Mathematical modeling and optimum design of zinc oxide nanostructures modified carbon fiber reinforced polymethylmethacrylate-based bone cement composite using machine learning methods

Abstract

A novel design-modeling strategy is proposed to enhance the mechanical properties of a medical polymethylmethacrylate (PMMA) bone cement (BC) under compressive and flexural loading conditions by considering the ratio of carbon fiber (CF), zinc (Zn)-coated carbon fiber (CF/Zn), and nanostructured zinc-oxide (ZnO) coated CF as design variables. A detailed study was carried out on multiple nonlinear neuro-regression analyses and revealed the advantages of the proposed method compared to Artificial Neural Networks (ANN). Polynomial, trigonometric and hybrid mathematical models are used to define the experimental process accurately. The boundedness of the candidate models is checked after the calculation of R²_training and R²_testing values to reveal whether the model is realistic or not. The results show that hybrid models are the most successful when the strength and strain are considered objective functions; the fourth-order polynomial model should be preferred when the module is considered objective. Also, it is seen that the most significant advantage of the Neuro-regression approach compared to artificial neural networks is that the mathematical models can be used directly without needing any transformation. This is not possible in neural networks and, therefore, significantly limits and complicates the use of models obtained using ANN.