# A Software Tool for a Stochastic Life Cycle Assessment and Costing of Buildings’ Energy Efficiency Measures

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}) emissions [4]. Thus, to reach the EU’s energy efficiency and climate objectives, the annual renovation rate of the building stock in the Member States, which today varies from 0.4 to 1.2%, will need at least to double [2]. However, this “renovation wave” will require costly investments whose returns are closely linked to highly uncertain future scenarios [5].

_{2}Emissions Optimization in Building Renovation”), for example, developed a specific tool named A56opt-tool able to perform both LCC and LCA evaluations of building renovation measures. The tool was specifically developed to support the decision-makers for the establishment of cost-optimized targets for energy use and carbon emissions related to building renovation, also considering different co-benefits [8,9].

## 2. Materials and Methods

#### 2.1. LCA Model

- IG is the Global Impact of the case study for a given LCA indicator (unit of indicator);
- $s{I}_{j}$ is the environmental impact related to production phase of the j-th system, Equation (2) (unit of indicator);
- ${s}_{j}$ is the number of replacements of the j-th system within the cp, considering its Service Life SL
_{j}(years); - ${EoLI}_{j}$ is the environmental impact related to the EoL phase of the j-th system, Equation (3) (unit of indicator);
- ${smI}_{j}$ is the environmental impact related to the periodic maintenance of the j-th system, Equation (4) (unit of indicator);
- i is each year of the calculation period;
- Q
_{H}is the building energy need (kWh/year); - $E{I}_{i}$ is the environmental impact of the energy carrier at the year I (unit of indicator). $s{I}_{j}$ is defined in the following Equation (2):

- UI
_{k}is the unitary production impact of the k-th material composing the j-th system (unit of indicator); - m
_{k}is the mass of the k-th material (kg).

_{k}is the unitary End of Life impact of the k-th material composing the j-th system (unit of indicator):

_{k}.

#### 2.2. LCC Model

- CI
_{j}is the initial investment cost of the j-th system (€); - CM
_{j,i}is the annual maintenance cost of the j-th system (€/year); - $C{S}_{j,t}$ is the replacement cost at a specific year t, assumed equal to the discounted investment costs for that year [€], whose frequency depends on the j-th system Service Life $S{L}_{j}$ (year) as follows: ${CS}_{j,t}=C{I}_{j}\xb7{R}_{{t}_{j}}^{disc}\xb7{R}_{{t}_{j}}^{L}{\text{},\text{}t}_{j}{=SL}_{j}+1{,\text{}2SL}_{j}+1,\text{}...{;\text{}SL}_{j}\text{}\text{}cp$;
- CE
_{i}is the annual energy cost (€/year), calculated multiplying the building annual energy consumption ${P}_{H}$ (kWh/year) for the energy tariff related to the specific energy carrier $EnT$ (€/kWh) (see Equation (6) for details); - ${R}_{i}^{disc}$ is the discount factor at the year i (-) defined as ${R}_{i}^{disc}={\displaystyle \prod}_{i=1}^{cp}\frac{1}{1+{i}_{i}^{R}}$, with ${i}_{i}^{R}$ the real interest rate;
- ${R}_{i}^{L}$ is the price development rate for human operation (labor cost) at year i (-) defined as ${R}_{i}^{L}={\displaystyle \prod}_{i=1}^{cp}\left(1+{e}_{i}^{L}\right)$, with ${e}_{i}^{L}$ the escalation factor for labor;
- ${R}_{i}^{E}$ is the price development rate for energy at year i (-) defined as ${R}_{i}^{E}={\displaystyle \prod}_{i=1}^{cp}\left(1+{e}_{i}^{E}\right)$, with ${e}_{i}^{L}$ the escalation factor for labor;
- $Va{l}_{j,\text{}cp}\text{}$ is the residual value of the system at the end of the calculation period, calculated based on straight-line depreciation of the initial investment or replacement cost of the system until the end of the calculation, discounted at the beginning of the evaluation period [€].

- ${P}_{H}\text{}$ indicates the building energy consumption expressed as ${P}_{H}={Q}_{H}/{\eta}_{H}$ (kWh/year), where ${\eta}_{H}$ is the building overall efficiency for heating (-);
- ${P}_{H}^{pre}$ is the building pre-renovation energy consumption (kWh/year);
- ${P}_{H}^{post}$ is the building post-renovation energy consumption (kWh/year);
- $EnT$ is the energy tariff of the specific energy carrier (€/kWh).

#### 2.3. Macroeconomic Scenarios

#### 2.4. Monte-Carlo Simulation for Uncertainty and Sensitivity Analysis

## 3. Results

#### 3.1. Description and Structure of the Software Tool

#### 3.1.1. Software Overview and Workflow

#### 3.1.2. Internal LCC/LCA Database

#### 3.1.3. Loading Data, Country Selection, and Pre-Processing

#### 3.1.4. Editing of Case Studies and Energy Sources

#### 3.1.5. LCA/LCC Run

#### 3.1.6. Advanced Functions

#### 3.2. Exemplary Applications

#### 3.2.1. The Case Studies

^{2}K. The thicknesses of the different internal insulation layers were calculated to achieve a similar U-value for the retrofitted walls, i.e., equal to or slightly lower than 0.36 W/m

^{2}K, according to the actual Italian law requirements [30], with slight differences due to the commercial insulation thicknesses available in the market.

^{2}and to obtain an average U-value ≤ 0.36 W/m

^{2}K with the minimum insulation thickness and for a calculation period of 30 years, assumed equal to the service lives of the insulation systems. For sake of simplicity, no maintenance or replacement operations are considered within this time horizon in these exemplary applications.

#### 3.2.2. A Single Stochastic LCA and LCC Analysis

_{2}-Eq., the AP from about 2.63 to 0.55 kg for the SO

_{2}-Eq., and the EP from 0.09 to 0.05 kg for the (PO

_{4})

^{3}-Eq. It should be noted that mean values are not always significant, especially in the case of the distribution that substantially differs from the normal one, as in the case of the EP indicator (see Figure 6).

#### 3.2.3. LCA and LCC Analysis under Alternative Scenarios

#### 3.2.4. Parametrizing Function

## 4. Discussion and Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**List of main used R packages**

## References

- European Commission. A Clear Planet for All–A European Strategic Long-Term Vision for a Prosperous, Modern, Competitive and Climate Neutral Economy; COM(2018) 773 Final; European Commission: Brussels, Belgium, 2018. [Google Scholar]
- European Commission. The European Green Deal; COM (2019) 640 Final; European Commission: Brussels, Belgium, 2019. [Google Scholar]
- Von der Leyen, U. A Union That Strives for More. My Agenda for Europe. Political Guidelines for the next European Commission; European Commission: Brussels, Belgium, 2019. [Google Scholar]
- European Commission Energy Performance of Buildings. Available online: https://ec.europa.eu/energy/en/topics/energy-efficiency/energy-performance-of-buildings (accessed on 3 March 2020).
- Hamdy, M.; Sirén, K.; Attia, S. Impact of financial assumptions on the cost optimality towards nearly zero energy buildings—A case study. Energy Build.
**2017**, 153, 421–438. [Google Scholar] [CrossRef] [Green Version] - OECD. OECD Guidance on Sustainability Impact Assessment; OECD: Paris, France, 2010. [Google Scholar]
- Amini Toosi, H.; Lavagna, M.; Leonforte, F.; Del Pero, C.; Aste, N. Life Cycle Sustainability Assessment in Building Energy Retrofitting; A Review. Sustain. Cities Soc.
**2020**, 60, 102248. [Google Scholar] [CrossRef] - Almeida, M.; Ferreira, M. Cost effective energy and carbon emissions optimization in building renovation (Annex 56). Energy Build.
**2017**, 152, 718–738. [Google Scholar] [CrossRef] - Dalla Mora, T.; Peron, F.; Romagnoni, P.; Almeida, M.; Ferreira, M. Tools and procedures to support decision making for cost-effective energy and carbon emissions optimization in building renovation. Energy Build.
**2018**, 167, 200–215. [Google Scholar] [CrossRef] - CEN EN 15459-1:2017 Energy Performance of Buildings–Economic Evaluation Procedure for Energy Systems in Buildings—Part 1: Calculation Procedures, Module M1-14; CEN: Brussels, Belgium, 2017.
- ISO 14040:2006 Environmental Management—Life Cycle Assessment—Principles and Framework; ISO: Geneva, Switzerland, 2006.
- ISO 14044:2006 Environmental Management—Life Cycle Assessment—Requirements and Guidelines; ISO: Geneva, Switzerland, 2006.
- CEN EN 15804: 2011 Sustainability of Construction Works–Environmental Product Declarations–Core Rules for the Product Category of Construction Products; CEN: Brussels, Belgium, 2011.
- CEN EN 15978: 2010. Sustainability of Construction Works–Sustainability Assessment of Buildings–Calculation Method; CEN: Brussels, Belgium, 2010.
- Di Giuseppe, E.; D’Orazio, M.; Du, G.; Favi, C.; Lasvaux, S.; Maracchini, G.; Padey, P. A Stochastic Approach to LCA of Internal Insulation Solutions for Historic Buildings. Sustainability
**2020**, 12, 1535. [Google Scholar] [CrossRef] [Green Version] - Baldoni, E.; Coderoni, S.; D’Orazio, M.; Di Giuseppe, E.; Esposti, R. The role of economic and policy variables in energy-efficient retrofitting assessment. A stochastic Life Cycle Costing methodology. Energy Policy
**2019**, 129, 1207–1219. [Google Scholar] [CrossRef] - Baldoni, E.; Coderoni, S.; D’Orazio, M.; Di Giuseppe, E.; Esposti, R. From cost-optimal to nearly Zero Energy Buildings’ renovation: Life Cycle Cost comparisons under alternative macroeconomic scenarios. J. Clean. Prod.
**2021**, 288, 125606. [Google Scholar] [CrossRef] - Di Giuseppe, E.; D’Orazio, M.; Favi, C.; Rossi, M.; Lasvaux, S.; Padey, P.; Favre, D.; Wittchen, K.; Du, G.; Nielsen, A.; et al. RIBuild, D5.1 Report and Tool: Probability Based Life Cycle Impact Assessment; Project No. 637268 European Union’s Horizon 2020; European Commission: Brussels, Belgium, 2017. [Google Scholar]
- Di Giuseppe, E.; Iannaccone, M.; D’Orazio, M.; Coderoni, S.; Baldoni, E.; Esposti, R.; Favre, D.; Padey, P.; Toczé, M.; Lasvaux, S.; et al. RIBuild, D5.2 Report and Tool: Probability Based Life Cycle Cost; Project No. 637268 European Union’s Horizon 2020; European Commission: Brussels, Belgium, 2018. [Google Scholar]
- Burhenne, S.; Tsvetkova, O.; Jacob, D.; Henze, G.P.; Wagner, A. Uncertainty quantification for combined building performance and cost-benefit analyses. Build. Environ.
**2013**, 62, 143–154. [Google Scholar] [CrossRef] - Copiello, S. Economic parameters in the evaluation studies focusing on building energy efficiency: A review of the underlying rationale, data sources, and assumptions. Energy Procedia
**2019**, 157, 180–192. [Google Scholar] [CrossRef] - Lütkepohl, H. New Introduction to Multiple Time Series Analysis, 1st ed.; Springer: Berlin/Heidelberg, Germany, 2006. [Google Scholar]
- Sobol, I.M. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math. Comput. Simul.
**2001**, 55, 271–280. [Google Scholar] [CrossRef] - Sobol’, I.M. On the distribution of points in a cube and the approximate evaluation of integrals. USSR Comput. Math. Math. Phys.
**1967**, 7, 86–112. [Google Scholar] [CrossRef] - Saltelli, A.; Ratto, M.; Andres, T.; Campolongo, F.; Cariboni, J.; Gatelli, D.; Saisana, M.; Tarantola, S. Global Sensitivity Analysis. The Primer; Wiley: Chichester, UK, 2008; ISBN 9780470059975. [Google Scholar]
- R Development Core Team. R: A Language and Environment for Statistical Computing; R Foundation for Statistical Computing: Vienna, Austria, 2008; ISBN 3-900051-07-0. Available online: http://www.R-project.org (accessed on 5 July 2021).
- Chang, W.; Cheng, J.; Allaire, J.; Xie, Y.; McPherson, J. shiny: Web Application Framework for R. R Package Version 1.0.3. Available online: https://cran.r-project.org/ (accessed on 5 July 2021).
- Wan, Z.; Hudak, P. Functional Reactive Programming from First Principles. Sigplan Not.
**2000**, 35, 242–252. [Google Scholar] [CrossRef] - Lacirignola, M.; Blanc, P.; Girard, R.; Pérez-López, P.; Blanc, I. LCA of emerging technologies: Addressing high uncertainty on inputs’ variability when performing global sensitivity analysis. Sci. Total Environ.
**2017**, 578, 268–280. [Google Scholar] [CrossRef] [PubMed] - Ministero dello Sviluppo Economico Decreto Interministeriale 26.06.2015–Applicazione Delle Metodologie di Calcolo Delle Prestazioni Energetiche e Definizione Delle Prescrizioni e dei Requisiti Minimi Degli Edifici; Ministero dello Sviluppo Economico: Roma, Italy, 2015.
- Eurostat Cooling and Heating Degree Days by NUTS 2 Regions–Annual Data. Available online: https://ec.europa.eu/eurostat/statistics-explained/index.php?title=Heating_and_cooling_degree_days_-_statistics (accessed on 5 July 2021).
- Di Giuseppe, E.; Maracchini, G.; Gianangeli, A.; Bernardini, G.; D’Orazio, M. Internal Insulation of Historic Buildings: A Stochastic Approach to Life Cycle Costing Within RIBuild EU Project. In Sustainability in Energy and Buildings; Springer: Singapore, 2020; pp. 349–359. ISBN 978-981-32-9868-2. [Google Scholar] [CrossRef]
- Bueno, C.; Hauschild, M.Z.; Rossignolo, J.A.; Ometto, A.R.; Mendes, N.C. Sensitivity analysis of the use of Life Cycle Impact Assessment methods: A case study on building materials. J. Clean. Prod.
**2016**, 112, 2208–2220. [Google Scholar] [CrossRef] [Green Version] - Mutel, C. Why Does the Ecoinvent Database Love the Lognormal Distribution? 2013. Available online: https://chris.mutel.org/ecoinvent-lognormal.html (accessed on 5 July 2021).
- Igos, E.; Benetto, E.; Meyer, R.; Baustert, P.; Othoniel, B. How to treat uncertainties in life cycle assessment studies? Int. J. Life Cycle Assess.
**2019**, 24, 794–807. [Google Scholar] [CrossRef]

**Figure 3.**“Editing” menu. Visualization of the summary data of a case study under the “Edit case study” Table (1) Identification of the case study; (2) Identification of the renovation systems applied to a case study; (3) Visualization/text editing of the input data included in the database.

**Figure 4.**“LCC Run” menu. Visualization of the input parameters needed to run a case study under the “LCC analysis”; Table (1) Identification of the case study; (2) Identification of the energy source; (3) Number of simulations to be run; (4) Calculation Period; (5) Economic scenarios where to perform the LCC assessment; (6) Specific setting for the escalation rates; (7) Graphical outputs and summary statistics at the end of the calculation.

**Figure 5.**“LCA Run” menu. Visualization of the input parameters needed to run a case study under the “LCA”; Table (1) Identification of the case study; (2) Identification of the energy source; (3) Number of simulations to be run; (4) Calculation Period; (5) Graphical outputs and summary statistics at the end of the calculation.

**Figure 6.**PDFs of the GWP (GI1), AP (GI2), and EP (GI3) indicators in pre- (

**a**) and post- (

**b**) renovation scenarios, and impact savings (

**c**) for the EPS internal insulation system.

**Figure 7.**LCA first order and total order sensitivity indices for the EPS case and each impact indicator: (

**a**) GWP; (

**b**) AP; (

**c**) EP. The error bars indicate the confidence level intervals at 95%.

**Figure 8.**PDF and CDF of the global cost obtained for the EPS case considering the natural gas energy source scenario and the regular growth macroeconomic scenario.

**Figure 9.**(

**a**) First order and total order sensitivity indices for global costs computed with “Method 1” for the EPS case; (

**b**) Total order sensitivity indices for global costs computed with “Method 2” for the EPS case. The error bars indicate the confidence level intervals at 95%.

**Figure 10.**Global cost and GWP (GI1) distributions obtained for the five insulation systems for the natural gas energy source scenario (LCA and LCC) under the four macroeconomic scenarios (LCC). 1: EPS, 2: CaSi, 3: AAC, 4: Cork, 5: RW.

**Figure 11.**Global cost and GWP (GI1) distributions obtained for the five insulation systems for the electricity energy source scenario (LCA and LCC) under the four macroeconomic scenarios (LCC). 1: EPS, 2: CaSi, 3: AAC, 4: Cork, 5: RW.

**Figure 12.**Energy share obtained for the five insulation systems for the natural gas energy source scenario under the four different macroeconomic scenarios. 1: EPS, 2: CaSi, 3: AAC, 4: Cork, 5: RW.

**Figure 13.**LCC results in terms of GC box plot for each analysis carried out with the “Parametrizing” tab.

LCA Stage (EN 15978 Nomenclature) | LCA Parameter | Data Frames | ||||
---|---|---|---|---|---|---|

Materials | Systems | Case Studies | Energy Sources | |||

Production stage (modules A1–A3) | Material | m_{k} (kg) | x | |||

UI_{k} (unit of indicator) | x | |||||

Use stage (modules B2, B4 and B6) | Maintenance | sl_{k} (years) | x | |||

Replacement | SL_{j} (years) | x | ||||

Energy need | ${Q}_{H}^{pre}$, ${Q}_{H}^{post}$(kWh/year) | x | ||||

Energy impact | $E{I}_{i}$(unit of indicator) | x | ||||

EoL stage (modules C1-C4) | EoL material impact | EOL_{k} (unit of indicator) | x |

LCC Category (EN 15459 Nomenclature) | LCC Parameter | Data Frames | ||||
---|---|---|---|---|---|---|

Materials | Systems | Case Studies | Energy Sources | |||

Investment Cost | CI_{j} (€) | x | ||||

Running Cost | Replacement cost | $S{L}_{j}$(years) | x | |||

$C{S}_{j,t}$(€) | x | |||||

Maintenance cost | CM_{j,i} (€/year) | x | ||||

Energy cost | ${Q}_{H}^{pre}$, ${Q}_{H}^{post}$(kWh/year) | x | ||||

${\eta}_{H}$(-) | x | |||||

$EnT$(€/kWh) | x |

**Table 3.**Mean (µ), median (χ), and standard deviation (σ) of GWP, AP, and EP indicators obtained from the LCA analysis for the natural gas energy source scenario.

Case Study | GWP (kgCO_{2}-Equation) | AP (kgSO_{2}-Equation) | EP (kg(PO_{4})^{3}-Equation) | ||||||
---|---|---|---|---|---|---|---|---|---|

µ | χ | σ | µ | χ | σ | µ | χ | σ | |

Pre | 7.68 × 10^{2} | 7.56 × 10^{2} | 1.34 × 10^{2} | 2.63 × 10^{0} | 2.44 × 10^{0} | 1.03 × 10^{0} | 8.63 × 10^{−2} | 8.52 × 10^{−2} | 1.43 × 10^{−2} |

EPS | 1.69 × 10^{2} | 1.67 × 10^{2} | 2.75 × 10^{1} | 5.53 × 10^{−1} | 5.09 × 10^{−1} | 2.64 × 10^{−1} | 4.60 × 10^{−2} | 2.39 × 10^{−2} | 1.39 × 10^{−1} |

CaSi | 2.46 × 10^{2} | 2.43 × 10^{2} | 3.81 × 10^{1} | 7.75 × 10^{−1} | 6.00 × 10^{−1} | 1.23 × 10^{0} | 1.24 × 10^{−1} | 3.30 × 10^{−2} | 7.84 × 10^{−1} |

AAC | 1.82 × 10^{2} | 1.80 × 10^{2} | 3.04 × 10^{1} | 5.95 × 10^{−1} | 5.05 × 10^{−1} | 8.09 × 10^{−1} | 7.66 × 10^{−2} | 2.37 × 10^{−2} | 5.19 × 10^{−1} |

Cork | 1.83 × 10^{2} | 1.80 × 10^{2} | 2.86 × 10^{1} | 6.04 × 10^{−1} | 5.20 × 10^{−1} | 6.26 × 10^{−1} | 6.85 × 10^{−2} | 2.77 × 10^{−2} | 2.73 × 10^{−1} |

RW | 1.67 × 10^{2} | 1.65 × 10^{2} | 2.75 × 10^{1} | 5.44 × 10^{−1} | 4.95 × 10^{−1} | 2.79 × 10^{−1} | 5.74 × 10^{−2} | 2.65 × 10^{−2} | 1.92 × 10^{−1} |

**Table 4.**Mean (µ), median (χ), and standard deviation (σ) of GC, PB, CI share, and energy costs’ share obtained from the LCC analysis for the natural gas energy source scenario and regular growth macroeconomic scenario.

Case Study | GC (€) | PB (Years) | CI (%) | Energy (%) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

µ | χ | σ | µ | χ | σ | µ | χ | σ | µ | χ | σ | |

EPS | 109.55 | 109.14 | 8.79 | 5.33 | 5.00 | 0.63 | 39.47 | 39.44 | 3.46 | 60.53 | 60.56 | 3.46 |

CaSi | 282.33 | 282.13 | 18.10 | 25.89 | 24.00 | 14.49 | 75.77 | 75.88 | 2.66 | 24.23 | 24.12 | 2.66 |

AAC | 151.25 | 151.03 | 10.24 | 9.97 | 10.00 | 1.26 | 58.17 | 58.21 | 3.57 | 41.83 | 41.79 | 3.57 |

Cork | 165.15 | 164.82 | 10.90 | 11.40 | 11.00 | 1.46 | 61.00 | 61.15 | 3.42 | 39.00 | 38.85 | 3.42 |

RW | 122.05 | 121.68 | 8.85 | 7.05 | 7.00 | 0.85 | 49.84 | 49.92 | 3.64 | 50.16 | 50.08 | 3.64 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Baldoni, E.; Coderoni, S.; Di Giuseppe, E.; D’Orazio, M.; Esposti, R.; Maracchini, G.
A Software Tool for a Stochastic Life Cycle Assessment and Costing of Buildings’ Energy Efficiency Measures. *Sustainability* **2021**, *13*, 7975.
https://doi.org/10.3390/su13147975

**AMA Style**

Baldoni E, Coderoni S, Di Giuseppe E, D’Orazio M, Esposti R, Maracchini G.
A Software Tool for a Stochastic Life Cycle Assessment and Costing of Buildings’ Energy Efficiency Measures. *Sustainability*. 2021; 13(14):7975.
https://doi.org/10.3390/su13147975

**Chicago/Turabian Style**

Baldoni, Edoardo, Silvia Coderoni, Elisa Di Giuseppe, Marco D’Orazio, Roberto Esposti, and Gianluca Maracchini.
2021. "A Software Tool for a Stochastic Life Cycle Assessment and Costing of Buildings’ Energy Efficiency Measures" *Sustainability* 13, no. 14: 7975.
https://doi.org/10.3390/su13147975