A Novel Modal Analysis Method Based on Fuzzy Sets

Abstract

A novel method of vibration modelling is proposed in this thesis. This method involves estimating the mode shapes of a general structure and describing these shapes in terms of fuzzy membership functions. These estimations or initial guesses are based on engineerâ s experience or physical insight into natural mode shapes assisted by end and boundary conditions and some rules. The guessed mode shapes were referred to as Mode Shape Forms (MSFs). MSFs are approximate mode shapes, therefore there are uncertainties involve with their values where this uncertainty is expressed by fuzzy sets. The deflection or displacement magnitude of the mode shape forms are described with Zero, Medium, and Large fuzzy linguistic terms and constructed using fuzzy membership functions and rules. Fuzzy rules are introduced for each MSF. In that respect fuzzy membership functions provides a means of dealing with uncertainty in measured data, it gives access to a large repertoire of tools available in fuzzy reasoning field. The second stage of the process addresses the issues of updating these curves by experimental data. This involves performing experimental modal analysis. The mode shapes derived from experimental FRFs collect a limited number of sampling points. When the fuzzy data is updated by experimental data, the method proposes that the points of the fuzzy data correspond to the sampling points of FRF are to be replaced by the experimental data. Doing this creates a new fuzzy curve which is the same as the previous one, except at those points. In another word a â spikedâ version of the original fuzzy curve is obtained. In the last stage of this process, neural network is used to â learnâ the spiked curve. By controlling the learning process (by preventing it from overtraining), an updated fuzzy curve is generated that is the final version of the mode shape. Examples are presented to demonstrate the application of the proposed method in modelling of beams, a plate and a structure (a three beams frame). The method is extended to evaluate the error where 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 guess available for the mode shape. In this situation the â closestâ MSF is selected among available MSFs. This MSF is modified by correcting the fuzzy rules that is used in constructing of the fuzzy MSF. Using engineering experience, heuristic knowledge and the developed MSF rules in this method are the capabilities that cannot be provided with any artificial intelligent system. This provides additional advantage relative to vibration modelling approaches that have been developed until now. Therefore this method includes all aspects of an effective analysis such as mixed artificial intelligence and experimental validation, plus human interface/intelligence. Another advantage is, MSF rules provide a novel approach in vibration modelling where enables the method to start and operate with unknown input parameters such as unknown material properties and imprecise structure dimensions. Hence the classical computational procedures of obtaining the vibration behaviour of the system, from these inputs, are not used in this approach. As a result, this method avoids the time consuming computational procedure that exhibit in existing vibration modelling methods. However, the validation procedure, using experimental tests (modal testing) is the same acceptable procedure that is used in any other available methods which proves the accuracy of the method. (This thesis was published in Dec 2005)