The Theoretical Approach And Experimental Study On The Inverse Problem Of Dynamic Force Identification In Time Domain

Accurately knowledge of the dynamic force acting on the structure during its designated life can be very important components in the design of mechanical systems, from the spacecraft and processing plants to electronic circuits. Regardless of actual application or the underlying physics, the expected force plays a key role in the structural health monitoring, the determination of the system properties or parameters, and the fatigue life estimationof operating systems. Unfortunately, in many practical situations, it is difficult, if not impossible, to perform direct measurements or calculations of the external forces acting on vibrating structures. For example, if the force gauges are inserted into force transfer path to measure those dynamic forces directly, they may either alter the system properties or intrude the load path. Instead, the vibration responses can often be conveniently measured. In such cases, indirect estimating these dynamic forces by using measured vibration responses in some sort of inverse model is sometimes necessary, which means that unknown force is established as the solution to an inverse problem, based on the measured vibration responses. The dynamic force identification, as the second type inverse problem in structural dynamics, has some splendent prospects in the state-of-art engineering design, and is also related to a variety of disciplines such as the numerical simulation, the dynamic vibration test and the theory of inverse problem. In this thesis the issues of basic applications of the dynamic force identification are studied, and the specific research works are as follows.Firstly, the force identification methods proposed by many researchers in the area of vibration and acoustics are reviewed, and the limitations of the current force identification methods are pointed out, and the idea of study on the force identification problem in the framework of theoretical and experimental study in time domain is established, and the interest areas in this thesis mainly focus on the ill-posedness of force identification problem, the foundation of precise force identification model, the stability of force identification algorithm, and the application of force identification technique.In general, the inverse problem of force identification is ill-posed, i.e. an arbitrarily small perturbation of the measured responses can cause arbitrarily large perturbation of the solution. In order to deal with this issue, the regularization technique of the mathematical theory to solve the inverse problem is utilized in this thesis to single out a useful and stable solution. The regularization technique, however, is only to cope with the ill-posed problem from the mathematical view, and not to completely eliminate the influence of errors in force identification model and the white noise in the measured vibration responses. Thus the establishment of proper force identification model is worth being concerned.In this thesis, three force identification models are established for the sake of reconstructing the input force of the structural systems. The force identification algorithm based on the precise computation for Markov parameters, is firstly presented to remove the numerical rounding errors of the dynamic force identification model, where a discrete moving average model of force identification is founded in state space, and the Markov parameter matrix is computed by the 2N type precise computation algorithm, and then the force identification model is recasted as Toeplitz matrix forms with a global multi-points distribution in time domain. The parameter estimation method for the force identification of the linear structural system is secondly proposed, in order to eliminate the effects of errors caused by the theoretical model or the truncated modal parameters in the experiment. The input force is expressed as a single base function, and the force identification problem is transformed into a problem of finding the parameters of the base function on the discrete time points. This force identification method is robust to improve the accuracy and the stability of the identified force. Finally, the force identification algorithm based on sensitivity analysis is proposed, where the input force is expressed as a series of parameters, and the sensitivity analysis method is used to iteratively update these parameters of input force in the inverse analysis. Furthermore, the sensitivity response matrix can be computed precisely when the input force is expressed as the harmonic functions. All these force identification methods presented in this thesis are still ill-posed, and the regularization process is necessary to suppress the fluctuations caused by the white noise in measured data.Finally, three force estimation experiments, corresponding to the force identification methods, are implemented, in order to verify that these force identification methods are valid. The forces, applied on the cantilever beam and the variable section beam in laboratory, are successfully reconstructed by the presented force identification methods in this thesis. Furthermore, the force identification program modules are developed and applied to estimate the input force acting on the high-speed aircraft in the launching process. The time history of harsh loads applied on the space aircrafts, are reconstructed by the telemetry response data, in order to optimize the design of high-speed aircrafts.