LAUSR

Abstract Time-delay estimation is an important step for soft sensor modeling. In practical industrial process, the transportation time of materials and the transmission time of signals are fluctuating, and the traditional static time-delay estimation (STDE) methods can no longer accurately extract the dynamic time-delay characteristics. In this paper, a weighted relevance vector machine model based on dynamic time-delay estimation (DTDE-WRVM) is proposed to realize the dynamic characteristic extraction and quality variable prediction. Firstly, a static delimitation-dynamic update (SD-DU) strategy is adopted for dynamic time-delay estimation, where the dynamic time-delay variation range can be determined based on the fuzzy curve analysis (FCA) method, and the dynamic time-delay characteristics between process variables can be captured based on improved sliding time window. Then, a weighted soft sensor model is established by setting the weights for the variables with different time-delays according to their importance to the output variable. Finally, a numerical example and a wastewater treatment plant (WWTP) case are studied to demonstrate the effectiveness of the DTDE-WRVM model. With the proposed method, the prediction accuracy of WWTP is significantly improved, e.g., the value of the root-mean-square error decreases by 55.7% from 0.0972 to 0.0431.