Neuro-fuzzy GMDH and its application to modelling grinding characteristics

Abstract

Mathematical models, in which many input variables are involved, require a range of input and output data, since the number of parameters increases with the input variables. GMDH (Group Method of Data Handling) has been used for the identificationof a mathematical model that has many input variables but limited data needs by using a hierarchical structure. This paper proposes a neuro-fuzzy GMDH model, adopting Gaussian radial basis functions (GRBF) as partial descriptions of GMDH. GRBF is reinterpreted as both a simplified fuzzy reasoning model and as a three-layered neural network. As an example of applying the algorithm, the wheel wear equation is identified, using data from experiments of abrasive cut-off. In the model, characteristics of work materials, grinding fluids, factors of wheels, wheel velocity and table feed are used as input variables, and the grinding ratio is the resulting output. The validity of the model is confirmed within the predicted accuracy by using additional data.

Limitations of Parametric Group Method of Data Handling and Empirical Improvements for the Application of Rainfall Modelling

“…The GRBF ↔ 𝑦 → a neural network composed of three layers (Poggio & Girosi, 1990). The neuro-fuzzy GMDH (NFGMDH) is formed through implementation of this fuzzy reasoning model as the PDs Mucciardi (1972, as cited in Nagasaka et al, 1995). NFGMDH follows the same paradigm as standard GMDH.…”

New insights into the methods for predicting ground surface roughness in the age of digitalisation

“…Thereafter, fuzzy basis function networks began to be widely used in the prediction of ground roughness. Nagasaka et al [112] proposed a neuro-fuzzy model based on the group method of data handling.…”

Application of improved neuro-fuzzy GMDH to predict scour depth at sluice gates

“…The GMDH approach has been used to identify behavior of non-linear systems such as forecasting of mobile communication, explosive cutting process, tool life testing in gun drilling, construction of optimal educational test, control engineering, marketing, economics and engineering geology (Astakhov and Galitsky, 2005;Hwang, 2006;Witczak et al, 2006;Amanifard et al, 2008;Srinivasan, 2008;Jamali et al, 2009;Abdel-Aal and El-Alfy, 2009;Mehrara et al, 2009;Kalantary et al, 2009). Nagasaka et al (1995) used a multi-stage fuzzy decision rule as neuro-fuzzy (NF) GMDH to model grinding characteristics, and Takashi et al (1998) proposed the orthogonal and successive projection approach for the learning of NF-GMDH. Hwang (2006) applied the NF-GMDH model to forecast the unreliable mobile communication, configured through the least square training method.…”