rubber hardness on the contact stress decreases significantly and the effects of other variables on the contact stress increase significantly, such as the hole center location and aperture.

(2) Coordinate deviation

The abscissa deviations are selected as ±0.2 mm, ±0.17 mm, ±0.15 mm and ±0.13 mm, respectively. The maximum and minimum limits of abscissas of hole centers can be obtained by adding these deviations with the mean values. The statistical characteristics of the other input variables are the same as those in Table 1. The same analysis method and sampling times as the above are used to get the sensitivity values of average contact stresses on the upper and bottom surfaces, as shown in Figure 7. From Figure 7, it can be obtained that the influence of the change of abscissas on the average contact stress on the bottom surface decreases if the abscissa deviation is strictly controlled. Because the variation range of sensitivity values is small, it may be due to the influence of rubber hardness on the contact stress is more significant than other variables when the tolerance of rubber hardness is in the range of ±5 degrees in this condition. If the abscissa position deviation is strictly controlled, the influence of the abscissa change of the 4th hole center on the average contact stress on the upper surface decreases and the change value of the sensitivity is 0.113. The change of other abscissas has little effect on the average surface contact stress.

From Table 2, it can be found that the ordinates of hole centers have little effect on the contact stress. Therefore, the influence of the change of the vertical position deviation on the contact stress sensitivity is not discussed in this paper.

(3) Aperture deviation

The maximum limit of aperture is kept as _{i}_{i}_{i}_{i}_{i}_{1} and _{4} deviations, the less influence on the average contact stress on the upper surface. The stricter the control of the _{2} and _{3} deviations, the more influence on the average contact stress on the upper surface. But the change extents are small because the rubber hardness has a greater effect on the contact stress than the aperture.

This paper focuses on the sensitivity analysis of elastic rubber gaskets in shield tunnel lining segments. In order to obtain the correlation between the parameters and the average contact stress of sealing gaskets, the ANSYS-PDS module is employed by combining the Monte Carlo method with the FEM, and the parameters of material hardness, hole center coordinates and apertures are selected as the random input variables. The analysis method and the results of this paper have a certain reference value on optimal design of elastic rubber gaskets in the future.

By controlling the tolerance of the parameters in turn, the influence of various parameters on the average contact stress of the sealing gasket is obtained. The mechanical parameters of rubber materials are the main factors that influence the water pressure resistance, especially _{10}. The influence of rubber hardness on the contact stress is the most significant when the tolerance of rubber hardness is in the range of ±5∼±3 degrees. When the rubber hardness tolerance is restricted in the range of ±2 degrees under strict production standards, the influence of the rubber hardness on the contact stress decreases significantly, while the influence of other parameters on the contact stress increases remarkably.

As for geometric parameters, the greatest impact on the contact stress is the position of bottom hole 1. The effect of the size of the two round holes in the middle part of the section on the surface contact stress is larger than that of the other round holes.

#### Statistical characteristics of random input variables

Variable name | Distribution pattern | Mean value | Standard deviation | Min limit value | Max limit value |
---|---|---|---|---|---|

_{01}/MPa | truncated normal | 0.035 | 0.05_{01} | 0.0279 | 0.044 |

_{10}/MPa | truncated normal | 0.700 | 0.05_{10} | 0.5578 | 0.88 |

_{i} | truncated normal | _{i} | 0.15 | _{i} | _{i} |

_{i} | truncated normal | _{i} | 0.15 | _{i} | _{i} |

_{i} | truncated normal | _{i} | 0.03 | _{i} | _{i} |

#### The sensitivity values of the input variables

Var. | _{01} | _{10} | _{1} | _{2} | _{3} | _{4} | _{1} | _{2} | _{3} | _{4} | _{1} | _{2} | _{3} | _{4} |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

0.049 | 0.971 | 0.126 | −0.102 | 0.094 | 0.011 | 0.010 | −0.019 | 0.010 | 0.032 | −0.072 | −0.040 | −0.138 | −0.102 | |

0.036 | 0.918 | 0.080 | −0.107 | 0.074 | −0.277 | −0.027 | 0.031 | −0.002 | 0.035 | −0.069 | 0.031 | −0.062 | −0.065 |

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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 Construction of an enterprise financial risk management system based on F-score model Research on education management system based on machine learning and multidimensional data modeling Multi-featured multi-scale combination of high-resolution remote sensing images for building extraction Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data Electronic properties of diamond semiconductor materials: based on response surface model Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching Deep learning techniques in modern women’s smart clothing design Nonlinear Differential Equations in Computer-Aided Modeling of Big Data Technology A study on the aesthetic characteristics of ethnic music based on radial basis neural network model The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Analysis of the application methods of film and television media and images in the era of big data cloud Air data computer simulation and design credibility assessment considering ADC calculation model Analysis of news communication strategies in the era of full media based on big data mining On the improvement, innovation and inheritance of stage makeup styling in opera under the background of big data Recognition of Electrical Control System of Flexible Manipulator Based on Transfer Function Estimation Method Evaluation Mechanism of Teaching Staff’s Building in Local Vocational Colleges Based on Big Data Technology 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 Research on detection of parking space based on the combination of magnetoresistance and microwave radar sensor under IoT platform Research on sustainable development 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and location of leakage points based on machine learning Analysis of higher education management strategy based on entropy and dissipative structure theory Grid data asset relationship and intelligent classification integrating knowledge graph and Internet of Things 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 Analysis of digital humanistic knowledge production based on natural language processing 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 The Construction of Judgment Model for Cultivating Intelligent Accounting Professionals in Universities Based on Logarithmic Periodic Power Law Model Action of Aut( G ) on the set of maximal subgroups ofp -groupsDigital Regeneration and Database Construction of Hunan Embroidery Needlework under the Perspective of Artificial Intelligence Research on the practice of innovation and entrepreneurship education in universities under the environment of big data Application of digital technology in environmental art design Research on loyalty prediction of e-commerce customer based on data mining Research on the evaluation system of tourism management classroom teaching based on multimedia big data analysis The application of ARCS motivation model in college oral English teaching Research on Innovation of Translation Teaching and Translation Strategies for College Students in Multimedia Background A multi-channel convolutional neural network based on attention mechanism fusion for facial expression recognition Exploring the development of cultural and creative tourism under the perspective of ecological theory of tourism destination management Modeling Analysis of User Consumption Data of Internet Culture Industry in the Context of Emerging Technologies Reference: An algorithm for recognizing the main melody of orchestral music based on artificial intelligence of music melody contour 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 The construction of a practical platform for party building and ideological and political education based on information fusion A study on the influence of the spread of Yangming Studies in Japan on the psychology of the Japanese people based on big data analysis Research on personalized recommendation algorithm for micromechanical sensors based on cloud model Research on the value of modern vernacular literature in contemporary rural construction based on ADDIE model Robust speech recognition based on deep learning for sports game review Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Model Construction of Influencing Factors of Physical Education Core Quality Cultivation Based on Multiple Linear Regression Application of Nonlinear Differential Equation in Electric Automation Control System Research on the operation and management mechanism of cross-border e-commerce shared practice training base Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Strategies for improving Chinese language proficiency based on artificial intelligence technology The success rate model of college students’ new entrepreneurship based on nonlinear differential equations Computational Algorithm to Solve Two–Body Problem Using Power Series in Geocentric System Research on the application of marketing strategy of national fitness exercise and dance events in the construction of sports culture based on big data technology Decisions of competing supply chain with altruistic retailer under risk aversion Strategies for constructing mathematical models of nonlinear systems based on multiple linear regression models Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations Research on human resource management performance evaluation based on BP algorithm 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 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Waterproof Performance of Elastic Rubber Gasket in Shield Tunnel Innovation of Economic Management Risk Control in Retailer Supply Chain Based on Differential Equation Model Statistical Model of College Ideological and Political Learning Based on Fractional Differential Equations Nonlinear Differential Equation in Anti-aging Test of Polymer Nanomaterials 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 University Ideological and Political Learning Model Based on Statistical Memory Curve Mathematical Equation 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 Conventional Algorithms in Sports Training Based on Fractional Differential Equations Dynamic Nonlinear System Based on Complex System Theory in the Development of Vocational Education The Algorithm Accuracy of Mathematical Model to Improve the Transmission Speed of E-commerce Platform The Security of Database Network Model Based on Fractional Differential Equations Electric Vehicle Mechanical Transmission System Based on Fractional Differential Equations The Practice System of Physics and Electronics Courses in Higher Vocational Colleges Based on Fractional Differential Equations The Economic Model of Rural Supply and Demand Under the Data Analysis Function Based on Ordered Probit 3D Modeling System of Indoor Environment Art Landscape Design under Statistical Equation Electronic Information Security Model of Nonlinear Differential Equations The Optimization Model of College Students' Physical Exercise Motivation and Self-control Ability Based on the Mathematical Model of Probability Theory 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 urban energy Internet planning based on fuzzy comprehensive method 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 intelligent path of college students’ network ideological and political education based on big data mining technology Research on the application of PLC technology in electrical automation engineering Application of matrix multiplication in signal sensor image perception 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 Research on the experimental principle of deep integration of LETS software and criminal procedure under the background of artificial intelligence VR-based computer maintenance practical training platform development design and application research Design and implementation of an integrated management system for discipline construction and postgraduate education in universities 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 Research on educational resource recommendation system based on MRLG Rec Visual analysis of the trend of mental health changes among Chinese college students in the context of the normalisation of the new crown epidemic A study on the phenomenon of anaphoric correction in college students’ English conversation 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 Research on the innovation of collaborative education model of scientific research and teaching in colleges and universities based on the theory of process reengineering AtanK-A New SVM Kernel for Classification The innovative path of diversified vocal music education reform in colleges and universities under the advanced educational concepts of China and the West Mechanical behaviour of continuous girder bridge with corrugated steel webs constructed by RW Rhino application in ceramic packaging design teaching Study of a linear-physical-programming-based approach for web service selection under uncertain service quality 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 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 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 Design and evaluation of intelligent teaching system on basic movements in PE Research on identifying psychological health problems of college students by logistic regression model based on data mining 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 Financial customer classification by combined model Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Retraction: Wei, Wei and Lu, Liu. “The influence of X fuzzy mathematics method in basketball tactics scoring” Applied Mathematics and Nonlinear Sciences, vol.7, no.1, 2022, pp.677-684 Retraction Retraction: Retraction of: Mundewadi, R. A. and S, Kumbinarasaiah. “Numerical Solution of Abel's Integral Equations using Hermite Wavelet” Applied Mathematics and Nonlinear Sciences, vol.4, no.2, 2019, pp.395-406