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Continuing Education Network Data Center Model Based on Fractional Differential Mathematical Equations

Published Online: 15 Jul 2022
Volume & Issue: AHEAD OF PRINT
Page range: -
Received: 26 Apr 2022
Accepted: 21 Jun 2022
Journal Details
License
Format
Journal
eISSN
2444-8656
First Published
01 Jan 2016
Publication timeframe
2 times per year
Languages
English
Introduction

Chinese online education has sprung up like mushrooms after rain. The “Internet + Education” model covers people of different levels, ages, and needs, showing a situation where a hundred flowers are blooming and competing for beauty. Online education in colleges and universities is the main force among them. It leads to the development trend of online education. Online education breaks through the limitations of space and time. It is more flexible and open. Its characteristics of shared educational resources and personalized teaching mode are also more conducive to students' knowledge acquisition [1]. However, the rapid development of online education has also caused many problems. On the one hand, there are problems such as the aging of the online learning platform, the inefficient use of resources caused by the unreasonable design, the poor quality of the courseware, and the repeated construction. On the other hand, the development of big data applications has not kept pace with the development of information technology. This makes it difficult for administrators to obtain technical support for decision-making in teaching and student support services, quality monitoring, and assurance. These problems have seriously affected and restricted the development of network education in colleges and universities.

Continuing education colleges urgently need reform and innovation. New technologies such as cloud computing and big data can be introduced. A new set of comprehensive management and unified learning platforms that adapt to the development of the times and technological changes can be launched. In this way, the original application can be integrated, and related services can be integrated to realize the integrated management of certification, learning, courses, examinations, training, grades, certificates, and payment. At the same time, we need to build a data center to ensure the homology of essential data, the return of original data, and the integration of business data. In this way, a modern information-based distance education system with big data as the core is realized.

At present, with the continuous growth of the number of continuing education network resources. This also gradually increases the requirements for multi-layer differential networks. Based on the multi-layer differential network, the distributed database can store the data of the original centralized database in a decentralized manner on multiple data storage nodes connected through the network [2]. This results in greater storage capacity and higher access. A multi-layer differential network's distributed data transmission process is also more complicated. This leads to security risks. This paper aims at the above problems to propose a real-time encryption method for distributed data in a multi-layer differential continuing education network based on fractional differential mathematical equations. The experimental results show that the stability of data transmission can be effectively controlled based on fractional differential equations. In this way, the operation efficiency of continuing education network data can be improved, and the encryption cost can be controlled.

Continuing education integrated management and unified learning platform

Figure 1 depicts the architecture of the college's comprehensive management and unified learning platform [3]. The new platform should avoid the defects of mixed management of students in current learning forms. The platform system manages each form of study's enrollment and student status separately. Another benefit of this approach is scalability. In the future, no matter which part of the college's business needs to be adjusted, it can be modified in its module. This will not affect the conduct of other businesses.

Figure 1

Architecture Design of College Integrated Management and Unified Learning Platform

The new integrated management and unified learning platform architecture are composed of multiple subsystems. To access each application system, users need to memorize multiple systems' user names and passwords. Multiple logins can affect efficiency. The platform must be able to standardize user management and provide unified authentication and login services. In the only data source, the platform conducts unified management of the entire life cycle of user information registration, distribution, authorization, change, and cancellation and synchronizes it to each information system. This ensures the consistency and synchronization of user data in each application system. Then the system provides a unified entry for each sub-application system through unified user identity management and single sign-on technology [4]. This avoids multiple verifications. This allows students or administrators to have no impact on the user experience.

Under this architecture, each business application system and its database are kept, independent. This modular model makes it convenient for the college to gradually and smoothly transfer work to the new platform by business unit.

Multi-layer differential network distributed data real-time encryption method

Any multi-layer differential network distributed network transmission should consider inserting private keys on the data [5]. According to the above analysis, the principle of multilayer difference network distributed data real-time encryption system. This paper combines the fractional differential equation encryption algorithm to encrypt distributed data in real-time.

Fractional differential equation encryption is an encryption method whose security is based on solving logarithmic solutions. It can be described as given a fractional differential equation E and two points G and Q, Q = xG = G + G + ⋯ + G on the curve. A total of x G are added. The problem we solve x is the problem of solving the discrete data of fractional differential equations.

Suppose F is a base field and x, y belongs to F such that y2 + axy + by = x3 + cx2 + dx + e. Adding an infinity point O forms a fractional differential equation. In general encryption algorithms, fractional differential equation equations located on a finite field Fp are usually used. which is expressed as E:y2=x3+ax+b E:{y^2} = {x^3} + ax + b

In the formula: a, b, x, y belongs to Fp, P and is a large prime number greater than 3. Our controller design process based on the nonlinear tracking control of the inversion wave function defines the curve data transmission error e1=ϑ=ϑr {e_1} = \vartheta = {\vartheta _r}

x3 is a new variable that interferes with the transmission of plaintext data. The fluctuation error caused by the disturbance is e˙1=ω2ϑ˙r {\dot e_1} = {\omega _2} - {\dot \vartheta _r}

Let b1, b2, b3, d3 be the known coefficients of the model. Δb1, Δb2, Δb3, Δd3 is the undetermined coefficient. fd1, fd2, fd3 is the interference signal. At this time, the inversion wave function is selected as ω2r=c1e1+ϑ˙rλ1ζ1 {\omega _{2r}} = - {c_1}{e_1} + {\dot \vartheta _r} - {\lambda _1}{\zeta _1}

Where c1, λ1 is more significant than zero. At the same time, the integral term ζ1 is introduced. This aims to enhance the robustness of distributed data transmission in the presence of disturbances and uncertain model parameters [6]. We define ζ1=0te1(τ)d(τ) {\zeta _1} = \int_0^t {{e_1}\left(\tau \right)d\left(\tau \right)} .

We perform global control over the data transmission stability of multi-layer differential networks. When t → ∞, the disturbance is a constant steady-state, the error will tend to zero. At this point, we get the multi-layer difference network distributed data real-time encryption error factor: e2=ω2ω2r=ω2+c1e1+λ1ζ1ϑ˙r {e_2} = {\omega _2} - {\omega _{2r}} = {\omega _2} + {c_1}{e_1} + {\lambda _1}{\zeta _1} - {\dot \vartheta _r}

Perform Laplace transform to get e˙1=e2c1e1λ1ζ1 {\dot e_1} = {e_2} - {c_1}{e_1} - {\lambda _1}{\zeta _1}

We use the principle of small perturbation to enable a multi-layer difference network distributed data transmission data stability model: V1=12e12 {V_1} = {1 \over 2}e_1^2

We design adaptive laws. We encrypt the fluctuation data nodes locally by inverting the fluctuation function [7]. The local encryption operator does not exceed the encryption key range. Then we reverse-engineer the adaptive law from the distributed data transmission δ˙^=ε1αV2e2 {\hat {\dot \delta}} = {\varepsilon _1}\alpha {V^2}{e_2}

We substitute the adaptive law. The purpose of this is to eliminate the impact of distributed data transmission on the stability of multi-layer differential networks V˙3=c1e12c2e220 {\dot V_3} = - {c_1}e_1^2 - {c_2}e_2^2 \le 0

We divide the duration (a, t) of the distributed information S(x) collected by the multi-layer difference network equally according to the time interval h. At this point we get n = (ta) / h. Thus we can obtain the fractional differential function of the operator concerning the intrinsic influence factor x based on the Grunwald-Letnikov definition αGDtυF(x)=limh0Fhυ(x)=hυk=0[tah](1)k(υk)F(xkh) _\alpha ^GD_t^\upsilon F\left(x \right) = \mathop {\lim}\limits_{h \to 0} F_h^\upsilon \left(x \right) = {h^{- \upsilon}}\sum\limits_{k = 0}^{\left[{{{t - a} \over h}} \right]} {{{\left({- 1} \right)}^k}\left({\matrix{\upsilon \cr k \cr}} \right)F\left({x - kh} \right)}

Where 0 ≤ n − 1 < υ < n, (υk) \left({\matrix{\upsilon \cr k \cr}} \right) is the binomial coefficient. (υk)=υ(υ1)(υ2)(υk+1)k!=[υk] \left({\matrix{\upsilon \cr k \cr}} \right) = {{\upsilon \left({\upsilon - 1} \right)\left({\upsilon - 2} \right) \cdots \left({\upsilon - k + 1} \right)} \over {k!}} = \left[{\matrix{{- \upsilon} \cr k \cr}} \right]

We substitute equation (6) into equation (5) to obtain the distributed data fusion algorithm model based on fractional differentiation defined by Grunwald-Letnikov αGDtυF(x)=limh0Fhυ(x)=hυk=0[tah](1)k[υk]F(xkh)=hυk=0[tah]wkυF(xkh) _\alpha ^GD_t^\upsilon F\left(x \right) = \mathop {\lim}\limits_{h \to 0} F_h^\upsilon \left(x \right) = {h^{- \upsilon}}\sum\limits_{k = 0}^{\left[{{{t - a} \over h}} \right]} {{{\left({- 1} \right)}^k}\left[{\matrix{{- \upsilon} \cr k \cr}} \right]F\left({x - kh} \right) = {h^{- \upsilon}}} \sum\limits_{k = 0}^{\left[{{{t - a} \over h}} \right]} {w_k^\upsilon F\left({x - kh} \right)}

In the formula wkυ w_k^\upsilon is the weight coefficient value and wkυ=(1)k[υk] w_k^\upsilon = {\left({- 1} \right)^k}\left[{\matrix{{- \upsilon} \cr k \cr}} \right] , and its calculation formula is w0υ=1,wkυ=(1υ+1k)wk1υ,k=1,2 w_0^\upsilon = 1,\,w_k^\upsilon = \left({1 - {{\upsilon + 1} \over k}} \right)w_{k - 1}^\upsilon,\,k = 1,2 \cdots

The data fusion model formula based on the fractional differential operator is as follows S(x)=Sυ(x)limh0hυr=013[υr]S(xrh)=hυ[S(x)υS(xh)υ(1υ)2!S(x2h) \matrix{{S^{'}\left(x \right) = {S^\upsilon}\left(x \right) \approx \mathop {\lim}\limits_{h \to 0} {h^{- \upsilon}}\sum\limits_{r = 0}^{13} {\left[{\matrix{{- \upsilon} \cr r \cr}} \right]S\left({x - rh} \right)}} \hfill \cr {= {h^{- \upsilon}}\left[{S\left(x \right) - \upsilon S\left({x - h} \right) - {{\upsilon \left({1 - \upsilon} \right)} \over {2!}}S\left({x - 2h} \right)} \right.} \hfill \cr} Vz={0,t<T1(Vzmax/2){1cos[2π(tT1Tz)]},T1tT1+Tz0,t>T1+T} {V_z} = \left\{{\matrix{{0,\,t\, < \,{T_1}} \hfill \cr {\left({{V_{z\,\max}}/2} \right)\left\{{1 - \cos \left[{2\pi \left({{{t - {T_1}} \over {{T_z}}}} \right)} \right]} \right\},\,{T_1} \le t \le {T_1} + {T_z}} \hfill \cr {0,\,t\, > \,{T_1} + T} \hfill \cr}} \right\}

T1, Tz represents the start time and duration of encryption, respectively. Vzmax is the maximum value of the stable transmission factor of distributed data.

Experimental Analysis

The experimental platform in this paper uses Windows 10 and i5 processors. The client uses JDK1.8 for real-time encryption of distributed data [8]. We store the ciphertext in the Tencent Cloud platform. The critical length statistics we set are shown in Table 1. The purpose is to verify that the method based on fractional differential equation encryption has the same security level as the traditional method.

Required critical lengths for the same security level.

N The average key length of the filtering algorithm (bit) An average key length of the clustering method (bit) The average key length (bit) of the method based on fractional differential equation encryption
10 522 207 52
20 778 232 72
30 702 270 72
40 848 220 72
50 807 300 82
60 859 325 75
70 985 335 79
80 997 372 75

It can be seen from Table 1 that the critical lengths of different methods are very different under the same security level. It is fully proved that the implementation steps of the method based on fractional differential equation encryption are more refined. It operates more efficiently.

Comparison of the average encryption time of different methods

N The average encryption time of the filtering algorithm (ms) Average encryption time of clustering method (ms) The average encryption time (ms) of the method based on fractional differential equation encryption
10 5.01 1.31 0.51
20 5.63 1.85 0.93
30 6.34 3.56 1.13
40 8.11 3.85 1.56
50 8.36 3.95 1.56
60 8.01 4.01 1.63
70 8.56 4.13 1.81
80 9.01 4.31 1.83

We compare the encryption time of the three methods through the data in Table 2. The specific data is shown in Figure 2. From the data in Table 2 and Figure 2, it can be seen that the encryption method based on fractional differential equation takes the shortest time. It has high operating efficiency.

Figure 2

Comparison of encryption time of different methods

Different encryption methods have differences in the stability of data transmission after distributed data encryption. We conduct experiments on three encrypted distributed data transmissions [9]. The experimental results are shown in Figure 3.

Figure 3

Comparison of the effects of different encryption methods on data transmission stability

It can be seen from Figure 3 that the stability of encrypted distributed data transmission increases with the increase in the number of times. The filtering algorithm encryption method is more stable than the clustering algorithm method for distributed data transmission after distributed data encryption [10]. The encryption method in this paper encrypts the distributed data, and the stability of the distributed data transmission is higher than that of the filtering algorithm encryption method. This fully proves that the data transmission stability of the method based on fractional differential equation encryption has been significantly improved. The algorithm increases the efficiency of continuing education platform network data operation.

Countermeasures for data center construction

Figure 4 shows the architectural design of the college data center construction. Before starting to build a data center, it is necessary to formulate the college's data management norms and systems. At the same time, we need to unify the college data storage and access standards. This paper proposes a parallel construction method for business platforms and data centers. We use data from various business systems as source data. Through the process of data extraction, cleaning, and transformation, we convert it into a unified data standard for the college and store it in the data warehouse [11]. The work of data extraction, cleansing, and transformation is carried out when the data warehouse is established and when the new business system is connected. During the platform's operation, we set up strategies according to different system requirements and execute them regularly.

Figure 4

Data Center Architecture Design of Continuing Education College

The operational data storage layer design is the same as the source data system structure and data granularity. It provides the role of temporary storage. It reduces the pressure of large-volume data query work in the business system. The data stored in it can be cleaned regularly according to business needs to save space.

Conclusion

Network education in colleges and universities needs to provide students with a platform with complete functions, easy operation, and stable services for online learning. At the same time, it is necessary to grasp and analyze the critical data of the entire business chain of the college to realize data mining, monitoring analysis, statistical query, and visual display to improve office efficiency and emergency response capabilities. The platform architecture and system proposed in this paper are used to construct and manage the Continuing Education College's unified learning platform and data center. At the same time, this paper proposes a real-time encryption method of multi-layer differential network distributed data based on fractional differential equations. Under the same security level condition, the encryption method based on a fractional differential equation has the shortest length. This shows that the encryption steps of the method are simple and easy to operate, and have strong operability. The study found that the data transmission stability of the method based on fractional differential equation encryption is higher than that of the traditional method. It improves operational efficiency

Figure 1

Architecture Design of College Integrated Management and Unified Learning Platform
Architecture Design of College Integrated Management and Unified Learning Platform

Figure 2

Comparison of encryption time of different methods
Comparison of encryption time of different methods

Figure 3

Comparison of the effects of different encryption methods on data transmission stability
Comparison of the effects of different encryption methods on data transmission stability

Figure 4

Data Center Architecture Design of Continuing Education College
Data Center Architecture Design of Continuing Education College

Comparison of the average encryption time of different methods

N The average encryption time of the filtering algorithm (ms) Average encryption time of clustering method (ms) The average encryption time (ms) of the method based on fractional differential equation encryption
10 5.01 1.31 0.51
20 5.63 1.85 0.93
30 6.34 3.56 1.13
40 8.11 3.85 1.56
50 8.36 3.95 1.56
60 8.01 4.01 1.63
70 8.56 4.13 1.81
80 9.01 4.31 1.83

Required critical lengths for the same security level.

N The average key length of the filtering algorithm (bit) An average key length of the clustering method (bit) The average key length (bit) of the method based on fractional differential equation encryption
10 522 207 52
20 778 232 72
30 702 270 72
40 848 220 72
50 807 300 82
60 859 325 75
70 985 335 79
80 997 372 75

Moaaz, O., Park, C., Muhib, A., & Bazighifan, O. Oscillation criteria for a class of even-order neutral delay differential equations. Journal of Applied Mathematics and Computing., 2020; 63(1): 607–617 MoaazO. ParkC. MuhibA. BazighifanO. Oscillation criteria for a class of even-order neutral delay differential equations Journal of Applied Mathematics and Computing 2020 63 1 607 617 10.1007/s12190-020-01331-w Search in Google Scholar

Sarhan, M. A., SHIHAB, S., & RASHEED, M. Some Results on a Two Variables Pell Polynomials. Al-Qadisiyah Journal of Pure Science., 2021;26(1): 55–70 SarhanM. A. SHIHABS. RASHEEDM. Some Results on a Two Variables Pell Polynomials Al-Qadisiyah Journal of Pure Science 2021 26 1 55 70 Search in Google Scholar

Gao, W., Veeresha, P., Prakasha, D. G., & Baskonus, H. M. New numerical simulation for fractional Benney–Lin equation arising in falling film problems using two novel techniques. Numerical Methods for Partial Differential Equations., 2021; 37(1): 210–243 GaoW. VeereshaP. PrakashaD. G. BaskonusH. M. New numerical simulation for fractional Benney–Lin equation arising in falling film problems using two novel techniques Numerical Methods for Partial Differential Equations 2021 37 1 210 243 10.1002/num.22526 Search in Google Scholar

Fernandez, A., & Mohammed, P. Hermite-Hadamard inequalities in fractional calculus defined using Mittag-Leffler kernels. Mathematical Methods in the Applied Sciences., 2021; 44(10): 8414–8431 FernandezA. MohammedP. Hermite-Hadamard inequalities in fractional calculus defined using Mittag-Leffler kernels Mathematical Methods in the Applied Sciences 2021 44 10 8414 8431 10.1002/mma.6188 Search in Google Scholar

İlhan, E., & Kıymaz, İ. O. A generalization of truncated M-fractional derivative and applications to fractional differential equations. Applied Mathematics and Nonlinear Sciences., 2020;5(1): 171–188 İlhanE. Kıymazİ. O. A generalization of truncated M-fractional derivative and applications to fractional differential equations Applied Mathematics and Nonlinear Sciences 2020 5 1 171 188 10.2478/amns.2020.1.00016 Search in Google Scholar

Gençoğlu, M. T., & Agarwal, P. Use of quantum differential equations in sonic processes. Applied Mathematics and Nonlinear Sciences., 2021; 6(1): 21–28 GençoğluM. T. AgarwalP. Use of quantum differential equations in sonic processes Applied Mathematics and Nonlinear Sciences 2021 6 1 21 28 10.2478/amns.2020.2.00003 Search in Google Scholar

El-Sayed, A. A., Baleanu, D., & Agarwal, P. A novel Jacobi operational matrix for numerical solution of multi-term variable-order fractional differential equations. Journal of Taibah University for Science., 2020; 14(1): 963–974 El-SayedA. A. BaleanuD. AgarwalP. A novel Jacobi operational matrix for numerical solution of multi-term variable-order fractional differential equations Journal of Taibah University for Science 2020 14 1 963 974 10.1080/16583655.2020.1792681 Search in Google Scholar

Phang, C., Kanwal, A., & Loh, J. R. New collocation scheme for solving fractional partial differential equations. Hacettepe Journal of Mathematics and Statistics., 2020; 49(3): 1107–1125 PhangC. KanwalA. LohJ. R. New collocation scheme for solving fractional partial differential equations Hacettepe Journal of Mathematics and Statistics 2020 49 3 1107 1125 10.15672/hujms.459621 Search in Google Scholar

Cui, Z., & Yan, C. Deep integration of health information service system and data mining analysis technology. Applied Mathematics and Nonlinear Sciences., 2020; 5(2): 443–452 CuiZ. YanC. Deep integration of health information service system and data mining analysis technology Applied Mathematics and Nonlinear Sciences 2020 5 2 443 452 10.2478/amns.2020.2.00063 Search in Google Scholar

Bakirova, E. A., Assanova, A. T., & Kadirbayeva, Z. M. A problem with parameter for the integro-differential equations. Mathematical Modelling and Analysis., 2021; 26(1): 34–54 BakirovaE. A. AssanovaA. T. KadirbayevaZ. M. A problem with parameter for the integro-differential equations Mathematical Modelling and Analysis 2021 26 1 34 54 10.3846/mma.2021.11977 Search in Google Scholar

Aubin-Frankowski, P. C., & Vert, J. P. Gene regulation inference from single-cell RNA-seq data with linear differential equations and velocity inference. Bioinformatics., 2020;36(18): 4774–4780 Aubin-FrankowskiP. C. VertJ. P. Gene regulation inference from single-cell RNA-seq data with linear differential equations and velocity inference Bioinformatics 2020 36 18 4774 4780 10.1093/bioinformatics/btaa57633026066 Search in Google Scholar

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