A Novel Modal Analysis Method Based on Fuzzy Sets

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.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

A novel modal analysis method based on fuzzy sets

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 engineer'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 'spiked' version of the original fuzzy curve is obtained. In the last stage of this process, neural network is used to 'learn' 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 'closest' 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.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Energy harvesting from suspension system using regenerative force actuators

In this paper harvesting vibration energy from suspension is investigated. Theoretical values for the harvested energy are calculated. Experimental evaluation of the energy is performed using vehicle road simulation facilities. An excitation signal in the frequency range of 0.5Hz to 20Hz is applied to the vehicle and the harvested power is calculated. Experimental results give a maximum harvested power of 984.4 W at the highest frequency, which is close to the theoretically computed value of 1106 W, for each suspension. Application of Regenerative Force Actuators (RFA) is explored for harvesting the vibration energy and controlling vibration. It is shown that the harvested power increases with the value of the actuator constant.Peer reviewe

Energy regeneration from suspension dynamic modes and self-powered actuation

Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.This paper concerns energy harvesting from vehicle suspension systems. The generated power associated with bounce, pitch and roll modes of vehicle dynamics is determined through analysis. The potential values of power generation from these three modes are calculated. Next, experiments are carried out using a vehicle with a four jack shaker rig to validate the analytical values of potential power harvest. For the considered vehicle, maximum theoretical power values of 1.1kW, 0.88kW and 0.97kW are associated with the bounce, pitch and roll modes, respectively, at 20 Hz excitation frequency and peak to peak displacement amplitude of 5 mm at each wheel, as applied by the shaker. The corresponding experimentally power values are 0.98kW, 0.74kW and 0.78kW. An experimental rig is also developed to study the behavior of regenerative actuators in generating electrical power from kinetic energy. This rig represents a quarter-vehicle suspension model where the viscous damper in the shock absorber system is replaced by a regenerative system. The rig is able to demonstrate the actual electrical power that can be harvested using a regenerative system. The concept of self-powered actuation using the harvested energy from suspension is discussed with regard to applications of self-powered vibration control. The effect of suspension energy regeneration on ride comfort and road handling is presented in conjunction with energy harvesting associated with random road excitations.Peer reviewedFinal Accepted Versio

Self-Powered Dynamic Systems in the Framework of Optimal Uncertainty Quantification

The energy that is needed for operating a self-powered device is provided by the energy excess in the system in the form of kinetic energy, or a combination of regenerative and renewable energy. This paper addresses the energy exchange issues pertaining to regenerative and renewable energy in the development of a self-powered dynamic system. A rigorous framework that explores the supply and demand of energy for self-powered systems is developed, which considers uncertainties and optimal bounds, in the context of optimal uncertainty quantification. Examples of regenerative and solar-powered systems are given, and the analysis of self-powered feedback control for developing a fully self-powered dynamic system is discussed