一种具有small world 特性的ESN 结构分析与设计

针对回声状态网络（ESN）结构设计复杂、参数选择难度大的问题,提出一种具有small world特性的ESN（SWESN）.首先采用神经元空间增长算法在平面区域生成small world拓扑网络;然后根据网络节点与基准点的Euclidean距离将网络节点进行重新排序,并将平面上的物理节点及其连接映射为SWESN的内部神经元连接矩阵,从而使动态神经元池具有small world特性.实验表明,SWESN动力学特性比常规ESN更为丰富,在鲁棒性、抗干扰能力等方面均优于常规的ESN.     

基于小世界回声状态网的时间序列预测

为了提高时间序列的预测精度, 提出了利用改进的小世界网络优化泄露积分型回声状态网(Leaky-integrator echo state network, Leaky ESN)的时间序列预测方法. 首先提出一个改进型小世界网络, 其加边概率是节点间距离的负指数函数. 然后, 利用加边概率直接表示Leaky ESN储备池两个神经节点的连接权值, 取值范围为[0,1], 表征了节点间的连接程度. 利用这个新型小世界网络改进Leaky ESN的储备池神经节点的连接方式, 有目的地实现了稀疏连接, 减小了Leaky ESN储备池随机稀疏连接的盲目性, 提高了储备池的适应性.最后, 利用改进的Leaky ESN预测典型的非线性时间序列, 并利用Matlab仿真软件验证了本文提出方法的有效性. 与Leaky ESN相比, 本文提出的方法具有更高的预测精度和更短的训练时间.     

Noise-Robust Automatic Speech Recognition Using a Predictive Echo State Network

Artificial neural networks have been shown to perform well in automatic speech recognition (ASR) tasks, although their complexity and excessive computational costs have limited their use. Recently, a recurrent neural network with simplified training, the echo state network (ESN), was introduced by Jaeger and shown to outperform conventional methods in time series prediction experiments. We created the predictive ESN classifier by combining the ESN with a state machine framework. In small-vocabulary ASR experiments, we compared the noise-robust performance of the predictive ESN classifier with a hidden Markov model (HMM) as a function of model size and signal-to-noise ratio (SNR). The predictive ESN classifier outperformed an HMM by 8-dB SNR, and both models achieved maximum noise-robust accuracy for architectures with more states and fewer kernels per state. Using ten trials of random sets of training/validation/test speakers, accuracy for the predictive ESN classifier, averaged between 0 and 20 dB SNR, was 81plusmn3%, compared to 61plusmn2% for an HMM. The closed-form regression training for the ESN significantly reduced the computational cost of the network, and the reservoir of the ESN created a high-dimensional representation of the input with memory which led to increased noise-robust classification.     

ESN 岭回归学习算法及混沌时间序列预测

ESN（回声状态网络）是一种新型的递归神经网络．可有效处理非线性系统辨识以及混沌时间序列预测问题．针对ESN学习算法中可能存在的解的奇异问题，利用岭回归方法代替原有的线性回归算法．通过贝叶斯或Bootstrap方法确定岭回归方法中的正则项系数．从而有效地控制输出权值的幅值，改善ESN的预测性能．该方法在月太阳黑子预测问题中显示出较好的结果．     

MULTI-LAYER CORRECTIVE CASCADE ARCHITECTURE FOR ON-LINE PREDICTIVE ECHO STATE NETWORKS

An architecture for on-line learning of time series prediction is presented which uses a series of echo state networks (ESNs). Each ESN learns to predict an error correction term for the previous ESN. This technique is demonstrated to improve prediction accuracy for on-line learning of the Mackey-Glass chaotic oscillator. The results are compared to other architectural configurations to show that the improved performance emerges from sequential ESN error correction. A new recurrent network structure is shown to be a useful simplification of the usual ESN reservoir.     

Modeling deterministic echo state network with loop reservoir

Echo state network (ESN), which efficiently models nonlinear dynamic systems, has been proposed as a special form of recurrent neural network. However, most of the proposed ESNs consist of complex reservoir structures, leading to excessive computational cost. Recently, minimum complexity ESNs were proposed and proved to exhibit high performance and low computational cost. In this paper, we propose a simple deterministic ESN with a loop reservoir, i.e., an ESN with an adjacent-feedback loop reservoir. The novel reservoir is constructed by introducing regular adjacent feedback based on the simplest loop reservoir. Only a single free parameter is tuned, which considerably simplifies the ESN construction. The combination of a simplified reservoir and fewer free parameters provides superior prediction performance. In the benchmark datasets and real-world tasks, our scheme obtains higher prediction accuracy with relatively low complexity, compared to the classic ESN and the minimum complexity ESN. Furthermore, we prove that all the linear ESNs with the simplest loop reservoir possess the same memory capacity, arbitrarily converging to the optimal value.     

Stock Price Forecasting: An Echo State Network Approach

Forecasting stock prices using deep learning models suffers from problems such as low accuracy, slow convergence, and complex network structures. This study developed an echo state network (ESN) model to mitigate such problems. We compared our ESN with a long short-term memory (LSTM) network by forecasting the stock data of Kweichow Moutai, a leading enterprise in China’s liquor industry. By analyzing data for 120, 240, and 300 days, we generated forecast data for the next 40, 80, and 100 days, respectively, using both ESN and LSTM. In terms of accuracy, ESN had the unique advantage of capturing nonlinear data. Mean absolute error (MAE) was used to present the accuracy results. The MAEs of the data forecast by ESN were 0.024, 0.024, and 0.025, which were, respectively, 0.065, 0.007, and 0.009 less than those of LSTM. In terms of convergence, ESN has a reservoir state-space structure, which makes it perform faster than other models. Root-mean-square error (RMSE) was used to present the convergence time. In our experiment, the RMSEs of ESN were 0.22, 0.27, and 0.26, which were, respectively, 0.08, 0.01, and 0.12 less than those of LSTM. In terms of network structure, ESN consists only of input, reservoir, and output spaces, making it a much simpler model than the others. The proposed ESN was found to be an effective model that, compared to others, converges faster, forecasts more accurately, and builds time-series analyses more easily.     

基于蚁群算法优化回声状态网络的研究

针对输出权值采用最小二乘法的回声状态网络(ESN),在随机选取输入权值和隐层神经元阈值时,存在收敛速度慢、预测精度不稳定等问题,提出了基于蚁群算法优化回声状态网络(ACO-ESN)的算法。该算法将优化回声状态网络的初始输入权值、隐层神经元阈值问题转化为蚁群算法中蚂蚁寻找最佳路径的问题,输出权值采用最小二乘法计算,通过蚁群算法的更新、变异、遗传等操作训练回声状态网络,选择出使回声状态网络预测误差最小的输入权值和阈值,从而提高其预测性能。将ACO-ESN与ELM、I-ELM、OS-ELM、B-ELM等神经网络的仿真结果进行对比,结果验证经过蚁群算法优化的回声状态网络加快了其收敛速度,改善了其预测性能,并增强了隐层神经元的敏感度。     

A new self-learning optimal control laws for a class of discrete-time nonlinear systems based on ESN architecture

A novel self-learning optimal control method for a class of discrete-time nonlinear systems is proposed based on iteration adaptive dynamic programming(ADP)algorithm.It is proven that the iteration costate functions converge to the optimal one,and a detailed convergence analysis of the iteration ADP algorithm is given.Furthermore,echo state network(ESN)architecture is used as the approximator of the costate function for each iteration.To ensure the reliability of the ESN approximator,the ESN mean square training error is constrained in the satisfactory range.Two simulation examples are given to demonstrate that the proposed control method has a fast response speed due to the special structure and the fast training process.     

基于层次化可塑性回声状态网络的混沌时间序列预测

为了提高回声状态网络对于混沌时间序列特征提取与预测的能力,提出一种层次化可塑性回声状态网络模型.该模型将多个储备池顺序连接,通过逐层特征变换的方式增强对非线性多尺度动态特征的提取能力.同时,引入神经科学中的内在可塑性机制模拟真实生物神经元的放电率分布,以最大化神经元的信息传递为目标对储备池进行预训练.层次化可塑性回声状态网络不仅能够增加模型的容量,降低随机投影所带来的不稳定性,而且也为理解储备池的表示、处理、记忆及储存操作提供一种新的思路.仿真实验结果表明,相比于其他7种改进的回声状态网络模型,所提出的模型在人造数据和真实数据所构成的混沌时间序列预测任务中均能取得最优的预测精度.     

基于增量式学习的正则化回声状态网络

针对回声状态网络(ESN)的结构设计问题,提出增量式正则化回声状态网络(IRESN).该网络由相互独立的子储备池模块构成,首先,子储备池根据奇异值分解方法生成,且可以保证每个子储备池权值矩阵的奇异值都小于1;其次,利用问题复杂度或者残差,将网络中逐一添加子储备池,直至满足预设的终止条件,在生成IRESN的过程中,回声状...     

Adaptive lasso echo state network based on modified Bayesian information criterion for nonlinear system modeling

Neural Computing and Applications - Echo state network (ESN), a novel recurrent neural network, has a randomly and sparsely connected reservoir. Since the reservoir size is very large, the...     

结合HS算法与ESN算法的光伏发电短期出力预测

为提高光伏发电系统短期出力预测的精度,提出了一种和声搜索(Harmony Search,HS)算法与回声状态网络(Echo State Network,ESN)算法相结合的预测模型。该模型以光伏电站的历史发电量数据和气象数据为基础。首先通过相似日选择算法挑选出预测日的相似日,将相似日的气象特征向量和预测日的气象特征向量的差值作为预测模型的输入变量;然后选择训练样本,并用和声搜索算法优化后的回声状态网络模型(HS-ESN)对样本进行训练和预测;最后以甘肃某光伏电站为例进行实例验证。实证分析表明,利用和声搜索算法优化回声状态网络预测模型的储备池参数可有效提高回声状态网络的预测精度,因此该模型具有较好的实用价值。     

基于Kalman滤波的储备池多元时间序列在线预报器

针对多元非线性时间序列, 结合回声状态网络和Kalman滤波提出一种新的在线自适应预报方法. 该方法将Kalman滤波应用于回声状态网络储备池高维状态空间中, 直接对网络的输出权值进行在线更新, 省去了传统递归网络扩展Kalman滤波中Jacobian矩阵的计算, 在提高预测精度的同时令算法的适用范围得到扩展. 在回声状态网络稳定时给出所提算法的收敛性证明. 仿真实例验证了所提方法的有效性.     

基于灵敏度分析的模块化回声状态网络修剪算法

针对回声状态网络（Echo state network,ESN）的结构设计问题,提出基于灵敏度分析的模块化回声状态网络修剪算法（Pruning algorithm for modular echo state network,PMESN）.该网络由相互独立的子储备池模块构成.首先利用矩阵的奇异值分解（Singular value decomposition,SVD）构造子储备池模块的权值矩阵,并利用分块对角阵原理生成储备池.然后利用子储备池模块输出和相应的输出层权值向量,定义学习残差对于子储备池模块的灵敏度以及网络规模适应度.利用灵敏度大小判断子储备池模块的贡献度,并根据网络规模适应度确定子储备池模块的个数,删除灵敏度低的子模块.在网络的修剪过程中,不需要缩放权值就可以保证网络的回声状态特性.实验结果说明,所提出的算法有效解决了ESN的网络结构设计问题,基本能够确定与样本数据相匹配的网络规模,具有较好的泛化能力和鲁棒性.     

基于延迟回声状态网的光伏电池板温度预测方法

光伏电池温度变化影响光伏系统输出的稳定性, 精准地预测光伏电池板温度的变化趋势, 对光伏系统智能运行具有重要意义. 为了更好地预测温度的变化趋势, 本文考虑了光伏电池板温度的迟滞效应, 将先前的温度输出作为延迟项引入回声状态网中, 提出了一种基于延迟回声状态网的光伏电池板温度预测模型. 给出一个延迟回声状态网具有回声状态特性的判定条件, 使得预测模型能够稳定地预测光伏电池板温度. 同时, 建立了一套光伏多传感器监测系统, 利用该监测系统采集的数据, 训练和验证模型的准确性. 与回声状态网(Echo state network, ESN), Leaky ESN (Leaky-integrator ESN)和VML ESN (ESN with variable memory length)相比, 仿真结果表明, 本文所提出的延迟回声状态网具有更好的预测性能, 平均绝对百分比误差甚至达到3.45%.     

基于储备池主成分分析的多元时间序列预测研究

提出一种基于回声状态网络储备池的非线性ＰＣＡ 方法,并将其应用于多元时间序列的预测中．由于多维输入变量间的相关性会影响建模效果,通过储备池将输入在原空间的非线性特征转化成高维空间的线性特征．在其中运用线性ＰＣＡ 技术寻找输入在储备池空间的最大方差方向,提取有效的多元变量综合信息．经储备池主成分分析处理后的输入与预测点呈动态线性映射,可使用线性方法建模．仿真结果表明了该方法的有效性．     

基于非线性STUKF滤波器和ESN算法的耦合预测模型

针对瓦斯浓度时间序列的混沌性,提出一种回声状态网络算法(ESN)和无迹卡尔曼滤波器(UKF)、强跟踪滤波器(STF)耦合的混沌时间序列预测模型.对于一维瓦斯浓度混沌时间序列,采用平均轨道周期的C-C算法在时间域确定重构空间的最佳时间延迟和嵌入维数,在相空间通过非线性回归预测模型拟合瓦斯涌出动力演化轨迹,提出带有渐消因子的非线性STUKF滤波器对ESN联合参数进行最优状态估计.试验结果表明:基于STUKF的ESN瓦斯涌出模型预测方法有效,在STUKF滤波器作用下增强了ESN算法的学习效率、提高了模型的跟踪能力,能达到精度高、鲁棒性好等优点.     

基于模块化回声状态神经网络光伏发电量预测

针对光伏发电的不确定性、间歇性给电力系统并网运行带来的安全问题,提出了一种基于模块化回声状态网络模型对发电量进行预测.首先利用模块化神经网络按季节建立预测子模型,再将子模型按相同日类型进行数据划分后,与平均气温一同作为样本,利用回声状态网络对子模型进行训练和发电量预测,最后集成输出结果.结果表明:此预测模型在日类型相同时预测误差较小,而在日类型不同时预测误差较大,但与ESN和BP预测模型相比均具有更高的预测精度和更快的预测速度.     

Artificial neural networks for water quality soft-sensing in wastewater treatment: a review

This paper aims to present a comprehensive survey on water quality soft-sensing of a wastewater treatment process (WWTP) based on artificial neural networks (ANNs). We mainly present problem formulation of water quality soft-sensing, common soft-sensing models, practical soft-sensing examples and discussion on the performance of soft-sensing models. In details, problem formulation includes characteristic analysis and modeling principle of water quality soft-sensing. The common soft-sensing models mainly include a back-propagation neural network, radial basis function neural network, fuzzy neural network (FNN), echo state network (ESN), growing deep belief network and deep belief network with event-triggered learning (DBN-EL). They are compared in terms of accuracy, efficiency and computational complexity with partial-least-square-regression DBN (PLSR-DBN), growing ESN, sparse deep belief FNN, self-organizing DBN, wavelet-ANN and self-organizing cascade neural network (SCNN). In addition, this paper generally discusses and explains what factors affect the accuracy of the ANNs-based soft-sensing models. Finally, this paper points out several challenges in soft-sensing models of WWTP, which may be helpful for researchers and practitioner to explore the future solutions for their particular applications.