In the complex industrial environment, data missing situation is often occurred in the process of data acquisition and transition. The major contribution of the paper is the proposal of a deep bidirectional echo state network (DBESN) framework for time series prediction with such incomplete dataset. Instead of data imputation methodology, a bidirectional fusion reservoir is here designed to extract the deep bidirectional feature along with forward and backward time scales, based on which a deep autoencoder echo state network (DAESN) and a deep bidirectional state echo state network (DBSESN) are constructed for the incomplete output and input samples, respectively. As for such two networks, a bidirectional echo state network (BESN) is proposed for connecting them to constitute the DBESN framework for prediction. To verify the effectiveness of the proposed method, one synthetic time series as well as two realworld industrial datasets are employed to conduct the comparative experiments. The experimental results demonstrate that the proposed method outperforms other comparative ones at various missing rates.

Introduction

With the development of modern industrial information technology, the amount of the industrial data accumulated in process of manufacturing is increasing at an unprecedented rate [1]. To monitor and analyze the state of energy utilization in industrial process, it is necessary to establish a prediction model for some crucial variables based on these process data [2]. Since, in the process of industrial data acquisition and transition, due to the collector faults, transmission errors, memory failures and human errors, the data absence phenomenon may occur, which often brings a huge challenge for data analysis and processing [3]. Furthermore, the existence of missing data may largely increase the difficulties to describe a system by using data-driven approaches [4]. Therefore, it becomes essential to construct a prediction model for the incomplete data to provide a significative guidance for energy scheduling to avoid energy waste in the industrial process. In literature, a series of researches exist on the time series prediction with incomplete dataset in recent years, but most of them only considered the issue of data imputation [5]. For example, a multiple imputation using Markov Chain Monte Carlo (MCMC) algorithm were adopted in [6] to impute the missing data by using partial least squares regression model. Besides, periodicity imputation method, mean imputation method and cubic spline imputation method were employed in [7] for incomplete time series data imputation before modeling, in which the differences between them were analyzed. Furthermore, a polyfit line-fitting algorithm [8], a Gaussian process [9] and a nearest neighbor method [10] were also applied to data imputation. However, one of the major drawbacks of data imputation lies in that the original feature of the data may be retorted by imputation, which could exhibit an adverse effect on the prediction accuracy.