Brussels Mat. Step 1.a Material Densities¶
The following code describes the process for the computation of material densities by m2 of floor space. These material densities are used for the estimation of total material demands for the building stock.
The following file describes the definition of building types for the residential rector for Brussels.
In [1]:
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
In [2]:
data = pd.DataFrame(
[np.nan, 0.03, 2.18, 0.02, np.nan, 0.02],
index=['Textiles', 'Metal', 'Minerals', 'Plastic', 'Chemicals', 'Wood'])
data.columns = [2013]
data.index.name = 'Material type'
In [3]:
data_years = pd.DataFrame(index=['Textiles', 'Metal', 'Minerals', 'Plastic', 'Chemicals', 'Wood'])
In [4]:
end_year = 2016
str_year = 1945
step = 5
diff = int((end_year - str_year -1) / step + 1)
rate = np.asarray([0, -0.0006, 0.015, -0.0006, 0, 0.001])
In [5]:
for e, year in enumerate(range(str_year, end_year, step)):
e += 1
a = (diff - e) / diff
data_years.loc[:, year] = data.loc[:, 2013] + a * rate
In [6]:
data_years
Out[6]:
| 1945 | 1950 | 1955 | 1960 | 1965 | 1970 | 1975 | 1980 | 1985 | 1990 | 1995 | 2000 | 2005 | 2010 | 2015 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Textiles | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
| Metal | 0.029440 | 0.029480 | 0.02952 | 0.029560 | 0.029600 | 0.02964 | 0.029680 | 0.029720 | 0.02976 | 0.029800 | 0.029840 | 0.02988 | 0.029920 | 0.029960 | 0.03 |
| Minerals | 2.194000 | 2.193000 | 2.19200 | 2.191000 | 2.190000 | 2.18900 | 2.188000 | 2.187000 | 2.18600 | 2.185000 | 2.184000 | 2.18300 | 2.182000 | 2.181000 | 2.18 |
| Plastic | 0.019440 | 0.019480 | 0.01952 | 0.019560 | 0.019600 | 0.01964 | 0.019680 | 0.019720 | 0.01976 | 0.019800 | 0.019840 | 0.01988 | 0.019920 | 0.019960 | 0.02 |
| Chemicals | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
| Wood | 0.020933 | 0.020867 | 0.02080 | 0.020733 | 0.020667 | 0.02060 | 0.020533 | 0.020467 | 0.02040 | 0.020333 | 0.020267 | 0.02020 | 0.020133 | 0.020067 | 0.02 |
In [7]:
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(15,5))
data_years.div(data_years.loc[:, 1945], axis=0).T.plot(ax=ax1)
ax1.set_ylabel('relative change in material density $[\%]$')
ax1.set_title('Material densities over time (benchmark year: 2015)')
data_years.sum().plot(ax=ax2)
ax2.set_ylabel('Material density $[t/m^2]$')
ax2.set_title('Total material density (benchmark year: 2015)');
In [8]:
typ = [
"Detached",
"Semi-detached",
"Terraced",
"Apartment - enclosed",
"Apartment - exposed"]
In [9]:
def formatnumbers(x):
x = str(x).replace(',', '.')
x = float(x)
return x
In [10]:
tabula = pd.read_excel('TABULA.xlsx', sheet_name='TABULA-2',
usecols=[0,2,3,4,5,6,7,8,9], index_col=[2,0,1],
skip_footer = 148,
converters = {
1: formatnumbers,
2: formatnumbers,
3: formatnumbers,
4: formatnumbers,
5: formatnumbers,
}
)
In [11]:
tabula.index.names = ['Construction Year', 'Construction Type', 'Size']
In [12]:
tabula.head()
Out[12]:
| Number of housing units | Floor surface area per housing unit (m2) | Protected volume (m³) | Total building envelope area (m²) | Roof (m²) | Exterior wall (m2) | |||
|---|---|---|---|---|---|---|---|---|
| Construction Year | Construction Type | Size | ||||||
| pre '46 | SFH | Detached | 1 | 279.0 | 766.0 | 599.2 | 158.4 | 228.9 |
| Semi-detached | 1 | 237.0 | 651.8 | 447.1 | 119.9 | 158.2 | ||
| Terraced | 1 | 225.9 | 621.3 | 323.0 | 90.0 | 92.0 | ||
| MFH | Small | 6 | 75.0 | 1716.0 | 558.8 | 165.0 | 114.7 | |
| Medium | 12 | 96.0 | 5166.6 | 1112.7 | 215.0 | 292.5 |
In [13]:
tabula.to_csv('data/tabula.csv')
In [14]:
facade = tabula.iloc[:, 5] / tabula.iloc[:, 0].mul(tabula.iloc[:, 1])
facade = facade.unstack(level=[1,2])
facade.index = [1970, 1990, 2005, 2016, 1946]
facade = facade.sort_index()
In [15]:
a = facade.plot(figsize=(15,5))
a.set_ylabel("Facade Floor-space ratio")
a.set_title("Facade floor-space ration for building typologies");
In [16]:
facade_plot = facade.loc[:, (['SFH '], ['Detached'])]
In [17]:
def make_trend(facade_plot, years_to_fit = [i for i in data_years.columns]):
if isinstance(facade_plot, pd.Series):
FFR = facade_plot
else:
FFR = np.asanyarray(facade_plot.iloc[:, 0])
z = np.polyfit(y=FFR, x=facade_plot.index, deg=1)
p = np.poly1d(z)
return p(years_to_fit)
In [18]:
trend_p = make_trend(facade_plot)
In [19]:
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(15,5))
facade_plot.plot(ax=ax1)
ax1.plot([i for i in data_years.columns], trend_p, label="trend line")
ax1.legend()
ax1.set_ylabel("Facade Floor-space ratio")
ax1.set_title('Facade foor-space ratio (SFH, Detached)')
#ax1.legend('off')
data_years.sum().plot(ax=ax2)
ax2.set_ylabel('Material density $[t/m^2]$')
ax2.set_title('Total material density (benchmark year: 2015)');
In [20]:
def _plot_fig(trend_md, ratio, years_to_fit = []):
fig, ax1 = plt.subplots(1, 1, figsize=(7,5))
if len(years_to_fit) >= 1:
ax1.plot(years_to_fit, trend_md)
ax1.set_xlabel('Construction year')
ax1.set_ylabel('Material density (MD) $[t/m^2]$')
ax1.set_title('Relationship between construction year and MD')
else:
ax1.plot(trend_md, ratio)
ax1.set_xlabel('Material density (MD) $[t/m^2]$')
ax1.set_title('Relationship between FFR and MD')
ax1.set_ylabel('Facade Floor-space ratio (FFR)')
In [21]:
z = np.polyfit(x=make_trend(facade.iloc[:, 0]), y=data_years.sum(), deg=1)
p = np.poly1d(z)
def get_MD(facade_plot, ratio = False, plot_fig = False, years_to_fit = []):
if len(years_to_fit) >= 1:
ratio = make_trend(facade_plot, years_to_fit = typ_years)
trend_md = p(ratio)
if plot_fig:
_plot_fig(trend_md, ratio, years_to_fit = years_to_fit)
return trend_md
In [22]:
typ_years = [1900, 1918, 1945, 1961, 1970, 1981, 1991, 2011, 2016, 2020, 2035]
FFR_typ = pd.DataFrame(index=typ_years)
for e, i in enumerate(facade):
if any(facade.iloc[:, e].isna()):
inx_nan = [e for e,i in enumerate(facade.iloc[:, e].isna()) if i]
if e >= 1:
facade.iloc[inx_nan, e] = facade.iloc[inx_nan, e-1]
else:
facade.iloc[inx_nan, e] = facade.iloc[inx_nan, e+1]
FFR = facade.iloc[:, e]
trend_md = get_MD(FFR, years_to_fit = typ_years)
inx = "".join(i)
FFR_typ.loc[:, inx] = trend_md
In [23]:
p = FFR_typ.plot(figsize=(15,5))
p.set_title("Total material density for building types")
p.set_ylabel('Material density (MD) $[t/m^2]$');
#p.set_ylim((2.2726, 2.273));
In [24]:
FFR_typ = FFR_typ.T
In [25]:
FFR_typ
Out[25]:
| 1900 | 1918 | 1945 | 1961 | 1970 | 1981 | 1991 | 2011 | 2016 | 2020 | 2035 | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| SFH Detached | 2.272693 | 2.269141 | 2.263813 | 2.260656 | 2.258880 | 2.256709 | 2.254736 | 2.250789 | 2.249803 | 2.249013 | 2.246053 |
| SFH Semi-detached | 2.264013 | 2.260413 | 2.255012 | 2.251812 | 2.250012 | 2.247812 | 2.245812 | 2.241811 | 2.240811 | 2.240011 | 2.237011 |
| SFH Terraced | 2.232643 | 2.231925 | 2.230848 | 2.230209 | 2.229850 | 2.229411 | 2.229012 | 2.228214 | 2.228014 | 2.227854 | 2.227256 |
| MFH Small | 2.197642 | 2.206479 | 2.219734 | 2.227589 | 2.232007 | 2.237408 | 2.242317 | 2.252136 | 2.254590 | 2.256554 | 2.263918 |
| MFH Medium | 2.207932 | 2.211288 | 2.216320 | 2.219302 | 2.220980 | 2.223030 | 2.224894 | 2.228622 | 2.229554 | 2.230300 | 2.233095 |
| MFH Large | 2.215709 | 2.216820 | 2.218487 | 2.219475 | 2.220030 | 2.220710 | 2.221327 | 2.222562 | 2.222870 | 2.223117 | 2.224043 |
In [26]:
data_years_nn = data_years.dropna()
In [27]:
def _get_p(data, i):
z = np.polyfit(x=data.columns, y=data.iloc[i], deg=1)
p = np.poly1d(z)
return p
In [28]:
all_shares = pd.DataFrame(index=typ_years)
for i in range(data_years_nn.shape[0]):
p = _get_p(data_years_nn, i)
shares = [p(y) for y in typ_years]
all_shares.loc[:, data_years_nn.index[i]] = shares
all_shares = all_shares.div(all_shares.sum(axis=1), axis=0)
In [29]:
densities = pd.DataFrame()
for i in range(FFR_typ.shape[0]):
temp = all_shares.mul(FFR_typ.iloc[i], axis=0)
#temp.index = ["a", temp.index]
tuples = [(FFR_typ.index[i], j) for j in temp.index]
index = pd.MultiIndex.from_tuples(tuples, names=['Building type', 'Construction year'])
temp.index = index
densities = densities.append(temp)
In [30]:
densities.head(15)
Out[30]:
| Metal | Minerals | Plastic | Wood | ||
|---|---|---|---|---|---|
| Building type | Construction year | ||||
| SFH Detached | 1900 | 0.029080 | 2.203000 | 0.019080 | 0.021533 |
| 1918 | 0.029224 | 2.199400 | 0.019224 | 0.021293 | |
| 1945 | 0.029440 | 2.194000 | 0.019440 | 0.020933 | |
| 1961 | 0.029568 | 2.190800 | 0.019568 | 0.020720 | |
| 1970 | 0.029640 | 2.189000 | 0.019640 | 0.020600 | |
| 1981 | 0.029728 | 2.186800 | 0.019728 | 0.020453 | |
| 1991 | 0.029808 | 2.184800 | 0.019808 | 0.020320 | |
| 2011 | 0.029968 | 2.180800 | 0.019968 | 0.020053 | |
| 2016 | 0.030008 | 2.179800 | 0.020008 | 0.019987 | |
| 2020 | 0.030040 | 2.179000 | 0.020040 | 0.019933 | |
| 2035 | 0.030160 | 2.176000 | 0.020160 | 0.019733 | |
| SFH Semi-detached | 1900 | 0.028969 | 2.194586 | 0.019007 | 0.021451 |
| 1918 | 0.029112 | 2.190940 | 0.019150 | 0.021211 | |
| 1945 | 0.029326 | 2.185470 | 0.019364 | 0.020852 | |
| 1961 | 0.029452 | 2.182229 | 0.019491 | 0.020639 |
In [31]:
densities.to_csv('data/densities.csv')
In [32]:
con = ["{}".format(i).strip() for i in tabula.index.droplevel([0,1])]
typ = ["{}".format(j).strip() for j in tabula.index.droplevel([0,2])]
In [33]:
tabula.loc[:, 'con'] = con
tabula.loc[:, 'typ'] = typ
/usr/lib/python3.6/site-packages/ipykernel/ipkernel.py:208: PerformanceWarning: indexing past lexsort depth may impact performance.
res = shell.run_cell(code, store_history=store_history, silent=silent)
In [34]:
tabula_reg = tabula.loc[:, ['Floor surface area per housing unit (m2)', 'con', 'typ']]
tabula_reg.columns = ['area', 'con', 'typ']
In [35]:
tabula.typ == "SFH"
Out[35]:
Construction Year Construction Type Size
pre '46 SFH Detached True
Semi-detached True
Terraced True
MFH Small False
Medium False
'46-'70 SFH Detached True
Semi-detached True
Terraced True
MFH Small False
Medium False
Large False
'71-'90 SFH Detached True
Semi-detached True
Terraced True
MFH Small False
Medium False
Large False
'91-'05 SFH Detached True
Semi-detached True
Terraced True
MFH Small False
Medium False
Large False
post '05 SFH Detached True
Semi-detached True
Terraced True
MFH Small False
Medium False
Large False
Name: typ, dtype: bool
In [36]:
p = tabula_reg.loc[tabula.typ == 'SFH', 'area'].unstack(2).plot.box(figsize=(8,8))
p.set_title("SQM area of SFH");
/usr/lib/python3.6/site-packages/ipykernel_launcher.py:1: PerformanceWarning: indexing past lexsort depth may impact performance.
"""Entry point for launching an IPython kernel.
In [37]:
p = tabula_reg.loc[tabula.typ == 'MFH', 'area'].unstack(2).plot.box(figsize=(8,8))
p.set_title("SQM area of MFH");
/usr/lib/python3.6/site-packages/ipykernel_launcher.py:1: PerformanceWarning: indexing past lexsort depth may impact performance.
"""Entry point for launching an IPython kernel.
In [38]:
tabula_reg.loc[tabula.typ == 'MFH', 'area'].unstack(2)
/usr/lib/python3.6/site-packages/ipykernel_launcher.py:1: PerformanceWarning: indexing past lexsort depth may impact performance.
"""Entry point for launching an IPython kernel.
Out[38]:
| Size | Large | Medium | Small | |
|---|---|---|---|---|
| Construction Year | Construction Type | |||
| '46-'70 | MFH | 105.0 | 88.0 | 70.0 |
| '71-'90 | MFH | 85.0 | 125.0 | 70.0 |
| '91-'05 | MFH | 105.0 | 110.0 | 155.0 |
| post '05 | MFH | 121.3 | 96.0 | 75.0 |
| pre '46 | MFH | NaN | 96.0 | 75.0 |
In [46]:
def get_year_lable(year, year_ranges, tabula):
inx_year = [e for e, i in enumerate(year_ranges) if year >= i[0] and year <= i[1]][0]
year_lable = tabula.index.get_level_values(0).unique()[inx_year]
return year_lable
def clean_year(y):
years = []
flip = False
highest = 0
for i in y.split("'"):
if 'post' in i: flip = True
if len(i) >= 1:
i = i.replace('-', '')
i = i.replace('pre', '-inf')
i = i.replace('post', 'inf')
i = float(i)
if i >= 40:
i += 1900
else:
i += 2000
if i <= highest:
i += 1
highest = i
years.append(i)
if flip:
years = years[::-1]
return years
def get_typ(year, construction, sqm, tabula = tabula):
construction += ' '
con_year = get_year_lable(2006, year_ranges, tabula)
temp = tabula.loc[(con_year, construction, slice(None)), "Floor surface area per housing unit (m2)"]
p = random.random()
temp_p = 1 - (abs(temp - sqm) / sum(abs(temp - sqm)))
temp_sel = temp_p.loc[temp_p >= p]
if temp_sel.shape[0] > 1:
temp_sel = temp_sel.loc[temp_sel == temp_sel.min()]
elif temp_sel.shape[0] == 0:
temp_sel = temp_p.loc[temp_p == temp_p.max()]
if temp_sel.shape[0] == 0:
print('error')
btyp = "{} {}".format(
temp_sel.index.get_level_values(1)[0].strip(),
temp_sel.index.get_level_values(2)[0].strip())
return(btyp)
def get_den(year, p, densities):
cyear_inx = densities.index.get_level_values(1).unique()
year_diff = [abs(int(i) - int(year)) for i in cyear_inx]
sel_inx = [e for e, i in enumerate(year_diff) if i == min(year_diff)][0]
den = densities.loc[(p, cyear_inx[sel_inx])]
return den
In [47]:
import random
year_ranges = [clean_year(i) for i in tabula.index.get_level_values(0).unique()]
In [48]:
sqm = 210
year = 1946
construction = "SFH"
random.seed(1234)
print("Tab. Material intensities of selected building typologies{sep}\
for construction year:\t{}{sep}\
and construction type:\t{}{sep}\
with a flor area of:\t{} m^2".format(year, construction, sqm, sep='\n'))
print("-" * 60)
print("| {:<20} | {:^6} | {:^6} | {:^6} | {:^6} |".format('Building Type', "Metals", "Mine.", "Plas.", "Wood"))
print("=" * 60)
for i in range(20):
p = get_typ(year, construction, sqm, tabula = tabula)
d = get_den(year, p, densities)
print("| {:<20} | {} |".format(p, " | ".join(["{:0.4f}".format(i) for i in d])))
print("-" * 60)
Tab. Material intensities of selected building typologies
for construction year: 1946
and construction type: SFH
with a flor area of: 210 m^2
------------------------------------------------------------
| Building Type | Metals | Mine. | Plas. | Wood |
============================================================
| SFH Terraced | 0.0290 | 2.1621 | 0.0192 | 0.0206 |
| SFH Semi-detached | 0.0293 | 2.1855 | 0.0194 | 0.0209 |
| SFH Detached | 0.0294 | 2.1940 | 0.0194 | 0.0209 |
| SFH Terraced | 0.0290 | 2.1621 | 0.0192 | 0.0206 |
| SFH Terraced | 0.0290 | 2.1621 | 0.0192 | 0.0206 |
| SFH Semi-detached | 0.0293 | 2.1855 | 0.0194 | 0.0209 |
| SFH Semi-detached | 0.0293 | 2.1855 | 0.0194 | 0.0209 |
| SFH Detached | 0.0294 | 2.1940 | 0.0194 | 0.0209 |
| SFH Terraced | 0.0290 | 2.1621 | 0.0192 | 0.0206 |
| SFH Detached | 0.0294 | 2.1940 | 0.0194 | 0.0209 |
| SFH Detached | 0.0294 | 2.1940 | 0.0194 | 0.0209 |
| SFH Terraced | 0.0290 | 2.1621 | 0.0192 | 0.0206 |
| SFH Detached | 0.0294 | 2.1940 | 0.0194 | 0.0209 |
| SFH Semi-detached | 0.0293 | 2.1855 | 0.0194 | 0.0209 |
| SFH Semi-detached | 0.0293 | 2.1855 | 0.0194 | 0.0209 |
| SFH Detached | 0.0294 | 2.1940 | 0.0194 | 0.0209 |
| SFH Detached | 0.0294 | 2.1940 | 0.0194 | 0.0209 |
| SFH Detached | 0.0294 | 2.1940 | 0.0194 | 0.0209 |
| SFH Detached | 0.0294 | 2.1940 | 0.0194 | 0.0209 |
| SFH Semi-detached | 0.0293 | 2.1855 | 0.0194 | 0.0209 |
------------------------------------------------------------