DOI: 10.3303/CET23103151 Paper Received: 12 June 2023; Revised: 18 July 2023; Accepted: 25 July 2023 Please cite this article as: Köck B., Elser M., Mihalyi B., 2023, Applications of Multivariate Statistics in the Context of Life Cycle Assessment, Chemical Engineering Transactions, 103, 901-906 DOI:10.3303/CET23103151 CHEMICAL ENGINEERING TRANSACTIONS VOL. 103, 2023 A publication of The Italian Association of Chemical Engineering Online at www.cetjournal.it Guest Editors: Petar S. Varbanov, Panos Seferlis, Yee Van Fan, Athanasios Papadopoulos Copyright © 2023, AIDIC Servizi S.r.l. ISBN 979-12-81206-02-1; ISSN 2283-9216 Applications of Multivariate Statistics in the Context of Life Cycle Assessment Bianca Köck*, Martin Elser, Bettina Mihalyi Institute of Chemical, Environmental and Bioscience Engineering, TU Vienna, Getreidemarkt 9, 1060 Vienna, Austria bianca.koeck@tuwien.ac.at LCA is essential for achieving the European Green Deal's targets and supporting sustainable development. As LCA tools become more complex, multivariate statistics can offer valuable solutions. However, their potential benefits in LCA are yet to be fully explored. Therefore, this review evaluates scientific publications combining both, focusing on evaluating the fields of application and potential of multivariate statistics in LCAs. Key findings were the identified use cases, which can be categorised as "Grouping of Products/Systems", "Reduction of Parameters", "Evaluation of Parameters", and "Support for Decision Makers". Among these, the evaluation of parameters was the most commonly used category, with Principal Component Analysis (PCA) being the most frequently used statistical method. Although the publications showed high potential for gaining information, there is a lack of publications combining both topics. They were often used for high Technology Readiness Levels and often based on small datasets, although large data sets are desirable for gaining reliable and robust results. Therefore, future work will need to validate the data requirements and statistical methods recommended per use case. 1. Introduction Multivariate statistics has emerged as a powerful extension of univariate statistics that enables the investigation of many variables together, leading to a new and improved quality of data evaluation. This approach has found widespread applications in diverse fields, including Chemometrics (Varmuza and Filzmoser, 2009), as well as in process engineering to evaluate the performance of different processes, for example, for residual biomass valorisation (Del Duca et al., 2022) or improvement seeking in the oil and gas industry (Foronda et al., 2023). Similar data complexity and uncertainties can also be observed when calculating LCAs, which could benefit from the use of multivariate statistical methods to provide additional context for the assessment. LCA is a stand- ardised method used to evaluate the environmental impact of products or systems throughout their whole life cycle (ISO, 2006). LCA holds significant prominence as a pivotal tool within the European Union, garnering escalating recognition in recent legislative endeavours, notably exemplified by the Green Deal or the Circular Economy Action Plan (Sala et al., 2021). By integrating LCA into legislative frameworks, the European Union aims to advance its sustainability objectives, foster eco-friendly practices, and promote informed decision-mak- ing that aligns with environmental stewardship and the pursuit of a greener and more sustainable future for its constituents and the global community. This increasing adoption of LCA also accentuates the need for further standardisation and innovative approaches to address the complex and multifaceted challenges concerning the data uncertainty and interpretation of results (e.g. analyze multiple environmental and non-environmental im- pacts). Overcoming these challenges empowers decision-makers to base their policies and strategies on robust data-driven insights, ensuring a more effective and impactful formulation of environmental policies. However, as the results of this review show, only 17 LCAs utilising multivariate statistics between 2005-2023 were found, with four of them having been published in the last three years. To learn from their use cases, this paper aims to explore the potential applications of multivariate statistics in LCA methodology through a literature review of existing applications. This study summarises the current information in publications for the given research ques- tion, “What application possibilities do multivariate statistical methods offer LCA?”. Additionally, the statistical method and objective, as well as the software used in the literature, are evaluated. 901 Table 1: Overview of the reviewed studies combining LCA and multivariate methods. Other used statistical methods, such as bivariate and univariate, are also included in the section “Statistical Methods” Study Topic Statistical Methods Data Amount A g ri c u lt u re & F o o d P ro d u c ti o n Fraterrigo Garofalo et al. (2023) Production optimization of omega- 3 oil from tuna viscera MLR, PCA 15 experiments González- Quintero et al. (2021) Environmental impact assess- ment of dual-purpose farms in Co- lombia PCA, HCPA, Krus- kal-Wallis & Kruskal- Nemenyi Data from 1,313 farms Michos et al. (2012) LCA of peach orchard farming systems in Greece PCA, ANOVA, MC, HCA, Mann-Whitney 16 farming systems Chen et al. (2015) LCA of trout farms in France PCA with non-para- metric bootstrap 24 trout farms Bava et al. (2014) Environmental impact analysis of dairy farms PCA, CA, PC 28 dairy farms Mu et al. (2017) Environmental performance of specialized dairy farms MLR, CCA, Outlier detection 55 specialized dairy farms Grados and Schrevens (2019) LCA of potato agricultural in the Central Peruvian Andes CA, LDA, EFA Data from 58 potato pi- lot plots M a te ri a l & E le m e n ts Smith et al. (2021) Chemical element sustainability index for piezoelectric materials PCA, Trend analysis, Monte Carlo Analy- sis 59 chemicals Rydh and Sun (2005) Simplification of LCAs at an early stage of product design LRA, PCA (Sartorius AG, 2023) data of 214 mechanical design materials S u p p ly C h a in Genovese et al. (2017) Reducing redundancies and iden- tifying relationships among indica- tors in LCA PCA LCA calculations on five random samples of 1,000 supply chains Pozo et al. (2012) Dimensionality reduction of envi- ronmental metrics for multi-objec- tive optimization PCA, Pareto solu- tions 2 supply chain cases: power plant and 14 re- cyclable products W a s te W a te r T re a tm e n t Flores- Alsina et al. (2010) Incorporating multiple criteria into a common LCA for wastewater treatment Normalisation tech- niques, HCA, PCA, FA, Discriminant Analyses 12 control strategies at plant level and environ- mental, legal, technical & economic indicators Guo et al. (2023) Relationships between GWP of waste/sludge treatment facilities PCA, uncertainty analysis Data from 660 cities O th e r Rowley et al. (2015) Unsupervised weighting algorithm using PCA for the Choquet inte- gral in two case studies PCA 135 Australian industry sectors and 8 biosolids management options Bersimis and Geor- gakellos (2013) Assessing environmental perfor- mance of beverage packaging (aluminum, glass, and PET) in the Greek market PC, PCA, con- sistency test 16 beverage containers and 5 impact categories Gutiérrez et al. (2010) Relationships of impact categories in two LCAs: wastewater treat- ment plants and cultivation sys- tems, and processing and con- sumption of mussels. PC, PCA, Multi- dimensionale Scaling 7 impact category re- sults from 13 wastewater treatment plants and 10 impact category results from 5 life stages of mussels. Basson and Petrie (2007) Decision-making under uncer- tainty in LCA while comparing bed combustion and refurbished exist- ing pulverized fuel boilers Latin Hypercube sampling, PCA Three scenarios for two power station reactiva- tion cases, including fi- nancial, social, and en- vironmental aspects 902 2. Materials and methods The first steps of the literature research were an unstructured search with Google Scholar to evaluate the avail- ability of publications and to define the range of search terms for the structured research, as well as searching via WTI-AG (2022) (no results) and ScienceDirect (Elsevier B.V., 2023) in 2021. An update search for new publications was performed on March 30 th 2023 as well. The inclusion criteria for the review were the language (English and German) and the type of publication (review articles and research articles in scientific journals). Subsequently, the identified literature was systematically categorised based on the specific topics of Life Cycle Assessment (LCA) under investigation, resulting in distinct groups such as agriculture and food production. Within each category, statistical methods employed, the corresponding utilisation cases, the extent of data avail- ability, and the software or programming languages utilised were meticulously recorded and analysed to discern prevailing patterns and trends in the application of multivariate statistics in LCA research. 3. Results The results summarize 17 scientific articles that employed multivariate statistical methods such as Principal Component Analysis (PCA), Multiple Linear Regression (MLR), Canonical-Correlation Analysis (CCA), Factor Analysis (FA), Exploratory Factor Analysis (EFA), Linear Discriminant Analysis (LDA), Hierarchical Cluster Anal- ysis (HCA), Hierarchical Clustering on Principal Components (HCPC) and other cluster analysis (CA) to analyse the environmental impact of various products and systems. Bivariate statistical tools, like Pearson Correlation (PC), Spearman Rank Correlations (SRC) and univariate tools, including Analysis of Variance (ANOVA), Linear Regression Analysis (LRA), as well as others like Monte Carlo Analysis (MC) were also used. A summary of the scope of the article, as well as the statistical methods used as well as the sample size, is visualised in Table 1. 3.1. Overview of multivariate statistical methods and software used Most publications were in the area of agriculture. Fifteen of the 17 studies used PCA, and eight other methods were also used, visible in Table 2. Table 2: Summary of publications by categories and statistical methods used by topic For the statistical part, the software used were Gurobi, GAMS, MATLAB, STATISTICA, Analytica, SAS, Chemo- metric Agile Tool, S+ and SPSS or it was just mentioned which programming language (and packages) were used like the FactoMineR package. The LCA was modelled in Excel and Simapro. No automation-like interface between the software for data transfer and no trend for the choice of statistic software could be observed. 4. Discussion The use cases for multivariate statistics could be identified as a grouping of products/systems, the reduction of parameters, the evaluation of parameters, and the support for decision-making. One approach discussed by González-Quintero et al. (2021) and Michos et al. (2012) involves using multivariate statistical techniques like PCA, HCA, and HCPC to group products or systems based on defined parameters. This provides an objective view of similarities between them, leading to new categorisations like organic, integrated, and conventional for other sectors. However, not all products can be easily differentiated through this method, and adaptation of input parameters may be necessary for better accuracy. Future studies are needed to validate these results. Another approach involves reducing parameters by employing multiple regression analysis and CCA (Mu et al., 2017), PCA (Genovese et al., 2017), as well as multidimensional scaling (Gutiérrez et al., 2010). This eliminates re- dundant information about the system and improves the cost-efficiency of evaluation. However, if multiple pa- rameters are added up without considering redundancies, it can lead to misleading results. It is important to note that the redundant parameters may still contain valuable data that was not selected for analysis initially. Several studies used multivariate statistics to evaluate parameters and gain insight into their significance com- pared to each other. Relationships between input values can be revealed, giving information about their inter- actions and modification effects. Linkages between different domains of objectives (environmental, economic, technical, and legal) can also be created, leading to improved control strategies. However, the locality should Topic Nr. of studies PCA CA HCA MLR (E)FA HCPA CCA LDA Agriculture and Farming 7 5 2 1 2 1 1 1 1 Materials and Elements 2 2 0 0 0 0 0 0 0 Supply Chain 2 2 0 0 0 0 0 0 0 Wastewater Treatment 2 2 0 1 0 1 0 0 0 Multiple and other Categories 4 4 0 0 0 0 0 0 0 Sum 17 15 2 2 2 1 1 1 1 903 be considered as an additional influencing factor in the decision of input parameters, and validation of the used publication on a larger scale is required to remove this problem (e.g. Basson and Petrie, 2007). Multivariate statistics can also support decision-makers by providing new categories for evaluation and creating a chemical element sustainability index (Smith et al., 2021) or a new evaluation method (Pozo et al., 2012). This gives stakeholders easier access to necessary information and tools to estimate new systems. Mathematical or statistical solutions allow a less subjective view of the evaluated system, but the risk of appearing perfect and complete should be questioned. Withholding information from decision-makers can consciously or subcon- sciously influence their actions. 5. Implications of Findings The findings of this literature review present a valuable foundation for future investigations to expand the scope of this research in various sectors and domains. Products evaluated can vary over different Technology Readi- ness Levels (TRL). However, most studies focused on higher TRL. Lower TRL appears to be a promising ave- nue for further exploration due to its growing importance and the lack of current studies in this area. However, like the literature sources examined (Table 1), these also often have limitations in terms of the amount of data. In multivariate analysis, a sufficiently large sample size is desirable to ensure reliable and robust results. A small sample size may affect the accuracy and generalisability of the results. The current trend in LCA research reveals a dearth of comprehensive testing and comparison of various statis- tical models, with a particular emphasis on the exclusive application of PCA. Furthermore, there is a high ne- cessity to explore specialised approaches such as Repeated Cross-Validation (Filzmoser et al., 2009), tailored for situations where data is scarce, and other techniques of machine learning, depending on the size of the data sets. As such, it is imperative to undertake comprehensive evaluations of these alternative methods compared to the commonly employed multivariate statistical models, with the aim of providing LCA practitioners with an effective toolkit suited to different use cases. Moreover, to enhance the accessibility of multivariate statistics to a wider audience of LCA practitioners, the implementation of integration for existing LCA software or interfaces between statistical and LCA software is proposed as a necessary step forward, which could, for example, be done by using the LCA software Brightway (Mutel, 2014), which is written in Python. Also, guidelines on how to include multivariate statistics for the different use cases (grouping of products/systems, reduction or evaluation of parameters and support for decision mak- ers) could lead to standardisation and, therefore, to higher quality and comparability of results in the future. However, as a first step, it should be clarified in which use cases multivariate statistic is beneficial for LCAs, and also an evaluation to compare it to other methods of Artificial Intelligence should be made in different data and use cases. 6. Conclusion Overall, this review demonstrates the usefulness of statistical multivariate analysis techniques for addressing the challenges of LCA, such as reducing the complexity of data and the identification of non-redundant impact categories and their relationships. The review of multivariate statistics in LCA highlights the benefits and appli- cations of using statistical multivariate analysis techniques in addressing the challenges of LCA. The findings of the literature review revealed several key points: • Use Cases: Multivariate statistical methods are utilised in LCA for various purposes, including grouping of products/systems, parameter reduction, parameter evaluation, and support for decision making. These approaches provide objective views of similarities between products/systems, reduce redundant information, evaluate parameter significance, and create new evaluation categories or indices. Other possible use cases which should be explored are o Uncertainty Analysis: Multivariate statistics can be leveraged to assess uncertainties by analys- ing the variability of input parameters and their impact on the overall results. This would enhance the robustness of LCA findings. o Time Series and Spatial Analysis: Time-dependent LCA data and geographical variations can be explored using multivariate techniques to identify trends, patterns, regional/temporal differences and correlations. This approach can offer insights into the dynamic nature of environmental im- pacts and guide strategies for continuous improvement. o Integration with Artificial Intelligence: Integrating multivariate statistics with machine learning al- gorithms, such as neural networks and genetic algorithms, can lead to enhanced predictive ca- pabilities in LCA. This integration could facilitate scenario modelling and aid in the identification of optimal solutions for sustainable product design and policy-making. 904 o Comparative LCA: Multivariate methods can support the comparison of LCA results across dif- ferent products or systems, even when they have varying numbers of parameters or dimensions. This will enable fair and comprehensive assessments. • The implications of the findings emphasise the need for further research in various sectors and do- mains, particularly exploring lower TRL and addressing the limitations of small sample sizes in multi- variate analysis. Comprehensive testing and comparison of statistical models beyond PCA is neces- sary. Integration of multivariate statistics into existing LCA software and the development of guidelines for different use cases can enhance accessibility and standardisation. 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