Availability prediction of solar water pumping system through stochastic modeling and nature-inspired algorithms

In many countries, agriculture is an essential part of the primary economic sector. For sustainable agriculture growth, the use of a solar water pumping system plays a vital role. The key objective of this paper is to present a novel scientific approach for evaluating the availability of a solar water pumping system, in which five components are connected in a series configuration. The stochastic framework of the system is established using Markov birth–death process, and the corresponding availability expression and estimation of the parameters is obtained using C-K differential equations. It is assumed that the failure and repair rates of each component are constant and time-independent in behavior. Further, the nature-inspired Algorithms, namely Ant Lion Optimizer (ALO), Genetic Algorithm (GA), and Grey Wolf Optimizer (GWO), are applied to predict the optimal availability of the system. The result of this study indicates that after the 200 iterations at 400, the population size system attained the highest availability i.e. 0.9132921 at coverage factor 0.5 by the Gray Wolf Optimizer. A convergence threshold for algorithm termination defined such that the optimization process stopped when the change in the objective function value fell below $${10}^{-6}$$ or when the maximum number of iterations reached. Also, to attain a stochastic variability and robustness each algorithm executed a total of 60 independent runs. The optimization computation performed with the help of R 4.3.1 on an Intel Core i7. For testing the significant difference among all three algorithms a non-parametric Freidman rank test was applied. Further, a Freidman post hoc analysis using the Wilcoxon signed-rank tests with Bonferroni correction implemented for pairwise comparison of algorithms. The results of this study showed that the calculated p value is significantly less than the 5% level of significant. This indicates all three algorithms are significantly different.