Structural Vibration Modeling Using a Neuro-Fuzzy Approach

A novel vibration modelling method based on fuzzy sets is presented in this paper. In this method, firstly the mode shapes of a structure are guessed using experience or the rules that are developed in this research. The guessed mode shapes are referred to as mode shape forms (MSFs). The MSFs are approximate mode shapes which only give the direction of motion of the particles of the elastic body. This qualitative information is expressed by fuzzy sets. The deflections or displacement magnitudes of the MSFs are described by fuzzy linguistic terms such as Zero, Medium and Large. In this respect, natural frequencies and structural dimensions constitute the fuzzy inputs while MSFs are the fuzzy outputs. Fuzzy rules are designed based on MSF rules or guessed mode shapes to relate the inputs to the output. In the second stage, fuzzy representations of MSFs are updated by experimental modal analysis. This modification creates a set of mode shape data. In the final step, neural networks are used as a tool to obtain an accurate version of the mode shape data by learning the target set of the data. The method is extended to evaluate the error when a wrong MSF is assumed for the mode shape. In this case the method finds the correct MSF among available guessed MSFs. A further extension of the method is proposed for cases where there is no suitable guess available for the mode shape. In this situation the "closest" MSF is selected among the available MSFs. The chosen MSF is modified by correcting the fuzzy rules that were used in constructing the fuzzy MSF. Human common sense, heuristic and general knowledge, past experience, and the MSF developed in this method are the capabilities that cannot be provided with existing artificial intelligent system. The approach developed in this paper provides additional advantages over the existing modelling approaches by incorporating effective analysis methods such as mixed artificial intelligence and experimental validation, together with human interface/intelligence. As an illustrative example, the result of a clamped-clamped beam is compared with the corresponding mathematical equation of motion. An acceptable distribution of results is obtained from the method developed in this paper.