*4.3. Statistical and Robustness Analysis*

This section provides the statistical evaluations based on mean, minimum, maximum, and standard deviation in terms of SSE for all earlier suggested methodologies, as well as a comparison with the accuracy and robustness of the various algorithms in a total of thirty runs, as shown in Table 7. The mean of the SSE is calculated to evaluate the algorithms' accuracy, and the standard deviation is calculated to evaluate the dependability of the implemented parameter estimation technique.


**Table 7.** Statistical results of Ballard Mark V Fuel cell.

The statistical analysis outcomes reveal that the developed OBAOA is the most accurate and efficient technique for parameter estimation because it has a very low standard deviation.

The Friedman rank test [67] is applied to determine the relevance of the data in addition to the conventional statistical analysis, i.e., best, mean, worst, and standard deviation. Furthermore, for each analyzed PV module, this non-parametric test is used to rank the algorithms. The null hypothesis H<sup>0</sup> (*p*-value > 5%) in the Friedman test suggests no notable change between the compared algorithms. The opposite hypothesis H<sup>1</sup> signifies a notable difference between the compared algorithms for all 30 runs. In this test, each algorithm is given a rank based on its performance. Small ranks determine the best algorithms. Table 8 displays the Friedman rank test results at a 95% confidence level. According to Table 8, the OBAOA has the first rank based on the Friedman ranking test results, followed by PSO, AOA, GSA, and AO.

**Table 8.** Friedman ranking test for Ballard Mark V PEMFC.

