Research On Computational Inverse Techniques In Dynamic Load Identification

In many practical engineering problems, such as the structural strength analysis, systemic health monitoring and fault diagnosis, structural dynamics modification and optimization design, to determinate the dynamic load acting on the structure is very important and necessary. Once the accurate dynamic external load is obtained, it is possible to apply various advanced methods to ensure the reliability and safety of engineering structures and satisfy the requirement of the modern industry and national defense. Nevertheless, in some cases, such as the tall building subjected to the wind load, the offshore platform subjected to the ice load, the vehicle subjected to the exciting force from road, direct measuring the dynamic load is generally difficult or even impossible due to the limitations of the technical and economic conditions. While the response measurement is comparatively easy and accurate, to develop some inverse analysis techniques for load identification from the measured responses has been the main stream of indirect method.Dynamic load identification is a solving deconvolution problem, and belongs to the second inverse problem of structural dynamics. Because the inverse problem of load identification is commonly ill-posed, the ill-conditioned kernel matrix and noisy responses will induce serious errors in the identified load. This dissertation conducts a systematical research to overcome the ill-posedness arising from dynamic load identification, and aims at contributing some useful researches and trials on load identification theories and practical computational inverse algorithms. The research routes of this dissertation are carried out from the three aspects of structural dynamic response equation, namely system kernel matrix, structural response and dynamic load. Firstly, in order to overcome the ill-condition of the kernel matrix, several general and improved regularization methods are studied. Secondly, in order to accurately describe the unknown dynamic force, the shape function method is presented. Thirdly, in order to fully utilize the measured structural responses and calculated kernel responses, the time domain Galerkin method is investigated. Additionally, the uncertainty from the modeling of load identification is considered and the interval analysis method is suggested to identify the upper and lower bounds of dynamic load acting on the uncertain structure. The major research works of this dissertation are as follows:(1) A computational inverse technique for dynamic load identification based on several general regularization methods is studied. The dynamic load is expressed as a series of impulse or step functions in time domain, and the structural response is the convolution integral of the kernel response and dynamic load. Through the discretization of the convolution integral, the forward model for load identification is established, and the ill-posedness arising from the inverse problem of load identification is analyzed. To overcome the difficulties of load identification directly using measured response with noise, several regularization methods and choosing regularization parameter methods are studied from various aspects of variational principles, spectrum decomposition and optimization iteration. These methods can effectively restrain the ill-posedness and stably realize the approximate reconstruction of the dynamic load.(2) Based on the sigular system theory of compact operator, two new regularization methods namely improved regularization and multi-level regularization are developed, in which the dynamic load can be more accurately and stably identified. For the form of the regularization operator, a modified regularization operator is constructed and proved, and the optimal convergence order of this regularized solution can be obtained further. For the structure of the regularization operator, the multi-level regularization method is suggested, in which the singular values of the kernel matrix is divided into different levels, and is corrected by different regularization parameters. In order to determine the boundary points of the singular values and the corresponding optimal parameters, a strategy that combines multi-objective genetic algorithm with L-curve criterion or generalized cross-validation criterion is presented. The regularization methods presented in this chapter can not only increase the accuracy of load identification, but also improve the stability of load identification.(3) A new method namely shape function method is proposed. Motivated by finite element method that discretized field variables in the spatial domain, the dynamic load is discretized into small elements in the time domain. In each element, it is assumed that the profile of the dynamic load varies with some functional form, and various shape functions of the dynamic load can be constructed through interpolation or fitting. The responses of the shape functions can be obtained based on a few finite element analyses, and assembled together with adjoining elements to form the global response equation for the whole time domain. Then, the shape function forward model for load identification is established. This new method can not only keep considerable accuracy as the sampling period increases, but also reduce the computational cost.(4) A new method namely time domain Galerkin method is developed. The measured structural responses and the calculated kernel function responses are also divided into small elements in the time domain and expressed by some basis functions. The coefficients of the basis functions can be obtained through least-square method. The fitting results are substituted into the convolution integral relation of structural dynamic response, and the basis functions are chosen as weight functions. Through minimizing the integral of internal residual multiplied by weight function, the time domain Galerkin forward model for load identification is established. The new method has strong noise-adaption ability and can efficiently ensure the accuracy of load identification.(5) Based on the interval analysis method, an efficient dynamic load identification method for uncertain structure is presented. The dynamic response relation of uncertain structure is established, and the interval is used to model and characterize the uncertainty parameters based on interval mathematics. Through interval analysis method, the load identification for uncertain structure can be transformed into two deterministic inverse problems, namely identifications for the midpoint load of the uncertain parameters and the first derivatives of the load. Then, regularization method is adopted to provide the efficient and stable solution of the two deterministic inverse problems, and through interval expanding operation the upper and lower bounds of dynamic load acting on the uncertain structure can be obtained. This method can objectively estimate and evaluate the influence of the uncertainty on load identification.(6) The experiment and software researches of dynamic load identification are developed. The impact load experiment system of cylindrical structure is established, and the impact load of hammer acting on the cylindrical structure is identified using the measured dynamic response and calculated kernel response through corresponding finite element model. The developed software of dynamic load identification integrates various kernel functions and regularization methods for convenience of engineering applications.