Presentation of regression analysis, GP and GMDH models to predict the pedestrian density in various urban facilities

Abstract

In this study, the relationship between space mean speed (SMS), flow rate and density of pedestrians was investigated in different pedestrian facilities, including 1 walkway, 2 sidewalks, 2 signalized crosswalks and 2 mid-block crosswalks. First, statistical analysis was performed to investigate the normality of data and correlation of variables. Regression analysis was then applied to determine the relationship between SMS, flow rate, and density of pedestrians. Finally, two prediction models of density were obtained using genetic programming (GP) and group method of data handling (GMDH) models, and k-fold and holdout cross-validation methods were used to evaluate the models. By the use of regression analysis, the mathematical relationships between variables in all facilities were calculated and plotted, and the best relationships were observed in flow rate-density diagrams. Results also indicated that GP had a higher R² than GMDH in the prediction of pedestrian density in terms of flow rate and SMS, suggesting that GP was better able to model SMS and pedestrian density. Moreover, the application of k-fold cross-validation method in the models led to better performances compared to the holdout cross-validation method, which shows that the prediction models using k-fold were more reliable. Finally, density relationships in all facilities were obtained in terms of SMS and flow rate.

Graphical abstract

Keywords

pedestrian density / regression analysis / GP model / GMDH model

References

[1] Haghighi M, Bakhtari F, Sadeghi-Bazargani H, Nadrian H. Strategies to promote pedestrian safety from the viewpoints of traffic and transport stakeholders in a developing country: A mixed-method study. Journal of Transport & Health, 2021, 22 : 101125–

[2] Chen S, Fu L, Fang J, Yang P. The effect of obstacle layouts on pedestrian flow in corridors: An experimental study. Physica A, 2019, 534 : 122333–

[3] Guidoni D L, Maia G, Souza F S H, Villas L A, Loureiro A A F. Vehicular traffic management based on traffic engineering for vehicular ad hoc networks. IEEE Access: Practical Innovations, Open Solutions, 2020, 8 : 45167– 45183

[4] World Health Organization. Global Status Report on Road Safety 2018. 2018

[5] Mohammadi A, Yousefi M, Taghipour A, Ebrahimipour H, Varmaghani M. Burden of disease caused by road traffic accidents in the city of mashhad. Health Scope, 2020, 9( 4): 101657–

[6] Hadaye R S, Rathod S, Shastri S. A cross-sectional study of epidemiological factors related to road traffic accidents in a metropolitan city. Journal of Family Medicine and Primary Care, 2020, 9( 1): 168– 172

[7] McIlroy R C, Kokwaro G O, Wu J, Jikyong U, Nam V H, Hoque M S, Preston J M, Plant K L, Stanton N A. How do fatalistic beliefs affect the attitudes and pedestrian behaviours of road users in different countries? A cross-cultural study.. Accident Analysis and Prevention, 2020, 139 : 105491–

[8] Hughes R L. A continuum theory for the flow of pedestrians. Transportation Research Part B: Methodological, 2002, 36( 6): 507– 535

[9] Helbing D, Johansson A, Al-Abideen H Z. Dynamics of crowd disasters: An empirical study. Physical Review. E, 2007, 75( 4): 046109–

[10] Liu W, Zhou H, He Q. Modeling pedestrians flow on stairways in Shanghai metro transfer station. In: 2008 International Conference on Intelligent Computation Technology and Automation (ICICTA). Changsha: IEEE, 2008

[11] Chen X, Ye J, Jian N. Relationships and characteristics of pedestrian traffic flow in confined passageways. Transportation Research Record: Journal of the Transportation Research Board, 2010, 2198( 1): 32– 40

[12] Plaue M, Chen M, Bärwolff G, Schwandt H. Trajectory extraction and density analysis of intersecting pedestrian flows from video recordings. In: ISPRS Conference on Photogrammetric Image Analysis. Berlin: Springer, 2011

[13] Shafabakhsh G, Mohammadi M, Mirzanamadi R. Analysis of pedestrians’ walking speed in Iran’s sidewalks (considering the elderly). Journal of Basic and Applied Scientific Research, 2013, 3( 3): 172– 182

[14] Rastogi R, Chandra S. Pedestrian flow characteristics for different pedestrian facilities and situations. European Transport, 2013, 53 : 1– 21

[15] Bargegol I, Gilani V, Jamshidpour F. Modeling pedestrian flow at central business district. Jurnal UMP Social Sciences and Technology Management, 2015, 3( 3): 217– 222

[16] Pinna F, Murrau R. Age factor and pedestrian speed on sidewalks. Sustainability, 2018, 10( 11): 4084–

[17] Sun Y. Kinetic Monte Carlo simulations of bi-direction pedestrian flow with different walk speeds. Physica A, 2020, 549 : 124295–

[18] Bargegol I, Gilani V N M, Jamshidpour F. Relationship between pedestrians’ speed, density and flow rate of crossings through urban intersections (case study: Rasht metropolis). International Journal of Engineering, 2017, 30( 12): 1814– 1821

[19] Najafzadeh M, Barani G A, Azamathulla H M. Prediction of pipeline scour depth in clear-water and live-bed conditions using group method of data handling. Neural Computing & Applications, 2014, 24( 3): 629– 635

[20] Guido G, Haghshenas S S, Haghshenas S S, Vitale A, Gallelli V, Astarita V. Development of a binary classification model to assess safety in transportation systems using GMDH-type neural network algorithm. Sustainability, 2020, 12( 17): 6735–

[21] Koopialipoor M, Nikouei S S, Marto A, Fahimifar A, Jahed Armaghani D, Mohamad E T. Predicting tunnel boring machine performance through a new model based on the group method of data handling. Bulletin of Engineering Geology and the Environment, 2019, 78( 5): 3799– 3813

[22] López J R, Gonzalez L C, Wahlstrom J, Montes y Gomez M, Trujillo L, Ramirez-Alonso G. A genetic programming approach for driving score calculation in the context of intelligent transportation systems. IEEE Sensors Journal, 2018, 18( 17): 7183– 7192

[23] Das S, Raju N, Maurya A K, Arkatkar S. Evaluating lateral interactions of motorized two-wheelers using multi-gene symbolic genetic programming. Transportation Research Record: Journal of the Transportation Research Board, 2020, 2674( 9): 1120– 1135

[24] Pattanaik M L, Choudhary R, Kumar B. Prediction of frictional characteristics of bituminous mixes using group method of data handling and multigene symbolic genetic programming. Engineering with Computers, 2020, 36( 4): 1875– 1888

[25] Blanca M J, Arnau J, López-Montiel D, Bono R, Bendayan R. Skewness and kurtosis in real data samples. Methodology, 2013, 9( 2): 78– 84

[26] Liu Y, Mu Y, Chen K, Li Y, Guo J. Daily activity feature selection in smart homes based on pearson correlation coefficient. Neural Processing Letters, 2020, 51( 2): 1– 17

[27] Xu H, Wu T, Liu Q, Li J. Research on the cut-throwing performance of chopper of sugarcane harvester. Computational Research Progress in Applied Science & Engineering (CRPASE), 2019, 05( 03): 85– 91

[28] Xu B, Lin B. Investigating drivers of CO₂ emission in China’s heavy industry: A quantile regression analysis. Energy, 2020, 206 : 118159–

[29] Ivakhnenko A G, Lapa V G. Cybernetic Predicting Devices. New York: CCM Information Corp., 1996

[30] Ahmadi M H, Mohseni-Gharyehsafa B, Ghazvini M, Goodarzi M, Jilte R D, Kumar R. Comparing various machine learning approaches in modeling the dynamic viscosity of CuO/water nanofluid. Journal of Thermal Analysis and Calorimetry, 2020, 139( 4): 2585– 2599

[31] Koza J R. Genetic Programming: On the Programming of Computers by Means of Natural Selection. Vol. 1. Cambridge, MA: MIT press, 1992

[32] Shahin M, Yun L, Chin C M M, Gao L, Wang C, Niu X, Goyal A, Garg A. An application of genetic programming for lithium-ion battery pack enclosure design: Modelling of mass, minimum natural frequency and maximum deformation case. IOP Conference Series: Earth and Environmental Science, 2019, 268( 1): 012065–

[33] Bai B, Guo Z, Zhou C, Zhang W, Zhang J. Application of adaptive reliability importance sampling-based extended domain PSO on single mode failure in reliability engineering. Information Sciences, 2021, 546 : 42– 59

[34] Zhao D, Liu L, Yu F, Heidari A A, Wang M, Liang G, Muhammad K, Chen H. Chaotic random spare ant colony optimization for multi-threshold image segmentation of 2D Kapur entropy. Knowledge-Based Systems, 2021, 216 : 106510–

[35] Hu J, Chen H, Heidari A A, Wang M, Zhang X, Chen Y, Pan Z. Orthogonal learning covariance matrix for defects of grey wolf optimizer: Insights, balance, diversity, and feature selection. Knowledge-Based Systems, 2021, 213 : 106684–

[36] Zhao X, Zhang X, Cai Z, Tian X, Wang X, Huang Y, Chen H, Hu L. Chaos enhanced grey wolf optimization wrapped ELM for diagnosis of paraquat-poisoned patients. Computational Biology and Chemistry, 2019, 78 : 481– 490

[37] Chen H, Heidari A A, Chen H, Wang M, Pan Z, Gandomi A H. Multi-population differential evolution-assisted Harris hawks optimization: Framework and case studies. Future Generation Computer Systems, 2020, 111 : 175– 198

[38] Cao Y, Li Y, Zhang G, Jermsittiparsert K, Nasseri M. An efficient terminal voltage control for PEMFC based on an improved version of whale optimization algorithm. Energy Reports, 2020, 6 : 530– 542

[39] Gao N, Luo D, Cheng B, Hou H. Teaching-learning-based optimization of a composite metastructure in the 0–10 kHz broadband sound absorption range. Journal of the Acoustical Society of America, 2020, 148( 2): EL125– EL129

[40] Sun G, Li C, Deng L. An adaptive regeneration framework based on search space adjustment for differential evolution. Neural Computing & Applications, 2021, 33( 15): 1– 17

[41] Liu J, Wu C, Wu G, Wang X. A novel differential search algorithm and applications for structure design. Applied Mathematics and Computation, 2015, 268 : 246– 269

[42] Zhang Y, Liu R, Heidari A A, Wang X, Chen Y, Wang M, Chen H. Towards augmented kernel extreme learning models for bankruptcy prediction: algorithmic behavior and comprehensive analysis. Neurocomputing, 2021, 430 : 185– 212

[43] Wang M, Chen H. Chaotic multi-swarm whale optimizer boosted support vector machine for medical diagnosis. Applied Soft Computing, 2020, 88 : 105946–

[44] Xu X, Chen H. Adaptive computational chemotaxis based on field in bacterial foraging optimization. Soft Computing, 2014, 18( 4): 797– 807

[45] Xu Y, Chen H, Luo J, Zhang Q, Jiao S, Zhang X. Enhanced Moth-flame optimizer with mutation strategy for global optimization. Information Sciences, 2019, 492 : 181– 203

[46] Li C, Hou L, Sharma B Y, Li H, Chen C S, Li Y, Zhao X, Huang H, Cai Z, Chen H. Developing a new intelligent system for the diagnosis of tuberculous pleural effusion. Computer Methods and Programs in Biomedicine, 2018, 153 : 211– 225

[47] Xia J, Chen H, Li Q, Zhou M, Chen L, Cai Z, Fang Y, Zhou H. Ultrasound-based differentiation of malignant and benign thyroid Nodules: An extreme learning machine approach. Computer Methods and Programs in Biomedicine, 2017, 147 : 37– 49

[48] Nguyen S, Mei Y, Zhang M. Genetic programming for production scheduling: A survey with a unified framework. Complex & Intelligent Systems, 2017, 3( 1): 41– 66

[49] Esmaeelzadeh R, Borhani Dariane A. Long-term streamflow forecasting by adaptive neuro-fuzzy inference system using k-fold cross-validation (Case study: Taleghan Basin, Iran). Journal of Water Sciences Research, 2014, 6( 1): 71– 83

[50] Wong T T, Yeh P Y. Reliable accuracy estimates from k-fold cross validation. IEEE Transactions on Knowledge and Data Engineering, 2020, 32( 8): 1586– 1594

[51] Nikbakhsh N, Dehghani G, Zamani F. Comparing classification algorithms of data mining in diagnosis of diabetes and assessing the effectiveness of k-fold cross validation in the accuracy of the constructed model. In: International Conference on Engineering and Computer Science. Najafabad: Islamic Azad University Najafabad Branch, 2016

[52] Yadav S, Shukla S. Analysis of k-fold cross-validation over hold-out validation on colossal datasets for quality classification. In: 2016 IEEE 6th International Conference on Advanced Computing (IACC). Bhimavaram: IEEE, 2016

[53] Elefteriadou L A. The highway capacity manual 6th edition: A guide for multimodal mobility analysis. Ite journal, 2016, 86( 4): 14– 18

[54] Zhang Y, Liu R, Wang X, Chen H, Li C. Boosted binary Harris hawks optimizer and feature selection. Engineering with Computers, 2021, 37( 4): 3741– 3770

[55] Tu J, Chen H, Liu J, Heidari A A, Zhang X, Wang M, Ruby R, Pham Q V. Evolutionary biogeography-based whale optimization methods with communication structure: Towards measuring the balance. Knowledge-Based Systems, 2021, 212 : 106642–

[56] Anitescu C, Atroshchenko E, Alajlan N, Rabczuk T. Artificial neural network methods for the solution of second order boundary value problems. Computers, Materials and Continua, 2019, 59( 1): 345– 359

[57] Gharahbash J, Jazani N. An intelligent method for understanding consumers’ perception of luxury hotel brands using convolutional neural networks. Computational Research Progress in Applied Science & Engineering (CRPASE), 2020, 06( 01): 9– 14

[58] Chen H, Chen A, Xu L, Xie H, Qiao H, Lin Q, Cai K. A deep learning CNN architecture applied in smart near-infrared analysis of water pollution for agricultural irrigation resources. Agricultural Water Management, 2020, 240 : 106303–

[59] Guo H, Zhuang X, Rabczuk T. A deep collocation method for the bending analysis of Kirchhoff plate. Computers, Materials and Continua, 2019, 59( 2): 433– 456

[60] Samaniego E, Anitescu C, Goswami S, Nguyen-Thanh V M, Guo H, Hamdia K, Zhuang X, Rabczuk T. An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications. Computer Methods in Applied Mechanics and Engineering, 2020, 362 : 112790–

[61] Zhuang X, Guo H, Alajlan N, Zhu H, Rabczuk T. Deep autoencoder based energy method for the bending, vibration, and buckling analysis of Kirchhoff plates with transfer learning. European Journal of Mechanics. A, Solids, 2021, 87 : 104225–

[62] Addeh A, Iri M. Brain tumor type classification using deep features of MRI images and optimized RBFNN. ENG Transactions, 2021, 2( 1): 1– 7

[63] Zhang X, Wang J, Wang T, Jiang R, Xu J, Zhao L. Robust feature learning for adversarial defense via hierarchical feature alignment. Information Sciences, 2021, 560 : 256– 270

[64] Golilarz N A, Gao H, Addeh A, Pirasteh S. ORCA optimization algorithm: A new meta-heuristic tool for complex optimization problems. In: 2020 17th International Computer Conference on Wavelet Active Media Technology and Information Processing (ICCWAMTIP). Chengdu: UESTC press, 2020, 198– 204

[65] Addeh A, Hemmati A, Lari A, Munir H. A hybrid diagnostic system to detect COVID-19 Based on selected deep features of chest CT images and SVM. ENG Transactions, 2021, 2( 2): 1– 18

RIGHTS & PERMISSIONS

2022 Higher Education Press 2022.