Predicting the dynamic behavior of a system with a neural state observer using nonlinear auto-regressive exogenous deep deterministic policy gradient: a case study on a washing machine

Abstract

This study presents a novel method for predicting the dynamic behavior of a system using a type of recurrent neural network as a state observer. This neural observer, which is trained with input–output data, is implemented on a washing machine. The problem under investigation is the detection of a coupled imbalanced state in washing machines, which is a difficult challenge. The proposed detection method in this study is named Nonlinear Auto-regressive exogenous Deep Deterministic Policy Gradient (NAR3PG). It has been shown that converting time series to images and teaching images to a convolutional neural network has acceptable results close to those of NAR3PG. Because of its inherent features and good results in detecting balance and coupled imbalance states, the NAR3PG neural method is the most suitable neural method used in this study. However, one of its main disadvantages is the long training time in the presence of many observations of the past, but it is the simplest method for converting the NAR3PG neural method to hardware code. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025.