Application of a Stochastic Gradient Descent-Based SVR Online Modeling Method to Time-Varying Forging Processes

Abstract

In practice, forging processes have many unknown dynamics and fast time-varying characteristics due to transient load variation. This often results in insufficient data samples. Usually, support vector regression (SVR) can accurately model small sample data due to its good sparsity. However, using of sequential minimum optimization (SMO) algorithms increases the computational costs during the solution process, making it difficult to model fast time-varying systems. Aiming to address this problem, we developed an approach using online stochastic gradient descent (SGD) to improve SVR modeling efficiency. First, we used loss coefficients derived from the loss function to represent support vector loss. This effectively ensured sparsity in the modeling process. In this way, the SVR solving process was transformed into a loss coefficient calculation. This calculation was easy to achieve using SGD; thus, the solving process complexity was greatly reduced compared to SMO. On this basis, we developed an online incremental strategy to adapt the time-varying dynamics using online updating of step length, loss coefficients and bias term. Additional analysis demonstrated the convergence of the proposed online modeling method. Furthermore, modeling effect of this method is verified by using actual experiments with a 40MN isothermal die forging press.