In this paper, we present a novel method for fault identification in the case of an incipient wheel fault in mobile robots. First, a three-layer neural networks is established to estimate the deviation of the robot dynamics due to the process fault. The estimate of the faulty dynamic model is based on a combination of the nominal dynamic model and the neural network output. Then, by replacing the faulty dynamic model with its estimate value, the primary estimates of the wheel radius appear as the solutions of two quadratic equations. Next, a simple and efficient way to perform these primary estimate selections is proposed in order to eliminate undesired primary estimates. A recursive nonlinear least squares is applied in order to obtain a smooth estimate of the wheel radius. Two computer simulation examples using Matlab/Simulink show that the proposed method is very effective for incipient fault identification in the setting of both left and right wheel faults.