污水处理系统是一个复杂的非线性、大时延的动态系统，由于工艺的复杂性、检测设备的不完备性以及经济成本的限制，一些重要的出水指标无法实现精准的检测。为解决此问题，文中提出了基于集合卡尔曼-Elman网络的软测量方法。传统动态神经网络具有能够处理时延信息数据的动态记忆能力，可用于基于数据驱动的软测量建模过程。但是，常规训练方法容易使神经网络陷入局部最小值，导致模型预测性能欠佳。鉴于此，文中引入集合卡尔曼滤波技术和对偶有限样本集合卡尔曼技术对典型的动态神经网络——Elman神经网络进行无梯度训练，构建新型软传感器模型，不仅有效提高了传统Elman神经网络的预测能力，而且提供了一种简单、无梯度的神经网络训练方法。将该方法在加州大学欧文分校的污水处理数据（UCI数据）上进行验证，结果表明，文中方法具有较好的预测性能，集合卡尔曼滤波技术可作为一种无梯度的替代方法来训练神经网络。

Wastewater treatment system is a dynamic system with complex nonlinearity and large time delay. Due to the complexity of the process, the incompleteness of the testing equipment and the constraint of economic cost, some important effluent indicators cannot be detected accurately. To solve this problem, this paper proposes a soft-sensor method based on an ensemble Kalman filter-Elman neural network. The traditional dynamic neural network has the dynamic memory ability to process time-delay data, so it can be used in data-driven soft sensing modeling. However, the conventional training method is easy to trap in a local minimum, resulting in poor prediction performance. This paper introduces the ensemble Kalman filter and the dual finite-size ensemble Kalman filter, and, together with the Elman neural network for gradient-free training, to construct two soft sensor models, which not only improve the prediction performance of Elman neural network but also provide a simple and gradient-free training method for neural network. The two models are then applied to a dataset of the University of California, Irvine (UCI data). The results show that the proposed method based on ensemble Kalman filter-Elman neural network possesses good prediction performance, and that the ensemble Kalman filter can be used as an alternative gradient-free method to train neural networks.