Mathematical Modeling for Predictive Maintenance: Leveraging AI and Machine Learning for System Optimization and Failure Prediction

Abstract

This paper presents a mathematical modeling framework for predictive maintenance using artificial intelligence (AI) and machine learning (ML) to improve system performance and accurately forecast component failures. The study integrates advanced mathematical tools-such as differential equations, optimization algorithms, and probabilistic models-with ML techniques to develop predictive insights for mechanical systems. A case study on engine life prediction demonstrates the application of Support Vector Machines (SVM) and Neural Networks (NN), showing how degradation over time can be effectively modeled and predicted using real-time data and simulations. The proposed model achieves failure prediction accuracy with error rates as low as 2.5 percent, along with notable improvements in operational efficiency. The research highlights the value of mathematical modeling in enhancing AI/ML-based maintenance systems and emphasizes its broad applicability in industrial settings.