Introducing Randomized High Order Fuzzy Cognitive Maps as Reservoir Computing Models: A Case Study in Solar Energy and Load Forecasting

Abstract

Fuzzy Cognitive Maps (FCMs) have emerged as an interpretable signed weighted digraph method consisting of nodes (concepts) and weights which represent the dependencies among the concepts. Although FCMs have attained considerable achievements in various time series prediction applications, designing an FCM model with time-efficient training method is still an open challenge. Thus, this paper introduces a novel univariate time series forecasting technique, which is composed of a group of randomized high order FCM models labeled R-HFCM. The novelty of the proposed R-HFCM model is relevant to merging the concepts of FCM and Echo State Network (ESN) as an efficient and particular family of Reservoir Computing (RC) models, where the least squares algorithm is applied to train the model. From another perspective, the structure of R-HFCM consists of the input layer, reservoir layer, and output layer in which only the output layer is trainable while the weights of each sub-reservoir components are selected randomly and keep constant during the training process. As case studies, this model considers solar energy forecasting with public data for Brazilian solar stations as well as Malaysia dataset, which includes hourly electric load and temperature data of the power supply company of the city of Johor in Malaysia. The experiment also includes the effect of the map size, activation function, the presence of bias and the size of the reservoir on the accuracy of R-HFCM method. The obtained results confirm the outperformance of the proposed R-HFCM model in comparison to the other methods. This study provides evidence that FCM can be a new way to implement a reservoir of dynamics in time series modelling.

A novel decomposition-based ensemble broad learning system for short-term load forecasting

“…For example, Orang et al proposed a novel univariate time series forecasting technique, called randomized high order FCM models (R-HFCM). The obtained results confirm the proposed R-HFCM model is superior to the other methods [7]. Haida et al proposed a regression-based daily peak load forecasting method and a conversion technique, which reduced the large forecasting error caused by the nonlinear characteristics [8].…”

Artificial Intelligence and Mathematical Models of Power Grids Driven by Renewable Energy Sources: A Survey

“…Finally, in the context of reservoir computing, Colla et al presented a novel application of the modeling of industrial processes in energy management [245]. Orang et al, in their paper, reported a time-series forecasting technique composed of a group of randomized high-order FCM models labeled R-HFCM using an RL algorithm [246].…”

Benchmarking Reservoir Computing for Residential Energy Demand Forecasting

“…Only a few compare them to other types of recurrent neural networks like LSTMs as well [27]. Even fewer publications consider multiple data sets or different types of data: In [33] the authors use deep ESN to predict energy consumption as well as wind power generation and in [34], high order fuzzy cognitive maps are used as reservoir computing models to predict solar energy as well as load. While there are first applications of RC for probabilistic load forecasting, like the authors show in [35] by coupling the ESN with multiple methods of uncertainty, we focus on determining point forecasts in this work.…”