As an S-curve concerns cumulative progress at a specific time point, the data set Aj should be further transformed to ACj as shown in Eq. (3):equation(3)ACj= AC1j,AC2j,AC3j,…,ACLj =A1j,∑i=1i=2Aij,∑i=1i=3Aij,…,∑i=1i=LAijwhere ACj stands for the data set of cumulative amount of construction waste disposal by the jth project, AC1j is the cumulative amount of construction waste disposal of the jth project at the first time point, and ACLj is the cumulative amount of construction waste disposal of the jth project at Lj.
It stands to reason that large-scale projects (e.g. construction volume, or longer duration) will normally generate more construction waste than small-scale counterparts. In order to reduce the impact of project scale, the original data set is standardized for further analyses. To this end, Eqs. (1) and (3) are standardized in the form of Eqs. (4) and (5) respectively:equation(4)TSj= TS1,TS2,TS3,…,TSLj =1Lj,2Lj,3Lj,…,1equation(5)ACSj=ACS1,ACS2,ACS3,…,ACSLj=AC1jACLj,AC2jACLj,AC3jACLj,…,1where TSj denotes the data set of standardized time of the jth project, and ACSj denotes the data set of standardized cumulative amount of construction waste generation of the jth project.
Apart from the time points and construction waste disposal amounts, the characteristics of the project are also collected. According to existing studies of CWM and S-curves (e.g. Lu and Yuan, 2010, Wang et al., 2010 and Chao and Chien, 2009), project characteristics such as duration, contract sum, location, project type, and client type (e.g. private or public) are important in influencing CWG. To identify the full list of project characteri###http://www.agarose-gpg-le.com/image/1-s2.0-S2405609X14000025-sc2.jpg####stics
that has significant influences on CWG would deserve another research paper(s). A wealth of research has been produced while it is still largely inconclusive. This study MLN4924
itself in existing studies to identify the project characteristics that matter. Another important consideration is the data availability.Step 2: Identifying the best form of S-curve to model CWG.
This step identifies an S-curve formula that best describes the data sets as shown in Eqs. (4) and (5). Numerous S-curve models of cost and value have been developed by previous studies. This study borrows such models to model a CWG S-curve. A unique feature of this study is that a wide range of S-curves is examined in order to find the one that best fits the data sets. This is possible given the computational power available today. Software programs are designed in Matlab ( MathWorks,
2012) to conduct curve fitting so as to select the best-fit S-curve formulas from the options as listed in Table 1.
Least-squares curve fitting analysis (LSCFA) is used to evaluate the fit of an S-curve to the data of a specific project (Lu et al., 2013). The mean-square error (MSE) is usually the specific indicator for the LSCFA, with:equation(6)MSEkj=∑i=1i=L(ACSij-ACSijk)2Ljwhere MSEkj denotes the MSE for the jth project when adopting the kth S-curve formula for curve fitting, Lj is the number of data points of the jth project, ACSij is the real standardized cumulative amount of CWG of the jth project at the i th time point, ACSijk is the standardized cumulative amount of construction waste generation of the jth project agreeing with the kth S-curve formula at the ith time point.
Based on Eq. (6), the average MSE (AMSE) for all available projects when adopting a specific S-curve formula is:equation(7)AMSEk=∑j=1j=JMSEkjJwhere AMSEk is the AMSE for all available projects when adopting the kth S-curve formula, and J is the number of projects under consideration. The best S-curve formula used to model the S-curve of CWG is the one that generates the minimal AMSE.
Step 3: Establishing the link between project characteristics and parameter values of CWG S-curve using ANN.
As a single and standard S-curve is insufficient to forecast CWG in different projects with different characteristics, a specific CWG S-curve needs to be developed by linking the standard CWG curve with the project characteristics. No previous research has been conducted to explore this link. Neither is Autosomes