Dynamic nonlinear state-space model with a neural network via improved sequential learning algorithm for an online real-time hydrological modeling

Abstract

Summary This paper proposes a dynamic nonlinear state-space model with a neural network that uses a sequential learning algorithm capable of online simulation, in which the model predicts and adapts to the arrival of each new item of hydrological data in a sequential manner (as opposed to a ‘batch’), thereby enabling online real-time hydrological modeling. The improved sequential extended Kalman filtering (EKF) learning algorithm is developed to train multi-layer perceptron (MLP) neural networks, and is known as the MLP-EKF method with updating of noise covariance (MLP-EKFQ). It is herein proposed to allow the evolution of the weight of a neural network sequentially in time while also computing the noise covariance matrices of the EKF algorithm automatically by maximizing the evidence density function with respect to the noise covariance matrices. The proposed MLP-EKFQ was used to develop an online real-time warning system to predict river temperatures affected by the discharge of cooling water 1 km downstream of a thermal power station, from real-time to 2 h ahead, sequentially on the arrival of each new item of hydrological, meteorological, and power station operational data at 10 min intervals. It is demonstrated that the proposed MLP-EKFQ is superior in terms of both model performance and computational efficiency to those models that adopt a batch learning algorithm such as a multi-layer perceptron (MLP) system trained using the back-prorogation learning algorithm (MLP-BP), or an adaptive neural-fuzzy inference system (ANFIS). Due to its computational efficiency, its online simulation capability, and the high levels of accuracy achieved by the proposed MLP-EKFQ method, there is a great deal of potential for its use as an online dynamic hydrological modeling tool that may be suitable for a variety of complex dynamic and/or real-time tasks.