XGBoost - $\rho-\mu-T$

Next-generation non-linear and collapse prediction models for short to long period systems via machine learning methods

The machine learning approach: Exterme Gradient Boosting (XGBoost)

Makes predictions for a strength ratio - ductility - period relationships

Key arguments:

• $R$ - strength ratio based on spectral acceleration
• $\rho$ - strength ratio based on average spectral acceleration
• $\mu$ - ductility
• $T$ - period

$$ R=\frac{Sa(T)}{Sa_y} $$

$$ \rho_2=\frac{Sa_{avg,2}(T)}{Sa_y} $$

$$ \rho_3=\frac{Sa_{avg,3}(T)}{Sa_y} $$

where

• $Sa(T)$ stands for spectral acceleration at fundamental period
• $Sa_y$ stands for spectral acceleration at yield
• $Sa_{avg,2}(T)$ stands for average spectral acceleration computed at periods $∈ [0.2T:2T]$
• $Sa_{avg,3}(T)$ stands for average spectral acceleration computed at periods $∈ [0.2T:3T]$

Installation

pip install xgb-rhomut

Example prediction

Example 1: Dynamic strength ratio prediction of non-collapse scenarios at a dynamic ductility level of 3.0:

import xgbrhomut
model = xgbrhomut.XGBPredict(im_type="sa_avg", collapse=False)
prediction = model.make_prediction(
  period=1, 
  damping=0.05, 
  hardening_ratio=0.02, 
  ductility=4, 
  dynamic_ductility=3.0
)

Example 2: Dynamic ductility prediction given a strength ratio of 3.0 (since im_type is "sa_avg", and collapse is False, \rho_2 is being estimated):

import xgbrhomut
model = xgbrhomut.XGBPredict(im_type="sa_avg", collapse=False)
prediction = model.make_prediction(
  period=1, 
  damping=0.05, 
  hardening_ratio=0.02, 
  ductility=4, 
  strength_ratio=3.0
)

prediction:

{
  "median": float,
  "dispersion": float
}

Other methods

xgbrhomut.r_mu_t.ec8.strength_ratio(mu=3, T=1, Tc=0.5)

Limitations

Limitations in terms of input parameters are:

• $T$ ∈ [0.01, 3.0] seconds
• $\mu$ ∈ [2.0, 8.0]
• $\xi$ ∈ [2.0, 20.0] %
• $a_h$ ∈ [2.0, 7.0] %
• $a_c$ ∈ [-30.0, -100.0] %
• $R$ ∈ [0.5, 10.0]

where

• $T$ stands for period
• $\mu$ stands for ductility
• $\xi$ stands for damping
• $a_h$ stands for hardening ratio
• $a_c$ stands for softening ratio (necessary to compute fracturing ductility, where collapse is assumed)

Predictions made using the non-linear analysis resutls of 7292 unique SDOF systems amounting in total to 26,000,000 observations (collapse + non-collapse).

References

• Shahnazaryan D., O'Reilly J.G., 2023, Next-generation non-linear and collapse prediction models for short to long period systems via machine learning methods, Under Review