For most Chinese schools and teachers, the teaching evaluation of spoken English is much more difficult than that of written English. Foreign language ability is a part of the national comprehensive quality, and the improvement of foreign language proficiency will help a nation gain more right to speak in the world. At present, English is the universal language in the world. Mastering English will have the tools to communicate with the world. The most important purpose of language learning is communication, and listening and speaking ability is the most important language skill .
In the early days, under the influence of the test-oriented education model, English teaching in China pays too much attention to the cultivation of reading and writing ability and neglected the training of oral expression ability. In English classes, teachers mainly talk about grammar and vocabulary, and there are few opportunities for oral expression. It can be said that oral language is basically not the focus of teaching, resulting in the common phenomenon of ‘dumb English’ and ‘Chinese English’ among Chinese students, which seriously affects the future development of students.
The difficulties in the teaching of spoken English in China can be summarised into three points. First, there are many students in large classes, and it is difficult for every student to have the opportunity to speak in class; second, there is no platform for students to practice oral English and get instant evaluation and feedback after class ; the organisation of the examination is very difficult. It requires a special voice computer room, supporting software and hardware computer test system, manual grading system and test question resources. Teachers need to spend several hours on correcting the written interview papers, in order to fully listen to the students' answering audio and give a rating. This situation is slowly changing. In recent years, in order to meet the needs of society and promote the reform of quality education, education authorities across China have actively explored the oral English test in the middle and high school entrance examinations. There are many types of questions in the oral English test of the middle and high school entrance examination, and the number of candidates is large. The traditional oral English test is conducted by manual face-to-face test or computer recording and manual scoring. This test method is difficult to organise and expensive to implement, and the scoring results are easily affected by the subjectivity of the scorers, which is not conducive to large-scale development.
Therefore, before 2011, the college entrance examination in each province only had an additional test for oral English, which was not included in the college entrance examination score. In 2011, Guangdong Province took the lead in not setting up an additional oral English test and directly included English listening and speaking scores into the total score of the college entrance examination. Candidates who take the English subject test must take the test, and the test results are obtained through manual double scoring. In 2014, the computer intelligent voice evaluation system developed by iFLYTEK was officially applied to the English listening and speaking test of the Guangdong college entrance examination. All the scoring work was completed within 2 days, which greatly reduced the difficulty of the organisation of the test and improved the scoring efficiency. The large-scale oral English test has become a reality, entering the era of computer intelligence evaluation, and it is feasible to promote it nationwide. At present, Canton phonetic evaluation technology helps oral English teaching, and voice evaluation technology helps oral English teaching and evaluation to be applied. Wenzhou and other 32 provinces and cities have included the English listening and speaking test into the senior high school entrance examination, and nearly 15 provinces and cities have included the results in the total score of the senior high school entrance examination. The computer intelligent scoring system of iFLYTEK has been widely used in auxiliary scoring.
Generally speaking, the measurement of confidence in the objective assessment of English pronunciation is obtained by calculating the correlation with the subjective assessment score. A high correlation coefficient indicates that the computer objective evaluation result is closer to the expert subjective evaluation, and the objective evaluation score is more reliable and more credible to reflect the quality of speech pronunciation. The low correlation coefficient indicates that the objective evaluation results of the computer are far away from the subjective evaluation results, so the reliability of the objective scores obtained by the computer is judged to be low . In order to obtain the objective evaluation score with high confidence, the traditional method is to obtain the pronunciation quality evaluation score goodness of pronunciation (GOP) of each speech frame through the forced matching algorithm, and the GOP score is weighted and mapped to the GOP of phonemes and words. The purpose is to obtain objective scores that are more consistent with subjective evaluations .
Speech signal is a typical time-varying signal . When the observation time is reduced to a small enough range, a series of approximately stable signals can be obtained. Therefore, when analysing the speech signal, we always assume that the speech signal is stationary within a time frame, which is the short-term analysis assumption of the speech signal. Usually a frame is about 20 ms or so. A set of features can be obtained by windowing a frame of signals and then performing feature analysis, and then processing the next frame by shifting the analysis window by an offset. There are related Hamming window or rectangular window functions in MATLAB speech signal processing. Practice has proved that this short-term stationary assumption is effective for the extraction of speech signal feature vectors. Feature vector extraction is an important part of speech evaluation. Feature vector extraction solves the digital representation of time-domain speech signals and provides data for the regression part.
Feature vector extraction is an important link in speech evaluation . Feature vector extraction addresses the digital representation of time-domain speech signals  and provides data for the regression part. The quality of feature extraction directly affects the performance of the regression machine.
There are various methods for extracting speech features, such as ZCR, LPC, LPCC and MFCC. The linear prediction coefficient (LPC) method has been successfully applied in speech recognition due to its robustness to environment and speaker changes. In this study, the LPC method is used to process the sound signal frame by frame, and the linear prediction cepstral coefficients (LPCCs) are used as the feature vector of audio information. The LPC uses a finite number of parameter models to linearly approximate the audio sequence x(n). These parameters are called LPCCs. The extraction process of the LPCC is as follows: first, pre-emphasise the sampling points contained in each audio frame, add a window function to the pre-emphasised audio intra-frame signal and then perform autocorrelation analysis on it, and apply this result to p. In order linear prediction calculation, the sequence of length p is obtained, which is the LPC-derived cepstral coefficient of the audio frame; the linear prediction cepstral feature is extracted from each short-term audio frame, which mainly reflects the short-term frame characteristics of the audio. In this study, the 10th-order LPCC is used as the feature vector of each frame of speech , and some other features can also be added according to the situation. The speech feature extraction process is shown in Figure 1.
In speech recognition, the maximum likelihood criterion is often used for the training of acoustic models [9, 10, 11], but the maximum likelihood criterion only considers increasing the likelihood of the correct category and does not consider the information of misclassification, which may cause problems in improving the correct category. At the same time as the similarity, the likelihood of the wrong category becomes higher. The discriminative training is not aimed at maximising the likelihood of the training corpus but focusses on how to adjust the classification surface between different models to improve the recognition ability of the model. In recent years, the discriminative training has significantly improved the performance of the speech recognition system. The representative training criteria are the maximum mutual information, minimum classification error and minimum word error. In order to further improve the generalisation of the model to improve the performance and robustness, the method similar to the large decision margin in machine learning is applied to the field of speech recognition to increase the distance between the correct recognition result and the wrong recognition result. For example, the maximum margin estimation criterion, the soft margin estimation criterion and enhanced confusing information methods mainly include enhanced maximum mutual information/minimum phoneme error and discriminative combinations between different models.
The data selection method based on the minimum phoneme error criterion proposed by Liu et al.  is based on the entropy value of the posterior probability of the Gaussian distribution in the state and selects training samples in the unit of time frame. A method of selecting data such as training sentences and candidate arcs in the expected phoneme accuracy field . However, the aforementioned data selection methods are not sufficiently related to the calculation of statistics required for the update process of the acoustic model. In order to improve the combination of data selection and statistics and the efficiency of discriminative training, this study adopts the dynamic weighting method, which combines the posterior probability and the expected phoneme accuracy rate field to select training samples and competing candidates. The discriminative training algorithm focusses on the contributing samples [14, 15, 16] to adjust the parameters of the acoustic model. This study firstly selects candidate paths and candidate arcs that contribute more to the model statistics in the posterior probability word graph, based on the error of the candidate paths. Then, according to the confusion information of the phoneme pair, the penalty weight is applied to calculate the phoneme accuracy. On this basis, the distribution of the expected phoneme accuracy of the candidate arcs is estimated, and the candidate arcs are weighted. Finally, the performance of the proposed method is discussed [17, 18, 19, 20].
Discriminative algorithms generally use word graphs to describe the competitive relationship between candidate words and calculate and adjust acoustic model statistics based on word graph information. The word graph contains many candidate paths, which effectively describe the correct recognition results and candidate words. The competitive relationship between them provides sufficient confusion information for discriminative training. Given a training sentence z, the objective function of the minimum phoneme error criterion is as follows:
The designed computer speech evaluation system can be divided into two parts: forced matching and score mapping. Force matching is used to get the GOP scores of phonemes, and score mapping maps the GOP scores of phonemes to words and sentences. The final evaluation system outputs an objective evaluation score of 0–100 based on phonemes, words and sentences.
First, the preprocessed learners' English pronunciation is verified by speech segment, including vowel segment cutting, establishment of verification system and reliability of verification system. The Viterbi algorithm cuts and decodes the speech segments and then sends the information including the extraction of evaluation parameters, the regularisation of evaluation parameters, the parameter association process and evaluation mechanism to the core of the English pronunciation evaluation system, that is, the pronunciation evaluation module. The weight of the evaluation parameters in the English pronunciation evaluation to reflects the opinions of human experts on the quality of English sentences and the feedback results provided to the learners including the comprehensive score and the correction opinions after the comparison of the expert knowledge base [23, 24, 25].
The so-called voice segment verification is to generate judgement thresholds for different evaluation voices and judge the correctness of the evaluation voice content according to the thresholds. After the verification system receives the evaluation speech segment, it performs pattern matching on each vowel, and then according to the distance of the matching result, combined with the verification mechanism, the final confidence threshold is given.
In this study, the forced alignment method commonly used in the Viterbi algorithm is used to cut the speech segment into smallest vowel pronunciation segments as much as possible. In this case, after the evaluation speech is cut, if the evaluation content and the standard pronunciation content are highly familiar, the number of vowel segments generated after cutting will be close to or equal to the number of standard pronunciation vowel segments. If the evaluation content is preceded by The n vowel consonant segments are the same as the standard pronunciation, and the following vowel consonant segments are speech segments outside the standard pronunciation library, so the number of vowel consonants after forced alignment is about n. After the vowel segment is cut, the number of vowel and consonant segments that can be cut out in the system is 15. For some speech segments that are not cut out, this study sets the confidence level to 0 to enhance the reliability of speech segment verification and make the recognition rate of the system higher. The pronunciation content of the upper part is the same as the standard pronunciation, and the system can cut out complete vowel segments; the pronunciation content of the lower part is partly different from the standard pronunciation, and the system can only cut out the vowel segments in the standard pronunciation library but cannot cut it. Vowel segments are outside the library.
The discriminative training method based on enhanced confusion information further improves the recognition performance. By weighting the candidate paths, the correct recognition result cannot be too close to the candidate word sequence with more errors, that is, for each training sentence, in the candidate word. In the sequence space, the greater the difference between a candidate word sequence and the correct recognition result, the stronger the discriminative information of the candidate word sequence, and its weight should be increased during training so as to be paid attention to when adjusting the acoustic model.
The dynamic weighting based on posterior probability and the discriminative training method based on enhanced confusion information use the same weighting factor
Due to the rich information in the word graph, the candidate paths that appear in the weighting process based on the posterior probability will be very huge, and most of the candidate words with too small posterior probability will make little contribution to the statistics and will increase significantly. Discriminative training is time-consuming and will affect the performance of recognition. In order to improve the efficiency of discriminative training, it is necessary to effectively trim the word graph and select useful samples for training. Commonly used trimming methods are mainly used in the decoding process of continuous speech recognition. However, unlike decoding in speech recognition, a unigram grammar is often used to generate word graph competition sets in discriminative training, and it is necessary to retain candidates. The starting and ending times of the arc are used to calculate the posterior probability of the arc in order to weight the Gaussian occupancy and statistics. In the likelihood-based Beam decoding process, only the states and paths whose cumulative likelihood is greater than the threshold are expanded, and the low state and path at the threshold will be clipped, which will cause many candidate words with high posterior probability, and competitive and confusing information to be removed due to the low likelihood score of the path. The degree of clipping is not suitable for discriminative training, but the Beam clipping algorithm is still a very effective word graph clipping method. Since the posterior probability has a great influence on the update of the model parameters and the recognition results, this study adopts a posterior-based method. The probabilistic Beam algorithm is used to trim word arcs, that is, the likelihood word graph describing the scores of the acoustic model, and the language model is converted into a posterior probability word graph and then trimmed on the posterior probability word graph [27, 28].
Based on the definition of the recognition error rate
Before speech cutting, an acoustic model should be established as the evaluation reference standard, then vowel segments should be cut out according to the standard pronunciation and evaluation pronunciation in the corpus, and then the trained standard pronunciation model should be used for evaluation and scoring. Acoustic Model Design:
The establishment of the acoustic model is the data preparation for the system development work. The quality of the model depends on the corpus, and the quality of the corpus directly affects the accuracy of the evaluation results. Based on the self-recorded corpus, this study uses the hidden Markov model (HMM) acoustic model to train the acoustic model of English standard pronunciation and the acoustic model of Chinese pronunciation, and establish a standard corpus and an evaluation corpus, respectively. The acoustic model of Chinese pronunciation can represent the pronunciation characteristics of users and is mainly used as the evaluation standard for learner training. The acoustic model of English standard pronunciation is used for pronunciation correction. In the feature parameter extraction of the training corpus, this study uses a 39-dimensional MFCC feature vector as the feature parameter of the acoustic model, compares the evaluation pronunciation with the standard pronunciation and calculates the distance to facilitate the operation of the evaluation mechanism . At present, most of the acoustic model designs use the HMM measured by the similarity with the reference speech model. Common HMMs include discrete HMM, continuous HMM and discrete–continuous HMM. According to the experimental conditions and objective effects, this study adopts the HMM without spanning from left to right; each vowel segment model has five states, and its model parameters are repeatedly calculated by the Baum–Welch algorithm:
English pronunciation assessment: English pronunciation assessment is the core of the whole learning system. In order to make the evaluation results more three-dimensional, this article proposes to obtain the evaluation results from four aspects: pronunciation integrity, that is, whether the speech signal is completely read out for short sentences; pitch period, that is, the fluctuation of the speech pitch; the speech rate of speech changes; and HMM logarithmic probability, that is, the logarithmic probability of each vowel obtained after the speech signal is recognised, represents the pronunciation content. Finally, all the aspects are comprehensively scored, and the evaluation weight of each aspect needs to be determined through theoretical calculation and experimental measurement. Parameter comparison method: In the evaluation parameter extraction mentioned before, the difference between the number of vowel segments obtained by cutting and the number of standard sentences represents completeness, and the time correlation (speech rate change) and HMM log-probability distance of each vowel are obtained by forced alignment. The extraction of the pitch period generally adopts the autocorrelation method and the method based on the short-time amplitude difference , but the effect is not ideal and the timeliness is poor. In this study, the pitch period is obtained according to the time-domain characteristics of the speech signal. The process is as follows: (1) obtain the maximum signal energy point in a frame and record its time-domain position; (2) search forward or backward for the position of the second maximum point, calculate the maximum point position distance; (3) standard judgement is made on the obtained distance: first, the normal pitch period range and then continue to search for the third largest point to check whether the distance is relatively close. The number of pitch periods obtained by this method is sufficiently abundant, which can comprehensively reflect the variation law of pitch periods during the pronunciation process. To obtain the effect of the pitch, the horizontal axis represents the time (s), the vertical axis represents the energy (corresponding to the red dot, which represents the pitch period value) and the red dotted line represents the pitch period change curve.
Due to the rich information in the word graph, the candidate paths that appear in the weighting process based on the posterior probability will be very huge, and most of the candidate words with too small posterior probability will make little contribution to the statistics and will increase significantly. Discriminative training is time-consuming and will affect the performance of recognition. In order to improve the efficiency of discriminative training, it is necessary to effectively trim the word graph and select useful samples for training. Commonly used trimming methods are mainly used in the decoding process of continuous speech recognition. However, unlike decoding in speech recognition, a unigram grammar is often used in discriminative training to generate word graph competition sets, and candidates need to be retained. The start and end times of the arc, and the posterior probability of the arc are calculated in order to weight the Gaussian occupancy and statistics.
In the likelihood-based Beam decoding process, only the states and paths whose cumulative likelihood is greater than the threshold value are expanded, and the states and paths lower than the threshold value will be precut, which will make many posterior probabilities relatively low. The candidate words with large, competitive and confusing information are removed due to the low likelihood score of the path, so the likelihood-based cropping is not suitable for discriminative training, but the Beam pre-cutting algorithm is still a very effective method for word graph pre-cutting.
Since the posterior probability has a great influence on the update of the model parameters and the recognition results, this study adopts the posterior probability-based Beam algorithm (PP Beam) to trim the word arcs, that is, to describe the likelihood words of the acoustic model and the language model score. The graph is converted into a posterior probability word graph, and clipping is performed on the posterior probability word graph. Let
In the formula,
Similar to the template matching algorithm for isolated word recognition, the forced matching algorithm for continuous speech of a given text  just replaces the matching template with a HMM string and then matches the HMM according to the VITERBI search algorithm. For each state, the steps are as follows:
Initialisation Induction End best score = max1≤ Backtracking
End best score = max1≤
In the aforementioned evaluation parameter extraction, the difference between the number of vowel segments obtained by cutting and the number of standard sentences is used to represent the completeness, and forced alignment is used to obtain the time correlation (speech rate change) and HMM log-probability distance of each vowel . The extraction of the pitch period generally adopts the autocorrelation method and the method based on short-time amplitude difference, but the effect is not ideal and the timeliness is poor. In this study, the pitch period is obtained according to the time domain characteristics of the speech signal, and the process is as follows:
Find the maximum point of signal energy in a frame and record its time domain position. Search the position of the second largest point forward or backward, and calculate the distance from the largest point position. Search the normal pitch period range and then continue to search for the third largest point to check whether the distance is relatively close. The number of pitch periods obtained by this method is sufficiently abundant, which can comprehensively reflect the variation law of pitch periods during the pronunciation process.
Find the maximum point of signal energy in a frame and record its time domain position.
Search the position of the second largest point forward or backward, and calculate the distance from the largest point position.
Search the normal pitch period range and then continue to search for the third largest point to check whether the distance is relatively close. The number of pitch periods obtained by this method is sufficiently abundant, which can comprehensively reflect the variation law of pitch periods during the pronunciation process.
After obtaining the degree of difference of each vowel in the four scoring parameters through the evaluation mechanism, the average degree of difference of a sentence is calculated according to the proportion, as shown in the following Table 1:
Top K confusion phone pairs and their weights
|1 ~ 10||11.77||27.84|
|11 ~ 20||6.79||16.06|
|21 ~ 30||4.88||11.54|
|31 ~ 40||3.56||8.42|
|41 ~ 50||3.25||7.69|
|51 ~ 60||2.95||6.98|
|61 ~ 70||2.62||6.20|
|71 ~ 80||2.37||5.61|
|81 ~ 90||2.13||5.04|
|91 ~ 100||1.95||4.61|
The computer objective speech evaluation system introduced in this study is designed for foreign language teaching and examination evaluation projects, and the purpose is to give evaluation scores that are more relevant to the subjective evaluation of experts. This study explores the use of discriminatively trained acoustic models to give evaluation scores that are more correlated with subjective expert evaluations. The mathematical theory of hypothesis testing proves that the discriminatively trained acoustic model can reduce the ‘false acceptance’ errors in the speech pronunciation evaluation system based on the VITERBI forced matching algorithm, thereby improving the confidence of the objective evaluation score. The relevant experiments based on the speech database collected in the fourth-level oral examination show that the discriminative acoustic model can give higher evaluation confidence scores than the acoustic model obtained by traditional maximum likelihood training.
Top K confusion phone pairs and their weights
|1 ~ 10||11.77||27.84|
|11 ~ 20||6.79||16.06|
|21 ~ 30||4.88||11.54|
|31 ~ 40||3.56||8.42|
|41 ~ 50||3.25||7.69|
|51 ~ 60||2.95||6.98|
|61 ~ 70||2.62||6.20|
|71 ~ 80||2.37||5.61|
|81 ~ 90||2.13||5.04|
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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 of p-groups 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 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