Time Series Estimation on Earthquake Events using ANFIS with Mapping Function

Abstract

Earthquake is a nonlinear process which is sensitive to the state of the large volume in the Earth. Time series prediction of earthquake events has been initiated about 100 years ago and at present it is still the subject of intensive research. Earthquake prediction is a challenging and difficult problem that needs an effective method to deal with highly nonlinear dynamics modeling. Adaptive Neuro Fuzzy Inference System (ANFIS) is a class of adaptive networks which enjoys many of the advantages claimed by neural networks and the linguistic interpretability of Fuzzy Inference Systems. The fixed membership functions used in the backward pass lead to a problem in minimizing discrepancy between the actual outputs and the desired outputs in highly nonlinear dynamics. A modified ANFIS algorithm in the backward pass by using a mapping function maps the inputs to all corrected values obtained via error correction rules in the first layer by means of an interpolation of the inputs. The corrected values in the first layer have been effectively overcome the problem in the standard ANFIS. Simulation results using earthquake data from the Sunda arc, Indonesia demonstrate the effectiveness of the proposed modified ANFIS in significantly reducing the discrepancy between the actual outputs and the desired outputs in time series prediction of earthquake parameters.