# American Institute of Mathematical Sciences

## Path prediction model of county urban growth boundary based on BP neural network

 1 School of Management, Xi'an University of Architecture and Technology, Xi'an 710055, China 2 School of Public Administration, Shaanxi Radio and Television University, Xi'an 710068, China

* Corresponding author: Huiqin Wang

Received  April 2019 Revised  May 2019 Published  January 2020

The city is the center of the regional system and the most influential space-time composite system. The spatial expansion of its land has become one of the main features of land use change in China. The problem of marginal growth of county cities is studied in depth in this paper. Firstly, the county urban land use information extraction method based on probabilistic neural network is used to obtain the geographic data of the county city. Then, through the optimized multi-feature fusion acquisition algorithm, the collected geographic data features of county cities are multi-featured. Finally, based on the characteristics of county city geographic data, the BP neural network-based path prediction model of the county urban growth boundary is established to predict the path of county urban growth boundary. The analysis shows that when the random variable is 1.1 and the threshold is 0.7, the prediction accuracy of this model is 99$\%$, which can effectively predict the growth boundary path of county cities. Compared with the similar prediction model, the prediction accuracy of this model is 99.87$\%$, which makes more accurate prediction of the future development of the city and can provide the basis for urban planning.

Citation: Zhiyuan Sun, Huiqin Wang, Ke Wang, Aorui Bi. Path prediction model of county urban growth boundary based on BP neural network. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020254
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##### References:
 [1] C. Bradley, N. Joyce and L. Garcia-Larrea, Adaptation in human somatosensory cortex as a model of sensory memory construction: A study using high-density eeg, Brain Structure and Function, 221 (2016), 421-431.  doi: 10.1007/s00429-014-0915-5.  Google Scholar [2] Y. Chen, Prediction algorithm of pm2.5 mass concentration based on adaptive bp neural network, Computing, 100 (2018), 825-838.  doi: 10.1007/s00607-018-0628-3.  Google Scholar [3] M. Colombo, D. Cumming and S. Vismara, Governmental venture capital for innovative young firms, Journal of Technology Transfer, 41 (2016), 10-24.   Google Scholar [4] T. Cong, J. Hong and O. Dong, Ntb branch predictor: Dynamic branch predictor for high-performance embedded processors, Journal of Supercomputing, 72 (2016), 1679-1693.   Google Scholar [5] M. Di, M. Mottolese and B. Di, The cytoskeleton regulatory protein hmena (enah) is overexpressed in human benign breast lesions with high risk of transformation and human epidermal growth factor receptor-2-positive/hormonal receptor-negative tumors, Clinical Cancer Research, 12 (2016), 1470-1478.   Google Scholar [6] M. Dorado-Moreno, A. Sianes and C. Hervás-Martínez, From outside to hyper-globalisation: An artificial neural network ordinal classifier applied to measure the extent of globalization, Quality and Quantity, 50 (2016), 549-576.  doi: 10.1007/s11135-015-0163-7.  Google Scholar [7] G. Frana, M. Almeida and S. Bonnet, Nowcasting model of low wind profile based on neural network using sodar data at guarulhos airport, brazil, International Journal of Remote Sensing, 39 (2018), 2506-2517.   Google Scholar [8] X. Fu, F. Wang and J. Shang, Optimized bp neural network algorithm based on multi-child genetic algorithm, Computer Simulation, 33 (2016), 258-263.   Google Scholar [9] J. Gao, X. Wu and W. Gao, Review on inductive contactless power transfer technology, Journal of Power Supply, 15 (2017), 166-178.   Google Scholar [10] M. Guerrero, D. Urbano and A. Fayolle, Entrepreneurial activity and regional competitiveness: Evidence from european entrepreneurial universities, Journal of Technology Transfer, 41 (2016), 105-131.  doi: 10.1007/s10961-014-9377-4.  Google Scholar [11] E. Jenelius and H. Koutsopoulos, Urban network travel time prediction based on a probabilistic principal component analysis model of probe data, IEEE Transactions on Intelligent Transportation Systems, 19 (2018), 436-445.  doi: 10.1109/TITS.2017.2703652.  Google Scholar [12] M. Joshanloo and W. Dan, Religiosity reduces the negative influence of injustice on subjective well-being: a study in 121 nations, Applied Research in Quality of Life, 11 (2016), 601-612.  doi: 10.1007/s11482-014-9384-5.  Google Scholar [13] S. Kim, K. Um and H. Kim, Hospital career management systems and their effects on the psychological state and career attitudes of nurses, Service Business, 10 (2016), 87-112.  doi: 10.1007/s11628-014-0257-7.  Google Scholar [14] W. Peng and Q. Huang, Research on complex information system evolution process, Journal of China Academy of Electronics and Information Technology, 12 (2017), 37-42.   Google Scholar [15] B. Song, Study on construction technology and engineering management of water conservancy and hydropower projects, Automation and Instrumentation, 10 (2017), 170-171.   Google Scholar [16] I. Szcs, B. Schlegelmilch and T. Rusch, Linking cause assessment, corporate philanthropy, and corporate reputation, Journal of the Academy of Marketing Science, 44 (2016), 376-396.  doi: 10.1007/s11747-014-0417-2.  Google Scholar [17] J. Tremblay and I. Abi-Zeid, Value-based argumentation for policy decision analysis: Methodology and an exploratory case study of a hydroelectric project in québec, Annals of Operations Research, 236 (2016), 233-253.  doi: 10.1007/s10479-014-1774-4.  Google Scholar [18] H. Uzun, Z. Yldz and J. Goldfarb, Improved prediction of higher heating value of biomass using an artificial neural network model based on proximate analysis, Bioresource Technology, 234 (2017), 122-130.  doi: 10.1016/j.biortech.2017.03.015.  Google Scholar [19] H. Wang and X. Zhang, Game theoretical transportation network design among multiple regions, Annals of Operations Research, 249 (2017), 97-117.  doi: 10.1007/s10479-014-1700-9.  Google Scholar [20] Y. Wang, S. Hu and F. Cao, Research prospect of cathode materials for lithium ion battery, Chinese Journal of Power Sources, 41 (2017), 638-640.   Google Scholar [21] S. Xu, Z. He and R. Long, Impacts of economic growth and urbanization on co2 emissions: Regional differences in china based on panel estimation, Regional Environmental Change, 16 (2016), 777-787.  doi: 10.1007/s10113-015-0795-0.  Google Scholar [22] J. Zhou and X. Hu, Knowledge sharing and life satisfaction: The roles of colleague relationships and gender, Social Indicators Research, 126 (2016), 379-394.   Google Scholar
Diagram of the Relation between Urban Growth Expansion and Economic Development at County Level
Modular structure of BP neural network
Prediction accuracy of models with different parameter settings
Contrast chart between predicted growth boundary path and actual growth boundary path of a city in 2015
Prediction of Urban Land Growth Change in the County in 2015 Based on Different Parameter Combinations in the Model
 Land type (a, T) 2015 -$\infty$, 0.7 1.1, +0.7 1.6, +0.7 2.1, +0.7 1.1, 0.8 The meas ure of area / $hm^{2}$ Growth rate /$\%$ The meas ure of area / $hm^{2}$ Growth rate /$\%$ The meas ure of area / $hm^{2}$ Growth rate /$\%$ The meas ure of area / $hm^{2}$ Growth rate /$\%$ The meas ure of area / $hm^{2}$ Growth rate /$\%$ Live 2399.59 2482.3 3.44 2620.82 9.21 2820.92 17.55 2943.3 22.65 2614.72 8.95 Comm ercial clothing 256.35 287.69 12.21 257.4 0.4 256.84 0.18 257.42 0.41 257.42 0.41 Working condi tion clothing storage 65.78 71.76 9.08 67.98 3.34 67.84 3.12 68.66 4.37 67.98 3.33 Road traffic 81.77 81.76 -0.01 82.62 1.03 84.19 2.95 82.6 1 82.61 1.02 Public manage ment and services 514.43 518.13 0.71 519.4 0.96 521.28 1.32 519.8 1.04 518.75 0.83 Waters 1.34 1.32 -1.71 1.4 4.58 1.4 4.47 1.44 7.24 1.4 4.24 Public green space 22.89 22.65 -1.05 22.78 -0.47 22.74 -0.65 22.63 -1.11 22.85 -0.18 Other 1722.61 1592.47 -7.54 1568.3 -8.95 1549.05 -10.07 1528.2 -11.3 1572.85 -9.68
 Land type (a, T) 2015 -$\infty$, 0.7 1.1, +0.7 1.6, +0.7 2.1, +0.7 1.1, 0.8 The meas ure of area / $hm^{2}$ Growth rate /$\%$ The meas ure of area / $hm^{2}$ Growth rate /$\%$ The meas ure of area / $hm^{2}$ Growth rate /$\%$ The meas ure of area / $hm^{2}$ Growth rate /$\%$ The meas ure of area / $hm^{2}$ Growth rate /$\%$ Live 2399.59 2482.3 3.44 2620.82 9.21 2820.92 17.55 2943.3 22.65 2614.72 8.95 Comm ercial clothing 256.35 287.69 12.21 257.4 0.4 256.84 0.18 257.42 0.41 257.42 0.41 Working condi tion clothing storage 65.78 71.76 9.08 67.98 3.34 67.84 3.12 68.66 4.37 67.98 3.33 Road traffic 81.77 81.76 -0.01 82.62 1.03 84.19 2.95 82.6 1 82.61 1.02 Public manage ment and services 514.43 518.13 0.71 519.4 0.96 521.28 1.32 519.8 1.04 518.75 0.83 Waters 1.34 1.32 -1.71 1.4 4.58 1.4 4.47 1.44 7.24 1.4 4.24 Public green space 22.89 22.65 -1.05 22.78 -0.47 22.74 -0.65 22.63 -1.11 22.85 -0.18 Other 1722.61 1592.47 -7.54 1568.3 -8.95 1549.05 -10.07 1528.2 -11.3 1572.85 -9.68
Comparison of Prediction Accuracy of Thirteen Models
 Direction Range left ($\bullet$) Area Covered by Real Growth Path($km^{2}$) Paper model Cellular Automata model Multi-agent model Predicted value ($km^{2}$) Area matching value D ($\%$) Predicted value ($km^{2}$) Area matching value D ($\%$) Predicted value ($km^{2}$) Area matching value D ($\%$) East 0-90 109.5 109.4 99.91$\%$ 103.1 94.16$\%$ 101.1 92.33$\%$ West 90-180 72.34 72.33 99.99$\%$ 70.21 97.06$\%$ 68.22 94.30$\%$ South 180-270 88.23 88.21 99.98$\%$ 85.34 96.75$\%$ 81.23 92.07$\%$ North 270-360 87.34 86.99 99.60$\%$ 85.23 97.58$\%$ 81.23 93.00$\%$ Whole 0-360 357.41 356.93 99.87$\%$ 343.88 96.21$\%$ 331.78 92.83$\%$
 Direction Range left ($\bullet$) Area Covered by Real Growth Path($km^{2}$) Paper model Cellular Automata model Multi-agent model Predicted value ($km^{2}$) Area matching value D ($\%$) Predicted value ($km^{2}$) Area matching value D ($\%$) Predicted value ($km^{2}$) Area matching value D ($\%$) East 0-90 109.5 109.4 99.91$\%$ 103.1 94.16$\%$ 101.1 92.33$\%$ West 90-180 72.34 72.33 99.99$\%$ 70.21 97.06$\%$ 68.22 94.30$\%$ South 180-270 88.23 88.21 99.98$\%$ 85.34 96.75$\%$ 81.23 92.07$\%$ North 270-360 87.34 86.99 99.60$\%$ 85.23 97.58$\%$ 81.23 93.00$\%$ Whole 0-360 357.41 356.93 99.87$\%$ 343.88 96.21$\%$ 331.78 92.83$\%$
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