Efficient Input Signal Design for Third-Order Volterra Model Identification

The present work addresses the identification of third-order Volterra models from input-output process data. Building on previous studies regarding input sequence design for third-order Volterra models (Soni and Parker, 2004), a new reduced-length sequence is designed to identify third-order sub-diagonal kernels. This input sequence leads to a 30 % reduction in the data required to accurately estimate the sub-diagonal kernel. Identification of second-and third-order off-diagonal kernels is carried out using a random binary sequence (RBS). These input sequences exploit the third-order Volterra model structure and use the prediction error variance expression as a measure of model fidelity. The utility of the proposed approach is demonstrated on an isothermal polymerization reactor case study. The reduced length sequence shows excellent performance and results in an 80 % improvement in the sum-squared error (SSE) value of the third-order sub-diagonal kernel.