A Generalized Perturbation Matrix-Based Fractional-Order Optimization Method of GM(r,2) for Inferring Driving Intention

Abstract

A fractional-order optimization method based on generalized perturbation matrix of GM(r,2) is proposed in this article. The smaller the perturbation bound, the more stable the model. By minimizing perturbation bound, a generalized perturbation matrix is given, which is the solving equation of the optimized fractional order. With different coefficients $\delta $ , different fractional orders can be calculated by a linear equation in one variable. Maximum relative error (RE) $e_{M}$ and mean absolute percentage error (MAPE) with different fractional orders can be obtained. Based on the smallest $e_{M}$ and the MAPE, the optimized fractional order of GM(r,2) can be determined. Compared with particle swarm optimization (PSO) and long short-term memory (LSTM) network transfer learning optimization methods, the MAPE of the proposed method is much smaller than that of PSO and slightly greater than LSTM network transfer learning optimization. The proposed method is superior to others without iteration calculation, and the convergence problem of PSO and the computational burden problem of transfer learning based on LSTM network optimization can be further improved. A GM(r,2) with optimized fractional order $r_{\mathrm { opt}}$ is evaluated in inferring driving intention of an active collision avoidance system for electric vehicles. Car-following simulations are performed to demonstrate the effectiveness of the proposed fractional-order optimization method with simple structure and flexible implementation.