Echo state networks (ESN) have been shown to be an effective alternative to conventional recurrent neural networks (RNNs) due to its fast training process and good performance in dynamic system modelling. However, the performance of ESN can be affected by the randomly generated reservoir. This paper presents nonlinear process modelling using ESN optimized by covariance matrix adaption evolutionary strategy (CMA-ES). CMA-ES is used to optimize the structural parameters of ESN: reservoir size, spectral radius, and leak rate. The proposed method is applied to three case studies: modelling a time series, modelling a conic tank, and modelling a fed-batch penicillin fermentation process. The results are compared with those from the original ESN, long short-term memory network, GA-ESN (ESN optimized by genetic algorithm), and feedforward neural networks. It is shown that the proposed method gives much better performance than the original ESN and other networks on all the three case studies.

回声状态网络（ESN）由于其快速的训练过程和在动态系统建模中的良好性能，已被证明是常规递归神经网络（RNN）的有效替代品。但是，ESN的性能会受到随机生成的油藏的影响。本文提出了使用ESN的非线性过程建模，该ESN是通过协方差矩阵适应进化策略（CMA-ES）优化的。CMA-ES用于优化ESN的结构参数：储层大小，光谱半径和泄漏率。所提出的方法应用于三个案例研究：对时间序列进行建模，对锥形罐进行建模以及对补料分批青霉素发酵过程进行建模。将结果与原始ESN，长短期记忆网络，GA-ESN（通过遗传算法优化的ESN）和前馈神经网络的结果进行比较。