With the rapid development of computer technology and the increasing expansion of the Internet scale, the network security problems are becoming more and more prominent. What's more, the number of security loopholes and security incidents is soaring rapidly. Hence, how to ensure the normal operation of the network effectively has become a critical problem. Luckily, network security situation awareness technology [1] is able to make full use of the existing network security technologies, coordinate and manage various security equipment, perceive the overall network security situation, identify the attacks by integrating all available information, and select an appropriate security defense mechanism.

The existing researches on overall network security situation assessment methods mainly focus on the following three categories:

Based on probability statistics, the typical methods include Bayesian inference, hidden Markov model, analytic hierarchy process and so on;

Based on logical reasoning, the typical methods include D-S evidence theory, fuzzy logic and so on;

Based on neural network, the typical methods include BP neural network, radial basis function network [2] and so on.

Fang Yan [3] proposed a quantitative evaluation method for network security based on Bayesian network. She combined Bayesian network and attack graphs to assess the overall and local network situation. The assessment result is somehow objective and accurate. Chen Hong [4] and her team put forward a security situation assessment system combined with multi-source data based on D-S evidence theory. The system comprehensively considers the information of nodes and links to realize its situation, and integrates multi-source data by using D-S evidence theory to obtain the overall security situation of the network.

Zhang Yong [5] came up with a method which improved the hidden Markov model. The model divides the situation awareness process into three levels: thematic level, element level and overall level. Different levels adopt different feature fusion methods. Hidden Markov model is used to thematic level and Markov game model to element level. The improved method is more objective and efficient. However, the assessment on the overall level is very subjective since the ratio is artificially allocated.

C Wang [6] raised a situation assessment model based on information fusion by using an improved D-S evidence theory. When doing the threat assessment, D-S evidence theory and dynamic Bayesian network were used to integrate multi-source sensor data. Wang Yongwei and his team [7] proposed a situation assessment model based on the improved D-S evidence theory, which includes four stages: rule measurement, evidence modification, rule integration and situation decisions. Evidence is integrated by calculating the dissimilitude degree among evidences to complete feature fusion and the calculation of security situation value. Compared with the traditional method of D-S evidence theory, this method could avoid the paradox problem in the fusion of situations based on the evidence theory. What is more, the results are more objective. Tang Yongli and his team [8] put up to use an optimized Back Propagation (BP) neural network based on genetic algorithm to capture the basic probability distribution (BPA) of D-S evidence theory.

It can be seen from the research status at home and abroad that, most of the existing research results have the problems of unitary methodology and large-scale subjective factors, further affecting the accuracy of situation assessment. Combined with the traditional network security technology, this paper sets up a three-layer evaluation index system, and puts forward an overall network security situation evaluation model based on hidden Markov model, PageRank algorithm and D-S evidence theory, through which, the overall situation is evaluated by different fusion algorithms in different fusion stages. And compared with the single fusion algorithm, this method is more accurate and comprehensive. Its validity and accuracy are verified by comparison experiments.

In order to assess the network security situation as fully as possible, this paper establishes a multilevel assessment framework, which is shown in Figure 1. At first, considering the multi-index data of network security situation assessment, the data information extracted from various data sources is taken as the information needing to be input to assess the situation from the factor level and the overall level.

The original data layer includes three data categories. The first one is system logs, security device logs, alarm logs and application logs, from which, threat events could be extracted. The second one is vulnerability scanning results, from which, vulnerability information in nodes could be extracted. The third one is the service information in the node, which could count out all assets contained in the nodes.

The extraction layer of situation indicator data: it is used to extract indicator data information needed by the element layer from original data layer.

The factor layer: Firstly, it uses the hidden Markov model to integrate the multi-source heterogeneous network security data, so as to obtain the threat situation weight, vulnerability situation weight and asset situation weight in each node. Then, it utilizes the PageRank algorithm to assign weights to each node. Hence the threat situation weight, vulnerability situation weight and asset situation weight in the whole network is obtained by weighting.

Overall layer: it uses D-S evidence theory to integrate three situation indicators including network threat, vulnerability and assets at the decision-making level to capture the overall network security situation.

The assessment indicators of network security situation should pay attention to all kinds of internal components of the network and their relationships. Network data may be generally divided into two types. One is the information reflecting the actual operation status of the network system, and the other is the information reflecting the security of the network system. Therefore, this paper constructs three first level indicators, namely threat, vulnerability and assets.

Threat is an indicator that reflects the attack status the network suffers. This could be obtained from logs or alarms in various security devices, such as intrusion detection systems, firewalls, web firewalls and so on.

Vulnerability, as an indicator, reflects the possible vulnerabilities provided by network equipment systems and network services, and it reflects their impacts as well.

Assets, as an indicator, reflect the asset information of each device on the network and their importance levels.

Among them, each first level indicator is represented by a certain number of second level indicators. Therefore, we make a list about index system of network security situation in Table 1.

The index system of network security situation

First level indicators | Second level indicators |
---|---|

Threat | The types and the number of attack events |

The frequency of attack events | |

The danger level of attack events | |

Vulnerability | Total number of vulnerabilities |

The number of vulnerabilities on different levels | |

The probability of vulnerabilities being successfully exploited | |

Assets | The number of services on target nodes |

The value level of each service on target nodes |

On the basis of the comprehensive analysis of various indicators in situation assessment, Hidden Markov Model (HMM) [9] is proposed as a first level indicator method for situation assessment. This method is mainly used to assess three situation elements of network nodes, namely threat, vulnerability and assets. Let's take the indicator of threat as an example. First, we set a hidden Markov model for the threat indicator of each node. Second, we find out the parameters of the model based on the Baum-Welch algorithm [10]. Then, we evaluate the threat situation weight of nodes based on the Viterbi algorithm [11]. The other two indicators as vulnerability and assets are of the same calculation method.

The situation weights of threat, vulnerability and asset on each node could be regarded as the hidden state of the hidden Markov model. As time goes on, they can be regarded as a changing Markov chain. The network attack information, vulnerability information and asset information of the nodes could be obtained through various detection methods. All of them could be considered as the observation sequence in the hidden Markov model. Hence, this problem can be described as to infer the hidden security state of the node from the observation sequence. As a result, the hidden Markov model is suitable for this assessment.

Firstly, we need to evaluate the threat situation weight of each node and set up the process of the hidden Markov model:

State pace

Observation state space _{1}, _{2},…,_{6}}. Among them, _{i}(1≤_{i}

Therefore, according to the six second level assessment indicators mentioned above and the three value ranges of each assessment indicator, the observation state space ^{6} states, that is ^{6}}

In observation sequence _{1},_{2},...,_{T}_{1},_{2},...,_{T}

The initial probability distribution of the system is _{1}, _{2}, _{3}, _{4}, _{5}}. It represents the probability distribution of the threat situation of the node respectively in five states at the initial moment

In the hidden state transition matrix _{ij}_{5×5}, _{ij}_{t+1} = _{t}

In the observation state transition matrix _{jk}_{L×5}, when _{ij}

The corresponding relationships between the statistical number of each second level indicator and the number of threat alarms

The statistical amount of each second level indicator | The number of threat alarms |
---|---|

Less | [0, 20) |

Medium | [20,50) |

More | [50, +∞) |

So far, the modeling about the node's threat weight has been completed, which is denoted as

Generally, Baum-welch algorithm is used for training. During the algorithm training process, the length of observation sequence _{1},_{2},...,_{T}_{i}_{i+1}. _{i}_{i+1} will be integrated through a certain proportion to get the equation as

After obtaining the parameters of hidden Markov model, the hidden state sequence can be solved. The hidden Markov model suffers a decoding problem and could be solved through Viterbi algorithm. Viterbi algorithm is a process used to search for the most possible hidden state sequence, the parameters of hidden Markov model and an observation sequence being given at that time. This algorithm adopts a dynamic programming optimized gradually from back to front in order to search for the best path of security situation change. Please refer to [13] for the specific process of the algorithm.

The evaluation algorithm using hidden Markov model to evaluate node's threat, vulnerability and assets situation weights is shown as follows:

Input: the observation sequence is consist of attack threat information, vulnerability information and asset information extracted from the extraction layer of situation indicator data.

Output: the threat, vulnerability and asset situation weight values of each network node.

Algorithm steps:

Build up the modeling of the threat situation of each node based on the hidden Markov model;

Train the hidden Markov model based on the Baum-Welch algorithm through sliding windows;

Find out the optimal hidden state sequence of hidden Markov model based on the Viterbi algorithm, and then calculate the threat situation weight of the node.

Adopt the same method as steps (2) and (3) to get the vulnerability and asset situation weight values of nodes.

As a result, the training and evaluation algorithms of hidden Markov model would be completed. And the overall evaluation process of the node's threat, vulnerability and asset situation weights is shown in Figure 3.

The purpose of using situation assessment method based on hidden Markov model is to evaluate the node's threat, vulnerability and asset situation weight values. Taking attack threat information, vulnerability information and asset information as data sources, based on sliding windows, the Baum-Welch algorithm and Viterbi algorithm are used respectively to evaluate the situation weights of nodes.

In this section, based on the hidden Markov model evaluating node's threat, vulnerability and asset situation weights, PageRank algorithm is introduced into multi-node network security situation assessment, in order to solve the calculation problem of node weights in complex network environment [14–15]. Through this algorithm, the weight information of each node can be calculated, and the threat, vulnerability and asset situation weights in the whole network can be calculated by weighting method.

The connection relations of each node in the network can be obtained through the network topology information, and the latter one can be abstracted into a directed graph. Let's assume the total number of nodes is _{i}

In this formula, _{pi}_{i}_{j}

This formula indicates that : (1) the more connections the network node _{i}_{i}_{i}_{i}_{i}

Finally, by integrating the situation elements and weights of each node, the threat, vulnerability and asset situation elements in the whole network will be obtained. Let's take the situation of threat as an example, its calculation formula being as follows:

In the formula, _{threat}_{i}_{threat}_{i}_{i}_{i}_{i}

On the basis of hidden Markov model and PageRank algorithm evaluating network's threat, vulnerability and asset situation elements, an overall evaluation method based on D-S evidence theory is proposed. This method mainly adopts the situation values of threat, vulnerability and assets to evaluate the overall network security situation. Firstly, the D-S evidence theory model is built according to the whole network situation. Secondly, the Basic Probability Assignment (BPA) required by the threat, vulnerability and assets in the D-S evidence theory is constructed. Finally, Dempster's composition rule is used to integrate three groups of evidences.

D-S evidence theory has the advantage of handling “uncertainty” at the decision level, and it could show the probability of the network security situation in each state, instead of a situation value, based on the reliability function and truth-like function. By constructing three evidence groups including threat, vulnerability and assets, the evidences of hidden Markov model's first-level evaluation results is synthesized to calculate the probability distribution of security situation in each state, which will finally help network security administrators to make decisions.

The process of overall network situation assessment based on D-S evidence theory is as follows.

Input: the output results of the threat, vulnerability and asset situation elements in the network based on the hidden Markov model and PageRank algorithm.

Output: the overall network security situation.

Algorithm steps:

Construct a hypothesis space

Based on the assessment results of the network situation elements including threat, vulnerability and assets, and based on the five situations of hypothesis space _{t}_{v}_{a}

(3) By the use of Dempster's composition rule, three evidence bodies are integrated. The new probability distributions

Dempster's composition rule about _{t}_{v}_{a}

(4) Determine the trust interval [_{i}_{i}

(5) Make decisions based on the results in step (4). When the situation assessment method based on D-S evidence theory is used, the overall security situation of the network could be evaluated. Taking the fusion results of hidden Markov model and PageRank algorithm as data sources, the final results are obtained by synthesizing the evidences and constructing the basic probability distributions on the basis of Dempster's composition rule. This method fits the situation of integrating decision-making levels, through which the assessment results become accurate and objective.

In order to test the effectiveness of the above method, DARPA 2000 dataset has been used as experimental data, since it is the most comprehensive dataset for attack tests and the standard test dataset which is widely recognized and used in the field of network security research.

This dataset includes the LLDOS 2.0 attack scenario which contains the following attack steps.

Scan the target network to search for any living hosts.

Detect if there is any living hosts with the sadmind vulnerability.

Invade and get the root access to the host 172.16.115.20 by making use of the sadmind vulnerability.

Install the Trojan horse on the host 172.16.115.20.

Invade another host 172.16.115.20 by taking the host 172.16.115.20 as a springboard.

Install the Trojan horse on the host 172.16.112.50.

The attacker controls host 172.16.115.20 and host 172.16.112.50 to launch an attack of DDoS on host 131.84.1.31.

However, the data set has not presented some information on the target network, such as the network topology, vulnerability, and service. So, on the basis of the experimental data provided in the literature [16], this article builds a key network topology structure, which is shown in Figure 4, from the alarm data set. And Table 3 and Table 4 also show the vulnerability information and service information of the network.

The vulnerability structure of the key nodes in DARPA 2000

ICMP Incorrectly Configured | √ | √ | √ | √ | √ | × |

SunPRC Incorrectly Configured | √ | √ | √ | × | × | × |

Sadmind Buffer overflow | √ | √ | √ | × | × | × |

RCP Incorrectly Configured | √ | √ | √ | × | × | × |

HINFO Query Incorrectly Configured | √ | × | × | × | × | × |

SYN Flood | × | × | × | × | × | √ |

The service information of the key nodes in DARPA 2000

Let's take the threat situation of node mill (172.16.115.20) as an example to present the evaluation process of hidden Markov model. Firstly, we set a hidden Markov model according to the method mentioned in the section 3.3.1. Since there is only IDS alarm data in DARPA 2000 data set, three second level evaluation indicators are used here: IDS mild alarm number, IDS moderate alarm number and IDS severe alarm number, the values of which are shown in Table 2, so there are 33=27 observation states. Then we observe the data at a same time interval, and then divide it into 7 steps according to different time intervals, the observation sequence _{t}

Based on the expert experience, the initial value of the parameters

On the basis of expert experience, Baum-Welch algorithm is used to optimize model parameters. Table 5 shows the changes of model parameters' log likelihood values for host “mill” in the iterative process of Baum-Welch algorithm.

The changes of the log likelihood values for the host

Interaction Times | 0 | 20 | 40 | 60 | 80 | 100 |

LL(log) | −257 | −64.1 | −50.3 | −46.1 | −43.7 | −43.4 |

It can be seen that, with the increasing number of iteration times, the log likelihood value of model parameters

In Figure 5, it shows the trend chart about the threat situation element of the host node “mill”, through which we can intuitively see the change trend of the host's threat situation during this period of time:(1) network attacks are mainly concentrated in the period of 4–9 and 14–15, during which network security is threatened and needs to be kept watch; However, in other periods, especially in the periods of 1–3 and 10–13, the security situation is often kept at a low level, which indicates that the network is relatively safe in these two periods. (2) By comparing two line graphs, it can be seen that the number of network attacks and the change trend of node's threat situation are almost the same, indicating that network attacks will directly have an impact on the threat situation element of host nodes.

The vulnerability and asset situations of the host node “mill” can be obtained by the same method, but they are different from the threat situation graph. Because of their particularity, their fluctuations are slight, so the trend graph is relatively stable, as shown in Figure 6.

Taking the evaluation on the threat situation in the network as an example, the network topology shown in Figure 4 is changed into the accessing relationship shown in Figure 7 for simplicity.

The accessing relationship of the sub network can be represented by an adjacency matrix:

The damping coefficient value is set as

The weight information of network nodes

Network Node | Weight |
---|---|

mill | 0.233 |

locke | 0.123 |

pascal | 0.123 |

hume | 0.123 |

robin | 0.123 |

0.275 |

From the Figure 8, it can be seen that :(1) the attacker invades the host “mill” (172.16.115.20) in the period of 3–6, and invades the host “pascal” (172.16.112.50) in the period of 7–10. The situation value of the former one was higher than that of the latter one, because host “mill” has a bigger weight and a higher importance. (2) The situation value of the network reaches to its highest during the period of 14–15. This is because the attacker controls the host “mill” and “pascal” during this period and attacks the host

From Figure 9, the fluctuation range of network's vulnerability and asset situations is small, which is different from the threat situation. That is to say, during this period, the vulnerability situation and asset situation in the network are relatively stable without big risks.

Taking the 15th period as an example, the experimental steps of evaluating the overall network security situation based on the D-S evidence theory are as follows. (1) According to experts' experience, the basic probability distributions of the three elements, namely threat _{t}_{v}_{a}

The basic probability distribution of threat

Situation value | The probability distribution of the threat evidence body { |
---|---|

1 | 0.65 0.15 0.10 0.06 0.04 |

2 | 0.25 0.35 0.25 0.10 0.05 |

3 | 0.10 0.23 0.34 0.23 0.10 |

4 | 0.05 0.10 0.25 0.35 0.25 |

5 | 0.04 0.06 0.10 0.15 0.65 |

The basic probability distribution of vulnerability

Situation value | The probability distribution of vulnerability evidence body { |
---|---|

1 | 0.50 0.22 0.13 0.10 0.05 |

2 | 0.30 0.30 0.25 0.10 0.05 |

3 | 0.10 0.25 0.30 0.25 0.10 |

0.10 0.25 0.30 0.30 | |

0.10 0.13 0.22 0.50 |

The basic probability distribution of assets

Situation Value | The probability distribution of the asset evidence body { |
---|---|

1 | 0.70 0.20 0.05 0.03 0.02 |

2 | 0.30 0.35 0.20 0.10 0.05 |

3 | 0.15 0.25 0.30 0.20 0.10 |

4 | 0.05 0.10 0.20 0.35 0.30 |

5 | 0.02 0.03 0.05 0.20 0.70 |

(2) Construct evidence bodies

According to the basic probability distributions of threat, vulnerability and assets in step (1), the probability distributions of three evidence types are shown as follows:

_{t}

_{v}

_{a}

(3) Synthesize evidences

Dempster's composition rule is used to integrate three evidence bodies, namely _{t}_{v}_{a}

_{t}_{v}

Similarly, Dempster's composition rule is used to integrate _{asset}

_{a}

(4) Determine the trust intervals.

The trust intervals _{t}_{v}_{a}

When the situation value is 2, the trust measure and likelihood measure are shown as follows:

When the situation value is 3, the trust measure and likelihood measure are shown as follows:

When the situation value is 4, the trust measure and likelihood measure are shown as follows:

When the situation value is 5, the trust measure and likelihood measure are shown as follows:

When the situation value of network is 1, the trust interval is [0, 0]; the trust interval is [0.02, 0.04] when the situation value is 2; the trust interval is [0.13, 0.20] when the situation value is 3; the trust interval is [0.55, 0.63] when the situation value is 4; and the trust interval is [0.21, 0.28] when the situation value is 5.

It can be seen from the results that, when the probability of security situation in the overall network is 4, it reaches to the highest and is followed by 5. Hence, the network here is dangerous, which needs some remedial measures in time. Meanwhile, the overall network situation value in the 15th period can be calculated as 4.14. The change trend of the overall network situation in the time period of 1–15 is shown in Figure 10.

From the Figure 10, it can be seen that the overall network situation value is between 3.1 and 4.6, and it maintains an upward trend after combining three situation indicators including threat, vulnerability and assets. This is almost similar with the change trend of network threat. The reason is that the network vulnerability and assets are stable in the selected time period, with its range ability being small. As a result, this method is proved to be effective since it accords with the expectation of the experimental results.

In order to verify the accuracy of the proposed method, this section makes a comparison with other evaluation techniques in the paper [4] and Paper [16] with DARPA 2000 data set as experimental data. In the paper [4], it evaluates the situation by analytic hierarchy method. While in the paper [16], it takes threat, vulnerability and service as evaluation indicators to evaluate situations based on the D-S evidence theory. The changing trend of the overall network situation calculated by the three methods is shown in Figure 11.

From the Figure 11, the experimental results indicate that: (1) The method in the paper [16] mainly considers network's threat indicator, but it does not pay much attention to the vulnerability indicator and asset indicator, so this method can reflect network's threat situation accurately. However, there are three elements for network risk assessment, namely threat, vulnerability and assets. Therefore, this method mainly reflects the network's threat situation but not the overall situation of the network. The method proposed in this paper can take the above three factors into consideration at the same time, which is more accurate and comprehensive. (2)The change of the method in the paper [4] is in doubt, so there is only a reasonable result shown in the graph. Since this method is easily affected by artificial factors when integrating the first and second level indicators, and the integration standards of various people are quite different, so each indicator will be assigned a specific fusion weight. As a result, this method is more difficult to adapt to the complex network environment. However, the method in this paper eliminates the artificial factors as much as possible, and comprehensively considers various factors such as threat, vulnerability, assets and network topology through self-learning. As a result, its ability of adapting to different network environments is stronger.

This paper mainly describes the process and methods about the overall situation assessment of network security, on the basis of a comprehensive assessment algorithm combined with hidden Markov model, PageRank algorithm and D-S evidence theory. It uses different fusion algorithms in different levels to assess the overall situation. Firstly, a technical framework of overall situation assessment is established, which could be divided into four layers, namely, from bottom to top, data source layer, data extraction layer of situation indicators, element layer and overall layer. Secondly, three first-level indicators including threat, vulnerability and assets, and several second-level indicators are given in the paper. Then, with the hidden Markov model, the second level indicators are integrated to evaluate the threat, vulnerability and asset situation elements of each node in the network. And when integrating the threat, vulnerability and asset situation elements of each node based on the PageRank algorithm, the whole network's threat, vulnerability and asset situation elements could be evaluated. Meanwhile, by integrating the threat, vulnerability and asset elements at the decision level based on the D-S evidence theory, the security situation of the whole network could be evaluated. And, in the simulation experiment, it shows that the assessment method proposed in this paper is more accurate, effective and suitable than the one in a single model.

#### The index system of network security situation

First level indicators | Second level indicators |
---|---|

Threat | The types and the number of attack events |

The frequency of attack events | |

The danger level of attack events | |

Vulnerability | Total number of vulnerabilities |

The number of vulnerabilities on different levels | |

The probability of vulnerabilities being successfully exploited | |

Assets | The number of services on target nodes |

The value level of each service on target nodes |

#### The weight information of network nodes

Network Node | Weight |
---|---|

mill | 0.233 |

locke | 0.123 |

pascal | 0.123 |

hume | 0.123 |

robin | 0.123 |

0.275 |

#### The corresponding relationships between the statistical number of each second level indicator and the number of threat alarms

The statistical amount of each second level indicator | The number of threat alarms |
---|---|

Less | [0, 20) |

Medium | [20,50) |

More | [50, +∞) |

#### The service information of the key nodes in DARPA 2000

#### The vulnerability structure of the key nodes in DARPA 2000

ICMP Incorrectly Configured | √ | √ | √ | √ | √ | × |

SunPRC Incorrectly Configured | √ | √ | √ | × | × | × |

Sadmind Buffer overflow | √ | √ | √ | × | × | × |

RCP Incorrectly Configured | √ | √ | √ | × | × | × |

HINFO Query Incorrectly Configured | √ | × | × | × | × | × |

SYN Flood | × | × | × | × | × | √ |

#### The basic probability distribution of threat

Situation value | The probability distribution of the threat evidence body { |
---|---|

1 | 0.65 0.15 0.10 0.06 0.04 |

2 | 0.25 0.35 0.25 0.10 0.05 |

3 | 0.10 0.23 0.34 0.23 0.10 |

4 | 0.05 0.10 0.25 0.35 0.25 |

5 | 0.04 0.06 0.10 0.15 0.65 |

#### The basic probability distribution of assets

Situation Value | The probability distribution of the asset evidence body { |
---|---|

1 | 0.70 0.20 0.05 0.03 0.02 |

2 | 0.30 0.35 0.20 0.10 0.05 |

3 | 0.15 0.25 0.30 0.20 0.10 |

4 | 0.05 0.10 0.20 0.35 0.30 |

5 | 0.02 0.03 0.05 0.20 0.70 |

#### The basic probability distribution of vulnerability

Situation value | The probability distribution of vulnerability evidence body { |
---|---|

1 | 0.50 0.22 0.13 0.10 0.05 |

2 | 0.30 0.30 0.25 0.10 0.05 |

3 | 0.10 0.25 0.30 0.25 0.10 |

0.10 0.25 0.30 0.30 | |

0.10 0.13 0.22 0.50 |

#### The changes of the log likelihood values for the host

Interaction Times | 0 | 20 | 40 | 60 | 80 | 100 |

LL(log) | −257 | −64.1 | −50.3 | −46.1 | −43.7 | −43.4 |

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agricultural economic development and optimisation measures under the strategy of rural revitalisation Study on the impact of forest fire prevention policy on the health of forest resources Value Creation of Real Estate Company Spin-off Property Service Company Listing Selection by differential mortality rates Digital model creation and image meticulous processing based on variational partial differential equation The modelling and implementation of the virtual 3D animation scene based on the geometric centre-of-mass algorithm The policy efficiency evaluation of the Beijing–Tianjin–Hebei regional government guidance fund based on the entropy method The transfer of stylised artistic images in eye movement experiments based on fuzzy differential equations Research on behavioural differences in the processing of tenant listing information: An eye-movement experiment Innovation of Economic Management Risk Control in Retailer Supply Chain Based on Differential Equation Model A review of the treatment techniques of VOC Some classes of complete permutation polynomials in the form of ( x ^{pm}−x +δ )^{s}+ax ^{pm}+bx overF _{p2m}The consistency method of linguistic information and other four preference information in group decision-making Statistical Model of College Ideological and Political Learning Based on Fractional Differential Equations Research on the driving principle and guiding strategy of the public's collaborative supervision of the sharing economy in my country Research on the willingness of Forest Land’s Management Rights transfer under the Beijing Forestry Development Nonlinear Differential Equation in Anti-aging Test of Polymer Nanomaterials A mathematical model of the fractional differential method for structural design dynamics simulation of lower limb force movement step structure based on Sanda movement Fractal structure of magnetic island in tokamak plasma Mechanics of Building Structural Materials Based on Lagrangian Mathematical Model Analysis 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ordinary differential equations Modeling of fractional differential equation in cloud computing image fusion algorithm Study on Establishment and Improvement Strategy of Aviation Equipment Research on Financial Risk Early Warning of Listed Companies Based on Stochastic Effect Mode Nonlinear strategic human resource management based on organisational mathematical model 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 A new variety from Sichuan, China— Paris polyphylla var.nullopetalina (Trilliaceae)Impact of ASEAN-China free trade area on fishery value chain based on difference-in-difference method Spatial–temporal graph neural network based on node attention A contrastive study on the production of double vowels in Mandarin Mathematical analysis of civil litigation and empirical research of corporate governance 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 TOPSIS missile target selection method supported by the posterior probability of target recognition The incentive contract of subject librarians in university library under the non-linear task importance Research on indoor environment design of comprehensive commercial shopping center based on numerical simulation Empirical analysis of the economic absolute income hypothesis based on mathematical statistics Realization of Book Collaborative Filtering Personalized Recommendation System Based on Linear Regression Equation Study on Interactive Relations between Enterprise Social Media and Decision Style Based on a vector Autoregressive Model Research on Dynamics of Flexible Multibody System with Deployable Antenna Based on Static Lagrangian Function The Optimization of Mathematics Teaching Models in Colleges and Universities Based on Nonlinear Differential Equations Study on spatial planning and design of learning commons in university libraries based on fuzzy matrix model The Stability Model of Piano Tone Tuning Based on Ordinary Differential Equations Construction and application of automobile user portrait based on k-mean clustering model The Homework Model of Screening English Teaching Courses Based on Fractional Differential Equations Research on a method of completeness index based on complex model Fake online review recognition algorithm and optimisation research based on deep learning Research on the sustainable development and renewal of Macao inner harbour under the background of digitisation Support design of main retracement passage in fully mechanised coal mining face based on numerical simulation Study on the crushing mechanism and parameters of the two-flow crusher Interaction design of financial insurance products under the Era of AIoT Modeling the pathway of breast cancer in the Middle East ARMA analysis of the green innovation technology of core enterprises under the ecosystem – Time series data Image design and interaction technology based on Fourier inverse transform Calculus Logic Function in Integrated Manufacturing Automation of Single Chip Microcomputer Football Offense Training Strategy Based on Fractional Differential Mathematical Modeling Research on China interregional industrial transformation slowdown and influencing factors of industrial transformation based on numerical simulation The medical health venture capital network community structure, information dissemination and the cognitive proximity The Mathematical Analysis Model of Educational System in Music Courses in Colleges and Universities Continuing Education Network Data Center Model Based on Fractional Differential Mathematical Equations A generative design method of building layout generated by path Analysis of the causes of the influence of the industrial economy on the social 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on the effect of generative adversarial network based on wavelet transform hidden Markov model on face creation and classification Research on Lightweight Injection Molding (CAE) and Numerical Simulation Calculate of New Energy Vehicle Power Flow Calculation in Smart Distribution Network Based on Power Machine Learning Based on Fractional Differential Equations Demonstration of application program of logistics public information management platform based on fuzzy constrained programming mathematical model Basketball Shooting Rate Based on Multiple Regression Logical-Mathematical Algorithm The Optimal Application of Lagrangian Mathematical Equations in Computer Data Analysis Similarity Solutions of the Surface Waves Equation in (2+1) Dimensions and Bifurcation Research on predictive control of students’ performance in PE classes based on the mathematical model of multiple linear regression equation Beam control method for multi-array antennas based on improved genetic algorithm The 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of B-theory for numerical method of functional differential equations in the analysis of fair value in financial accounting Research on the influence of fuzzy mathematics simulation model in the development of Wushu market Study on audio-visual family restoration of children with mental disorders based on the mathematical model of fuzzy comprehensive evaluation of differential equation Difference-in-differences test for micro effect of technological finance cooperation pilot in China Application of multi-attribute decision-making methods based on normal random variables in supply chain risk management Exploration on the collaborative relationship between government, industry, and university from the perspective of collaborative innovation The impact of financial repression on manufacturing upgrade based on fractional Fourier transform and probability AtanK-A New SVM Kernel for Classification Validity and reliability analysis of the Chinese version of planned happenstance career inventory based on mathematical statistics Visual positioning system for marine industrial robot assembly based on complex variable function Mechanical behaviour of continuous girder bridge with corrugated steel webs constructed by RW Study of a linear-physical-programming-based approach for web service selection under uncertain service quality The Relationship Between College Students’ Taekwondo Courses and College Health Based on Mathematical Statistics Equations A mathematical model of plasmid-carried antibiotic resistance transmission in two types of cells Fractional Differential Equations in the Exploration of Geological and Mineral Construction AdaBoost Algorithm in Trustworthy Network for Anomaly Intrusion Detection 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 Calculating university education model based on finite element fractional differential equations and macro-control analysis Educational research on mathematics differential equation to simulate the model of children's mental health prevention and control system Analysis of enterprise management technology and innovation based on multilinear regression model Verifying the validity of the whole person model of mental health education activities in colleges based on differential equation RETRACTION NOTE 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 Determination of the minimum distance between vibration source and fibre under existing optical vibration signals: a study Nonlinear differential equations based on the B-S-M model in the pricing of derivatives in financial markets 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 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 MCM of Student’s Physical Health Based on Mathematical Cone Sports health quantification method and system implementation based on multiple thermal physiology simulation Research on visual optimization design of machine–machine interface for mechanical industrial equipment based on nonlinear partial equations 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 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 Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory Mathematical function data model analysis and synthesis system based on short-term human movement Human gait modelling and tracking based on motion functionalisation The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Financial Accounting Measurement Model Based on Numerical Analysis of Rigid Normal Differential Equation and Rigid Functional Equation Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate Differential equation model of financial market stability based on Internet big data 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Children’s cognitive function and mental health based on finite element nonlinear mathematical model 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 Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups ofp -groupsThe internal mechanism of corporate social responsibility fulfillment affecting debt risk in China: analysis of intermediary transmission effect based on degree of debt concentration and product market competitive advantage Study on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Asymptotic stability problem of predator–prey system with linear diffusion Research on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Research on threat assessment problems of island air defence system based on the leader-follower model 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 Study on inefficient land use determination method for cities and towns from a city examination perspective A sentiment analysis method based on bidirectional long short-term memory networks Evaluation of ecosystem health in Futian mangrove wetland based on the PSR-AHP model A study of local smoothness-informed convolutional neural network models for image inpainting Towards more efficient control of the ironmaking blast furnace: modelling gaseous reduction of iron ores in H _{2}-N_{2}atmosphereAlgorithm of overfitting avoidance in CNN based on maximum pooled and weight decay 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 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 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 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 Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model