**4. Predicting CO2 Emissions Using a Monte Carlo Simulation**

#### *4.1. Monte Carlo Simulation*

In this study, Monte Carlo simulation was adopted for probabilistic estimation of CO2 emissions. Monte Carlo simulation was used because it is one of the essential techniques used for probabilistic analysis and it generates a stochastic model for uncertain variables and presents statistical results from the simulated experiment [25]. These statistical results enable effective decision-making under uncertain conditions.

In this study, Crystal Ball software was used to effectively perform Monte Carlo simulations. This software supports probabilistic model analysis and simulation testing of the data required for Monte Carlo simulations. For the application of Monte Carlo simulations in this study, CO2 emissions of one work cycle were set as the result value. In addition, the variables that affect the resultant value were set at CO2 emissions for each activity. Afterward, the Kolmogorov–Smirnov (K–S) test was performed on the activity data to derive the probability distribution model for CO2 emissions from the activities. A correlation analysis was performed between the CO2 emission data for each activity. The simulation was performed by generating random numbers using the correlation analysis results. As a result, the probability model of the resultant value was derived, and the CO2 emissions were analyzed for each activity.

#### *4.2. The Kolmogorov–Smirnov (K–S) Test*

In this study, the K–S test was used to focus on a typical situation where the number of observations is higher than in certain situations where the equipment takes a long time to run. Comparing the K–S test with the Anderson–Darling test, the K–S test has the advantage that it is more sensitive in the middle distribution than in the tail [26]. In the K–S test, 14 types of probability distributions are available in the Crystal Ball software. The K–S test was used to test the goodness-of-fit of the emissions data from the measured operation time.

Since the test statistic of the critical value has a significance level of 0.05 and an N value of 21, it is confirmed to be 0.287 for the K–S test for goodness of fit [27]. The test results indicated that the null hypothesis of the K–S test method adopted in Table 5 for all the sub-tasks is lower than the critical value of 0.287. Therefore, the probability model of each variable derived from this section sufficiently reflects the distribution of actual data. Analysis showed that the distributions for stopping after entering, waiting after stopping, and leaving activities followed a log normal distribution, whereas pouring concrete followed a logistic distribution, and pumping concrete followed an extremum value distribution (Figure 1).

**Table 5.** Kolmogorov–Smirnov (K–S) test of CO2 emissions by activities.

**Figure 1.** The plots of distribution by activities.

#### *4.3. Correlation Analysis*

In this section, correlation analysis is performed to derive the correlation coefficients for the emission amount of each activity and to reflect them in the simulation. The correlation analysis indicated the magnitude of the correlation among the activities through a correlation coefficient. The correlation coefficient range is from −1 to +1, and the signs of the coefficients indicated whether the relationship of the two variables is proportional or inversely proportional. The absolute value of the coefficient indicates the strength of the relationship. Thus, any value close to +1 or −1 indicates a strong correlation.

This study investigated the correlation between each variable, determined through the Spearman correlation coefficient. The Spearman correlation coefficient is a non-parametric measure of the degree of qualitative correlation of the increase or decrease when the distribution of two successive variables fits a normal distribution or provides rank-scale data. Therefore, the application of Spearman's correlation coefficient can be suitably considered a detailed work-specific fit distribution model that was verified in the previous section.

As a result of the correlation analysis with a significance level of 0.05, it was confirmed that the correlation between stopping after entering and pouring concrete, stopping after entering and leaving, pumping concrete and waiting after stopping, pumping concrete and pouring concrete was significant

(Table 6). The highest correlation was found between pumping concrete and pouring concrete with a correlation coefficient of 0.806 because the concrete pump car can pump concrete while concrete pouring work is underway. The correlations between pouring concrete and stopping after entering (0.524), and between stopping after entering and leaving (0.469) appeared to be strongly positive. The reason for the two positive correlations is that these activities are particularly affected by the proficiency of handling the equipment at a busy construction site and of the concrete mixer truck driver. The correlation between waiting after stopping and pumping was −0.469, indicating a strong negative correlation. This is because the waiting time is longer as the concrete pumping work is delayed.


**Table 6.** Results of correlation analysis between activities.

\* Significant at 0.05 level of significance. \*\* Significant at 0.01 level of significance.

#### *4.4. Simulation Test Results and Analysis*

In this study, we executed the simulation test 10,000 times at a 95% confidence interval. To calculate the confidence interval, instead of a mathematical formula, we used an analytical bootstrapping method [28]. The simulation tests were performed by taking into account the probability distribution model obtained from the fit and the calculated correlation coefficient. The random values were generated considering the correlation to the probability distribution of a particular activity, and the results were obtained stochastically. The upper and lower limits of emissions were determined by adjusting the confidence interval.

The results of the simulation were similar to the corresponding figures of the measured operating time-based emissions data (Table 7). However, in the case of kurtosis and skewness, a significant difference was noticed in the corresponding figures in the CO2 emission data based on the measured operating hours. The significant differences are because the tendency in the form of CO2 emission distribution was strongly reflected by the performance of the repeated imitating experiment. The degree of deviation was significantly different from the corresponding values of the emission data based on the measured operating time of equipment.

As a result of the simulation, the CO2 emission probability model of the pouring work follows the log normal distribution (Figure 2). At a 95% confidence interval, the lower limit of emissions is 4171.7 g CO2, the upper limit is 11,705.4 g CO2, and the average is 7329.7 g CO2.

This study analyzed CO2 emissions estimated by current deterministic methods as a single value using the derived probability distribution model. The results of the analysis of the estimated current CO2 emissions were outside the 95% confidence interval of the probability distribution model or about 20% different from the mean value (Figure 3). In the probability distribution model, the probability of CO2 emissions being less than those estimated by the CECET was found to be about 0.6% (i). Therefore, it is estimated that there is a risk of underestimating emissions because the level of emissions was estimated at a level that exceeds the 95% confidence interval of the simulation results. In addition, the probability of actual measured CO2 emissions being less than the estimated CO2 emissions using a bill of quantity was 73.2% in the probability distribution model (iii). The value of the result is within the 95% confidence interval of the probability distribution model. However, it is considered that the CO2 emission calculation method using a bill of quantity may over-calculate compared to actual CO2

emissions because the corresponding probability differs by more than 20% from the average value of the probability distribution model.


\* 95% confidence interval.

**Figure 2.** The probability model of CO2 emissions in concrete pouring work according to simulation results.

Consequently, using actual measured data, probability-based estimation and analysis of CO2 emissions will be more realistic and accurate for the construction planning phase as well as for the construction phase. The current methods of estimating CO2 emissions are analyzed to have differences with actual CO2 emissions, so further verification or improvement of the current methods of estimation is needed. It is also possible to assess quantitatively whether CO2 emissions are likely to be over- or under-estimated by reviewing the probability distribution model for specific construction work.


**Figure 3.** Analysis of CO2 emissions using the probability model.

#### **5. Conclusions**

This study gathered data on the operation time of construction equipment at the activity level and performed a probabilistic analysis using Monte Carlo simulations to determine the variability of CO2 emissions during the construction phase.

This study used actual activity data to account for variability in the construction phase, and probabilistic estimation showed that the current deterministic methods are insufficient to predict CO2 emissions at the planning and design phases. It is suggested that actual activity data collection and probabilistic analyses for activity data are necessary to present highly reliable CO2 emission estimation. Risk information from the probabilistic emission calculation methods presented in this study may support decision makers to establish more realistic reduction goals in developing greenhouses gas and energy consumption reduction strategies.

This study dealt with the CO2 emissions of the construction process stage within the life-cycle assessment (LCA) system boundaries. The CO2 emissions from the construction process stage are known to account for less than those of the operational use stage in the building life cycle. Thus, the variability of the construction phase covered in this study may not have a significant impact on the CO2 emissions of the whole life cycle. Nevertheless, the importance of embedded carbon, including CO2 emissions from the current construction process stage, has been emphasized. In particular, according to the zero-energy building concept, which has recently become a reality, CO2 emissions from the operational use stage will be close to zero in the future, and the calculation of carbon emissions from the construction process stage will be important.

However, this study was limited to the activity data gathered from concrete work only and considered variability at the activity level only in terms of construction equipment operation time. In future studies, we will gather further actual activity data during the construction process. In addition, we will derive the additional factors affecting CO2 emissions during the construction phase and calculate the derived weights of the factors. The CO2 emissions from the construction process will also be implemented as a probabilistic model with calculated weights.

**Author Contributions:** Data curation, C.N.; Formal analysis, D.L. and C.N.; Investigation, D.L. and C.N.; Methodology, D.L., G.K. and C.N.; Project administration, H.C and K.-I.K.; Supervision, K.-I.K.; Writing—original draft, D.L.; Writing—review & editing, D.L., G.K. and H.C.; funding acquisition, K.-I.K.

**Funding:** This research was funded by National Research Foundation of Korea grant number 2016R1A2B3015348 and Architecture & Urban Development Research Program funded by the Ministry of Land, Infrastructure and Transport of the Korean Government grant number 19AUDP-B121595-04.

**Acknowledgments:** This research was supported by National Research Foundation of Korea grant number 2016R1A2B3015348 and Architecture & Urban Development Research Program funded by the Ministry of Land, Infrastructure and Transport of the Korean Government grant number 19AUDP-B121595-04.

**Conflicts of Interest:** The authors declare no conflict of interest.
