# Fuzzy-Based Multivariate Analysis for Input Modeling of Risk Assessment in Wind Farm Projects
## 1 Introduction  
Wind and solar energy are expected to lead the future transformation of the global electricity sector, with onshore and offshore wind predicted to produce about 35% of total electricity demands by 2050 [1]. To reach the targeted installation capacity, considerable investments in the construction of renewable energy infrastructure are being made [1]. In Alberta, Canada, $3.6 billion will be invested through the renewable electricity program (REP) to add 5000 megawatts of renewable energy by 2030 [2; 3]. As a relatively novel type of infrastructure, wind farm construction is characterized by a lack of relevant literature and a scarcity of historical data. The development of risk management plans for these types of projects, therefore, are highly dependent on the collection of expert knowledge [4]. While the boom in the wind energy industry has encouraged new contractors to engage in the construction of these projects, a lack of data represents a challenge for new contractors when conducting risk management. Inadequate risk identification and assessment can have a detrimental impact on these large-scale projects, resulting in negative effects on cost, time, quality, and safety, while simultaneously discouraging contractors from engaging in wind farm construction. Risk assessment is necessary during all phases of a wind farm project, including design, construction, operation, maintenance, and life cycle planning [5]. Although there are several types of qualitative and quantitative methods for reliability-based risk assessment, determining which approach to apply in each phase of the project's life cycle will depend on the amount and/or type of data available at a particular phase [5]. Qualitative approaches (e.g., failure mode and effect analysis (FMEA), fault tree analysis (FTA), event tree analysis (EVA), and risk matrices), are better suited to the planning and early construction phases of a project when data are limited [5]. However, as projects progress and as more data are gathered, quantitative methods (e.g., analytical methods, stochastic methods, and Bayesian approaches) are favored because of their comprehensive capabilities [5]. Monte Carlo simulation (MCS) is a widely applied stochastic quantitative approach for risk assessment. It is an extremely powerful tool used for understanding and quantifying the potential effects of uncertainty on a project [6], and has been widely applied to simulate cost and time in construction [7]. As with many quantitative methods, however, the application of MCS is constrained by the need for variables to be input as probability density functions, limiting its use in the planning and early construction phases of a project. Currently, there are two primary approaches for developing the probability density functions that are input into MCS-based risk assessment models (Figure 1). As classified by [PERSON] [8], the two approaches are categorized based on data availability. The first approach can be adopted when there is sufficient historical data available for a particular variable [8]. In this case, a probability distribution is fit to the data and is then input into the risk assessment model. The second approach is adopted when there is an absence of data. This approach uses elicitation methods to construct the input distribution [8], where the risk analyst can decide to use either (1) a probabilistic approach by choosing either triangular, uniform, or PERT distributions [9; 10], or (2) a possibility approach, where fuzzy numbers are used to represent the impact of a risk factor [11]. Wind farm construction does not have sufficient historical data available to complete a risk assessment using the first approach. Nevertheless, there is a substantial amount of detailed subjective  
Figure 1: Levels of data available and accompanying methods used for input modeling. knowledge available [4]. The second approach, however, cannot make use of this knowledge, thereby missing an opportunity to enhance the reliability of risk assessment results.