In this paper, Kernel density estimation method is used to analyze the distribution characteristics of continuing education resources and reveal the distribution pattern of resources in different communities. On this basis, CCR model and BCC model are introduced to optimize the DEA model of data envelopment analysis and evaluate the resource allocation of continuing education institutions. The resource allocation optimization and dynamic planning system of continuing education is further constructed, and the system dynamics simulation method is used to simulate the optimization process of resource allocation, which provides a scientific basis for the governance of community education. The results show that: continuing education resource input is polarized in quantity, its performance level is not high, regional differences are significant, and scale efficiency is a key factor restricting quality improvement. This paper constructs a system dynamics model for the quality and user use of educational information resources, and in view of the difficulties of optimization and dynamic planning of the allocation of continuing education information resources, it is proposed that the managerial and digital educational resource platform construction-based inputs such as teachers’ information technology application ability, assessment system construction, etc. should be improved to promote the high-quality and balanced development of continuing education informatization.

Aiming at the bridge monitoring system, some of the monitoring data are abnormal due to equipment failure and environmental impacts. In this paper, the time-frequency domain convolutional neural network method is applied to the calculation of monitoring data and the risk assessment of bridge structure. The data collected by the acceleration sensor is firstly sliced and sampled and visualized. Then wavelet analysis is used to preprocess the cluttered data, and Wigner-Ville distribution and Fast Fourier Transform are introduced to extract time-frequency features from the collected data. A convolutional neural network is proposed and the network is trained on dual channel images fusing time and frequency domain images. By analyzing the spectrogram and and time-frequency diagram of the bridge monitoring data, the method of this paper classifies the bridge health condition into three kinds: no disease, slight disease and disease, which can accurately determine the health condition of different bridges, and the assessment accuracy of the risk assessment model based on the fusion of time-frequency domain information reaches 97.78%, which indicates that the high efficiency and feasibility of the bridge inspection data computation and the risk assessment model in this paper can meet the actual engineering construction needs of bridge inspection.

As the global climate change problem is getting more and more serious, carbon emission quota allocation is more and more emphasized by countries all over the world, while the traditional carbon quota allocation program has the problem of single objective. In order to improve the scientificity and acceptability of the carbon quota allocation scheme, this paper constructs indicators and forms multiobjective functions to formulate the carbon quota allocation scheme from the three perspectives of efficiency, fairness and sustainability, and builds a multi-objective optimization model for carbon quota allocation and decision support. Aiming at the solution problem of the carbon quota allocation model, an improved hybrid swarm algorithm based on Gaussian perturbation, tournament selection strategy and proposed Newtonian local optimization search operator (L-BFGS) is proposed. The model is used to explore the quota allocation scheme for cities in the Bohai Economic Rim in 2030. In the three single-target pre-allocation schemes based on the principles of efficiency, fairness, and sustainability, the difference between the cities with the largest and smallest quotas is 319 Mt, 289 Mt, and 256 Mt, respectively, which lacks scientificity and rationality. In contrast, the allocation results of the multi-objective pre-allocation scheme proposed by the carbon quota allocation model in this paper are relatively balanced and the difference is small, which can eliminate the conflict between multiple principles.

This paper establishes a multi-objective optimization model for the process of yoga course ideology and politics in colleges and universities through the group paper technology, and adopts an improved genetic algorithm to solve the model. Integrating the online and offline hybrid teaching mode, the paper’s group paper technology is placed in the online assessment to realize the all-round reform of yoga course Civics teaching. The research results show that the improved genetic algorithm (IGA) in this paper has a higher grouping efficiency and quality compared with the traditional genetic algorithm (GA), and saves about 52.7% in the grouping time. At the same time, using the social network analysis method to analyze the online-offline hybrid teaching mode of this paper, we are able to derive the student objects that need to be focused on based on the results of the analysis of the centrality of the point degree and the centrality of the middle of the point degree. The experimental class adopting the teaching mode of this paper has an excellent class performance rate of 100% under the test of group paper technology, which fully demonstrates that the teaching reform method proposed in this paper for the ideology of yoga course in colleges and universities has significant practical application effects.

This paper constructs an overall framework for vulnerability mining, covering the whole process from code collection to vulnerability remediation. The word vector technique is used to transform code fragments into vector form, thus preserving the semantic information of the code. A vulnerability mining system based on semantic graph of source code is further designed, which generates a semantic graph of code by constructing an abstract syntax tree (SAT), and analyzes the semantic graph by using graph neural network to accurately locate potential vulnerabilities. At the same time, a vulnerability repair method based on thought chain is proposed. The results show that the model in this paper can accurately mine the vulnerabilities of web service software, and it consumes short latency and has strong stability. The results of web service software vulnerability detection show that the accuracy rate of the model always stays above 85% under different network structures. In addition, this paper obtains that the integration degree centrality measure and 60 iteration rounds have the best effect on the detection of vulnerabilities of the model. Finally, the vulnerability repair experiments show that at Beams=15, the model in this paper repairs each vulnerability function with a PPP metric of 61.52% and an average time of 3.168 seconds, which is the best for vulnerability repair.

Because of their inherent vulnerability, small States are in a relatively weak position in global economic relations. In order to survive and develop, regional cooperation is an important way for small countries to safeguard and promote their national interests. Taking Malta as an example, this paper utilizes the international trade data of some major countries along the “Belt and Road” from 2004 to 2018, and adopts the social network analysis method to construct the trade network of 37 countries in each year, and explores the formation of the trade network of the “Belt and Road” through the gravity model. The gravity model explores the major trade subgroups formed in the “Belt and Road” trade network and reveals the cooperation and interaction paths of small countries in the global economic system. Among them, Malta’s position and role in the countries along the “Belt and Road”, Malta still participated in global economic cooperation through Russia in 2004, and in 2018, in the more closely linked global economic network system, Malta strengthened its economic ties with China, which has a core degree of 0.897, further enhancing its own position in the global economic network. The economic scale and institutional differences between countries have different impacts on the trade of different products, and small countries have limited resources, so it is more important to formulate different economic development strategies according to different influencing factors and product types, and strengthen trade cooperation with neighboring countries.

The professional development of physical education teachers is the direction and basic requirement of modern education development, which is better promoted by strengthening the tracking and prediction of the trajectory of the professional development of physical education teachers. In this paper, a combined ARIMA-LSTM model is established to visualize the PE teachers’ professional development trajectory by predicting their professional development scores, using the advantages of ARIMA model in handling linear time series data, while combining the powerful ability of LSTM network in capturing the long-term dependency of data. Three physical education teachers were randomly selected as research subjects to predict their PE teacher professional development trajectories. The root mean square error (RMSE) and mean absolute percentage error (MAPE) values were used as the assessment indexes of the model, and the MAPE and RMSE of the ARIMA-LSTM model were less than those of the ARIMA model and the LSTM model for the physical education teachers in No. 1 and No. 3. And on the prediction of physical education teacher No. 2, the MAPE comparison of ARIMA-LSTM model and LSTM model increased by 1.12%, but the RMSE decreased by 73.4563, and the prediction curve of the professional development score was close to the original sequence, and the ARIMA-LSTM model still showed better prediction effect.

In order to improve the accuracy of enterprise financial risk early warning and realize the risk control of enterprise capital chain under digital transformation, this paper adopts the Long Short-Term Memory (LSTM) neural network algorithm to establish the enterprise financial risk early warning model. First analyze the enterprise financial risk early warning indicators, use factor analysis for indicator screening, determine the indicator weights through the Delphi method and the improved hierarchical analysis method, and select the indicators with high importance to construct the enterprise financial risk early warning feature samples. Then after LSTM neural network training, the enterprise financial risk early warning model is obtained, and the model is evaluated for performance and practical use. The experiment proves that the accuracy of the LSTM neural network model on the training set and test set is 91.48% and 88.62% respectively, which indicates that the model can effectively predict the enterprise financial risk. By comparing with the commonly used enterprise financial risk warning algorithms, the algorithm in this paper has the highest warning accuracy, shorter prediction time, and better warning performance in dealing with large-scale enterprise samples. This study provides an effective financial risk early warning method for enterprises, which can help them better carry out capital chain wind control in the process of digital transformation.

Vocal music is an art about the perception and expression of sound. Successful vocal music teaching is to cultivate students’ unique singing personality, so this paper constructs a personalized vocal music teaching mode with the help of AI algorithm. Subsequently, it describes the problem of service object learners under personalized learning path recommendation, proposes a personalized learning path recommendation strategy based on ant colony optimization algorithm, and verifies the recommendation effect of personalized path through simulation experiments. Then the cognitive diagnosis model based on KM-VDINA is proposed to diagnose students’ vocal music knowledge under personalized learning path. The article concludes through experiments that the personalized vocal music teaching model based on AI algorithms requires the integration of online and offline teaching, while focusing on the integration of teaching inside and outside the classroom. The vocal music learning path of most students can be expressed as (000000)→(100001)→(101001)→(101100)→(111100)→(101110)→(111111). Students have multiple trajectories to master the attributes of vocal music knowledge, so teachers can explain the attributes of knowledge that are easier to master according to the actual situation, and then explain the attributes of knowledge that are difficult for students to master.

The purpose of this paper is to study the multidimensional computational optimization problem of enterprise organization structure. Based on the value dimension, this paper designs a kind of enterprise organizational structure which contains six dimensions such as demand deϐinition, sales and so on. And the optimization model of enterprise organizational structure is studied by taking a demand-pull enterprise as an example. In the iterative process of the algorithm, the particle swarm optimization (PSO) algorithm and ant colony optimization (ACO) algorithm are run alternately to form the PSACO algorithm to solve the optimization model of enterprise organizational structure constructed in this paper. The experimental results show that the PSACO algorithm used in this paper can maintain stable and good convergence performance under different demand sizes. The enterprise organizational structure optimization model and solving algorithm in this paper can achieve ideal resource allocation scheme and effect, and can still achieve good solving effect in large-scale enterprise organizational structure optimization adjustment. It provides good decision support for the optimization and improvement of enterprise organizational structure in the era of digital economy, and has important application value.