Solution of Inverse Problems: Source and System Identification
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The aim of the present chapter is to use the formulated spectral elements of the previous chapters to solve some difficult practical problems of great industrial significance. To start with, one important application of the spectral formulation is in solving inverse problems, e.g., source identification and parameter estimation. Because of the frequency domain formulation of spectral elements, where the input and output responses are algebraically connected through the transfer function, force (external disturbance) reconstruction can be performed with relative ease compared to any FE based methods. Similarly, material property identification by a classical optimization based method, which requires multiple evaluation of the objective function (in this case spectral solution), is computationally feasible because of small spectral system sizes. The SLE developed in Section 6.1 is used in the following example to reconstruct the applied broadband force. Similarly, the SLE developed in Section 7.1 for inhomogeneous layered media is used to identify background homogeneous material properties and inhomogeneous parameters.
KeywordsInverse Problem Structural Health Monitoring Spectral Element Classical Optimization Spectral Formulation
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