An improved adaptive gradient-based optimization algorithm for estimating the parameters of three-parameter Weibull distribution: an application of aero-engine reliability assessment

The reliability assessment of long-life and high-quality products such as aero-engines under smaller sample size conditions is essential for maintaining structural integrity. Parameter estimation for the three-parameter Weibull distribution should be particularly emphasized in reliability assessment of aero-engine life. Optimization algorithms have emerged as an effective strategy for solving multivariate nonlinear equations in maximum likelihood estimation of parameters for the three-parameter Weibull distribution. This study proposes a novel metaheuristic optimization algorithm based on adaptive gradient optimization principles for determining the parameters of the three-parameter Weibull distribution. Initially, the proposed algorithm optimizes the initial confidence intervals by utilizing the correlation coefficient and Bootstrap methods. Furthermore, due to the pseudo-random nature of traditional initialization parameters, the Halton random initialization method is employed to facilitate low-discrepancy sequence sampling. Subsequently, the Gradient Search Rule and the Local Escaping Operator are incorporated to enhance the computational efficiency and the capability to escape local optima. Therefore, global optimal parameter estimation of Weibull parameters is achieved. Extensive Monte-Carlo simulations are conducted to validate the proposed method. The simulation results indicate that the proposed method exhibits superior performance compared to existing methodologies. Ultimately, the proposed method is implemented to evaluate the reliability of actual failure data from the aero-engine and confirm the applicability.