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Prediction evaluation of Global damage index of RC dual system buildings by support vector regression method

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Abstract

Evaluation of Global damage index (GDI) of the reinforced concrete (RC) shear wall buildings under seismic conditions through nonlinear dynamic analyses is very important. Determination of GDI is done using park and Ang approach but the evaluation is very time consuming, therefore, the application of support vector regression (SVR) method can help in this regards. Hence, in this current study, an effort is made to predict the GDI of RC shear wall buildings using SVR Method. A total of 176 samples were collected from RC shear wall buildings through nonlinear dynamic analysis (NDA) using SAP2000V21 software, and is used to introduced the SVR model. IDR, roof displacement, joint rotation and hysteresis energy are considered as the input parameters and GDI as the output parameter in both the perpendicular direction of the RC shear wall building. Three kernel parameters have been employed in this study, i.e. Polynomial function (PF), Exponential and Gaussian radial basis function (ERBF, GRBF) for SVR modelling. ERBF performed best among all the considered kernels. Therefore, it has been concluded that, the ERBF performance for SVR model is more suitable in comparison to other two considered kernels for predicting the evaluation of RC frame shear wall buildings. Also, the SVR model performance has been compared with the multi-variable regression (MVR) analysis results. Additionally, a correlation matrix is also introduced to see the influence of the considered parameters on GDI.

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Abbreviations

GDI:

Global damage index

RC:

Reinforced concrete

SVR:

Support vector regression

NDA:

Nonlinear dynamic analysis

IDR:

Inter-story drift

PF:

Polynomial function

ERBF:

Exponential radial basis function

GRBF:

Gaussian radial basis function

MVR:

Multi-variable regression

DI:

Damage Index

UPBD:

Unified performance-based design

SCGM:

Spectrum compatible ground motions

EDPs:

Engineering demand parameters

SVM:

Support vector machines

ANN:

Artificial neural networks

LDI or SDI:

Local or storey wise damage index

DDBD:

Direct displacement-based design

ESDOF:

Equivalent single degree of freedom

MDOF:

Multi-degree of freedom

SSI:

Soil structure interaction

LS:

Life safety

PL:

Performance level

GMs:

Ground motions

N:

Number of the storey

SRM:

Minimization of structural risk

ERM:

Minimization of empirical risk

R:

Correlation coefficient

MAE:

Mean absolute error

RMSE:

Root mean square error

MAPE:

Mean absolute percentage error

\({\theta }_{d}\) :

Design drift

\({\theta }_{yw}\) :

Yield rotation of the wall

\({\theta }_{pw}\) :

Plastic rotation of the wall

\({\phi }_{yw}\) :

Yield curvature

\({h}_{\mathrm{inf}}\) :

Inflection height

\({\upvarepsilon }_{\mathrm{y}}\) :

Yield strain of rebar

\({L}_{w}\) :

The horizontal length of the wall

\({t}_{w}\) :

The thickness of the wall

\({V}_{\mathrm{Wall}}\) :

Shear carried by the walls

\({\tau }_{c}\) :

Permissible shear stress of concrete

\({h}_{b}\) :

Beam depth

\({\theta }_{pb}\) :

Allowable plastic rotation of the beam

\({\Delta }_{d}\) :

Design displacement

\({m}_{e}\) :

Effective mass

\({h}_{e}\) :

Equivalent height

\({m}_{i}\) :

Mass of i-th storey

\({\Delta }_{iyw}\) :

Yield displacements of the wall in i-th storey

\({\Delta }_{i}\) :

Profile displacement

\({\mu }_{w}\) :

Displacement ductility of the wall

\({\mu }_{f}\) :

Displacement ductility of the frame

\({\Delta }_{\mathrm{he}, y}\) :

Yield displacement of the wall

\({M}_{w}\) :

Wall moment

\({\xi }_{w}\) :

Wall damping moment

\({M}_{\mathrm{ot},f}\) :

Frame overturning moment

\({\xi }_{f}\) :

Frame damping

\({T}_{e,\mathrm{trial}}\) :

Trial effective time period

\(r\) :

Post-yield stiffness ratio

\(\eta \) :

Reduction factor corresponding to the damping

\({K}_{e}\) :

Effective stiffness

\({V}_{b}\) :

Base shear

\(\mathrm{DL},\mathrm{LL},{F}_{x},{F}_{y}\) :

Dead load, live load, seismic load in the x-direction and y-direction

\({\delta }_{M}\) :

Optimum deformation under earthquake loading

\({\delta }_{u}\) :

Optimum deformation monotonic loading

dE:

Hysteresis energy

\({Q}_{y}\) :

Yield strength

β :

Non-negative parameter

\({E}_{\mathrm{storey},i}\) :

Hysteretic dissipated energy of i-th storey

\({E}_{i}\) :

Hysteretic dissipation energy of \(i-\mathrm{th}\) member

Lε :

Function ε-insensitive loss

W 0 :

Weight peak value

b 0 :

Bias peak value

C :

Penalty function

d :

Kernel parameters

σ :

Sigma parameter

ε :

Loss function parameter

\({\xi }_{i}^{*}, {\xi }_{i}\) :

Slack variables

R :

Correlation coefficient

MAE:

Mean absolute error

RMSE:

Root mean square error

MAPE:

Mean absolute percentage error

O i :

Calculated value

Pi :

Predicted values of GDI

N :

Total samples

\(\overline{O }\) and \(\overline{P }\) :

Mean values of Oi and Pi

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Authors and Affiliations

  1. Department of Civil Engineering, National Institute of Technology Silchar, Silchar, India

    Durga Mibang & Satyabrata Choudhury

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  1. Durga Mibang
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  2. Satyabrata Choudhury
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Correspondence to Durga Mibang.

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Mibang, D., Choudhury, S. Prediction evaluation of Global damage index of RC dual system buildings by support vector regression method. Innov. Infrastruct. Solut. 7, 169 (2022). https://doi.org/10.1007/s41062-022-00772-5

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