Recurrent stochastic configuration networks (RSCNs) are a class of randomized learner models that have shown promise in modelling nonlinear dynamics. In many fields, however, the data generated by industry systems often exhibits nonstationary characteristics, leading to the built model performing well on the training data but struggling with the newly arriving data. This paper aims at developing a self-organizing version of RSCNs, termed as SORSCNs, to enhance the continuous learning ability of the network for modelling nonstationary data. SORSCNs can autonomously adjust the network parameters and reservoir structure according to the data streams acquired in real-time. The output weights are updated online using the projection algorithm, while the network structure is dynamically adjusted in the light of the recurrent stochastic configuration algorithm and an improved sensitivity analysis. Comprehensive comparisons among the echo state network (ESN), online self-learning stochastic configuration network (OSL-SCN), self-organizing modular ESN (SOMESN), RSCN, and SORSCN are carried out. Experimental results clearly demonstrate that the proposed SORSCNs outperform other models with sound generalization, indicating great potential in modelling nonlinear systems with nonstationary dynamics.

Reservoir computing (RC) offers efficient temporal data processing with a low training cost by separating recurrent neural networks into a fixed network with recurrent connections and a trainable linear network. The quality of the fixed network, called reservoir, is the most important factor that determines the performance of the RC system. In this paper, we investigate the influence of the hierarchical reservoir structure on the properties of the reservoir and the performance of the RC system. Analogous to deep neural networks, stacking sub-reservoirs in series is an efficient way to enhance the nonlinearity of data transformation to high-dimensional space and expand the diversity of temporal information captured by the reservoir. These deep reservoir systems offer better performance when compared to simply increasing the size of the reservoir or the number of sub-reservoirs. Low frequency components are mainly captured by the sub-reservoirs in later stage of the deep reservoir structure, similar to observations that more abstract information can be extracted by layers in the late stage of deep neural networks. When the total size of the reservoir is fixed, tradeoff between the number of sub-reservoirs and the size of each sub-reservoir needs to be carefully considered, due to the degraded ability of individual sub-reservoirs at small sizes.