In this paper, two-stage approaches are proposed to study damage detection, localization and quantification in Functionally Graded Material (FGM) plate structures. Metal and Ceramic FGM plates are considered using three different composite materials: Al/Al2O3, Al/ZrO2-1, and Al/ZrO2-2. The FGM plates are modelled using IsoGeometric Analysis (IGA), which is more efficient than the classical Finite Element Method (FEM). Using a power-law distribution of the volume fractions of the plate constituents, the material properties of the plates are expected to vary continuously through their thickness. Improved damage indicator based on Frequency Response Function (FRF) is employed to predict the damaged elements in the first stage. A robust and efficient Improved Artificial Neural Network using Arithmetic Optimization Algorithm (IANN-AOA) is implemented for damage quantification problem in the second stage. The main idea is based on eliminating the healthy elements from the numerical model by the improved indicator. Next, collected data from damaged element based on damage index of an improved indicator is used as input and damage level as output. To prove the robustness of IANN-AOA, a Balancing Composite Motion Optimization (BCMO) is considered to improve ANN (IANN-BCMO) and is used for comparison. The results show that the improved indicator can predict the damaged elements with high precision. For damage quantification, IANN-AOA provides more accurate results than IANN-BCMO.