Multi-Resolution Convolutional Dictionary Learning for Riverbed Dynamics Modeling

This work proposes a novel formulation of convolutional-sparse-coded dynamic mode decomposition (CSC-DMD) incorporating a deep learning framework. CSC-DMD is a high-dimensional data analysis method with a convolutional synthesis dictionary and applicable to analyze dynamics such as seismic motions and river flows. An authors’ previous work has shown the effectiveness of CSC-DMD for riverbed state estimation. However, there still remains a room to improve the performance in expressing evolution of temporal and spatial changes in riverbed shape. Hence, this work proposes to adopt multi-resolution convolutional dictionary by introducing a deep learning framework so that the capability of simultaneously capturing local and global features is added to CSC-DMD. The significance of the proposed method is verified by evaluation of riverbed state estimation for time-series data of water surface and riverbed shape obtained through an experimental setup of river model.

1. INTRODUCTION

In recent years, advances in sensing, networking, and computer technologies have contributed greatly to the analysis of complex dynamic phenomena. In addition, modeling of high-dimensional data is required in many fields such as engineering, physics and biology [1]–[3]. Extended dynamic mode decomposition (EDMD), one of the data-driven analysis methods, has been applied in various fields [4]–[7]. In the field of civil engineering, modeling of river channel fluctuations has attracted much attention. The reason for this is that climate change has increased the frequency of heavy rainfall in recent years, increasing the risk of water-related disasters. A lot of residential areas around the world were damaged by flood of rivers due to heavy rains [8], [9]. These disasters have caused tremendous damage such as loss of social assets and human lives. For this reason, there is a need for immediate response to disaster mitigation and prevention. The main causes of river disasters are overflow due to water level rise and bank collapse due to channel fluctuations. For the former, it is important to predict the location and start time of the overflow, and for the latter, it is important to suppress and prevent channel fluctuations. To give some measure for these problems, it is quite helpful to express the time evolution of river dynamics. However, the mathematical model that governs the dynamics is expected to be non-linear and high-dimensional. Thus, it is not trivial to establish a formula for river dynamics according to a hypothesis on physics.