Bahram Shafai, Mario Sznaier, Luca Caracoglia
Date of Award
Doctor of Philosophy
Department or Academic Unit
College of Engineering. Department of Civil and Environmental Engineering.
Civil engineering, Zeros, Transfer function
Signal processing -- Mathematics, Discrete-time systems
Civil and Environmental Engineering
This study examines conditions where one can estimate the zeros of transfer functions from response measurements. It is shown in the literature that the cepstrum can be exploited to estimate the poles and zeros of a system from its response measurements provided that the system is excited at a single point with an input which has a flat logspectrum and the location of the input is known. Poles and zeros are estimated by curvefitting an analytical expression of the transfer function to the region of the cepstrum where the contribution of the input is minimal. Since the source and input information cannot be separated completely anywhere in the cepstrum, the approach is always approximate even in the case of noise-free data. This dissertation improves the cepstrum technique such that the requirement on the characteristics of the input is completely eliminated provided that the number of measurements is more than one. Although the improved technique cannot estimate the poles, it can estimate the zeros exactly in the case of noise-free data. The main shortcoming of the cepstrum approach to the estimation of zeros in the unknown input case is the requirement of a single input. In many civil engineering applications systems are constantly excited by unknown forces such as wind, traffic and passengers that act at many locations so the cepstrum technique is not applicable. A second objective of the dissertation is to devise a technique which can estimate the zeros from response measurements in the case of multiple inputs. The technique that has been developed is for systems whose mass matrices can be approximated as diagonal. Assuming the measured responses are due to collocated forces, the technique makes use of state-space matrices A and C which are obtained from stochastic system identification and estimates a surrogate matrix for the missing input matrix (B) connected with a collocated distribution of forces. The approach works by forcing two constraints: (1) the off-diagonal terms of the mass matrix are zero, (2) the fact that there is no direct transmission term relating forces to velocity or displacement measurements. The technique yields exact results provided that mass matrix is diagonal and the system matrices A and C are not truncated and the number of sensors is larger than a certain threshold. Otherwise, the technique is approximate.
Omer Faruk Tigli
Tigli, Omer Faruk, "Estimation of zeros from response measurements" (2008). Civil Engineering Dissertations. Paper 3. http://hdl.handle.net/2047/d10017914
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