Levenberg–Marquardt Backpropagation Training of Multilayer Neural Networks for State Estimation of a Safety-Critical Cyber-Physical System

As an important safety-critical cyber-physical system (CPS), the braking system is essential to the safe operation of the electric vehicle. Accurate estimation of the brake pressure is of great importance for automotive CPS design and control. In this paper, a novel probabilistic estimation method of brake pressure is developed for electrified vehicles based on multilayer artificial neural networks (ANNs) with Levenberg-Marquardt backpropagation (LMBP) training algorithm. First, the high-level architecture of the proposed multilayer ANN for brake pressure estimation is illustrated. Then, the standard backpropagation (BP) algorithm used for training of the feed-forward neural network (FFNN) is introduced. Based on the basic concept of BP, a more efficient training algorithm of LMBP method is proposed. Next, real vehicle testing is carried out on a chassis dynamometer under standard driving cycles. Experimental data of the vehicle and the powertrain systems are collected, and feature vectors for FFNN training collection are selected. Finally, the developed multilayer ANN is trained using the measured vehicle data, and the performance of the brake pressure estimation is evaluated and compared with other available learning methods. Experimental results validate the feasibility and accuracy of the proposed ANN-based method for braking pressure estimation under real deceleration scenarios.