def calculate_fragility(capacity_curves, idealised_capacity, damage_model, MC,
Sa_ratios):
allSa, allbTSa, allLR50, allbLR = [], [], [], []
no_capacity_curves = len(capacity_curves['Vb'])
g = 9.81
w = capacity_curves['weights']
Tav = capacity_curves['mean_period']
for icc in range(0, no_capacity_curves):
# Derive median Sa value (median of Sa) of capacity for each Limit State and corresponding overall dispersion std(log(Sa))
T = capacity_curves['periods'][icc]
Gamma = capacity_curves['gamma'][icc]
if len(damage_model['median']) < no_capacity_curves:
EDPlim = damage_model['median'][0]
bUthd = damage_model['dispersion'][0]
else:
EDPlim = damage_model['median'][icc]
bUthd = damage_model['dispersion'][icc]
SPO = idealised_capacity[icc]
[ISDvec, Sdvec] = sdof_utils.from_ISD_to_Sd(capacity_curves, icc)
RDvec = Sdvec * Gamma
[SaT50, bTSa] = simplified_bilinear(T, Gamma, EDPlim, ISDvec, RDvec,
SPO, bUthd, g, MC)
# Converting the Sa(T1) to Sa(Tav), the common IM
SaTlogmean_av, bTSa_av = np.log(SaT50) * Sa_ratios[icc], np.array(
bTSa) * Sa_ratios[icc]
allSa.append(SaTlogmean_av)
allbTSa.append(bTSa_av)
# Combine the fragility of each building in a single lognormal curve with
# mean = weighted_mean(means) and std = SRSS(weighted_std(means),weighted_mean(stds))
logmeans, logstddev = [], []
for i in range(0, len(EDPlim)):
SaLS = [ele[i] for ele in allSa]
StdSaLS = [ele[i] for ele in allbTSa]
#log_meanSa.append(np.average(SaLS,weights = w)) # weighted log-mean mean(log(Sa))
log_m = np.average(SaLS, weights=w)
#log_stSa.append(np.sqrt(np.sum(w*(np.power((SaLS-log_meanSa[i]),2)+np.power(StdSaLS,2))))) # weighted log-std (dispersion)
log_s = np.sqrt(
np.sum(w * (np.power((SaLS - log_m), 2) + np.power(StdSaLS, 2))))
logmeans.append(log_m)
logstddev.append(log_s)
fragility_model = {
'damage_states': None,
'logmean': None,
'logstddev': None,
'IMT': None
}
fragility_model['damage_states'] = damage_model['damage_states']
fragility_model['logmean'] = logmeans
fragility_model['logstddev'] = logstddev
fragility_model['IMT'] = 'Sa(' + str(Tav) + ')'
return fragility_model
def calculate_fragility(capacity_curves, idealised_capacity, damage_model, MC, Sa_ratios, corner_periods):
Tc, Td = corner_periods
allSa, allbTSa, allLR50, allbLR = [],[],[],[]
no_capacity_curves = len(capacity_curves['Vb'])
g = 9.81
w = capacity_curves['weights']
Tav = capacity_curves['mean_period']
for icc in range(0,no_capacity_curves):
# Derive median Sa value (median of Sa) of capacity for each Limit State and corresponding overall dispersion std(log(Sa))
T = capacity_curves['periods'][icc]
Gamma = capacity_curves['gamma'][icc]
if len(damage_model['median'])<no_capacity_curves:
EDPlim = damage_model['median'][0]
bUthd = damage_model['dispersion'][0]
else:
EDPlim = damage_model['median'][icc]
bUthd = damage_model['dispersion'][icc]
SPO = idealised_capacity[icc]
if len(SPO) == 3:
SPO.insert(2,SPO[1])
SPO.insert(3,SPO[1])
SPO.insert(-1,SPO[-1])
SPO.insert(-1,SPO[-1])
[ISDvec, Sdvec] = sdof_utils.from_ISD_to_Sd(capacity_curves,icc)
RDvec = Sdvec*Gamma
[mc,a,ac,r,mf] = get_spo2ida_parameters(SPO, T, Gamma) # Convert MDoF into SDoF
[SaT50,bTSa] = DFfragility(T, Gamma, EDPlim, ISDvec, RDvec, SPO, bUthd, mc, r, g, Tc, Td, MC)
# Converting the Sa(T1) to Sa(Tav), the common IM
SaTlogmean_av, bTSa_av = np.log(SaT50)*Sa_ratios[icc], np.array(bTSa)*Sa_ratios[icc]
allSa.append(SaTlogmean_av)
allbTSa.append(bTSa_av)
# Combine the fragility of each building in a single lognormal curve with
# mean = weighted_mean(means) and std = SRSS(weighted_std(means),weighted_mean(stds))
fragility_model = []
logmeans, logstddev = [],[]
for i in range(0,len(EDPlim)):
SaLS = [ele[i] for ele in allSa]
StdSaLS = [ele[i] for ele in allbTSa]
log_m = np.average(SaLS,weights = w)
log_s = np.sqrt(np.sum(w*(np.power((SaLS-log_m),2)+np.power(StdSaLS,2))))
logmeans.append(log_m)
logstddev.append(log_s)
fragility_model = {'damage_states': None, 'logmean': None, 'logstddev': None,
'IMT': None}
fragility_model['damage_states'] = damage_model['damage_states']
fragility_model['logmean'] = logmeans
fragility_model['logstddev'] = logstddev
fragility_model['IMT'] = 'Sa('+str(Tav)+')'
return fragility_model
def define_deformed_shape(capacity_curves, filename):
ISD_vectors, Sd_vectors = [],[]
for icc in range(len(capacity_curves['no_storeys'])):
[ISDvec, Sdvec] = sdof_utils.from_ISD_to_Sd(capacity_curves, icc)
ISD_vectors.append(ISDvec)
Sd_vectors.append(Sdvec)
sdof_utils.save_deformed_shape(ISD_vectors,Sd_vectors,filename)
return [ISD_vectors, Sd_vectors]
def calculate_fragility(capacity_curves, idealised_capacity, damage_model, MC,
Sa_ratios, plotflag):
pw = 1
filletstyle = 3
linew = 1
fontsize = 11
N = 10
allSa, allbTSa, allLR50, allbLR = [], [], [], []
no_capacity_curves = len(capacity_curves['Vb'])
g = 9.81
w = capacity_curves['weights']
Tav = capacity_curves['mean_period']
for icc in range(0, no_capacity_curves):
# Derive median Sa value (median of Sa) of capacity for each Limit State and corresponding overall dispersion std(log(Sa))
T = capacity_curves['periods'][icc]
Gamma = capacity_curves['gamma'][icc]
if len(damage_model['median']) < no_capacity_curves:
EDPlim = damage_model['median'][0]
bUthd = damage_model['dispersion'][0]
else:
EDPlim = damage_model['median'][icc]
bUthd = damage_model['dispersion'][icc]
SPO = idealised_capacity[icc]
if len(SPO) == 3:
SPO.insert(2, SPO[1])
SPO.insert(3, SPO[1])
SPO.insert(-1, SPO[-1])
SPO.insert(-1, SPO[-1])
[ISDvec, Sdvec] = sdof_utils.from_ISD_to_Sd(capacity_curves, icc)
RDvec = Sdvec * Gamma
[mc, a, ac, r,
mf] = get_spo2ida_parameters(SPO, T, Gamma) # Convert MDoF into SDoF
[idacm,
idacr] = spo2ida_allT(mc, a, ac, r, mf, T, pw, plotflag, filletstyle,
N, linew, fontsize) # apply SPO2IDA procedure
[SaT50, bTSa] = spo2ida_method(idacm, idacr, mf, T, Gamma, g, EDPlim,
ISDvec, RDvec, SPO, bUthd, MC)
# Converting the Sa(T1) to Sa(Tav), the common IM
SaTlogmean_av, bTSa_av = np.log(SaT50) * Sa_ratios[icc], np.array(
bTSa) * Sa_ratios[icc]
allSa.append(SaTlogmean_av)
allbTSa.append(bTSa_av)
# Combine the fragility of each building in a single lognormal curve with
# mean = weighted_mean(means) and std = SRSS(weighted_std(means),weighted_mean(stds))
logmeans, logstddev = [], []
for i in range(0, len(EDPlim)):
SaLS = [ele[i] for ele in allSa]
StdSaLS = [ele[i] for ele in allbTSa]
#log_meanSa.append(np.average(SaLS,weights = w)) # weighted log-mean mean(log(Sa))
log_m = np.average(SaLS, weights=w)
#log_stSa.append(np.sqrt(np.sum(w*(np.power((SaLS-log_meanSa[i]),2)+np.power(StdSaLS,2))))) # weighted log-std (dispersion)
log_s = np.sqrt(
np.sum(w * (np.power((SaLS - log_m), 2) + np.power(StdSaLS, 2))))
logmeans.append(log_m)
logstddev.append(log_s)
fragility_model = {
'damage_states': None,
'logmean': None,
'logstddev': None,
'IMT': None
}
fragility_model['damage_states'] = damage_model['damage_states']
fragility_model['logmean'] = logmeans
fragility_model['logstddev'] = logstddev
fragility_model['IMT'] = 'Sa(' + str(Tav) + ')'
return fragility_model
