Document Type : Research Note

**Authors**

Department of Civil Engineering, National Institute of Technology Rourkela, Odisha, India-769008

**Abstract**

Proper assessment of wind load enables durable design of structures under varying wind load conditions. The accurate prediction of pressure coefficient on any irregular plan shaped buildings is essential for the assessment of wind loads and the structural design. The main objective of this study is to present an equation in the line of Multivariate Adaptive Regression Spline (MARS) approach using experimental data of surface mean pressure coefficient. This developed equation can be used satisfactorily for the prediction of pressure coefficient values accurately on the surfaces of C-shaped buildings. An extensive experimentation was carried out to obtain coefficient of pressure over the surfaces of C-shaped models under varying sizes, corner curvature and angle of incidence in a sub-sonic wind tunnel. The predicted values of pressure coefficient of different C-shaped buildings using developed model are compared with equations developed by Swami and Chandra’s (S&C) and Muehleisen and Patrizi’s (M&P). The comparison indicates that the proposed MARS model predicts pressure coefficient values more accurately than those by S&C and M&P models on frontal as well as side surfaces. Further, the model is used to validate with the actual building, Tokyo Polytechnic University (TPU) data to show the applicability of the proposed equation.

**Keywords**

References:

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7. Zhou, Y. and Stathopoulos, T. "A new technique for the numerical simulation of wind flow around buildings", Journal of Wind Engineering and Industrial Aerodynamics, 72, pp. 137-147 (1997).

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10. Lou, W., Jin, H., Chen, Y., Cao, L., and Yao, J. "Wind tunnel test study on wind load characteristics for double-skin facade building with rectangular shape", Journal of Building Structure, 26(1), pp. 65-70 (2005).

11. Lu, S., Chen, S.F., Li, J.H., and Jiao, Y.F. "Numerical study on the effects of curved annex on the wind loads on a spherical tall building", Engineering Mechanics, 2, p. 021 (2007).

12. Chakraborty, S., Dalui, S.K., and Ahuja, A.K. "Experimental and numerical study of surface pressure on '+' plan shape tall building", International Journal of Construction Materials and Structures, 8(3), pp. 251- 262 (2013).

13. Gomes, M.G.R., Rodrigues, A.M., and Mendes, P. "Experimental and numerical study of wind pressures on irregular-plan shapes", Journal of Wind Engineering and Industrial Aerodynamics, 93(10), pp. 741-756 (2005).

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17. Chakraborty, S., Dalui, S.K., and Ahuja, A.K. "Wind load on irregular plan shaped tall building-a case study", Wind Struct., 19(1), pp. 59-73 (2014).

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19. Bhattacharyya, B. and Dalui, S.K. "Investigation of mean wind pressures on 'E' plan shaped tall building", Wind and Structures, 26(2), pp. 99-114 (2018).

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34. Costola, D., Blocken, B., Ohba, M., and Hensen, J.L.M. "Uncertainty in air flow rate calculations due to the use of surface-averaged pressure coefficients", Energy and Buildings, 42(6), pp. 881-888 (2010).

35. Muehleisen, R.T. and Patrizi, S. "A new parametric equation for the wind pressure coefficient for low-rise buildings", Energy and Buildings, 57, pp. 245-249 (2013).

36. Deo, R.C. and Sahin, M. "Application of the extreme learning machine algorithm for the prediction of monthly effective drought index in eastern Australia", Atmospheric Research, 153, pp. 512-525 (2015).

37. Samadi, M., Jabbari, E., Azamathulla, H.M., and Mojallal, M. "Estimation of scour depth below free overfall spillways using multivariate adaptive regression splines and artificial neural networks", Engineering Applications of Computational Fluid Mechanics, 9(1), pp. 291-300 (2015).

38. Suman, S., Mahamaya, M., and Das, S.K. "Prediction of maximum dry density and unconfined compressive strength of cement stabilised soil using artificial intelligence techniques", International Journal of Geosynthetics and Ground Engineering, 2(2), p. 11 (2016).

39. Mehdizadeh, S., Behmanesh, J., and Khalili, K. "Application of gene expression programming to predict daily dew point temperature", Applied Thermal Engineering, 112, pp. 1097-1107 (2017).

40. Milukow, H.A., Binns, A.D., Adamowski, J., Bonakdari, H., and Gharabaghi, B. "Estimation of the darcy-weisbach friction factor for ungauged streams using gene expression programming and extreme learning machines", Journal of Hydrology, 568, pp. 311-321 (2018).

41. Mohanta, A., Patra, K.C., and Sahoo, B. "Anticipate Manning's coefficient in meandering compound channels", Hydrology, 5(3), p. 47 (2018).

42. Najafzadeh, M., Rezaie-Balf, M., and Tafarojnoruz, A. "Prediction of riprap stone size under overtopping flow using data-driven models", International Journal of River Basin Management, 16(4), pp. 1-8 (2018).

43. Shende, S. and Chau, K.W. "Forecasting safe distance of a umping well for effective riverbank filtration", Journal of Hazardous, Toxic, and Radioactive Waste, 23(2), p. 04018040 (2018).

44. Varvani, J. and Khaleghi, M.R. "A performance evaluation of neuro-fuzzy and regression methods in estimation of sediment load of selective rivers", Acta Geophysica, 67(1), pp. 205-214 (2018). https://doi.org/10.1007/s11600-018-0228-9.

45. Sheikh Khozani, Z., Bonakdari, H., and Zaji, A.H. "Mean bed shear stress estimation in a rough rectangular channel using a hybrid genetic algorithm based on an artificial neural network and genetic programming", Scientia Iranica, 25(1), pp. 152-161 (2018).

46. Bui, D.T., Hoang, N.D., and Samui, P. "Spatial pattern analysis and prediction of forest fire using new machine learning approach of multivariate adaptive regression splines and differential flower pollination optimization: a case study", at Lao Cai province (Viet Nam). Journal of Environmental Management, 237, pp. 476-487 (2019).

47. Zaji, A.H., Bonakdari, H., and Shamshirband, S. "Standard equations for predicting the discharge coefficient of a modified high-performance side weir", Scientia Iranica, 25(3), pp. 1057-1069 (2018).

48. Samui, P., Das, S., and Kim, D. "Uplift capacity of suction caisson in clay using multivariate adaptive regression spline", Ocean Engineering, 38(17-18), pp. 2123-2127 (2011).

49. Samui, P. and Kurup, P. "Multivariate adaptive regression spline (MARS) and least squares support vector machine (LSSVM) for OCR prediction", Soft Computing, 16(8), pp. 1347-1351 (2012).

50. Samui, P. "Multivariate adaptive regression spline (Mars) for prediction of elastic modulus of jointed rock mass", Geotechnical and Geological Engineering, 31(1), pp. 249-253 (2013).

51. Cheng, M.Y. and Cao, M.T. "Accurately predicting building energy performance using evolutionary multivariate adaptive regression splines", Applied Soft Computing, 22, pp. 178-188 (2014).

52. Koc, E.K. and Bozdogan, H. "Model selection in multivariate adaptive regression splines (MARS) using information complexity as the fitness function", Machine Learning, 101(1-3), pp. 35-58 (2015).

53. Zhang, W. and Goh, A.T. "Multivariate adaptive regression splines and neural network models for prediction of pile drivability", Geoscience Frontiers, 7(1), pp. 45-52 (2016).

54. Mukhopadhyay, T. "A multivariate adaptive regression splines based damage identification methodology for web core composite bridges including the effect of noise", Journal of Sandwich Structures & Materials, 20(7), pp. 885-903 (2017). https://doi.org/10.1177/1099636216682533.

55. Bhattacharya, S., Murakonda, P., and Das, S. "Prediction of uplift capacity of suction caisson in clay using functional network and multivariate adaptive regression spline", Scientia Iranica, 25(2), pp. 517-531 (2018).

56. Mirabbasi, R., Kisi, O., Sanikhani, H., and Meshram, S.G. "Monthly long-term rainfall estimation in Central India using M5Tree, MARS, LSSVR, ANN and GEP models", Neural Computing and Applications, 31(10), pp. 6843-6862 (2019). https://doi.org/10.1007/s00521-018-3519-9.

57. Goh, A.T.C., Zhang, W., Zhang, Y., Xiao, Y., and Xiang, Y. "Determination of earth pressure balance tunnel-related maximum surface settlement: a multivariate adaptive regression splines approach", Bulletin of Engineering Geology and the Environment, 77(2), pp. 489-500 (2018).

58. Zhang, W., Zhang, R., and Goh, A.T. "Multivariate adaptive regression splines approach to estimate lateral wall deflection profiles caused by braced excavations in clays", Geotechnical and Geological Engineering, 36(2), pp. 1349-1363 (2018).

59. Friedman, J.H. "Multivariate adaptive regression splines", Annals of Statistics, 19(1), pp. 1-67 1991). https://doi.org/10.1214/aos/1176347963.

60. Friedman, J.H. and Roosen, C.B., An Introduction to Multivariate Adaptive Regression Splines, Sage Publications Sage CA: Thousand Oaks, CA (1995).

61. Leathwick, J.R., Rowe, D., Richardson, J., Elith, J., and Hastie, T. "Using multivariate adaptive regression splines to predict the distributions of New Zealand's freshwater diadromous fish", Freshwater Biology, 50(12), pp. 2034-2052 (2005).

62. Craven, P. andWahba, G. "Smoothing noisy data with spline functions", Numerische Mathematik, 31(4), pp. 377-403 (1978).

63. Barati, R., Rahimi, S., and Akbari, G.H. "Analysis of dynamic wave model for flood routing in natural rivers", Water Science and Engineering, 5(3), pp. 243- 258 (2012).

64. Barati, R. "Application of excel solver for parameter estimation of the nonlinear Muskingum models", KSCE Journal of Civil Engineering, 17(5), pp. 1139- 1148 (2013).

65. Akbari, G.H. and Barati, R. "Comprehensive analysis of flooding in unmanaged catchments", Proceedings of the Institution of Civil Engineers-Water Management, pp. 229-238 (2012).

66. Gandomi, A.H., Yun, G.J., and Alavi, A.H. "An evolutionary approach for modelling of shear strength of RC deep beams", Materials and Structures, 46(12), pp. 2109-2119 (2013).

67. Ebtehaj, I., Bonakdari, H., Zaji, A.H., Azimi, H., and Khoshbin, F. "GMDH-type neural network approach for modeling the discharge coefficient of rectangular sharp-crested side weirs", Engineering Science and Technology, an International Journal, 18(4), pp. 746- 757 (2015).

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2. Macdonald, A.J., Wind Loading on Buildings, Halsted Press (1975).

3. Meroney, R.N. "Wind-tunnel modelling of the flow about bluff bodies", Journal of Wind Engineering and Industrial Aerodynamics, 29(1-3), pp. 203-223 (1988).

4. Cook, N.J. "The designer's guide to wind loading of building structures", Building Research Establishment Report, Part 2: Static Structures, Butterworths, London (1990).

5. Suresh Kumar, K., Irwin, P.A., and Davies, A. "Design of tall building for wind: wind tunnel vs. codes/standards", Third National Conference on Wind Engineering, Calcutta, India, pp. 318-325 (2006).

6. Stathopoulos, T. and Zhou, Y.S. "Numerical simulation of wind-induced pressures on buildings of various geometries", Computational Wind Engineering, 1, Elsevier, pp. 419-430 (1993).

7. Zhou, Y. and Stathopoulos, T. "A new technique for the numerical simulation of wind flow around buildings", Journal of Wind Engineering and Industrial Aerodynamics, 72, pp. 137-147 (1997).

8. Ahmad, S. and Kumar, K. "Interference effects on wind loads on low-rise hip roof buildings", Engineering Structures, 23(12), pp. 1577-1589 (2001).

9. Ho, T.C.E., Surry, D., and Davenport, A.G. "The variability of low building wind loads due to surrounding obstructions", Journal of Wind Engineering and Industrial Aerodynamics, 36, pp. 161-170 (1990).

10. Lou, W., Jin, H., Chen, Y., Cao, L., and Yao, J. "Wind tunnel test study on wind load characteristics for double-skin facade building with rectangular shape", Journal of Building Structure, 26(1), pp. 65-70 (2005).

11. Lu, S., Chen, S.F., Li, J.H., and Jiao, Y.F. "Numerical study on the effects of curved annex on the wind loads on a spherical tall building", Engineering Mechanics, 2, p. 021 (2007).

12. Chakraborty, S., Dalui, S.K., and Ahuja, A.K. "Experimental and numerical study of surface pressure on '+' plan shape tall building", International Journal of Construction Materials and Structures, 8(3), pp. 251- 262 (2013).

13. Gomes, M.G.R., Rodrigues, A.M., and Mendes, P. "Experimental and numerical study of wind pressures on irregular-plan shapes", Journal of Wind Engineering and Industrial Aerodynamics, 93(10), pp. 741-756 (2005).

14. Amin, J.A. and Ahuja, A.K. "Experimental study of wind pressures on irregular plan shape buildings", BBAA VI International Colloquium on: Bluff Bodies Aerodynamics and Applications, Milano, Italy, pp. 20- 24 (2008).

15. Amin, J.A. and Ahuja, A.K. "Experimental study of wind-induced pressures on buildings of various geometries", International Journal of Engineering, Science and Technology, 3(5), pp. 1-19 (2011). https://www.ajol.info/index.php/ijest/issue/view/ 8314.

16. Kim, Y.C. and Kanda, J. "Wind pressures on tapered and set-back tall buildings", Journal of Fluids and Structures, 39, pp. 306-321 (2013).

17. Chakraborty, S., Dalui, S.K., and Ahuja, A.K. "Wind load on irregular plan shaped tall building-a case study", Wind Struct., 19(1), pp. 59-73 (2014).

18. Bhattacharyya, B., Dalui, S.K., and Ahuja, A.K. "Wind induced pressure on E plan shaped tall buildings", Jordon Journal of Civil Engineering, 8(2), pp. 120-134 (2014).

19. Bhattacharyya, B. and Dalui, S.K. "Investigation of mean wind pressures on 'E' plan shaped tall building", Wind and Structures, 26(2), pp. 99-114 (2018).

20. Yi, J. and Li, Q.S. "Wind tunnel and full-scale study of wind effects on a super-tall building", Journal of Fluid Structure, 58, pp. 236-253 (2015).

21. Li, Y. and Li, Q. "Across-wind dynamic loads on L-shaped tall buildings", Wind Structure, 23(5), pp. 385-403 (2016).

22. Mallick, M., Mohanta, A., Kumar, A., and Raj, V. "Modelling of wind pressure coefficients on Cshaped building models", Modelling and Simulation in Engineering, 2018, Article ID 6524945, 13 pages (2018). https://doi.org/10.1155/2018/6524945.

23. Akins, R.E. "Wind pressures on buildings", CER; 76/77-15 (1976).

24. Walton, G.N. "Air flow and multiroom thermal analysis", ASHRAE Transactions, 88, pp. 78-91 (1982).

25. Walker, I.S. and Wilson, D.J. "Evaluating models for superposition of wind and stack effect in air infiltration", Building and Environment, 28(2), pp. 201-210 (1993).

26. Ginger, J.D. and Letchford, C.W. "Net pressures on a low-rise full-scale building", Journal of Wind Engineering and Industrial Aerodynamics, 83(1-3), pp. 239-250 (1999).

27. Ohkuma, T., Marukawa, H., Niihori, Y., and Kato, N. "Full-scale measurement of wind pressures and response accelerations of a high-rise building", Journal of Wind Engineering and Industrial Aerodynamics, 38(2-3), pp. 185-196 (1991).

28. Swami, M.V. and Chandra, S. "Procedures for calculating natural ventilation air flow rates in buildings", ASHRAE Final Report FSEC-CR-163-86, ASHRAE Research Project (1987).

29. Swami, M.V. and Chandra, S. "Correlations for pressure distribution on buildings and calculation of natural-ventilation air

ow", ASHRAE Transactions, 94(3112), pp. 243-266 (1988).

30. Grosso, M. "Wind pressure distribution around buildings: a parametrical model", Energy and Buildings, 18(2), pp. 101-131 (1992).

31. Crawley, D.B., Lawrie, L.K., Winkelmann, F.C., Buhl, W.F., Huang, Y.J., Pedersen, C.O., Strand, R.K., Liesen, R.J., Fisher, D.E., and Witte, M.J. "EnergyPlus: creating a new-generation building energy simulation program", Energy and Buildings, 33(4), pp. 319-331 (2001).

32. Cook, N., Designers' Guide to EN 1991-1-4 Eurocode 1: Actions on Structures, general actions part 1-4. Wind actions, Thomas Telford Publishing (2007).

33. Costola, D., Blocken, B., and Hensen, J.L.M. "Overview of pressure coefficient data in building energy simulation and air flow network programs", Building and Environment, 44(10), pp. 2027-2036 (2009).

34. Costola, D., Blocken, B., Ohba, M., and Hensen, J.L.M. "Uncertainty in air flow rate calculations due to the use of surface-averaged pressure coefficients", Energy and Buildings, 42(6), pp. 881-888 (2010).

35. Muehleisen, R.T. and Patrizi, S. "A new parametric equation for the wind pressure coefficient for low-rise buildings", Energy and Buildings, 57, pp. 245-249 (2013).

36. Deo, R.C. and Sahin, M. "Application of the extreme learning machine algorithm for the prediction of monthly effective drought index in eastern Australia", Atmospheric Research, 153, pp. 512-525 (2015).

37. Samadi, M., Jabbari, E., Azamathulla, H.M., and Mojallal, M. "Estimation of scour depth below free overfall spillways using multivariate adaptive regression splines and artificial neural networks", Engineering Applications of Computational Fluid Mechanics, 9(1), pp. 291-300 (2015).

38. Suman, S., Mahamaya, M., and Das, S.K. "Prediction of maximum dry density and unconfined compressive strength of cement stabilised soil using artificial intelligence techniques", International Journal of Geosynthetics and Ground Engineering, 2(2), p. 11 (2016).

39. Mehdizadeh, S., Behmanesh, J., and Khalili, K. "Application of gene expression programming to predict daily dew point temperature", Applied Thermal Engineering, 112, pp. 1097-1107 (2017).

40. Milukow, H.A., Binns, A.D., Adamowski, J., Bonakdari, H., and Gharabaghi, B. "Estimation of the darcy-weisbach friction factor for ungauged streams using gene expression programming and extreme learning machines", Journal of Hydrology, 568, pp. 311-321 (2018).

41. Mohanta, A., Patra, K.C., and Sahoo, B. "Anticipate Manning's coefficient in meandering compound channels", Hydrology, 5(3), p. 47 (2018).

42. Najafzadeh, M., Rezaie-Balf, M., and Tafarojnoruz, A. "Prediction of riprap stone size under overtopping flow using data-driven models", International Journal of River Basin Management, 16(4), pp. 1-8 (2018).

43. Shende, S. and Chau, K.W. "Forecasting safe distance of a umping well for effective riverbank filtration", Journal of Hazardous, Toxic, and Radioactive Waste, 23(2), p. 04018040 (2018).

44. Varvani, J. and Khaleghi, M.R. "A performance evaluation of neuro-fuzzy and regression methods in estimation of sediment load of selective rivers", Acta Geophysica, 67(1), pp. 205-214 (2018). https://doi.org/10.1007/s11600-018-0228-9.

45. Sheikh Khozani, Z., Bonakdari, H., and Zaji, A.H. "Mean bed shear stress estimation in a rough rectangular channel using a hybrid genetic algorithm based on an artificial neural network and genetic programming", Scientia Iranica, 25(1), pp. 152-161 (2018).

46. Bui, D.T., Hoang, N.D., and Samui, P. "Spatial pattern analysis and prediction of forest fire using new machine learning approach of multivariate adaptive regression splines and differential flower pollination optimization: a case study", at Lao Cai province (Viet Nam). Journal of Environmental Management, 237, pp. 476-487 (2019).

47. Zaji, A.H., Bonakdari, H., and Shamshirband, S. "Standard equations for predicting the discharge coefficient of a modified high-performance side weir", Scientia Iranica, 25(3), pp. 1057-1069 (2018).

48. Samui, P., Das, S., and Kim, D. "Uplift capacity of suction caisson in clay using multivariate adaptive regression spline", Ocean Engineering, 38(17-18), pp. 2123-2127 (2011).

49. Samui, P. and Kurup, P. "Multivariate adaptive regression spline (MARS) and least squares support vector machine (LSSVM) for OCR prediction", Soft Computing, 16(8), pp. 1347-1351 (2012).

50. Samui, P. "Multivariate adaptive regression spline (Mars) for prediction of elastic modulus of jointed rock mass", Geotechnical and Geological Engineering, 31(1), pp. 249-253 (2013).

51. Cheng, M.Y. and Cao, M.T. "Accurately predicting building energy performance using evolutionary multivariate adaptive regression splines", Applied Soft Computing, 22, pp. 178-188 (2014).

52. Koc, E.K. and Bozdogan, H. "Model selection in multivariate adaptive regression splines (MARS) using information complexity as the fitness function", Machine Learning, 101(1-3), pp. 35-58 (2015).

53. Zhang, W. and Goh, A.T. "Multivariate adaptive regression splines and neural network models for prediction of pile drivability", Geoscience Frontiers, 7(1), pp. 45-52 (2016).

54. Mukhopadhyay, T. "A multivariate adaptive regression splines based damage identification methodology for web core composite bridges including the effect of noise", Journal of Sandwich Structures & Materials, 20(7), pp. 885-903 (2017). https://doi.org/10.1177/1099636216682533.

55. Bhattacharya, S., Murakonda, P., and Das, S. "Prediction of uplift capacity of suction caisson in clay using functional network and multivariate adaptive regression spline", Scientia Iranica, 25(2), pp. 517-531 (2018).

56. Mirabbasi, R., Kisi, O., Sanikhani, H., and Meshram, S.G. "Monthly long-term rainfall estimation in Central India using M5Tree, MARS, LSSVR, ANN and GEP models", Neural Computing and Applications, 31(10), pp. 6843-6862 (2019). https://doi.org/10.1007/s00521-018-3519-9.

57. Goh, A.T.C., Zhang, W., Zhang, Y., Xiao, Y., and Xiang, Y. "Determination of earth pressure balance tunnel-related maximum surface settlement: a multivariate adaptive regression splines approach", Bulletin of Engineering Geology and the Environment, 77(2), pp. 489-500 (2018).

58. Zhang, W., Zhang, R., and Goh, A.T. "Multivariate adaptive regression splines approach to estimate lateral wall deflection profiles caused by braced excavations in clays", Geotechnical and Geological Engineering, 36(2), pp. 1349-1363 (2018).

59. Friedman, J.H. "Multivariate adaptive regression splines", Annals of Statistics, 19(1), pp. 1-67 1991). https://doi.org/10.1214/aos/1176347963.

60. Friedman, J.H. and Roosen, C.B., An Introduction to Multivariate Adaptive Regression Splines, Sage Publications Sage CA: Thousand Oaks, CA (1995).

61. Leathwick, J.R., Rowe, D., Richardson, J., Elith, J., and Hastie, T. "Using multivariate adaptive regression splines to predict the distributions of New Zealand's freshwater diadromous fish", Freshwater Biology, 50(12), pp. 2034-2052 (2005).

62. Craven, P. andWahba, G. "Smoothing noisy data with spline functions", Numerische Mathematik, 31(4), pp. 377-403 (1978).

63. Barati, R., Rahimi, S., and Akbari, G.H. "Analysis of dynamic wave model for flood routing in natural rivers", Water Science and Engineering, 5(3), pp. 243- 258 (2012).

64. Barati, R. "Application of excel solver for parameter estimation of the nonlinear Muskingum models", KSCE Journal of Civil Engineering, 17(5), pp. 1139- 1148 (2013).

65. Akbari, G.H. and Barati, R. "Comprehensive analysis of flooding in unmanaged catchments", Proceedings of the Institution of Civil Engineers-Water Management, pp. 229-238 (2012).

66. Gandomi, A.H., Yun, G.J., and Alavi, A.H. "An evolutionary approach for modelling of shear strength of RC deep beams", Materials and Structures, 46(12), pp. 2109-2119 (2013).

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Transactions on Mechanical Engineering (B)

November and December 2020Pages 2967-2984