# Fuzzy-Based Multivariate Analysis for Input Modeling of Risk Assessment in Wind Farm Projects
## 4 Application and Results
### Data Processing
#### 4.2.2 Validation of the Marginal Distribution  
Two approaches, namely sensitivity analysis and expert validation, were used to investigate the proposed methodology. In the sensitivity analysis, the influence of input parameters on the fitted distribution was investigated, while the expert validation analysis was performed to evaluate the proposed approach from the perspective of an expert. * Sensitivity Analysis  
Sensitivity analysis is a powerful technique for testing the internal consistency and reliability of models [63] by analyzing the model behavior in response to variations in input values or parameters. Figure 8: Marginal Beta distribution of schedule-risk impact. Figure 7: Marginal Beta distribution of cost-risk impact. The purpose of conducting a sensitivity analysis is to assess how the input variables of a model affect the resulting probability distribution, allowing analysts to identify the input variables with the greatest influence on the output of a model or system [64]. Two approaches are commonly used to conduct a sensitivity analysis: local (also known as absolute [65]) and global. The local approach allows only one variable of a model to be assessed at a time, while fixing all other variables to their original values [64]. Conversely, global sensitivity allows all input factors to vary simultaneously, where the sensitivity is evaluated over the entire range of each input factor [64]. This study applied a local approach to investigate sensitivity of three input variables: (1) selection of linguistic variables; (2) membership values of the linguistic variables; and (3) membership values for calibrating and mapping the risk impact range. Sensitivity was calculated manually by changing the values of the targeted parameters and examining the effect on the resulting marginal Beta distribution. Parameters resulting in the greatest change were deemed to have the greatest impact on outputs. Thus, experts are encouraged to remain cognizant of such parameters during the application of the proposed method. Sensitivity of these parameters was tested on the parameters of the Beta distribution. The selection of linguistic terms is at the discretion of the analyst [61]; however, the range that each linguistic term represents must be investigated. The illustrative case study was investigated again using different membership values for (\(F\)) and (\(C\)). First, the sensitivity of frequency of occurrence (\(F\)) was tested by introducing a new membership function, adopted from [50], where the same linguistic terms are used but the membership values were changed. Results are detailed in Table 10.  
The shape parameters \(\alpha=0.389\) and \(\beta=0.392\) and the fitted Beta distribution is shown in Figure 9. Differences between the original distribution and the one derived following the change the in membership function of the frequency of occurrence (\(F\)) were minimal. The results demonstrate that small variations in membership values have little effect on the output distribution. Next, the influence of changing the membership function of the adverse consequence (\(C\)) was investigated by introducing a new trapezoidal membership function, as shown in Table 11. The shape parameters \(\alpha=0.592\) and \(\beta=0.713\) and the fitted Beta distribution are presented in Figure 10. Again, the differences between the original distribution and the one derived following the change in the membership function of the adverse consequence (\(C\)) were minimal. The results demonstrate that the output distribution is not sensitive to changes in the membership function of the adverse consequence (\(C\)).