2.1. Methodology of the Research
The partial least squares regression (PLSR) method, based on the results of the NIPALS (nonlinear partial least squares) iterative algorithm [
25,
26,
27,
28,
29], was used to determine the damage intensity index of large-block and large-panel buildings.
Basically, the PLSR method can be divided into two simultaneous procedures [
25]. The first involves identification of the principal components in the input variable space, and the second the relationships binding these components with the dependent variable. As part of this study, the PLSR method was used at the level of individual principal components and their subsequent verification. Such a course of action allows finding one of the most efficient linear combinations between input variables.
The PLSR method assumes that both the variables from the input space
X and output space
Y can be written as the sum of the linear combinations of the vectors
t and
p as well as
q and
u, i.e., the scores and loadings. These relationships have the following form [
26]:
where:
—the input variable space,
—the output variable space,
a—arbitrarily determined number of principal components,
—parameters of linear combinations: scores,
—parameters of linear combinations: loadings,
T, Q—block scoring matrix (n X a),
—block loading matrix (a X m).
The PLSR method, in the classical form based on the NIPALS iterative algorithm, leads to finding vectors
w and
c (normalized vectors
t and
u) in order to consequently maximize the covariance between the projected input and output variable space to the normalized directions
t and
u, respectively (w and c) [
27]:
As a result, using the NIPALS iterative procedure [
25] the decomposition of the vectors of the state of the input variables and the dependent variable (1) and (2) was obtained, as assumed at the beginning. The individual component vectors of the matrix
P are the tangent coefficients of the subsequent principal components identified during the construction of the PLSR model.
2.2. Database of Buildings
The information used in this research was collected during technical condition inventories of 138 buildings with reinforced concrete prefabricated structure carried out in 2002, 2007 and 2012. 64 of these structures were built in the large-block system (
Figure 1a) and 74 were built in large-panel system (
Figure 1b). All buildings located in the database constitute buildings in the mining area of the Legnica-Głogów Copper District (LGCD). In addition to construction data, the database contains information on indicators describing the risk of mining impacts.
2.2.1. Technical Characteristics of Large-Block Buildings
Among the 64 large-block buildings collected in the database, 50 have a residential function, 13 are public utility buildings, while one object has a residential-commercial function. The public facilities were built in the school large block (SLB) system and the rest in the large block (LB) system. Most of the large-block objects are located in multi-segment buildings. In 93.7% of cases, these buildings have no more than five stories. The dominant construction system is the transverse system of load-bearing walls. The described buildings are characterized by high stiffness, which results from the nature of the reinforced concrete prefabricated structure made of what is called “Żerań brick”. The structure consists of wall plates connected to each other by vertical joints and horizontally stiffened by floor slabs connected to the walls by tie beam. The foundation and basement walls of all investigated buildings are made as RC or concrete. The ceilings are made as precast reinforced concrete.
2.2.2. Technical Characteristics of Large-Panel Buildings
All 74 large-panel buildings collected in the database have a residential function. A total of 42 of them were erected in WWP system, and the rest in Wk-70 or Wk-70/SG system. A major part of the buildings was erected in semi-compact (40.5%) or compact (28.4%) development. In 87.8% of cases, these buildings have four or five storeys. In the remaining cases it is eleven storeys. The dominant system of load-bearing walls, similar as in the case of large-block buildings, is transverse. The described group of buildings is characterized by construction consisting of precast reinforced concrete elements, wall panels connected with each other with, e.g., steel connectors and concrete. Horizontal stiffness in the WWP system is ensured by reinforced concrete slabs, while in the Wk-70 system there are hollow-core slabs which are also used in large-block systems. The foundation and basement walls of described objects were made as RC or concrete.
2.2.3. Building Technical Condition Indicators
Degree of Technical Wear
The measure of the technical condition of a building structure is its technical wear
sz (e.g., [
9]). In this study, the degree of technical wear was determined for individual buildings using the weighted average method, considering individual constructional and technological solutions. The examined objects are characterized by the degree of wear with average values from 17.8% in 2002 to 25.1% in 2012 for large-panel, and from 27.4% in 2002 to 36.7% in 2012 for large-block buildings.
Damage Intensity Index
In order to investigate the contribution of damage to the technical wear of buildings, changes in damage intensity over time and the relationship between the extent of damage and the impact of mining exploitation, a qualitative index of damage intensity
wui was determined for individual structural and non-structural elements (e.g., [
21,
22]). A total of 22 elements were identified (
Table 1), for which this index was defined on a 6-point scale, in which
wui = 0 means no damage,
wui = 1—insignificant damage (range from 0 to 10%),
wui = 2—moderate damage (range from above 10 to 30%),
wui = 3—intensive damage (range from above 30 to 50%),
wui = 4 (and 5)—very intensive damage (range above 50%).
Figure 2 shows examples of damage to the load-bearing structure and secondary components.
The analysis of the value of the damage intensity index wui for individual building elements in the studied groups showed that there was insignificant, moderate or, in individual cases, intensive damage.
The damage intensity index of entire buildings was then determined as linear combinations of the indices describing the damage of their component parts. The partial least squares regression (PLSR) approach from data mining presented in
Section 2 was used to update the generalized damage index formula
wu.
Taking into account the specificity of the studied buildings, it was found that the description of the generalized damage index
wu for the studied groups of buildings are linear combinations (
Table 2) of the damage indices of structural and finishing elements
wui with the general form of the formula:
The formula calculated for large-block buildings does not take into account the values of indicators wu9, wu20, wu22, as contrary to large-panel buildings, they turned out to be insignificant in this group. The wu values determined for particular buildings fall within the categories of insignificant and moderate.
The average rate of technical wear presented in
Table 3 and
Figure 3 indicates a very similar rate of wear growth between 2002 and 2007 in the group of large-block (by 4.3% over five years) and large-panel buildings (by 4.1% over five years). Between 2007 and 2012, an increase in the rate of consumption growth was recorded in the group of large-block (up to 5.0% over five years) and a decrease in the group of large-panel buildings (down to 3.2% over five years). This situation may be caused by differences in the quality of maintenance of buildings. In the group of large-block buildings, between 2002 and 2007 there was a much higher number of renovations carried out than between 2007 and 2012. This is particularly true for public utility buildings (including schools), which are exposed to accelerated wear due to their operating conditions.
In 2002, the average values of the damage intensity index in the compared groups of buildings were similar at the level of 5.9 ÷ 6.0% (
Figure 4). In the group of large-block buildings, a similar rate of increase of the damage index was observed between 2002 and 2012, at the level of 0.6 ÷ 0.7%, while among the large-panel buildings an increase of the index by 1.4% until 2007 and by 0.6% until 2012 was observed.
2.2.4. Indicators Describing the Risk of Mining Impacts on Buildings