Parameter Estimation of a Non-Homogeneous Inverse Exponential Process Using Classical, Metaheuristic, and Deep Learning Approaches

The proposed research technique implements Inverse Exponential distribution as its intensity function for modelling and estimating NHPP occurrence rates. The main research target evaluates parameter identification capabilities between traditional methods and metaheuristic algorithm and deep learning approaches in this newly created stochastic process. This research analyses parameter estimation through a combination of Maximum Likelihood Estimation (MLE) with Ordinary Least Squares (OLS) classical methods and Firefly Algorithm (FFA) and Grey Wolf Optimization (GWO) as well as Long Short-Term Memory (LSTM) networks and Artificial Neural Networks (ANN) as deep learning models. Performance evaluation of parameter identification methods depends on Root Mean Squared Error (RMSE) calculations in the simulation experiment. The researcher tested the model using failure time data that was extracted from the Mosul Dam power station during the time period from January 2017 through January 2020. Research data shows Artificial Neural Networks with Long Short-Term Memory networks produce superior outcomes than traditional techniques because ANN achieved the lowest Root Mean Squared Error across all sample numbers. The proposed research uses hybrid intelligent methods to improve stochastic process parameter estimation through examples that can benefit reliability engineering alongside temporal modelling of data.