Recurrent stochastic configuration networks (RSCNs) have shown promise in modelling nonlinear dynamic systems with order uncertainty due to their advantages of easy implementation, less human intervention, and strong approximation capability. This paper develops the original RSCNs with block increments, termed block RSCNs (BRSCNs), to further enhance the learning capacity and efficiency of the network. BRSCNs can simultaneously add multiple reservoir nodes (subreservoirs) during the construction. Each subreservoir is configured with a unique structure in the light of a supervisory mechanism, ensuring the universal approximation property. The reservoir feedback matrix is appropriately scaled to guarantee the echo state property of the network. Furthermore, the output weights are updated online using a projection algorithm, and the persistent excitation conditions that facilitate parameter convergence are also established. Numerical results over a time series prediction, a nonlinear system identification task, and two industrial data predictive analyses demonstrate that the proposed BRSCN performs favourably in terms of modelling efficiency, learning, and generalization performance, highlighting their significant potential for coping with complex dynamics.

翻译：循环随机配置网络（RSCNs）因其易于实现、人工干预少和逼近能力强等优点，在具有阶次不确定性的非线性动态系统建模中显示出潜力。本文通过引入块增量结构发展了原始RSCNs，称为块循环随机配置网络（BRSCNs），以进一步提升网络的学习能力和效率。BRSCNs在构建过程中能够同时添加多个储备池节点（子储备池）。每个子储备池根据监督机制配置独特结构，确保网络的通用逼近特性。储备池反馈矩阵经过适当缩放以保证网络的回声状态特性。此外，输出权重采用投影算法进行在线更新，并建立了促进参数收敛的持续激励条件。通过时间序列预测、非线性系统辨识任务以及两个工业数据预测分析的数值实验表明，所提出的BRSCN在建模效率、学习能力和泛化性能方面表现优异，凸显了其处理复杂动态系统的巨大潜力。